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https://huijzer.xyz/posts/writing-checklist/	HUIJZER.XYZ # Writing checklist 2020-07-29 I keep forgetting lessons about writing. After writing a text, my usual response is to declare it as near perfect and never look at it again. In this text, I will describe a checklist, which I can use to quickly debunk the declaration. I plan to improve this checklist over time. Hopefully, text which passes the checklist in a few dozen years from now will, indeed, be near perfect. The list is roughly ordered by importance. The text should: 1. Ensure that the writing is valuable to the community of readers. 2. Be simple or be made as simple as possible, but not simpler[1]. This is also known as Occam's razor, kill your darlings or the KISS principle. 3. Be polite, that is, not contain a career limiting move. For example, do not "write papers proclaiming the superiority of your work and the pathetic inadequacy of the contributions of A, B, C, ..." . 4. Be consistent. For example, either use the Oxford comma in the entire text or do not use it at all. 5. Avoid misspellings. 6. Avoid comma splices. 7. Place the object before the action, so write "the boy hit the ball" instead of "the ball was hit by the boy". 8. Flow naturally; just like a normal conversation. This is, for me, contradictory to writing when programming. 9. Provide a high-level overview of the text. This can be a summary, abstract, a few sentences in the introduction or a combination of these. 10. Prefer common collocations. A list of common collocations is The Academic Collocation List. 11. Use simple verbs, for example, prefer "stop" over "cease to move on" or "do not continue". 12. Avoid dying metaphors such as "stand shoulder to shoulder with" . Metaphors aim to "assist thought by evoking a visual image" . Dying metaphors do not evoke such an image anymore due to overuse . 13. Avoid pretentious diction such as dressing up simple statements, inappropriate adjectives and foreign words and expressions . For example, respectively "effective", "epic" and "status quo" . 14. Avoid meaningless words, that is, words for which no clear definition exists. For example, "democracy" and "freedom" have "several different meanings which cannot be reconciled with one another" . ## Writing when programming In programming, one of the main goals is to avoid code duplication. Code is deduplicated by introducing functions. This deduplication is good, but can introduce functions which meaning can only be explained as a helper for deduplication. For example, f("A") g("A") f("B") g("B") ... is replaced by process(s) = f(s); g(s) process("A") process("B") ... Programmers are used to these kind of functions. However, outside of programming duplication is allowed if it improves readability. Synonyms should be used to avoid boring the reader with the duplicates. [1] This statement is likely to be attributed to Einstein . ## References Orwell, George (1946). Politics and the English Language. Retrieved July 29, 2020, from https://www.orwell.ru/library/essays/politics/english/e_polit Adams, Scott (2015). The Day You Became A Better Writer. Retreived April 23, 2021, from https://www.scottadamssays.com/2015/08/22/the-day-you-became-a-better-writer-2nd-look/.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.7424670457839966, "perplexity": 3183.0704220654584}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710503.24/warc/CC-MAIN-20221128102824-20221128132824-00145.warc.gz"}
http://community.wolfram.com/groups/-/m/t/1353471?sortMsg=Votes	# From Intersecting Cylinders to Ambiguous Rings GROUPS: Erik Mahieu 9 Votes Intrigued by the Ambiguous Cylinder Illusion, of prof. Kokichi Sugihara, I started looking for explanations with the help of Wolfram Language. The "ambiguous cylinder" can, for purposes of the viewing illusion, be reduced to its upper rim. We call the rim an "ambiguous ring". This ring can be seen as a circle or a square, depending on the viewpoint. Almost perpendicular, viewpoints can be achieved with the help of a mirror.Looking parallel to the axis of the circular cylinder or of the square cylinder (prism) will show a circle or a square respectively. A possible mathematical expression for this "ambiguous curve" can be obtained by investigating the intersection of a circular with a square cylinder. My Wolfram demonstrations Intersection of Circular and Polygonal Cylinders 1] and [Ambiguous Rings 1: Polygon Based illustrate the different intersection curves obtained by changing the geometry of the cylinders. For these intersection curves to form a ring, a tight fit between the square cylinder inside the circular one is required. The circumradius of a perfectly fitted square inside a circle of radius 1 is: fittedradius4[t_] := Module[{n}, n = 2 Floor[4 (.5 t + \[Pi]/8)/\[Pi]] - 1; Cos[t - (n + 1) \[Pi]/4]] As can be seen in this simple Manipulate: Manipulate[ ParametricPlot[ 1/Sqrt[2] Sec[ 1/2 ArcTan[Cot[2 (\[Theta] - \[Theta]0)]]] {Cos[\[Theta]], Sin[\[Theta]]}, {\[Theta], 0, 2 \[Pi]}, PlotStyle -> Directive[AbsoluteThickness[4], Orange], PlotRange -> 1.25, ImageSize -> Small, TicksStyle -> 6, Prolog -> {{Thick, Dotted, Circle[]}, Cyan, AbsoluteThickness[4], Line[{{-5, fittedradius4[\[Theta]0]}, {5, fittedradius4[\[Theta]0]}}], Line[{{-5, -fittedradius4[\[Theta]0]}, {5, \ -fittedradius4[\[Theta]0]}}], AbsolutePointSize[5], Black, Point[{0, 0}]}], {{\[Theta]0, 0.5, "axial rotation\nsquare cylinder"}, 0, 10 \[Pi], ImageSize -> Tiny}, TrackedSymbols :> Manipulate] Based on [1], this is the function for a polygonal ringset: polyRingsetCF = Compile[{{\[Theta], _Real}, {r, _Real}, {\[Theta]0, _Real}, {d, \ _Real}, {n, _Integer}, {\[Alpha], _Real}}, Module[{t}, t = Sec[2 ArcTan[Cot[1/2 n (\[Theta] - \[Theta]0)]]/ n]; {(part1){Cos[\[Pi]/n] Cos[\[Theta]] t, Cos[\[Pi]/n] t Sin[\[Theta]], Sec[\[Alpha]] Sqrt[-d^2 + r^2 + 2 d Cos[\[Pi]/n] t Sin[\[Theta]] - Cos[\[Pi]/n]^2 t^2 Sin[\[Theta]]^2] - Cos[\[Pi]/n] Cos[\[Theta]] t Tan[\[Alpha]]}, {(part 2)Cos[\[Pi]/n] Cos[\[Theta]] t, Cos[\[Pi]/ n] t Sin[\[Theta]], -Sec[\[Alpha]] Sqrt[-d^2 + r^2 + 2 d Cos[\[Pi]/n] t Sin[\[Theta]] - Cos[\[Pi]/n]^2 t^2 Sin[\[Theta]]^2] - Cos[\[Pi]/n] Cos[\[Theta]] t Tan[\[Alpha]]}}]]; ParametricPlot3D[ polyRingsetCF[t, 1., 0.5, 0., 4, 0.], {t, -\[Pi], \[Pi]}, PlotStyle -> {{Red, Tube[.035]}}, PlotPoints -> 500, PerformanceGoal -> "Quality", SphericalRegion -> True, PlotRange -> 1.1, Background -> Lighter[Gray, 0.5], ImageSize -> 300, PlotTheme -> "Marketing"] If we now use fittedRadius[[Theta]0] as the circumradius for the square cylinder, we can create closed ringsets as a function the axial rotation [Theta]0 of the suare cylinder. This is a GIF scrolling through all possible fitted square cylinders inside a circular cylinder of radius 1 :These intersection curves are composite curves (ringsets) consisting each of two separate curves (rings). We can select one of these two rings by introducing the cutoff angles (t1 and t2) in the parametric plot [2]. polyRingCF = Compile[{{\[Theta], _Real}, {\[Theta]0, _Real}, {r, _Real}, \ {\[Alpha], _Real}, {n, _Integer}, {d, _Real}, {t1, _Real}, {t2, \ _Real}},(t1 and t2 are the values of \[Theta] for switching between \ parts) Module[{t},(selection of parts of a composite curve) t = Sec[2 ArcTan[Cot[1/2 n (\[Theta] - \[Theta]0)]]/n]; {Cos[\[Pi]/n] Cos[\[Theta]] t, Cos[\[Pi]/n] Sin[\[Theta]] t,(select part1 or part 2) Piecewise[{{1, \[Theta] <= t1 \[Pi] + 2 \[Theta]0 \|\| \[Theta] > t2 \[Pi] + 2 \[Theta]0}}, -1]*(Sec[\[Alpha]] Sqrt[-d^2 + r^2 + 2 d Cos[\[Pi]/n] t Sin[\[Theta]] - Cos[\[Pi]/n]^2 t^2 Sin[\[Theta]]^2]) - Cos[\[Pi]/n] Cos[\[Theta]] t Tan[\[Alpha]]}]] printring4 = ParametricPlot3D[ polyRingCF[\[Theta], 0., fittedradius4[0.], 0., 4, 0., -.5, .5], {\[Theta], -\[Pi], \[Pi]}, SphericalRegion -> True, PlotStyle -> {Green, Tube[.05]}, Boxed -> False, Axes -> False, PlotRange -> 1.05, PlotPoints -> 100, ImageSize -> Small, PlotTheme -> "ThickSurface"] This is a GIF showing the different views of this ring: among them a circle, a square, a "lemniscate", etc...To test this "ambiguous ring" in a mirror setup, we use Printout3D to send the file to Sculpteo for 3D-printing: Printout3D[printring4, "Sculpteo", RegionSize -> Quantity[5, "cm"]] And when reflected in an experimental mirror setup: The physical ring looks like a circle while the reflected ring looks like a square.For those who like to print this ring themselves, This is the link to the Sculpteo file.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30636486411094666, "perplexity": 11364.82555350837}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864957.2/warc/CC-MAIN-20180623093631-20180623113631-00298.warc.gz"}
https://infoscience.epfl.ch/record/229913	Infoscience Journal article # Bactericide effects of transparent polyethylene photocatalytic films coated by oxides under visible light This review addresses catalytic/photocatalytic films under visible light inducing fast bacterial inactivation. These films present uniform, stable and adhesive surfaces able to inactivate bacteria within minutes. Uniform sputtered polyethylene-TiO2 (PE-TiO2) films absorbing mainly in the UV-region were later followed by studies on PE-FeOx and PE-FeOx-TiO2 absorbing light in the visible region. The amount of TiO2 sputtered on PE was significantly increased by RF-plasma pre-treatment due to the additional polar binding sites introduced on the PE-film. The hydrophobic to hydrophilic conversion of the PE-TiO2 films under light irradiation was observed to be concomitant with the bacterial inactivation time. The TiO2 diffuse reflectance spectra (DRS) of TiO2-PE-films were extensively modified by the sputtering of FeOx. The structure of the sputtered layers revealed a random deposition of FeOx-TiO2 on PE. The oxidative radical species generated on semiconductor surfaces were identified by appropriate scavenging experiments. By photoelectron spectroscopy (XPS), the redox processes occurring on the photocatalysts were evaluated. Repetitive bactericide cycling was possible for the three films discussed in this review. Bacterial inactivation mechanisms were suggested for the different films presented in this review.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8631139397621155, "perplexity": 15784.078082329746}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824357.3/warc/CC-MAIN-20171020211313-20171020231313-00331.warc.gz"}
https://ask.sagemath.org/questions/42416/revisions/	# Revision history [back] ### Sum using coefficients of a expansion I'm trying to sum over the coefficients of a expansion but the sum gives zero. I use the taylor method to expand a function f: f=sin(x) ft=f.taylor(x,0,6) then I need to use the coefficients in a sum, but if I for example do the following: sum(x^(i)ft.coefficient(x,i),i,0,5) I get zero. Any idea why this is happening? ### Sum using coefficients of a expansion I'm trying to sum over the coefficients of a an expansion but the sum gives zero. I use the taylor method to expand a function f: f=sin(x) ft=f.taylor(x,0,6) then I need to use the coefficients in a sum, but if I for example do the following: sum(x^(i)ft.coefficient(x,i),i,0,5) I get zero. Any idea why this is happening? happening?	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9096959829330444, "perplexity": 480.06458645607984}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195527458.86/warc/CC-MAIN-20190722010436-20190722032436-00557.warc.gz"}
https://quics.umd.edu/research/publications?page=6&s=title&amp%3Bf%5Bag%5D=G&o=desc&f%5Bauthor%5D=1075	# Publications Export 2 results: Author [ Title] Type Year Filters: Author is M. S. Safronova [Clear All Filters] O , Optimizing the fast Rydberg quantum gate, Physical Review A, vol. 67, no. 4, 2003.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8148967623710632, "perplexity": 10970.893632169678}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146562.94/warc/CC-MAIN-20200226211749-20200227001749-00316.warc.gz"}
https://www.physicsforums.com/threads/determine-acceleration-from-position-vs-time-graph.205098/	# Determine Acceleration from Position vs. Time Graph 1. Dec 17, 2007 ### petern The position vs. time graph is wavy and I assume the only point where there is acceleration is where there is a curve, right? It seems like the acceleration is also 0 at the curve though. Is it even possible? 2. Dec 17, 2007 ### MrJingles For a position as a function of time graph, simply find the derivative at the point which you wish to find the velocity for. Find the second derivative of the function for the acceleration. Perhaps if you uploaded an image of the particular graph in question I could be of more use. (The acceleration will equal zero at any point where the f(t) graph changes concavity) 3. Dec 17, 2007 ### petern and this: I don't really understand most of it. 4. Dec 17, 2007 ### MrJingles Your first assertion, that acceleration occurs only at curves is correct. Velocity is only equal to zero when it (the position function) has zero slope (ie, no motion--- straight lines and relative max/mins) and acceleration equals zero when the velocity is constant (velocity is a straight line) and when the position graph switches concavity (inflection point). It is important to note that, though velocity may =0 at some point, acceleration may not (although it can). When the function is concave (up) its derivative (in this case velocity) is increasing, which means that its acceleration is positive When it's convex (concave down) its derivative is decreasing which means that its acceleration is negative Last edited: Dec 17, 2007 5. Dec 17, 2007 ### petern Thanks for the advice but for the 1st page, can u tell me where each bullet goes? Which interval does it go to?	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9181612730026245, "perplexity": 876.3035147117789}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721415.7/warc/CC-MAIN-20161020183841-00420-ip-10-171-6-4.ec2.internal.warc.gz"}
https://arxiv.org/abs/1703.05042	cs.PL # Title:A Relational Logic for Higher-Order Programs Abstract: Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for reasoning about a broad range of properties, including equivalence and refinement, and specialized notions such as continuity, information flow security or relative cost. In a higher-order setting, relational program verification can be achieved using relational refinement type systems, a form of refinement types where assertions have a relational interpretation. Relational refinement type systems excel at relating structurally equivalent terms but provide limited support for relating terms with very different structures. We present a logic, called Relational Higher Order Logic (RHOL), for proving relational properties of a simply typed $\lambda$-calculus with inductive types and recursive definitions. RHOL retains the type-directed flavour of relational refinement type systems but achieves greater expressivity through rules which simultaneously reason about the two terms as well as rules which only contemplate one of the two terms. We show that RHOL has strong foundations, by proving an equivalence with higher-order logic (HOL), and leverage this equivalence to derive key meta-theoretical properties: subject reduction, admissibility of a transitivity rule and set-theoretical soundness. Moreover, we define sound embeddings for several existing relational type systems such as relational refinement types and type systems for dependency analysis and relative cost, and we verify examples that were out of reach of prior work. Comments: Submitted to ICFP 2017 Subjects: Programming Languages (cs.PL) Cite as: arXiv:1703.05042 [cs.PL] (or arXiv:1703.05042v1 [cs.PL] for this version) ## Submission history From: Alejandro Aguirre [view email] [v1] Wed, 15 Mar 2017 09:32:27 UTC (72 KB)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6259340643882751, "perplexity": 3008.264739046731}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232254751.58/warc/CC-MAIN-20190519101512-20190519123512-00150.warc.gz"}
http://blekko.com/wiki/Orthocenter?source=672620ff	# Altitude (triangle) From Wikipedia, the free encyclopedia - View original article (Redirected from Orthocenter) Jump to: navigation, search Three altitudes intersecting at the orthocenter In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. forming a right angle with) a line containing the base (the opposite side of the triangle). This line containing the opposite side is called the extended base of the altitude. The intersection between the extended base and the altitude is called the foot of the altitude. The length of the altitude, often simply called the altitude, is the distance between the base and the vertex. The process of drawing the altitude from the vertex to the foot is known as dropping the altitude of that vertex. It is a special case of orthogonal projection. Altitudes can be used to compute the area of a triangle: one half of the product of an altitude's length and its base's length equals the triangle's area. Thus the longest altitude is perpendicular to the shortest side of the triangle. The altitudes are also related to the sides of the triangle through the trigonometric functions. In an isosceles triangle (a triangle with two congruent sides), the altitude having the incongruent side as its base will have the midpoint of that side as its foot. Also the altitude having the incongruent side as its base will form the angle bisector of the vertex. It is common to mark the altitude with the letter h (as in height). In a right triangle, the altitude with the hypotenuse as base divides the hypotenuse into two lengths p and q. If we denote the length of the altitude by h, we then have the relation $h=\sqrt{pq}$. ## The orthocenter The three altitudes intersect in a single point, called the orthocenter of the triangle. The orthocenter lies inside the triangle if and only if the triangle is acute (i.e. does not have an angle greater than or equal to a right angle). See also orthocentric system. If one angle is a right angle, the orthocenter coincides with the vertex of the right angle. Thus for acute and right triangles the feet of the altitudes all fall on the triangle. The orthocenter, along with the centroid, circumcenter and center of the nine-point circle all lie on a single line, known as the Euler line. The center of the nine-point circle lies at the midpoint between the orthocenter and the circumcenter, and the distance between the centroid and the circumcenter is half that between the centroid and the orthocenter. The isogonal conjugate and also the complement of the orthocenter is the circumcenter. Four points in the plane such that one of them is the orthocenter of the triangle formed by the other three are called an orthocentric system or orthocentric quadrangle. Let A, B, C denote the angles of the reference triangle, and let a = \|BC\|, b = \|CA\|, c = \|AB\| be the sidelengths. The orthocenter has trilinear coordinates sec A : sec B : sec C and barycentric coordinates $\displaystyle ((a^2+b^2-c^2)(a^2-b^2+c^2) : (a^2+b^2-c^2)(-a^2+b^2+c^2) : (a^2-b^2+c^2)(-a^2+b^2+c^2)).$ Denote the vertices of a triangle as A, B, and C and the orthocenter as H, and let D, E, and F denote the feet of the altitudes from A, B, and C respectively. Then: • The sum of the ratios on the three altitudes of the distance of the orthocenter from the base to the length of the altitude is 1:[1] $\frac{HD}{AD} + \frac{HE}{BE} + \frac{HF}{CF} = 1.$ • The sum of the ratios on the three altitudes of the distance of the orthocenter from the vertex to the length of the altitude is 2:[1] $\frac{AH}{AD} + \frac{BH}{BE} + \frac{CH}{CF} = 2.$ • The product of the lengths of the segments that the orthocenter divides an altitude into is the same for all three altitudes:[2] $AH \cdot HD = BH \cdot HE = CH \cdot HF.$ • If any altitude, say AD, is extended to intersect the circumcircle at P, so that AP is a chord of the circumcircle, then the foot D bisects segment HP:[2] $HD = DP.$ Denote the orthocenter of triangle ABC as H, denote the sidelengths as a, b, and c, and denote the circumradius of the triangle as R. Then[3] $a^2+b^2+c^2+AH^2+BH^2+CH^2 = 12R^2.$ In addition, denoting r as the radius of the triangle's incircle, ra, rb, and rc as the radii if its excircles, and R again as the radius of its circumcircle, the following relations hold regarding the distances of the orthocenter from the vertices:[4] $r_a+r_b+r_c+r=AH+BH+CH+2R,$ $r_a^2+r_b^2+r_c^2+r^2=AH^2+BH^2+CH^2+(2R)^2.$ ## Orthic triangle Triangle abc is the orthic triangle of triangle ABC If the triangle ABC is oblique (not right-angled), the points of intersection of the altitudes with the sides of the triangle form another triangle, A'B'C', called the orthic triangle or altitude triangle. It is the pedal triangle of the orthocenter of the original triangle. Also, the incenter (that is, the center for the inscribed circle) of the orthic triangle is the orthocenter of the original triangle.[5] The orthic triangle is closely related to the tangential triangle, constructed as follows: let LA be the line tangent to the circumcircle of triangle ABC at vertex A, and define LB and LC analogously. Let A" = LB ∩ LC, B" = LC ∩ LA, C" = LC ∩ LA. The tangential triangle, A"B"C", is homothetic to the orthic triangle. The orthic triangle provides the solution to Fagnano's problem, posed in 1775, of finding for the minimum perimeter triangle inscribed in a given acute-angle triangle. The orthic triangle of an acute triangle gives a triangular light route.[6] Trilinear coordinates for the vertices of the orthic triangle are given by • A' = 0 : sec B : sec C • B' = sec A : 0 : sec C • C' = sec A : sec B : 0 Trilinear coordinates for the vertices of the tangential triangle are given by • A" = −a : b : c • B" = a : −b : c • C" = a : b : −c ## Some additional altitude theorems ### Altitude in terms of the sides For any triangle with sides a, b, c and semiperimeter s = (a+b+c) / 2, the altitude from side a is given by $h_a=\frac{2\sqrt{s(s-a)(s-b)(s-c)}}{a}.$ This follows from combining Heron's formula for the area of a triangle in terms of the sides with the area formula (1/2)×base×height, where the base is taken as side a and the height is the altitude from a. ### Equilateral triangle theorem For any point P within an equilateral triangle, the sum of the perpendiculars to the three sides is equal to the altitude of the triangle. This is Viviani's theorem. ### Inradius theorems Consider an arbitrary triangle with sides a, b, c and with corresponding altitudes α, β, η. The altitudes and incircle radius r are related by $\displaystyle \frac{1}{r}=\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\eta}.$ Let c, h, s be the sides of three squares associated with the right triangle: the square on the hypotenuse, and the triangle's two inscribed squares respectively. The sides of these squares (c>h>s) and the incircle radius r are related by a similar formula: $\displaystyle \frac{1}{r}=-{\frac{1}{c}}+\frac{1}{h}+\frac{1}{s}.$ ### Relation among altitudes of right triangle In a right triangle the three altitudes α, β, η (the first two of which coincide with the legs b and a respectively) are related according to[7][8] $\frac{1}{\alpha ^2}+\frac{1}{\beta ^2}=\frac{1}{\eta ^2}.$ ### Relation among sides of squares on and in a right triangle Also in the case of the right triangle, the sides c, h, s of the three above-mentioned squares are related to each other by the symphonic theorem, which states that[9] $\frac{1}{c^2}+\frac{1}{h^2}=\frac{1}{s^2}.$ ### Area theorem Denoting the altitudes of any triangle from sides a, b, and c respectively as $h_a$, $h_b$, and $h_c$,and denoting the semi-sum of the reciprocals of the altitudes as $H = (h_a^{-1} + h_b^{-1} + h_c^{-1})/2$ we have[10] $\mathrm{Area}^{-1} = 4 \sqrt{H(H-h_a^{-1})(H-h_b^{-1})(H-h_c^{-1})}.$ ## In-line references 1. ^ a b 2. ^ a b "Orthocenter of a triangle" 3. ^ http://mathworld.wolfram.com/Orthocenter.html Weisstein, Eric W. "Orthocenter." From MathWorld--A Wolfram Web Resource.] 4. ^ Bell, Amy, "Hansen’s right triangle theorem, its converse and a generalization", Forum Geometricorum 6, 2006, 335–342. 5. ^ William H. Barker, Roger Howe (2007). "§ VI.2: The classical coincidences". Continuous symmetry: from Euclid to Klein. American Mathematical Society Bookstore. p. 292. ISBN 0-8218-3900-4. See also: Corollary 5.5, p. 318. 6. ^ Bryant, V., and Bradley, H., "Triangular Light Routes," Mathematical Gazette 82, July 1998, 298-299. 7. ^ Voles, Roger, "Integer solutions of $a^{-2}+b^{-2}=d^{-2}$," Mathematical Gazette 83, July 1999, 269–271. 8. ^ Richinick, Jennifer, "The upside-down Pythagorean Theorem," Mathematical Gazette 92, July 2008, 313–317. 9. ^ Price, H. Lee and Bernhart, Frank R. "Pythagorean Triples and a New Pythagorean Theorem" (2007), arXiv 0701554 [1] 10. ^ Mitchell, Douglas W., "A Heron-type formula for the reciprocal area of a triangle," Mathematical Gazette 89, November 2005, 494.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 20, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9166755676269531, "perplexity": 725.4670677343113}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609525991.2/warc/CC-MAIN-20140416005205-00227-ip-10-147-4-33.ec2.internal.warc.gz"}
https://quant.stackexchange.com/questions/9051/examples-of-spectral-risk-measures/45316	# Examples of Spectral Risk Measures Let's take the usual definition of a spectral risk measure. If we look at the integral we see that spectral risk measures have the property that the risk measure of a random variable $X$ can be represented by a combination of the quantiles of $X$. Since the quantile function is rather friendly one gets that every spectral risk measure is also a coherent risk measure. Examples are the expected value and the expected shortfall (CVaR). In those cases, the spectral representation yields a very convenient way to approximate the measure by simply weighing the quantiles of our dataset. That yields the following questions: Are there any other known measures that have a spectral representation? If we relax the assumptions on the spectrum $\phi$, can we obtain (approximative sequences of) other (possibly non-coherent) risk measures? EDIT: In reaction to the comment by @Joshua Ulrich I want to provide an example of what I want to achieve and some more details. • Example: The Conditional Value at Risk. We have the following formula: $\text{CVaR}_\alpha(X) = -\frac{1}{\alpha}\int_0^{\alpha}F^{-1}_X(p)dp$. From sample $X_i$, $i=1,\ldots,N$, we can calculate the CVaR by taking the order statistics that are in the $\alpha$-tail of the sample, average, and divide by $\alpha$. We can see that this is measure has a spectral representation with $\phi(p) = \frac{1}{\alpha}$ for $p \in [0,\alpha]$ and $\phi(p) = 0$ for $p \in (\alpha, 1]$. So its easy to check: The CVaR is a spectral measure. Obviously, the "order statistics + weighted average" procedure does not only work for the CVaR, it works for all spectral measures: From the definition of spectral measure we see that, after discretizing the integral, we have an approximation of the measure that is a linear combination of quantiles which is very easy to compute. In fact its so easy that I would like to compute as many risk measures as possible this way (very easy if you do monte carlo or scenarios for example). For the computation only, I dont need all the assumptions about $\phi$ so lets forget about them for a moment and see what else we can calculate this way. • This is a bit broad, and could lead to list-like answers. Could you provide more details on what you're actually trying to accomplish? Oct 20, 2013 at 12:32 • Well, I am not sure I understand what you want but what is clear is that $CVAR_{\alpha}$ works as $\Phi(p)=\frac{1}{\alpha} \cdot 1_{p \in [0,\alpha]}$ which is a density of probability. So you can build any other risk measure chosing for $\Phi$ any density on the compact set $[0,1]$, and by scaling on a compact set. I would try a "hat function" first, then sinusoids... Oct 21, 2013 at 12:20 • Quite a few risk measures seem unlikely to have a representation like this, since their units differ. For example, annualized volatility. Some risk measures, such as scenario playbacks of the '97 Asian crisis, will trivially have a spectral representation but not in any computationally useful way. Oct 21, 2013 at 13:38 • @statquant Well, the aim is not to try a different spectrum $\phi$ but rather to identify the spectra of other well known risk measures. Brian B: I dont understand your comment about units. The units are irrelevant for a risk measure as far es the spectral property is concerned, right? Oct 23, 2013 at 6:47 I believe that Prospect Theory (as defined by Kahneman, Amos, and Tversky) implicitly makes use spectral risk measures. Though I am not able to find any literature linking the two, I think there is clear link between the intuitions regarding loss aversion. The key difference is that spectral risk measures are normative; we assume that the utility function is known. Prospect Theory, on the other hand, is inherently descriptive (i.e., reflects observed behaviors). Also, I am aware that spectral risk measures are extended to portfolio risk, while Prospect Theoretic measures deal with generic utility. source: Wikipedia. Prospect Theory Again, while I haven't seen any literature on the topic, it would be interesting if someone were to show that Prospect Theoretic risk measures (which are typified by Exhibit A) meet the coherence standards for a spectral risk measure given by: ${\displaystyle \rho :{\mathcal {L}}\to \mathbb {R} }$ satisfies: • Positive Homogeneity: for every portfolio X and positive value ${\displaystyle \lambda >0} \lambda >0$, ${\displaystyle \rho (\lambda > X)=\lambda \rho (X)}$; • Translation-Invariance: for every portfolio X and $\alpha \in \mathbb {R}$, ${\displaystyle \rho (X+a)=\rho (X)-a}$; • Monotonicity: for all portfolios X and Y such that ${\displaystyle X\geq Y}$ , ${\displaystyle \rho (X)\leq \rho (Y)}$; • Sub-additivity: for all portfolios X and Y, ${\displaystyle \rho (X+Y)\leq \rho (X)+\rho (Y)}$; • Law-Invariance: for all portfolios X and Y with cumulative distribution functions ${\displaystyle F_{X}}$ and ${\displaystyle > F_{Y}}$ respectively, if ${\displaystyle F_{X}=F_{Y}}$ then ${\displaystyle \rho (X)=\rho (Y)}$; • Comonotonic Additivity: for every comonotonic random variables X and Y, ${\displaystyle \rho (X+Y)=\rho (X)+\rho (Y)}$. Note that X and Y are comonotonic if for every ${\displaystyle \omega _{1},\omega > _{2}\in \Omega :\;(X(\omega _{2})-X(\omega _{1}))(Y(\omega _{2})-Y(\omega _{1}))\geq 0}$ • Interesting thought but thats kindof the sad story about prospect theory. It does not fulfill the necessary requirements that we have in our models. Clearly, the function above is not subadditive. Take X and -X as an example. Mar 2, 2018 at 12:26 • @vanguard2k I think the function in the illustration is for a single asset, so it really doesn't say anything about how things behave in a portfolio. Regardless, my point was that if you merge the intuitions of behavioral finance into a coherent risk measure, you get something that looks a lot like a spectral risk measure. Mar 3, 2018 at 18:16 As I know, I think that spectral risk measure is a new kind of measure developed from the CVaR (weighted average value of VaR) and in the framework of coherent risk measures. If you can prove that a risk measure is coherent then you can add any types of weighted function $$\phi$$ to make it a spectral risk measure. The underlying idea is that the sum of any number of coherent measures is also a coherent risk measure. • Utility functions just make them reflect attitude to risk of investors and sound more like behavioural finance. Apr 26, 2019 at 9:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9420799612998962, "perplexity": 458.6905733390614}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337680.35/warc/CC-MAIN-20221005234659-20221006024659-00306.warc.gz"}
https://www.homebuiltairplanes.com/forums/members/bifft.9807/	B Reaction score 108 Profile posts Latest activity Postings About • Thanks for letting me know about that. Since I'm using an RV component, I have been keeping up with all relevant issues/SBs etc. for the tailplane I am using so I was aware of it and will be incorporating the appropriate mod as required. I appreciate you taking the time to let me know. That's very kind of you. Cheers, Dave	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8582687377929688, "perplexity": 1175.978627534187}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738653.47/warc/CC-MAIN-20200810072511-20200810102511-00336.warc.gz"}
https://brilliant.org/problems/foundations-part-15/	# Foundations, part 15 Geometry Level 2 One leg of a right angled triangle is double of the other leg. If the hypotenuse is $H$, what is the area of the triangle? ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7739778161048889, "perplexity": 601.6869966081155}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178373761.80/warc/CC-MAIN-20210305214044-20210306004044-00391.warc.gz"}
https://www.physicsforums.com/threads/need-some-help-answering-this-problem-thanks.303608/	# Need some help answering this problem thanks 1. Mar 29, 2009 ### nsingh947 hi just wondering how you would solve this problem A 3 kg toy car with a speed of 6 m/s collides head on with a 2kg car traveling in the opposite direction with a speed of 4 m/s. If the cars are locked together after the collision with a speed of 2 m/s, how much kinetic energy is lost? 2. Mar 29, 2009 ### rock.freak667 Find the kinetic energies before impact. Then find the kinetic energy when the two stick together after impact. Find the difference. 3. Mar 29, 2009 ### danb Momentum is conserved, and kinetic energy is easy to calculate for each object. Incidentally, the problem is overspecified. They could have asked you to calculate the final speed from the masses and initial speeds. Similar Discussions: Need some help answering this problem thanks	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8855653405189514, "perplexity": 617.7674201258618}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886102967.65/warc/CC-MAIN-20170817053725-20170817073725-00588.warc.gz"}
https://www.varsitytutors.com/ap_physics_1-help/electric-force-between-point-charges	# AP Physics 1 : Electric Force Between Point Charges ## Example Questions ← Previous 1 ### Example Question #1 : Electricity Two point charges, each having a charge of +1C, are 2 meters apart. If the distance between them is doubled, by what factor does the force between them change? The force between the charges remains constant Explanation: This is a question where knowing how to effectively sift through a problem statement and choose only the information you need will really help. We are given a bunch of values, but only need to know one thing, which is that the distance between the two charges is doubled. Coulomb's law is as follows: We can rewrite this for the initial and final scenarios: We can divide one equation by the other to set up a ratio: We know that the final radius is double the intial, which is written as: Substituting this in we get: Rerranging for the final force, we get: ### Example Question #1 : Electric Force Between Point Charges What is the force exerted on a point charge of by a point charge of that is located away? Explanation: Use Coulomb's law. Plug in known values and solve. Note that a positive value for electric force corresponds to a repulsive force. This should make sense since the charge on both particles are the same sign (positive). ### Example Question #2 : Electric Force Between Point Charges If we have 2 charges, and , that are apart, what is the force exerted on by if we know that has a charge of and has a charge of ? Explanation: Use Coulomb's law. Note that the electric force between two charges of the same sign (both positive or both negative) is a positive value. This indicates a repulsive force. ### Example Question #3 : Electric Force Between Point Charges Determine the magnitude of the electric force between 2 protons that are 3nm apart. Also determine if this force is attractive or repulsive. ; attractive ; repulsive ; repulsive ; repulsive ; repulsive Explanation: Recall that Coulomb's law tells us that the magnitude of force between two point charges is given as: Here, is force between two particles, are the charges of each of the two particles, and is the distance between the two charges. In our case, and are identical since each is the charge of a proton which is given as:, and Thus, plug in known values and solve. To determine if the force is attractive or repulsive, we only need to examine the sign of the charges. Since both protons have the same sign for their charge (positive charges) they will repel. ### Example Question #4 : Electric Force Between Point Charges A point charge of magnitude is located 0.01m away from a point charge of magnitude . What is the electric force between the point charges? Explanation: Use Coulomb's law to find the electric force between the charges: ### Example Question #5 : Electric Force Between Point Charges A point charge of magnitude is 2nm away from a point charge of identical charge. What is the electric force between the point charges? Explanation: The electric force between two point charges is given by Coulomb's law: Now, plug in the given charges (both the same magnitude), the given constant, and the distance between the charges (in meters) to get our answer: ### Example Question #1231 : Ap Physics 1 What is the magnitude of the electric force between two charged metals that are 3m apart, that have absolute value of the charges being 1C and 3C? Explanation: We are given all the necessary information to find the magnitude of the electric force by using Coulomb's law: Where is Coulomb's constant given by and are the respective charges, and is the distance between the charges. In our case: ### Example Question #7 : Electric Force Between Point Charges Three charges are shown in the given figure. Find the net force on the "top" charge due to the other two (both magnitude and direction). Let and assume all charges are away from each other. Let be the bottom left particle, be the top particle and be the bottom right particle. Note the axis. Explanation: The method to solving Coulomb's law problems with electrostatic configurations is to find the magnitude of the force and then assign a direction based of what is known about the charges. Coulomb's law is given as: Where and are the two particles we are finding the force between and is the electric constant and is: Notice that the distances between and is the same as the and . Since the magnitudes of all charges are the same, that means that the magnitudes of the forces (not directions) are the same. So the force exerted on from is the same magnitude as the force exerted on from . A sketch of the forces is shown below: Remember that there are always equal and opposite force pairs. We only care about the forces acting on and the last picture shows the two forces that act on it from and . Notice that the vector arrows are of equal length (force magnitudes are equal) and in different directions. Coulomb forces obey the law of superposition and we can add them. Before we do that let's calculate the magnitude of the two forces pictured. Remember to convert distances to meters and charge magnitudes to Coulombs so the units work out and you are not off by any factors of . Both the red vector arrow and the blue vector arrow have magnitudes of . Notice in the diagram below that if the charges are spaced equidistant, the will form an equilateral triangle. The angle is the same angle that each vector on the right has relative to the line drawn. In order to add the vectors together we need to separate the components of the vectors into their x- and y-components and add the respective components. This is where symmetry can be handy to make the problem easier. Since the particles are equidistant and the charge magnitudes are all equal, this lead to the force magnitudes to be equal. By inspection it can be shown that the y-components must be equal and opposite and therefore cancel. This means that total magnitude of the force acting on is just the sum of the x-component forces. To get the x-components we can use the cosine of the angle. Since the angles are equal and the magnitudes are equal, the final answer will be: The final answer is in the positive x-direction, denoted by the positive answer and the to indicate in the x-direction. The answer must have a magnitude and direction to describe the net force acting on the particle. ### Example Question #8 : Electric Force Between Point Charges A mole of electrons have a charge of , which is called Faraday's constant. Given that Faraday's constant is , determine the electric force per mole exerted by individual moles of electrons on one another separated by by . Assume charges are static. Use Coulomb's law, and assume that moles of electrons behave like a point charge. Explanation: From Coulomb's Law: Where is the distance between point charges, , and and are charges of the electrons. In our case, ### Example Question #9 : Electric Force Between Point Charges If , and , then what is the magnitude of the net force on charge 2? Explanation: First lets set up two axes. Have be to the right of charge 3 and 2 in the diagram and be above charges 1 and 2 in the diagram with charge 2 at the origin. Coloumb's law tells us the force between point charges is The net force on charge 2 can be determined by combining the force on charge 2 due to charge 1 and the force on charge 2 due to charge 3. Since charge 1 and charge 2 are of opposite polarities, they have an attractive force; therefore, charge 2 experiences a force towards charge 1 (in the direction). By using Coloumb's law, we can determine this force to be in the direction Since charge 2 and 3 have the same polarities, they have a repulsive force; therefore, charge 2 experiences a force away from charge 2 (in the direction). By using Coloumb's law, we can determine this force to be: in the -direction If we draw out these two forces tip to tail, we can construct the net force: From this, we can see that and create a right triangle with the net force on charge 2 as the hypotenuse. By using the Pythagorean theorem, we can calculate the magnitude of the net force: ← Previous 1	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9846778512001038, "perplexity": 520.9742315986465}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039742978.60/warc/CC-MAIN-20181116045735-20181116071735-00521.warc.gz"}
https://link.springer.com/article/10.1007%2Fs00706-018-2243-6	Monatshefte für Chemie - Chemical Monthly , Volume 149, Issue 9, pp 1693–1699 # Monitoring of n-butanol vapors biofiltration process using an electronic nose combined with calibration models • Bartosz Szulczyński • Piotr Rybarczyk • Jacek Gębicki Open Access Original Paper ### Abstract Malodorous odors, by definition, are unpleasant, irritating smells being a mixture of volatile chemical compounds that can be sensed at low concentrations. Due to the increasing problem of odor nuisance associated with odor sensations, and thus the need to remove them from the air, deodorization techniques are commonly used. Biofiltration is one of the methods of reducing odorants in the air stream. In the paper, the possibility of using an electronic nose as an alternative method to gas chromatography for the online monitoring and evaluation of efficiency of the n-butanol vapors biofiltration process in a transient state was investigated. Three calibration models were used in the research, i.e., multiple linear regression, principal component regression, and partial least-square regression. The obtained results were compared with the theoretical values. ## Keywords Odorous substances Sensors Mathematical modeling Alcohols ## Introduction Among various methods of controlling volatile organic compounds’ (VOCs) emissions, biological techniques seem to be very promising due to low operating costs, possibility to treat gases with low concentration of odorants and very low secondary pollution generation. The use of biological methods for air purification has been known for over 60 years. Devices called biofilters are most commonly used for this purpose [1]. A typical biofilter is a column-type bioreactor packed with a bed made from either natural or synthetic materials. The process of biofiltration consists in the decomposition of contaminants by bacteria or other microorganisms located in the biofilm formed on the filter bed elements. The contaminated gas is humidified prior to entering the biofilter. The mechanism of biofiltration involves the diffusion of pollutants from the gas phase to the biofilm, covering the surface of the packing element. The compounds absorbed in the biofilm undergo biodegradation and the clean gas leaves the biofilter [2, 3]. Elements of a biofilter bed are moisturized with an aqueous phase. Therefore, the biofilm formed on the surface of such elements of bed allows for the absorption of hydrophilic compounds, as it is in the case of n-butanol. n-Butanol belongs to the group of VOCs, concentrations of which need to be controlled in the environment. Emissions of n-butanol are identified, i.e., from processes of thermal regeneration of adsorbents, from wastewater treatment plants, and waste disposal plants, coal mines, and other industrial activities [4, 5]. n-Butanol is characterized by harsh and alcoholic-like odor type [6], and it is irritating and hazardous to human health when inhaled. The effectiveness of the removal of such kind of compounds in the biofilters depends mainly on the rate of their biodegradation by microorganisms inhabiting the biofilm. This is so because the process limitation with respect to mass transfer of the hydrophilic compounds from the gas to liquid phase is negligibly small [7]. The most crucial parameters affecting the biofiltration efficiency include the type and porosity of the bed, the pressure drop through the bed, pH value, gas flow rate, temperature, and concentration of pollutants in the gas phase [8]. Mathematical modeling is a useful tool for the prediction of a biofilter performance. Biofiltration models usually follow a transfer-reaction scheme [9]. Such an approach requires the knowledge of physical (i.e., gas–liquid equilibrium and transfer coefficients) as well as biological (kinetics and efficiency of biodegradation) parameters. One of the first and the most popular models describing biofiltration was proposed by Ottengraf [10, 11]. According to [10], the Ottengraf model is based on the following assumptions: (1) the mass transfer resistance in the gas phase is negligible comparing to the mass transfer resistance in the liquid phase; (2) the biofilm thickness is much smaller than the diameter of a bed element; (3) the biofilm may be treated as a planar surface; (4) substrate transport through the biofilm occurs by diffusion; (5) the interface between the gas and the liquid phases is in the equilibrium; (6) biodegradation may be described by the Michaelis–Menten kinetics or by the Monod equation; (7) constant kinetic constants may be used due to the net growth of biomass in the biofilm which is controlled to be zero; (8) the biomass is uniformly distributed in the biofilter; (9) the biofilter is treated as a plug flow reactor. The Ottengraf model, proposed in 1983, is a rather simple model predicting the performance of the biofilter; however, it is still treated as a reference for other models and their modifications [12]. When modifying or developing a new model for the description of biofiltration, following problems must be taken into consideration: (1) an influence of unstable conditions during the biofiltration, (2) the possibility of interactions between the gas-mixture components, and (3) the identification of biodegradation inhibitors. Until the steady-state process conditions are established, the system is subjected to both first- and zero-order reactions. In addition, for a given moment of the process duration at two different horizontal cross-sections of the biofilter, the occurring reactions proceed with different rates and may follow the kinetics of different order. Therefore, it is impossible to determine the order of reactions in the initial period of the biofiltration process, because the process occurs in unsteady-state conditions. For this reason, the model proposed by Świsłowski [13] was used in this paper to predict the theoretical values of the time-dependent distribution pattern of n-butanol concentrations in the biofilter outlet gas stream. The calculation algorithm is shown schematically in Fig. 1. The determination of concentration of a compound at the inlet and outlet of a biofilter allows to calculate the efficiency of the process: $$\eta = 1 - \frac{{C_{\text{outlet}} }}{{C_{\text{inlet}} }},$$ (1) where η is the biofiltration efficiency; Cinlet/outlet is the concentration of the odorous compound in the inlet and outlet streams. The most popular methods used for the evaluation of the biofiltration efficiency are chromatographic methods, i.e., gas chromatography coupled with mass spectrometer or flame ionization detector. However, due to the high operating costs, the need to provide high purity gas or vacuum, these techniques are mainly exploited for laboratory tests and are rarely used for the monitoring of industrial biofiltration processes in the online mode. In recent years, there has been a significant increase in the interest in using electronic noses for quantitative and qualitative analyses for environmental monitoring [14, 15]. Due to the short time and low cost of a single analysis, electronic noses have become an alternative to gas chromatography. Electronic noses (e-noses) are devices that are supposed to mimic the human sense of smell and are used in many areas of human activity [16, 17, 18, 19, 20]. Such devices consist of four main components, as given in Fig. 2. The applied sampling system eliminates possible undesirable factors affecting the sensor response, and provides stable and reproducible measurement conditions (temperature, humidity, and gas flow velocity). Detection system is a set of sensors located in the measurement chamber. The most commonly used sensor types are commercially available sensors for the detection of volatile organic compounds, e.g., metal oxide sensors (MOS) [21]. Such sensors exhibit different selectivity and sensitivity, but, when coupled in a sensor matrix, produce a characteristic chemical image of the gas mixture (“fingerprint”). This image is transferred to the data collection system, which is responsible for the digital signal processing. The last but the most important element of the electronic nose system is a pattern recognition system, which assigns the received set of signals to one of the pattern classes or predicts the concentrations using the appropriate mathematical calibration model. The most commonly used models include multiple linear regression (MLR), principal components regression (PCR), and partial least-squares regression (PLSR). Construction of the above models utilizes a set of explaining variables (signals from the sensors comprising an electronic nose) and a set of dependent variables (values of substance concentrations in a gas mixture). A task for the calibration method is to develop a model allowing for the quantitative evaluation of a particular property or the properties based on the set of explaining variables. These methods find successful applications for the monitoring of the changes of concentrations of odorous compounds during biofiltration or sewage treatment [22, 23, 24, 25]. Multiple linear regression generates a linear relationship between a single dependent variable (y) and a set of several explanatory variables (x): $$y = a_{0} + a_{1} \cdot x_{1} + a_{2} \cdot x_{2} + \cdots + a_{n} \cdot x_{n} .$$ (2) The model can be used when the number of variables is smaller than the number of samples and when these variables are poorly correlated. In other cases, it is impossible to determine the regression coefficients (a), which are obtained by the least-squares method [26]. Principal component regression assumes reducing the number of explanatory variables by selecting few first principal components (PCs) in the place of the primary variables. The guiding idea of this method is to formulate a relationship between PCs and the expected property of the sample. The method may be applied in two stages and the first stage allows for the determination of the principal components using the principal component analysis (PCA) method. It allows to obtain uncorrelated matrix of variables. The second stage assumes the development of the MLR model with the use of principal components as variables: $$y = a_{0} + a_{1} \cdot {\text{PC}}_{1} + a_{2} \cdot {\text{PC}}_{2} + \cdots + a_{n} \cdot {\text{PC}}_{n} .$$ (3) The number of principal components (n) most often needs to be selected experimentally. The proper choice is of a great importance for the prognostic capabilities of the model. In the case when too few main components, the calibration model contains insufficient information necessary for the correct forecasting. However, if the number of main factors is excessive, unwanted information such as a noise or experimental errors is introduced to the model. The partial least-squares regression is the most commonly used method for the development of multidimensional calibration models. The task of the PLS method, like PCR, is the design of the model based on the mutually orthogonal factors. In the PLS method, such factors are created in different way than in the PCR method. In the PCR method, factors are the principal components created on the basis of the variables matrix only, while, in the PLS method, the relationship between variables and dependent variables matrices is taken into account. Each factor in the PLS method explains the maximum covariance between factors for the variables and factors for the dependent variables. Covariance combines a high variance of the variables matrix with a high correlation of the property of interest [27, 28, 29]. In the present paper, an electronic nose prototype combined with three types of calibration models (MLR, PCR, and PLSR) is used for the monitoring of n-butanol vapors biofiltration process. Research results are compared with theoretical values. ## Results and discussion For the data calibration, three models were developed, i.e., MLR, PCR, and PLSR. As a visual method of assessing the fit of the models to the experimental data, the correlation plots were prepared (Figs. 3, 4, 5). The root-mean-square error of prediction (RMSEP) was chosen as the numerical tool for the selection of the optimal model. The values of RMSEP for the developed models are given in Table 1. Table 1 Root-mean-square error of prediction (RMSEP) values for the developed models Model RMSEP/ppm Multiple linear regression (MLR) 7.5 Principal component regression (PCR) 12.8 Partial least-square regression (PLSR) 5.4 The results of the conducted research indicate that the most suitable calibration model for the determination of the n-butanol concentration is the PLS model (i.e., characterized by the lowest value of RMSEP = 5.4), and the least suitable model is PCR with the RMSEP value of 12.8. The obtained results show that, with a relatively small number of training data, PLSR models perform better than in the case of PCR methods. The multiple linear regression method, in terms of the value of mean square error, is placed between PLSR and PCR. It can be concluded that its estimation of the explained variable is relatively good (RMSEP = 7.5), taking into account a small number of degrees of freedom of the model. Good predictive capabilities of the developed models allowed to investigate the possibility of using the e-nose as a tool for monitoring and assessing the effectiveness of the n-butanol biofiltration process in unsteady-state conditions. In this part of the work, also the three models were applied (i.e., MLR, PCR, and PLSR). Using the electronic nose, the concentrations of n-butanol vapors at the inlet and outlet of the biofilter were determined for the process duration time from the start-up until reaching the stable process conditions. The obtained results (the ratio of the outlet-to-inlet concentrations) as a function of time are shown in Figs. 6, 7, and 8. Presented figures contain also the theoretical values of process efficiency calculated on the basis of the biofiltration model described in Fig. 1. Very good correlation between the experimental and theoretical results was obtained. The PLSR model presents the best fit to the theoretical curve. For the process duration time longer than about 5–6 h, the MLR and PCR models predicted lower values for the outlet concentration of n-butanol (CG) than the theoretical values. The largest discrepancies were observed for the PCR model which may be due to the presence of water vapor released from the filter bed, which was not present in the calibration samples. This problem has not been observed for the PLSR mode, which is the least susceptible to changes in the sample matrix composition among the investigated models. ## Conclusions It was found that the constructed electronic nose prototype together with the developed mathematical calibration models (MLR, PCR, and PLSR) can be successfully applied for the monitoring and efficiency assessment of the n-butanol vapors biofiltration process. The proposed models were characterized by a high compliance with the theoretical values. The best fit quality was obtained for the PLSR model. The obtained results confirm that the use of electronic noses as an alternative method to gas chromatography for the online monitoring of the biofiltration process is possible. Due to the low cost of the prototype and short time as well as low cost of a single analysis, the use of e-noses seems to be justified and purposeful for such applications. The possibility of obtaining the results in the online mode highlights the perspective of using e-noses as measuring elements in the automation systems for control and management of air biofiltration processes. ## Experimental Two research systems were used in the investigations: the first was used to develop calibration models for the electronic nose (Fig. 9) and the second system was used for the evaluation of a biofilter performance (Fig. 10). Mixtures of air and n-butanol vapors were generated using the bubbling phenomenon. Purified and dried air was passed through a vial containing n-butanol (Sigma-Aldrich). The formed mixture was diluted with a zero air stream to achieve the desired concentration of n-butanol in the mixture. The concentration was determined by measuring the weight loss of n-butanol in a vial according to the relationship: $$C = \frac{\Delta m}{V \cdot t},$$ (4) where C is the concentration, Δm is the vial mass change, V is the air flow rate, and t is the time. The air flow rates through the vial and the diluting air were controlled by mass flow controllers. Switching the three-way valve, the generated mixture was directed to the electronic nose working in the stop-flow mode (flow time: 30 s; stop time: 15 s). Then, the valve was switched again and zero air was introduced to the e-nose for sensors regeneration (for the time interval equal to 10 min). Measurements were made for five concentrations of n-butanol in the mixture: 15, 30, 60, 120, and 240 ppm. Each measurement was repeated three times. The biofiltration of n-butanol vapors was carried out using the system shown in Fig. 10. A mixture of air and n-butanol with a concentration of 240 ppm, generated as described above, was fed to the biofilter. The volumetric flow rate of the mixture through the packed bed was 1.2 dm3 min−1. Column biofilter was used during the investigations (outside diameter/inside diameter: 0.05/0.04 m, h = 1 m). Pine bark elements with an average size of 4–7 mm were used a biofilter packing material. Before starting the process, the bed was sprinkled with an aqueous solution of mineral salts. After the process start-up (process duration time: 12 h), every 15 min, the gas samples were collected and analyzed using the electronic nose prototype, constructed in the Department of Chemical and Process Engineering, Faculty of Chemistry, Gdańsk University of Technology. The device worked with eight TGS metal oxide sensors manufactured by Figaro Inc: TGS 2104, TGS 2106, TGS 2180, TGS 2201, TGS 2600, TGS 2602, TGS 2603, and TGS 2611. The collected sensor signals were saved on the computer using the Simex SIAi-8 analog-to-digital converter. The electronic nose operated in a stop-flow mode. The sample flow time through the chamber was 30 s, while the stop time was 15 s. For the calculations of a sensor signal (S), the quotient form was chosen: $$S = \frac{\Delta S}{{S_{0} }} = \frac{{S_{ \hbox{max} } - S_{0} }}{{S_{0} }},$$ (5) where Smax is the maximal value of the signal and S0 is the sensor baseline value. Data analysis and other calculations were performed using RStudio Desktop (v. 1.0.143) software. ## Notes ### Acknowledgements The investigations were financially supported by the Grant No. UMO-2015/19/B/ST4/02722 from the National Science Centre, Poland. ## References 1. 1. Sonil N, Prakash KS, Jayanthi A (2012) J Soil Sci Environ Manag 3:28Google Scholar 2. 2. Mudliar S, Giri B, Padoley K, Satpute D, Dixit R, Bhatt P, Pandey R, Juwarkar A, Vaidya A (2010) J Environ Manag 91:1039 3. 3. Ferdowski M, Avalos Ramirez A, Jones PJ, Heitz M (2017) Int Biodeterior Biodegrad 119:336 4. 4. Schmidt T, Anderson WA (2017) Environments 4:57 5. 5. Lee SH, Li C, Heber AJ, Ni J, Huang H (2013) Bioresour Technol 127:366 6. 6. Lewkowska P, Cieślik B, Dymerski T, Konieczka P, Namieśnik J (2016) Environ Res 151:573 7. 7. Cheng Y, He H, Yang C, Zeng G, Li X, Chen H, Yu G (2016) Biotechnol Adv 34:1091 8. 8. McNevin D, Barford J (2000) Biochem Eng J 5:231 9. 9. Pineda J, Auria R, Perez-Guevara F, Revah S (2000) Bioprocess Biosyst Eng 23:479 10. 10. Lim KH, Lee EJ (2003) Korean J Chem Eng 20:315 11. 11. Zarook SM, Shaikh AA (1997) Chem Eng J 65:55 12. 12. Qasim M, Shareefdeen Z (2013) Adv Chem Eng Sci 3:26479 13. 13. Świsłowski M (2002) Removal of organic vapors from the air in a biofilter with natural packing materials, Ph.D. Dissertation. Faculty of Chemistry, Gdańsk University of Technology, GdańskGoogle Scholar 14. 14. Capelli L, Sironi S, Del Rosso R (2014) Sensors 14:19979 15. 15. Szulczyński B, Wasilewski T, Wojnowski W, Majchrzak T, Dymerski T, Namieśnik J, Gębicki J (2017) Sensors 17:2671 16. 16. Gancarz M, Wawrzyniak J, Gawrysiak-Witulska M, Wiącek D, Nawrocka A, Tadla M, Rusinek R (2017) Measurement 103:227 17. 17. Wojnowski W, Majchrzak T, Dymerski T, Gębicki J, Namieśnik J (2017) Meat Sci 131:119 18. 18. Schnabel RM, Boumans MLL, Smolinska A, Stobberingh EE, Kaufmann R, Roekaerts PMHJ, Bergmans DCJJ (2015) Respir Med 109:1454 19. 19. Peris M, Escuder-Gilabert L (2016) Trends Food Sci Technol 58:40 20. 20. Romero-Flores A, McConnell LL, Hapeman CJ, Ramirez M, Torrents A (2017) Chemosphere 186:151 21. 21. Szulczyński B, Gębicki J (2017) Environments 4:21 22. 22. López R, Cabeza IO, Giráldez I, Díaz MJ (2011) Bioresour Technol 102:7984 23. 23. Romain AC, Nicolas J, Cobut P, Delva J, Nicks B, Philippe F-X (2013) Atmos Environ 77:935 24. 24. Littarru P (2007) Waste Manag 27:302 25. 25. Szulczyński B, Gębicki J, Namieśnik J (2018) Chem Papers 72:527 26. 26. Wise B, Gallagher N (1996) J Process Control 6:329 27. 27. Arnold MA, Burmeister JJ, Chung H (1998) Photochem Photobiol 67:50 28. 28. Malin F, Ruchti TL, Blank TB, Thennadil SN, Monfre SL (1999) Clin Chem 45:1651 29. 29. 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https://online.stat.psu.edu/stat501/book/export/html/965	# 10.1 - What if the Regression Equation Contains "Wrong" Predictors? 10.1 - What if the Regression Equation Contains "Wrong" Predictors? Before we can go off and learn about the two variable selection methods, we first need to understand the consequences of a regression equation containing the "wrong" or "inappropriate" variables. Let's do that now! There are four possible outcomes when formulating a regression model for a set of data: • The regression model is "correctly specified." • The regression model is "underspecified." • The regression model contains one or more "extraneous variables." • The regression model is "overspecified." Let's consider the consequence of each of these outcomes on the regression model. Before we do, we need to take a brief aside to learn what it means for an estimate to have the good characteristic of being unbiased. ### Unbiased estimates An estimate is unbiased if the average of the values of the statistics determined from all possible random samples equals the parameter you're trying to estimate. That is, if you take a random sample from a population and calculate the mean of the sample, then take another random sample and calculate its mean, and take another random sample and calculate its mean, and so on — the average of the means from all of the samples that you have taken should equal the true population mean. If that happens, the sample mean is considered an unbiased estimate of the population mean $$\mu$$. An estimated regression coefficient $$b_i$$ is an unbiased estimate of the population slope $$\beta_i$$ if the mean of all of the possible estimates $$b_i$$ equals $$\beta_i$$. And, the predicted response $$\hat{y}_i$$ is an unbiased estimate of $$\mu_Y$$ if the mean of all of the possible predicted responses $$\hat{y}_i$$ equals $$\mu_Y$$. So far, this has probably sounded pretty technical. Here's an easy way to think about it. If you hop on a scale every morning, you can't expect that the scale will be perfectly accurate every day —some days it might run a little high, and some days a little low. That you can probably live with. You certainly don't want the scale, however, to consistently report that you weigh five pounds more than you actually do — your scale would be biased upward. Nor do you want it to consistently report that you weigh five pounds less than you actually do — errr..., scratch that, maybe you do — in this case, your scale would be biased downward. What you do want is for the scale to be correct on average — in this case, your scale would be unbiased. And, that's what we want! ### The four possible outcomes ##### Outcome 1 A regression model is correctly specified if the regression equation contains all of the relevant predictors, including any necessary transformations and interaction terms. That is, there are no missing, redundant or extraneous predictors in the model. Of course, this is the best possible outcome and the one we hope to achieve! The good thing is that a correctly specified regression model yields unbiased regression coefficients and unbiased predictions of the response. And, the mean squared error (MSE) — which appears in some form in every hypothesis test we conduct or confidence interval we calculate — is an unbiased estimate of the error variance $$\sigma^{2}$$. ##### Outcome 2 A regression model is underspecified if the regression equation is missing one or more important predictor variables. This situation is perhaps the worst-case scenario, because an underspecified model yields biased regression coefficients and biased predictions of the response. That is, in using the model, we would consistently underestimate or overestimate the population slopes and the population means. To make already bad matters even worse, the mean square error MSE tends to overestimate $$\sigma^{2}$$, thereby yielding wider confidence intervals than it should. Let's take a look at an example of a model that is likely underspecified. It involves an analysis of the height and weight of martians. The Martian dataset — which was obviously contrived just for the sake of this example — contains the weights (in g), heights (in cm), and amount of daily water consumption (0, 10 or 20 cups per day) of 12 martians. If we regress $$y = \text{ weight}$$ on the predictors $$x_1 = \text{ height}$$ and $$x_2 = \text{ water}$$, we obtain the following estimated regression equation: ##### Regression Equation weight = -1.220 + 0.28344 height + 0.11121 water and the following estimate of the error variance $$\sigma^{2}$$: MSE = 0.017 If we regress $$y = \text{ weight}$$ on only the one predictor $$x_1 = \text{ height}$$, we obtain the following estimated regression equation: ##### Regression Equation weight = -4.14 + 0.3889 height and the following estimate of the error variance $$\sigma^{2}$$: MSE = 0.653 Plotting the two estimated regression equations, we obtain: The three black lines represent the estimated regression equation when the amount of water consumption is taken into account — the first line for 0 cups per day, the second line for 10 cups per day, and the third line for 20 cups per day. The blue dashed line represents the estimated regression equation when we leave the amount of water consumed out of the regression model. The second model — in which water is left out of the model — is likely an underspecified model. Now, what is the effect of leaving water consumption out of the regression model? • The slope of the line (0.3889) obtained when height is the only predictor variable is much steeper than the slopes of the three parallel lines (0.28344) obtained by including the effect of water consumption, as well as height, on martian weight. That is, the slope likely overestimates the actual slope. • The intercept of the line (-4.14) obtained when height is the only predictor variable is smaller than the intercepts of the three parallel lines (-1.220, -1.220 + 0.11121(10) = -0.108, and -1.220 + 0.11121(20) = 1.004) obtained by including the effect of water consumption, as well as height, on martian weight. That is, the intercept likely underestimates the actual intercepts. • The estimate of the error variance $$\sigma^{2}$$ (MSE = 0.653) obtained when height is the only predictor variable is about 38 times larger than the estimate obtained (MSE = 0.017) by including the effect of water consumption, as well as height, on martian weight. That is, MSE likely overestimates the actual error variance $$\sigma^{2}$$. This contrived example is nice in that it allows us to visualize how an underspecified model can yield biased estimates of important regression parameters. Unfortunately, in reality, we don't know the correct model. After all, if we did we wouldn't have a need to conduct the regression analysis! Because we don't know the correct form of the regression model, we have no way of knowing the exact nature of the biases. ##### Outcome 3 Another possible outcome is that the regression model contains one or more extraneous variables. That is, the regression equation contains extraneous variables that are neither related to the response nor to any of the other predictors. It is as if we went overboard and included extra predictors in the model that we didn't need! The good news is that such a model does yield unbiased regression coefficients, unbiased predictions of the response, and an unbiased SSE. The bad news is that — because we have more parameters in our model — MSE has fewer degrees of freedom associated with it. When this happens, our confidence intervals tend to be wider and our hypothesis tests tend to have lower power. It's not the worst thing that can happen, but it's not too great either. By including extraneous variables, we've also made our model more complicated and hard to understand than necessary. ##### Outcome 4 If the regression model is overspecified, then the regression equation contains one or more redundant predictor variables. That is, part of the model is correct, but we have gone overboard by adding predictors that are redundant. Redundant predictors lead to problems such as inflated standard errors for the regression coefficients. (Such problems are also associated with multicollinearity, which we'll cover in Lesson 12). Regression models that are overspecified yield unbiased regression coefficients, unbiased predictions of the response, and an unbiased SSE. Such a regression model can be used, with caution, for prediction of the response, but should not be used to describe the effect of a predictor on the response. Also, as with including extraneous variables, we've also made our model more complicated and hard to understand than necessary. ### A goal and a strategy Okay, so now we know the consequences of having the "wrong" variables in our regression model. The challenge, of course, is that we can never really be sure which variables are "wrong" and which variables are "right." All we can do is use the statistical methods at our fingertips and our knowledge of the situation to help build our regression model. Here's my recommended approach to building a good and useful model: 1. Know your goal, know your research question. Knowing how you plan to use your regression model can assist greatly in the model building stage. Do you have a few particular predictors of interest? If so, you should make sure your final model includes them. Are you just interested in predicting the response? If so, then multicollinearity should worry you less. Are you interested in the effects that specific predictors have on the response? If so, multicollinearity should be a serious concern. Are you just interested in summary description? What is it that you are trying to accomplish? 2. Identify all of the possible candidate predictors. This may sound easier than it actually is to accomplish. Don't worry about interactions or the appropriate functional form — such as $$x^{2}$$ and log x — just yet. Just make sure you identify all the possible important predictors. If you don't consider them, there is no chance for them to appear in your final model. 3. Use variable selection procedures to find the middle ground between an underspecified model and a model with extraneous or redundant variables. Two possible variable selection procedures are stepwise regression and best subsets regression. We'll learn about both methods here in this lesson. 4. Fine-tune the model to get a correctly specified model. If necessary, change the functional form of the predictors and/or add interactions. Check the behavior of the residuals. If the residuals suggest problems with the model, try a different functional form of the predictors or remove some of the interaction terms. Iterate back and forth between formulating different regression models and checking the behavior of the residuals until you are satisfied with the model. 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https://worldbuilding.stackexchange.com/questions/47891/why-is-this-creature-afraid-of-water-but-not-of-body-or-plant-fluids/47907	# Why is this creature afraid of water but not of body or plant fluids? I have a creature or more accurately creatures that I have a problem with. I can't figure out why it is afraid of water. They are landbased tiny tiny little piranha like organisms that work in unison. Each individual organism is about the size of phytoplankton and plankton. They work together almost like a hivemind but have no evil queen to rule them. Each individual creature is not intelligent and acts more on instinct and signals from others. Think of eusocial insects using chemicals and pheromones. Because you never see one alone and only in large clusters, they always appear like a low-lying mist or fog. Let's call a cluster of these creatures the Mistraille. Mistraille can consume all living plants and animals by entering the victim through a cut/wound/tear etc. and leave behind a desicated husk (I believe they consume everything, bones, muscles, all plant matter except the outer covering/skin but this can be changed if necessary). The plant/animal can still be alive when the Mistraille enters. After a time the Mistraille can actually move the animal around like a 'meatsuit' (this could allow isolated cases of Mistraille in areas not normally associated with it). A small amount of Mistraille enters the body, reproduces while consuming the body and emerges in greater numbers. The Mistraille therefore leaves a fairly desolate empty environment behind them. They appear to live in deserts — which came first, Mistraille or the desert? (rhetorical question). I didn't want an entire desert wasteland of a planet, so I have tried to limit Mistraille range by giving it two major weaknesses; light and water. Mistraille normally take cover during daylight hours, either by hiding deep in the desert sands, deep shadows (like basements, caves, inside empty shoes etc.) or in their latest victim. They are also physically constrained by large water bodies and can be temporarily repelled by water sprinkled at them (more on this later). EDIT I had already figured this would also limit their climate range as well. ie it would be limited to the dry, 'desert' mid latitudinal regions of the planet. Extreme variations in the day/night cycle, rain, humidity, and even soil moisture would hinder them. Equatorial regions would probably be too wet. High latitudinal areas can have deserts. If the Mistraille had managed to use a 'meatsuit' or darkness to travel there (by accident) it would then have to cope with the longer summer day cycles (only a brief dry night cycle) and the 'wetter' winter cycles. I still don't think high latitudes like tundra would be the best location. Same for the polar desert regions - 'eternal' day is not what this little critter is all about! EDIT See this climate map from Wikipedia as a reference to habitat location (thankfully this creature is not on Earth, so sleep peacefully!) Two minor restrictions are they cannot hide in or travel through rock/solid surfaces. Porous rock yes, solid rock no. Mistraille also cannot consume a victim from the outside. It has to get inside the body first. So any cuts, wounds, open sores are a way in. To further limit this I feel that natural orifices like mouths, noses, ears, bums, skin or plant pores should be off limits to entry (reasoning not completely worked out yet). I need limiting factors to stop the spread and range of said Mistraille as well as some way to keep it at bay at night by 'intelligent' creatures. ## Extra information incase it influences the answer I have figured out several constraints and reasoning behind their light weakness. • Mistraille actually are in deadly danger to any length of exposure to the UV spectrum of light. • Due to their limited exposure to daylight they have an unfounded fear of the entire visible spectrum of light (almost a pavlovan response). • They can be repelled at night by artificial light sources such as fire, or modern day torches (it is the light not the heat that they avoid). This won't prevent the Mistraille from crossing the barrier of light if it really decides to go at you. • I have figured that the parts of the plants that photosynthesize during the day would be off limits. Therefore Mistraille can only hideout during the day in deep shadows, animals and in the more solidish parts of the plants Eg. tree trunks. (I know that there are light and dark phases of the photosynthesis cycle, but hopefully you get my reasoning). ## Related information to question In working out the details on water I have figured out some constraints but not the reasoning. • I want to limit their spread, so I made them unable to cross large bodies of water; oceans, seas, rivers, and perhaps marshes. Mistraille could possibly create 'bridges' to cross little trickles or very tiny streams. Eg. ants working together to cross a small river but this might involve sacrificing those in the water. • At night or in the deep shadows you can temporarily 'repel' Mistraille by 'sprinkling' water at them. A deluge would also work, but you are in a desert so you don't want to use all the water at once. What I can't figure out is why they are afraid of water! They go inside animal and plant bodies that are made up of a large proportion of water. How can I reasonably explain the fear of the one but not the other? My question is: why are my creatures, Mistraille, afraid of water outside their victims but not when they are inside their victims? I've been thinking that maybe the water would interfere with their hivemind communication, isolating each creature from the cluster. But how would they then communicate inside their victims? Maybe something in the chemical makeup of the victims body fluids could trigger a delayed transformation to a form more adapted to the fluid environment. But with that reasoning it can't be related to the freshness or saltiness of the fluid and can't be plant /animal species specific. Hopefully you see my conundrum. I'm not looking for idea generation per say, just a somewhat valid reasoning on how I can explain my creatures actions. And if necessary alternate solutions. These are very tiny creatures, so their body structure would be fairly basic and not too complex. (I don't think they would be similar or based on felides. Sorry!). Something along the lines of this image by Sanja Zamuda ... I had been toying with a caste structure but now think I will definitely need one. Highly eusocial creatures are defined as having a job role bases on the creatures body characteristics from birth. No changing a worker into a queen or a queen onto a worker. I believe Mistraille would be 'primitively eusocial' - their job roles aren't defined from birth, they can have multiple generations, shared care for the young, etc. So using that basis I believe I can make Mistraille have different sets of body characteristics based on the surrounding environment. When they are travelling outside any victims they could be fairly similar to each other. Each simple creature communicating via pheromones and the larger collective consciousness a sort of hivemind with no queen directing any actions. These outside Mistraille move by either crawling/hopping or 'flying' on very basic proto wings. No swimming. The best image I have, in my head, is the classic sediment transport image by bouncing, rolling, dragging, and suspension etc. It is this 'outside' form that would be the most vulnerable to light and water (a holdover from their 'inside' forms?). When they encounter a victim, they enter and then this would trigger a process of transformation to occur. This transformation would result in a better adaptation for 'liquid' interiors but the reasoning so far of narrow osmosis range/required toxin would still hold (or a similar reason not yet mentioned). They could transform into several specialised bodytypes suited to what they are munching on Eg animal or plant AND bone, muscle, organs, plant fibres etc. They would also lose any proto wings they have and develop 'claws', 'razorsharp teeth' and 'swimming' abilities. The 'nests' where the Queens and child-rearing occur would be in locations safe from light (so in plants, in the protected areas not involved in photosynthesis). As I mentioned before, this transformation requirement from 'travel' mode to 'attack' mode (as @Drenzel called it) would explain why they can't eat a victim from the outside. It could also explain why natural orifices are off limits. They would still communicate by chemicals and pheromones but might be directed by several Queens. I don't believe the hivemind is as developed as each creature knowing and experiencing the others experiences (as these are very simple creatures) but rather each individual creature influencing and been influenced by the collective consciousness. THANK YOU VERY MUCH FOR THE ANSWERS SO FAR I'll be taking a little bit from most of them. • How does the swarm move? Do they fly/crawl/float? You say that they appear like a low-lying mist or fog and are land based, but could possibly "bridge" across trickles of water. This suggests they crawl / have appendages to link together (I'm imagining tiny insect-like creatures). – kwah Jul 21 '16 at 10:43 • I got interested in the light part. Beware the Vashta Nerada. They stalk not in every shadow but ANY shadow. (You should watch Doctor Who S04E09-S04E10, "Silence in the library", if you haven't already. You should ALL do) – xDaizu Jul 21 '16 at 12:06 • Oh my! I hadn't even made the connection! That was a good episode. 'hey, who turned off the lights?!' – EveryBitHelps Jul 21 '16 at 13:45 • Perhaps the water is what triggers them from 'travel' mode to 'attack' mode. So if they come into contact without actually been inside a person, they would switch into attack mode.... then die on the floor. Would give them a reason to fear water that isn't inside what they want to feed on. Also this means any area with decent levels of humidity would be pretty much immune to them as their small size would mean even humidity would cause an issue. – Drenzul Jul 21 '16 at 14:48 • Distinction between porosity and permeability (very important to soft-rock geologists in particular): porous rocks have interstitial gaps in the structure, but possibly not connected; permeable rocks have connected interstitial gaps in the structure, allowing substances of sufficiently low viscosity to flow through the rock. Many rocks are porous without being permeable. – Pieter Geerkens Jul 23 '16 at 14:49 As a hive mind species, one of their greatest fears is isolation of the individual units from the rest of the hive, this would often mean death for the individual units, and if all of them are scattered, death for the hive. Large bodies of water, especially flowing or moving water (rivers, waterfalls, waves) have tended to separate them from one another, killing or severely injuring those hives who encounter fast moving water. Over time they have developed an innate fear of all large concentrations of water, but especially indications of fast moving water. A misting of water, especially a directional spray, often corresponds to a large moving body of water, like a waterfall or river rapids. This signals one of their primal fears, causing them to contract as a group and retreat from the source. • Can I +2? I really like the directional spray idea. Thanks! – EveryBitHelps Jul 20 '16 at 13:53 • This could also be coupled with the rain if you want to keep them inside or cause them to act less predictably. – David Starkey Jul 20 '16 at 16:49 • Just thought of a new scenario. Would an arterial spurt of blood scare them off to? It's fast moving directional spray! Could lead to some interesting scenarios. – EveryBitHelps Jul 24 '16 at 13:24 Maybe something in the chemical makeup of the victims body fluids could trigger a delayed transformation to a form more adapted to the fluid environment. But with that reasoning it can't be related to the freshness or saltiness of the fluid and can't be plant /animal species specific. Let's not be specific, then, and let's look at something that does kill some animals in our own real world. The salinity of our bloodstream is different from that of most bodies of water. The same can be said for the sap in plants. That's because living beings accumulate many different ions in their organisms to some extent, but also eliminate excesses to some extent. For example, our blood has as much salt content as saline - 9 grams per liter. For salinity purposes, our blood is within the range of brackish water (between 0.5 and 30 grams per liter). That's more salty than fresh water, but less salty than seawater. So let's say that your Mistrailles have a bodily salt content like our own. But unlike many animals and plants, they can't regulate the salt in their organisms like we do. The range of salinity they can tolerate is narrower. If they are immersed in drinking water, their cells will each individually absorb a lot of water and pop, just like our own red blood cells in a cup of drinking water. You could also see this happening to a sea jellyfish if you take it out of the sea and place it in a bucket full of drinking water, but if you do that you have no soul. If they are immersed in seawater, the water will run out of their cells and they will die dehydrated. Just like our own red blood cells in a cup of seawater. You can also see this happening to a river hydra (poor cnidaria have very narrow salinity ranges they can live with) if you take it from a river and put it into a bucket full of salty water, but if you do that I am going to dennounce you to PETA. And that's why they can't stand water, unless it has been carefully treated to have exactly the amount of saltiness they will tolerate. You should probably be really careful around your Saline IV storages. • Imagine accidently injecting someone with infected saline water! urghhhh, I just made myself shudder in horror! – EveryBitHelps Jul 20 '16 at 17:44 • I love that your answer is both scientifically based in the real world, and also made me chuckle! – Taegost Jul 20 '16 at 20:34 • A desert animal needs to keep the water inside of it, so just topic exposure to water won't trigger an osmotic damage any more than what a human (land animal) can survive in water with the head out. – Davidmh Jul 21 '16 at 12:23 • But this osmotic answer plus the directional spray answer could explain why the topical exposure DOES work. – EveryBitHelps Jul 21 '16 at 13:55 • @Davidmh the creatures described in the question are microscopic. What would be a topical exposure to us would be complete immersion for them. – Renan Jul 21 '16 at 14:01 They communicate through chemicals in the air, and I think this is the solution. While flesh contains a lot of water, it mainly isn't in a liquid state, being stored in the tissues. Even though blood is liquid, it isn't an excessive amount. Any chemicals that they release to communicate with each other and keep their hive mind like link going are going to be contained in their victims body. But a river or a large body of water would dilute and wash away all of the communication chemicals cutting them off from the rest. Being a very social creature, this silencing effect is very disconcerting for them, causing a lot of fear, and so they avoid it instinctively. • The concentration/diluting of these communication chemicals could influence why it takes awhile to get to work eating the victims insides. Thanks! – EveryBitHelps Jul 20 '16 at 13:41 • You would also have to have them "go to ground" during a rain shower, though in their desert like environment this may be a rare occurrence. Heavy fog/mist may affect them as well. Might keep them down in the early morning when there is dew on the ground (so they are active in early to middle night, not pre-dawn morning). – Jason K Jul 20 '16 at 13:50 • @JasonK Going to ground during rain would definitely be a thing, since rain is good at clearing particulates out of the air. I don't know about fog though, if that's even a problem in the desert, since it's suspended in the air. It may mute the chemical communication, but it does that with sound to some extent too. I don't think dew would be a problem. They don't have a problem with small amounts of water, just larger amounts. – AndyD273 Jul 20 '16 at 15:38 • My thoughts exactly! – JDługosz Jul 21 '16 at 6:03 One option is that the water is mostly fresh and the Mistraille can not manage cellular integrity due to osmotic pressure. The salt in their systems would leach out and water enters in killing them if they are immersed. The blood of the host contains a similar amount of minerals / salts but entering the fresh water causes their cells to burst. Even sprinkling of water greatly weakens them, stopping them from entering the host. Salt water could be missing important salts / minerals or contain predators that like to eat them. The water could also contain viruses or bacteria that are deadly to the Mistraille but that the host immune system destroys. Either way this shall fuel my nightmares for some time. Consider that, like their irrational fear of general light because of a vulnerability to a specific range of light wavelength, the Mistraille are only vulnerable to something commonly found in the world's water bodies. In that event, any of the following could apply: • Natural predator lives in or near bodies of water (believability: low-moderate; why is a natural predator of a desert creature dependent on bodies of water?) • A toxin is released by flora or fauna that appears frequently around bodies of water, but the amount in the water is only a danger to very small organisms; larger organisms filter it out and/or tolerate it (believability: moderate-high; some creatures are immune to Mistraille because they let the toxin into their blood, others store the toxin in an organ they avoid) • Mistraille are dependent on a toxin that must exist in the right quantity within an organism and the toxin breaks down quickly in bodies of water, so organisms don't have a chance to absorb it (believability: moderate; kind of sounds like the Mistraille are an engineered creature run amok intended to clean up an industrial spill) [courtesy AmiralPatate] These were off the top of my head. If I come up with any more, I will add them in later. • why is a natural predator of a desert creature dependent on bodies of water It may not be that they are specifically sought out, but rather that they happen to be not very distinguishable from plankton, and therefore get eaten before they can reach any destination. Or maybe they can't swim. – AmiralPatate Jul 20 '16 at 13:31 • And since I'm full of comments, an alternative take on the toxin would be to flip it. Maybe they need the toxin and it can only be found in the desert. Whatever they eat must have the right amount of toxin. So a plant that produces the toxin would have too much of it and be left alone. Oceans wouldn't have enough and be left alone as well. Other plants or creatures would ingest/inhale toxin (no negative effect necessary) and become an acceptable treat. You're free to use that one in your answer. – AmiralPatate Jul 20 '16 at 13:39 They can consume all living plants and animals by entering the victim through a cut/wound/tear etc. and leave behind a desicated husk (I believe they consume everything, bones, muscles, plant matter except the outer covering but this can be changed if necessary). They need a cut/wound/tear to enter victim but they can consume bones, that may be because they have two different "stances", lets say migration and feeding so when they are in migration mode they have a normal solid shell-type body, but in contact a liquid they dissolve like a slime which is useful to enter in other organism via circulatory system and just dissolve/control-it but not so when you just spread away in water with huge solubility and nothing to feed of. Well, do your creatures crawl, do they fly? Can they swim? Can they "breathe" underwater? Maybe they can fly but just short distances. Too short to cross a large body of water. They'd drown. So they don't even try. Just like a grasshopper (insert any short-range flying creature) wouldn't try to jump over a mile-wide river or an ocean. Maybe they can fly long distances but they can't dive into the water (because they can't breathe underwater or because it hurts them otherwise), so they know that they would starve over a sea or ocean, like locust. Maybe they can even swim/dive but they are really slow and it's hard to catch fish for them so why bother when there's easier meat on land. A major plot point in the novel Fragment is that (significant spoiler warning!) salt water is fatally toxic to the Henders Is. wildlife, seemingly on contact, due to osmosis action. The novel is an interesting read in its own right, but may be especially useful for your project. Some additional thought or incorporation of other ideas suggested may improve this point to apply in your built world. Maybe water makes them unable to move? Dry sand or flour can be even moved by wind, but it sticks together when wet. So when you spray water at them, they stick to each other and fall to the ground. And in the larger bodies of water they have trouble keeping together. But in the human body they either slowly move inside the muscles/other solid things (while eating them) or are transported by the blood flow. They are a group, and they are small so they might not want to go in water because: 1. They get split, and a single mistraille would probably die 2. On land, they can easily see predators coming but in the water they move so fast they might accidentally land in the mouth of a predator I think they might be scared because water is the only fluid that cleans their surface from hormones, or something like that, that they need to orient itself and that might cause death, while other fluids like blood don't do that. For example, scout ants leave a trace of hormones when looking for food, so when they come back other ants can follow the trace an bring food back, lets say this "cretures" have hormones all around its body that they use to find their own, or the hormones may do many things like give them a sense, for example if we don't have saliva, we lose the taste in our tongue, these are just some ideas without closing so you can do the rest • This is only a single sentence. Can you flesh out this answer some? – kingledion Feb 22 '18 at 17:06 • edited answer with some examples – user32608 Mar 15 '18 at 13:13 • Welcome to WorldBuilding! If you have a moment please take the tour and visit the help center to learn more about the site. Have fun! – Sec SE - clear Monica's name Mar 15 '18 at 14:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2641524076461792, "perplexity": 2132.4877907589944}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251696046.73/warc/CC-MAIN-20200127081933-20200127111933-00362.warc.gz"}
http://math.stackexchange.com/questions/272821/quadratic-equation-with-matricial-coefficients	# Quadratic equation with matricial coefficients If I have a equation in the form $${\lambda ^2}{I_N} + \lambda {M_1} + {M_2} = {0_N}$$ where ${I_N}$ is the identity matrix of order $N$, $M_1$ and $M_2$ are matrices of ($N\times N$) order and $\lambda \in \mathbb C$ belongs to the complex numbers . What are the mathematical tools or the mathematical framework to solve this kind of equations? - Looking at the equation for one coefficient gives you two possible values for $\lambda$. You can test both of them to see if they solve the equation. – Quimey Jan 8 '13 at 14:18 For the equation to have a solution, your matrices $M_1$ and $M_2$ must necessarily commute. This would only be one requirement. To see this, consider the case for diagonalizable $M_2$ so that $PM_2P^{-1} = D$ for some invertible $P$ and diagonal $D$. \begin{align} P\left(\lambda^2 I_N + \lambda M_1 + M_2 = 0_N\right)P^{-1} \\ \lambda^2 I_N + \lambda PM_1P^{-1} + D = 0_N \end{align} Here we can see that $M_1$ must not only have the same spectrum as $M_2$ (since otherwise the non-zero elements in the off-diagonal would not be canceled in the sum), but it must have appropriate eigenvalues such that the single $\lambda$ simultaneously solves for each diagonal term. tl:dr: solve for $\lambda_1$ and $\lambda_2$ at any desired coordinate. Check if either one works globally. If not, then there is no solution. - I've comproved that this eq does not have solution, this because M1 and M2 do not commute and they do not share the same spectra. Thanks a lot. – Daniel.B. Jan 10 '13 at 10:17 +1 and thanks for noting me that gap there. – Babak S. Jan 16 '13 at 15:56 @Babak Thanks, and let me know when to delete my other comments on your question, I will look up and refresh my memory on the array syntax in the meantime – adam W Jan 16 '13 at 16:04 You noted me a very important thing and I want you to accept my thanks. Let them be there. Your comments contain some useful points I didn't know them. ;-) – Babak S. Jan 16 '13 at 16:08 If the equality is to be true, we need to check that for $\{M_1\}_{ij}$ and $\{M_2\}_{ij}$ we have $$\lambda^2 \delta_{ij} + \lambda \{M_1\}_{ij} + \{M_2\}_{ij} = 0$$ where $\delta_{ij}$ is the Kronecker delta and $1 \leq i,j \leq n$. There's probably a better way of investigating it - I'm having a think about that now. Certainly, from the $i \neq j$ case, we are left with a single variabled equation, so at most we have one $\lambda$ as a solution. - The determinant does not distribute over the sum. – Quimey Jan 8 '13 at 15:11 Indeed - I guess I thought that the determinant was a ring homomorphism. – Andrew D Jan 8 '13 at 15:15 Indeed, by adam W's answer, $M_1$ is without loss of generality in Jordan canonical form, so that $M_1 = \bigoplus_{k=1}^M (\mu_k I_{n_k} + N_{n_k})$ for $\mu_k$ the eigenvalues (counted with the relevant notion of multiplicity) and $N_{n_k}$ the appropriate nilpotent matrices. Then $$\lambda^2 I_N + \lambda M_1 = \bigoplus_{k=1}^M ((\lambda^2 + \lambda\mu_k) I_{n_k} + \lambda N_{n_k}),$$ so that $M_2$ must necessarily have the analogous block diagonal form $$M_2 = \bigoplus_{k=1}^M (\alpha_k I_{n_k} + \beta N_{n_k})$$ for some constants $\alpha_k$ and $\beta$. Hence, when the dust settles, you're left with the system of quadratic equations $$\lambda^2 + \mu_k \lambda - \alpha_k =0$$ together with the additional equation $\lambda = \beta$ whenever $M_1$ (and hence also $M_2$) is not diagonal. I think this should be correct? -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9555039405822754, "perplexity": 302.1932952811522}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422121833101.33/warc/CC-MAIN-20150124175033-00016-ip-10-180-212-252.ec2.internal.warc.gz"}
http://www.algebra.com/cgi-bin/show-question-source.mpl?solution=142642	Question 190084 <font face="Garamond" size="+2"> You can go through the process of finding all of the possible factors of -15 and 10, blah blah blah, but there is a much simpler and quicker method. Use the idea that if [tex \LARGE x = a] is a root of the equation formed when you set the polynomial equal to zero, then [tex \LARGE x - a] must be a factor of the polynomial. Since this is a quadratic trinomial, you can set it equal to zero and use the quadratic formula to find the roots -- then the factors become obvious. Step 1: Set the trinomial equal to zero. [tex \LARGE \ \ \ \ \ \ \ \ \ \ 10w^2-19w-15=0] Step 2: Solve with the quadratic formula: [tex \LARGE \ \ \ \ \ \ \ \ \ \ w = \frac{-b \pm sqrt{b^2 - 4ac}}{2a} = \frac{-(-19) \pm sqrt{(-19)^2 - 4(10)(-15)}}{2(10)} = \frac{19 \pm sqrt{961}}{20} = \frac{19 \pm 31}{20} ] So [tex \LARGE \ \ \ \ \ \ \ \ \ \ w = \frac{19 + 31}{20} = \frac{50}{20} =\frac{5}{2} \ \ \Rightarrow\ \ 2w - 5 = 0] Or [tex \LARGE \ \ \ \ \ \ \ \ \ \ w = \frac{19 - 31}{20} = \frac{-12}{20} =\frac{-3}{5} \ \ \Rightarrow\ \ 5w + 3 = 0] Verifying that [tex \LARGE \ \ \ \ \ \ \ \ \ \ (2w - 5)(5w + 3) = 10w^2-19w-15] is left as an exercise for the student. By the way, if you end up with a pair irrational roots, then the trinomial is not factorable over the rational numbers. John [tex \LARGE e^{i\pi} + 1 = 0] </font>	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.982337474822998, "perplexity": 406.4470280357851}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368698063918/warc/CC-MAIN-20130516095423-00067-ip-10-60-113-184.ec2.internal.warc.gz"}
https://meta.stackexchange.com/questions/68388/there-should-be-universal-latex-mathjax-guide-for-sites-supporting-it/70559	# There should be universal LaTeX/MathJax guide for sites supporting it Currently, stats, math, cstheory and physics have MathJax support which turns LaTeX code into equation. At least on math, occasionally there are users that do not know this feature or don't know it's possible to use LaTeX (MathJax), resulting a badly formatted post. I suggest that there should be a common "LaTeX/MathJax typesetting help" page for those sites that enabled MathJax support, like the "Markdown editing help" that is present on all sites. Preferably, there should also be a line • LaTeX equations $\sin^2 \theta$ in the "How to Format" on the right hand side. ### See also: The MathJax help link should point to a more specific guide • Wait. Geeks aren't born knowing LaTeX? – dmckee Oct 23 '10 at 15:36 • You mean a MathJaX help. MathJaX =/= LaTeX. – Loop Space Oct 23 '10 at 15:41 • @AndrewStacey: well, MathJax ≈ LaTeX-surrounded-by-dollar-signs – Kip Nov 17 '10 at 14:16 • @Kip: shakes head sadly at the ignorance of youth. I \emph{guess} it depends on what \textbf{you} mean by \LaTeX\ really. – Loop Space Nov 17 '10 at 14:24 • @Kip: Even in LaTeX editors, $-signs work, just not if there are too many things in math mode. . – Abhimanyu Pallavi Sudhir Jul 18 '13 at 4:41 ## 4 Answers This is basically completed, but I can't find a good help / demos page to link to for MathJaX. There is this: http://www.mathjax.org/demos/ but oddly it requires users to "view source" before showing them the markup required, which is ... annoying. Per suggestion, I am now changing it to http://www.math.harvard.edu/texman/ • Maybe you can pop a question on meta.math.se and ask the good people there to write one? Not sure how much work it would take though. – Yi Jiang Nov 19 '10 at 6:50 • @YiJiang: meta.stackexchange.com/questions/68388/…. (I'm putting it here instead of meta.math.SE as this is not just a math.SE feature.) – kennytm Nov 19 '10 at 19:26 • I found the Wikipedia formula-writing page very helpful: en.wikipedia.org/wiki/Help:Displaying_a_formula – Kip Nov 20 '10 at 3:17 • Jeff, this was added as a comment to the meta.math post, but I'll repeat it here so you're more likely to see it- the help box is almost perfect, but MathJax will render the $\sin^2 \theta$ in it, so what the user actually sees is "MathJax equation sin² θ", which isn't correct. It has to be wrapped between <code/> tags or <span class="tex2jax_ignore"/> tags to avoid MathJax parsing it. – Kip Nov 20 '10 at 3:19 • I just spent 15 minutes trying to figure out how to do a simple subscript. Sending me off to mathjax.org/demos frankly wasted my time as I vainly clicked around looking for help. Please don't provide that link any more as there's no obvious way to get any syntax help! I wrote the MathJax people directly and they suggested math.harvard.edu/texman. Would you please consider changing your link on the question-asking page to point there instead? It will save your users much wasted time and frustration. – ErikE Jan 21 '11 at 20:19 • @emt sure I can change it to that, checking that change in now. – Jeff Atwood Jan 22 '11 at 0:51 • Thanks a lot. There may be better resources out there (in fact, the MathJax folks asked me to keep them posted if a better one is found) but for now that one is at least adequate and did have syntax help like I was expecting. – ErikE Jan 22 '11 at 2:22 Let's write our own help page for our use of MathJax. Here is a start. It is based on Stack Overflow's own Markdown editing help, the FAQ for typing math on math.SE and Math Overflow, and "Using LaTeX" on ask NRICH. Characters in bold italics indicate highlighting. # MathJax turns LaTeX markup into beautiful formulae This site supports typesetting mathematical formula with AMS-LaTeX markup, powered by the MathJax rendering engine. ## Entering math mode Surround the TeX code with dollar signs to insert an inline equation The integers$x,y,z$form a Pythagorean triplet when$x^2 + y^2 = z^2$. and use double dollar signs to insert an equation in its own line The Bessel functions$J_n(x)$and$Y_n(x)$are solutions to the Bessel equation $$x^2 y'' + x y' + (x^2 - n^2) y = 0$$ where$n$is a constant. ## Basic LaTeX markup • Superscript and subscript — x^2, a_n, a_{n+1}, H_n^{(2)} • Spacing — a\ b (text space). Other kinds of spacing. • Square root and radicals — \sqrt{x}, \sqrt[3]{x} • Fraction — \frac{a}{b} • Sum and integral — \sum_{k=0}^n k^2, \int_0^1 x^3 dx • Greek letters — \alpha (α) to \omega (ω); \Gamma (Γ) to \Omega (Ω) • Symbols — \ne (≠), \ge (≥), \le (≤), \sim (∼), \pm (±), \to (→), \infty (∞), etc. • Function names — \sin, \cos, \log, \lim, etc. Visit Detexify2 to lookup command for a symbol. Check the MathJax documentation for the complete list of commands supported. ## Show source Right-clicking on any equations should reveal a context menu. Clicking "Show source" will open up a new window showing the LaTeX markup that generates it. ## Need More Detail? The Not So Short Introduction to LaTeX2e is a good beginner's guide on the LaTeX system. • Let's get this up! Right now the link provided is not helping anybody. – ErikE Jan 21 '11 at 20:20 • Lack of proper docs & examples is actually getting worse, as even more fantasy-themed sites such as Worldbuilding are supporting it, but only link to mathjax.org, which only links to docs.mathjax.org which has LaTeX links to the glossary of docs.mathjax.org which links to wikipedia.org/wiki/LaTeX... 15 clicks and 3 deliberate searches later to find something that resembles respectable docs just to type $\Delta\$. This may be the opportunity for SO Docs to step up as the de-facto resource. – IT Bear Feb 14 '17 at 20:47 I brought this up on meta.math and was directed to this question. I thought I'd share the mockup here too, showing what I'd like: A much much more detailed MathJax tutorial/reference has been created on Math.SE: MathJax basic tutorial and quick reference	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5801709890365601, "perplexity": 4924.700694083696}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039746061.83/warc/CC-MAIN-20181119171420-20181119193420-00284.warc.gz"}
https://www.intechopen.com/books/medical-imaging-in-clinical-practice/clinical-applications-of-nuclear-medicine/	InTechOpen uses cookies to offer you the best online experience. By continuing to use our site, you agree to our Privacy Policy. Medicine » Diagnostics » "Medical Imaging in Clinical Practice", book edited by Okechukwu Felix Erondu, ISBN 978-953-51-0986-0, Published: February 20, 2013 under CC BY 3.0 license. © The Author(s). # Clinical Applications of Nuclear Medicine By Sonia Marta Moriguchi, Kátia Hiromoto Koga, Paulo Henrique Alves Togni and Marcelo José dos Santos DOI: 10.5772/53029 Article top ## Overview Figure 1. Normal salivary gland imaging. Dynamic images are performed during 30 minutes and citric stimulus is on first fifteen minutes. Region of interest are placed on right and left parotid (red and dark blue) and submandibulary (yellow and light blue) glands and time activity curves are created showing quantitative uptake and excretion analyses. Figure 2. Anormal salivary gland imaging. Absence uptake and non excretion in parotid glands confirmed by quantitative curves by region of interest (red and dark blue). Figure 3. Scintigraphy on esophageal transit. Normal, adynamia and adynamia with incordination patterns, respectivelly. Figure 4. Gastroesophageal reflux scintigraphy. A single episode with a short time, reaching the upper esophageal segment (black arrow) and during a long time (red arrow). Figure 5. Liver-spleen scintigraphy. Focal nodular hyperplasia. Anterior and posterior images. Focal uptake increased in liver (black arrow). Spleen increased too (red arrow). Figure 6. Myocardial perfusion scintigraphy with 99mTc-sestamibi. A: Pre-angioplasty: ischemia of the apex and the middle and apical regions of the anteroseptal wall of the left ventricle. B: Post-angioplasty: a study without evidence of myocardial ischemia. Figure 7. Imaging of myocardial infarction with 99mTc-pyrophosphate. 99mTc: trasmural infarction in the anterolateral wall of the left ventricle. Figure 8. Normal pulmonary scintigraphy.Inhalation and perfusion images are compared. Homogeneous uptake in lungs. Matched findings. Figure 9. Dynamic renal scintigraphy with 99mTc-DTPA: flow, normal function and nonobstructive excretory pathways. Figure 10. Dynamic renal scintigraphy with 99mTc-DTPA and use of diuretic: Deficit of flow and left renal function associated with obstructive hydronephrosis. Figure 11. Normal renal scintigraphy with 99mTc-DMSA. Figure 12. Renal scintigraphy with 99mTc-DMSA, renal scars. Figure 13. Radionuclide cystography: right vesicoureteral reflux. Figure 14. Bone scintigraphy in children. A. normal scan: Symmetric uptake on the skeletal and presence of physiological osteoblastic activity in the growth cartilage. B. Acute phase of avascular necrosis in right femoral head. Vascular permeability decreased (green arrow) and photopenic area (brown arrow) in right femoral head. C. Three phase bone scan. Osteosarcoma in the right humerus. Flow, vascular permeability and osteoblastic activity increased in right humerus (red arrows). Figure 15. Bone scintigraphies in adults. A. Normal scan: symmetric uptake on the sckeletal. B. Single bone metastasis on left rib. C. Multiple bone metastasis. Multiple focal uptake on skull, scapulas, ribs, spine, pelvis and right femur. D. Monostotic Paget Disease on right humerus. Intense uptake on right humerus. E. Hyperparathyroidism. Intense uptake on skull and focal uptake on ribs. Figure 16. Whole body scan with gallium 67. A. normal scintigraphy. B. Lymphoma with lymphonodopathy. Uptake in left axillary lymphonode. C. Lymphoma with lymphonodapathy in right axillary, supravicular and mediastinal chain and left lung. D. Lymphoma in inguinopelvic lymphonode and soft tissue in right leg. Figure 17. Scintimammgraphy. Breast carcinoma in right and left side (black arrows) and lymphonodal metastase (red arrow). Figure 18. Dacrioscintigraphy. Normal exam. Radiotracer reachs right nasal cavity (black arrows). Total retention in billateral lacrimal sacs. Right lacrimal sac (red arrows) and left lacrimal sac (light blue arrows). Figure 19. Breast lymphoscintigraphy. Anterior and left lateral images. After injection of radiopharmaceutical substance in left breast (yellow arrows) and SLN in left axillary lymphatic chair ( light blue arrows). Figure 20. Billateral breast lymphoscintigraphy. Two sentinel lymph nodes are identified in left and in right axillary lymphatic chain. Figure 21. Thyroid scintigraphies. A. Graves’ Disease. Diffuse thyroid uptake. B. Plummer’s Disease. Nodular uptake on left thyoid lobe with suppression of the gland. Figure 22. Whole body scan post radioiodine therapy. Radioidine on thyroid tissue and on cervical lymphodes (red arrows). In another patient, notice lymphonode (green arrows and lung (light blue arrows) metastasis. Figure 23. Phaeochromocytoma. Focal uptake in posterior abdomen aspect (red arrows). Late images are better to identify the lesion. Figure 24. Bone scan. Bone metastasis.Multiple focal uptake on skeletal, # Clinical Applications of Nuclear Medicine Sonia Marta Moriguchi1, 2, Kátia Hiromoto Koga2, Paulo Henrique Alves Togni1, 3 and Marcelo José dos Santos4 ## 1. Introduction Nuclear Medicine is a medical specialty in which radioactive substances are used for diagnostic and therapeutic purposes. Historically, its major development occurred after the Second World War. After the attack on Pearl Harbor, the United States developed nuclear reactors to produce atomic bombs, which were subsequently dropped on the Japanese cities of Hiroshima and Nagasaki. After the end of the war, the United States was involved in the campaign for application of Atomic Energy for Peace, which stimulated implementation of knowledge of nuclear energy for medical applications, among other beneficial actions. There is no doubt that this was the greatest advance in the production and distribution of radionuclides for medical purposes. The first radionuclide for medical applications was iodine-131, and this was followed by several others. Artificial production of technetium for diagnostic purposes was a milestone in the history of nuclear medicine. Today, this radioisotope is used the one most for producing imaging. In the beginning, the images were documented using rectilinear scanner and subsequently using scintillation cameras or so-called gamma cameras, with images of poor definition. With technological development, improvements to gamma cameras became possible. The acquisition of functional images, which had previously only been done on a two-dimensional plane, became tomographic with three-dimensional reconstruction. This was named Single-Photon Emission Computed Tomography (known as SPECT), and it increased the sensitivity of detecting abnormalities or lesions. More recently, gamma cameras have been coupled with computed tomography (CT) or magnetic resonance imaging (MRI), thereby forming hybrid machines and increasing the effectiveness of identifying lesions or functionally abnormal tissues, at their sites. Technological advances have also been important for Positron Emission Tomography (known as PET), thereby massively increasing the applicability of this method, especially related to oncologic processes, with molecular imaging. The diagnostic and therapeutic applications are based on the kind of radiation used. In general, gamma emitters are used for diagnosis, and technetium-99m is the most common agent for this purpose. For therapy, beta radiation emitters such as iodine-131 are the agents most used. Scintigraphy is a noninvasive imaging diagnosis method using low doses of radiation, it is painless, has reasonable cost and availability, and enables functional or metabolic assessment of organs or structures. Its advantage is clear, especially when the possibility of analysis using other methods is limited. It is based on administration of radiation-emitting substances to patients, with detection by scanning using a scintillation camera. These radioactive substances may migrate to the organs themselves or, when that does not happen, they may bind to other substances, thus forming complexes called radiopharmaceuticals that are taken up by the target organ. There are specific pharmaceuticals for each organ, e.g. MDP, DTPA, sestamibi, etc., thus making it possible to perform bone, renal or cardiac scintigraphy, respectively. The great majority of radiotracers represent the physiology or metabolic activity of some part of the body, but without altering the function of these structures or forming part of the metabolism. The main characteristic of scintigrams is that they provide information on the functioning and metabolism of organs and structures. Hence, they differ from other imaging methods such as ultrasound, CT scans or MRI, which are anatomical, and thus complement the diagnostic investigation. From this perspective, it is important to distinguish between the diagnostic approaches for benign or malignant diseases. In benign lesions, the most important information comes from functional assessment of each organ. This may show that the organ function is normal or is deviating from normal, and this is assessed together with the evolution of the disease or the post-intervention changes. Malignancies are assessed based on metabolic activity and findings of active primary or metastatic tumors. Details relating to residual tumors, viable tumors, recurrence, or disease progression are important and can be differentiated. Based on this information, the clinical application of nuclear medicine is to highlight the physiological or metabolic structures or organs involved. This chapter does not aim to teach the methodology for performing scintigraphy, but to provide some knowledge for professionals who are not specialists in this field, so that the usefulness of this method in relation to various diseases can be seen. This chapter is divided into applications and therapy using conventional scintigraphy with single-photon emitters. The radionuclide most used for performing single-photon scintigraphy is technetium 99m, which is a pure gamma radiation emitter, with energy of 140 keV. This is considered to be a low energy level with ideal characteristics for producing images. It can be administered alone or coupled with pharmaceuticals to form complexes with specific characteristics relating to the preferential uptake for various human organs or structures. For each type of scintigraphy, there is a specific radiotracer uptake mechanism that interfaces with the metabolism or excretion of the organ. In the following, most of the applications of diagnostic nuclear medicine in different systems of the human body are presented. The general precautions to be taken in cases of pregnancy, breastfeeding, breastfed infants and young children, for all the procedures in nuclear medicine, are indicated. This should be discussed on a case-by-case basis. ## 2. Gastrointestinal system Application of nuclear medicine to the gastrointestinal (GI) system is very useful for investigating many diseases. This is a noninvasive and painless examination, with administration of low doses of radiation to patients. It is easy to perform and is indicated for diagnosing and following up gastrointestinal diseases. The long acquisition time for most examinations increases the sensitivity for detecting gastrointestinal abnormalities. Scintigraphy is generally of use for assessing organ function and the kinetics of gastrointestinal transit or excretion. ### 2.1. Salivary gland imaging This assesses the function and excretion of the salivary glands, both in the initial diagnosis and in post-treatment follow-up. The main indications include: tumors, cysts, inflammatory or infectious diseases, calculosis and Sjögren’s syndrome. The radioisotope used is pertechnetate, an anion that is concentrated and secreted by the epithelial cells of the salivary glands in the same way as seen with the anions that make up the saliva. Thus, this substance reflects the production and physiological secretion of the saliva. This radiotracer is administered intravenously, and sequential images of the head are acquired for 30 minutes. Over the first ten minutes, increasing concentration of radiotracer in the salivary glands is observed, which represents the function. After administration of citric stimulus, generally using lemon, the excretion phase begins. The uptake peak usually occurs five to ten minutes after starting to administer the radiotracer, and complete excretion begins immediately after the stimulation with lemon (Figure 1). ### Figure 1. Normal salivary gland imaging. Dynamic images are performed during 30 minutes and citric stimulus is on first fifteen minutes. Region of interest are placed on right and left parotid (red and dark blue) and submandibulary (yellow and light blue) glands and time activity curves are created showing quantitative uptake and excretion analyses. The scintigraphic abnormalities depend on the type and severity of disease. Most tumors present diminished or absence of uptake radiotracer, except for Warthin’s tumor. Acute inflammatory and infectious diseases present uptake increased because of the increased vascularization and diminished secretion. Abscesses and cysts do not show any uptake. Patients with Sjögren’s syndrome either do not concentrate radioactive material or concentrate very little of it (Figure 2). ### Figure 2. Anormal salivary gland imaging. Absence uptake and non excretion in parotid glands confirmed by quantitative curves by region of interest (red and dark blue). Other agents that are used to assess the salivary glands include gallium-67 and 111 In/99mTc-labeled white blood cells, in cases of inflammatory or infectious diseases. ### 2.2. Scintigraphy on esophageal transit and emptying Scintigraphy on the esophageal transit is a noninvasive examination with oral administration of radiotracer that supplies information on esophageal motility, in relation to the duration of esophageal transit and segmental motor abnormalities such as adynamia and lack of coordination. It is indicated for patients with suspected primary or secondary motor disorders, both for diagnosis and for follow-up of therapeutic interventions, in conditions such as achalasia, scleroderma, diffuse esophageal spasm, nutcracker esophagus, diabetic enteropathy, nonspecific motor disorders, Chagas’ disease, neoplasm, systemic lupus erythematosus, polymyositis, myasthenia gravis, myotonic dystrophy, esophagitis, alcoholism and others. The radiopharmaceuticals indicated for these assessments are those that are not absorbed by the esophageal mucosa, such as colloids and chelates: technetium-99mTc-sulfur colloid and diethylenetriamine pentaacetic acid (DPTA). The radiopharmaceuticals are administered orally, diluted in 10 ml of water, and deglutition is stimulated every 20 seconds with the patient in either a supine or an upright position. The transit time for the entire esophagus and in its three segments (upper, middle and lower) is quantified and the motor abnormality pattern (adynamia or lack of coordination) is determined (Figure 3). ### Figure 3. Scintigraphy on esophageal transit. Normal, adynamia and adynamia with incordination patterns, respectivelly. ### 2.3. Investigation of gastroesophageal reflux Scintigraphy is the most sensitive noninvasive method for detecting gastroesophageal reflux, especially in children. Colloids with low absorption rates in the esophageal and gastric mucosa are used, thereby reflecting the kinetics of the tracer within the digestive system. After oral administration of 99mTc colloid, and with a field of view covering the stomach and esophagus, episodes of gastroesophageal reflux are identified and information on the quantity and duration of the reflux and the point that it reaches are obtained (Figure 4). It has the advantage of continuous and more prolonged acquisition, which increases the sensitivity of the method. Other additional information obtained includes assessment of pulmonary aspiration, in the event that the reflux of the ingested material reaches the pulmonary tree. ### Figure 4. Gastroesophageal reflux scintigraphy. A single episode with a short time, reaching the upper esophageal segment (black arrow) and during a long time (red arrow). ### 2.4. Gastric emptying This is a noninvasive examination performed after intake of solid foods, liquids or a mixture of these. The emptying time and kinetics of the radiotracer in the stomach depend on the composition of the food ingested. Several pharmacological materials can be labeled with the radioactive substance, and the composition of both the food and the radiotracer depends on the standard adopted by each laboratory as the reference value. Computer acquisition is required to determine the half-time of emptying and/or percent of emptying and to generate gastric emptying time-activity curves. The main indications include diabetic gastroparesis, anorexia nervosa, gastroesophageal reflux, gastritis, gastric ulcer, duodenal ulcer, Zollinger-Ellison disease, connective tissue disorders and others, along with postsurgical evaluations, vagotomy and gastrectomy. ### 2.5. Liver-spleen imaging Other imaging methods such as MRI, CT and ultrasound offers better information about the anatomic display of liver and spleen than does this exam. The radionuclide colloid imaging is capitalized by phagocitosis by Kupffer cells of liver and spleen. The uptake and distribution of 99mTc-colloid in liver and spleen reflects perfusion and the distribution of functioning reticulendothelial cells. Usually, the information of liver-spleen scan include the size, shape and position, the distribution aspect of activity within the organs, as homogeneity or non-homogeneity, presence of any or many focal defects in activity and relative distribution of colloid among the liver, spleen and bone marrow. Most of the masses seen on MRI, CT or US, which take up 99mTc colloid contain Kupffer cells, and are benign. These present with increased hepatic uptake and include: focal nodular hyperplasia (Figure 5), cirrhosis with regenerating nodule, Budd-Chiari syndrome and Superior vena caval obstruction. Masses with decreased hepatic uptake can be benign or malignant. These include: hepatoma, metastasis, cyst, adenoma, hemangioma, abcess, and pseudotumor. The most common causes of focal defects in the spleen include: abcess, cyst, infarct, lymphoma, and hematoma. ### Figure 5. Liver-spleen scintigraphy. Focal nodular hyperplasia. Anterior and posterior images. Focal uptake increased in liver (black arrow). Spleen increased too (red arrow). ### 2.6. Hepatic blood pool imaging This exam is indicated for evaluating hemangiomas. These lesions are clusters or large blood filled sinuses. They are usually asymptomatic, and are found as incidental findings during MRI, CT or US performed for others indications. The radiotracer used is 99mTc-red blood cells (RBC), injected intravenously. The typical appearance of 99mTc-RBC scan is a focal area of decreased perfusion on the first study (flow phase), and in the immediate images because the flow with 99mTc-RBC is relatively low compared to the hemangioma. About 1 or 2 hours later, the radiolabelled cells reach the hemangioma vessels, and then these lesions present as a focal hot spot, with intensity similar to the heart. This method is highly specific to confirm hemangioma. ### 2.7. Gastrointestinal bleeding imaging The common causes of lower GI bleeding in adults include neoplasms, inflammatory bowel disease, diverticular disease and angiodysplasia. The GI Imaging is a noninvasive method that provides information especially of lower GI bleeding. The effective therapy for acute GI bleeding depends on accurate localization of the site of bleeding. There are two radiotracer that localize the GI bleeding; 99mTc-RBC and 99mTc-colloid. The first one is preferred in the investigation of GI hemorrhage, especially in cases of intermittent or slow bleeding, because the radiotracer remains in the intravascular space. Imaging may be performed over a period of 24 hours. The second one is high, specifically to identify the bleeding site, but the sensitivity is low, because it is performed for a short time and the bleeding needs to be present at the moment of scintigraphy. ## 3. Cardiovascular system Nuclear medicine examinations play an important role in the noninvasive evaluation of cardiac physiology. ### 3.1. Myocardial perfusion imaging Myocardial perfusion imaging (MPI) has high sensitivity to evaluate perfusion in the left ventricular wall and thus indirectly assess coronary flow. The ischemic cascade is the basis and the best justification for the use of nuclear medicine examinations in the evaluation of coronary artery disease. Myocardial perfusion imaging can be performed with thallium-201 chloride and Pharmaceuticals labelled with 99mTc (sestamibi, tetrofosmim and teboroxime). To use thallium-201 chloride it is necessary to fast for at least 4 hours. Radiopharmaceuticals labelled with 99mTc have advantages and disadvantages when compared to thallium-201 chloride, as best rate of counts and less sensitivity to assess viability, respectively. The stress phase can be accomplished by exercise or by the use of drugs such as dipyridamole, adenosine, and dobutamine. The sensitivity and specificity of these types of stress are similiar. Clinical applications of the study with thallium-201 chloride are: diagnosis of coronary artery disease, assessing the extent and severity of coronary stenosis, myocardial viability assessment and therapeutic efficacy (CABG and angioplasty). Radiopharmaceutical labelled with 99mTc are usually associated with cardiac monitoring during image acquisition, thus allowing quantitative analysis with motility evaluation of the left ventricular wall and ejection fraction. Clinical applications of the study using radiopharmaceuticals labelled with 99mTc are: a diagnosis of coronary artery disease, risk stratification post-myocardial infarction and therapeutic efficacy (Figure 6). ### Figure 6. Myocardial perfusion scintigraphy with 99mTc-sestamibi. A: Pre-angioplasty: ischemia of the apex and the middle and apical regions of the anteroseptal wall of the left ventricle. B: Post-angioplasty: a study without evidence of myocardial ischemia. ### 3.2. Myocardial viability imaging The principle objective of myocardial viability assessment is to identify patients eligible for coronary artery bypass grafting (CABG). Several criteria were used to determine the clinical impact of CABG: improvement in regional left ventricular function, in global left ventricular function (ejection fraction), symptoms, functional capacity, in cardiac remodeling and long term prognosis [1]. Imaging with thallium-201 chloride and home-redistribution protocol can be used to assess the presence of viable myocardium. Using the protocol stress-rest-reinjection, in addition to similar information, the presence of ischemia can be evaluated. ### 3.3. Myocardial infarction imaging Currently this study has been little used, due to advances in methods of enzymatic detection of acute myocardial infarction. Radiopharmaceuticals used can be 99mTc-pyrophosphate and Antimyosin-Fab-DTPA-In-111. The maximum uptake of 99mTc-pyrophosphate occurs 24 to 72 hours after the event. Planar imaging with 99mTc pyrophosphate detect acute transmural with a sensitivity of at least 90% and a specificity of 70% (Figure 7). Tomographic imaging (SPECT) can improve the specificity to around 80%. ### Figure 7. Imaging of myocardial infarction with 99mTc-pyrophosphate. 99mTc: trasmural infarction in the anterolateral wall of the left ventricle. Antimyosin has an overall sensitivity of 92% for the detection of acute MI [2]. ### 3.4. Multi Gated Acquisition (MUGA) The objective is to assess the global and regional ventricular function. The radiopharmaceutical used is 99mTc-red blood cells (RBC), erythrocytes labeled with 99mTc. The parameters evaluated in this study are: motility of the ventricular wall, left ventricular ejection fraction, analysis of phase and amplitude. The clinical indications are: acute myocardial infarction, coronary artery disease, cardiomyopathy, valvular disease, congenital heart disease, therapeutic efficacy assessment and evaluation of cardiotoxic drugs. The sympathetic and parasympathetic innervation of the heart plays an important role in regulating the cardiac function [3]. The activation of sympathetic innervation causes increased heart rate (chronotropic effect), contractility (inotropic effect) and conduction atrioventricular [4]. Norepinephrine is produced and stored in presynaptic vesicles in sympathetic nerve terminals [5]. Thus, the radionuclide used for cardiac adrenergic imaging is 123I-MIBG (metaiodobenzylguanidine) that is an guanethidine analogue which mimics norepinefrina [6]. The clinical indications are: heart failure, cardiomyopathy, cardiac transplantation, ischemia and myocardial infarction and ventricular tachyarrhythmias. ## 4. Pulmonary system Pulmonary embolism (PE) is an important and treatable illness caused by migration of thrombus to the pulmonary circulation, commonly from the veins of the lower extremities. Untreated, PE can cause death [7]. The treatment includes oral anticoagulants, heparin and thrombolytic agents. The clinical presentation of PE is variable, from asymptomatic to sudden death, including cough, hemoptysis, chest pain, breathlessness, syncope, palpitations, tachypnoea, cyanosis, tachycardia, pulmonary hypertension and right heart failure. But, these symptoms are not specific of PE, needing more tests to confirm or refuse the PE diagnostic. Recently, Bajc et al, purposed a clinical algorithm for the investigation of patients with suspected PE. If the clinical likelihood of PE is low and the quantitative D-dimer is negative, a diagnosis of PE is unlikely and further investigations are not required. If the clinical likelihood of PE is low and the quantitative D-dimer is positive, further investigations for a range of diagnoses including PE may be required, particularly if the D-dimer level is markedly elevated. If the clinical probability is other than low, it seems more appropriate to skip the D-dimer test and refer the patient directly to the appropriate imaging technique. This may be Ventilation (V) and perfusion (P) imaging (V/PSCAN) or multidetector computed tomography of the pulmonary arteries (MDCT) depending on the local availability, medical expertise, and the patient’s clinical condition. V/PSCAN has virtually no contraindications and yields a substantially lower radiation burden than MDCT [8]. A combined ventilation and perfusion study increases the specificity for PE diagnosis. A combined 1-day protocol is preferred. The scan can be with planar lung imaging (anterior, posterior, left and right lateral and left and right posterior oblique) or Spect imaging. In pregnancy only a perfusion scan is recommended. ### 4.1. Ventilation lung scintigraphy (V) Ventilation studies, in general, are performed after inhalation of inert gases 133Xe and 81mKr, radiolabelled aerosols 99mTc-DTPA and 99mTc-labelled Technegas. It is performed for mapping regional ventilation. ### 4.2. Perfusion lung scintigraphy (P) Perfusion scintigraphy is accomplished by microembolization with radiolabelled particles injected into a peripheral vein. The commercially used particles are MAA, which are labelled with 99mTc. The particle distribution accurately defines regional lung perfusion. V/PSCAN exploits the unique pulmonary arterial segmental anatomy. Each bronchopulmonary segment is supplied by a single end-artery. In principle, conical bronchopulmonary segments have their apex towards the hilum and base projecting onto the pleural surface. Occlusive thrombi, affecting individual pulmonary arteries, therefore produce characteristic lobar, segmental or subsegmental peripheral wedge-shaped defects with the base projecting to the lung periphery. V/P mismatch within bronchopulmonary segment(s) defected by PE, ventilation is usually preserved. This pattern of preserved ventilation and absent perfusion within a lung segment gives rise to the fundamental signiture for PE diagnosis using V/PSCAN, known as V/P mismatch. Follow-up of PE using imaging is essential to assess the effect of therapy, differentiate between new and old PE on suspicion of PE recurrence and investigate physical incapacity after PE [9]. ### Figure 8. Normal pulmonary scintigraphy.Inhalation and perfusion images are compared. Homogeneous uptake in lungs. Matched findings. ## 5. Genitourinary tract imaging In nuclear medicine the studies of genitourinary system can be divided into superior and inferior genitourinary tract. Studies evaluating the superior genitourinary tract include the kidneys, allowing evaluation of several characteristics such as blood flow, function, anatomy and integrity of the collection system, aiding in the diagnosis of different pathologies. For the lower genitourinary tract studies are represented by radionuclide cystography and testicular scintigraphy. Renal radiopharmaceuticals commonly used to meet the various pathologies are 99mTc-MAG3, 99mTc-DTPA, 99mTc-GHA and 99mTc-DMSA, being dependent on the indication of particular characteristics. 99mTc-MAG3 has as a main uptake mechanism tubular secretion (98% tubular secretion, 2% of glomerular filtration and extraction fraction of 40-50%). the 99mTc-DTPA has as a main uptake mechanism glomerular filtration (100% filtration and extraction fraction of 20%). 99mTc-GHA has a mixed uptake mechanism, being, glomerulo-tubular (10-20% tubular secretion and 80-90% glomerular filtration). The 99mTc-DMSA is attached to the renal cortical (40-50% cortical binding in 2 hours). ### 5.1. Clinical applications in the superior genitourinary tract Dynamic renal scintigraphy renogram represents the study commonly used to evaluate the various pathologies associated with superior genitourinary tract. #### 5.1.1. Obstruction of the genitourinary tract It is the main indication of renal dynamic studies. The exam is simple, painless, easy to perform and only prior hydration is necessary. It lasts 30 to 50 minutes, and such variation is associated with the use of diuretics (Figures 9 and 10). ### Figure 9. Dynamic renal scintigraphy with 99mTc-DTPA: flow, normal function and nonobstructive excretory pathways. #### 5.1.2. Hypertension of renovascular origin For this condition, the renal dynamic study is done in two phases: one utilizing a stimulus by angiotensin converting enzyme inhibitor, one hour before administration of the radiopharmaceutical and the other from the merely studying renal dynamic without stimulus considered study baseline. According to the pathophysiology of renovascular disease, the standard pattern of diagnosis is an abnormal study with stimulation of the angiotensin converting enzyme inhibitorassociated with a normal baseline study. #### 5.1.3. Renal transplant In renal transplant, renal dynamic study is mainly used for evaluation of its most common complications such as acute tubular necrosis and rejection. The scintigraphic pattern of acute tubular necrosis and acute rejection are very similar, with preserved or slightly reduced flow and reduced glomerular filtration rate. The time and symptoms are the key to diagnosis. In serial renal studies, the renal graft dysfunction secondary to acute tubular necrosis should improve or remain unchanged, while the rejection demonstrates progressive deterioration. Currently, ultrasound is the method of choice for renal transplant dysfunction [10]. ### Figure 10. Dynamic renal scintigraphy with 99mTc-DTPA and use of diuretic: Deficit of flow and left renal function associated with obstructive hydronephrosis. #### 5.1.4. Acute pyelonephritis and renal scarring The renal cortical scintigraphy with 99mTc-DMSA is the procedure of choice for evaluating acute pyelonephritis and renal scarring. The image acquisition takes place 2 to 3 hours after intravenous administration of the radiopharmaceutical so that attachment occurs at the same cortical. The scintigraphic patterns in acute pyelonephritis are focal involvement of a single area or multiple areas and diffuse involvement of the kidney. It has 100% sensitivity and specificity above 87% [11]. Renal scarring is a consequence of acute pyelonephritis, which may develop in 37% to 80% of children after an episode of infection [11,12] (Figures 11 and 12). ### Figure 11. Normal renal scintigraphy with 99mTc-DMSA. ### Figure 12. Renal scintigraphy with 99mTc-DMSA, renal scars. ### 5.2. Clinical applications in the lower genitourinary tract #### 5.2.1. Assessment of vesicoureteral reflux Radionuclide cystography permits visualization of very small volumes of reflux, and is probably more sensitive than contrast cystography [13]. The procedure is performed by infusion of saline and radiopharmaceuticals within the bladder through the catheter, thereby evaluating the presence of reflux (Figure 13). #### 5.2.2. Testicular torsion Testicular torsion is considered a surgical emergency and the availability of this tissue is mainly related to ischemic time. The testicular ultrasound is a simple method and easily performed for evaluation of this condition, however, in children evaluating the flow can be difficult, testicular scintigraphy is indicated. The scintigraphic findings depend on the stage of testicular torsion, in the early phase there is a normal flow, reduced or absent and the still image is a slight reduction in uptake of the radiotracer within the testicle, followed by an increase in flow and static image appearance of halo of mildly increased activity around a centrally cold testicle, ending with testicular infarction, in which there is an increased flow rate and persistent halo of increased activity around a cold center. ## 6. Musculoskeletal system ### 6.1. Bone scintigraphy Bone scintigraphy identifies single or multiple focal or diffuse areas with increased osteoblastic activity, which reflects local bone remodeling. It is a highly sensitive examination for detecting such abnormalities, but its specificity is limited. It needs to be analyzed in conjunction with other imaging examinations. It is indicated for both adults and children, but should be interpreted differently for these two groups, given that the normal distribution of radiopharmaceutical in the skeleton differs between adults and children, particularly because of the presence of physiological osteoblastic activity in the growth cartilage of children. These bone scans are based on the principle of phosphonate uptake in bone tissue, especially in blastic lesions. For example, from this principle, the presence of osteoblastic metastases from breast tumors or prostate tumors can be seen, among others. Likewise, changes typical of benign diseases such as bone infections, inflammatory activity of rheumatic diseases, and prosthesis complications like loosening, infection, etc., can be seen. The radiopharmaceutical used most, which is called 99mTc-methylene diphosphonate (99mTc-MDP), binds to the amorphous phase of hydroxyapatite crystals by means of chemoadsorption. It is administered intravenously as a bolus. Images can be acquired immediately afterwards when information on the blood supply and vascular permeability is important, like in cases of infectious or tumor growth processes. They may also only be acquired later on, after 2-3 hours of injection, with acquisition of whole-body images in the anterior and posterior projections, in order to acquire information on osteoblastic activity. It is worth emphasizing that this examination shows low sensitivity to predominantly lytic pathological conditions or to conditions with low bone remodeling, except in cases associated with significant osteoblastic abnormalities, such as in investigations of associated fractures, for example, in patients with multiple myeloma. The great advantage of this method is that it assesses the whole body in a single examination with high sensitivity, and it guides other examinations that are more specific. #### 6.1.1. Clinical applications for children Based on informations above, the mean indications of bone scan include: primary benign or malignant bone tumors and bone metastases; acute osteomyelitis versus soft-tissue inflammation; subacute and chronic osteomyelitis; septic arthritis as a complication of osteomyelitis; and aseptic arthritis; aseptic necrosis (Legg-Calvé-Perthes disease) and sickle cell disease; equivocal radiographic findings after trauma; stress fractures; occult fractures; child abuse; multiple trauma; complications of fractures and therapy; and Sudeck’s atrophy; surgeryguided by bone scintigraphy, like as osteoid osteoma; bone dysplasia; Camurati-Engelmann disease; evaluations on skeletal involvement (brown tumors); and hyperparathyroidism; arthritis and bone pain [14]. Scintigraphies in children are showed in figure 14. ### Figure 14. Bone scintigraphy in children. A. normal scan: Symmetric uptake on the skeletal and presence of physiological osteoblastic activity in the growth cartilage. B. Acute phase of avascular necrosis in right femoral head. Vascular permeability decreased (green arrow) and photopenic area (brown arrow) in right femoral head. C. Three phase bone scan. Osteosarcoma in the right humerus. Flow, vascular permeability and osteoblastic activity increased in right humerus (red arrows). #### 6.1.2. Clinical applications for adults A little difference is observed between the chindrens and adultsindications of bone scan. In this last group, the pathologies include: primary and metastatic bone tumors: staging, follow-up and post-therapy evaluation; distribution of osteoblastic activity prior to radiometabolic therapy (89Sr, 153Sm-EDTMP and 186Re-HEDP); osteomyelitis; Paget’s disease, osteoporosis and hyperparathyroidism; arthropathy, low back pain and sacroiliitis; fibrous dysplasia and other rare congenital conditions; stress fractures, shin splints, occult fractures; avascular necrosis and loose or infected joint prosthesis [15] (Figure 15). ### Figure 15. Bone scintigraphies in adults. A. Normal scan: symmetric uptake on the sckeletal. B. Single bone metastasis on left rib. C. Multiple bone metastasis. Multiple focal uptake on skull, scapulas, ribs, spine, pelvis and right femur. D. Monostotic Paget Disease on right humerus. Intense uptake on right humerus. E. Hyperparathyroidism. Intense uptake on skull and focal uptake on ribs. ## 7. Scintigraphy with gallium-67 citrate Because of the characteristics of gallium-67 uptake in tissues, this radiotracer can be used in relation to neoplastic diseases, especially lymphomas, and in cases of chronic inflammatory or infectious processes, such as those in fever of unknown origin or in patients with acquired immunodeficiency. The radiotracer is administered intravenously 48 hours before producing whole-body initial images in the supine position, in the anterior and posterior projections. Delayed images, produced at least from 72 hours and up to 5 days after injection, may be needed to differentiate normal colonic activity from lesions in the abdomen. This allows clearance of nonspecific activity from the body, and enhancement of the target in relation to the background in the images. The technologist or physician should give the patient a thorough explanation about the examination. Food and liquid restrictions are not mandatory. Bowel preparation is optional. In patients with constipation, oral laxatives prior to imaging may decrease the activity in the bowel. In this case, laxatives should be given on the day before gallium-67 scintigraphy (at least 18 hours prior to scanning). Gallium-67 scanning should be avoided within 24 hours of blood transfusion or gadolinium-enhanced MRI, which could interfere with gallium-67 biodistribution. It is also advisable to wait 3-4 weeks after chemotherapy before performing follow-up imaging. Management of patients with lymphoma is very useful, especially in intermediate or high-grade tumors. Low-grade lymphomas may not uptake gallium-67 and therefore may not benefit from this method. Although anatomical diagnostic methods such as CT and MRI are superior to gallium-67 for initially staging the patients, an initial examination using gallium-67 is important because it serves as the basis for post-therapy monitoring of patients and indicates which patients may benefit from this method. If the tumor does not concentrate gallium-67 in the first examination, this radiotracer should not be used for the follow-up. For lymphomas that concentrate gallium-67, this tool becomes very useful for assessing the response to the treatment, since gallium accurately assesses tumor viability and the extent of the disease, indicates the prognosis and, especially, is important for restaging, given that the anatomical changes that occur after the treatment make it difficult to interpret anatomical images. Other tumors that may benefit from this method are lung cancer, head and neck tumors, hepatocellular carcinoma, germ cell tumors, neuroblastomas, sarcomas, multiple myelomas and melanomas. These tumors present avidity for gallium-67, but the use of this imaging method in these tumors is not well defined (Figure 16). #### Figure 16. Whole body scan with gallium 67. A. normal scintigraphy. B. Lymphoma with lymphonodopathy. Uptake in left axillary lymphonode. C. Lymphoma with lymphonodapathy in right axillary, supravicular and mediastinal chain and left lung. D. Lymphoma in inguinopelvic lymphonode and soft tissue in right leg. In addition, gallium-67 has been used to detect infections or inflammations such as osteomyelitis, sarcoidosis and myocarditis, and to evaluate interstitial lung disease and examine patients with acquired immunodeficiency syndrome (AIDS). It has been suggested that gallium-67 may be clinically useful for assessing adults presenting fever of unknown origin because of the possibility of locating pathological uptake (both malignant and benign). Precautions need to be taken in relation to cases of suspected or confirmed pregnancy. If diagnostic procedures are performed on such patients, a clinical decision weighing the benefits against the possible harm from carrying out the procedure is necessary. Moreover, if diagnostic procedures are performed on breastfeeding mothers, the breastfeeding should be discontinued. Because of the high radiation exposure, children aged less than 14 years should not undergo gallium-67 scintigraphy, except when there is clear evidence of malignancy. In laboratories with PET/CT the gallium scintigraphy was replaced by 18F-FDG in the pathologies described above, because of the best accuracy of the PET. ## 8. Scintimammography Scintimammography was approved by the FDA in 1987 as a complementary examination for use when mammography is indeterminate in investigating malignant breast tumors. It is not used for screening, although new technologies for the equipment have improved the accuracy of this method. On the other hand, it is now indicated when mammography presents limitations in investigating tumor processes, such as in cases of dense breasts, asymmetrical density, architectural distortion acquired after the procedures or belonging to the breast, detection of tumor viability or recurrence, and very small breasts, particularly in men when breast compression cannot be performed. Lymph node status is also assessed, although with low sensitivity. 99mTc-Sestamibi (a cation with affinity for malignant tumor processes) is used, with summing of factors such as negative transmembrane potential, activity, mitochondrial density, cell count and cell mitotic activity. #### Figure 17. Scintimammgraphy. Breast carcinoma in right and left side (black arrows) and lymphonodal metastase (red arrow). ## 9. Dacryoscintigraphy This examination is indicated for cases of epiphora. It is a simple and easy-to-perform examination, with administration of microdrops of pertechnetate in the epicanthus of the eyes. In a normal examination, the radiotracer is expected to progressively pass through the palpebral fissure, lacrimal canaliculi, lacrimal sac, nasolacrimal ducts and nasal cavity. The retention or obstruction patterns do not show progression of the radiotracer. #### Figure 18. Dacrioscintigraphy. Normal exam. Radiotracer reachs right nasal cavity (black arrows). Total retention in billateral lacrimal sacs. Right lacrimal sac (red arrows) and left lacrimal sac (light blue arrows). Radioguided procedures were introduced in the 80s, and are based on the search of concentrated lesions of radioactive material guided by a small detector. There are three types of procedures: the search for occult and/or radioguided lesion (ROLL), the search of sentinel lymph node (SLN), and the association of the two methods (SNOLL). ROLL are lesions with difficult to be found when is necessary to be located for biopsy. The mean indications are: nonpalpable breast lesions, like a small lesions, deep lesions or microcalcifications; for biopsy of parathyroid, osteoma, bone metastasis and so on. SNL is the first lymph node to be reached by neoplasms cells from the primary tumor. When the lymph node was not metastatic, the second lymph nodes are not. Then, the total lymphadenectomy can be avoided (Figure 19 and figure 20). #### Figure 19. Breast lymphoscintigraphy. Anterior and left lateral images. After injection of radiopharmaceutical substance in left breast (yellow arrows) and SLN in left axillary lymphatic chair ( light blue arrows). #### Figure 20. Billateral breast lymphoscintigraphy. Two sentinel lymph nodes are identified in left and in right axillary lymphatic chain. ## 11. Therapy Radioiodine therapy consists of oral administration of iodine-131 to treat benign and malignant diseases of the thyroid. Iodine-131 is a beta-emitting radionuclide with a physical half-life of 8.1 days. The main gamma rays have energy of 364 keV and the beta radiation has maximum energy of 0.61 MeV, mean energy of 0.192 MeV and tissue reach of 0.8 mm. Because of cellular damage it is necessary to have some precautions. Mean absolute contraindications include: Pregnancy: Female patients of fertile age should ideally undergo a pregnancy test 72 hours or less before radioiodine therapy. Occasionally, when the patient’s history clearly demonstrates that there is no possibility of pregnancy, the test may not have to be done; Breastfeeding: Patients who are breastfeeding have to be advised to postpone radioiodine therapy until lactation ceases. This has the aim of minimizing the radiation absorbed by the breast. Lactation ceases between four and six weeks after delivery when there is no breastfeeding, and four to six weeks after the end of breastfeeding. This milk should not be stored. Mean relative contraindications are: Urinary incontinence that is difficult to manage: The physician should obtain confirmation of the patient’s urinary incontinence in order to take the necessary measures to avoid contamination through the urine; uncontrollable hyperthyroidism; active exophthalmia. The clinical indications for benign disease of thyroid including: hyperthyroidism: Graves’ disease, toxic multinodular goiter and autonomous nodules; non-toxic multinodular goiter: therapy with iodine-131 has been successfully used to reduce non-toxic multinodular goiter [15,16](Figure 21). And for malignant thyroid diseases, specially for: well-differentiated neoplasms of the thyroid that synthesize thyroglobulin. In these cases, iodine-131 has been used to ablate the remains of the thyroid after total thyroidectomy, and to treat residual cancer and metastatic disease after total thyroidectomy. Cerebral metastases have to be assessed carefully, since there is a risk of bleeding and cerebral edema. In general, the more invasive the cancer is, the bigger the dose will be. ### Figure 21. Thyroid scintigraphies. A. Graves’ Disease. Diffuse thyroid uptake. B. Plummer’s Disease. Nodular uptake on left thyoid lobe with suppression of the gland. ### Figure 22. Whole body scan post radioiodine therapy. Radioidine on thyroid tissue and on cervical lymphodes (red arrows). In another patient, notice lymphonode (green arrows and lung (light blue arrows) metastasis. ### 11.2. 131I-meta-iodobenzylguanidine therapy (131I-mIBG) This consists of 131I-mIBG intravenous infusion, selectively accumulated by neuroectodermal tissue, including tumours of neuroectodermal origin. Uptake occurs by active via and passive diffusion. mIBG is a meta isomer of the guanethidine derivative iodobenzylguanidine, stored within cytoplasmic storage granules and 131I. Common indications include: neuroectodermal tumours derived from the primitive neural crest, and showing uptake and retention of labeled mIBG, especially in inoperable or malignant phaeochromocytoma (Figure 23), inoperable or malignant paraganglioma, inoperable or malignant carcinoid tumour Stage III or IV neuroblastoma, inoperable, malignant medullary thyroid cancer. ### Figure 23. Phaeochromocytoma. Focal uptake in posterior abdomen aspect (red arrows). Late images are better to identify the lesion. ### 11.3.Treatment of refractory metastatic bone pain Bone pain is a common symptom of metastatic disease in cancer, experienced with various intensities during the development of their disease, generally in the terminal phases. In addition to other therapies, such as analgesics, bisphosphonates, chemotherapy, hormonal therapy and external beam radiotherapy, bone-seeking radiopharmaceuticals are also used for the palliation of pain from bone metastases (Figure 24). Substantial advantages of bone palliation radionuclide therapy include the ability to simultaneously treat multiple sites of disease with a more probable effect in earlier phases of metastatic disease. The tissue destruction is also based on beta-emitting radionuclide. This therapy consists of intravenous administration of 89Sr-chloride in aqueous solution, 153Sm-EDTMP or 186Re-HEDP that reaches the osteoblastic or mixed metastasis from prostate, breast, lung or any other tumor with osteoblastic presentation. Caution is necessary because this therapy develops myelotoxicity. Usually the bone pain decreased after two weeks depending on the radionuclide administered [17]. ### Figure 24. Bone scan. Bone metastasis.Multiple focal uptake on skeletal, ## 12. Conclusion In conclusion, the information about the nuclear medicine applications, based on metabolic and functional evaluations, make this method a co-adjuvant of the others anatomic exams on investigation of many pathologies, without competition with them and being preferred on the functional lesion follow up, metastasis screening and viable tumor issue. ## References 1 - Schinkel, AFL, Poldermans D, Elhendy A, Bax JJ. Assessment of myocardial viability in patients with heart failure. J Nucl Med 2007; 48: 1135-1146. 2 - Manspeaker P, Weisman HF, Schaible TF. Cardiovascular applications: Current status of immunoscintigraphy in the detection of myocardial necrosis using antimyosin (R11D10) and deep venous thrombosis using antifibrin (T2G1s). Semin Nucl Med 1993; 23: 133-47. 3 - Patel AD, Iskandrian AE. MIBG imaging. J Nucl Cardiol 2002; 9: 75-94. 4 - Carrio I. Cardiac neurotransmission imaging. J Nucl Med 2001; 42: 1062-1076. 5 - Kelesidis I, Travin MI. Use of cardiac radionuclide imaging to identify patients at risk for arrhythmic sudden cardiac death. J Nucl Cardiol 2012; 19: 142-52. 6 - 6. Chen W, Botvinick EH, Alavi A, Zhang Y, Yang S, Perini R, et al. Age-related decrease in cardiopulmonary adrenergic neuronal function in children as assessed by the I-123 metaiodobenzylguanidine imaging. Nucl J Cardiol 2008; 15: 73-79. 7 - Barritt, D.W. & Jordan, S.C. Anticoagulant drugs in the treatment of pulmonary embolism. A controlled trial. Lancet. 1960; 1:1309–12. ISSN: 0140-6736. 8 - Bajc, M., Neilly, J.B., Miniati, M., Schuemichen, C., Meignan, M. & B. Jonson, B. EANM guidelines for ventilation/perfusion scintigraphy. Part 1. Pulmonary imaging with ventilation/perfusion single photon emission tomography. Eur J Nucl Med Mol Imaging. 2009; 6(36):1356–70. E ISSN: 1619-7089. (a) 9 - Bajc, M., Neilly, J.B., Miniati, M., Schuemichen, C., Meignan, M. & B. Jonson, B. EANM guidelines for ventilation/perfusion scintigraphy. Part 2. Eur J Nucl Med Mol Imaging. 2009; 6(36):1528–38. E ISSN: 1619-7089.(b) 10 - Boubaker A, Prior JO, Meuwly JY, Delaloye AB. Radionuclide investigations of the urinary tract in the era of multimodality imaging. J Nucl Med 2006; 47: 1819-1836. 11 - Chiou YY, Wang ST, Tang MJ, Lee BF, Chiu NT. Renal fibrosis: prediction from acute pyelonephritis focus volume measured at 99mTc dimercaptosuccinic acid SPECT. Radiology 2001; 221: 366-370. 12 - Hitzel A, Liard A, Véra P, Manrique A, Ménard JF, Dacher JN. Color and power Doppler sonography versus DMSA scintigraphy in acute pyelonephritis and in prediction of renal scarring. J Nucl Med 2002; 43: 27-32. 13 - Eggli DF, Tulchinski M. Scintigraphic evaluation of pediatric urinary tract infection. Semin Nucl Med 1993; 23(3): 199-218. 14 - Stauss J, Hahn K, Mann M, Palma D. Guidelines for paediatric bone scanning with 99mTc-labeled radiopharmaceuticals and 18F-fluoride. Eur J Nucl Med Mol Imaging. 2010; 37: 1621-28. 15 - EANM procedures guidelines for therapy benign thyroid disease, 2010; 37:2218-28. 16 - EANM procedures guidelines for therapy with iodine 131. Eur J Nucl Med Mol Imaging. 2003; 30: BP27-BP31. 17 - Bodei, L., Marnix Lam, M., Chiesa, C., Flux, G., Brans, B., Chiti, A. & Giammarile, F. (2008). EANM procedure guideline for treatment of refractory metastatic bone pain. Eur J Nucl Med Mol Imaging. 2008, 35:1934–40. Eletronic ISSN: 1619-7089.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44860124588012695, "perplexity": 15377.84086497479}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647498.68/warc/CC-MAIN-20180320150533-20180320170533-00004.warc.gz"}
http://ilcdoc.linearcollider.org/record/20131	Preprint / physics.ins-det arXiv:0902.2067 R&D status of FPCCD VTX Abstract: As a candidate of the vertex detector for experiments at ILC, fully depleted fine pixel CCDs (FPCCDs) are under development. We describe the basic concept of the FPCCD and report on preliminary results of the performance study of the first prototype FPCCD sensors. Note: Comments: 3 pages, 3 figures, LCWS2008 Proceedings The record appears in these collections: Documentation > Articles & Preprints > Preprints	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8379414081573486, "perplexity": 12085.22118414001}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463612327.8/warc/CC-MAIN-20170529130450-20170529150450-00110.warc.gz"}
http://stackoverflow.com/questions/21629012/python-3-valueerror-intbase-must-be-2-and-36	# Python 3 - ValueError int()base must be >=2 and <=36 [closed] I very much a noob so please forgive my scruffy confusing code. I am trying to make a game engine of my own for text based adventures with combat and such. here is the code: import random def drawBoard(board): # This function prints out the board that it was passed. # "board" is a list of 29 strings representing the board (ignore index 0) print('\|---+---+---+---+---+---+---\|') print('\| \| \| \| \| \| \| \|') print('\| ' + board[1] + ' \| ' + board[2] + ' \| ' + board[3] + ' \| ' + board[4] + ' \| ' + board[5] + ' \| ' + board[6] + ' \| ' + board[7] + ' \| ') print('\| \| \| \| \| \| \| \|') print('\|---+---+---+---+---+---+---\|') print('\| \| \| \| \| \| \| \|') print('\| ' + board[8] + ' \| ' + board[9] + ' \| ' + board[10] + ' \| ' + board[11] + ' \| ' + board[12] + ' \| ' + board[13] + ' \| ' + board[14] + ' \| ') print('\| \| \| \| \| \| \| \|') print('\|---+---+---+---+---+---+---\|') print('\| \| \| \| \| \| \| \|') print('\| ' + board[15] + ' \| ' + board[16] + ' \| ' + board[17] + ' \| ' + board[18] + ' \| ' + board[19] + ' \| ' + board[20] + ' \| ' + board[21] + ' \| ') print('\| \| \| \| \| \| \| \|') print('\|---+---+---+---+---+---+---\|') print('\| \| \| \| \| \| \| \|') print('\| ' + board[22] + ' \| ' + board[23] + ' \| ' + board[24] + ' \| ' + board[25] + ' \| ' + board[26] + ' \| ' + board[27] + ' \| ' + board[28] + ' \| ') print('\| \| \| \| \| \| \| \|') print('\|---+---+---+---+---+---+---\|') def whoGoesFirst(): if random.randint(0, 1) == 0: # coin flip 50/50 who starts combat firstToSpawn = enemy lastToSpawn = player else: firstToSpawn = player lastToSpawn = enemy # following chunk works out the spawn points of the first to enter #and the last to enter, respectively. It then places them on the #board in their respective spawn points, represented by their symbol while firstToSpawn not in theBoard and lastToSpawn not in theBoard: boardSpawn = '1 2 3 4 5 6 7 14 21 28 27 26 25 24 23 22 15 8'.split() boardSpawnResult = random.choice(boardSpawn) theBoard[int(boardSpawnResult)] = firstToSpawn print(firstToSpawn + ' has entered the room.') else: if firstToSpawn in theBoard and lastToSpawn not in theBoard: boardHalf = len(boardSpawn) / 2 boardHalf = int(boardHalf) lastToSpawnPosition = int(boardSpawnResult) + boardHalf if lastToSpawnPosition > len(boardSpawn): lastToSpawnPosition = lastToSpawnPosition - len(boardSpawn) lastToSpawnPosition = boardSpawn[lastToSpawnPosition] theBoard[int(lastToSpawnPosition)] = lastToSpawn print(lastToSpawn + ' has entered the room.') if firstToSpawn == player: playerLocale = int(boardSpawnResult) global playerLocale else: playerLocale = int(lastToSpawnPosition) global playerLocale print(drawBoard(theBoard)) def shoot(): shotChance = int(playerStats[1]) - int(gangerStats[3]) didItHit = random.randint(int(shotChance), 100) if didItHit < 65: print(playerName + ' Missed the shot!') elif didItHit >= 65: didItCrit = random.randint(int(playerStats[5], 85)) if didItCrit >= 85: shotDamage = 25 + weaponsGlock print('Critical hit! ' + shotDamage) else: shotDamage = weaponsGlock print(playerName + ' Hit the enemy for ' + shotDamage) gangerStats[0] - shotDamage if gangerStats[0] < 1: print(playerName + ' killed the Ganger!') #declaring globals and starting the program while True: theBoard = [' ']* 29 player = ' ' enemy = '!' playerName = input() player = playerName[0].upper() playerLocale = ' ' playerStats = '100 50 2 10 5 2'.split() gangerStats = '65 20 1 5 3 5'.split() weaponsGlock = 30 whoGoesFirst() shoot() while int(gangerStats[0]) > 0: command = input('Type shoot to attack again:').lower if command == 'shoot': shoot() else: if int(gangerStats[0]) <= 0: command = input('Type "searchbody" to loot dead enemies:').lower The errors keep appearing for me in my shoot() function on the line where the randint is rolled for the didItCrit variable. Here's a copy of the error: Traceback (most recent call last): File "<string>", line 420, in run_nodebug File "C:\Python33\practice programs\textAdventure\combatmodule.py", line 163, in <module> shoot() File "C:\Python33\practice programs\textAdventure\combatmodule.py", line 133, in shoot didItCrit = random.randint(int(playerStats[5], 85)) ValueError: int() base must be >= 2 and <= 36 Any help would be massively appreciated. - ## closed as off-topic by Wooble, soon, devnull, lanzz, GabeFeb 7 '14 at 13:33 This question appears to be off-topic. The users who voted to close gave this specific reason: • "This question was caused by a problem that can no longer be reproduced or a simple typographical error. While similar questions may be on-topic here, this one was resolved in a manner unlikely to help future readers. This can often be avoided by identifying and closely inspecting the shortest program necessary to reproduce the problem before posting." – Wooble, soon, devnull, lanzz, Gabe If this question can be reworded to fit the rules in the help center, please edit the question. Why are you using '65 20 1 5 3 5'.split() instead of just [65, 20, 1, 5, 3, 5]? – Gabe Feb 7 '14 at 13:35 simply because it means not having to type the list out. That's not a bad thing is it? – Coned_Stoding Feb 7 '14 at 13:47 You misplaced a ): random.randint(int(playerStats[5], 85)) calls int() with 2 arguments. Instead, you want: random.randint(int(playerStats[5]), 85) which calls randint() with 2 arguments, 1 of which is the result of calling int() with 1 argument. - Thanks a lot for the help, much appreciated - problem fixed and it's back to simply moderately buggy now :D Cheers – Coned_Stoding Feb 7 '14 at 13:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4867866337299347, "perplexity": 5884.184968958438}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988065.26/warc/CC-MAIN-20150728002308-00061-ip-10-236-191-2.ec2.internal.warc.gz"}
https://www.gamedev.net/forums/topic/542238-stl-list-containing-iterators/	# STL list containing iterators This topic is 3340 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts Hi, I'd like to make two linked lists with elements that can reference each other: typedef list< pair<xy, iter> >::iterator iter; list< pair<xy, iter> > list1; list< pair<xy, iter> > list2; iter it = list1.insert(list1.begin(), make_pair(xy(0,0), NULL)); list2.insert(list2.begin, make_pair(xy(0,0), it)); As you can see, I cannot define the iterator type since the list itself needs to be defined, which needs the iterator, and so on. Is there a base type of iterator that I can use, or anything I can cast between? I tried void* but it can't be casted. I can store a pointer to the address of an iterator (by casting (&it) to void ), but this would involve making a vector of iterators. Is this the best way? ##### Share on other sites It works well to make a vector of iterators and store in the list the index within the vector (pair<xy, int>). It's a little extra work but it's pretty clean. ##### Share on other sites Why do you need linked lists with cross links? The awkwardness and lack of clarity may be a sign you need a different data structure. ##### Share on other sites Great, I've been pondering on this for 15 minutes, and now I have a knot in my brain :) ##### Share on other sites List nodes never change their location in memory, so you can just obtain and store pointers to elements. But what is the cross-linking for? ##### Share on other sites A pointer to the elements gives me the data, but I need the node in the linked list so that I can traverse forwards and backwards within the list. The problem is to calculate intersecting polygons. I store each vertex in a linked list, so that I can travel forwards/backwards, and efficiently remove or add vertices on the fly. I find all the intersection points, and add them to the lists for both polygons as I go. For each intersection, I need the cross-link information of how to get to the associated vertex on the other polygon. Then, to find the subtraction of two polygons, I can travel one counter-clockwise until I find an intersection, switch over to the other polygon, and travel that clockwise. This approach works, but I ran into trouble in the special cases, like when I try and subtract a polygon from itself, or deal with colinear edges. I found a nice library called GPC (Generic Polygon Clipper) which works very well so far. ##### Share on other sites I think you've over complexified. I know "just use a simple pointer" is considered scary advice in some circles, but if you have element A and B in separate lists, and you want to get from A to B, having A simply point to B seems simple and obvious. Intrusive, yes, but that's not as evil as some make it out to be. It's possible that what you really want is a lattice, where the intersection points have two parents and two children and everything else is essentially linked lists, but I don't know if STL supports them directly. I had a problem that involved computing many unions and intersections of simple polygons (and sometimes circles), and I went far, far out of my way to avoid solving the polygon intersection problem in pure form. Ask yourself if you need* to do this. I found I didn't. ##### Share on other sites Can't you just make a third list that contains a pair of iterators? [source language="cpp"]typedef std::list<point> poly_type;typedef std::pair<poly_type::iterator, poly_type::iterator> iter_pair;typedef std::list<iter_pair> intersection_type;poly_type poly1;poly_type poly2;intersection_type intersection;bool done = false;while (!done){ //By searching poly1 and poly2 in parallel, suppose you find that //the line formed by v_a and v_b from poly1 intersect the line formed //by v_k and v_j from poly2, at the point x. Furthermore, since these //vertices were found by searching through the lists, WLOG we can assume //that v_k, v_j, v_a, and v_b are iterators into their respective lists, //rather than actual points. //If the intersection point was in poly1, don't re-insert it. Either way //when this is done v_k is an iterator inside poly1 to the intersection //point and the insert operation takes constant time due to the hint. if (v_a != x) v_a = poly1.insert(v_a, x); //If the intersection point was in poly2, don't re-insert it. Either way //when this is done v_k is an iterator inside poly2 to the intersection //point and the insert operation takes constant time due to the hint. if (v_k != x) v_k = poly2.insert(v_k, x); intersection.insert(std::make_pair(v_a, v_k));} Now you can iterate over the list "intersection", which will contain iterators into each of the respective lists ##### Share on other sites Why not just create the subtraction as a separate list? Are you familiar with the .splice() member function? You might find it useful here. 1. 1 2. 2 3. 3 frob 20 4. 4 Rutin 19 5. 5 • 32 • 13 • 10 • 11 • 9 • ### Forum Statistics • Total Topics 632558 • Total Posts 3007077 ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22345514595508575, "perplexity": 2434.029700197925}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267155676.21/warc/CC-MAIN-20180918185612-20180918205612-00508.warc.gz"}
http://community.wolfram.com/groups/-/m/t/1081009	BinListsBy - Binning data with associate data GROUPS: Note that I changed the code a bit on May 8th, 2017. Now the function is always mapped--independent of the dimensions of the input data. A common problem is that you want to bin data by (e.g.) the x coordinate, while maintaining some associated data y with it. We can define a new function BinListsBy to bin n-dimensional data in m dimensions: ClearAll[BinListsBy] BinListsBy[data_List,binspecs__List]:=Module[{fs,idata,len,out}, len=Length[data]; fs={binspecs}; If[AllTrue[fs, MatchQ[#, {_, _?NumericQ, _?NumericQ} \| {_, _?NumericQ, _?NumericQ, _?NumericQ}] &], idata=Table[Map[f,data],{f,fs[[All,1]]}]; AppendTo[idata,Range[len]]; out=BinLists[Transpose[idata],Sequence@@(Rest/@fs),{0,len+1,len+1}]; out=Part[out,Sequence@@ConstantArray[All,Length[fs]],1,All,-1]; Map[data[[#]] &, out, {Length[fs]}] , Print["Your specification is incorrect\[Ellipsis]"]; ] ] ?BinListsBy Basic Examples Bin 2D data in only 1 dimension: data={{29,48},{76,70},{37,78},{60,63},{83,0},{42,44},{26,77},{59,91},{93,46},{38,24},{30,97},{76,60},{98,50},{35,2},{22,17},{90,90},{90,67},{34,22},{97,26},{78,85},{70,55},{59,92},{15,66},{30,84},{45,48},{91,13},{69,94},{10,100},{97,40},{91,87},{74,24},{66,91},{9,93},{67,2},{44,22},{54,96},{67,13},{23,12},{88,2},{35,82},{76,64},{84,32},{62,5},{56,84},{88,68},{25,99},{41,13},{23,4},{40,14},{89,90}}; out=BinListsBy[data,{First,0,100,10}] out//Grid The data can be of any type: data={{1.2,"This"},{5.1,"is"},{4.5,"just"},{3.1,"some"},{2.4,"test"},{7.1,"data"},{6.2,"from"},{3.14,"Sander"},{-0.7,"ok?"}}; BinListsBy[data,{First,-3,10}] Column[%, Frame -> All] will output: {{},{},{{-0.7,ok?}},{},{{1.2,This}},{{2.4,test}},{{3.1,some},{3.14,Sander}},{{4.5,just}},{{5.1,is}},{{6.2,from}},{{7.1,data}},{},{}} such that it is binned using the first element, and the associate data is kept. Bin based on the length of a string: data={"This","is","just","some","test","data","from","Sander","ok?"}; BinListsBy[data,{StringLength,1,10}] giving: {{},{is},{ok?},{This,just,some,test,data,from},{},{Sander},{},{},{}} Of course we can also bin 2D data in a single dimension based on the length of a string: data={{1.2,"This"},{5.1,"is"},{4.5,"just"},{3.1,"some"},{2.4,"test"},{7.1,"data"},{6.2,"from"},{3.14,"Sander"},{-0.7,"ok?"}}; BinListsBy[data,{StringLength@Last,1,10}] Column[%,Frame->All] giving: {{},{{5.1,is}},{{-0.7,ok?}},{{1.2,This},{4.5,just},{3.1,some},{2.4,test},{7.1,data},{6.2,from}},{},{{3.14,Sander}},{},{},{}} where now strings of equal length are binned using a {1,10} specification. Scope We can also do higher number of dimensions: data={{1.2,2.3,"This"},{5.1,1.2 ,"is"},{4.5,3.1,"just"},{3.1,1.87,"some"},{2.4,1.6,"test"},{7.1,1.4,"data"},{6.2,7.3,"from"},{3.14,9.1,"Sander"},{-0.7,0.8,"ok?"}}; BinListsBy[data,{First,-2,8},{#[[2]]&,0,10},{StringLength@Last,1,7,1}]; Grid[Map[Column,%,{2}],Frame->All] which nicely outputs a 3D list of binned data. Using Composition and RightComposition or pure functions can make elaborate functionality. Here we bin based on number of unique characters: data={"This","is","just","some","test","data","from","Sander","ok?"}; BinListsBy[data,{Length@DeleteDuplicates@Characters@ToLowerCase,1,10}] giving: {{},{is},{test,data,ok?},{This,just,some,from},{},{Sander},{},{},{}} Note that the data can have different lengths and types or structures: data={{1.3,{1,1}},{2.3,{1,1,1}},{4.14,1,2,"test"},{2.5,{2,1},2},{4.3}}; BinListsBy[data,{First,0,6}]; Column[%] Or by a criteria that works based on aggregate functions (Total, Mean): data={{1,2},{4,5},{-2,5},{3,6},{2,3},{1,1}} BinListsBy[data,{Total,1,10}]; Column[%] Properties & Relations If the data is purely numeric, real, and not ragged, one can specify very large bins for BinLists to capture all the data in the other dimension: data={{29,48},{76,70},{37,78},{60,63},{83,0},{42,44},{26,77},{59,91},{93,46},{38,24},{30,97},{76,60},{98,50},{35,2},{22,17},{90,90},{90,67},{34,22},{97,26},{78,85},{70,55},{59,92},{15,66},{30,84},{45,48},{91,13},{69,94},{10,100},{97,40},{91,87},{74,24},{66,91},{9,93},{67,2},{44,22},{54,96},{67,13},{23,12},{88,2},{35,82},{76,64},{84,32},{62,5},{56,84},{88,68},{25,99},{41,13},{23,4},{40,14},{89,90}}; BinLists[data,{0,100,10},{-10000,10000,20000}][[All,1]]===BinListsBy[data,{First,0,100,10}] Neat Examples One can bin 1D data in 2D: data={"This","is","just","some","test","data","from","Sander","ok?"}; BinListsBy[data,{Length@DeleteDuplicates@Characters@ToLowerCase,1,10},{StringLength,0,10}]//Grid So we first bin by unique characters, and then by string length: Final thoughts I've been advocating for this functionality for a while, it is basically BinLists but with an extra By like GatherBy and SortBy such that nD data can be binned in mD (which is currently not possible!). It is indeed very useful for data processing where it is very common to bin by a certain value, while wanting to maintain some auxiliary data (for example an ID of the data, or time-stamp or ...). 2 months ago 5 Replies Vincent Virgilio 1 Vote I've wanted something like this for a long time too. It has been a while since I've needed it, but if I recall correctly, the application was a sliding window of fixed time-width across irregularly sampled data.However, I think recent improvements in the TimeSeries subsystem have addressed my specific need. 2 months ago I've used quite often actually, and coded the same thing in multiple ways over the years... It can also be implemented by a GatherBy route; you use GatherBy to do the hard work, and then make bins yourself and replace the values.... Sander Huisman 2 Votes Hi Vincent,Good point, the last version was not optimized for speed. I changed the code slightly above; the old code is included as a comment... This new code is quite a bit faster than the previous one: ClearAll[BinListsByOld] BinListsByOld[data_List,binspecs__List]:=Module[{fs,idata,len,out}, len=Length[data]; fs={binspecs}; If[AllTrue[fs,2<=Length[#]<=4&], idata=Table[Map[f,data],{f,fs[[All,1]]}]; AppendTo[idata,Range[len]]; out=BinLists[Transpose[idata],Sequence@@(Rest/@fs),{0,len+1,len+1}]; out=Part[out,Sequence@@ConstantArray[All,Length[fs]],1,All,-1]; out/.Thread[Range[len]->data] , Print["Your specification is incorrect\[Ellipsis]"]; ] ] ClearAll[BinListsBy] BinListsBy[data_List,binspecs__List]:=Module[{fs,idata,len,out}, len=Length[data]; fs={binspecs}; If[AllTrue[fs,2<=Length[#]<=4&], idata=Table[Map[f,data],{f,fs[[All,1]]}]; AppendTo[idata,Range[len]]; out=BinLists[Transpose[idata],Sequence@@(Rest/@fs),{0,len+1,len+1}]; out=Part[out,Sequence@@ConstantArray[All,Length[fs]],1,All,-1]; Map[data[[#]]&,out,{Length[fs]}] , Print["Your specification is incorrect\[Ellipsis]"]; ] ] ClearAll[RandomString] RandomString[chars_List,n_Integer]:=StringJoin[RandomChoice[chars,n]] RandomString[n_Integer]:=RandomString[CharacterRange["a","z"],n] Now doing the benchmark: timings=Table[ data=Transpose[{RandomInteger[100,n],Table[RandomString[RandomInteger[{5,10}]],{n}]}]; {{n,AbsoluteTiming[out=BinListsBy[data,{First,0,100,10}];][[1]]}, {n,AbsoluteTiming[out=BinListsByOld[data,{First,0,100,10}];][[1]]}},{n,Round[PowerRange[10,5 10^4,1.2]]}]; Show[{ListLogLogPlot[Transpose[timings], Frame -> True, FrameLabel -> {"size", "timing"}, PlotLegends -> {"BinListsBy New", "BinListsBy Old"}], LogLogPlot[{0.000003 x, 0.00000003 x^2}, {x, 10, 10^5}]}] You can see that the new code performs much better actually, moreover, it scales much better: linearly versus quadratically!In order to compare it with 'regular' binning, we can do a problem that can also be done by regular BinLists: timings2=Table[ data=Transpose[{RandomInteger[100,n],RandomReal[100,n]}]; {{n,AbsoluteTiming[BinListsBy[data,{First,0,100,10}];][[1]]}, {n,AbsoluteTiming[BinListsByOld[data,{First,0,100,10}];][[1]]}, {n,AbsoluteTiming[BinLists[data,{0,100,10},{-1000,1000,2000}][[All,1]];][[1]]}},{n,Round[PowerRange[10,5 10^4,1.2]]}]; Show[{ListLogLogPlot[Transpose[timings2], Frame -> True, FrameLabel -> {"size", "timing"}, PlotLegends -> {"BinListsBy New", "BinListsBy Old", "BinLists"}], LogLogPlot[{0.000003 x, 0.00000003 x^2, 0.0000017 x}, {x, 10, 10^5}]}] You can see that both the regular BinLists and the new BinListsBy are very close, and both scale linearly (as expected). It is slightly slower than BinLists, but that is expected because it uses BinLists internally + some extra stuff.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2587261497974396, "perplexity": 4465.675685363682}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424148.78/warc/CC-MAIN-20170722202635-20170722222635-00717.warc.gz"}
https://datascience-enthusiast.com/R/dates.html	# Fisseha Berhane, PhD #### Data Scientist 443-970-2353 [email protected] CV Resume ### Working with Dates and Times in R using Power Consumption Data Here data from the UC Irvine Machine Learning Repository, a popular repository for machine learning datasets, will be used to show how to work with dates in R. In particular, I am using the “Individual household electric power consumption Data Set”. The Data Set Information and Attribute Information below are taken from the website ### Data Set Information:¶ This archive contains 2075259 measurements gathered between December 2006 and November 2010 (47 months). Notes: 1.(global_active_power*1000/60 - sub_metering_1 - sub_metering_2 - sub_metering_3) represents the active energy consumed every minute (in watt hour) in the household by electrical equipment not measured in sub-meterings 1, 2 and 3. 2.The dataset contains some missing values in the measurements (nearly 1,25% of the rows). All calendar timestamps are present in the dataset but for some timestamps, the measurement values are missing: a missing value is represented by the absence of value between two consecutive semi-colon attribute separators. For instance, the dataset shows missing values on April 28, 2007. ### Attribute Information:¶ 1.date: Date in format dd/mm/yyyy 2.time: time in format hh:mm:ss 3.global_active_power: household global minute-averaged active power (in kilowatt) 4.global_reactive_power: household global minute-averaged reactive power (in kilowatt) 5.voltage: minute-averaged voltage (in volt) 6.global_intensity: household global minute-averaged current intensity (in ampere) 7.sub_metering_1: energy sub-metering No. 1 (in watt-hour of active energy). It corresponds to the kitchen, containing mainly a dishwasher, an oven and a microwave (hot plates are not electric but gas powered). 8.sub_metering_2: energy sub-metering No. 2 (in watt-hour of active energy). It corresponds to the laundry room, containing a washing-machine, a tumble-drier, a refrigerator and a light. 9.sub_metering_3: energy sub-metering No. 3 (in watt-hour of active energy). It corresponds to an electric water-heater and an air-conditioner. In [5]: if(!file.exists('data.zip')){ url<-"http://archive.ics.uci.edu/ml/machine-learning-databases/00235/household_power_consumption.zip" } In [8]: unzip("data.zip") # This creates the file "household_power_consumption.txt" Read the data in to R In [10]: data<-read.table("household_power_consumption.txt",header = TRUE, sep= ";") Looking at the attributes of the datset In [11]: names(data) Out[11]: 1. "Date" 2. "Time" 3. "Global_active_power" 4. "Global_reactive_power" 5. "Voltage" 6. "Global_intensity" 7. "Sub_metering_1" 8. "Sub_metering_2" 9. "Sub_metering_3" In [12]: lapply(data, class) Out[12]: $Date "factor"$Time "factor" $Global_active_power "factor"$Global_reactive_power "factor" $Voltage "factor"$Global_intensity "factor" $Sub_metering_1 "factor"$Sub_metering_2 "factor" $Sub_metering_3 "numeric" Many of them are factor vaiables and we will change them to numeric when we are working with them. Let's see the first few values of Date and Time In [13]: data$Date[1:10] Out[13]: 1. 16/12/2006 2. 16/12/2006 3. 16/12/2006 4. 16/12/2006 5. 16/12/2006 6. 16/12/2006 7. 16/12/2006 8. 16/12/2006 9. 16/12/2006 10. 16/12/2006 In [14]: data$Time[1:10] Out[14]: 1. 17:24:00 2. 17:25:00 3. 17:26:00 4. 17:27:00 5. 17:28:00 6. 17:29:00 7. 17:30:00 8. 17:31:00 9. 17:32:00 10. 17:33:00 Let's use strptime to change the factor Date and Time values in to yyyy-mm-dd hh:mm:ss. First, let's create a variables by concatenating Date and Time. In [16]: data$DateTime<-paste(data$Date, data$Time) Let's see the help document of strptime In [36]: ?strptime Out[36]: strptime {base} R Documentation ## Date-time Conversion Functions to and from Character ### Description Functions to convert between character representations and objects of classes "POSIXlt" and "POSIXct" representing calendar dates and times. ### Usage ## S3 method for class 'POSIXct' format(x, format = "", tz = "", usetz = FALSE, ...) ## S3 method for class 'POSIXlt' format(x, format = "", usetz = FALSE, ...) ## S3 method for class 'POSIXt' as.character(x, ...) strftime(x, format = "", tz = "", usetz = FALSE, ...) strptime(x, format, tz = "") ### Arguments x An object to be converted: a character vector for strptime, an object which can be converted to "POSIXlt" for strftime. tz A character string specifying the time zone to be used for the conversion. System-specific (see as.POSIXlt), but "" is the current time zone, and "GMT" is UTC. Invalid values are most commonly treated as UTC, on some platforms with a warning. format A character string. The default for the format methods is "%Y-%m-%d %H:%M:%S" if any element has a time component which is not midnight, and "%Y-%m-%d" otherwise. If options("digits.secs") is set, up to the specified number of digits will be printed for seconds. ... Further arguments to be passed from or to other methods. usetz logical. Should the time zone be appended to the output? This is used in printing times, and more reliable than using "%Z". ### Details The format and as.character methods and strftime convert objects from the classes "POSIXlt" and "POSIXct" to character vectors. strptime converts character vectors to class "POSIXlt": its input x is first converted by as.character. Each input string is processed as far as necessary for the format specified: any trailing characters are ignored. strftime is a wrapper for format.POSIXlt, and it and format.POSIXct first convert to class "POSIXlt" by calling as.POSIXlt (so they also work for class "Date"). Note that only that conversion depends on the time zone. The usual vector re-cycling rules are applied to x and format so the answer will be of length of the longer of these vectors. Locale-specific conversions to and from character strings are used where appropriate and available. This affects the names of the days and months, the AM/PM indicator (if used) and the separators in formats such as %x and %X, via the setting of the LC_TIME locale category. The ‘current locale’ of the descriptions might mean the locale in use at the start of the R session or when these functions are first used. The details of the formats are platform-specific, but the following are likely to be widely available: most are defined by the POSIX standard. A conversion specification is introduced by %, usually followed by a single letter or O or E and then a single letter. Any character in the format string not part of a conversion specification is interpreted literally (and %% gives %). Widely implemented conversion specifications include %a Abbreviated weekday name in the current locale. (Also matches full name on input.) %A Full weekday name in the current locale. (Also matches abbreviated name on input.) %b Abbreviated month name in the current locale. (Also matches full name on input.) %B Full month name in the current locale. (Also matches abbreviated name on input.) %c Date and time. Locale-specific on output, "%a %b %e %H:%M:%S %Y" on input. %C Century (00–99): the integer part of the year divided by 100. %d Day of the month as decimal number (01–31). %D Date format such as %m/%d/%y: ISO C99 says it should be that exact format. %e Day of the month as decimal number (1–31), with a leading space for a single-digit number. %F Equivalent to %Y-%m-%d (the ISO 8601 date format). %g The last two digits of the week-based year (see %V). (Accepted but ignored on input.) %G The week-based year (see %V) as a decimal number. (Accepted but ignored on input.) %h Equivalent to %b. %H Hours as decimal number (00–23). As a special exception strings such as 24:00:00 are accepted for input, since ISO 8601 allows these. %I Hours as decimal number (01–12). %j Day of year as decimal number (001–366). %m Month as decimal number (01–12). %M Minute as decimal number (00–59). %n Newline on output, arbitrary whitespace on input. %p AM/PM indicator in the locale. Used in conjunction with %I and not with %H. An empty string in some locales (and the behaviour is undefined if used for input in such a locale). Some platforms accept %P for output, which uses a lower-case version: others will output P. %r The 12-hour clock time (using the locale's AM or PM). Only defined in some locales. %R Equivalent to %H:%M. %S Second as decimal number (00–61), allowing for up to two leap-seconds (but POSIX-compliant implementations will ignore leap seconds). %t Tab on output, arbitrary whitespace on input. %T Equivalent to %H:%M:%S. %u Weekday as a decimal number (1–7, Monday is 1). %U Week of the year as decimal number (00–53) using Sunday as the first day 1 of the week (and typically with the first Sunday of the year as day 1 of week 1). The US convention. %V Week of the year as decimal number (01–53) as defined in ISO 8601. If the week (starting on Monday) containing 1 January has four or more days in the new year, then it is considered week 1. Otherwise, it is the last week of the previous year, and the next week is week 1. (Accepted but ignored on input.) %w Weekday as decimal number (0–6, Sunday is 0). %W Week of the year as decimal number (00–53) using Monday as the first day of week (and typically with the first Monday of the year as day 1 of week 1). The UK convention. %x Date. Locale-specific on output, "%y/%m/%d" on input. %X Time. Locale-specific on output, "%H:%M:%S" on input. %y Year without century (00–99). On input, values 00 to 68 are prefixed by 20 and 69 to 99 by 19 – that is the behaviour specified by the 2004 and 2008 POSIX standards, but they do also say ‘it is expected that in a future version the default century inferred from a 2-digit year will change’. %Y Year with century. Note that whereas there was no zero in the original Gregorian calendar, ISO 8601:2004 defines it to be valid (interpreted as 1BC): see http://en.wikipedia.org/wiki/0_(year). Note that the standards also say that years before 1582 in its calendar should only be used with agreement of the parties involved. For input, only years 0:9999 are accepted. %z Signed offset in hours and minutes from UTC, so -0800 is 8 hours behind UTC. Values up to +1400 are accepted as from R 3.1.1: previous versions only accepted up to +1200. (Standard only for output.) %Z (Output only.) Time zone abbreviation as a character string (empty if not available). This may not be reliable when a time zone has changed abbreviations over the years. Where leading zeros are shown they will be used on output but are optional on input. Names are matched case-insensitively on input: whether they are capitalized on output depends on the platform and the locale. Note that abbreviated names are platform-specific (although the standards specify that in the C locale they must be the first three letters of the capitalized English name: this convention is widely used in English-language locales but for example French month abbreviations are not the same on any of Linux, OS X, Solaris and Windows). When %z or %Z is used for output with an object with an assigned time zone an attempt is made to use the values for that time zone — but it is not guaranteed to succeed. Not in the standards and less widely implemented are %k The 24-hour clock time with single digits preceded by a blank. %l The 12-hour clock time with single digits preceded by a blank. %s (Output only.) The number of seconds since the epoch. %+ (Output only.) Similar to %c, often "%a %b %e %H:%M:%S %Z %Y". May depend on the locale. For output there are also %O[dHImMUVwWy] which may emit numbers in an alternative locale-dependent format (e.g., roman numerals), and %E[cCyYxX] which can use an alternative ‘era’ (e.g., a different religious calendar). Which of these are supported is OS-dependent. These are accepted for input, but with the standard interpretation. Specific to R is %OSn, which for output gives the seconds truncated to 0 <= n <= 6 decimal places (and if %OS is not followed by a digit, it uses the setting of getOption("digits.secs"), or if that is unset, n = 3). Further, for strptime %OS will input seconds including fractional seconds. Note that %S ignores (and not rounds) fractional parts on output. The behaviour of other conversion specifications (and even if other character sequences commencing with % are conversion specifications) is system-specific. Some systems document that the use of multi-byte characters in format is unsupported: UTF-8 locales are unlikely to cause a problem. ### Value The format methods and strftime return character vectors representing the time. NA times are returned as NA_character_. strptime turns character representations into an object of class "POSIXlt". The time zone is used to set the isdst component and to set the "tzone" attribute if tz != "". If the specified time is invalid (for example "2010-02-30 08:00") all the components of the result are NA. (NB: this does means exactly what it says – if it is an invalid time, not just a time that does not exist in some time zone.) ### Printing years Everyone agrees that years from 1000 to 9999 should be printed with 4 digits, but the standards do not define what is to be done outside that range. For years 0 to 999 most OSes pad with zeros or spaces to 4 characters, and Linux outputs just the number. OS facilities will probably not print years before 1 CE (aka 1 AD) ‘correctly’ (they tend to assume the existence of a year 0: see http://en.wikipedia.org/wiki/0_(year), and some OSes get them completely wrong). Common formats are -45 and -045. Years after 9999 and before -999 are normally printed with five or more characters. Some platforms support modifiers from POSIX 2008 (and others). On Linux the format "%04Y" assures a minimum of four characters and zero-padding. The internal code (as used on Windows and by default on OS X) uses zero-padding by default, and formats %_4Y and %_Y can be used for space padding and no padding. ### Time zone offsets Offsets from GMT (also known as UTC) are part of the conversion between timezones and to/from class "POSIXct", but cause difficulties as they often computed incorrectly. They conventionally have the opposite sign from time-zone specifications (see Sys.timezone): positive values are East of the meridian. Although there have been time zones with offsets like 00:09:21 (Paris in 1900), and 00:44:30 (Liberia until 1972), offsets are usually treated as whole numbers of minutes, and are most often seen in RFC 822 email headers in forms like -0800 (e.g., used on the Pacific coast of the US in winter). Format %z can be used for input or output: it is a character string, conventionally plus or minus followed by two digits for hours and two for minutes: the standards say that an empty string should be output if the offset is unknown, but some systems use the offsets for the time zone in use for the current year. ### Note The default formats follow the rules of the ISO 8601 international standard which expresses a day as "2001-02-28" and a time as "14:01:02" using leading zeroes as here. (The ISO form uses no space to separate dates and times: R does by default.) For strptime the input string need not specify the date completely: it is assumed that unspecified seconds, minutes or hours are zero, and an unspecified year, month or day is the current one. Some components may be returned as NA (but an unknown tzone component is represented by an empty string). If the time zone specified is invalid on your system, what happens is system-specific but it will probably be ignored. Remember that in most time zones some times do not occur and some occur twice because of transitions to/from ‘daylight saving’ (also known as ‘summer’) time. strptime does not validate such times (it does not assume a specific time zone), but conversion by as.POSIXct will do so. Conversion by strftime and formatting/printing uses OS facilities and may return nonsensical results for non-existent times at DST transitions. Much less comprehensive support for output specifications was provided on Windows before R 3.1.0. In a C locale %c is required to be "%a %b %e %H:%M:%S %Y". As Windows does not comply (and uses a date format not understood outside N. America), that format is used by R on Windows in all locales. That %A %a %B %b on input match both full and abbreviated names caused problems in some locales prior to R 3.0.3: e.g. in French on OS X juillet was matched by jui, the abbreviation for June. ### References International Organization for Standardization (2004, 2000, ...) ISO 8601. Data elements and interchange formats – Information interchange – Representation of dates and times. For links to versions available on-line see (at the time of writing) http://dotat.at/tmp/ISO_8601-2004_E.pdf and http://www.qsl.net/g1smd/isopdf.htm; for information on the current official version, see http://www.iso.org/iso/iso8601. The POSIX 1003.1 standard, which is in some respects stricter than ISO 8601. DateTimeClasses for details of the date-time classes; locales to query or set a locale. Your system's help page on strftime to see how to specify their formats. (On some systems, including Windows, strftime is replaced by more comprehensive internal code.) ### Examples ## locale-specific version of date() format(Sys.time(), "%a %b %d %X %Y %Z") ## time to sub-second accuracy (if supported by the OS) format(Sys.time(), "%H:%M:%OS3") ## read in date info in format 'ddmmmyyyy' ## This will give NA(s) in some locales; setting the C locale ## as in the commented lines will overcome this on most systems. ## lct <- Sys.getlocale("LC_TIME"); Sys.setlocale("LC_TIME", "C") x <- c("1jan1960", "2jan1960", "31mar1960", "30jul1960") z <- strptime(x, "%d%b%Y") ## Sys.setlocale("LC_TIME", lct) z ## read in date/time info in format 'm/d/y h:m:s' dates <- c("02/27/92", "02/27/92", "01/14/92", "02/28/92", "02/01/92") times <- c("23:03:20", "22:29:56", "01:03:30", "18:21:03", "16:56:26") x <- paste(dates, times) strptime(x, "%m/%d/%y %H:%M:%S") ## time with fractional seconds z <- strptime("20/2/06 11:16:16.683", "%d/%m/%y %H:%M:%OS") z # prints without fractional seconds op <- options(digits.secs = 3) z options(op) ## time zones name are not portable, but 'EST5EDT' comes pretty close. (x <- strptime(c("2006-01-08 10:07:52", "2006-08-07 19:33:02"), "%Y-%m-%d %H:%M:%S", tz = "EST5EDT")) attr(x, "tzone") strptime("Tue, 23 Mar 2010 14:36:38 -0400", "%a, %d %b %Y %H:%M:%S %z") [Package base version 3.1.3 ] Then, let's chnage DateTime to yyyy-mm-dd hh:mm:ss In [17]: data$DateTime<-strptime(data$DateTime, "%d/%m/%Y %H:%M:%S") Let's work with the data for dates 2007-02-01 and 2007-02-02. In [20]: start<-which(data$DateTime==strptime("2007-02-01", "%Y-%m-%d")) end<-which(data$DateTime==strptime("2007-02-02 23:59:00", "%Y-%m-%d %H:%M:%S")) data2<-data[start:end,] Now, we can plot some of the observations. In [28]: hist(as.numeric(as.character(data2$Global_active_power)), # note we used as.character and as numeric since # the variable is factor variable. main="Global Active Power", xlab="Global Active Power (kilowatts)", col="red") In [43]: plot(data2$DateTime, as.numeric(as.character(data2$Global_active_power)), type='l',ylab="Global Active Power (Kilowatts)", xlab="") In [44]: plot(data2$DateTime, as.numeric(as.character(data2$Sub_metering_1)),type='l', ylab ="Energy sub metering", xlab="") lines(data2$DateTime, as.numeric(as.character(data2$Sub_metering_2)),type='l', col='red') lines(data2$DateTime, data2$Sub_metering_3,type='l', col="blue") legend('topright', c("Sub_metering_1","Sub_metering_2","Sub_metering_3"), lty=c(1,1,1) ,col=c("black","red","blue")) In [45]: par(mfcol=c(2,2)) plot(data2$DateTime, as.numeric(as.character(data2$Global_active_power)),type='l',ylab="Global Active Power", xlab="") plot(data2$DateTime, as.numeric(as.character(data2$Sub_metering_1)),type='l', xlab="",ylab ="Energy sub metering") lines(data2$DateTime, as.numeric(as.character(data2$Sub_metering_2)),type='l', col='red') lines(data2$DateTime, data2$Sub_metering_3,type='l', col="blue") legend('topright', c("Sub_metering_1","Sub_metering_2","Sub_metering_3"), lty=c(1,1,1),col=c("black","red","blue")) plot(data2$DateTime, as.numeric(as.character(data2$Voltage)),type='l', ylab="Voltage",xlab="datetime" ) plot(data2$DateTime, as.numeric(as.character(data2\$Global_reactive_power)),type='l', ylab="Global_reactive_power",xlab="datetime" )	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2740308940410614, "perplexity": 5904.56886887872}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991737.39/warc/CC-MAIN-20210514025740-20210514055740-00374.warc.gz"}
http://math.stackexchange.com/questions/292837/rectify-image-from-congruent-planar-shape-objects/295409	Rectify image from congruent planar shape objects I am implementing an algorithm to remove projective distortions on the following image. I understand this is possible by applying the following transformation: $$\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ l_1 & l_2 & l_3 \\ \end{matrix}$$ Where $$l_\infty=(\begin{matrix}l_1 & l_2 & l_3 \end{matrix})^T$$ is the line at the infinity. In a perspective image of a plane, the line at infinity on the world plane is imaged as the vanishing line of the plane. The vanishing line can be computed by intersecting two vanishing points which can be computed in the following ways: 1. From the intersection of two sets of imaged parallel lines. But seems there are no two sets of imaged parallel lines on the image. 2. Given two intervals on a imaged line $$\lt0,a^\prime,a^\prime+b^\prime\gt$$ with a known length ratio $$d(0,a^\prime):d(a^\prime,a^\prime+b^\prime)=0:a^\prime$$ Where I need to solve the system (up to scale) $$\left(\begin{matrix}0 \\ 1\end{matrix}\right)=\left(\begin{matrix}h11 & h12 \\ h21 & h22\end{matrix}\right) \left(\begin{matrix}0 \\ 1\end{matrix}\right)$$ $$\left(\begin{matrix}a \\ 1\end{matrix}\right)=\left(\begin{matrix}h11 & h12 \\ h21 & h22\end{matrix}\right) \left(\begin{matrix}a^\prime \\ 1\end{matrix}\right)$$ $$\left(\begin{matrix}a+b \\ 1\end{matrix}\right)=\left(\begin{matrix}h11 & h12 \\ h21 & h22\end{matrix}\right) \left(\begin{matrix}a^\prime+b^\prime \\ 1\end{matrix}\right)$$ And compute the vanishing point as $$x^\prime=\left(\begin{matrix}h11 & h12 \\ h21 & h22\end{matrix}\right) \left(\begin{matrix}0 \\ 1\end{matrix}\right)$$ But I don't understand this approach as I don't have the world points $$\lt0,a,a+b\gt$$ and I don't know what serves me for knowing the length ratio. 3. Using the cross ratio. Which I totally don't understand how could be possible to use in this case. Edit: isn't necessary to follow any particular approach just remind that the planar objects are irregular (no orthogonal angles in real world) congruent shapes (they have the same shape in real world) - I have written an answer on SO about how to compute a projective transform given four points and their images. You can use vanishing points for my approach, but don't have to. – MvG Feb 4 '13 at 15:36 Thanks for your answer, well actually using directly a projective approach based on four points is an oversepecification of the geometry (8 degrees of freedom instead of 4). Furthermore i don't count with such 4 pairs of points for which i know its shape in world frame; the piece of paper under the rightmost pen might not be rectangular or even may not exist. – gantzer89 Feb 5 '13 at 12:05 I see I haven't read your question carefully enough, but now I have a proper solution for you, posted as an answer. If that answer is what you are looking for, then perhaps you should modify the title of this question, since you don't necessarily need to use cross ratios for this. Nor some real vanishing points, come to think of it. So “Reconstruct perspective from congruent shapes” or something like this would better describe the task you have at hand. Except you really want a solution based on cross ratios, that is… – MvG Feb 5 '13 at 14:18 I will assume that the two depicted bright polygons are congruent in the world plane. If they are not, then I guess you won't have enough information to reconstruct anything. The first step is finding a projective transformation which maps one of the polygons onto the other. That transformation is uniquely defined using four points and their images, and I've described this computation in detail in another post. So choosing any four pairs of matching corners will give you that matrix. Originally I had assumed that this is the transformation you were interested in, but I had not read the question carefully enough. The transformation you just found describes the rotation of one polygon onto the other in the image plane. Next, you look for fixed points of the transformation. You find these as eigenvectors of the transformation matrix. In $\mathbb C\mathrm P^2$ you should get three fixed points, one of them real and two complex and conjugate to one another. The real one is your center of rotation. The complex fixed points correspond to the ideal circle points $I=(1,i,0)^T$ and $J=(1,-i,0)^T$, which remain fixed under every similarity transformation. By the way: The join of the two complex points corresponds to the vanishing line. Which in your image is way outside the picture area. But knowing the vanishing line is less useful than knowing the locations of $I$ and $J$ as we do, since these points can be used to define angles, so they will help you avoid skewing. Now you can again choose four points and their images to define a projective transformation. This time, you map the complex fixed points to $I$ and $J$, and you map the center of rotation to wherever you want it to lie in your reconstructed image, e.g. the origin. You still have one point which you can choose arbitrarily. Its image will fix the scale and orientation of the reconstructed image. Strictly speaking, you don't have to take the center of rotation as one preimage point either: as long as you correctly map $I$ and $J$ from image coordinates to world coordinates, you can choose any two pairs of real points to uniquely define the projective transformation. Counting degrees of freedom, the two arbitrarily chosen points above amount to four real degrees of freedom, matching the four degrees of freedom of a similarity transformation. Everything else is fixed. In particular, not only parallel lines but also angles are reconstructed. I've just implemented the above description as a proof of concept using Cinderella. The center of rotation, drawn in green, appears to coincide with the upper boundary of your picture. The points P1, P2 and R2 were chosen arbitrarily. - Thanks a lot for your answer its been very helpful. I am writing because I got some issues: 1) When mapping the complex fixed points to the ideal points I am obtaining a complex transformation matrix, is it correct? 2) How should I choose the fourth point? despite the fact of being complex I am applying the projective transformation to the planar objects vertices but it reflects horizontally and vertically. 3) I tried to apply the transformation to the complex fixed points but they didn't transformed onto the ideal points, is it correct? – gantzer89 Feb 6 '13 at 2:48 @gantzer89: 1) The transformation matrix should be real, as you map conjugate points onto conjugate points. 2) Choose the fourth pair of preimage and image both as real points. Apart from that, tweak it to control the size and rotation of the reconstruction. If you get "two reflections", then you get a rotation, so rotate P2 around R2 (in my example) to align the image any way you want. 3) If the pairs of points defining the transformation don't end up as preimage and image under said transformation, you made a mistake computing its matrix. The complex fixpoints should map to $I$ and $J$. – MvG Feb 6 '13 at 3:00 Thank you for your patience answering my questions, I continue having problems with the projective transformation, in this other question I am showing the matrices I am using for the computation of the transformation. – gantzer89 Feb 6 '13 at 15:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8584201335906982, "perplexity": 296.03527813976797}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500830834.3/warc/CC-MAIN-20140820021350-00033-ip-10-180-136-8.ec2.internal.warc.gz"}
http://www.journaltocs.ac.uk/index.php?action=browse&subAction=subjects&publisherID=8&journalID=9523&pageb=3&userQueryID=&sort=&local_page=&sorType=&sorCol=	Subjects -> MATHEMATICS (Total: 1105 journals) - APPLIED MATHEMATICS (88 journals) - GEOMETRY AND TOPOLOGY (23 journals) - MATHEMATICS (814 journals) - MATHEMATICS (GENERAL) (45 journals) - NUMERICAL ANALYSIS (25 journals) - PROBABILITIES AND MATH STATISTICS (110 journals) MATHEMATICS (814 journals) First \| 1 2 3 4 5 Showing 401 - 538 of 538 Journals sorted alphabetically Journal of Computational Physics (Followers: 70) Journal of Computational Physics : X (Followers: 1) Journal of Computer Engineering, System and Science (CESS) Journal of Contemporary Mathematical Analysis Journal of Cryptology (Followers: 3) Journal of Difference Equations and Applications Journal of Differential Equations (Followers: 1) Journal of Discrete Algorithms (Followers: 4) Journal of Discrete Mathematics (Followers: 1) Journal of Dynamics and 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Mathematics Education, Science and Technology (Followers: 1) Nagoya Mathematical Journal Nano Research (Followers: 4) Nanotechnologies in Russia (Followers: 1) Natural Resource Modeling (Followers: 1) New Mathematics and Natural Computation Nonlinear Analysis : Modelling and Control (Followers: 1) Nonlinear Analysis : Theory, Methods & Applications (Followers: 1) Nonlinear Analysis: Hybrid Systems Nonlinear Analysis: Real World Applications (Followers: 2) Nonlinear Differential Equations and Applications NoDEA Nonlinear Engineering Nonlinear Oscillations (Followers: 1) North Carolina Journal of Mathematics and Statistics Similar Journals manuscripta mathematicaJournal Prestige (SJR): 1.053 Citation Impact (citeScore): 1Number of Followers: 0 Hybrid journal (It can contain Open Access articles) ISSN (Print) 1432-1785 - ISSN (Online) 0025-2611 Published by Springer-Verlag [2626 journals] • A note on fibrations of $$G_2$$ G 2 -manifolds • Abstract: In this note, we first give some constructions of torsion-free $$G_2$$ -structures on some topological product manifolds. Then we provide a sufficient condition of 3-Calabi–Yau fibrations for $$G_2$$ -manifolds. Next we study the Gukov–Yau–Zaslow horizontal lifting for hyperKähler firbations of $$G_2$$ -manifolds, and discuss when the Gukov-Yau-Zaslow metric on this fibration is a $$G_2$$ -metric. PubDate: 2019-03-22 • Evolution of the Steklov eigenvalue under geodesic curvature flow • Abstract: On a two-dimensional compact Riemannian manifold with boundary, we prove that the first nonzero Steklov eigenvalue is nondecreasing along the unnormalized geodesic curvature flow if the initial metric has positive geodesic curvature and vanishing Gaussian curvature. Using the normalized geodesic curvature flow, we also obtain some estimate for the first nonzero Steklov eigenvalue. On the other hand, we prove that the compact soliton of the geodesic curvature flow must be the trivial one. PubDate: 2019-03-21 • The generalized algebraic conjecture on spherical classes • Abstract: Let X be a pointed CW-complex. The generalized conjecture on spherical classes states that, the Hurewicz homomorphism $$H: \pi _{}(Q_0 X) \rightarrow H_{}(Q_0 X)$$ vanishes on classes of $$\pi _* (Q_0 X)$$ of Adams filtration greater than 2. Let $$\varphi _s: Ext _{\mathcal {A}}^{s}(\widetilde{H}^(X), \mathbb {F}_2) \rightarrow {(\mathbb {F}_2 \otimes _{{\mathcal {A}}}R_s\widetilde{H}^(X))}^$$ denote the sth Lannes–Zarati homomorphism for the unstable $${\mathcal {A}}$$ -module $$\widetilde{H}^(X)$$ . This homomorphism corresponds to an associated graded of the Hurewicz map. An algebraic version of the conjecture states that the sth Lannes–Zarati homomorphism vanishes in any positive stem for $$s>2$$ and any CW-complex X. We construct a chain level representation for the Lannes–Zarati homomorphism by means of modular invariant theory. We show the commutativity of the Lannes–Zarati homomorphism and the squaring operation. The second Lannes–Zarati homomorphism for $$\mathbb {R}\mathbb {P}^{\infty }$$ vanishes in positive stems, while the first Lannes-Zatati homomorphism for any space is basically non-zero. We prove the algebraic conjecture for $$\mathbb {R}\mathbb {P}^{\infty }$$ and $$\mathbb {R}\mathbb {P}^{n}$$ with $$s=3$$ , 4. We discuss the relation between the Lannes–Zarati homomorphisms for $$\mathbb {R}\mathbb {P}^{\infty }$$ and $$S^0$$ . Consequently, the algebraic conjecture for $$X=S^0$$ is re-proved with $$s=3$$ , 4, 5. PubDate: 2019-03-19 • The concavity of Rényi entropy power for the parabolic p -Laplace equations and applications • Abstract: In this paper, we prove that the concavity of Rényi entropy power of positive solutions to the parabolic p-Laplace equations on compact Riemannian manifold with nonnegative Ricci curvature. As applications, we derive the improved $$L^p$$ -Gagliardo-Nirenberg inequalities. PubDate: 2019-03-16 • A Note on Generic Transversality of Euclidean Submanifolds • PubDate: 2019-03-15 • Bernstein theorem for translating solitons of hypersurfaces • Abstract: In this paper, we prove a monotonicity formula and some Bernstein type results for translating solitons of hypersurfaces in $$\mathbb {R}^{n+1}$$ , giving some conditions under which a translating soliton is a hyperplane. We also show a gap theorem for the translating soliton of hypersurfaces in $$R^{n+k}$$ , namely, if the $$L^n$$ norm of the second fundamental form of the soliton is small enough, then it is a hyperplane. PubDate: 2019-03-15 • A square root of Hurwitz numbers • Abstract: We exhibit a generating function of spin Hurwitz numbers analogous to (disconnected) double Hurwitz numbers that is a tau function of the two-component BKP (2-BKP) hierarchy and is a square root of a tau function of the two-component KP (2-KP) hierarchy defined by related Hurwitz numbers. PubDate: 2019-03-15 • On the density theorem related to the space of non-split tri-Hermitian forms II • Abstract: Let $${\widetilde{k}}$$ be a fixed cubic field, F a quadratic field and $$L=\widetilde{k}\cdot F$$ . In this paper and its companion paper, we determine the density of more or less the ratio of the residues of the Dedekind zeta functions of L, F where F runs through quadratic fields. PubDate: 2019-03-14 • Erratum to: A note on Galois embeddings of abelian varieties • Abstract: The original Theorem in the article is revised in this erratum based on a referee’s request. PubDate: 2019-03-01 • Motivic multiplicative McKay correspondence for surfaces • Abstract: We revisit the classical two-dimensional McKay correspondence in two respects: The first one, which is the main point of this work, is that we take into account of the multiplicative structure given by the orbifold product; second, instead of using cohomology, we deal with the Chow motives. More precisely, we prove that for any smooth proper two-dimensional orbifold with projective coarse moduli space, there is an isomorphism of algebra objects, in the category of complex Chow motives, between the motive of the minimal resolution and the orbifold motive. In particular, the complex Chow ring (resp. Grothendieck ring, cohomology ring, topological K-theory) of the minimal resolution is isomorphic to the complex orbifold Chow ring (resp. Grothendieck ring, cohomology ring, topological K-theory) of the orbifold surface. This confirms the two-dimensional Motivic Crepant Resolution Conjecture. PubDate: 2019-03-01 • On path-components of the mapping spaces $$M(\mathbb {S}^m,\mathbb {F}P^n)$$ M ( S m , F P n ) • Abstract: We estimate the number of homotopy types of path-components of the mapping spaces $$M(\mathbb {S}^m,\mathbb {F}P^n)$$ from the m-sphere $$\mathbb {S}^m$$ to the projective space $$\mathbb {F}P^n$$ for $$\mathbb {F}$$ being the real numbers $$\mathbb {R}$$ , the complex numbers $$\mathbb {C}$$ , or the skew algebra $$\mathbb {H}$$ of quaternions. Then, the homotopy types of path-components of the mapping spaces $$M(E\Sigma ^m,\mathbb {F}P^n)$$ for the suspension $$E\Sigma ^m$$ of a homology m-sphere $$\Sigma ^m$$ are studied as well. PubDate: 2019-03-01 • Local energy inequalities for mean curvature flow into evolving ambient spaces • Abstract: We establish a local monotonicity formula for mean curvature flow into a curved space whose metric is also permitted to evolve simultaneously with the flow, extending the work of Ecker (Ann Math (2) 154(2):503–525, 2001), Huisken (J Differ Geom 31(1):285–299, 1990), Lott (Commun Math Phys 313(2):517–533, 2012), Magni, Mantegazza and Tsatis (J Evol Equ 13(3):561–576, 2013) and Ecker et al. (J Reine Angew Math 616:89–130, 2008). This formula gives rise to a monotonicity inequality in the case where the target manifold’s geometry is suitably controlled, as well as in the case of a gradient shrinking Ricci soliton. Along the way, we establish suitable local energy inequalities to deduce the finiteness of the local monotone quantity. PubDate: 2019-03-01 • On the isometry group of $$RCD^(K,N)$$ R C D ∗ ( K , N ) -spaces • Abstract: We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition, $$RCD^(K,N),$$ is a Lie group. We obtain an optimal upper bound on the dimension of this group, and classify the spaces where this maximal dimension is attained. PubDate: 2019-03-01 • A fractional elliptic problem in $$\mathbb {R}^n$$ R n with critical growth and convex nonlinearities • Abstract: In this paper we prove the existence of a positive solution of the nonlinear and nonlocal elliptic equation in $$\mathbb {R}^n$$ \begin{aligned} (-\Delta )^s u =\varepsilon h u^q+u^{2_s^-1} \end{aligned} in the convex case $$1\le q<2_s^-1$$ , where $$2_s^={2n}/({n-2s})$$ is the critical fractional Sobolev exponent, $$(-\Delta )^s$$ is the fractional Laplace operator, $$\varepsilon$$ is a small parameter and h is a given bounded, integrable function. The problem has a variational structure and we prove the existence of a solution by using the classical Mountain-Pass Theorem. We work here with the harmonic extension of the fractional Laplacian, which allows us to deal with a weighted (but possibly degenerate) local operator, rather than with a nonlocal energy. In order to overcome the loss of compactness induced by the critical power we use a Concentration-Compactness principle. Moreover, a finer analysis of the geometry of the energy functional is needed in this convex case with respect to the concave–convex case studied in Dipierro et al. (Fractional elliptic problems with critical growth in the whole of $$\mathbb {R}^n$$ . Lecture Notes Scuola Normale Superiore di Pisa, vol 15. Springer, Berlin, 2017). PubDate: 2019-03-01 • Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity • Abstract: We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Caratheodory reaction term which is resonant both at zero and $$\pm \infty$$ . Using the Lyapunov–Schmidt reduction method and critical groups (Morse theory), we show that the problem has at least two nontrivial smooth solutions. PubDate: 2019-03-01 • On invariant Riemannian metrics on Ledger–Obata spaces • Abstract: We study invariant metrics on Ledger–Obata spaces $$F^m/{\text {diag}}(F)$$ . We give the classification and an explicit construction of all naturally reductive metrics, and also show that in the case $$m=3$$ , any invariant metric is naturally reductive. We prove that a Ledger–Obata space is a geodesic orbit space if and only if the metric is naturally reductive. We then show that a Ledger–Obata space is reducible if and only if it is isometric to the product of Ledger–Obata spaces (and give an effective method of recognising reducible metrics), and that the full connected isometry group of an irreducible Ledger–Obata space $$F^m/{\text {diag}}(F)$$ is $$F^m$$ . We deduce that a Ledger–Obata space is a geodesic orbit manifold if and only if it is the product of naturally reductive Ledger–Obata spaces. PubDate: 2019-03-01 • Algebraic surfaces with $$p_g$$ p g = q = 1, $$K^2$$ K 2 = 4 and genus 3 Albanese fibration • Abstract: In this paper, we study the Gieseker moduli space $$\mathcal {M}_{1,1}^{4,3}$$ of minimal surfaces with $$p_g=q=1, K^2=4$$ and genus 3 Albanese fibration. Under the assumption that direct image of the canonical sheaf under the Albanese map is decomposable, we find two irreducible components of $$\mathcal {M}_{1,1}^{4,3}$$ , one of dimension 5 and the other of dimension 4. PubDate: 2019-03-01 • Tautological ring of strata of differentials • Abstract: Strata of k-differentials on smooth curves parameterize sections of the k-th power of the canonical bundle with prescribed orders of zeros and poles. Define the tautological ring of the projectivized strata using the $$\kappa$$ and $$\psi$$ classes of moduli spaces of pointed smooth curves along with the class $$\eta = \mathcal O(-1)$$ of the Hodge bundle. We show that if there is no pole of order k, then the tautological ring is generated by $$\eta$$ only, and otherwise it is generated by the $$\psi$$ classes corresponding to the poles of order k. PubDate: 2019-03-01 • Classifying Fano complexity-one T -varieties via divisorial polytopes • Authors: Nathan Ilten; Marni Mishna; Charlotte Trainor Abstract: The correspondence between Gorenstein Fano toric varieties and reflexive polytopes has been generalized by Ilten and Süß to a correspondence between Gorenstein Fano complexity-one T-varieties and Fano divisorial polytopes. Motivated by the finiteness of reflexive polytopes in fixed dimension, we show that over a fixed base polytope, there are only finitely many Fano divisorial polytopes, up to equivalence. We classify two-dimensional Fano divisorial polytopes, recovering Huggenberger’s classification of Gorenstein del Pezzo $$\mathbb {K}^$$ -surfaces. Furthermore, we show that any three-dimensional Fano divisorial polytope is equivalent to one involving only eight functions. PubDate: 2018-05-14 DOI: 10.1007/s00229-018-1036-x • Hölder regularity for bounded solutions to a class of anisotropic operators • Authors: Stella Piro-Vernier; Francesco Ragnedda; Vincenzo Vespri Abstract: In this note we show the Hölder regularity for bounded solutions to a class of anisotropic elliptic operators. This result is the dual of the one proved by Liskevich and Skrypnik (Nonlinear Anal 71:1699–1708, 2009). PubDate: 2018-05-02 DOI: 10.1007/s00229-018-1034-z JournalTOCs School of Mathematical and Computer Sciences Heriot-Watt University Edinburgh, EH14 4AS, UK Email: journaltocs@hw.ac.uk Tel: +00 44 (0)131 4513762	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8962690234184265, "perplexity": 3845.2435544239247}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107894203.73/warc/CC-MAIN-20201027140911-20201027170911-00470.warc.gz"}
https://mathoverflow.net/questions/366768/how-to-estimate-the-order-of-this-integral-with-parameter	# How to estimate the order of this integral with parameter Some introduction: Given a homogeneous structure called "dilation" in $$R^n$$: For $$t\geq 0$$ $$D_t: R^n\rightarrow R^n$$ $$D_t(x)=(t^{a_1}x_1,...,t^{a_n}x_n)$$ where $$1=a_1\leq...\leq a_n$$, and $$a_i$$ are all integers. And we call $$Q=a_1+...+a_n$$ the homogeneous dimension. In our problem, we only consider when $$Q>n\geq 2$$. Now consider the integral: $$J(r)=\int_{[0,1]^n}\frac{dx}{P(x,r)}=\int_{[0,1]^n}\frac{dx}{f_n(x)r^n+f_{n+1}(x)r^{n+1}+...+f_Q(x)r^Q}$$ where $$f_k(x)$$ satisfies: (1) $$f_k(D_t(x))=t^{Q-k}f_k(x)$$ for all $$x\in R^n$$ and $$t\geq0$$ (2) $$f_k(x)$$ is the combination of some positive monomials. (Examples will be shown below) (3) $$f_Q(x)=Constant>0$$. (This property follows from other theorems and propositions, but they are too many so I don't describe them here.) Four examples are the followings: (ex1) In $$R^2$$, $$D_t(x)=(tx_1,t^2x_2)$$, so $$Q=3$$. And Let $$P(x,r)=x_1r^2+r^3$$. (ex2) In $$R^3$$, $$D_t(x)=(tx_1,tx_2,t^2x)$$, so $$Q=4$$. Let $$P(x,r)=(x_1+x_2)r^3+r^4$$ (ex3) In $$R^3$$, $$D_t(x)=(t^{1}x_1,t^2x_2,t^{3}x_3)$$, so $$Q=6$$. Let $$P(x,r)= x_1^3r^3+(x_2+3x_1^2)r^4+5x_1r^5+3r^6$$ (ex4) In $$R^3$$, $$D_t(x)=(t^{1}x_1,t^2x_2,t^{3}x_3)$$, so $$Q=6$$. Let $$P(x,r)= x_1x_2r^3+(x_2+2x_1^2)r^4+3x_1r^5+r^6$$ (You will find that $$x_n$$ doesn't make effort. In my work $$x_n$$ do make no sense in the integral but this follows from other theorems, and it doesn't matter here. ) Problem: Find the order of $$J(r)$$ when $$r$$ goes to $$0^+$$. Like the following description. Attempt and information: I guess $$J(r)=\frac{1}{r^\alpha}I(r)$$, where the $$\alpha$$ is the "critical value", that is: (i) $$\liminf_\limits{r\rightarrow0^+}I(r)>0$$. (ii) for any $$\epsilon>0$$, $$\lim_\limits{x\rightarrow0^+}r^\epsilon I(r)=0$$. I will give the reason why I guess so in the below. I can show that $$g_p(r)=r^p J(r)$$, then there exists $$p_0$$ s.t. when $$a, $$\lim_\limits{r\rightarrow0^+}g_a(r)>0$$ and when $$a>p_0$$, $$\lim_\limits{r\rightarrow0^+}g_a(r)=0$$. But I can't show $$\lim_\limits{r\rightarrow0^+}g_{p_0}(r)>0$$, that is, I can't show the (i) above. (see https://math.stackexchange.com/questions/3769564/how-to-find-the-critical-index-a-of-xafx) One gave a counterexample for the proposition in that link. But its counterexample will not appear in this problem. Because this is a rational fractional integral. The $$I(r)$$ I guess will be like the combination of $$\log$$ and $$\arctan$$. The four example have the order estimates: (ex1) We can calculate directly: $$J(r)=\frac{1}{r^2}\ln(1+\frac{1}{r})=\frac{1}{r^2}I(r)$$ where $$I(r)$$ satisfies (i)(ii) above. (ex2) $$J(r)=\frac{1}{r^3}I(r)$$ where $$I(r)$$ can be calculate or one can use Dominate convergence theorem to estimate that $$I(r)$$ satisfies (i)(ii) (ex3) $$J(r)=\frac{1}{r^{3+2/3}}I(r)$$ see https://math.stackexchange.com/questions/3718932/estimate-a-integral-with-parameter (ex4) $$J(r)=\frac{1}{r^{3}}I(r)$$ First $$J(r)=\frac{1}{r^3}\int_{[0,1]^2}\frac{dxdy}{xy+(y+2x^2)r+3xr^2+r^3}=\frac{1}{r^3}I(r)$$ we can show $$I(r)$$ satisfies (i)(ii): (i) change variables: $$I(r)=\int_{0}^{1/r^2}\int_{0}^{1/r}\frac{dxdy}{xy+(y+2x^2)+3x+1}$$ and then obviously. (ii) for $$3>\epsilon>0$$ (the part $$\epsilon\geq 3$$ follows from the part $$3>\epsilon>0$$), $$r^\epsilon I(r)=\int_{[0,1]^2}\frac{r^\epsilon}{xy+(y+2x^2)r+3xr^2+r^3}dxdy=\int_{[0,1]^2}h_r(x,y)dxdy=\int_{(0,1)^2}h_r(x,y)dxdy$$ Pointwisely $$\lim_\limits{r\rightarrow0^+}h_r(x,y)=0$$ in $$(0,1)^2$$. Now look for a dominating function in $$(0,1)^2$$: $$\frac{1}{h_r(x,y)}\geq \frac{xy}{r^\epsilon}+r^{3-\epsilon}\geq C(xy)^{1-\frac{\epsilon}{3}}$$ So $$h_r(x,y)\leq \frac{C}{(xy)^{1-\frac{\epsilon}{3}}}$$ in $$(0,1)^2$$, which is integrable. By DCT, we have $$I(r)$$ satisfying (i)(ii). But this method doesn't work in other examples like (ex3). Based on the four examples, I guess $$J(r)=\frac{1}{r^\alpha}I(r).$$ But I can't show how to find the critical value $$\alpha$$ and even it's difficult to show the existence of critical value It looks like you care only about the order of magnitude (i.e., an answer up to a constant factor), in which case it is fairly easy. First, ignore all coefficients. Setting them to $$1$$ just changes the answer at most constant number of times. Now, suppose we have the denominator of the form $$\sum_{(\alpha,\beta)} x^\alpha r^\beta$$ where $$\alpha$$ is a multi-index with real entries and $$\beta$$ is a real number. The sum is assumed to be finite. Make the change of variable $$x_j=e^{-y_j}$$. Now, at each point, only the maximal term matters (up to a factor that is the total number of terms). In terms of $$y$$'s, the condition of maximality of $$x^\alpha r^\beta$$ is $$y_j\ge 0$$, $$\langle y,\alpha-\alpha'\rangle\le (\beta'-\beta)\log(1/r)$$ for all $$(\alpha',\beta')\ne(\alpha,\beta)$$. This domain is just a fixed polyhedron $$P_{\alpha,\beta}$$ stretched $$\log(1/r)$$ times (we keep only those with non-empty interiors in what follows; also I call it a "polyhedron" though, technically, it can be unbounded). Thus, $$J(r)\asymp\sum_{(\alpha,\beta)}r^{-\beta}\int_{(log\frac 1r)P_{\alpha,\beta}}e^{\psi_{\alpha,\beta}(y)}\,dy$$ where $$\psi_{\alpha,\beta}(y)=\langle \alpha-e,y\rangle$$, $$e=(1,\dots,1)$$. Now the life becomes straightforward. All you need is to find the order of magnitude of each integral. I'll drop the indices $$\alpha,\beta$$ for brevity. Let $$F$$ be the face of $$P$$ on which $$\psi$$ attains its maximum $$p$$ and let $$d$$ be the dimension of $$F$$. If $$\psi\equiv 0$$ (i.e., $$\alpha=e$$), we just have $$F=P$$ and $$\int_{(\log\frac 1r)P}e^{\psi}=V(P)\log^d(1/r)$$. Consider now the non-trivial situation when $$\psi$$ is not $$0$$. Then we can rotate and shrink the coordinate system so that $$-\psi(y)$$ becomes a new variable $$t$$. Also we can shift $$P$$ along this coordinate so that the face $$F$$ lies on the corresponding coordinate hyperplane $$\{t=0\}$$. Then the integral in question is just $$e^{p\log(1/r)}(\log^{D-1}\frac 1r)\int_{0}^\infty e^{-t}S_P(\frac t{\log{1/r}})\,dt$$ where $$S_P(\tau)$$ is the $$D-1$$-dimensional volume of the cross-section of $$P$$ by the hyperplane $$\{t=\tau\}$$. By the general convex geometry nonsense, for small $$\tau$$, $$S_P(\tau)=v_d\tau^{D-1-d}+v_{d-1}\tau^{D-d}+\dots+v_0\tau^{D-1}$$ where $$v_d>0$$ and then it becomes smaller (look up "mixed volumes" on Google if you are interested in the details), whence the leading term in the integral becomes $$\log^d\frac 1r$$ with some coefficient depending on $$P$$. Thus, the final answer for the integral we are interested in with the factor $$r^{-\beta}$$ is $$\asymp r^{-p_{\alpha,\beta}-\beta}\log^{d_{\alpha,\beta}}\frac 1r$$ We have several competing terms like that, so the winning one is the one with largest $$p+\beta$$ and among those the one with the largest $$d$$. In your last example $$x_1x_2+x_1^2r+x_2r+x_1r^2+r^3$$ (I ignore $$r^3$$ that can be carried out and all the coefficients), we have $$5$$ polyhedra and functionals (I drop the trivial restrictions $$y_1,y_2\ge 0$$): $$P_{1,1,0}=\{-y_1+y_2\le 1, y_1\le 1, y_2\le 2, y_1+y_2\le 3\}, \\ \psi_{1,1,0}(y)=0 \\ P_{2,0,1}=\{y_1-y_2\le -1, 2y_1-y_2\le 0, y_1\le 1,2y_1\le 2\}, \\ \psi_{2,0,1}(y)=y_1-y_2 \\ et\ cetera.$$ Here $$P_{1,1,0}$$ dominates and yields $$\log^2\frac 1r$$ but it may be instructive to find the contribution of $$P_{2,0,1}$$. In this case (just draw the picture) $$p=-1$$, $$\beta=1$$, $$d=1$$, so we get $$\log\frac 1r$$. • @Houa Oops, I forgot about $r^\beta$ in my final answer. I edited. So the contribution of $P_2$ is actually $\log(1/r)$. However, it is still $P_1$ that dominates (contributing $\log^2(1/r)$, so $J(r)\asymp r^{-3}\log^2(1/r)$ in full agreement with what you wrote). As to question 1, by my (corrected) formula the integral is $\asymp r^{-1}\int_{\log(1/r)P_{0,1}}e^{-y}dy+\int_{\log(1/r)P_{1,0}}1dy$. From the definition with linear inequalities (just drop $\log(1/r)$ on the RHS), $P_{1,0}=\{0\le y\le 1\}=[0,1]$ and $P_{0,1}=\{y>0,-y\le-1\}=[1,+\infty]$ so you get your $\log(1/r)+1\asymp\log(1/r)$ – fedja Jul 29 at 12:02 • @Houa Is it clearer now? If not, what should I clarify? (I addressed two explicit questions you asked but I suspect more clarification may be still needed, so don't hesitate to ask for it but try to explain what exactly you are confused about) – fedja Jul 29 at 12:25 • (3) Yes, of course. As I said "ignore everything with empty interior". (4) It follows from the physical meaning of your particular problem: since you have a constant term, the integral should converge, and if $\psi$ is unbounded (or the face $F$ on which the maximum is attained is unbounded), you'll certainly just get $+\infty$ immediately. This can happen in the general setting I considered but your particular case is tame. (5) Yes, you can think of it as first rotating the rectangle and then shifting it or you can think of first shifting the origin and then rotating the coordinate frame. – fedja Jul 30 at 14:17 • @Houa (6) Yes, it is related to it (read the previous comment for (3-5); I forgot to address it to you). As to the integral, just integrate term by term. The claim is that if $f(t)$ is any function that equals $p(t)=\sum_k c_kt^k$ ($c_k>0$) near the origin and is always between $0$ and $p(t)$, then $\int_0^\infty f(\delta t)e^{-t}\,dt\approx \sum_k k!c_k\delta^k$ as $\delta\to 0$. – fedja Jul 30 at 14:24 • @Houa That's all right, but note that I also first shifted the origin to the point where the maximum is attained (so I should rather say "making $t=p-\psi(y)$ a new coordinate" if I had used the original $y$, not $y$ with respect to the shifted origin), in which case the shift in the argument of $S_P$ disappears and our formulae agree. I apologize for being somewhat confusing here – fedja Jul 31 at 14:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 133, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999200105667114, "perplexity": 2066.5531622907533}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107884322.44/warc/CC-MAIN-20201024164841-20201024194841-00590.warc.gz"}
http://mathhelpforum.com/calculus/18992-second-fundamental-theorem-calculus-print.html	# Second Fundamental Theorem of Calculus • September 15th 2007, 10:37 AM Fourier Second Fundamental Theorem of Calculus Is it possible to use the Second Fundamental Theorem of Calculus on $C(x)$ to find $C'(x)$, if $C(x)=\sum_{j=1}^{n}{\bigg\|N_{j}\int_{x}^{x_j}{k(s) ds}\bigg\|}$, where $N_j$ is some constant, and $k(s)$ is integrable over every interval? • September 15th 2007, 12:31 PM CaptainBlack Quote: Originally Posted by Fourier Is it possible to use the Second Fundamental Theorem of Calculus on $C(x)$ to find $C'(x)$, if $C(x)=\sum_{j=1}^{n}{\bigg\|N_{j}\int_{x}^{x_j}{k(s) ds}\bigg\|}$, where $N_j$ is some constant, and $k(s)$ is integrable over every interval? Yes RonL • September 15th 2007, 01:38 PM Fourier Would $C'(x)$ be $C'(x)=\sum_{j=1}^{n}{\bigg\|N_j k(x_j)\bigg\|} \textrm{ ?}$ If this is correct, then it implies that the derivative is always nonnegative and increasing as the sum increases from 1 to n. • September 17th 2007, 08:16 AM Fourier Can anyone check my work? Thanks	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9826605916023254, "perplexity": 501.4534305301673}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644063881.16/warc/CC-MAIN-20150827025423-00107-ip-10-171-96-226.ec2.internal.warc.gz"}
http://mathematica.stackexchange.com/questions/36843/using-a-mathematica-function-to-define-a-new-function	# using a Mathematica function to define a new function I'd like to define a function of three variables which produces a new, named function of a single variable, where this final variable is not a member of the first three. So I'd like something where I have f0[x_ , y_ , z_] := << complicated function >> which gives f1[p_] Furthermore, I'd like to have the functions be defined in such a way that when I write IN:= f0[x0,y0,z0] I get OUT:= fx0y0z0[p_] so that I can easily identify which inputs produced the function. So, basically, I'd like to wind up with a function produced via Interpolation and I'd like that function to have a specific name defined by my inputs. For instance, let's say I'm creating a numerical function by writing down a table in two variables (say, p and q) that requires x, y, and z as inputs. Then I'd like to integrate over q and interpolate over p so that my final function is just a function over q only. So, let's say that my first function is g[x_,y_,z_,p_,q_] := (x + y + z) p / q Now I'd like to tabulate this over p and q for given values of x, y, and z. Then I'd like to integrate over p and have a function of q only. I can for instance do the following f1[x_,y_,z_] := NIntegrate[ Interpolation[ Flatten[Table[{q, p, g[x,y,z,p,q]}, {p,p0,p1}, {q,q0,q1}],1]][#, p], {p, p0, p1}] & and then this is a well-behaved function of q which I can make tables of, which I can then plot, integrate, etc. just by writing f1[x0,y0,x0][q]. But this is not very convenient for me since it requires me to write out a new function name every time I want to examine the behavior as a function of different values of x, y, and z, and I will ultimately need many values of x, y, and z. Is there any way to write a meta-function that is capable of producing a brand new interpolating function of q only, with the name including the input values of x, y, and z? Thanks for your help, Sam - A solution like the one to this question might be useful to you. – episanty Nov 12 '13 at 19:00 I typically use pure functions for this type of meta programming. For example: generator[p_,q_] := Function[{x,y,z}, Evaluate[ Integrate[ (x+y+z)/(p+q), {p,p0,p1},{q,q0,q1}] ] ] Then one can use it as fpXqY = generator[X,Y] And then fpXqY will be a pure function you can use. This only works for function that can be treated as pure functions. However, one can also do something similar by just calling SetDelayed[] (which is the full form of :=) within your generator to create a new function. So something like: generator2[p_,q_] := SetDelayed[ ToExpression[ StringJoin[ "fp", ToString[p], "q", ToString[q]]][x_, y_, z_] , Integrate[ (x+y+z)/(p+q), {p,p0,p1},{q,q0,q1}] ] And then call it as generator2[X,Y] and you should then find you can use fpXqY as your evaluator. Note that you can either use Set or SetDelayed as you need. - Thanks -- this seems to be on the right track. However, my goal is to produce a function with an entirely new name. Say I have g[x_,y_,z_,p_,q_]:=(x+y+z)p/q f1[x_,y_,z_] := NIntegrate[Interpolation[Flatten[Table[{q,p,g[x,y,z,p,q]},{p,10}, {q,10}],1]][#,p],{p,1,10}]& as before. What is wrong with the following? generator[x_,y_,z_]:=SetDelayed[ToExpression[ToString[StringForm["f1",x,y,z]]][‌#]&,Interpolation[Table[f1[x,y,z][p],{p,10}]]] I'd like to produce, e.g., f1323 = Interpolation[Table[f1[3,2,3][x],{x,10}]]; which is easily identifiable and very fast. Thank you for your help! – user1451632 Nov 12 '13 at 16:43 @user1451632 right sorry, let me fix that -- see the updated generator 2. In general, you should avoid using StringForm for producing function names -- the *Form sometimes introduces odd quirks – tkott Nov 12 '13 at 17:31 Terrific! This really helps. Thank you for your time. – user1451632 Nov 12 '13 at 21:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8292410373687744, "perplexity": 760.2934362867456}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609526252.40/warc/CC-MAIN-20140416005206-00023-ip-10-147-4-33.ec2.internal.warc.gz"}
https://forum.allaboutcircuits.com/threads/weird-women.70814/	# weird women ? #### Mathematics! Joined Jul 21, 2008 1,036 So, I was at a club yesterday And I meet this girl and her friends... I basically chilled with them for most of the night. what I am trying to figure out is I know this girl likes me but I cann't figure her completely out yet. First she kept touching my inner thigh and that usually in my book is a good thing. So I basically tried to kiss her but she mostly gave me the side of her cheek. So I didn't persist that much with it and just kept it touchy feely. So also would tell me extra info or private info like I am really from etc etc but I am just telling those guys I am from yada yada And for like 15 mins or longer she went to the bathroom with her sister... Then we went to the club I did ask her and all her friend when I first sat down who was involved/had boyfriends.... The girl that I am talking about said she was just just starting a relation ship... I kiddingly said was it with a guy by the name of my name...etc jokingly she just laughed but didn't say No. So after all this we went dancing and at the end of the night they asked for my phone number so I gave it to them... I felt I did to much already so I left it up to her (that might of been a poor mistake but F it if she likes me she will call at least once ) On another note: The other girl a few nights ago I asked for her name and number though we didn't spend more then 5 minutes together. I gave that one a call and she hasn't got back to me yet so I felt that I would try it the other way around. I already got shot down with the kiss (a little bit) so I figured why not let her call me. Though I am curious why she was so touch feely but not kissing friendly maybe she really does have a new relation ship but even if she does then why would she be feeling me up and accepting being felt up by me. She even showed me her underwear but that was after I showed her mine because of been asked to show. Any comments on what is going on here.... Anyway if she doesn't call then F it again I am going back to try and pick up another one. I have to say she was older but very very hot (supermodel hot)... And I am getting better about this stuff. Basically have just one light drink to make you less nervous but not drunk The don't think to hard just act if a bad outcome occurs just move on... Smile and ask open ended questions / listen ,...etc I am actually so glad that I am learning to just not fear any girl situations Even around some of there guys I have had them say sometime shes with me ...etc etc Normally if it starts to get more involved then that a simple just move along... I have been shot down a ton and I have to say each time I just see it as less of an issue and laugh it off... And I am finding more and more I am getting closer and closer to my goal Which is being the most attractive confident guy in the places. I have to say I can see right through most girls intentions its funny how girls can pretty much get at least one guy to give them what they want. Question 1 So how far should I give them what they want ... even though I know some of them are just toying with me a little. If I don't given in at all they may just say F it I will just find somebody else.... if I give in to much they might say F it this guy is P whipped. So there must be a time when to give and went to not.... I can tell you all the toy games ,...etc but I cann't tell you in what situations will you not play into them. The girl that I am talking about in this thread she never really played to many games with me to much... Except one another guy in the dance club came up behind her dancing and she whispered get this guy off me/ lose this guy. Also at the bar she would always rest her head on my chest which I kind of liked. The only problem with her is if I found out she had kids... for me I don't care how hot you are I am not getting in a relation ship with kids (especially not mine). Last edited: #### maxpower097 Joined Feb 20, 2009 816 Sounds like you just gotta seperate her from the heard then take her down like an antelope. They will do those kinds of moves to let you know they're a freak and interested but they don't wanna hear if from their friends so anything PDA they will shun, but the hand on the inside theigh is an obvious sign. So take the number and single her out. Probably won't even have to buy her dinner. #### loosewire Joined Apr 25, 2008 1,686 There are dates and players, Mathematics,do the math. Players are more worldly,dates are local ,from the Interview of the lady that had the boat captain to lose it at sea. You got to many projects going,do you have time to take on another.There better advice here,you will get it. #### VoodooMojo Joined Nov 28, 2009 505 Never back your attack by sacking the WAC or by riding the breast of the WAVE. Sit in the sand and run it by hand and think of the money you'll save. #### monster_catfish Joined Mar 17, 2011 116 Sounds like you just gotta seperate her from the heard then take her down like an antelope. . Ha ha ha ha This timeless quote made my day. Now if I had a free grope for every time I FAILED to separate her from the herd, I'd probably have gotten laid a whole lot more than I ever did ha ha ha #### DerStrom8 Joined Feb 20, 2011 2,390 The other girl a few nights ago I asked for her name and number though we didn't spend more then 5 minutes together. I gave that one a call and she hasn't got back to me yet so I felt that I would try it the other way around. DON'T call them. Let them call you. Also, there's a conventional "3-day waiting period" before one should call the other. It's a standard. It allows each party to think about what (who) they really want, and if they think it's a good idea to continue building a relationship. That's my 2 cents on this. Can't say much about the rest. #### MrChips Joined Oct 2, 2009 21,664 Mathematics! you are weird man! You can see right through most girls intentions but don't you think they can see right through you? Building a long term relationship ain't the same as scoring. If you want a genuine relationship, be genuine yourself. Touching or kissing the first time you meet a girl? Not in my books. Holding hands, maybe. Take it easy and get to know the person first. The rest will fit into place when the time comes. Call me old fashioned. Last edited: #### Rbeckett Joined Sep 3, 2010 208 The question is basically do you want a relationship or a sport lay. Depending on that answer you will have two very different approaches. If youre really into the lady, do not hesitate, call her up, make a date, show her a great time and be the ultimate Prince Gallahad. Once she is comfortable she will let you know what she wants. It may be casual, freaky or white picket fence and 2 kids with a dog. Investigate as you would any other piece of merchandise or equipment. She may end up being around to rock your world for a long long time. My wife and I have been together nearly 20 years and married nearly 10, and she rocks my world like a 18 YO nypho freak every time (i'm 50 plus and 100% disabled too).... Just sayin. Wheelchair Bob #### Mathematics! Joined Jul 21, 2008 1,036 I hear what you guys are saying And I myself haven't quite figured out if I just want to score or a relationship. Probably a little of both... But now that I think about it it was probably a bad idea to try kissing... But I don't know in the big picture of things would this have ruined it for me? Also I don't know if not taking her number and just giving my number was a mistake also Probably so.... But I will see how it pans out. With each new mistake you learn not to make it twices.... Honestly the way she was acting around me short of almost implied trying to kiss would be ok. But maybe I am wrong. Though I said I can read what most girls are trying to do... obviously not all and obviously I can make mistakes.... I have to say from her point of view I could have been coming off as somebody that just wanted to get laid... But then again how could anybody not if you saw how hot she was and the way she was acting... Of course she could be a teaser ... But all I have to say is whatever I had fun that night regardless weather she calls me back or not. And I am quite aware of the rules like the 3 day before calling ,don't kiss on first date ,...etc But obviously those don't always work in every context my friend got married to a girl he meet walking down the street. He got her number that day called her the next day and the rest is history.... Anyway not going to worry about weather I made a mistake that night or not you cann't change the passed... Question 1) Though any good advice for the future if she does call back ? Question 2) I am pretty good with the rules of trying to start a long term relationship but what happens if I just want a short term fooling around relationship... Is there any rules or tips in being successful with this area ? Like is there any boundaries or can you basically say do you want to fool around ...etc etc As well what do you think is the most likely way of getting into a short term relationship? I am more kicking myself for not getting her number though... should you always get the number and call even when you think you did to much already like kiss ,...etc. Because the way I was think is give her my number and leave it up to her to call me initially to maybe show that I am not totally stuck on her. Normally I always get the number and call the girl the first time but is it wrong/doesn't work if you do it the other way around... Well I am going to find out. And also this wasn't technically a planned date so I don't know if the rules still apply in all cases to this situation. You can see right true most girls intentions but don't you think they can see right through you? Not saying they don't see my intentions they where pretty obvious though I don't think they see all of my intentions either since there are boundaries that I have as well that know girl could control ,...etc etc Anyway I am not trying to hide my intentions I would have took her home that night she knows this I think. But I also would have planned another date to go out with her again so I basically left it up to her if she wants to proceed then just call my number that simple. Last edited: #### R!f@@ Joined Apr 2, 2009 9,734 U blew it big time #### Wendy Joined Mar 24, 2008 22,155 Patience, man, patience. If you are only interested in sex then there are other ways. I'm hearing you want a girlfriend. This means relationship. This in turns means going slow. Some guys are blessed with whatever it is that allows them to talk a woman into the sack, I think it is partly pheromones, partly attitude. The fact is most of the guys like this are total aes, part of why they succeed is they don't care about anyone but themselves. Is this what you want to be? Any woman who is that easy is likely to give you something permanent. Drug resistant gonorrhea is on the rise, for example. It is for life again, if you get the wrong strain. Easy women don't care either. IMO a girlfriend is definitely better, more rewarding, and a heck of a lot more fun. And yes, a lot more work. Last edited: #### MrChips Joined Oct 2, 2009 21,664 First time you meet a girl and there is mutual interest, exchange phone numbers. Wait for three days if she doesn't call and then you call and invite her for coffee/snack/lunch not dinner (at a local deli/coffee shop/snack bar). #### loosewire Joined Apr 25, 2008 1,686 Quote from interview.....at midnight players and feral cats are Hard to find,...Players ,play the players..know no shame. A good lnterview, the real world. A part of coming safely home from Player trip. #### strantor Joined Oct 3, 2010 5,322 [translation] The question is basically do you want a relationship or a sport lay. Depending on that answer you will have two very different approaches. "The question is, are you going fishing or are you going hunting? Because if you're going hunting you need a gun and if you're going fishing you need a rod." And I myself haven't quite figured out if I just want to score or a relationship. Probably a little of both... "I haven't decided yet" [as he walks off into the woods with blunt stick and a large rock] #### nerdegutta Joined Dec 15, 2009 2,676 Be yourself. You cannot pretend to be someone/something else. Eventually the truth will come. #### R!f@@ Joined Apr 2, 2009 9,734 that's me !!! #### maxpower097 Joined Feb 20, 2009 816 U blew it big time Thats what I though with hand on the inner thiegh. Women are weird about pda when their in a heard. Thats why you gotta seperate her. Cause a couple of her friends will be jealous and talk crap about you. The other will be annoyed this was supposed to be girls night out, blah blah blah. Just get her alone and spring the trap. #### THE_RB Joined Feb 11, 2008 5,438 Man you need to learn a bit about women. Be rude to her female friends and look at them like they are crap, then look at her like she's hot and you want her, but remain aloof and give off the signal that you're not going to do her like she's not quite up to your standard. Then she'll practically make it her mission in life to track you down and get with you. Of course this relies on you being at least reasonably alpha, ie fit, strong and not too ugly. #### count_volta Joined Feb 4, 2009 435 Here is a cynical reply from a very cynical person. All women are weird.... Which is why we love them..... #### Mathematics! Joined Jul 21, 2008 1,036 well, I had a good time none the less. If she calls then great if not then whatever I will learn from this mistake....etc (its a learning process before getting great at it) As such if she was dirty then I didn't really want to fool around once. More into girl friend or long term friends with benefits not one night stand wuth STD no matter how hot they are. It just shows though if I could get somebody this hot then I shouldn't limit myself into think I cann't do it again.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1683598756790161, "perplexity": 1845.9568035987543}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400221382.33/warc/CC-MAIN-20200924230319-20200925020319-00460.warc.gz"}
https://socratic.org/precalculus/functions-defined-and-notation/symmetry	Precalculus Topics # Symmetry ## Key Questions It is a line about which the shape/curve is repeated as if it had rotated about it by ${180}^{o}$ See diagram/graph #### Explanation: $\textcolor{g r e e n}{\text{The line of symmetry is the y axis}}$ $f \left(x , y\right) = {x}^{2} + x y + {y}^{2}$ $g \left(x , y , z\right) = x y + y z + z x + \frac{1}{{x}^{2} + {y}^{2} + {z}^{2}}$ #### Explanation: A symmetric function is a function in several variable which remains unchanged for any permutation of the variables. For example, if $f \left(x , y\right) = {x}^{2} + x y + {y}^{2}$, then $f \left(y , x\right) = f \left(x , y\right)$ for all $x$ and $y$. How many times is the same shape seen if a figure is turned through 360° #### Explanation: Symmetry means that there is a 'sameness' about two figures THere are two types of symmetry - line symmetry and rotational symmetry. Line symmetry means if you draw a line thorugh the middle of a figure, the one side is a mirror image of the other. Rotational symmetry is the symmetry of turning. If you turn a shape though 360°, sometimes the identical shape is seen again during the turn. This is called rotational symmetry. For example, a square has 4 sides, but the square will look exactly the same no matter which of its sides is at the top. Rotational symmetry is described by the number of times the same shape is seen during the 360° rotation. A square has rotational symmetry of order 4, An equilateral triangle has rotational symmetry of order 3. A rectangle and a rhombus have rotational symmetry of order 2. A regular pentagon has rotational symmetry of order 5.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8255053758621216, "perplexity": 495.48876464141495}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249490870.89/warc/CC-MAIN-20190223061816-20190223083816-00170.warc.gz"}
https://www.lessonplanet.com/teachers/match-uppercase-to-lowercase-letters-f-g-h-i-and-j	# Match Uppercase to Lowercase-- Letters F, G, H, I and J In this matching letters worksheet, students draw lines to match upper and lower case examples of letters F, G, H, I and J.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9171276092529297, "perplexity": 2362.07757823056}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818690035.53/warc/CC-MAIN-20170924152911-20170924172911-00588.warc.gz"}
https://www.katzentante.at/wordpress-tips-change-permalinks/	As suggested by several websites I wanted to change my permalinks from the structure p=123 to structure /post-title/ because it should be easier to find my content using a search engine. First you have to go to you wordpress admin panel. Then you do the following: 1. Click on “Settings” 3. Apply the changes you want (I changed the link structure and the base for categories) 4. Click “Save changes”. It might be that you need to create redirects for which I found this tool. For my blog the tool said “You don’t have to do any redirects, WordPress will do it for you.”. But, if wordpress does not have write access to your .htaccess file (A message is generated after you “Save changes” on the top of the “Permalinks” page), you have to add this manually (in my case I just had to uncomment it because the lines were already there): RewriteEngine On RewriteBase / RewriteRule ^index\.php\$ - [L] RewriteCond %{REQUEST_FILENAME} !-f RewriteCond %{REQUEST_FILENAME} !-d My .htaccess file is located at /etc/wordpress. This might be different depending on the OS of your server but in general you will find it there (make sure to look for hidden files as well). Now everything should work! To test it, you can do the following: • Click on an old link and try if it redirects • Click on any category / tag in case you changed the structure for them as well • Click on a post in the overview to see if the new links work Good luck!	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20141802728176117, "perplexity": 1810.8286199452461}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514576122.89/warc/CC-MAIN-20190923064347-20190923090347-00407.warc.gz"}
https://www.healthline.com/nutrition/maple-syrup	# Maple Syrup: Healthy or Unhealthy? Written by Kris Gunnars, BSc on June 4, 2017 One of the more popular sweeteners today is maple syrup. It is a 100% natural sweetener that is claimed to be more nutritious and healthier than sugar. There are many claims about maple syrup online and I'd like to separate the facts from the fiction. ## What Is Maple Syrup and How Is It Made? Maple syrup is made from the sugary circulating fluid (sap) of maple trees. It has been consumed for many centuries in North America... since the times of Native Americans. Over 80% of the world's supply is now produced in Canada. Maple syrup is made in a natural 2-step process: 1. A hole is drilled in the maple tree. Then the sugary circulating fluid leaks out and is collected into a container. 2. The sugary fluid is boiled until most of the water evaporates, leaving a thick sugary syrup, which is then filtered to remove impurities. If you want to see how incredibly simple it is to make maple syrup, then check out this cool video (opens in new tab) of a guy making his own from wild maple trees. Bottom Line: Maple syrup is made by evaporating the sugary circulating fluid (sap) from maple trees, leaving a thick syrup. It has been consumed for many centuries in North America. ## Different Grades of Maple Syrup There are several different "grades" of maple syrup, depending on the color. The exact way they are classified can vary between countries. In the United States, maple syrup is either classified as grade A or grade B (1). • Grade A is further categorized into 3 groups: Light Amber, Medium Amber and Dark Amber. • Grade B is the darkest of them all. The main difference between them, is that the darker syrups are made from sap that is extracted later in the harvesting season. The dark syrups have a stronger maple flavor and are usually used for baking or in recipes, while the lighter ones are rather used directly as syrups... for example on pancakes. If you're going to buy maple syrup, then make sure to get actual maple syrup, not just maple-flavored syrup... which can be loaded with refined sugar or high fructose corn syrup. As with any other food, make sure to read the label. Bottom Line: There are several different grades of maple syrup, depending on the color. Grade B is the darkest, with the strongest maple flavor. ## It Contains Some Vitamins and Minerals, But is Also High in Sugar The main thing that sets maple syrup apart from refined sugar, is the fact that it also contains some minerals and antioxidants. 100 grams of maple syrup contain (2): • Calcium: 7% of the RDA. • Potassium: 6% of the RDA. • Iron: 7% of the RDA. • Zinc: 28% of the RDA. • Manganese: 165% of the RDA. True, maple syrup does contain a decent amount of some minerals, especially manganese and zinc, but keep in mind that it also contains a whole bunch of sugar. Maple syrup is about 2/3rds sucrose (as in table sugar) and a 100 grams of it therefore supply around 67 grams of sugar. Really... sugar can be seriously harmful. Consumed in excess, it is believed to be among the leading causes of some of the world's biggest health problems, including obesity, type 2 diabetes and heart disease (3, 4, 5). The fact that maple syrup contains some minerals is a very poor reason to eat it, given the high sugar content. Most people are already eating way too much sugar. The best way to get these minerals is to eat real foods. If you eat a balanced diet of plants and animals, then your chances of lacking any of these minerals is very low. But if you're going to eat a sugar-based sweetener anyway, then replacing refined sugar in recipes with an identical amount of maple syrup will cut the total sugar content by a third. The glycemic index of maple syrup seems to be around 54, compared to table sugar which has a glycemic index of around 65 (6). This is a good thing and implies that maple syrup raises blood sugar slower than regular sugar. Bottom Line: Maple syrup contains a small amount of minerals, especially manganese and zinc. However, it is also very high in sugar (about 67%). ## Maple Syrup Contains at Least 24 Different Antioxidants Oxidative damage is believed to be among the mechanisms behind ageing and many diseases. It consists of undesirable chemical reactions that involve free radicals... that is, molecules with unstable electrons. Antioxidants are substances that can neutralize free radicals and reduce oxidative damage, potentially lowering the risk of some diseases. Several studies have found that maple syrup is a decent source of antioxidants. One study found 24 different antioxidant substances in maple syrup (7). The darker syrups (like Grade B) contain more of these beneficial antioxidants than the lighter syrups (8). However, same as with the minerals, the total amount of antioxidants is still low compared to the large amounts of sugar. One study estimates that replacing all the refined sugar in the average diet with "alternative" sweeteners like maple syrup will increase the total antioxidant load of the diet similar to eating a single serving of nuts or berries (9). If you need to lose weight or improve your metabolic health, then you would be better off skipping caloric sweeteners altogether instead of going for a "less bad" version of sugar. Bottom Line: There are a number of antioxidant substances found in maple syrup, but the amount is still low compared to the large amount of sugar. ## Maple Syrup Has Been Studied in Test Tubes, But no Human Studies are Available Numerous potentially beneficial substances have been found in maple syrup. Some of these compounds are not present in the maple tree, but they form when the sugary fluid is boiled to form the syrup. One of these is a compound called quebecol, named after Quebec, a province in Canada that produces large amounts of maple syrup. The active compounds in maple syrup have been shown to help reduce the growth of cancer cells and may slow down the breakdown of carbohydrates in the digestive tract (10, 11, 12, 13, 14). But really... these test tube studies are almost meaningless when it comes to human health. They tell us absolutely nothing about what happens in a living, breathing person. ## The Bottom Line: It's Slightly "Less Bad" Than Sugar Even though maple syrup does contain some nutrients and antioxidants, it is also very high in sugar. Calorie for calorie (and sugar gram for sugar gram), maple syrup is a very poor source of nutrients compared to "real" foods like vegetables, fruits and unprocessed animal foods. Replacing refined sugar with pure, quality maple syrup is likely to yield a net health benefit, but adding it to your diet will just make things worse. Maple syrup is a "less bad" version of sugar... kind of like honey and coconut sugar. That does NOT make it healthy. As with all sugar-based sweeteners, if you're going to eat it, make sure to do so in moderation only. An evidence-based nutrition article from our experts at Authority Nutrition. 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http://stats.stackexchange.com/questions/46588/why-are-gaussian-process-models-called-non-parametric	# Why are Gaussian process models called non-parametric? I am a bit confused. Why are Gaussian processes called non parametric models? They do assume that the functional values, or a subset of them, have a Gaussian prior with mean 0 and covariance function given as the kernel function. These kernel functions themselves have some parameters (i.e., hyperparameters). So why are they called non parametric models? - I know of several definitions of "Gaussian processes," so it's not apparent what your question is really asking about. But as you consider how to clarify it, ask yourself this: exactly how would you parametrize the Gaussian process you have in mind? If you cannot do it in a natural way with a finite number of real parameters, then it should be considered nonparametric. – whuber Dec 27 '12 at 16:15 @whuber. AFAIK, the main parameters of gaussian processes are the mean and the covariance functions. But as we keep on adding data points, they keep on increasing. So it keeps on increasing. Is that why gaussian processes are termed as non parametric? – user34790 Dec 27 '12 at 17:04 @whuber If I have millions of training data points, then my GP f ~ N(m,k) will be a million dimensional multivariate gaussian distribution. Isn't that too big? I mean as new training data comes it gets bigger and bigger. Doesn't it give rise to computational issue? – user34790 Dec 27 '12 at 17:06 "Parametric" versus "non-parametric" are terms that do not apply to particular processes: they apply to the entire family of processes that could be fit to data. Although I still do not know what family you have in mind, it sounds like although the number of parameters may be finite in any circumstance, there is no limit to the number of parameters that may appear among members of the family: ergo, the problem is non-parametric. – whuber Dec 27 '12 at 17:35 I'll preface this by saying that it isn't always clear what one means by "nonparametric" or "semiparametric" etc. In the comments, it seems likely that whuber has some formal definition in mind (maybe something like choosing a model $M_\theta$ from some family $\{M_\theta: \theta \in \Theta\}$ where $\Theta$ is infinite dimensional), but I'm going to be pretty informal. Some might argue that a nonparametric method is one where the effective number of parameters you use increases with the data. I think there is a video on videolectures.net where (I think) Peter Orbanz gives four or five different takes on how we can define "nonparametric." Since I think I know what sorts of things you have in mind, for simplicity I'll assume that you are talking about using Gaussian processes for regression, in a typical way: we have training data $(Y_i, X_i), i = 1, ..., n$ and we are interested in modeling the conditional mean $E(Y\|X = x) := f(x)$. We write $$Y_i = f(X_i) + \epsilon_i$$ and perhaps we are so bold as to assume that the $\epsilon_i$ are iid and normally distributed, $\epsilon_i \sim N(0, \sigma^2)$. $X_i$ will be one dimensional, but everything carries over to higher dimensions. If our $X_i$ can take values in a continuum then $f(\cdot)$ can be thought of as a parameter of (uncountably) infinite dimension. So, in the sense that we are estimating a parameter of infinite dimension, our problem is a nonparametric one. It is true that the Bayesian approach has some parameters floating about here and there. But really, it is called nonparametric because we are estimating something of infinite dimension. The GP priors we use assign mass to every neighborhood of every continuous function, so they can estimate any continuous function arbitrarily well. The things in the covariance function are playing a role similar to the smoothing parameters in the usual frequentist estimators - in order for the problem to not be absolutely hopeless we have to assume that there is some structure that we expect to see $f$ exhibit. Bayesians accomplish this by using a prior on the space of continuous functions in the form of a Gaussian process. From a Bayesian perspective, we are encoding beliefs about $f$ by assuming $f$ is drawn from a GP with such-and-such covariance function. The prior effectively penalizes estimates of $f$ for being too complicated. Edit for computational issues Most (all?) of this stuff is in the Gaussian Process book by Rasmussen and Williams. Computational issues are tricky for GPs. If we proceed niavely we will need $O(N^2)$ size memory just to hold the covariance matrix and (it turns out) $O(N^3)$ operations to invert it. There are a few things we can do to make things more feasible. One option is to note that guy that we really need is $v$, the solution to $(K + \sigma^2 I)v = Y$ where $K$ is the covariance matrix. The method of conjugate gradients solves this exactly in $O(N^3)$ computations, but if we satisfy ourselves with an approximate solution we could terminate the conjugate gradient algorithm after $k$ steps and do it in $O(kN^2)$ computations. We also don't necessarily need to store the whole matrix $K$ at once. So we've moved from $O(N^3)$ to $O(kN^2)$, but this still scales quadratically in $N$, so we might not be happy. The next best thing is to work instead with a subset of the data, say of size $m$ where inverting and storing an $m \times m$ matrix isn't so bad. Of course, we don't want to just throw away the remaining data. The subset of regressors approach notes that we can derive the posterior mean of our GP as a regression of our data $Y$ on $N$ data-dependent basis functions determined by our covariance function; so we throw all but $m$ of these away and we are down to $O(m^2 N)$ computations. A couple of other potential options exist. We could construct a low-rank approximation to $K$, and set $K = QQ^T$ where $Q$ is $n \times q$ and of rank $q$; it turns inverting $K + \sigma^2 I$ in this case can be done by instead inverting $Q^TQ + \sigma^2 I$. Another option is to choose the covariance function to be sparse and use conjugate gradient methods - if the covariance matrix is very sparse then this can speed up computations substantially. - Generally speaking, the "nonparametric" in Bayesian nonparametrics refers to models with an infinite number of (potential) parameters. There are a lot of really nice tutorials and lectures on the subject on videolectures.net (like this one) which give nice overviews of this class of models. Specifically, the Gaussian Process (GP) is considered nonparametric because a GP represents a function (i.e. an infinite dimensional vector). As the number of data points increases ((x, f(x)) pairs), so do the number of model 'parameters' (restricting the shape of the function). Unlike a parametric model, where the number of parameters stay fixed with respect to the size of the data, in nonparametric models, the number of parameters grows with the number of data points. - This is exactly what I was assuming. So my assumption is right I guess. But my question is if I have million points(observed data). Then my f will also be of million dimension. So wouldn't I have computational issues. Further my covariance matrix will also be of size 1millionx1million. So what should I do in this case? – user34790 Dec 27 '12 at 22:07 @user34790 yes, you would have computational issues. Computational challenges are quite big deal for GPs. Rasmussen and Williams have a book on GPs with an entire chapter dedicated to this, and if you google hard enough you can find it online for free. See my updated post for some minimal details. – guy Dec 28 '12 at 4:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8189270496368408, "perplexity": 294.0272394727482}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936461988.0/warc/CC-MAIN-20150226074101-00014-ip-10-28-5-156.ec2.internal.warc.gz"}
http://physics.stackexchange.com/questions/57523/do-you-use-the-magnitude-equation-to-get-speed-from-an-accelerometer	# Do you use the magnitude equation to get speed from an accelerometer? A guy suggested to me that getting speed from an accelerometer required the use of this equation: $\text{speed} = \sqrt{x^2 + y^2 + z^2}$ This does not make any sense to me, all that you would get from this equation would be the magnitude in $m/s^2$ of the acceleration in the $x, y$ and $z$ axes. Am I correct? Or is my reasoning flawed? - A link to the original claim would be nice. – Chris White Mar 21 '13 at 3:57 I added the link into the question for you, mathisnotmyforte, but just remember for the future that when you have additional information to add to a question, edit it in, don't leave it in a comment. – David Z Mar 21 '13 at 6:09 Basically yes. 1) Acceleration is a change over time in velocity. Since velocity has units of distance per unit time (like meters per second), acceleration has units of distance per unit time per unit time (like $\mathrm{m}/\mathrm{s}^2$). So the accepted answer is mistaken on that point. 2) Just to make sure everyone is on the same page with notation: From reading the question, and better yet the accepted answer to the original question, one can see that all throughout, $x$, $y$, and $z$ are referring to components of acceleration, not speed (or position, as a physicist would assume given those names). I imagine that mistaken answerer just used "speed" and "acceleration" interchangeably - unfortunately. 3) But the answer has the right idea. The quantity $$\sqrt{x^2 + y^2 + z^2}$$ is indeed the magnitude of the vector with components $x$, $y$, and $z$, assuming those components are in orthogonal positions (which they are). If all three are accelerations in $\mathrm{m}/\mathrm{s}^2$, then the result will be too. If the device is otherwise not moving (or even if it is moving, but at a constant speed and in an unchanging direction), then the only acceleration it will feel will be due to the Earth's gravity, which (assuming we are not inside the mantle or as far away as the Moon or something) is pretty constant at $9.8~\mathrm{m}/\mathrm{s}^2$. Thus one would hope the square-rooted quantity we calculated comes out to $9.8$. If it doesn't, you need to tweak the calibrations more. - You're correct. That equation is for the magnitude of the acceleration vector, not the speed. Measuring speed using just an accelerometer can be tricky. You essentially have to integrate the measured acceleration by multiplying that acceleration (minus gravity) by the time between measurements and summing them for three components of the velocity, then finding the magnitude with that equation. I don't have experience with doing this, but if you're serious about measuring speed, you could combine that measurement with GPS coordinates using something like a Kalman filter. - Thanks for answering my question. I'm going to use this paper as a guide – mathisnotmyforte Mar 21 '13 at 4:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8679831624031067, "perplexity": 293.23903630336264}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049278385.58/warc/CC-MAIN-20160524002118-00034-ip-10-185-217-139.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/varying-the-action-with-respect-to-a_-mu.784867/	# Varying the action with respect to A_\mu 1. Nov 30, 2014 ### PhyAmateur Was reading a paper and trying to work out the author's calculations: I am trying to vary the action, $$S_A= \int d^3x \left[ \, -\frac{1}{4}F_{\mu\nu}(A)F^{\mu\nu}(A) +\frac{1}{2}m\, \epsilon^{\mu\nu\rho}A_\mu F_{\nu\rho}(A) \right]$$ with respect to $$A_\mu$$. I am finding difficulty deriving this because $$A_\mu$$ is embedded in $$F_{\mu \nu}$$. So my attempt was writing this all in terms of $$A_\mu$$: $$S_A= \int d^3x \, \left[ -\frac{1}{4}(\partial_\mu A_\nu - \partial_\nu A_\mu) (\partial^\mu A^\nu - \partial^\nu A^\mu) +\frac{1}{2}m\, \epsilon^{\mu\nu\rho}A_\mu (\partial_\nu A_\rho - \partial_\rho A_\nu) \right]$$ and then I got stuck. If you could please lead me from here. Reference, section 2: http://arxiv.org/pdf/hep-th/9705122.pdf 2. Dec 5, 2014	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9106631278991699, "perplexity": 435.8062119348272}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863684.0/warc/CC-MAIN-20180520190018-20180520210018-00544.warc.gz"}
https://portal.research.lu.se/sv/publications/effect-of-bilayer-charge-on-lipoprotein-lipid-exchange	# Effect of bilayer charge on lipoprotein lipid exchange Kathryn Louise Browning, Tania Kjellerup Lind, Selma Maric, Robert David Barker, Marité Cárdenas, Martin Malmsten Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskriftPeer review 5 Citeringar (SciVal) ## Sammanfattning Lipoproteins play a key role in the onset and development of atherosclerosis, the formation of lipid plaques at blood vessel walls. The plaque formation, as well as subsequent calcification, involves not only endothelial cells but also connective tissue, and is closely related to a wide range of cardiovascular syndromes, that together constitute the number one cause of death in the Western World. High (HDL) and low (LDL) density lipoproteins are of particular interest in relation to atherosclerosis, due to their protective and harmful effects, respectively. In an effort to elucidate the molecular mechanisms underlying this, and to identify factors determining lipid deposition and exchange at lipid membranes, we here employ neutron reflection (NR) and quartz crystal microbalance with dissipation (QCM-D) to study the effect of membrane charge on lipoprotein deposition and lipid exchange. Dimyristoylphosphatidylcholine (DMPC) bilayers containing varying amounts of negatively charged dimyristoylphosphatidylserine (DMPS) were used to vary membrane charge. It was found that the amount of hydrogenous material deposited from either HDL or LDL to the bilayer depends only weakly on membrane charge density. In contrast, increasing membrane charge resulted in an increase in the amount of lipids removed from the supported lipid bilayer, an effect particularly pronounced for LDL. The latter effects are in line with previously reported observations on atherosclerotic plaque prone regions of long-term hyperlipidaemia and type 2 diabetic patients, and may also provide some molecular clues into the relation between oxidative stress and atherosclerosis. Originalspråk engelska 117-125 9 Colloids and Surfaces. B, Biointerfaces 168 https://doi.org/10.1016/j.colsurfb.2018.01.043 Published - 2018 aug 1 ## Fingeravtryck Utforska forskningsämnen för ”Effect of bilayer charge on lipoprotein lipid exchange”. Tillsammans bildar de ett unikt fingeravtryck.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.809516191482544, "perplexity": 10519.604749803006}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662519037.11/warc/CC-MAIN-20220517162558-20220517192558-00751.warc.gz"}
http://www.thespectrumofriemannium.com/tag/polylogarithmic-functions/	LOG#162. Polylogia flashes(IV). In this final post (by the moment) in the polylogia series we will write some additional formulae for polylogs and associated series. Firstly, we have (1) and now, if (2) (3) The next identity also holds … Continue reading LOG#161. Polylogia flashes(III). In the third post of this series I will write more fantastic identities related to our friends, the polylogs! (1) and by analytic continuation that equation can be extended to all . In fact (2) such as , … Continue reading	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9623979330062866, "perplexity": 4980.289567510609}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104692018.96/warc/CC-MAIN-20220707124050-20220707154050-00527.warc.gz"}
https://brilliant.org/discussions/thread/help-me-5/	# Help me!! Consider the situation as shown in the figure. When the point mass (1 kg) is released, it will start accelerating downwards due to gravity and by the time it moves through 30 m it will rebound upwards due to the string. Find the maximum height it reaches. Consider ideal conditions. Note by Shantanu Lautre 6 years, 6 months ago This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science. When posting on Brilliant: • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused . • Ask specific questions about the challenge or the steps in somebody's explanation. 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MarkdownAppears as italics or _italics_ italics bold or __bold__ bold - bulleted- list • bulleted • list 1. numbered2. list 1. numbered 2. list Note: you must add a full line of space before and after lists for them to show up correctly paragraph 1paragraph 2 paragraph 1 paragraph 2 [example link](https://brilliant.org)example link > This is a quote This is a quote # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" MathAppears as Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting. 2 \times 3 $2 \times 3$ 2^{34} $2^{34}$ a_{i-1} $a_{i-1}$ \frac{2}{3} $\frac{2}{3}$ \sqrt{2} $\sqrt{2}$ \sum_{i=1}^3 $\sum_{i=1}^3$ \sin \theta $\sin \theta$ \boxed{123} $\boxed{123}$ Sort by: EDITED The horizontal distance was 30cm Now let us consider the system ,, Let us make the following observations-- 1) Initially there was no tension in string as it wasnt taut 2) So the mass falls vertically freely under gravity till it becomes taut. 3) And since the mass was not at the same position as that of hinge initially,, surely it would not become taut 3m below the hinge point 4) When it becomes taut,, the ball's component of velocity paralell to the string becomes 0 , and the other component that is perpendicular to it remains (can be established through angular momentum conservation) (or qualitatively) 5) So the remaining energy of ball will bring it up again and from there we can decide the maximim height it reaches So heres what i think is gonna happen, Please Check if i am correct When the ball falls vertically till string becomes Taut, Applying energy conservation-- (note the $\theta$ is the angle between string and vertical when it becomes taut) $mglcos\theta \quad =\quad \frac { m{ v }^{ 2 } }{ 2 }$ Now it falls vertically till then, so its velocity will be downward,, so its component perpendicular to string is $v\quad sin\theta \\ \\ \quad$ which is $\sqrt { 2glcos\theta } sin\theta$ Now with this velocity it continues further motion as a circle about the hinge point,, thus again applying energy conservation we get $mglcos\theta \quad (sin\theta )^{ 2 }\quad =\quad mgh\quad \\ h=lcos\theta \quad (sin\theta )^{ 2 }$ Now as the lateral distance is 30 cm ,, so the angle $\theta$ is approx 37 degrees,, (thats irrelevant,, let it be arc sin (0.6) ) either way it means the answer is 72/5 cm,, @Ronak Agarwal am i correct, if answer does not matter, just tell if there is anything wrong with the method,, thankyou NOTE - I assumed that as string is inextensible,, the whole component of velocity paralell to it is cancelled (that is no rebounce occurs, or string does not behave as a spring even for a second) - 6 years, 6 months ago According to my calculation the answer should be : ${ h }_{ ground }\quad =\quad 50\quad -\quad 30{ (\cfrac { \sqrt { { 30 }^{ 2 }-{ d }^{ 2 } } }{ 30 } ) }^{ 3 }$. where d = initial distance of the Point mass from the point of suspension. And I think 'd' should be mentioned in this question. here is diagram of this question: ( it is rough figure don't take it seriously :P ) Diagram - 6 years, 6 months ago I got the same answer. - 6 years, 6 months ago @Mvs Saketh Actually the horizontal distance is 30 cm and the length of the string is 50 cm . It is given wrong in the diagram. Now can please you please post your solution again then it can be checked whether it is correct or not.Refer to the values given by me. I know this question as I have said I have seen it in fiitjee grandmasters package. - 6 years, 6 months ago I have edited it accordingly, check now - 6 years, 6 months ago Also the question was asking the speed of the ball at the lowest point. - 6 years, 6 months ago Your method is absolutely correct @Mvs Saketh this is the correct method needed to solve the question. But can you solve for the velocity at the lowest point of the trajectory. - 6 years, 6 months ago Yes i will use conservation of energy again after the "Taut" instant because the tension in string only acts perpendicular to the direction of motion after it has become taut and thus does no work,, so i will use change in mgh= gain in KE and find out - 6 years, 6 months ago see if we consider just vertical motion then when the string becomes taut it'll provide impulse to the particle in opposite direction to its motion (i.e., upward direction) , then what do you think the value of the impulse will be.?? - 6 years, 6 months ago No please observe my answer carefully,, impulse is not provided in vertical direction but along the string,, (tension acts along the string ) so the component of velocity paralell to string gets cancelled completely or the impulse provided is the momentum of the particle along the string which is mvcos(x) ,,, see my solution carefully , - 6 years, 6 months ago Gotcha.......Thank you a million.! - 6 years, 6 months ago I got that too...... - 6 years, 6 months ago This question I saw in grand masters package of fiitjee. - 6 years, 6 months ago	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 15, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9823077917098999, "perplexity": 1532.921684356295}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991648.40/warc/CC-MAIN-20210514060536-20210514090536-00018.warc.gz"}
http://mathhelpforum.com/calculus/195690-limit-two-variables.html	# Math Help - limit (two variables) 1. ## limit (two variables) lim {(3x^2y)}/{(x^2+y^2)} (x,y) -> (0,0) My question is how can i solve it by formal defenition? Attached Thumbnails	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9550862312316895, "perplexity": 16154.49763328721}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413558066650.89/warc/CC-MAIN-20141017150106-00302-ip-10-16-133-185.ec2.internal.warc.gz"}
https://bioconductor.org/packages/3.11/bioc/vignettes/parody/inst/doc/parody.html	# 1 Introduction Outliers are data points that seem anomalous. Precise quantitative measurement of anomalousness is easiest when a parametric probability model is adopted. Significant statistical and computational research has been devoted to devising and rationalizing criteria for outlyingness that do not require adoption of a parametric probability model. This package provides interfaces to various methods presented in the literature of statistical methods for measuring outlyingness in univariate and multivariate samples. It is offered as a resource through bioconductor.org because formal testing for outliers is a common concern of genome scale data analysis, in many different contexts. # 2 Univariate samples Davies and Gather (1992) present a detailed study of criteria for outlyingness in univariate samples. Inlier boundaries are defined, with form $$(\hat{m}-c(n)\hat{s}, \hat{m} + c(n) \hat{s})$$, where $$\hat{m}$$ is a location parameter estimate, $$\hat{s}$$ is a scale parameter estimate, and $$c(n)$$ are multipliers depending on sample size. Candidates for $$m$$ are trimmed mean, median, midpoint of shorth; candidates for $$s$$ include trimmed standard deviation, median absolute deviation (MAD), length of shorth. The familiar boxplot outlier labeling rules do not fall immediately into this framework, as the left and right inlier boundaries may not be equidistant from the location parameter value. This package provides functions implementing components of the various labeling rules; users may mix components to define their own procedures. We define a dataset presented in Rosner (1983). The data concern tapping frequencies achieved by children with various exposures to lead. We can use a boxplot to visualize the distribution. This includes an outlier labeling criterion, and the dots beyond the whiskers are declared to be outlying. The first formal assessment uses the familiar boxplot rules. For this, we need to supply a scaling function as described in the manual page. ## $ind ## [1] 34 35 1 ## ##$val ## [1] 13 14 83 ## ## $outlier.region ## [1] 18.16667 76.83333 We can see that this agrees with the R visualization. Theoretical work on the calibration of the boxplot rule is deployed when is set to . See the manual page for references. ## Warning in tukeyorinds(x = x, alpha = alpha, g = g): no data values in outlier ## region ##$ind ## [1] NA ## ## $val ## [1] NA ## ##$outlier.region ## [1] 7.808079 87.191921 Another procedure that does not fit in the Davies and Gather framework is the generalized extreme studentized deviate procedure due to B Rosner. In this procedure, we prespecify the number of possibly outlying points $$k$$ (which may be any number less than half the sample size), and the $$k$$ most extreme studentized deviates are obtained and recorded from the highest to lowest value. Then repeated `outward testing’ is conducted using analytic critical values that bound the rate of false outlier labeling for the entire testing procedure, whether or not outliers are present. Here we apply Rosner’s procedure: ## $ind ## [1] 1 34 35 ## ##$val ## [1] 83 13 14 It gives results that agree with the standard boxplot. Davies and Gather characterize a rule based on median and MAD using scaling functions $$c(n)$$ that they associate with Hampel. This procedure uses the scaling function defined in their expression (3). ## $ind ## [1] 34 35 1 ## ##$val ## [1] 13 14 83 ## ## $outlier.region ## [1] 14.92932 81.07068 Finally we use the shorth-based detector. ## Warning in rououtinds(x = x, alpha = alpha, g = g): no data values in outlier ## region ##$ind ## [1] NA ## ## $val ## [1] NA ## ##$outlier.region ## [1] 6.215225 94.784775 # 3 Multivariate samples A sample dataset called is supplied with the package. Before visualizing, we compute a default multivariate outlier criterion, due to Caroni and Prescott, that generalizes Rosner’s GESD: ## $inds ## [1] 21 9 ## ##$vals ## fuel repair capital ## 21 26.16 17.44 16.89 ## 9 29.11 15.09 3.28 ## ## $k ## [1] 17 ## ##$alpha ## [1] 0.05 We see that indices 9 and 21 are flagged. Let’s create a pairs plot with coloring. Another display of interest employs principal components: To get a sense of the robustness (or lack thereof) of the biplot, let us replot after removing the datapoints that were marked as outliers by the Caroni and Prescott procedure.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7126809358596802, "perplexity": 2429.968277706154}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370497042.33/warc/CC-MAIN-20200330120036-20200330150036-00516.warc.gz"}
https://au.mathworks.com/help/fuzzy/what-is-sugeno-type-fuzzy-inference.html	Documentation ### This is machine translation Translated by Mouseover text to see original. Click the button below to return to the English version of the page. ## What Is Sugeno-Type Fuzzy Inference? This topic discusses the Sugeno, or Takagi-Sugeno-Kang, method of fuzzy inference. Introduced in 1985 [1], this method is similar to the Mamdani method in many respects. The first two parts of the fuzzy inference process, fuzzifying the inputs and applying the fuzzy operator, are the same. The main difference between Mamdani and Sugeno is that the Sugeno output membership functions are either linear or constant. A typical rule in a Sugeno fuzzy model has the form: If Input 1 is x and Input 2 is y, then Output is z = ax + by + c For a zero-order Sugeno model, the output level z is a constant (a = b = 0). Each rule weights its output level, zi, by the firing strength of the rule, wi. For example, for an AND rule with Input 1 = x and Input 2 = y, the firing strength is `${w}_{i}=AndMethod\left({F}_{1}\left(x\right),{F}_{2}\left(y\right)\right)$` where F1,2(.) are the membership functions for Inputs 1 and 2. The final output of the system is the weighted average of all rule outputs, computed as where N is the number of rules. A Sugeno rule operates as shown in the following diagram. ### Note Sugeno systems always use product implication and sum aggregation. The preceding figure shows the fuzzy tipping model developed in Fuzzy Inference Process adapted for use as a Sugeno system. Fortunately, it is frequently the case that singleton output functions are sufficient for the needs of a given problem. As an example, the system `tippersg.fis` is the Sugeno-type representation of the now-familiar tipping model. If you load the system and plot its output surface, you see that it is almost the same as the Mamdani system you have previously seen. ```fis = readfis('tippersg'); gensurf(fis)``` The easiest way to visualize first-order Sugeno systems is to think of each rule as defining the location of a moving singleton. That is, the singleton output spikes can move around in a linear fashion in the output space, depending on what the input is. This also tends to make the system notation compact and efficient. Higher-order Sugeno fuzzy models are possible, but they introduce significant complexity with little obvious merit. Sugeno fuzzy models whose output membership functions are greater than first order are not supported by Fuzzy Logic Toolbox™ software. Because of the linear dependence of each rule on the input variables, the Sugeno method is ideal for acting as an interpolating supervisor of multiple linear controllers that are to be applied, respectively, to different operating conditions of a dynamic nonlinear system. For example, the performance of an aircraft may change dramatically with altitude and Mach number. Linear controllers, though easy to compute and suited to any given flight condition, must be updated regularly and smoothly to keep up with the changing state of the flight vehicle. A Sugeno fuzzy inference system is suited to the task of smoothly interpolating the linear gains that would be applied across the input space; it is a natural and efficient gain scheduler. Similarly, a Sugeno system is suited for modeling nonlinear systems by interpolating between multiple linear models. To see a specific example of a system with linear output membership functions, consider the one-input, one-output system stored in `sugeno1.fis`. Load the system and view the properties of its output variable. ```fis = readfis('sugeno1'); fis.Outputs(1)``` ```ans = fisvar with properties: Name: "output" Range: [0 1] MembershipFunctions: [1x2 fismf] ``` The output variable has two membership functions. View the properties of the first membership function. `fis.Outputs(1).MembershipFunctions(1)` ```ans = fismf with properties: Name: "line1" Type: "linear" Parameters: [-1 -1] ``` View the properties of the second membership function. `fis.Outputs(1).MembershipFunctions(2)` ```ans = fismf with properties: Name: "line2" Type: "linear" Parameters: [1 -1] ``` Further, these membership functions are linear functions of the input variable. The membership function `line1` is defined by the equation: `$output=\left(-1\right)×input+\left(-1\right)$` and the membership function `line2` is: `$output=\left(1\right)×input+\left(-1\right)$` The input membership functions and rules define which of these output functions are expressed and when: `fis.Rules` ```ans = 1x2 fisrule array with properties: Description Antecedent Consequent Weight Connection Details: Description _________________________________ 1 "input==low => output=line1 (1)" 2 "input==high => output=line2 (1)" ``` The function `plotmf` shows us that the membership function `low` generally refers to input values less than zero, while `high` refers to values greater than zero. The function `gensurf` shows how the overall fuzzy system output switches smoothly from the line called `line1` to the line called `line2`. ```subplot(2,1,1) plotmf(fis,'input',1) subplot(2,1,2) gensurf(fis)``` As this example shows, Sugeno-type system gives you the freedom to incorporate linear systems into your fuzzy systems. By extension, you could build a fuzzy system that switches between several optimal linear controllers as a highly nonlinear system moves around in its operating space. ## References [1] Sugeno, M., Industrial applications of fuzzy control, Elsevier Science Pub. Co., 1985.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6977279186248779, "perplexity": 1052.2292443856188}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525500.21/warc/CC-MAIN-20190718042531-20190718064531-00555.warc.gz"}
http://math.stackexchange.com/questions/17343/what-is-the-speed-of-a-divergent-series?answertab=oldest	what is the speed of a divergent series? How to characterize the speed of a divergent series ? I have a divergent series with a parameter $x$ in it. How can i characterize the speed of divergence for different $x$ ? - While there are various rates of convergence, based on big-O, little-o, etc. notations, it will not make equal sense to talk about "speed of divergence". A divergent series need not grow uniformly. It might oscillate. Or there might be subsequences that grow and subsequences that oscillate in bounded fashion. One way to impose some consistency on the behavior of nonconvergent sequences is to look at its lim sup and lim inf. Perhaps you should explain the purpose of the characterization you seek. – hardmath Jan 13 '11 at 4:57 @hardmath : the series is non-decreasing – Rajesh D Jan 13 '11 at 5:22 This is a very vague question. Why don't you show us what series you have... – Aryabhata Jan 13 '11 at 5:30 @Moron : I don't really have any series to work with, the only restriction is that it is non decreasing. – Rajesh D Jan 13 '11 at 5:41 I guess ‘big O notation’ and its relatives are what you’re after, or something like that? If $(a_n)$ is a sequence with $a_n \rightarrow \infty$ as $n \rightarrow \infty$, then this notation defines statements like $(a_n) = O(n^2)$, formalising the idea that “in the long run, the sequence $(a_n)$ grows no faster than the sequence $(n^2)$”. (The use of ‘=’ in this notation is slightly confusing: the precise statement doesn’t assert that any two things are equal.) - Under the given circumstances (the sequence $\{a_n\}$ tends monotonically to plus infinity), faster rate of divergence (growth) would be equivalent to faster convergence of $\{1/a_n\}$ to zero. – hardmath Jan 13 '11 at 6:12 This is related to Hausdorff's "Pantachie" problem. Suppose $x_i$ is a monotone decreasing sequence whose sum is divergent. We say that a similar sequence $y_i$ diverges slower if $x_i/y_i \rightarrow \infty$. Example: $\sum n^{-1}$ diverges slower then $\sum n^{-0.5}$. Similarly, if $x_i$ is a monotone decreasing sequence whose sum is convergent, a similar sequence $y_i$ converges more slowly if $y_i/x_i \rightarrow \infty$. Example: $\sum n^{-2}$ converges more slowly than $\sum n^{-3}$. Hausdorff proved the following theorem: For any sequence of divergent (convergent) series, there's a sequence diverging (converging) slower than any of them. That means that there is no "expressible by finite strings" characterization of the speed of divergence (convergence), since such a characterization would not allow any series which is diverging (converging) slower. For more on the subject, look up Hausdorff gaps. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9407497048377991, "perplexity": 525.3099430562444}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988310.3/warc/CC-MAIN-20150728002308-00067-ip-10-236-191-2.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/147543/is-this-number-random	# Is this number random? I'm trying to create a random 6 digit code. If I generate a random number between 0 and 999999 and then pad it with zeros to make it 6 digits is it random or is it biased in some way? E.g It generates 750 so it is then padded to 000750 It generates 28149 so it is padded to 028149 Does this achieve the same as generating a random integer between 0 and 9 six times and then putting the numbers together in a string? Thanks. - The title of this question amused me. I imagined it to go something like, "Here is a number: 9. Is this number random?" – Rahul May 20 '12 at 22:45 It makes no difference, provided that in both cases you’re generating the numbers with uniform distribution. Consider, for instance, the probability of generating a number that starts with at least three zeroes. The first method gives you $1000$ such numbers out of $1,000,000$ possibilities, so the probability of getting one is $\frac{1000}{1,000,000}=\frac1{1000}$. In the second method you must generate three zeroes in succession to start, after which you don’t care: the probability of that is $\left(\frac1{10}\right)^3=\frac1{1000}$. More generally, each of the $10^6$ possible six-digit numbers has one chance in a million of being generated under either scheme. The two procedures should both yield "random" strings of $6$ digits, with all strings equally likely. There may be subtle differences, since we are using pseudo-random number generators.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7036014199256897, "perplexity": 377.08953637341625}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500831565.57/warc/CC-MAIN-20140820021351-00148-ip-10-180-136-8.ec2.internal.warc.gz"}
http://mathhelpforum.com/advanced-statistics/79440-distribution-probabilty-parent-sample.html	# Math Help - Distribution and probabilty - parent and sample 1. ## Distribution and probabilty - parent and sample Ok I am completely lost, can anyone help me out? I have done the first question, and the second one is based on it. The first question said: The parent distribution of x is normal with mean 80 and standard deviation 9. Based on samples of size n=25, find the mean and standard error of the sampling distribution of $\bar{x}$. I said: $\mu_{\bar{x}}$ = 80 $\sigma_{\bar{x}}$ = 9/5 The second question is where I am lost. It says find: A. P(62 < x < 80) B. P(71 < $\bar{x}$ < 77) C. x' such that P( $\bar{x}$ > x') = .05 2. Is n=25 or 225? Because $\sigma_{\bar{x}}={\sigma \over\sqrt{n}}$. Or, did you mean $\sigma_{\bar{x}}={9\over 5}$ 3. n=25 it is the number in the sample $\sigma\bar{x}$ = 9/5 (thats what I got) sorry 4. $P(62. $P(71<\bar X<77)=P\biggl({71-80\over 9/5}. Can you finish these? I'll check on you later. $.05=P(\bar X so ${a-80\over 9/5}=-1.645$. 5. P[(-5) < z < (-5/3)] It was supposed to be P( $\bar{x}$ > x') SORRY P( $\bar{x}$ > $x'-80\over 9/5$) ? Can you tell me what formula you used to find that last one? Did you use these for the first two? Z= $X-\mu\over \sigma$ and Z= $\bar{x}-\mu\over \sigma / \sqrt n$ 6. Let X be a random variable with mean $\mu$ and standard deviation $\sigma$. Then $Z={X-\mu\over \sigma}$ has mean zero and standard deviation 1. And if X was a normal random variable, then Z is a standard normal random variable and you can use your Z table. We did that for both X and $\bar X$. 7. Thank you SO much for your help. It helped me a lot on my test. Thanks a hundred times. You are a really nice person	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 21, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9497736692428589, "perplexity": 1320.6045859857793}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510261958.8/warc/CC-MAIN-20140728011741-00024-ip-10-146-231-18.ec2.internal.warc.gz"}
http://www.perimeterinstitute.ca/seminar/emergent-gravity-dark-energy-and-dark-matter	# From Emergent Gravity to Dark Energy and Dark Matter The observed deviations from the laws of gravity of Newton and Einstein in galaxies and clusters can logically speaking be either due to the presence of unseen dark matter particles or due to a change in the way gravity works in these situations. Until recently there was little reason to doubt that general relativity correctly describes gravity in all circumstances. In the past few years insights from black hole physics and string theory have lead to a new theoretical framework in which the gravitational laws are derived from the quantum entanglement of the microscopic information that is underlying space-time. An essential ingredient in the derivation is of the Einstein equations is that the vacuum entanglement obeys an area law, a condition that is known to hold in Anti-de Sitter space due to the work of Ryu and Takayanagi. We will argue that in de Sitter space due to the positive dark energy, that the microscopic entanglement entropy also contains also a volume law contribution in addition to the area law. This volume law contribution is related to the thermal properties of de Sitter space and leads to a total entropy that precisely matches the Bekenstein-Hawking formula for the cosmological horizon. We study the effect of this extra contribution on the emergent laws of gravity, and argue that it leads to a modification compared to Einstein gravity. We provide evidence for the fact that this modification explains the observed phenomena in galaxies and clusters currently attributed to dark matter. Collection/Series: Event Type: Seminar Scientific Area(s): Speaker(s): Event Date: Wednesday, October 4, 2017 - 14:00 to 15:30 Location: Time Room Room #: 294	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9713998436927795, "perplexity": 243.06640815171482}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647327.52/warc/CC-MAIN-20180320091830-20180320111830-00322.warc.gz"}
http://bib-pubdb1.desy.de/collection/VDB?ln=en	# Publications database 2019-05-2314:17 [PUBDB-2019-02359] Book/Report/Master Thesis Steder, L. Systematic studies of a cavity quench localization system [DESY-THESIS-2019-010] Hamburg : Verlag Deutsches Elektronen-Synchrotron, DESY-THESIS 120 pp. (2019) [10.3204/PUBDB-2019-02359] = Masterarbeit, Universität Hamburg, 2019 Several tools for quench localization at Superconducting Radio Frequency cavities exist. One of these techniques uses the excitation of temperature waves in liquid Helium below the lambda point. [...] OpenAccess: MasterThesis_B_Bein - PDF PDF (PDFA); desy-thesis-19-010.title - PDF PDF (PDFA); 2019-05-2114:21 [PUBDB-2019-02325] Report/Journal Article et al Search for vector-like quarks in events with two oppositely charged leptons and jets in proton-proton collisions at $\sqrt{s} =$ 13 TeV [arXiv:1812.09768; CMS-B2G-17-012; CERN-EP-2018-290] A search for the pair production of heavy vector-like partners $\mathrm {T}$ and $\mathrm {B}$ of the top and bottom quarks has been performed by the CMS experiment at the CERN LHC using proton–proton collisions at $\sqrt{s} = 13\,\text {Te}\text {V}$ . The data sample was collected in 2016 and corresponds to an integrated luminosity of 35.9 $\,\text {fb}^{-1}$ . [...] OpenAccess: PDF PDF (PDFA); 2019-05-2114:17 [PUBDB-2019-02324] Report/Journal Article et al Measurement of the $\mathrm{t}\overline{\mathrm{t}}$ production cross section, the top quark mass, and the strong coupling constant using dilepton events in pp collisions at $\sqrt{s} =$ 13 TeV [arXiv:1812.10505; CMS-TOP-17-001; CERN-EP-2018-317] A measurement of the top quark–antiquark pair production cross section $\sigma _{\mathrm {t}\overline{\mathrm {t}}}$ in proton–proton collisions at a centre-of-mass energy of 13 $\,\text {Te}\text {V}$ is presented. The data correspond to an integrated luminosity of $35.9{\,\text {fb}^{-1}}$ , recorded by the CMS experiment at the CERN LHC in 2016. [...] OpenAccess: PDF PDF (PDFA); 2019-05-2114:14 [PUBDB-2019-02323] Report/Journal Article et al Measurement of inclusive very forward jet cross sections in proton-lead collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV [arXiv:1812.01691; CMS-FSQ-17-001; CERN-EP-2018-325] Journal of high energy physics 1905(05), 043 (2019) [10.1007/JHEP05(2019)043] Measurements of differential cross sections for inclusive very forward jet production in proton-lead collisions as a function of jet energy are presented. The data were collected with the CMS experiment at the LHC in the laboratory pseudorapidity range $-$6.6$<\eta<-$5.2. [...] OpenAccess: PDF PDF (PDFA); 2019-05-2114:10 [PUBDB-2019-02322] Report/Journal Article et al Measurement of the energy density as a function of pseudorapidity in proton-proton collisions at $\sqrt{s} =$ 13 TeV [arXiv:1812.04095; CMS-FSQ-15-006; CERN-EP-2018-308] A measurement of the energy density in proton–proton collisions at a centre-of-mass energy of s√=13 TeV is presented. The data have been recorded with the CMS experiment at the LHC during low luminosity operations in 2015. [...] OpenAccess: PDF PDF (PDFA); External link: Fulltext 2019-05-2114:00 [PUBDB-2019-02321] Report/Journal Article et al Search for an $L_{\mu}-L_{\tau}$ gauge boson using Z$\to4\mu$ events in proton-proton collisions at $\sqrt{s} =$ 13 TeV [arXiv:1808.03684; CMS-EXO-18-008; CERN-EP-2018-208] Physics letters / B 792, 345 - 368 (2019) [10.1016/j.physletb.2019.01.072] A search for a narrow Z$'$ gauge boson with a mass between 5 and 70 GeV resulting from an $L_{\mu}-L_{\tau}$ $U(1)$ local gauge symmetry is reported. Events containing four muons with an invariant mass near the standard model Z boson mass are analyzed, and the selection is further optimized to be sensitive to the events that may contain Z$\to$Z$'\mu\mu\to4\mu$ decays. [...] OpenAccess: PDF PDF (PDFA); External link: Fulltext 2019-05-2020:52 [PUBDB-2019-02319] Journal Article/Contribution to a conference proceedings HERMES Collaboration Medium-indused modification of kaons spectra measured in SIDIS at HERMES 24th International Baldin Seminar on High Energy Physics Problems, ISHEPP 2018, DubnaDubna, Russia, 17 Sep 2018 - 22 Sep 2018 The predicted high sensitivity of the nuclear modification factor for K$^−$ in SIDIS due to the QCD based effect of medium-induced flavour conversion in the fragmentation function is studied at HERMES experiment. Unlike π+, π− and K$^+$ nuclear modification factor for K$^−$ is assumed to increase at high value of Bjorken variable $x_B$ and a hadron fraction energy $z$. [...] OpenAccess: PDF PDF (PDFA); External link: Fulltext 2019-05-2016:18 [PUBDB-2019-02318] Report/Journal Article et al Constraining the Magnetic Field in the TeV Halo of Geminga with X-Ray Observations [arXiv:1904.11438] The astrophysical journal / 1 Part 1 875(2), 149 (2019) [10.3847/1538-4357/ab125c] Recently, the High Altitude Water Cherenkov (HAWC) collaboration reported the discovery of a TeV halo around the Geminga pulsar. The TeV emission is believed to originate from the inverse Compton scattering of pulsar-injected electrons/positrons off cosmic microwave background photons [...] Restricted: PDF PDF (PDFA); 2019-05-2016:09 [PUBDB-2019-02317] Report/Journal Article et al Secondary neutrino and gamma-ray fluxes from SimProp and CRPropa [arXiv:1901.01244] The interactions of ultra-high energy cosmic rays (UHECRs) with background photons in extragalactic space generate high-energy neutrinos and photons. Simulating UHECR propagation requires assumptions about physical quantities such as the spectrum of the extragalactic background light (EBL) and photodisintegration cross sections. [...] Restricted: PDF PDF (PDFA); 2019-05-2013:29 [PUBDB-2019-02314] Poster Bakhshiansohi, H. Exotic decay of the Higgs boson to a pair of light pseudoscalars in the CMS experiment 7th Conference of Large Hadron Collider Physics, LHCP2019, PueblaPuebla, Mexico, 20 May 2019 - 25 May 2019 The Standard Model is one of the most successful theories at describing the strong, weak, and electromagnetic forces and the interactions between the elementary particles.The scalar boson discovered in 2012 at the Large Hadron Collider (LHC) might be consistent with the Higgs boson predicted by the Standard Model, thus validating the Higgs mechanism and therefore representing a further confirmation of this theoretical framework. However, the experimental data still leave plenty of room to determine whether or not an extension of the scalar sector is allowed.The LHC combination of the SM Higgs boson measurements at 7 and 8 TeV allows Higgs boson decays to BSM states with a rate of up to 34% at 95% confidence level.Presence of new physics within the context of the Two-Higgs-Double-Model and NMSSM theories allows the exotic decay of the Higgs boson into a pair of light pseudoscalars. [...] OpenAccess: PDF PDF (PDFA); External link: Fulltext	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9954367876052856, "perplexity": 3556.1997659183917}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232259327.59/warc/CC-MAIN-20190526165427-20190526191427-00004.warc.gz"}
https://grocid.net/2011/05/07/stack-algorithm-in-python/	# Stack algorithm in Python A commonly used algorithm for sequential decoding is the stack algorithm. It was invented by Zigangirov and Jelinek in the 60’s. The algorithm is a depth-first algorithm with non-deterministic complexity: Algorithm (Stack algorithm) 1. Put the root node in the list $\mathcal{S}$. 2. Remove top node. Place its successors in $\mathcal{S}$. Sort $\mathcal{S}$ in (Fano) metric order. 3. If top path leads to end of tree, stop and output the path as decoded codeword. Otherwise, go to Step 2. This Python code does the job (using an infinite stack which is OK for smaller instances): import random import bisect import itertools from math import log def CreateGeneratorMatrix(SubMatrix, Length): G = [] for j in range(0,Length): for i in range(0,len(SubMatrix)): row = [0]j(len(SubMatrix[0]))+SubMatrix[i]+[random.randint(0,1) for k in range((j+1)len(SubMatrix[0]), Lengthlen(SubMatrix[0]))] G.append(row) return G def Encode(Sequence, Generator): Codeword = [] for i in range(0, len(Generator[0])): Parity = 0 for j in range(0,len(Sequence)): Parity ^= Generator[j][i]&Sequence[j] Codeword.append(Parity) return Codeword def Metric(Sequence, Codeword, Generator, Rate, FanoMetrics): Metric = 0 for i in range(Rate[1](len(Sequence)/Rate[0]-1), Rate[1]len(Sequence)/Rate[0]): Parity = 0 for j in range(0,len(Sequence)): Parity ^= Generator[j][i]&Sequence[j] Metric += (Codeword[i]^Parity)FanoMetrics[1] + (Codeword[i]^Parity^1)FanoMetrics[0] return Metric def Decode(Codeword, Generator, Rate, ErrorProbability): Permutations = [list(seq) for seq in itertools.product([0,1], repeat=Rate[0])] Stack = [] FanoMetrics = [log(1-ErrorProbability, 2)+(1-Rate[1]/Rate[0]), log(ErrorProbability, 2)+ (1-Rate[1]/Rate[0])] for Permutation in Permutations: bisect.insort(Stack,[Metric(Permutation, Codeword, Generator, Rate, FanoMetrics), Permutation]) while(len(Stack[0][1]) < len(Generator)): BestSequence = Stack.pop(0) for Permutation in Permutations: bisect.insort(Stack, [BestSequence[0]+Metric(BestSequence[1]+Permutation, Codeword, Generator, Rate, FanoMetrics), BestSequence[1]+Permutation]) while len(Stack) > 100: Stack.pop(0) return Stack.pop()[1] An example using the code above for index in map(int,(sample(xrange(len(Message)),Weight))): Message[index] ^= 1 return Message SubMatrix = [[1,0,1],[0,1,1]] G = CreateGeneratorMatrix(SubMatrix,15) Message = [random.randint(0,1) for k in range(0,len(SubMatrix)*15)] where we create random time-varying rate $R = 2/3$ convolutional code with infinite memory and generate a random message. Then we add two errors to some arbitrary positions and decode.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 4, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5227078199386597, "perplexity": 15766.045330351311}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314732.59/warc/CC-MAIN-20190819114330-20190819140330-00151.warc.gz"}
https://projecteuclid.org/euclid.em/1128371759	## Experimental Mathematics ### Extremal modular lattices, McKay Thompson series, quadratic iterations, and new series for $\pi$ Kok Seng Chua #### Abstract We give 20 new Ramanujan-type formulae and 20 quadratic approximations to {\small $\pi$}, parameterized by extremal modular lattices of minimal square norm 2 and 4, at the ten special levels corresponding to square-free orders of the Mathieu group {\small $M_{23}$}. An algorithm for uncovering rational relations between two given power series that we used to discover some of the explicit relations is also given. Explicit relations parameterized by modular lattices between McKay Thompson series for the group {\small $\Gamma_0(\ell)^+$} and {\small $\Gamma_0(2\ell)+p_j$}, where {\small $p_j$} range over all odd primes dividing the special level {\small $\ell$}, are uncovered. #### Article information Source Experiment. Math., Volume 14, Issue 3 (2005), 343-357. Dates First available in Project Euclid: 3 October 2005 Chua, Kok Seng. Extremal modular lattices, McKay Thompson series, quadratic iterations, and new series for $\pi$. Experiment. Math. 14 (2005), no. 3, 343--357. https://projecteuclid.org/euclid.em/1128371759	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5014887452125549, "perplexity": 2562.207076415741}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232262029.97/warc/CC-MAIN-20190527065651-20190527091651-00477.warc.gz"}
https://www.nature.com/articles/s41586-022-04472-z?error=cookies_not_supported&code=84e728b1-5f8b-4f04-9cd5-210e8820ec7a	Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. Light-induced ferromagnetism in moiré superlattices Abstract Many-body interactions between carriers lie at the heart of correlated physics. The ability to tune such interactions would allow the possibility to access and control complex electronic phase diagrams. Recently, two-dimensional moiré superlattices have emerged as a promising platform for quantum engineering such phenomena1,2,3. The power of the moiré system lies in the high tunability of its physical parameters by adjusting the layer twist angle1,2,3, electrical field4,5,6, moiré carrier filling7,8,9,10,11 and interlayer coupling12. Here we report that optical excitation can highly tune the spin–spin interactions between moiré-trapped carriers, resulting in ferromagnetic order in WS2 /WSe2 moiré superlattices. Near the filling factor of −1/3 (that is, one hole per three moiré unit cells), as the excitation power at the exciton resonance increases, a well-developed hysteresis loop emerges in the reflective magnetic circular dichroism signal as a function of magnetic field, a hallmark of ferromagnetism. The hysteresis loop persists down to charge neutrality, and its shape evolves as the moiré superlattice is gradually filled, indicating changes of magnetic ground state properties. The observed phenomenon points to a mechanism in which itinerant photoexcited excitons mediate exchange coupling between moiré-trapped holes. This exciton-mediated interaction can be of longer range than direct coupling between moiré-trapped holes9, and thus magnetic order arises even in the dilute hole regime. This discovery adds a dynamic tuning knob to the rich many-body Hamiltonian of moiré quantum matter13,14,15,16,17,18,19. This is a preview of subscription content Access options \$32.00 All prices are NET prices. Data availability The data that support the plots within this paper are available from the corresponding authors upon reasonable request. Source data are provided with this paper. References 1. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011). 2. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018). 3. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018). 4. Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020). 5. Ghiotto, A. et al. Quantum criticality in twisted transition metal dichalcogenides. Nature 597, 345–349 (2021). 6. Li, T. et al. Continuous Mott transition in semiconductor moiré superlattices. Nature 597, 350–354 (2021). 7. Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020). 8. Xu, Y. et al. Correlated insulating states at fractional fillings of moiré superlattices. Nature 587, 214–218 (2020). 9. Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020). 10. Huang, X. et al. Correlated insulating states at fractional fillings of the WS2/WSe2 moiré lattice. Nat. Phys. 17, 715–719 (2021). 11. Li, H. et al. Imaging two-dimensional generalized Wigner crystals. Nature 597, 650–654 (2021). 12. Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019). 13. Zang, J. et al. Hartree-Fock study of the moiré Hubbard model for twisted bilayer transition metal dichalcogenides. Phys. Rev. B 104, 075150 (2021). 14. Hu, N. C. & MacDonald, A. H. Competing magnetic states in transition metal dichalcogenide moiré materials. Phys. Rev. B 104, 214403 (2021). 15. Wu, F. et al. Hubbard model physics in transition metal dichalcogenide moiré bands. Phys. Rev. Lett. 121, 026402 (2018). 16. Zhang, Y. et al. Electronic structures, charge transfer, and charge order in twisted transition metal dichalcogenide bilayers. Phys. Rev. B 103, 155142 (2021). 17. Zhu, Z. & White, S. R. Spin liquid phase of the S = ½ J1J2 Heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). 18. Devakul, T., Crépel, V., Zhang, Y. & Fu, L. Magic in twisted transition metal dichalcogenide bilayers. Nat. Commun. 12, 6730 (2021). 19. Pan, H. et al. Quantum phase diagram of a Moiré-Hubbard model. Phys. Rev. B 102, 201104 (2020). 20. Miao, S. et al. Strong interaction between interlayer excitons and correlated electrons in WSe2/WS2 moiré superlattice. Nat. Commun. 12, 3608 (2021). 21. Liu, E. et al. Excitonic and valley-polarization signatures of fractional correlated electronic phases in a WSe2/WS2 moire superlattice. Phys. Rev. Lett. 127, 037402 (2021). 22. Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020). 23. Zhou, Y. et al. Bilayer Wigner crystals in a transition metal dichalcogenide heterostructure. Nature 595, 48–52 (2021). 24. Fausti, D. et al. Light-induced superconductivity in a stripe-ordered cuprate. Science 331, 189–191 (2011). 25. Kogar, A. et al. Light-induced charge density wave in LaTe3. Nat. Phys. 16, 159–163 (2020). 26. Xu, X. et al. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343–350 (2014). 27. Seyler, K. L. et al. Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019). 28. Baek, H. et al. Highly energy-tunable quantum light from moiré-trapped excitons. Sci. Adv. 6, eaba8526 (2020). 29. Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019). 30. Tran, K. et al. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019). 31. Alexeev, E. M. et al. Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures. Nature 567, 81–86 (2019). 32. Hong, X. et al. Ultrafast charge transfer in atomically thin MoS2/WS2 heterostructures. Nat. Nanotechnol. 9, 682–686 (2014). 33. Rivera, P. et al. Observation of long-lived interlayer excitons in monolayer MoSe2–WSe2 heterostructures. Nat. Commun. 6, 6242 (2015). 34. Piermarocchi, C. et al. Optical RKKY interaction between charged semiconductor quantum dots. Phys. Rev. Lett. 89, 167402 (2002). 35. Fernández-Rossier, J. et al. Coherently photoinduced ferromagnetism in diluted magnetic semiconductors. Phys. Rev. Lett. 93, 127201 (2004). 36. Li, W. et al. Optical control of the valley Zeeman effect through many-exciton interactions. Nat. Nanotechnol. 16, 148–152 (2021). 37. Jiang, C. et al. Optical spin pumping induced pseudomagnetic field in two-dimensional heterostructures. Phys. Rev. B 98, 241410 (2018). 38. Li, Y. et al. Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2. Phys. Rev. B 90, 205422 (2014). Acknowledgements We thank B. Spivak, T. Cao, J.-H. Chu, D. Cobden, M. Yankowitz, C. Dean and A. N. Pasupathy for helpful discussions. Research on the observation of ferromagnetism near −1/3 moiré superlattice filling is primarily supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443. Optically induced magnetism of dilute electron/hole gas is mainly supported by the DOE BES under award DE-SC0018171. Sample fabrication and piezoresponse force microscopy characterization are partially supported by the ARO MURI programme (grant no. W911NF-18-1-0431). Monte carlo simulation by D.X. was partially supported by the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA). The AFM-related measurements were performed using instrumentation supported by the US National Science Foundation through the UW Molecular Engineering Materials Center, a Materials Research Science and Engineering Center (DMR-1719797). W.Y. and C.X. acknowledge support by the Croucher Foundation (Croucher Senior Research Fellowship) and the University Grant Committee/Research Grants Council of Hong Kong SAR (AoE/P-701/20). Bulk WSe2 crystal growth and characterization by J.Y. is supported by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, grant number JPMXP0112101001, JSPS KAKENHI grant number JP20H00354 and CREST (JPMJCR15F3), JST. X.X. acknowledges support from the State of Washington funded Clean Energy Institute and from the Boeing Distinguished Professorship in Physics. Author information Authors Contributions X.X. and W.Y. conceived the project. H.P. and X.W. fabricated and characterized the samples, assisted by J.Z. X.W. performed the magneto-optical measurements, assisted by J.Z. X.W., X.X., W.Y., D.X. and D.R.G. analysed and interpreted the results. C.X. and W.Y. performed calculations of optically induced magnetic exchange interactions. C.W. and D.X. performed Monte Carlo simulations of correlated states. T.T. and K.W. synthesized the hBN crystals. J.Y. synthesized and characterized the bulk WSe2 crystals. X.X., X.W., W.Y., D.X. and D.R.G. wrote the paper with input from all authors. All authors discussed the results. Corresponding authors Correspondence to Wang Yao or Xiaodong Xu. Ethics declarations Competing interests The authors declare no competing interests. Peer review Peer review information Nature thanks David Ruiz-Tijerina, Tomasz Smolenski and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Extended data figures and tables Extended Data Fig. 1 Determination of filling factors. a, Gate dependent photoluminescence (PL) spectra obtained at 7 K. The excitation wavelength is 740 nm with 50 nW power. Charge neutrality is assigned with the voltage corresponding to the brightest PL with symmetric spectra on the electron and hole sides. b, Gate-dependent differential reflectance spectra (ΔR/R) near the WSe2 exciton resonance, measured at base temperature 1.6 K. The power used for reflectance spectroscopy is 15 nW. c, Gate-dependent differential reflectance spectra differentiated with respect to photon energy (the same data as in Fig. 1c). All three figures share the same y-axis. Gate voltages are labelled at the left axis of panel (a). Assigned filling factors are labelled at the right axis of panel (c). The optical doping effect is negligible. The data of panels (a)–(c) are taken at a different spot of the same sample. d, Monte Carlo simulation of correlated insulating states at fractional moiré miniband fillings. The transition temperature of charge ordered states in the vertical axis is determined as the temperature where the specific heat is maximum in Monte Carlo simulations. Extended Data Fig. 2 Excitation Energy dependent RMCD at selected filling factors. a, Excitation Energy dependent RMCD signal at v = −1. b, Excitation Energy dependent RMCD at v = Harding Text1/7. Maximized RMCD signals are observed when the excitation energy is between 1.676-1.678 eV (739-740 nm) as indicated by the dash lines. Extended Data Fig. 3 RMCD signal near v = −1 and its dependence on optical excitation power. a, RMCD signal with a few selected filling factors near ν = −1 at T = 1.6 K. The excitation wavelength is 739.2 nm. Laser power is 24 nW. b, Power dependence of RMCD signal at the condition ν = −1. The RMCD signals barely changes by varying the excitation power. c, RMCD amplitude, i.e., saturation RMCD signal difference on the positive and negative sides of magnetic field, as a function of optical excitation power. The saturation amplitude of RMCD signal reduces slightly as optical excitation power increases. Extended Data Fig. 4 Hysteresis loop width as a function of filling factors and temperature. a, Extracted hysteresis loop width vs filling factor of the sample in the main text. b, Temperature dependent hysteresis loop width of RMCD signal at filling factor v = −1/7, showing similar instrument determined offset at high temperature. The loop width is determined by the difference between the magnetic fields at which the RMCD signal crosses zero as µoH is swept back and forth. The error bar is the standard deviation obtained by averaging over 5 data points. The set of data in a were taken at different thermal cycles. This causes a slight offset of loop width in (a) compared with those at the same filling factors in (b) and Fig. 2d in the main text. Extended Data Fig. 5 RMCD signal near ν = −1/3 and its dependence on the magnetic field scanning rate. a. RMCD signal vs µoH in a narrow doping regime near v = −1/3, showing typical ferromagnetic behavior. Data are extracted from Fig. 1d. b. Magnetic field sweeping rate dependent RMCD hysteresis loops at v = −1/3 with 76 nW excitation. Extended Data Fig. 6 Data from an additional device at near zero twist angle on sapphire substrate. It resembles the main results observed in the device presented in the maintext. a, RMCD signal as a function of filling factor v and magnetic field μoH. Temperature: 1.6K. Optical excitation power: 590 nW. b, RMCD signal vs µ0H measured sweeping back and forth at selected filling factors. c, Power dependent RMCD at v = −1/3. d, Temperature dependent RMCD at v = −1/3 and optical excitation power of 590 nW. The data in (c) and (d) are offset for clarity. Extended Data Fig. 7 Calculated Exciton mediated exchange interaction J. a–c, shows the J amplitude plot as a function of the separation r between moiré trapped holes and exciton density with exciton temperature of (a) 10 K, (b) 20 K and (c) 50 K. Extended Data Fig. 8 Excitation power dependent RMCD at v = −1/7. a, Line cuts of Fig. 4b in the main text at three different optical excitation power (indicated in the panels). b–c, RMCD signal vs temperature at optical excitation power of (b) 253 nW and (c) 26 nW. Extended Data Fig. 9 RMCD signal as a function of filling factor and magnetic field at select temperatures. The excitation power is 200 nW at a wavelength of 739.2 nm. Extended Data Fig. 10 Extracted RMCD signal amplitude as a function of temperature and filling factor. a, The same plot of Fig. 4d in the main-text. b, replot of panel (a) with the RMCD signal normalized to its maximum at each fixed filling factor. The enhanced magnetic response at v = −1/3 becomes visible. Supplementary information Supplementary Information This file contains Supplementary text, equations 1–18 and references. Rights and permissions Reprints and Permissions Wang, X., Xiao, C., Park, H. et al. Light-induced ferromagnetism in moiré superlattices. Nature 604, 468–473 (2022). https://doi.org/10.1038/s41586-022-04472-z • Accepted: • Published: • Issue Date: • DOI: https://doi.org/10.1038/s41586-022-04472-z	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8552146553993225, "perplexity": 6597.851269008939}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103646990.40/warc/CC-MAIN-20220630001553-20220630031553-00122.warc.gz"}
https://brilliant.org/practice/probability-theory-level-2-challenges/?subtopic=mathematics-prerequisites&chapter=probability-theory	Quantitative Finance # Probability Theory: Level 2 Challenges How many 4 -digit positive integers have 2 or more zeroes? A fair coin is tossed until it lands heads up. What is the probability that heads first appears on an odd numbered toss? Alice and Carla are playing a dice game. Here's how it works: • Each person rolls a die, and the highest number rolled of the two is recorded. • If the highest number rolled is a 1, 2, 3 or 4, Alice wins. • If the highest number rolled is a 5 or a 6, Carla wins. On average, who is more likely to win: Alice, Carla, or are the probabilities equal? 1% of people have a rare cancer, and there is a test for this cancer which is "90% accurate"; that is: • If you have the cancer there is a 90% chance the test will be positive. • If you don't have the cancer there is a 90% chance the test will be negative. If you take the test and test positive, what is the approximate probability that you have the cancer? A restaurant offers 5 choices of appetizer, 10 choices of the main course and 4 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses. Assuming that all food choices are available, how many different possible meals does the restaurant offer? Note: When you eat a course, you only pick one of the choices. ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 4, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7596063017845154, "perplexity": 577.51231314868}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998690.87/warc/CC-MAIN-20190618063322-20190618085322-00393.warc.gz"}
http://knotphysics.net/faq.html	# FAQ The following are some important advantages of this theory: 1. There is a small set of fundamental assumptions with very few independent parameters. This implies that almost all of the parameters can be derived from first principles. This has already been done for the fine structure constant. 2. In this theory, quantum properties are a consequence of the dynamics of the branched manifold. We show that the discrete behavior of the branched manifold can be modeled using a continuous approximation, which is a path integral. Because the underlying system is discrete and finite, the pathological infinities of the path integral never appear. 3. From the fundamental assumptions, we show that the manifold can spontaneously produce pairs of knots of the form $$\mathbb{R}^3 \# (S^1 \times P^2)$$. We show that these knots have the properties of the elementary fermions. Different embedding types of these knots explain the different generations of fermions. We therefore find that the theory spontaneously produces the elementary particles without additional assumptions. Furthermore, the theory tightly constrains the types of knots that can be created, and we therefore can mathematically constrain the types of possible particles. 4. The spacetime manifold is constrained by our assumptions, but it is under-constrained. We therefore expect the manifold to maximize entropy. Using this principle of entropic maximization, we can derive a description of the dynamics of the spacetime manifold. We find that the manifold behavior is best described by a Lagrangian. In that Lagrangian, we find terms for gravity (scalar curvature $$R$$) and electromagnetism (the term $$F^{\mu\nu} F_{\mu\nu}$$. Including the effects of particle geometry and topology produces electroweak and strong forces. In this theory, we assume a few constraints on the spacetime manifold. One important result of those constraints is that the ways that the manifold can change topology are tightly constrained. If particles are knots on the manifold, then every production of particle/anti-particle pair is a change of topology of the manifold. Therefore a particular topology is only a viable particle topology if it can be created on the spacetime manifold subject to the constraining assumptions. We prove that it is possible to produce pairs of knots of the form $$\mathbb{R}^3 \# (S^1 \times P^2)$$ subject to our constraining assumptions. The type $$\mathbb{R}^3 \# (S^1 \times P^2)$$ is relatively simple, analogous to a twist in the manifold. We then go on to show that those knots have the same properties as the elementary fermions. It remains to be shown that no other topology type is possible. It may be that there are other possible particle topologies and the only reason we see just the type $$\mathbb{R}^3 \# (S^1 \times P^2)$$ is that it has the lowest energy. While it is possible to mathematically eliminate many classes of particle topology, a complete list of possible particle topologies has not yet been determined. The mathematical theory of knot theory has a very specific meaning for the word "knot". A knot is an embeddding of $$S^n$$ in $$S^{n+2}$$. The constraint on the dimensions (an $$n$$-manifold in an $$n$$+2-manifold) is a tight constraint. For any other dimensionality, the embedding would not be knotted. For example, a knot of the form $$S^n$$ in $$S^{n+3}$$ would spontaneously untie. Every elementary fermion in this theory has topology $$\mathbb{R}^3 \# (S^1 \times P^2)$$. This is not a knot in the sense of knot theory. Also, this 3-dimensional topology can be embedded in $$\mathbb{R}^n$$ for $$n \geq 5$$. A hadron, for example a proton, contains linked copies of $$\mathbb{R}^3 \# (S^1 \times P^2)$$, each of which is a quark. Those quarks will remain linked to each other only if the 3 spatial dimensions of the spacetime manifold are embedded in a 5-dimensional space. For that reason, we see that the dimension of the embedding space is perfectly constrained by the particle topology of hadrons. In this theory, we need a word to describe particle topology. There are two reasons that we use the word "knot". The first reason is that the word is convenient and approximately describes the particle topology. The second reason is that, for hadrons, the 3-dimensional particle topology must be embedded in an 5-dimensional space, which is the same constraint ($$n=3$$ and $$n+2=5$$) that applies in the mathematical theory of knot theory. In this theory, all elementary fermions are knots in the spacetime manifold that have topology $$\mathbb{R}^3 \# (S^1 \times P^2)$$. Leptons are elementary fermions and therefore they also have this topology. In this theory, we assume that the spacetime manifold is constrained by Ricci flatness, and we find that Ricci flatness strongly constrains the geometry of the particles. In particular, as charged leptons approach other particles, Ricci flatness forces the lepton radius to shrink. As the distance of approach goes to zero, the lepton radius also goes to zero. For this reason, leptons appear to be pointlike in collisions. This description allows us to describe the spin angular momentum of leptons in familiar terms. For the case of pointlike leptons, spin angular momentum must be considered to be an inherent quantity that is not obtained in the normal sense of $$p \times r$$, because the calculation would be meaningless if the lepton radius is $$r=0$$. In this description, radius is non-zero and the spin angular momentum can be calculated as a function of field strength from first principles. The description of quantum mechanics here is very different from the usual description. We assume that the spacetime manifold is branched and we get all of our quantumness from that property. The viewpoint we adopt is that the path integral of quantum mechanics is useful because it is a convenient simplification of the complex dynamical system, which is the branched manifold. This is similar to saying that the heat equation is a convenient simplification of the transfer of heat energy through the vibrating molecules of an atomic lattice. The heat equation has certain pathological properties, for example energy is transferred faster than light speed. The path integral has certain pathological properties, for example various infinities that are difficult to tame. We hypothesize that the pathology results from modeling a discrete system as a continuous one. With the branched manifold, a single branch of the manifold is analogous to a single atom of the atomic lattice, and we do not try to know its random contribution. We just try to model the ensemble statistically. If we model the ensemble using a continuous approximation, the result reproduces the path integral of quantum mechanics. So far all the key properties of physics (all four forces, quantum mechanics, and the known particles) have been shown to follow without requiring additional assumptions. There is a very short list of assumptions, even in comparison to the Standard Model, and the consequences of those assumptions have been adequate to describe every physical phenomenon that has been attempted. Interestingly, over the course of the development of the theory, the set of assumptions has become ever smaller as previously distinct descriptions were shown to be unified by ever simpler models. You can reach us at: We welcome any questions, comments, or interest in research collaboration.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9330724477767944, "perplexity": 259.9919557256813}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578593360.66/warc/CC-MAIN-20190423054942-20190423075946-00053.warc.gz"}
http://mathoverflow.net/questions/2128/youngs-lattice-and-the-weyl-algebra/58676	# Young's lattice and the Weyl algebra Let L be the lattice of Young diagrams ordered by inclusion and let Ln denote the nth rank, i.e. the Young diagrams of size n. Say that lambda > mu if lambda covers mu, i.e. mu can be obtained from lambda by removing one box and let C[L] be the free vector space on L. The operators U lambda = summu > lambda mu D lambda = sumlambda > mu mu are a decategorification of the induction and restriction operators on the symmetric groups, and (as observed by Stanley and generalized in the theory of differential posets) they have the property that DU - UD = I; in other words, Young's lattice along with U, D form a representation of the Weyl algebra. Is this a manifestation of a more general phenomenon? What's the relationship between differential operators and the representation theory of the symmetric group? Edit: Maybe I should ask a more precise question, based on the comment below. As I understand it, in the language of Coxeter groups the symmetric groups are "type A," so the Weyl algebra can be thought of as being associated to type A phenomena. What's the analogue of the Weyl algebra for types B, C, etc.? - In type B, the poset of ordered pairs of Young diagrams describes the branching rules for the hyperoctahedral group. Here, the corresponding relation is DU - UD = 2I. Is there a natural way to rescale one of the variables so that these are "differential operators" in a sensible way? – Sammy Black Oct 23 '09 at 18:31 If I'm not mistaken you can take U = x - dx, D = x + dx, but I don't know if this is the "natural" interpretation. – Qiaochu Yuan Oct 23 '09 at 18:38 EDIT (3/16/11): When I first read this question, I thought "hmmm, Weyl algebra? Really? I feel like I never hear people say they're going to categorify the Weyl algebra, but it looks like that's what the question is about..." Now I understand what's going on. Not to knock the OP, but there's a much bigger structure here he left out. If you have any $S_n$ representation $M$, you get a functor $$\operatorname{Ind}_{S_m\times S_n}^{S_{m+n}}-\otimes M: S_m-\operatorname{rep}\to S_{m+n}-\operatorname{rep}$$ and these functors all have adjoints which I won't bother writing down. All of these together categorify a Heisenberg algebra, which is what Khovanov proves in the paper linked below (though cruder versions of these results on the level the OP was talking about are much older, at least as far back as Leclerc and Thibon). There is a much more general story here, though one my brain is not very up to explaining it this afternoon, and unfortunately, I don't know of anywhere it's summarized well for beginners. So, how you you prove the restriction rule you mentioned above? You note that the restriction of a $S_n$ rep to an $S_{n-1}$ rep has an action of the Jucys-Murphy element $X_n$ which commutes with $S_{n-1}$. The different $S_{n-1}$ representations are the different eigenspaces of the J-M element. So, one can think of "restrict and take the m-eigenspace" as a functor $E_m$; this defines a direct sum decomposition of the functor of restriction. Of course, this functor has an adjoint: I think the best way to think about this is as $F\_m=(k[S\_n]/(X\_n-m)) \otimes\_{k[S\_{n-1}]} V$. These functors E_m,F_m satsify the relations of the Serre relations for $\mathfrak{sl}(\infty)$. Over characteristic 0, these are all different, and you can think of this as an $\mathfrak{sl}(\infty)$. If instead, you take representations over characteristic p, then E_m=E_{m+p} so you can think of them as being in a circle, an affine Dynkin diagram, so one gets an action of $\widehat{\mathfrak{sl}}(p)$. Similar categorifications of other representations can deconstructed in general by looking at representations of complex reflection groups given by the wreath product of the symmetric group with a cyclic group. So, Sammy, you shouldn't rescale, you should celebrate that you found a representation with a different highest weight (also, if you really care, you should go talk to Jon Brundan or Sasha Kleshchev; they are some of the world's experts on this stuff). EDIT: Khovanov has actually just posted a paper which I think might be relevant to your question. - In the OP's defense, nothing is really lost by only considering the Weyl algebra since the basic representation of affine sl_p is irreducible on restriction to the Heisenberg subalgebra. – David Hill Mar 16 '11 at 23:12 Sasha Kleshchev's book "Linear and Projective Representations of Symmetric Groups" is the reference I'd suggest. Chapter 1 contains the connection with Young's lattice, and the subsequent chapters develop the functors that Ben described above. The second half of the book develops the theory for spin representations of symmetric groups which is an honest type B analogue (The functors $E_m$ and $F_m$ in Ben's answer satisfy the Serre relations for the Kac-Moody algebra of type $B_\infty$). To add a little more detail to Ben's answer, the right level of generality to think about these questions is the affine Hecke algebra (either the degenerate or nondegenerate varieties). I'll describe the degenerate case: Let $F$ be an algebraically closed field of characteristic $p$. As a vector space the (degenerate) affine Hecke algebra is a tensor product of a polynomial algebra with the group algebra of the symmetric group: $H_d=F[x_1,\ldots,x_d]\otimes FS_d$. Multiplication is defined so that each tensor summand is a subalgebra, and $H_d$ satisfies the mixed relations $s_ix_j=x_js_i$ for $j\neq i,i+1$ (here $s_i=(i,i+1)$), and $s_ix_i=x_{i+1}s_1-1$. Note that in addition to being a subalgera, $FS_d$ is also a quotient of $H_d$ obtained by mapping $s_i\mapsto s_i$ and $x_1\mapsto 0$ (so that the $x_i$ map to Jucys-Murphy elements). The polynomial subalgebra forms a maximal commutative subalgebra, so given a finite dimensional $H_d$-module $M$, we may decompose $$M=\bigoplus_{(a_1,\ldots,a_d)\in F^d}M_{(a_1,\ldots,a_d)},$$ where $$M_{(a_1,\ldots a_d)}=\lbrace m\in M\|(x_i-a_i)^Nm=0,\mbox{ for }N\gg0\mbox{ and }i=1,\ldots,d \rbrace$$ is the generalized $(a_1,\ldots,a_d)$-eigenspace for the action of $x_1,\ldots,x_d$. Let $I=\mathbb{Z}1_F\subset F$ and $Rep_IH_d$ be the category of finite dimensional $H_d$-modules which are integral in the sense that if $M\in Rep_IH_d$, and $M_{(a_1,\ldots,a_d)}\neq 0$, then $(a_1,\ldots,a_d)\in I^d$. Now, let $K_d=K_0(Rep_IH_d)$, and $K=\bigoplus_d K_d$. Then, the categorification statement is that parabolic induction and restriction give $K$ the structure of a bialgebra, and as such $$K\cong U_{\mathbb{Z}}(\mathfrak{n}).$$ In the above statement, $\mathfrak{n}\subset \mathfrak{g}$ is the maximal nilpotent subalgebra of the Kac-Moody algebra $\mathfrak{g}$ generated by the Chevalley generators $e_i$, where, if $char F=p$, then $\mathfrak{g}=\hat{sl}(p)$, and if $char F=0$, $\mathfrak{g}=\mathfrak{gl}(\infty)$. In both cases $U_{\mathbb{Z}}(\mathfrak{g})$ denotes the Kostant-Tits $\mathbb{Z}$-subalgebra of the universal enveloping algebra. Note here that the Chevalley generators are indexed by $I$. Now, for each dominant integral weight $\Lambda=\sum_{i\in I}\lambda_i\Lambda_i$ ($\Lambda_i$ the fundamental dominant weights) for $\mathfrak{g}$, define the polynomial $$f_\Lambda=\prod_{i\in I}(x_1-i)^{\lambda_i}.$$ Then, the algebra $H_d^\Lambda=H_d/(H_d f_\Lambda H_d)$ is finite dimensional. In the case $\Lambda=\Lambda_0$, $H_d^\Lambda\cong FS_d$. One can form $K_d(\Lambda)$ and $K(\Lambda)$ as above corresponding to the category $H_d^\Lambda-mod$. Then, the categorification statement is $$K(\Lambda)\cong V_{\mathbb{Z}}(\Lambda)$$ as $\mathfrak{g}$-modules, where $V(\Lambda)$ is the irreducible $\mathfrak{g}$-module of highest weight $\Lambda$ generated by a highest weight vector $v_+$, and $V_{\mathbb{Z}}(\Lambda)=U_\mathbb{Z}(\mathfrak{g})v_+$ is an admissible lattice. The action of the Chevalley generators on $K$ are analogues of the functors in Ben's answer. The action of the Weyl module corresponds to the action of $D=\sum_{i\in I}e_i$ and $U=\sum_{i\in I}f_i$ (in characteristic 0, this is defined in the completion $\mathfrak{a}(\infty)$ of $\mathfrak{gl}(\infty)$. One can generalize this story to $\hat{\mathfrak{sl}}_\ell$ by working with the (nondegenerate) affine Hecke algebra $H_d(t)$, where $t$ is a primitive $\ell$-th root of unity. In this case, the finite dimensional quotients are Hecke algebras of complex reflection groups. The hyperoctohedral group corresponds to the highest weight $\Lambda=2\Lambda_0$. Then $V(\Lambda)$ is a level 2 representation, hence the central element acts by $2\cdot Id$ as in Sammy's comment). In the second half of Kleshchev's book, the Hecke algebra is replaced by the so-called Hecke-Clifford (or Sergeev) algebra, and $\mathfrak{g}$ is of type $B_\infty$ or $A_{2\ell}^{(2)}$ depending on the ground field (or one can work in the non-degenerate case so that $\ell$ needn't be prime. The algebras introduced by Khovanov-Lauda and Rouquier generalize this story to arbitrary symmetrizable Kac-Moody algebra. These algebras are graded, so one gets a categorification of the quantum group $U_q$, where $q$ keeps track of the grading . . . - Passing from towers of algebras to graded dual Hopf algebras is done by using induction and restriction on the Grothendieck groups, and then using structure constants one gets edge multiplicities for a graded graph. Dual graded graphs are generalizations of differential posets (the definig rule is $D_{\Gamma} U_{\Gamma'}-U_{\Gamma}D_{\Gamma'}=r Id$). This generalizes the way one can start with the tower of symmetric group algebras $\bigoplus_{n\geq 0}\mathbb{C} \mathfrak{S}_n$ and get the ring of symmetric functions which is a self dual graded Hopf algebra (construction of the Hopf structure in terms of the Grothendieck groups by Zelevinsky) and finally obtain the Young lattice through Pieri rules on the ring of symmetric functions (equivalently the branching rules for the symmetric group).	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9586575627326965, "perplexity": 215.6740886138987}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999652955/warc/CC-MAIN-20140305060732-00071-ip-10-183-142-35.ec2.internal.warc.gz"}
https://stats.stackexchange.com/questions/396406/post-hoc-test-for-chi-squared-with-given-unequal-probabilities	# Post hoc test for chi-squared with given (unequal) probabilities I am conducting a chi-squared test to see whether the categories survey respondents mention match the distribution of categories in the population. This test is significant, but I am wondering how to run post hoc tests to determine which of the categories significantly deviates from the known probability. responses <- matrix(c(1247,1362, 184, 224), ncol=4) colnames(responses) <- c("Cat 1", "Cat 2", "Cat 3", "Cat 4") responses<-as.table(responses) proportions <- c(0.39, 0.40, 0.10, 0.11) chisq.test(responses, p = proportions) Lukas There are some ideas at this Cross Validated post I believe looking at the standardized residuals from the analysis is appropriate in the case of chi-square goodness-of-fit test with unequal theoretical proportions. A standardized residual >1.96 or <-1.96 indicates an interesting observation corresponding to the alpha = 0.05 level. A problem with this approach with your data is that your sample size is large enough that relatively small differences between the theoretical and observed proportions are likely to be significant. The logical approach here, then, is to report the differences in proportions in some way, and assess whether these differences are large enough to be practically meaningful. responses <- matrix(c(1247,1362, 184, 224), ncol=4) colnames(responses) <- c("Cat 1", "Cat 2", "Cat 3", "Cat 4") responses<-as.table(responses) proportions <- c(0.39, 0.40, 0.10, 0.11) chisq.test(responses, p = proportions) Test = chisq.test(responses, p = proportions) StdRes = Test\$stdres names(StdRes) = colnames(responses) StdRes ### Cat 1 Cat 2 Cat 3 Cat 4 ### 2.626653 5.767644 -7.142785 -6.276560 Pval = 2 * pnorm(abs(StdRes), lower.tail=F) Pval ### Cat 1 Cat 2 Cat 3 Cat 4 ### 8.622926e-03 8.038742e-09 9.145890e-13 3.461461e-10 observed.prop = responses / sum(responses) XT = rbind(proportions, observed.prop) rownames(XT)[1]="Theoretical" rownames(XT)[2]="Observed" XT ### Cat 1 Cat 2 Cat 3 Cat 4 ### Theoretical 0.3900000 0.4000000 0.10000000 0.11000000 ### Observed 0.4133245 0.4514418 0.06098774 0.07424594 barplot(XT, beside = T, xlab = "Group", col = c("cornflowerblue","blue"), legend = rownames(XT)) • Thank you, that is very helpful! I completely agree that substantive interpretations matter more with this sample size, but the journal I am submitting to wants p-values as well ... – Lukas Wallrich Mar 9 at 19:15	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4815518856048584, "perplexity": 3305.8890910598375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999620.99/warc/CC-MAIN-20190624171058-20190624193058-00045.warc.gz"}
https://mcejp.github.io/2020/09/27/cs4954.html	The CS4954 is a long-obsolete NTSC/PAL Digital Video Encoder by Cirrus Logic. Despite being out of production, it is a nice chip, and is being used on the CLONE BUINO DUAL to drive the composite video output. CS4954 block diagram, courtesy of Cirrus Logic. Out of its many inputs and outputs, we only care about a few, highlighted in bold. ## Hello world? To get video output on the composite (CVBS) port with minimum effort, these are the steps to take: • Apply power to the chip • Provide 27MHz reference clock • Via I2C, change the following control flags (preserve the defaults for other flags and other registers): • CONTROL_0: Set MSTR=1 (Master Mode) • CONTROL_4: Set COMDAC_PD=0 (composite DAC: power up) • CONTROL_5: Set EN_COM=1, LOW_IMP=1 (enable composite DAC, enable composite output) • CONTROL_3: Set CBAR=1 (enable internal color bar generator) • Note that the default output format is NTSC-M ITU-R.BT601. If this is not what you want, you can consult Table 4 of the datasheet which describes register configuration for other formats. Tip: you might want to make use of cs4954.h. That should be enough to get you the familiar color bars: Here captured through a USB digitizer dongle Another thing to try is to set CBAR=0 and then varying the BKG_COLOR register. You should get a screen filled with a solid color that changes accordingly. The BKG_COLOR register is encoded as a 3:3:2-bit RGB value, no need to worry about any YCbCr bullshit. Thanks to Master Mode, we don’t have to worry about providing any synchronization signals – everything is taken care of internally. ## Next steps Color bars are a nice start, but what if we want to display our own picture? For this, we need to first gain understanding of the input format(s) understood by the video encoder. In fact, with the CS4954, we have 2 choices of input encoding: ### ITU-R BT.601 (spec) In this mode, the inputs go in as 8-bit words in the pattern Cb–Y1–Cr–Y2. This pattern repeats 360 times during the visible part of a scanline, yielding 720 pixels of luminance resolution and 360 pixels of chrominance resolution. This is also known as 4:2:2 chroma subsampling. Conversion between the RGB and YCbCr color spaces is conceptually simple, but requires matrix multiplication, which is not a problem on PC, but can be tricky or expensive in embedded systems. The coefficients can be found here. Note the “interesting” ranges of values: 16–235 for Y, 16-240 for Cb and Cr. Legend says that these have something to do with analog representation of the signals and under/overshoot concerns. The CS4954 gives us a choice of a Master or a Slave mode. In Master mode, the chip generates HSYNC & VSYNC signals and provides them as digital outputs; conversely, to use Slave Mode, HSYNC and VSYNC must be fed to the video encoder along with pixel data. #### Timing In NTSC (interlaced) mode, a frame consists of 2 fields. You get 29.97 frames, so 59.94 fields per second. One frame consists of: 3 blank lines ( 1.. 3) 3 VSYNC lines ( 4.. 6) 15 blank lines ( 7.. 21) 240 picture lines ( 22..261) 4.5 blank lines (262, 263, 264, 265 + 1st half of 266) 3 VSYNC lines (middle of 266 .. middle of 269) 15.5 blank lines (2nd half of 269 + 270..284) 240 picture lines (285..524) 1 blank line (525) The numbers in brackets are 1-based and inclusive. As for horizontal timing: 128 HSYNC cycles ( 1.. 128) 116 blank cycles ( 129.. 244) 1440 pixel cycles ( 245..1684) encoding 720 horizontal pixels 32 blank cycles (1685..1716) A quick verification: 1716 * 525 * (30 / 1.001) = 27,000,000 cycles per second, which is exactly the reference frequency used by the CS4954. ### ITU-R BT.656 (spec) The BT.656 spec is freely available, but I found the wording just a little bit ambiguous. On the other hand, the application note from Intersil (mirrored here) is crystal clear and presents data in a format useful for encode implementation. BT.656 encodes pixel data in the same way as BT.601, but it also embeds synchronization in the data stream instead of requiring additional discrete signals. The vertical timing becomes much simpler, with no silly half-lines: 21 blank lines ( 1.. 21) 240 picture lines ( 22..261) 23 blank lines (262..284) 240 picture lines (285..524) 1 blank line (525) As for horizontal timing: 4 EAV cycles [FF, 00, 00, XY] 268 dummy cycles [80, 10, ...] 4 SAV cycles [FF, 00, 00, XY] 1440 pixel cycles [Cb, Y1, Cr, Y2] yielding the same grand total of 1716 cycles/line. The XY word is a bit more involved: from MSB to LSB its 8 bits read as 1FVHPPPP. Fortunately, we can pretty much ignore the meaning of the individual bits, thanks to this handy decoding table: Line number, 1-based, inclusive F V H (EAV) H (SAV) 1-3 1 1 1 0 4-20 1 0 1 1 0 21-263 0 0 1 0 264-265 0 1 1 0 266-282 1 1 1 0 283-525 1 0 1 0 Sanity-preserving table courtesy of Intersil engineers And what about PPPP? These bits encode 4-bit parity which allows correction of any single-bit error no one seems to care about, at least for inter-IC applications. Again, you can find more details in the Intersil application note. Since BT.656 mode needs 2 pins fewer than BT.601, it should be the more convenient way forward. This background should be enough to generate a valid BT.656 stream from our FPGA. Next time. ## Open questions 1. Is there a drop-in replacement chip with better availability? ## Footnotes 1. Beware that the BT.601 spec says that the odd-field vertical sync flag should last up to and including line 19, not 20. In practice, this difference does not seem to cause any issues; in fact, it seems that every revision of the standard changes this number somewhat randomly.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4980757534503937, "perplexity": 4639.1439740059495}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662604495.84/warc/CC-MAIN-20220526065603-20220526095603-00053.warc.gz"}
https://hal-centralesupelec.archives-ouvertes.fr/hal-02419167	State observers for reaction systems with improved convergence rate Abstract : The problem of designing state observers for reaction systems whose convergence rate is faster than the standard asymptotic observers [7] is addressed in this paper. It is assumed that the reaction functions are known and that there are more measurements than “independent” reactions. If the unmeasurable state enters linearly in the reaction functions we propose an observer that converges in finite-time, under very weak excitation assumptions. If this dependence is nonlinear, we additionally assume that there is an element of the reaction functions vector that depends only on one unmeasurable state and that these functions are strictly monotonic. Under these conditions, a state observer that ensures exponential convergence of the states that appear in the reaction functions is designed. For the unmeasurable states that do not appear in these functions, the convergence is similar to the one of the asymptotic observers. Document type : Journal articles Domain : https://hal-centralesupelec.archives-ouvertes.fr/hal-02419167 Contributor : Myriam Baverel <> Submitted on : Thursday, December 19, 2019 - 12:59:59 PM Last modification on : Wednesday, September 16, 2020 - 4:50:33 PM Citation Romeo Ortega, Alexey Bobtsov, Denis Dochain, Nikolay Nikolayev. State observers for reaction systems with improved convergence rate. Journal of Process Control, Elsevier, 2019, 83, pp.53-62. ⟨10.1016/j.jprocont.2019.08.003⟩. ⟨hal-02419167⟩ Record views	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.948207676410675, "perplexity": 1263.089652457247}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703522150.18/warc/CC-MAIN-20210121004224-20210121034224-00371.warc.gz"}
https://www.physicsforums.com/threads/electrolytic-reduction-of-iron-ore-stoichiometry.346185/	# Homework Help: Electrolytic reduction of iron ore - Stoichiometry 1. Oct 16, 2009 ### ThetaPi 1. The problem statement, all variables and given/known data Calculate the maximum mass of aluminum that can be made from 408 tonnes of alumina, assuming that aluminum is produced by electrolysis. 2. Relevant equations At the cathode: $$Al^{3+} (l) + 3e^{-} \Rightarrow Al (l)$$. At the anode: $$O^{2-} (l) \Rightarrow O_2 (g) + 4e^{-}$$. Is the oxide ion from aluminum oxide in liquid or gaseous state? 3. The attempt at a solution Is there any limiting reagent of sorts? I have never done any stoichiometric calculations on metallurgy. Postscript. How do we input chemistry using LaTeX? (Especially the chemical equations and symbols, e.g. how to make Al not italicized.) Last edited: Oct 16, 2009 2. Oct 16, 2009 ### cepheid Staff Emeritus Regarding formatting, LaTeX posts on PF are automatically in math mode, which means that all letters are italicized (which is the conventional way to typeset mathematical variables). However, the following LaTeX output (without the spaces in the tex tags) will generate the result given below it: [ tex ] \textrm{Al}^{3+}_{(\textrm{l})} +3e^{-} \longrightarrow \textrm{Al}_{(\textrm{l})} [ /tex ] $$\textrm{Al}^{3+}_{(\textrm{l})} +3e^{-} \longrightarrow \textrm{Al}_{(\textrm{l})}$$ where the \textrm{} enviroment takes us out of math mode and into normal text mode using the roman font. 3. Oct 16, 2009 ### cepheid Staff Emeritus Regarding the problem, it's been a while since I've done chemistry, but isn't it merely a matter of: 1. Figuring out how many moles of aluminum oxide correspond to 408 tonnes of it. 2. Figuring out how many moles of Al are produced per mole of aluminum oxide 3. Converting that many moles of Al into a mass, assuming all of it is converted? Edit, and here's a non LaTeX alternative which might or might not be easier for chemistry (your choice). Use the sup and sub tags for superscripts and subscripts respectively This input, without spaces in the tags, produces the output below it: Al[ sub ](l)[ /sub ][ sup ]3+[ /sup ] + 3e[ sup ]-[ /sup ] → Al [ sub ] (l) [ /sub ] Al(l)3+ + 3e- → Al(l)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9389857053756714, "perplexity": 4901.825378523361}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867977.85/warc/CC-MAIN-20180527004958-20180527024958-00233.warc.gz"}
http://openstudy.com/updates/4f28afb8e4b049df4e9d73f0	Here's the question you clicked on: 55 members online • 0 viewing ## anonymous 4 years ago What is the mass of 5.00 L of whole blood? densiry of blood is 1.05g/cm^3 Delete Cancel Submit • This Question is Closed 1. anonymous • 4 years ago Best Response You've already chosen the best response. 0 $5.00L(\frac{1000ml}{1 L})(\frac{1.05 g}{1 ml})=5250g$ 2. anonymous • 4 years ago Best Response You've already chosen the best response. 0 1ml is equal to 1 cm^3 3. anonymous • 4 years ago Best Response You've already chosen the best response. 0 Strange i wrote out a factor label solution but it's not loading. Let me rewrite it 4. anonymous • 4 years ago Best Response You've already chosen the best response. 0 5.00 L (1000 ml/ 1 L)(1.05 g/ 1 ml)=5250g 5. Not the answer you are looking for? Search for more explanations. • Attachments: Find more explanations on OpenStudy ##### spraguer (Moderator) 5→ View Detailed Profile 23 • Teamwork 19 Teammate • Problem Solving 19 Hero • You have blocked this person. • ✔ You're a fan Checking fan status... Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9995914101600647, "perplexity": 17541.177715901715}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720967.29/warc/CC-MAIN-20161020183840-00442-ip-10-171-6-4.ec2.internal.warc.gz"}
https://benjaminziepert.com/teaching/introduction-into-r-for-social-scientists/r-basics-statistical-analysis/	Introduction Into R for Social Scientists # 1 Instructions For the current session you will practice common statistical methods such as correlation, regression, etc. For this session you will need the material from the website https:\\benjaminziepert.com\teaching and your knowledge from the datacamp assignments. During the session you will create a R script file which is necessary for passing this course. You have to submit the working R script file before 5th December 2018 to pass the R lectures. To do so, please reply to my last e-mail. All steps that are in bold in the current handout have to be included in the script. # 2 Research For our analysis we will use data from experiments that studied the relationship between movement and cognition. Students had the task to transport supposed cocaine or flour and had to avoid border guards. You can see the movement data, measured with GPS, below. The students walked three or fours rounds and after each round they filled in a questionnaire about their feelings and thoughts. For instance, we were checking whether participants would walk closer together when they had the feeling they would do something illegal. https://analyse-gps.com/wp-content/uploads/2018/02/smuggle1.gif The following animation shows a participant walking four rounds from the start (left) to the finish (right). When the path is white then the participant transported flour and when the path is black then the participant transported cocaine. After passing the finish to the right, the participants would answer questionnaires. https://analyse-gps.com/wp-content/uploads/2016/10/black-and-white.gif Source: # 3 Loading the data Please download all files for today’s session from benjaminziepert.com/teaching. Afterwards, load the data from the file “S02D02-SPSS-Data.sav” into R and save it in the variable “data”. To do this please follow the steps from the datacamp course. Remember, you have to load the package “haven” first. For loading a package you can use the library() function. # 4 Exploring the data You can check the “data” variable in the Environment view on the top right. To see more details you can click on the arrow next to the “data” variable. Moreoever, if you click on the variable itself you can see actual data. Alternatively, you can also run the code below to view the data. View(data) To see all columns in the “data” data frame you can use the function names() as illustrated below. names(data) ## [1] "team" "exp" ## [3] "ppn" "round" ## [5] "sexe" "age" ## [7] "nationality" "cocaine" ## [9] "id" "ah_mean_kmh" ## [11] "ah_sd_kmh" "ah_mean_team_distance" ## [13] "ah_mean_deviation_route" "ah_sd_deviation_route" ## [15] "com_sat" "com_awc" ## [17] "com_ssas" "com_fright" ## [19] "com_impulse" "com_dt" ## [21] "com_awp" "com_hi_check" ## [23] "sat1" "sat2" ## [25] "sat3" "sat4" ## [27] "sat5" "dt1" ## [29] "dt2" "dt3" The columns starting with “com_” are the measurements (components) from the questionnaire. All items were measured with a likert scale from 1 to 7. The columns sat1 - sat5 are the questions for the component com_sat and the columns dt1 - dt3 are the questions for com_dt. Further, the columns starting with “ah_” are the measurements from the movement (GPS) sensors. To see the labels of the columns you can run the following code. Please load the “Hmisc” package to make the code work. as.matrix(label(data)) ## [,1] ## team "Team" ## exp "Experiment" ## ppn "Participant" ## round "Round" ## sexe "Sexe" ## age "Age" ## nationality "Nationality" ## cocaine "Illegal Card Selection" ## id "Track ID" ## ah_mean_kmh "Speed" ## ah_sd_kmh "Speed Variation" ## ah_mean_team_distance "Intra-Team Distance" ## ah_mean_deviation_route "Route Deviation" ## ah_sd_deviation_route "Variation Route Deviation" ## com_sat "Alertness to Being Target of Guards" ## com_awc "Cognitive Self-Regulation" ## com_ssas "Situational Self Awareness" ## com_fright "Frightened by Presence of Guards" ## com_impulse "Suppressed Impulses to Change Movement" ## com_dt "Contemplation of Hostile Intent" ## com_awp "Awareness Movement Change in Presence of Guard" ## com_hi_check "Hostile Intent" ## sat1 "I had the feeling the border guard(s) targeted me" ## sat2 "I thought I had attracted the border guards’ attention" ## sat3 "I had a feeling that I was going to be stopped" ## sat4 "I felt like I was the one being addressed by the border guard(s)" ## sat5 "I had the idea that the others were paying attention to me" ## dt1 "I was wondering whether I looked suspicious to the border guards" ## dt2 "I was thinking about what I had to hide from the border guards" ## dt3 "I was wondering whether I was doing something that I was not allowed to do" Feel free to also inspect the file in SPSS and compare if you can find the same information in R. # 5 Descriptives To get a first understanding of the variables, please generate the descriptives of all collumns in data in the same way you did the in the first session. The example below shows for instance the descriptives of age, average walking speed and “Suppressed Impulses to Change Movement”. ## age ah_mean_kmh com_impulse ## Min. :18.00 Min. :0.4554 Min. :1.000 ## 1st Qu.:20.00 1st Qu.:4.3013 1st Qu.:1.600 ## Median :21.00 Median :4.6458 Median :2.600 ## Mean :21.61 Mean :4.6010 Mean :2.756 ## 3rd Qu.:22.00 3rd Qu.:4.9592 3rd Qu.:3.800 ## Max. :37.00 Max. :6.3679 Max. :6.600 ## NA's :8 NA's :63 Please answer the follwing questions • What is the average distance of a participants to the team members? • How frightened was the most frightened participant? To write an answer in your script you can use the comment indicator #. If you start a line with a # then this line will not executed by R. Please check the example below. # How frightened was the most frightened participant? # The most frightened participant reported a score of ... # 6 Reliability To measure the internal reliability of our questions we can calculate Cronbach’s alpha with the function alpha() from the package “psych”. Be aware, we also use the package “ggplot2” and both, “ggplot2” and “psych”, have a function alpha(). To tell R that we want to use alpha() from “psych” we can add “psych::” before the function psych::alpha(). Since we want to measure the internal reliability of all questions from the component “Alertness to Being Target of Guards” we select the columns with the questions sat1 - sat5. library("psych") ## ## Attaching package: 'psych' ## The following object is masked from 'package:Hmisc': ## ## describe ## The following objects are masked from 'package:ggplot2': ## ## %+%, alpha psych::alpha(data[,c("sat1", "sat2", "sat3", "sat4", "sat5")]) ## ## Reliability analysis ## Call: psych::alpha(x = data[, c("sat1", "sat2", "sat3", "sat4", "sat5")]) ## ## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r ## 0.89 0.88 0.89 0.6 7.6 0.011 3.7 1.7 0.64 ## ## lower alpha upper 95% confidence boundaries ## 0.87 0.89 0.91 ## ## Reliability if an item is dropped: ## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r ## sat1 0.84 0.84 0.83 0.56 5.2 0.0154 0.0311 0.53 ## sat2 0.84 0.83 0.80 0.56 5.0 0.0161 0.0149 0.56 ## sat3 0.87 0.86 0.87 0.61 6.2 0.0130 0.0392 0.59 ## sat4 0.85 0.84 0.83 0.57 5.4 0.0150 0.0253 0.56 ## sat5 0.91 0.91 0.90 0.72 10.1 0.0093 0.0081 0.68 ## ## Item statistics ## n raw.r std.r r.cor r.drop mean sd ## sat1 192 0.89 0.88 0.86 0.81 4.0 2.2 ## sat2 192 0.91 0.90 0.90 0.84 3.7 2.2 ## sat3 192 0.82 0.82 0.74 0.71 4.0 2.0 ## sat4 192 0.88 0.87 0.86 0.80 3.7 2.2 ## sat5 192 0.64 0.66 0.52 0.49 3.1 1.7 ## ## Non missing response frequency for each item ## 1 2 3 4 5 6 7 miss ## sat1 0.19 0.16 0.11 0.07 0.14 0.16 0.17 0.24 ## sat2 0.25 0.16 0.08 0.09 0.10 0.19 0.12 0.24 ## sat3 0.17 0.10 0.15 0.13 0.12 0.21 0.12 0.24 ## sat4 0.22 0.16 0.12 0.08 0.10 0.18 0.12 0.24 ## sat5 0.21 0.21 0.24 0.11 0.09 0.10 0.04 0.24 We are interested in the standardized alphas “std.alpha” if an item is dropped. We do so, to check how the items effect the overall reliability of a component. When we are satisfied with the result and you don’t want to perform a factor analysis / principal component analysis then you can create the “com_sat” component with the function rowMeans. In order that we don’t overwrite our current component, we will create a new component called “com_sat2”. data[,"com_sat2"] <- rowMeans(data[,c("sat1", "sat2", "sat3", "sat4", "sat5")]) Please perform a internal reliability analysis for the questions of “Contemplation of Hostile Intent” and create the component “com_dt2”. Please report the standardized alpha levels of “Contemplation of Hostile Intent” for each question if dropped. If you had to remove an item from “Contemplation of Hostile Intent” which would you choose? What are the pros and cons of removing the item and would you do it? # 7 Histogram Please create a histogram for the speed of the participants. You can look in the handout of session 1 for an example and the result should look like the image below. ## stat_bin() using bins = 30. Pick better value with binwidth. ## Warning: Removed 8 rows containing non-finite values (stat_bin). # 8 Scatter plot Please create a scatter plot of “Alertness to Being Target of Guards” and “Speed Variation” with a regression line. The “Alertness to Being Target of Guards” measured how much participants had the feeling that the guards would stop them to check their supposed contraband of cocaine or flour. The “Speed Variation” indicates how much the participants changed their walking speed. ## Warning: Removed 69 rows containing non-finite values (stat_smooth). ## Warning: Removed 69 rows containing missing values (geom_point). # 9 Correlation Please correlate “Alertness to Being Target of Guards” and “Speed Variation”. What can you say about the relationship of “Alertness to Being Target of Guards” and “Speed Variation”? ## x y ## x 1.00 0.32 ## y 0.32 1.00 ## ## n ## x y ## x 192 184 ## y 184 245 ## ## P ## x y ## x 0 ## y 0 Tip: you can run ?rcorr to open the help page for this function. Under the heading “value” you can read what for information the function returns. # 10 Regression To perform a regression analysis you have to formulate the formula of the regression. You start with the dependent variable and sepearte it with ~ from the predictor. The generalized form of the formula is y ~ x. To save the formula we use fit <- lm(y ~ x, data = data) where data is a data frame or matrix with the columns x and y. Finally, we run summary(fit) to show the results of the regression analysis. For instance, if you want to know whether “Alertness to Being Target of Guards” is a significant predictor for “Speed” then you can run the following code. fit <- lm(ah_mean_kmh ~ com_sat, data = data) summary(fit) ## ## Call: ## lm(formula = ah_mean_kmh ~ com_sat, data = data) ## ## Residuals: ## Min 1Q Median 3Q Max ## -4.2105 -0.3027 0.0068 0.2978 1.6845 ## ## Coefficients: ## Estimate Std. Error t value Pr(>\|t\|) ## (Intercept) 4.71264 0.10419 45.229 <2e-16 * ## com_sat -0.02920 0.02557 -1.142 0.255 ## --- ## Signif. codes: 0 '' 0.001 '' 0.01 '' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.5975 on 182 degrees of freedom ## (69 observations deleted due to missingness) ## Multiple R-squared: 0.007118, Adjusted R-squared: 0.001663 ## F-statistic: 1.305 on 1 and 182 DF, p-value: 0.2548 As you can see in the coefficients table above, the predictor com_sat is not a significant predictor for ah_mean_kmh with p = .255. For the next step you will perform your own regression analysis with “Suppressed Impulses to Change Movement” as predictor and “Variation Route Deviation” as dependent variable. “Suppressed Impulses to Change Movement” is the attempt of participants to walk normal in the precense of the guards in order not to give themselves away as smugglers with supposed cocaine. Further, “Variation Route Deviation” is an indicator how often particiapnts changed their route. Please perform the regression analysis with “Suppressed Impulses to Change Movement” and “Variation Route Deviation”. Is “Suppressed Impulses to Change Movement” a significant predictor for “Variation Route Deviation”? Please write your answer in the same manner as you would do in a result section of your thesis. However, formatting such as italic is not necessary.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3428771495819092, "perplexity": 5565.474908802534}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988882.7/warc/CC-MAIN-20210508121446-20210508151446-00596.warc.gz"}
http://mathhelpforum.com/advanced-algebra/29941-groups.html	# Math Help - Groups 1. ## Groups Hi. Hope someone can help with my problem. Let G be a group with identity e. If A and B are subgroups of G then, from the Direct Product of Groups Theory, AxB is a subgroup of GxG. Use this result througout. a) Show that, if A and B are two normal subgroups of G, then AxB is normal subgroup of GxG (Not sure if I am to prove that A and B are two normal subgroups as well as proving AxB is a normal subgroup of GxG). b) Let H be the subset H={(g,g):g E G} Show that H is a subgroup of GxG Normally I can do these type of questions, it's just the Gx G and AxB bit has confused me a bit. Thanx 2. Originally Posted by bex23 a) Show that, if A and B are two normal subgroups of G, then AxB is normal subgroup of GxG (Not sure if I am to prove that A and B are two normal subgroups as well as proving AxB is a normal subgroup of GxG). You need to prove $(g_1,g_2)(a,b)(g_1^{-1},g_2^{-1})\in A\times B$ thus $(g_1ag_1^{-1},g_2bg_2^{-1})\in A\times B$ because $g_1ag_1^{-1}\in A$ and $g_2bg_2^{-1} \in B$. 3. Originally Posted by ThePerfectHacker You need to prove $(g_1,g_2)(a,b)(g_1^{-1},g_2^{-1})\in A\times B$ thus $(g_1ag_1^{-1},g_2bg_2^{-1})\in A\times B$ because $g_1ag_1^{-1}\in A$ and $g_2bg_2^{-1} \in B$. I seem to be having a brain dead day, as I can't even remember how to do that 4. ## Groups Right, I think I have figured out part a) it's just part b) that is giving me problems. I know that to prove that H is a subgroup of GxG, I need to prove the three subgroup axioms Closure, Identity and Inverse. So far I have only gone so far as Closure and even then I am not sure that this is correct any help will be greatly appreciated. Closure: Let (g_1, g_2) and (g_3, g_4) be any two elments of GxG. By the definition of GxG, we know that g_1, g_2, g_3 and g_4 are elemnts of G. Since G is a group, it is closed under the operation o and we have (g_1,g_2)o(g_3,g_4)=(g_1 o g_3, g_2 o g_4) which belongs to H So the closue axiom holds. Is this correct and if it is (which I don't think it is) can you help me get started with the other two axioms. Thanx Bex 5. It is correct. For identity element consider $(e,e)$, show it is identity element. For inverse, note $(g_1,g_2)^{-1} = (g_1^{-1},g_2^{-1})$. 6. ## Groups Identity: To prove the identity axiom we use the identity element (e,e) which belongs to GxG and the arbitrary element (g_1,g_2) which also belongs to GxG, Thus (e,e) o (g_1,g_2)= (e o g_1, e o g_2) =(g_1,g_2) which belongs to H Inverse: For this I have two methods (neither which I am very confidant on). Method1: To prove the inverse axiom, let (g_1,g_2) be and element of GxG where g_1^-1 and g_2^-1 are the inverses respectively. Proving that (g_1^-1, g_2^-1) is the inverse of (g_1,g_2) in GxG this will prove the inverse axiom (I hope!!). We have (g_1,g_2)o(g_1^-1, g_2^-1)=(g_1og_1^-1, g_2og_2^-1) =(e,e) Also (g_1^-1, g_2^-1)o(g_1,g_2)=(e,e) Hence, (g_1^-1,g_2^-1) is the inverse of (g_1,g_2) Method 2: Let (g_1,g_2) be an element of GxG then the inverse is (g_1^-1,g_2^-1), which belongs to H as it is of the form (g,g) for g E G. I think method 2 is the more wrong of the two but put in in here just in case. Have I gone completly off the mark here. I was surprised when you said that the first part was right, and so now the rest will probably be all wrong. Lol!! Can you just tell me if I have gone in the right direction, and if not point me in the right one. Thanx Bex	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9684237241744995, "perplexity": 618.2251356352376}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999673608/warc/CC-MAIN-20140305060753-00050-ip-10-183-142-35.ec2.internal.warc.gz"}
http://mathoverflow.net/questions/179408/when-does-convolution-preserve-the-size-of-a-function	# When does convolution preserve the `size' of a function? For a positive function $f$ and positive measures $\mu, \nu$, does $$\mu\ast f\leq \nu\ast f \Rightarrow \\|\mu\\|\leq \\|\nu\\|?$$ More details: Let $G$ be a locally compact group, $C(G)$ be the space of continuous functions on $G$, $M(G)$ be the finite, Borel measures on $G$. The convolution of a measure and function is defined by $$\mu\ast f(x) = \int f(y^{-1}x)d\mu (y)$$. If $0\neq f\in C(G)$ is positive and compactly supported, and $\mu, \nu\in M(G)^+$ then the above implication holds. Simply take the Haar integral and evaluate the first inequality to find the second. A similar approach works if $G$ is amenable and $f$ has nonzero mean value. My questions: Does the implication above hold for all (edit: bounded) $f\in C(G)^+$ if $G$ is amenable? If $G$ is not amenable, what are the functions for which it is true? - It seems that Justin Moore has some results on single functions witnessing non-amenability in his answer to his question mathoverflow.net/questions/60247/… – Ben Willson Aug 27 '14 at 1:38 In the non-topological setting, I think this question is very closely related to supramenability. – Ben Willson Nov 12 '14 at 2:36 Do you want to require $f$ to be bounded? Otherwise there are easy counterexamples: take $G = \mathbb{Z}$, $\mu(1) = 2$, $\nu(0) = 1$, and $\mu$ and $\nu$ zero at all other points, and $f(n) = 2^n$. Then $\mu * f = \nu*f$ but $\\|\mu\\| = 2 > 1 = \\|\nu\\|$. Thanks. I am mostly interested in bounded $f$, but it is good to be reminded of unbounded examples. – Ben Willson Aug 26 '14 at 7:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9502367377281189, "perplexity": 311.17110893138243}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430456360595.57/warc/CC-MAIN-20150501045920-00002-ip-10-235-10-82.ec2.internal.warc.gz"}
https://imcmy.me/d3-selection-memo/	There is a code snippet in the tutorials of d3.js. It will create a bar chart in the div. <body> <div class="chart"> </div> </body> d3.select(".chart") .selectAll("div") .data(data) .enter().append("div") .style("width", function(d) { return d * 10 + "px"; }) .text(function(d) { return d; }); However, when I tries to modify the selection part to d3.select("div").data(data) or d3.select(".chart).data(data), it fails. Searching for the reason, and on StackOverflow, there is a post explains the reason. The implementation of enter.select is then specialized such that nodes are inserted into the group’s parent, replacing the placeholder. This is why it is critical to call selection.selectAll prior to a data join: it establishes the parent node for entering elements. In other words, calling selectAll('div') at this point is to get the parent node so that append('div') knows where to put it. So the first selector is to select the DOM element, and the second selector is to get the parent node.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35950595140457153, "perplexity": 1535.330625725725}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315258.34/warc/CC-MAIN-20190820070415-20190820092415-00234.warc.gz"}
https://economics.stackexchange.com/questions/10099/what-is-the-difference-between-herfindahl-index-and-the-concentration-ratio/10103	# What is the difference between Herfindahl Index and the Concentration Ratio I was recently reading about the Herfindahl Index and from what I've learned so far, is that HHI is preferred over the Concentration Ratio. However, I didn't quite understand the reasoning that lead to this conclusion. What impact does squaring have on the final result? Any hints or suggestions for further reading will be appreciated. From the Industrial Organization by Belleflame and Petiz (Page 34/35, Chapter 2): While the m-firm concentration ratio adds market shares of a small number of firms in the market, the so-called Herfindahl index (also known as Herfindahl–Hirschman index) considers the full distribution of market shares. We can conclude that the mathematical approach in HHI is more adequate for a full market setup, rather than observing a particular concentration ratio in one firm. Also from the same book the Herfindahl index provides a better measure of concentration as it captures both the number of firms and the dispersion of the market shares. Hence the squared market shares. For your information, there is another concentration measure called the Lerner Index, although the Lerner index is a snapshot of the intensity of competition. You can calculate L by finding the difference between price and marginal costs as a percentage of the price. More formally: $L=\frac{p-C'}{p}$ But it is easily observed that L ignores some dynamics of the markets. Lower prices do not necessarily mean high levels of competition.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8922759890556335, "perplexity": 897.2365210777605}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540511946.30/warc/CC-MAIN-20191208150734-20191208174734-00156.warc.gz"}
https://documen.tv/question/consider-75-3-which-two-statements-are-correct-a-the-quotient-is-25-b-the-quotient-is-25-c-3-det-22298181-74/	## Consider −75/3. Which TWO statements are correct? A) The quotient is 25. B) The quotient is −25. C) 3 determines the Question Consider −75/3. Which TWO statements are correct? A) The quotient is 25. B) The quotient is −25. C) 3 determines the quotient’s sign. D) −75 determines the quotient’s sign. E) The integer with the greatest absolute value always determines the quotient’s sign. in progress 0 5 months 2021-08-11T11:06:07+00:00 2 Answers 9 views 0	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8307551741600037, "perplexity": 7527.59331618095}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305260.61/warc/CC-MAIN-20220127103059-20220127133059-00315.warc.gz"}
https://en.formulasearchengine.com/wiki/Distributed_source_coding	# Distributed source coding Distributed source coding (DSC) is an important problem in information theory and communication. DSC problems regard the compression of multiple correlated information sources that do not communicate with each other.[1] By modeling the correlation between multiple sources at the decoder side together with channel codes, DSC is able to shift the computational complexity from encoder side to decoder side, therefore provide appropriate frameworks for applications with complexity-constrained sender, such as sensor networks and video/multimedia compression (see distributed video coding[2]). One of the main properties of distributed source coding is that the computational burden in encoders is shifted to the joint decoder. ## History In 1973, David Slepian and Jack Keil Wolf proposed the information theoretical lossless compression bound on distributed compression of two correlated i.i.d. sources X and Y.[3] After that, this bound was extended to cases with more than two sources by Thomas M. Cover in 1975,[4] while the theoretical results in the lossy compression case are presented by Aaron D. Wyner and Jacob Ziv in 1976.[5] Although the theorems on DSC were proposed on 1970s, it was after about 30 years that attempts were started for practical techniques, based on the idea that DSC is closely related to channel coding proposed in 1974 by Aaron D. Wyner.[6] The asymmetric DSC problem was addressed by S. S. Pradhan and K. Ramchandran in 1999, which focused on statistically dependent binary and Gaussian sources and used scalar and trellis coset constructions to solve the problem.[7] They further extended the work into the symmetric DSC case.[8] Syndrome decoding technology was first used in distributed source coding by the DISCUS system of SS Pradhan and K Ramachandran (Distributed Source Coding Using Syndromes).[7] They compress binary block data from one source into syndromes and transmit data from the other source uncompressed as side information. This kind of DSC scheme achieves asymmetric compression rates per source and results in asymmetric DSC. This asymmetric DSC scheme can be easily extended to the case of more than two correlated information sources. There are also some DSC schemes that use parity bits rather than syndrome bits. The correlation between two sources in DSC has been modeled as a virtual channel which is usually referred as a binary symmetric channel.[9][10] Starting from DISCUS, DSC has attracted significant research activity and more sophisticated channel coding techniques have been adopted into DSC frameworks, such as Turbo Code, LDPC Code, and so on. Similar to the previous lossless coding framework based on Slepian–Wolf theorem, efforts have been taken on lossy cases based on the Wyner–Ziv theorem. Theoretical results on quantizer designs was provided by R. Zamir and S. Shamai,[11] while different frameworks have been proposed based on this result, including a nested lattice quantizer and a trellis-coded quantizer. Moreover, DSC has been used in video compression for applications which require low complexity video encoding, such as sensor networks, multiview video camcorders, and so on.[12] With deterministic and probabilistic discussions of correlation model of two correlated information sources, DSC schemes with more general compressed rates have been developed.[13][14][15] In these non-asymmetric schemes, both of two correlated sources are compressed. Under a certain deterministic assumption of correlation between information sources, a DSC framework in which any number of information sources can be compressed in a distributed way has been demonstrated by X. Cao and M. Kuijper.[16] This method performs non-asymmetric compression with flexible rates for each source, achieving the same overall compression rate as repeatedly applying asymmetric DSC for more than two sources. Then, by investigating the unique connection between syndromes and complementary codewords of linear codes, they have translated the major steps of DSC joint decoding into syndrome decoding followed by channel encoding via a linear block code and also via its complement code,[17] which theoretically illustrated a method of assembling a DSC joint decoder from linear code encoders and decoders. ## Theoretical bounds The information theoretical lossless compression bound on DSC (the Slepian–Wolf bound) was first purposed by David Slepian and Jack Keil Wolf in terms of entropies of correlated information sources in 1973.[3] They also showed that two isolated sources can compress data as efficiently as if they were communicating with each other. This bound has been extended to the case of more than two correlated sources by Thomas M. Cover in 1975.[4] Similar results were obtained in 1976 by Aaron D. Wyner and Jacob Ziv with regard to lossy coding of joint Gaussian sources.[5] ### Slepian–Wolf bound Distributed Coding is the coding of two or more dependent sources with separate encoders and joint decoder. Given two statistically dependent i.i.d. finite-alphabet random sequences X and Y, Slepian–Wolf theorem includes theoretical bound for the lossless coding rate for distributed coding of the two sources as below:[3] ${\displaystyle R_{X}\geq H(X\|Y),\,}$ ${\displaystyle R_{Y}\geq H(Y\|X),\,}$ ${\displaystyle R_{X}+R_{Y}\geq H(X,Y).\,}$ If both the encoder and decoder of the two sources are independent, the lowest rate we can achieve for lossless compression is ${\displaystyle H(X)}$ and ${\displaystyle H(Y)}$ for ${\displaystyle X}$ and ${\displaystyle Y}$ respectively, where ${\displaystyle H(X)}$ and ${\displaystyle H(Y)}$ are the entropies of ${\displaystyle X}$ and ${\displaystyle Y}$. However, with joint decoding, if vanishing error probability for long sequences is accepted, the Slepian–Wolf theorem shows that much better compression rate can be achieved. As long as the total rate of ${\displaystyle X}$ and ${\displaystyle Y}$ is larger than their joint entropy ${\displaystyle H(X,Y)}$ and none of the sources is encoded with a rate larger than its entropy, distributed coding can achieve arbitrarily small error probability for long sequences. A special case of distributed coding is compression with decoder side information, where source ${\displaystyle Y}$ is available at the decoder side but not accessible at the encoder side. This can be treated as the condition that ${\displaystyle R_{Y}=H(Y)}$ has already been used to encode ${\displaystyle Y}$, while we intend to use ${\displaystyle H(X\|Y)}$ to encode ${\displaystyle X}$. The whole system is operating in an asymmetric way (compression rate for the two sources are asymmetric). ### Wyner–Ziv bound Shortly after Slepian–Wolf theorem on lossless distributed compression was published, the extension to lossy compression with decoder side information was proposed as Wyner–Ziv theorem.[5] Similarly to lossless case, two statistically dependent i.i.d. sources ${\displaystyle X}$ and ${\displaystyle Y}$ are given, where ${\displaystyle Y}$ is available at the decoder side but not accessible at the encoder side. Instead of lossless compression in Slepian–Wolf theorem, Wyner–Ziv theorem looked into the lossy compression case. Wyner–Ziv theorem presents the achievable lower bound for the bit rate of ${\displaystyle X}$ at given distortion ${\displaystyle D}$. It was found that for Gaussian memoryless sources and mean-squared error distortion, the lower bound for the bit rate of ${\displaystyle X}$ remain the same no matter whether side information is available at the encoder or not. ## Virtual channel Deterministic model Probabilistic model ## Asymmetric DSC vs. symmetric DSC Asymmetric DSC means that, different bitrates are used in coding the input sources, while same bitrate is used in symmetric DSC. Taking a DSC design with two sources for example, in this example ${\displaystyle X}$ and ${\displaystyle Y}$ are two discrete, memoryless, uniformly distributed sources which generate set of variables ${\displaystyle \mathbf {x} }$ and ${\displaystyle \mathbf {y} }$ of length 7 bits and the Hamming distance between ${\displaystyle \mathbf {x} }$ and ${\displaystyle \mathbf {y} }$ is at most one. The Slepian–Wolf bound for them is: ${\displaystyle R_{X}+R_{Y}\geq 10}$ ${\displaystyle R_{X}\geq 5}$ ${\displaystyle R_{Y}\geq 5}$ This means, the theoretical bound is ${\displaystyle R_{X}+R_{Y}=10}$ and symmetric DSC means 5 bits for each source. Other pairs with ${\displaystyle R_{X}+R_{Y}=10}$ are asymmetric cases with different bit rate distributions between ${\displaystyle X}$ and ${\displaystyle Y}$, where ${\displaystyle R_{X}=3}$, ${\displaystyle R_{Y}=7}$ and ${\displaystyle R_{Y}=3}$, ${\displaystyle R_{X}=7}$ represent two extreme cases called decoding with side information. ## Practical distributed source coding ### Slepian–Wolf coding – lossless distributed coding It was understood that Slepian–Wolf coding is closely related to channel coding in 1974,[6] and after about 30 years, practical DSC started to be implemented by different channel codes. The motivation behind the use of channel codes is from two sources case, the correlation between input sources can be modeled as a virtual channel which has input as source ${\displaystyle X}$ and output as source ${\displaystyle Y}$. The DISCUS system proposed by S. S. Pradhan and K. Ramchandran in 1999 implemented DSC with syndrome decoding, which worked for asymmetric case and was further extended to symmetric case.[7][8] The basic framework of syndrome based DSC is that, for each source, its input space is partitioned into several cosets according to the particular channel coding method used. Every input of each source gets an output indicating which coset the input belongs to, and the joint decoder can decode all inputs by received coset indices and dependence between sources. The design of channel codes should consider the correlation between input sources. A group of codes can be used to generate coset partitions,[18] such as trellis codes and lattice codes. Pradhan and Ramchandran designed rules for construction of sub-codes for each source, and presented result of trellis-based coset constructions in DSC, which is based on convolution code and set-partitioning rules as in Trellis modulation, as well as lattice code based DSC.[7][8] After this, embedded trellis code was proposed for asymmetric coding as an improvement over their results.[19] After DISCUS system was proposed, more sophisticated channel codes have been adapted to the DSC system, such as Turbo Code, LDPC Code and Iterative Channel Code. The encoders of these codes are usually simple and easy to implement, while the decoders have much higher computational complexity and are able to get good performance by utilizing source statistics. With sophisticated channel codes which have performance approaching the capacity of the correlation channel, corresponding DSC system can approach the Slepian–Wolf bound. Although most research focused on DSC with two dependent sources, Slepian–Wolf coding has been extended to more than two input sources case, and sub-codes generation methods from one channel code was proposed by V. Stankovic, A. D. Liveris, etc. given particular correlation models.[20] #### General theorem of Slepian–Wolf coding with syndromes for two sources Theorem: Any pair of correlated uniformly distributed sources, ${\displaystyle X,Y\in \left\{0,1\right\}^{n}}$, with ${\displaystyle \mathbf {d_{H}} (X,Y)\leq t}$, can be compressed separately at a rate pair ${\displaystyle (R_{1},R_{2})}$ such that ${\displaystyle R_{1},R_{2}\geq n-k,R_{1}+R_{2}\geq 2n-k}$, where ${\displaystyle R_{1}}$ and ${\displaystyle R_{2}}$ are integers, and ${\displaystyle k\leq n-\log(\sum _{i=0}^{t}{n \choose i})}$. This can be achieved using an ${\displaystyle (n,k,2t+1)}$ binary linear code. Proof: The Hamming bound for an ${\displaystyle (n,k,2t+1)}$ binary linear code is ${\displaystyle k\leq n-\log(\sum _{i=0}^{t}{n \choose i})}$, and we have Hamming code achieving this bound, therefore we have such a binary linear code ${\displaystyle \mathbf {C} }$ with ${\displaystyle k\times n}$ generator matrix ${\displaystyle \mathbf {G} }$. Next we will show how to construct syndrome encoding based on this linear code. Suppose there are two different input pairs with the same syndromes, that means there are two different strings ${\displaystyle \mathbf {u^{1},u^{2}} \in \left\{0,1\right\}^{k}}$, such that ${\displaystyle \mathbf {u^{1}G+c_{s}=e} }$ and ${\displaystyle \mathbf {u^{2}G+c_{s}=e} }$. Thus we will have ${\displaystyle \mathbf {(u^{1}-u^{2})G=0} }$. Because minimum Hamming weight of the code ${\displaystyle \mathbf {C} }$ is ${\displaystyle 2t+1}$, the distance between ${\displaystyle \mathbf {u_{1}G} }$ and ${\displaystyle \mathbf {u_{2}G} }$ is ${\displaystyle \geq 2t+1}$. On the other hand, according to ${\displaystyle w(\mathbf {e} )\leq t}$ together with ${\displaystyle \mathbf {u^{1}G+c_{s}=e} }$ and ${\displaystyle \mathbf {u^{2}G+c_{s}=e} }$, we will have ${\displaystyle d_{H}(\mathbf {u^{1}G,c_{s}} )\leq t}$ and ${\displaystyle d_{H}(\mathbf {u^{2}G,c_{s}} )\leq t}$, which contradict with ${\displaystyle d_{H}(\mathbf {u^{1}G,u^{2}G} )\geq 2t+1}$. Therefore, we cannot have more than one input pairs with the same syndromes. Therefore, we can successfully compress the two dependent sources with constructed subcodes from an ${\displaystyle (n,k,2t+1)}$ binary linear code, with rate pair ${\displaystyle (R_{1},R_{2})}$ such that ${\displaystyle R_{1},R_{2}\geq n-k,R_{1}+R_{2}\geq 2n-k}$, where ${\displaystyle R_{1}}$ and ${\displaystyle R_{2}}$ are integers, and ${\displaystyle k\leq n-\log(\sum _{i=0}^{t}{n \choose i})}$. Log indicates Log2. #### Slepian–Wolf coding example Take the same example as in the previous Asymmetric DSC vs. Symmetric DSC part, this part presents the corresponding DSC schemes with coset codes and syndromes including asymmetric case and symmetric case. The Slepian–Wolf bound for DSC design is shown in the previous part. ##### Asymmetric case (${\displaystyle R_{X}=3}$, ${\displaystyle R_{Y}=7}$) In this case, the length of an input variable ${\displaystyle \mathbf {y} }$ from source ${\displaystyle Y}$ is 7 bits, therefore it can be sent lossless with 7 bits independent of any other bits. Based on the knowledge that ${\displaystyle \mathbf {x} }$ and ${\displaystyle \mathbf {y} }$ have Hamming distance at most one, for input ${\displaystyle \mathbf {x} }$ from source ${\displaystyle X}$, since the receiver already has ${\displaystyle \mathbf {y} }$, the only possible ${\displaystyle \mathbf {x} }$ are those with at most 1 distance from ${\displaystyle \mathbf {y} }$. If we model the correlation between two sources as a virtual channel, which has input ${\displaystyle \mathbf {x} }$ and output ${\displaystyle \mathbf {y} }$, as long as we get ${\displaystyle \mathbf {y} }$, all we need to successfully "decode" ${\displaystyle \mathbf {x} }$ is "parity bits" with particular error correction ability, taking the difference between ${\displaystyle \mathbf {x} }$ and ${\displaystyle \mathbf {y} }$ as channel error. We can also model the problem with cosets partition. That is, we want to find a channel code, which is able to partition the space of input ${\displaystyle X}$ into several cosets, where each coset has a unique syndrome associated with it. With a given coset and ${\displaystyle \mathbf {y} }$, there is only one ${\displaystyle \mathbf {x} }$ that is possible to be the input given the correlation between two sources. In this example, we can use the ${\displaystyle (7,4,3)}$ binary Hamming Code ${\displaystyle \mathbf {C} }$, with parity check matrix ${\displaystyle \mathbf {H} }$. For an input ${\displaystyle \mathbf {x} }$ from source ${\displaystyle X}$, only the syndrome given by ${\displaystyle \mathbf {s} =\mathbf {H} \mathbf {x} }$ is transmitted, which is 3 bits. With received ${\displaystyle \mathbf {y} }$ and ${\displaystyle \mathbf {s} }$, suppose there are two inputs ${\displaystyle \mathbf {x_{1}} }$ and ${\displaystyle \mathbf {x_{2}} }$ with same syndrome ${\displaystyle \mathbf {s} }$. That means ${\displaystyle \mathbf {H} \mathbf {x_{1}} =\mathbf {H} \mathbf {x_{2}} }$, which is ${\displaystyle \mathbf {H} (\mathbf {x_{1}} -\mathbf {x_{2}} )=0}$. Since the minimum Hamming weight of ${\displaystyle (7,4,3)}$ Hamming Code is 3, ${\displaystyle d_{H}(\mathbf {x_{1}} ,\mathbf {x_{2}} )\geq 3}$. Therefore the input ${\displaystyle \mathbf {x} }$ can be recovered since ${\displaystyle d_{H}(\mathbf {x} ,\mathbf {y} )\leq 1}$. Similarly, the bits distribution with ${\displaystyle R_{X}=7}$, ${\displaystyle R_{Y}=3}$ can be achieved by reversing the roles of ${\displaystyle X}$ and ${\displaystyle Y}$. ##### Symmetric case In symmetric case, what we want is equal bitrate for the two sources: 5 bits each with separate encoder and joint decoder. We still use linear codes for this system, as we used for asymmetric case. The basic idea is similar, but in this case, we need to do coset partition for both sources, while for a pair of received syndromes (corresponds to one coset), only one pair of input variables are possible given the correlation between two sources. Suppose we have a pair of linear code ${\displaystyle \mathbf {C_{1}} }$ and ${\displaystyle \mathbf {C_{2}} }$ and an encoder-decoder pair based on linear codes which can achieve symmetric coding. The encoder output is given by: ${\displaystyle \mathbf {s_{1}} =\mathbf {H_{1}} \mathbf {x} }$ and ${\displaystyle \mathbf {s_{2}} =\mathbf {H_{2}} \mathbf {y} }$. If there exists two pair of valid inputs ${\displaystyle \mathbf {x_{1}} ,\mathbf {y_{1}} }$ and ${\displaystyle \mathbf {x_{2}} ,\mathbf {y_{2}} }$ generating the same syndromes, i.e. ${\displaystyle \mathbf {H_{1}} \mathbf {x_{1}} =\mathbf {H_{1}} \mathbf {x_{2}} }$ and ${\displaystyle \mathbf {H_{1}} \mathbf {y_{1}} =\mathbf {H_{1}} \mathbf {y_{2}} }$, we can get following(${\displaystyle w()}$ represents Hamming weight): where ${\displaystyle \mathbf {e_{3}} =\mathbf {e_{2}} +\mathbf {e_{1}} }$ and ${\displaystyle w(\mathbf {e_{3}} )\leq 2}$. That means, as long as we have the minimum distance between the two codes larger than ${\displaystyle 3}$, we can achieve error-free decoding. The two codes ${\displaystyle \mathbf {C_{1}} }$ and ${\displaystyle \mathbf {C_{2}} }$ can be constructed as subcodes of the ${\displaystyle (7,4,3)}$ Hamming code and thus has minimum distance of ${\displaystyle 3}$. Given the generator matrix ${\displaystyle \mathbf {G} }$ of the original Hamming code, the generator matrix ${\displaystyle \mathbf {G_{1}} }$ for ${\displaystyle \mathbf {C_{1}} }$ is constructed by taking any two rows from ${\displaystyle \mathbf {G} }$, and ${\displaystyle \mathbf {G_{2}} }$ is constructed by the remaining two rows of ${\displaystyle \mathbf {G} }$. The corresponding ${\displaystyle (5\times 7)}$ parity-check matrix for each sub-code can be generated according to the generator matrix and used to generate syndrome bits. ### Wyner–Ziv coding – lossy distributed coding In general, a Wyner–Ziv coding scheme is obtained by adding a quantizer and a de-quantizer to the Slepian–Wolf coding scheme. Therefore, a Wyner–Ziv coder design could focus on the quantizer and corresponding reconstruction method design. Several quantizer designs have been proposed, such as a nested lattice quantizer,[21] trellis code quantizer[22] and Lloyd quantization method.[23] ### Large scale distributed quantization Unfortunately, the above approaches do not scale (in design or operational complexity requirements) to sensor networks of large sizes, a scenario where distributed compression is most helpful. If there are N sources transmitting at R bits each (with some distributed coding scheme), the number of possible reconstructions scales ${\displaystyle 2^{NR}}$. Even for moderate values of N and R (say N=10, R = 2), prior design schemes become impractical. Recently, an approach,[24] using ideas borrowed from Fusion Coding of Correlated Sources, has been proposed where design and operational complexity are traded against decoder performance. This has allowed distributed quantizer design for network sizes reaching 60 sources, with substantial gains over traditional approaches. The central idea is the presence of a bit-subset selector which maintains a certain subset of the received (NR bits, in the above example) bits for each source. Let ${\displaystyle {\mathcal {B}}}$ be the set of all subsets of the NR bits i.e. ${\displaystyle {\mathcal {B}}=2^{\{1,...,NR\}}}$ Then, we define the bit-subset selector mapping to be ${\displaystyle {\mathcal {S}}:\{1,...,N\}\rightarrow {\mathcal {B}}}$ Note that each choice of the bit-subset selector imposes a storage requirement (C) that is exponential in the cardinality of the set of chosen bits. ${\displaystyle C=\sum _{n=1}^{N}2^{\|{\mathcal {S}}(n)\|}}$ This allows a judicious choice of bits that minimize the distortion, given the constraints on decoder storage. Additional limitations on the set of allowable subsets are still needed. The effective cost function that needs to be minimized is a weighted sum of distortion and decoder storage ${\displaystyle J=D+\lambda C}$ The system design is performed by iteratively (and incrementally) optimizing the encoders, decoder and bit-subset selector till convergence. ## Non-asymmetric DSC for more than two sources The syndrome approach can still be used for more than two sources. Let us consider ${\displaystyle a}$ binary sources of length-${\displaystyle n}$ ${\displaystyle \mathbf {x} _{1},\mathbf {x} _{2},\cdots ,\mathbf {x} _{a}\in \{0,1\}^{n}}$. Let ${\displaystyle \mathbf {H} _{1},\mathbf {H} _{2},\cdots ,\mathbf {H} _{s}}$ be the corresponding coding matrices of sizes ${\displaystyle m_{1}\times n,m_{2}\times n,\cdots ,m_{a}\times n}$. Then the input binary sources are compressed into ${\displaystyle \mathbf {s} _{1}=\mathbf {H} _{1}\mathbf {x} _{1},\mathbf {s} _{2}=\mathbf {H} _{2}\mathbf {x} _{2},\cdots ,\mathbf {s} _{a}=\mathbf {H} _{a}\mathbf {x} _{a}}$ of total ${\displaystyle m=m_{1}+m_{2}+\cdots m_{a}}$ bits. Apparently, two source tuples cannot be recovered at the same time if they share the same syndrome. In other words, if all source tuples of interest have different syndromes, then one can recover them losslessly. General theoretical result does not seem to exist. However, for a restricted kind of source so-called Hamming source [25] that only has at most one source different from the rest and at most one bit location not all identical, practical lossless DSC is shown to exist in some cases. For the case when there are more than two sources, the number of source tuple in a Hamming source is ${\displaystyle 2^{n}(an+1)}$. Therefore, a packing bound that ${\displaystyle 2^{m}\geq 2^{n}(an+1)}$ obviously has to satisfy. When the packing bound is satisfied with equality, we may call such code to be perfect (an analogous of perfect code in error correcting code).[25] A simplest set of ${\displaystyle a,n,m}$ to satisfy the packing bound with equality is ${\displaystyle a=3,n=5,m=9}$. However, it turns out that such syndrome code does not exist.[26] The simplest (perfect) syndrome code with more than two sources have ${\displaystyle n=21}$ and ${\displaystyle m=27}$. Let	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 206, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8688565492630005, "perplexity": 569.355195546627}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943750.71/warc/CC-MAIN-20230322051607-20230322081607-00244.warc.gz"}
https://cstheory.stackexchange.com/questions/16700/finding-minimum-weight-k-cliques-in-a-complete-graph	# Finding minimum weight $k$ cliques in a complete graph For an undirected weighted complete graph $G = (V, E)$. Assuming the edge weight indicates the similarity between different nodes, the smaller $w_{ij}$ is, it means $i$ and $j$ are more similar towards each other. I'm trying to find a subset of size $k$ nodes such that they look not so "similar" towards one another, $\textrm{i.e.}$ $k$ nodes $G_k = (V_k, E_k)$ s.t. $\sum_{(i,j) \in E_k} w_{ij}$ is maximized. I'm not looking for an exact solution but I do want to know whether there is an approximation algorithm that is easy to implement and can still have some kind of performance guarantee. • Do you really want an approximation algorithm that is NOT easy to implement? – Yoshio Okamoto Mar 2 '13 at 4:07 • Negative of the function you are trying to maximize can be shown to be a submodular function on the set of nodes. So your problem can be stated as a submodular minimization problem, which has been well studied. There must be some approximation algorithms for minimizing over subsets of fixed size $k$. – polkjh Mar 2 '13 at 5:57 • @YoshioOkamoto: Oops...should be "easy to implement". :) – derekhh Mar 2 '13 at 6:11 • The submodular function we get in your case is even more special, it is an increasing function. It might be possible to use that too. But these are some papers on minimizing general submodular functions with constraints on size of subsets. algorithmofsaintqdd.googlecode.com/svn/trunk/Papers/ML/ICML2011/… and arxiv.org/pdf/0805.1071v3.pdf – polkjh Mar 2 '13 at 7:13 • In fact, it seems your problem is a standard one, called densest $k$-subgraph problem. citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.9443 – polkjh Mar 2 '13 at 7:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8618831038475037, "perplexity": 281.43068787453467}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145774.75/warc/CC-MAIN-20200223123852-20200223153852-00440.warc.gz"}
https://www.science.gov/topicpages/a/agent-inhibited+acetylcholinesterase+ache.html	#### Sample records for agent-inhibited acetylcholinesterase ache 1. Comparison of oxime reactivation and aging of nerve agent-inhibited monkey and human acetylcholinesterases. PubMed Luo, Chunyuan; Tong, Min; Maxwell, Donald M; Saxena, Ashima 2008-09-25 Non-human primates are valuable animal models that are used for the evaluation of nerve agent toxicity as well as antidotes and results from animal experiments are extrapolated to humans. It has been demonstrated that the efficacy of an oxime primarily depends on its ability to reactivate nerve agent-inhibited acetylcholinesterase (AChE). If the in vitro oxime reactivation of nerve agent-inhibited animal AChE is similar to that of human AChE, it is likely that the results of an in vivo animal study will reliably extrapolate to humans. Therefore, the goal of this study was to compare the aging and reactivation of human and different monkey (Rhesus, Cynomolgus, and African Green) AChEs inhibited by GF, GD, and VR. The oximes examined include the traditional oxime 2-PAM, two H-oximes HI-6 and HLo-7, and the new candidate oxime MMB4. Results indicate that oxime reactivation of all three monkey AChEs was very similar to human AChE. The maximum difference in the second-order reactivation rate constant between human and three monkey AChEs or between AChEs from different monkey species was 5-fold. Aging rate constants of GF-, GD-, and VR-inhibited monkey AChEs were very similar to human AChE except for GF-inhibited monkey AChEs, which aged 2-3 times faster than the human enzyme. The results of this study suggest that all three monkey species are suitable animal models for nerve agent antidote evaluation since monkey AChEs possess similar biochemical/pharmacological properties to human AChE. 2. Peripheral site ligand conjugation to a non-quaternary oxime enhances reactivation of nerve agent-inhibited human acetylcholinesterase. PubMed de Koning, Martijn C; van Grol, Marco; Noort, Daan 2011-09-25 Commonly employed pyridinium-oxime (charged) reactivators of nerve agent inhibited acetylcholinesterase (AChE) do not readily pass the blood brain barrier (BBB) because of the presence of charge(s). Conversely, non-ionic oxime reactivators often suffer from a lack of reactivating potency due to a low affinity for the active site of AChE. It was therefore hypothesized that an extra contribution in affinity may be achieved by covalently connecting a peripheral site ligand (PSL) to a non-ionic reactivator, which may result in a higher reactivation potency of the total construct. This validity of this approach, which proved successful for charged pyridinium oximes in earlier work, is now further exemplified with the covalent linkage of a neutral PSL via a spacer to a non-ionic and otherwise almost non-reactivating α-ketoaldoxime. It is demonstrated that the linkage of the PSL resulted in a remarkable increase in reactivation potency of the hybrid compounds. Although the molecules reported here are still inefficient reactivators compared to the current pyridinium oximes, the presented approach holds promise for the future design and synthesis of non-ionic oxime reactivators with improved BBB penetration and may be suited as well for non-oxime reactivators thus further widening the scope in the ongoing search for broad-spectrum reactivators. PMID:21504785 3. Circannual rhythms of acetylcholinesterase (AChE) activity in the freshwater fish Cnesterodon decemmaculatus. PubMed Menéndez-Helman, Renata J; Ferreyroa, Gisele V; dos Santos Afonso, Maria; Salibián, Alfredo 2015-01-01 The use of biomarkers as a tool to assess responses of organisms exposed to pollutants in toxicity bioassays, as well as in aquatic environmental risk assessment protocols, requires the understanding of the natural fluctuation of the particular biomarker. The aim of this study was to characterize the intrinsic variations of acetylcholinesterase (AChE) activity in tissues of a native freshwater teleost fish to be used as biomarker in toxicity tests, taking into account both seasonal influence and fish size. Specific AChE activity was measured by the method of Ellman et al. (1961) in homogenates of fish anterior section finding a seasonal variability. The highest activity was observed in summer, decreasing significantly below 40% in winter. The annual AChE activity cycle in the anterior section was fitted to a sinusoidal function with a period of 11.2 months. Moreover, an inverse relationship between enzymatic activity and the animal size was established. The results showed that both the fish length and seasonal variability affect AChE activity. AChE activity in fish posterior section showed a similar trend to that in the anterior section, while seasonal variations of the activity in midsection were observed but differences were not statistically significant. In addition, no relationship between AChE and total tissue protein was established in the anterior and posterior sections suggesting that the circannual rhythms observed are AChE-specific responses. Results highlight the importance of considering both the fish size and season variations to reach valid conclusions when AChE activity is employed as neurotoxicity biomarker. 4. Acetylcholinesterase (AChE) inhibition aggravates fasting-induced triglyceride accumulation in the mouse liver. PubMed Yokota, Shin-Ichi; Nakamura, Kaai; Ando, Midori; Kamei, Hiroyasu; Hakuno, Fumihiko; Takahashi, Shin-Ichiro; Shibata, Shigenobu 2014-01-01 Although fasting induces hepatic triglyceride (TG) accumulation in both rodents and humans, little is known about the underlying mechanism. Because parasympathetic nervous system activity tends to attenuate the secretion of very-low-density-lipoprotein-triglyceride (VLDL-TG) and increase TG stores in the liver, and serum cholinesterase activity is elevated in fatty liver disease, the inhibition of the parasympathetic neurotransmitter acetylcholinesterase (AChE) may have some influence on hepatic lipid metabolism. To assess the influence of AChE inhibition on lipid metabolism, the effect of physostigmine, an AChE inhibitor, on fasting-induced increase in liver TG was investigated in mice. In comparison with ad libitum-fed mice, 30 h fasting increased liver TG accumulation accompanied by a downregulation of sterol regulatory element-binding protein 1 (SREBP-1) and liver-fatty acid binding-protein (L-FABP). Physostigmine promoted the 30 h fasting-induced increase in liver TG levels in a dose-dependent manner, accompanied by a significant fall in plasma insulin levels, without a fall in plasma TG. Furthermore, physostigmine significantly attenuated the fasting-induced decrease of both mRNA and protein levels of SREBP-1 and L-FABP, and increased IRS-2 protein levels in the liver. The muscarinic receptor antagonist atropine blocked these effects of physostigmine on liver TG, serum insulin, and hepatic protein levels of SREBP-1 and L-FABP. These results demonstrate that AChE inhibition facilitated fasting-induced TG accumulation with up regulation of the hepatic L-FABP and SREBP-1 in mice, at least in part via the activation of muscarinic acetylcholine receptors. Our studies highlight the crucial role of parasympathetic regulation in fasting-induced TG accumulation, and may be an important source of information on the mechanism of hepatic disorders of lipid metabolism. PMID:25383314 5. A selective molecularly imprinted polymer for immobilization of acetylcholinesterase (AChE): an active enzyme targeted and efficient method. PubMed Demirci, Gökhan; Doğaç, Yasemin İspirli; Teke, Mustafa 2015-11-01 In the present study, we immobilized acetylcholinesterase (AChE) enzyme onto acetylcholine removed imprinted polymer and acetylcholine containing polymer. First, the polymers were produced with acetylcholine, substrate of AChE, by dispersion polymerization. Then, the enzyme was immobilized onto the polymers by using two different methods: In the first method (method A), acetylcholine was removed from the polymer, and then AChE was immobilized onto this polymer (acetylcholine removed imprinted polymer). In the second method (method B), AChE was immobilized onto acetylcholine containing polymer by affinity. In method A, enzyme-specific species (binding sites) occurred by removing acetylcholine from the polymer. The immobilized AChE reached 240% relative specific activity comparison with free AChE because the active enzyme molecules bounded onto the polymer. Transmission electron microscopy results were taken before and after immobilization of AChE for the assessment of morphological structure of polymer. Also, the experiments, which include optimum temperature (25-65 °C), optimum pH (3-10), thermal stability (4-70 °C), kinetic parameters, operational stability and reusability, were performed to determine the characteristic of the immobilized AChE. 6. Effect of pharmaceuticals exposure on acetylcholinesterase (AchE) activity and on the expression of AchE gene in the monogonont rotifer, Brachionus koreanus. PubMed Rhee, Jae-Sung; Kim, Bo-Mi; Jeong, Chang-Bum; Park, Heum Gi; Leung, Kenneth Mei Yee; Lee, Young-Mi; Lee, Jae-Seong 2013-11-01 Pharmaceuticals are widely used in human and veterinary medicine. However, they are emerging as a significant contaminant in aquatic environments through wastewater. Due to the persistent and accumulated properties of pharmaceuticals via the food web, their potential harmful effects on aquatic animals are a great concern. In this study, we investigated the effects of six pharmaceuticals: acetaminophen, ATP; atenolol, ATN; carbamazepine, CBZ; oxytetracycline, OTC; sulfamethoxazole, SMX; and trimethoprim, TMP on acetylcholinesterase (AChE; EC 3.1.1.7) activity and its transcript expression with chlorpyrifos (as a positive control) in the monogonont rotifer, Brachionus koreanus. ATP, CBZ, and TMP exposure also remarkably inhibited Bk-AChE activity at 100 μg/L (24 h) and 1000 μg/L (12 h and 24 h). ATP, CBZ, and TMP exposure showed a significant decrease in the Bk-AChE mRNA level in a concentration-dependent manner. However, in the case of OTC and SMX, a slight decrease in Bk-AChE mRNA expression was found but only at the highest concentration. The time-course experiments showed that ATP positively induced Bk-AChE mRNA 12 h after exposure at both 100 and 1000 μg/L, while the Bk-AChE mRNA expression was significantly downregulated over 6 to 24 h after exposure to 1000 μg/L of CBZ, OTC, SMX, and TMP. Our findings suggest that Bk-AChE would be a useful biomarker for risk assessment of pharmaceutical compounds as an early signal of their toxicity in aquatic environments. Particularly, ATP, CBZ, and TMP may have a toxic cholinergic effect on rotifer B. koreanus by inhibiting AChE activity. PMID:24028855 7. Acetylcholinesterase (AChE) gene modification in transgenic animals: functional consequences of selected exon and regulatory region deletion. PubMed Camp, Shelley; Zhang, Limin; Marquez, Michael; de la Torre, Brian; Long, Jeffery M; Bucht, Goran; Taylor, Palmer 2005-12-15 AChE is an alternatively spliced gene. Exons 2, 3 and 4 are invariantly spliced, and this sequence is responsible for catalytic function. The 3' alternatively spliced exons, 5 and 6, are responsible for AChE disposition in tissue [J. Massoulie, The origin of the molecular diversity and functional anchoring of cholinesterases. Neurosignals 11 (3) (2002) 130-143; Y. Li, S. Camp, P. Taylor, Tissue-specific expression and alternative mRNA processing of the mammalian acetylcholinesterase gene. J. Biol. Chem. 268 (8) (1993) 5790-5797]. The splice to exon 5 produces the GPI anchored form of AChE found in the hematopoietic system, whereas the splice to exon 6 produces a sequence that binds to the structural subunits PRiMA and ColQ, producing AChE expression in brain and muscle. A third alternative RNA species is present that is not spliced at the 3' end; the intron 3' of exon 4 is used as coding sequence and produces the read-through, unanchored form of AChE. In order to further understand the role of alternative splicing in the expression of the AChE gene, we have used homologous recombination in stem cells to produce gene specific deletions in mice. Alternatively and together exon 5 and exon 6 were deleted. A cassette containing the neomycin gene flanked by loxP sites was used to replace the exon(s) of interest. Tissue analysis of mice with exon 5 deleted and the neomycin cassette retained showed very low levels of AChE expression, far less than would have been anticipated. Only the read-through species of the enzyme was produced; clearly the inclusion of the selection cassette disrupted splicing of exon 4 to exon 6. The selection cassette was then deleted in exon 5, exon 6 and exons 5 + 6 deleted mice by breeding to Ella-cre transgenic mice. AChE expression in serum, brain and muscle has been analyzed. Another AChE gene targeted mouse strain involving a region in the first intron, found to be critical for AChE expression in muscle cells [S. Camp, L. Zhang, M. Marquez, B 8. Modelling interactions between Loop1 of Fasciculin2 (Fas2) and Torpedo californica acetylcholinesterase ( Tc AChE) Wang, Jing; Gu, Jiande; Leszczynski, Jerzy 2006-11-01 Four interaction models for the binding of Torpedo californica acetylcholinesterase ( TcAChE) with Loop1 of Fasciculin2 are investigated at the B3LYP/6-311G(d,p) level of theory. The total binding energy of three fragments (P1-P3) which belong to the omega loop Cys67-Cys94 of TcAChE contributes almost 67% of the entire binding, suggesting the domination of this omega loop on the interaction between AChE and Loop1 of Fas2. The energy decomposition illustrates that the interactions mainly consist of electrostatic components. The polar solvent which reduces the binding energies of the studied models implies the significant impact of the solvent on the binding of Fas2 and AChE. 9. Acetylcholinesterase Regulates Skeletal In Ovo Development of Chicken Limbs by ACh-Dependent and -Independent Mechanisms PubMed Central Spieker, Janine; Ackermann, Anica; Salfelder, Anika; Vogel-Höpker, Astrid; Layer, Paul G. 2016-01-01 Formation of the vertebrate limb presents an excellent model to analyze a non-neuronal cholinergic system (NNCS). Here, we first analyzed the expression of acetylcholinesterase (AChE) by IHC and of choline acetyltransferase (ChAT) by ISH in developing embryonic chicken limbs (stages HH17-37). AChE outlined formation of bones, being strongest at their distal tips, and later also marked areas of cell death. At onset, AChE and ChAT were elevated in two organizing centers of the limb anlage, the apical ectodermal ridge (AER) and zone of polarizing activity (ZPA), respectively. Thereby ChAT was expressed shortly after AChE, thus strongly supporting a leading role of AChE in limb formation. Then, we conducted loss-of-function studies via unilateral implantation of beads into chicken limb anlagen, which were soaked in cholinergic components. After varying periods, the formation of cartilage matrix and of mineralizing bones was followed by Alcian blue (AB) and Alizarin red (AR) stainings, respectively. Both acetylcholine (ACh)- and ChAT-soaked beads accelerated bone formation in ovo. Notably, inhibition of AChE by BW284c51, or by the monoclonal antibody MAB304 delayed cartilage formation. Since bead inhibition of BChE was mostly ineffective, an ACh-independent action during BW284c51 and MAB304 inhibition was indicated, which possibly could be due to an enzymatic side activity of AChE. In conclusion, skeletogenesis in chick is regulated by an ACh-dependent cholinergic system, but to some extent also by an ACh-independent aspect of the AChE protein. PMID:27574787 10. Acetylcholinesterase Regulates Skeletal In Ovo Development of Chicken Limbs by ACh-Dependent and -Independent Mechanisms. PubMed Spieker, Janine; Ackermann, Anica; Salfelder, Anika; Vogel-Höpker, Astrid; Layer, Paul G 2016-01-01 Formation of the vertebrate limb presents an excellent model to analyze a non-neuronal cholinergic system (NNCS). Here, we first analyzed the expression of acetylcholinesterase (AChE) by IHC and of choline acetyltransferase (ChAT) by ISH in developing embryonic chicken limbs (stages HH17-37). AChE outlined formation of bones, being strongest at their distal tips, and later also marked areas of cell death. At onset, AChE and ChAT were elevated in two organizing centers of the limb anlage, the apical ectodermal ridge (AER) and zone of polarizing activity (ZPA), respectively. Thereby ChAT was expressed shortly after AChE, thus strongly supporting a leading role of AChE in limb formation. Then, we conducted loss-of-function studies via unilateral implantation of beads into chicken limb anlagen, which were soaked in cholinergic components. After varying periods, the formation of cartilage matrix and of mineralizing bones was followed by Alcian blue (AB) and Alizarin red (AR) stainings, respectively. Both acetylcholine (ACh)- and ChAT-soaked beads accelerated bone formation in ovo. Notably, inhibition of AChE by BW284c51, or by the monoclonal antibody MAB304 delayed cartilage formation. Since bead inhibition of BChE was mostly ineffective, an ACh-independent action during BW284c51 and MAB304 inhibition was indicated, which possibly could be due to an enzymatic side activity of AChE. In conclusion, skeletogenesis in chick is regulated by an ACh-dependent cholinergic system, but to some extent also by an ACh-independent aspect of the AChE protein. PMID:27574787 11. An acetylcholinesterase (AChE) biosensor with enhanced solvent resistance based on chitosan for the detection of pesticides. PubMed Warner, John; Andreescu, Silvana 2016-01-01 Solvent tolerance of immobilized enzymes is important for many biosensing and biotechnological applications. In this paper we report an acetylcholinesterase (AChE) biosensor based on chitosan that exhibits high solvent resistance and enables sensitive detection of pesticides in presence of a high content of organic solvents. The solvent effect was established comparatively for the enzyme immobilized in chitosan and covalently cross-linked with glutaraldehyde. The activity of the immobilized AChE was dependent on the immobilization method and solvent type. The enzyme entrapped in chitosan fully conserved its activity in up to 25% methanol, 15% acetonitrile and 100% cyclohexane while the enzyme cross-linked with glutaraldehyde gradually lost its activity starting at 5% acetonitrile and methanol, and showed variable levels in cyclohexane. The detection limits of the biosensor for paraoxon were: 7.5 nM in 25% methanol, 100 nM in 15% acetonitrile and 2.5 μM in 100% cyclohexane. This study demonstrates that chitosan provides an excellent immobilization environment for AChE biosensors designed to operate in environments containing high amounts of organic solvents. It also highlights the effect of the immobilization material and solvent type on enzyme stability. These findings can enable future selection of the immobilization matrix and solvent type for the development of organic phase enzyme based systems. 12. An acetylcholinesterase (AChE) biosensor with enhanced solvent resistance based on chitosan for the detection of pesticides. PubMed Warner, John; Andreescu, Silvana 2016-01-01 Solvent tolerance of immobilized enzymes is important for many biosensing and biotechnological applications. In this paper we report an acetylcholinesterase (AChE) biosensor based on chitosan that exhibits high solvent resistance and enables sensitive detection of pesticides in presence of a high content of organic solvents. The solvent effect was established comparatively for the enzyme immobilized in chitosan and covalently cross-linked with glutaraldehyde. The activity of the immobilized AChE was dependent on the immobilization method and solvent type. The enzyme entrapped in chitosan fully conserved its activity in up to 25% methanol, 15% acetonitrile and 100% cyclohexane while the enzyme cross-linked with glutaraldehyde gradually lost its activity starting at 5% acetonitrile and methanol, and showed variable levels in cyclohexane. The detection limits of the biosensor for paraoxon were: 7.5 nM in 25% methanol, 100 nM in 15% acetonitrile and 2.5 μM in 100% cyclohexane. This study demonstrates that chitosan provides an excellent immobilization environment for AChE biosensors designed to operate in environments containing high amounts of organic solvents. It also highlights the effect of the immobilization material and solvent type on enzyme stability. These findings can enable future selection of the immobilization matrix and solvent type for the development of organic phase enzyme based systems. PMID:26695264 13. Sesquiterpenes and a monoterpenoid with acetylcholinesterase (AchE) inhibitory activity from Valeriana officinalis var. latiofolia in vitro and in vivo. PubMed Chen, Heng-Wen; He, Xuan-Hui; Yuan, Rong; Wei, Ben-Jun; Chen, Zhong; Dong, Jun-Xing; Wang, Jie 2016-04-01 Acetylcholinesterase Inhibitor (AchEI) is the most extensive in all anti-dementia drugs. The extracts and isolated compounds from the Valeriana genus have shown anti-dementia bioactivity. Four new sesquiterpenoids (1-4) and a new monoterpenoid (5) were isolated from the root of Valeriana officinalis var. latiofolia. The acetylcholinesterase (AchE) inhibitory activity of isolates was evaluated by modified Ellman method in vitro. Learning and memory ability of compound 4 on mice was evaluated by the Morris water maze. The contents of acetylcholine (Ach), acetylcholine transferase (ChAT) and AchE in mice brains were determined by colorimetry. The results showed IC50 of compound 4 was 0.161 μM in vitro. Compared with the normal group, the learning and memory ability of mice and the contents of Ach and ChAT decreased in model group mice (P<0.01), while the AchE increased (P<0.01). Compared with the model group, Ach and ChAT in the positive control group, the high-dose group and the medium-dose group increased (P<0.01), while the AchE decreased (P<0.01). Compound 4 can improve the learning and memory abilities of APPswe/PSΔE9 double-transgenic mice, and the mechanism may be related to the regulation of the relative enzyme in the cholinergic system. PMID:26976216 14. Acetylcholinesterase (AChE) is an important link in the apoptotic pathway induced by hyperglycemia in Y79 retinoblastoma cell line PubMed Central Masha'our, R. Shehadeh; Heinrich, R.; Garzozi, H. J.; Perlman, I. 2012-01-01 Acetylcholinesterase (AChE) expression was found to be induced in the mammalian CNS, including the retina, by different types of stress leading to cellular apoptosis. Here, we tested possible involvement of AChE in hyperglycemia-induced apoptosis in a retinal cell line. Y79 retinoblastoma cells were incubated in starvation media (1% FBS and 1 mg/ml glucose) for 16–24 h, and then exposed to hyperglycemic environment by raising extracellular glucose concentrations to a final level of 3.5 mg/ml or 6 mg/ml. Similar levels of mannitol were used as control for hyperosmolarity. Cells were harvested at different time intervals for analysis of apoptosis and AChE protein expression. Apoptosis was detected by the cleavage of Poly ADP-ribose polymerase (PARP) using western blot, and by Terminal deoxynucleotidyl-transferase-mediated dUTP nick-end-labeling (TUNEL) assay. AChE protein expression and activity was detected by western blot and by the Karnovsky and Roots method, respectively. MissionTM shRNA for AChE was used to inhibit AChE protein expression. Treating Y79 cells with 3.5 mg/ml of glucose, but not with 3.5 mg/ml mannitol, induced apoptosis which was confirmed by TUNEL assay and by cleavage of PARP. A part of the signaling pathway accompanying the apoptotic process involved up-regulation of the AChE-R variant and an N-extended AChE variant as verified at the mRNA and protein level. Inhibition of AChE protein expression by shRNA protected Y79 cell from entering the apoptotic pathway. Our data suggest that expression of an N-extended AChE variant, most probably an R isoform, is involved in the apoptotic pathway caused by hyperglycemia in Y79 cells. PMID:22685426 15. Acetylcholinesterase (AChE) is an important link in the apoptotic pathway induced by hyperglycemia in Y79 retinoblastoma cell line. PubMed Masha'our, R Shehadeh; Heinrich, R; Garzozi, H J; Perlman, I 2012-01-01 Acetylcholinesterase (AChE) expression was found to be induced in the mammalian CNS, including the retina, by different types of stress leading to cellular apoptosis. Here, we tested possible involvement of AChE in hyperglycemia-induced apoptosis in a retinal cell line. Y79 retinoblastoma cells were incubated in starvation media (1% FBS and 1 mg/ml glucose) for 16-24 h, and then exposed to hyperglycemic environment by raising extracellular glucose concentrations to a final level of 3.5 mg/ml or 6 mg/ml. Similar levels of mannitol were used as control for hyperosmolarity. Cells were harvested at different time intervals for analysis of apoptosis and AChE protein expression. Apoptosis was detected by the cleavage of Poly ADP-ribose polymerase (PARP) using western blot, and by Terminal deoxynucleotidyl-transferase-mediated dUTP nick-end-labeling (TUNEL) assay. AChE protein expression and activity was detected by western blot and by the Karnovsky and Roots method, respectively. Mission(TM) shRNA for AChE was used to inhibit AChE protein expression. Treating Y79 cells with 3.5 mg/ml of glucose, but not with 3.5 mg/ml mannitol, induced apoptosis which was confirmed by TUNEL assay and by cleavage of PARP. A part of the signaling pathway accompanying the apoptotic process involved up-regulation of the AChE-R variant and an N-extended AChE variant as verified at the mRNA and protein level. Inhibition of AChE protein expression by shRNA protected Y79 cell from entering the apoptotic pathway. Our data suggest that expression of an N-extended AChE variant, most probably an R isoform, is involved in the apoptotic pathway caused by hyperglycemia in Y79 cells. PMID:22685426 16. Combined 3D-QSAR, molecular docking, and molecular dynamics study of tacrine derivatives as potential acetylcholinesterase (AChE) inhibitors of Alzheimer's disease. PubMed Zhou, An; Hu, Jianping; Wang, Lirong; Zhong, Guochen; Pan, Jian; Wu, Zeyu; Hui, Ailing 2015-10-01 Acetylcholinesterase (AChE) is one of the key targets of drugs for treating Alzheimer's disease (AD). Tacrine is an approved drug with AChE-inhibitory activity. In this paper, 3D-QSAR, molecular docking, and molecular dynamics were carried out in order to study 60 tacrine derivatives and their AChE-inhibitory activities. 3D-QSAR modeling resulted in an optimal CoMFA model with q(2) = 0.552 and r(2) = 0.983 and an optimal CoMSIA model with q(2) = 0.581 and r(2) = 0.989. These QSAR models also showed that the steric and H-bond fields of these compounds are important influences on their activities. The interactions between these inhibitors and AChE were further explored through molecular docking and molecular dynamics simulation. A few key residues (Tyr70, Trp84, Tyr121, Trp279, and Phe330) at the binding site of AChE were identified. The results of this study improve our understanding of the mechanisms of AChE inhibitors and afford valuable information that should aid the design of novel potential AChE inhibitors. Graphical Abstract Superposition of backbone atoms of the lowest-energy structure obtained from MD simulation (magenta) onto those of the structure of the initial molecular docking model (green). 17. Acetylcholinesterase (AChE) and heat shock proteins (Hsp70) of gypsy moth (Lymantria dispar L.) larvae in response to long-term fluoranthene exposure. PubMed Mrdaković, Marija; Ilijin, Larisa; Vlahović, Milena; Matić, Dragana; Gavrilović, Anja; Mrkonja, Aleksandra; Perić-Mataruga, Vesna 2016-09-01 Polycyclic aromatic hydrocarbons (PAHs) may affect biochemical and physiological processes in living organisms, thus impairing fitness related traits and influencing their populations. This imposes the need for providing early-warning signals of pollution. Our study aimed to examine changes in the activity of acetylcholinesterase (AChE) and the concentration of heat shock proteins (Hsp70) in homogenates of brain tissues of fifth instar gypsy moth (Lymantria dispar L.) larvae, exposed to the ubiquitous PAH, fluoranthene, supplemented to the rearing diet. Significantly increased activity of AChE in larvae fed on the diets with high fluoranthene concentrations suggests the necessity for elucidation of the role of AChE in these insects when exposed to PAH pollution. Significant induction of Hsp70 in gypsy moth larvae reared on the diets containing low fluoranthene concentrations, indicate that changes in the level of Hsp70 might be useful as an indicator of pollution in this widespread forest species. PMID:27343862 18. Acetylcholinesterase (AChE) and heat shock proteins (Hsp70) of gypsy moth (Lymantria dispar L.) larvae in response to long-term fluoranthene exposure. PubMed Mrdaković, Marija; Ilijin, Larisa; Vlahović, Milena; Matić, Dragana; Gavrilović, Anja; Mrkonja, Aleksandra; Perić-Mataruga, Vesna 2016-09-01 Polycyclic aromatic hydrocarbons (PAHs) may affect biochemical and physiological processes in living organisms, thus impairing fitness related traits and influencing their populations. This imposes the need for providing early-warning signals of pollution. Our study aimed to examine changes in the activity of acetylcholinesterase (AChE) and the concentration of heat shock proteins (Hsp70) in homogenates of brain tissues of fifth instar gypsy moth (Lymantria dispar L.) larvae, exposed to the ubiquitous PAH, fluoranthene, supplemented to the rearing diet. Significantly increased activity of AChE in larvae fed on the diets with high fluoranthene concentrations suggests the necessity for elucidation of the role of AChE in these insects when exposed to PAH pollution. Significant induction of Hsp70 in gypsy moth larvae reared on the diets containing low fluoranthene concentrations, indicate that changes in the level of Hsp70 might be useful as an indicator of pollution in this widespread forest species. 19. R86Q, a mutation in BmAChE3 yielding a Rhipicephalus microplus organophosphate-insensitive acetylcholinesterase Technology Transfer Automated Retrieval System (TEKTRAN) Mutations were identified in the sequence encoding the acetylcholinesterase, BmAChE3, in strains of Rhipicephalus (Boophilus) microplus (Canestrini) resistant or susceptible to orgaonphosphorus acaricide. The mutation which appeared most frequently in the organophosphorus-resistant San Román strain... 20. Identification and Expression of Acetylcholinesterase in Octopus vulgaris Arm Development and Regeneration: a Conserved Role for ACHE? PubMed Fossati, Sara Maria; Candiani, Simona; Nödl, Marie-Therese; Maragliano, Luca; Pennuto, Maria; Domingues, Pedro; Benfenati, Fabio; Pestarino, Mario; Zullo, Letizia 2015-08-01 Acetylcholinesterase (ACHE) is a glycoprotein with a key role in terminating synaptic transmission in cholinergic neurons of both vertebrates and invertebrates. ACHE is also involved in the regulation of cell growth and morphogenesis during embryogenesis and regeneration acting through its non-cholinergic sites. The mollusk Octopus vulgaris provides a powerful model for investigating the mechanisms underlying tissue morphogenesis due to its high regenerative power. Here, we performed a comparative investigation of arm morphogenesis during adult arm regeneration and embryonic arm development which may provide insights on the conserved ACHE pathways. In this study, we cloned and characterized O. vulgaris ACHE, finding a single highly conserved ACHE hydrophobic variant, characterized by prototypical catalytic sites and a putative consensus region for a glycosylphosphatidylinositol (GPI)-anchor attachment at the COOH-terminus. We then show that its expression level is correlated to the stage of morphogenesis in both adult and embryonic arm. In particular, ACHE is localized in typical neuronal sites when adult-like arm morphology is established and in differentiating cell locations during the early stages of arm morphogenesis. This possibility is also supported by the presence in the ACHE sequence and model structure of both cholinergic and non-cholinergic sites. This study provides insights into ACHE conserved roles during processes of arm morphogenesis. In addition, our modeling study offers a solid basis for predicting the interaction of the ACHE domains with pharmacological blockers for in vivo investigations. We therefore suggest ACHE as a target for the regulation of tissue morphogenesis. 1. Identification and Expression of Acetylcholinesterase in Octopus vulgaris Arm Development and Regeneration: a Conserved Role for ACHE? PubMed Fossati, Sara Maria; Candiani, Simona; Nödl, Marie-Therese; Maragliano, Luca; Pennuto, Maria; Domingues, Pedro; Benfenati, Fabio; Pestarino, Mario; Zullo, Letizia 2015-08-01 Acetylcholinesterase (ACHE) is a glycoprotein with a key role in terminating synaptic transmission in cholinergic neurons of both vertebrates and invertebrates. ACHE is also involved in the regulation of cell growth and morphogenesis during embryogenesis and regeneration acting through its non-cholinergic sites. The mollusk Octopus vulgaris provides a powerful model for investigating the mechanisms underlying tissue morphogenesis due to its high regenerative power. Here, we performed a comparative investigation of arm morphogenesis during adult arm regeneration and embryonic arm development which may provide insights on the conserved ACHE pathways. In this study, we cloned and characterized O. vulgaris ACHE, finding a single highly conserved ACHE hydrophobic variant, characterized by prototypical catalytic sites and a putative consensus region for a glycosylphosphatidylinositol (GPI)-anchor attachment at the COOH-terminus. We then show that its expression level is correlated to the stage of morphogenesis in both adult and embryonic arm. In particular, ACHE is localized in typical neuronal sites when adult-like arm morphology is established and in differentiating cell locations during the early stages of arm morphogenesis. This possibility is also supported by the presence in the ACHE sequence and model structure of both cholinergic and non-cholinergic sites. This study provides insights into ACHE conserved roles during processes of arm morphogenesis. In addition, our modeling study offers a solid basis for predicting the interaction of the ACHE domains with pharmacological blockers for in vivo investigations. We therefore suggest ACHE as a target for the regulation of tissue morphogenesis. PMID:25112677 2. Acetylcholinesterase-Fc Fusion Protein (AChE-Fc): A Novel Potential Organophosphate Bioscavenger with Extended Plasma Half-Life. PubMed Noy-Porat, Tal; Cohen, Ofer; Ehrlich, Sharon; Epstein, Eyal; Alcalay, Ron; Mazor, Ohad 2015-08-19 Acetylcholinesterase (AChE) is the physiological target of organophosphate nerve agent compounds. Currently, the development of a formulation for prophylactic administration of cholinesterases as bioscavengers in established risk situations of exposure to nerve agents is the incentive for many efforts. While cholinesterase bioscavengers were found to be highly effective in conferring protection against nerve agent exposure in animal models, their therapeutic use is complicated by short circulatory residence time. To create a bioscavenger with prolonged plasma half-life, compatible with biotechnological production and purification, a chimeric recombinant molecule of HuAChE coupled to the Fc region of human IgG1 was designed. The novel fusion protein, expressed in cultured cells under optimized conditions, maintains its full enzymatic activity, at levels similar to those of the recombinant AChE enzyme. Thus, this novel fusion product retained its binding affinity toward BW284c5 and propidium, and its bioscavenging reactivity toward the organophosphate-AChE inhibitors sarin and VX. Furthermore, when administered to mice, AChE-Fc exhibits exceptional circulatory residence longevity (MRT of 6000 min), superior to any other known cholinesterase-based recombinant bioscavengers. Owing to its optimized pharmacokinetic performance, high reactivity toward nerve agents, and ease of production, AChE-Fc emerges as a promising next-generation organophosphate bioscavenger. 3. Biochemical effects of glyphosate based herbicide, Excel Mera 71 on enzyme activities of acetylcholinesterase (AChE), lipid peroxidation (LPO), catalase (CAT), glutathione-S-transferase (GST) and protein content on teleostean fishes. PubMed Samanta, Palas; Pal, Sandipan; Mukherjee, Aloke Kumar; Ghosh, Apurba Ratan 2014-09-01 Effects of glyphosate based herbicide, Excel Mera 71 at a dose of 17.20mg/l on enzyme activities of acetylcholinesterase (AChE), lipid peroxidation (LPO), catalase (CAT), glutathione-S-transferase (GST) and protein content were measured in different tissues of two Indian air-breathing teleosts, Anabas testudineus (Bloch) and Heteropneustes fossilis (Bloch) during an exposure period of 30 days under laboratory condition. AChE activity was significantly increased in all the investigated tissues of both fish species and maximum elevation was observed in brain of H. fossilis, while spinal cord of A. testudineus showed minimum increment. Fishes showed significant increase LPO levels in all the tissues; highest was observed in gill of A. testudineus but lowest LPO level was observed in muscle of H. fossilis. CAT was also enhanced in both the fishes, while GST activity in liver diminished substantially and minimum was observed in liver of A. testudineus. Total protein content showed decreased value in all the tissues, maximum reduction was observed in liver and minimum in brain of A. testudineus and H. fossilis respectively. The results indicated that Excel Mera 71 caused serious alterations in the enzyme activities resulting into severe deterioration of fish health; so, AChE, LPO, CAT and GST can be used as suitable indicators of herbicidal toxicity. PMID:24927388 4. Biochemical effects of glyphosate based herbicide, Excel Mera 71 on enzyme activities of acetylcholinesterase (AChE), lipid peroxidation (LPO), catalase (CAT), glutathione-S-transferase (GST) and protein content on teleostean fishes. PubMed Samanta, Palas; Pal, Sandipan; Mukherjee, Aloke Kumar; Ghosh, Apurba Ratan 2014-09-01 Effects of glyphosate based herbicide, Excel Mera 71 at a dose of 17.20mg/l on enzyme activities of acetylcholinesterase (AChE), lipid peroxidation (LPO), catalase (CAT), glutathione-S-transferase (GST) and protein content were measured in different tissues of two Indian air-breathing teleosts, Anabas testudineus (Bloch) and Heteropneustes fossilis (Bloch) during an exposure period of 30 days under laboratory condition. AChE activity was significantly increased in all the investigated tissues of both fish species and maximum elevation was observed in brain of H. fossilis, while spinal cord of A. testudineus showed minimum increment. Fishes showed significant increase LPO levels in all the tissues; highest was observed in gill of A. testudineus but lowest LPO level was observed in muscle of H. fossilis. CAT was also enhanced in both the fishes, while GST activity in liver diminished substantially and minimum was observed in liver of A. testudineus. Total protein content showed decreased value in all the tissues, maximum reduction was observed in liver and minimum in brain of A. testudineus and H. fossilis respectively. The results indicated that Excel Mera 71 caused serious alterations in the enzyme activities resulting into severe deterioration of fish health; so, AChE, LPO, CAT and GST can be used as suitable indicators of herbicidal toxicity. 5. Oxime-mediated in vitro reactivation kinetic analysis of organophosphates-inhibited human and electric eel acetylcholinesterase. PubMed Sahu, Arvind Kumar; Sharma, Rahul; Gupta, Bhanushree; Musilek, Kamil; Kuca, Kamil; Acharya, Jyotiranjan; Ghosh, Kallol K 2016-06-01 Organophosphate (OP)-based pesticides and nerve agents are highly toxic compounds which interrupt the catalytic mechanism of acetylcholinesterase (AChE) by phosphorylating the hydroxyl moiety of serine residue. The inhibited enzyme can be reactivated by the nucleophilic action of oxime reactivators. To analyze the effect of different AChE sources on reactivation efficacy of reactivators, several in vivo studies have carried out using variety of AChE sources like pig, rat and monkey. Investigations on species differences provide a better insight for the development of new reactivators. Hence, present study was mainly targeted on comparative analysis of the reactivation of electric eel and human AChE inhibited by different OP. A series of butene-linked bis-pyridinium mono oximes which vary in functional groups present at the second pyridinium ring have been examined against sarin, VX, tabun and ethyl-paraoxon-poisoned AChE. In case of tabun-inhibited AChEs, tested oximes were better than reference oximes. For VX-poisoned human AChE, reactivator K251 (kr2;1.51 mM (-) (1 )min (-) (1)) showed good reactivation efficacy with standard oximes. Studies stipulated that butene-linked oximes consisting of different functional moieties are good reactivators and found to have better efficacy to reactivate nerve agent-inhibited human AChE in comparison to eel AChE. PMID:27101948 6. Acute toxicity of a commercial glyphosate formulation on European sea bass juveniles (Dicentrarchus labrax L.): gene expressions of heme oxygenase-1 (ho-1), acetylcholinesterase (AChE) and aromatases (cyp19a and cyp19b). PubMed Prevot-D'Alvise, N; Richard, S; Coupé, S; Bunet, R; Grillasca, J P 2013-12-31 Acute toxicity of Roundup, a commercial glyphosate--based herbicide, was evaluated in a teleost marine fish, the European sea bass, after 96 h of exposure. The LC50 96-h value of Roundup was 529 mg/L. Juveniles (Dicentrarchus labrax L.) were exposed to a sublethal concentration (35% of the LC50, i.e. 193 mg/L) of Roundup for 96-h. The study of heme oxygenase-1 (ho-1) gene expression was performed in four tissues (liver, gills, brain and gonads) and highlighted the disruption of antioxidant defence system. Results showed that ho-1 mRNA levels in liver and gills significantly decreased (p<0.001 and p<0.01 respectively) in fish exposed to 193 mg/L of Roundup, whereas in brain and gonads, ho-1 mRNA level was not altered. The analysis of acetylcholinesterase expression was used to evaluate the overall neurotoxicity of the herbicide and aromatase genes to assess the alteration of the endocrine system. Results showed that AChE and cyp19b gene transcriptions significantly increased (p<0.01) in brain of sea bass, whereas aromatase gene expression (cyp19a) in gonads was not significantly altered. Our results showed complex tissue-specific transcriptional responses after 96 h of exposure to a sublethal concentration. All these disruptions confirmed the deleterious effects of this glyphosate-based herbicide in a marine species. PubMed Sánchez-Osuna, María; Yuste, Victor J 2015-06-01 DNA hydrolysis is a biochemical process often associated with different forms of cell death, including apoptosis. In a recent paper published in Cell Discovery, Du et al. report that synaptic acetylcholinesterase (AChE-S) shows an unexpected enzymatic activity as DNase switched on after cytotoxic insults. PMID:25930710 8. AOP description: Acetylcholinesterase inhibition EPA Science Inventory This adverse outcome pathway (AOP) leverages existing knowledge in the open literature to describe the linkage between inhibition of acetylcholinesterase (AChE) and the subsequent mortality resulting from impacts at cholinergic receptors. The AOP takes a chemical category approa... 9. Reactivation of nerve agent-inhibited human acetylcholinesterase by obidoxime, HI-6 and obidoxime+HI-6: Kinetic in vitro study with simulated nerve agent toxicokinetics and oxime pharmacokinetics. PubMed Worek, Franz; Koller, Marianne; Thiermann, Horst; Wille, Timo 2016-03-28 Despite extensive research for decades no effective broad-spectrum oxime for the treatment of poisoning by a broad range of nerve agents is available. Previous in vitro and in vivo data indicate that the combination of in service oximes could be beneficial. To investigate the ability of obidoxime, HI-6 and the combination of both oximes to reactivate inhibited human AChE in the presence of sarin, cyclosarin or tabun we adopted a dynamic in vitro model with real-time and continuous determination of AChE activity to simulate inhalation nerve agent exposure and intramuscular oxime administration. The major findings of this kinetic study are that the extent and velocity of reactivation is dependent on the nerve agent and the oxime-specific reactivating potency. The oxime-induced reactivation of inhibited human AChE in the presence of nerve agents is markedly impaired and the combination of obidoxime and HI-6 had no additive effect but could broaden the spectrum. In conclusion, these data indicate that a combination of obidoxime and HI-6 would be beneficial for the treatment of poisoning by a broad spectrum of nerve agents and could present an interim solution until more effective and broad-spectrum reactivators are available. 10. Role of acetylcholinesterase in lung cancer PubMed Central Xi, Hui-Jun; Wu, Ren-Pei; Liu, Jing-Jing; Zhang, Ling-Juan; Li, Zhao-Shen 2015-01-01 Acetylcholinesterase (AChE) plays a key role in catalytic hydrolysis of cholinergic neurotransmitters. Intensive research has proven the involvement of this protein in novel functions, such as cell adhesion, differentiation, and proliferation. In addition, several recent studies have indicated that acetylcholinesterase is potentially a marker and regulator of apoptosis. Importantly, AChE is also a promising tumor suppressor. In this review, we briefly summarize the involvement of AChE in apoptosis and cancer, focusing on the role of AChE in lung cancer, as well as the therapeutic consideration of AChE for cancer therapy. PMID:26273392 11. Reactivation of organophosphate-inhibited human, Cynomolgus monkey, swine and guinea pig acetylcholinesterase by MMB-4: A modified kinetic approach SciTech Connect Worek, Franz; Wille, Timo; Aurbek, Nadine; Eyer, Peter; Thiermann, Horst 2010-12-15 Treatment of poisoning by highly toxic organophosphorus compounds (OP, nerve agents) is a continuous challenge. Standard treatment with atropine and a clinically used oxime, obidoxime or pralidoxime is inadequate against various nerve agents. For ethical reasons testing of oxime efficacy has to be performed in animals. Now, it was tempting to investigate the reactivation kinetics of MMB-4, a candidate oxime to replace pralidoxime, with nerve agent-inhibited acetylcholinesterase (AChE) from human and animal origin in order to provide a kinetic basis for the proper assessment of in vivo data. By applying a modified kinetic approach, allowing the use of necessary high MMB-4 concentrations, it was possible to determine the reactivation constants with sarin-, cyclosarin-, VX-, VR- and tabun-inhibited AChE. MMB-4 exhibited a high reactivity and low affinity towards OP-inhibited AChE, except of tabun-inhibited enzyme where MMB-4 had an extremely low reactivity. Species differences between human and animal AChE were low (Cynomolgus) to moderate (swine, guinea pig). Due to the high reactivity of MMB-4 a rapid reactivation of inhibited AChE can be anticipated at adequate oxime concentrations which are substantially higher compared to HI-6. Additional studies are necessary to determine the in vivo toxicity, tolerability and pharmacokinetics of MMB-4 in humans in order to enable a proper assessment of the value of this oxime as an antidote against nerve agent poisoning. 12. Inhibition of acetylcholinesterase activity by essential oil from Citrus paradisi. PubMed Miyazawa, M; Tougo, H; Ishihara, M 2001-01-01 Inhibition of acetylcholinesterase (AChE) activity by essential oils of Citrus paradisi (grapefruit pink in USA) was studied. Inhibition of AChE was measured by the colorimetric method. Nootkatone and auraptene were isolated from C. paradisi oil and showed 17-24% inhibition of AChE activity at the concentration of 1.62 microg/mL. PMID:11858553 13. Russian VX: inhibition and reactivation of acetylcholinesterase compared with VX agent. PubMed Kuca, Kamil; Jun, Daniel; Cabal, Jiri; Hrabinova, Martina; Bartosova, Lucie; Opletalova, Veronika 2006-04-01 Organophosphorus compounds such as nerve agents inhibit, practically irreversibly, cholinesterases by their phosphorylation in the active site of these enzymes. Current antidotal treatment used in the case of acute nerve agent intoxications consists of combined administration of anticholinergic drug (usually atropine) and acetylcholinesterase (AChE, EC 3.1.1.7) reactivator (HI-6, obidoxime, pralidoxime), which from a chemical view is a derivative from the group of pyridinium or bispyridinium aldoximes (commonly called "oxime"). Oximes counteract acetylcholine increase, resulting from AChE inhibition. In the human body environment these compounds are powerful nucleophiles and are able to break down the bond between AChE and nerve agent molecule. This process leads to renewal of enzyme functionality -- to its reactivation. The usefulness of oxime in the reactivation process depends on its chemical structure and on the nerve agent whereby AChE is inhibited. Due to this fact, selection of suitable reactivator in the treatment of intoxications is very important. In our work, we have compared differences in the in vitro inhibition potency of VX and Russian VX on rat, pig and human brain, and subsequently we have tested reactivation of rat brain cholinesterase inhibited by these agents using oxime HI-6, obidoxime, pralidoxime, trimedoxime and methoxime. The results showed that no major differences in the reactivation process of both VX and Russian VX-inhibited cholinesterase. The similarity in reactivation was caused by analogous chemical structure of either nerve agent; and that oxime HI-6 seems to be the most effective reactivator tested, which confirms that HI-6 is currently the most potent reactivator of AChE inhibited by nerve agents. The results obtained in our study should be considered in the future development of new AChE reactivators. 14. Genetic factors potentially reducing fitness cost of organophosphate-insensitive acetylcholinesterase(s) in Rhipicephalus (Boophilus) microplus (Acari: Ixodidae) Technology Transfer Automated Retrieval System (TEKTRAN) Acaricidal activity of organophosphate (OP) and carbamate acaricides is believed to result from inhibition of acetylcholinesterase (AChE). Previous studies in Rhipicephalus (Boophilus) microplus demonstrated the presence of three presumptive AChE genes (BmAChEs). Biochemical characterization of re... 15. Mechanism-Based Analysis of Acetylcholinesterase Inhibitory Potency of Organophosphates, Carbamates, and Their Analogs EPA Science Inventory Acetylcholinesterase (AChE) is a key enzyme in the nervous system of animals, terminating impulse transmission by rapid hydrolysis of the neurotransmitter acetylcholine. Organophosphate (OP) and carbamate esters can inhibit acetylcholinesterase (AChE) by binding covalently to a s... 16. Efforts toward treatments against aging of organophosphorus-inhibited acetylcholinesterase. PubMed Zhuang, Qinggeng; Young, Amneh; Callam, Christopher S; McElroy, Craig A; Ekici, Özlem Dogan; Yoder, Ryan J; Hadad, Christopher M 2016-06-01 Aging is a dealkylation reaction of organophosphorus (OP)-inhibited acetylcholinesterase (AChE). Despite many studies to date, aged AChE cannot be reactivated directly by traditional pyridinium oximes. This review summarizes strategies that are potentially valuable in the treatment against aging in OP poisoning. Among them, retardation of aging seeks to lower the rate of aging through the use of AChE effectors. These drugs should be administered before AChE is completely aged. For postaging treatment, realkylation of aged AChE by appropriate alkylators may pave the way for oxime treatment by neutralizing the oxyanion at the active site of aged AChE. The other two strategies, upregulation of AChE expression and introduction of exogenous AChE, cannot resurrect aged AChE but may compensate for lowered active AChE levels by in situ production or external introduction of active AChE. Upregulation of AChE expression can be triggered by some peptides. Sources of exogenous AChE can be whole blood or purified AChE, either from human or nonhuman species. PMID:27327269 17. AChE inhibition: one dominant factor for swimming behavior changes of Daphnia magna under DDVP exposure. PubMed Ren, Zongming; Zhang, Xu; Wang, Xiaoguang; Qi, Pingping; Zhang, Biao; Zeng, Yang; Fu, Rongshu; Miao, Mingsheng 2015-02-01 As a key enzyme that hydrolyzes the neurotransmitter acetylcholine in cholinergic synapses of both vertebrates and invertebrates, acetylcholinesterase (AChE) is strongly inhibited by organophosphates. AChE inhibition may induce the decrease of swimming ability. According to previous research, swimming behavior of different aquatic organisms could be affected by different chemicals, and there is a shortage of research on direct correlation analysis between swimming behavior and biochemical indicators. Therefore, swimming behavior and whole-body AChE activity of Daphnia magna under dichlorvos (DDVP) exposure were identified in order to clarify the relationship between behavioral responses and AChE inhibition in this study. In the beginning, AChE activity was similar in all treatments with the control. During all exposures, the tendency of AChE activity inhibition was the same as the behavioral responses of D. magna. The AChE activity of individuals without movement would decrease to about zero in several minutes. The correlation analysis between swimming behavior of D. magna and AChE activity showed that the stepwise behavioral response was mainly decided by AChE activity. All of these results suggested that the toxicity characteristics of DDVP as an inhibitor of AChE on the swimming behavior of organisms were the same, and the AChE activity inhibition could induce loss of the nerve conduction ability, causing hyperactivity, loss of coordination, convulsions, paralysis and other kinds of behavioral changes, which was illustrated by the stepwise behavioral responses under different environmental stresses. 18. Acetylcholinesterases of Blood-feeding Flies and Ticks Technology Transfer Automated Retrieval System (TEKTRAN) Acetylcholinesterase (AChE) is the biochemical target of organophosphate (OP) and carbamate pesticides for invertebrates, vertebrate nerve agents, and AChE inhibitors used to reduce effects of Alzheimer’s disease. Organophosphate pesticides (OPs) are widely used to control blood-feeding arthropods, ... 19. Introducing Dynamic Combinatorial Chemistry: Probing the Substrate Selectivity of Acetylcholinesterase ERIC Educational Resources Information Center Angelin, Marcus; Larsson, Rikard; Vongvilai, Pornrapee; Ramstrom, Olof 2010-01-01 In this laboratory experiment, college students are introduced to dynamic combinatorial chemistry (DCC) and apply it to determine the substrate selectivity of acetylcholinesterase (AChE). Initially, the students construct a chemical library of dynamically interchanging thioesters and thiols. Then, AChE is added and allowed to select and hydrolyze… 20. Acetylcholinesterase inhibition by flavonoids from Agrimonia pilosa. PubMed Jung, Mankil; Park, Moonso 2007-09-03 In a bioassay-guided search for acetylcholinesterase (AChE) inhibitors from 180 medicinal plants, an ethyl acetate extract of whole plants of Agrimonia pilosa ledeb yielded tiliroside (1), 3-methoxy quercetin (2), quercitrin (3) and quercetin (4). We report herein for the first time that all four flavonol compounds showed significant inhibitory effects on AChE, particularly quercetin (4), which showed twice the activity of dehydroevodiamine (DHED). 1. Overexpression of acetylcholinesterase gene in rice results in enhancement of shoot gravitropism. PubMed Yamamoto, Kosuke; Shida, Satoshi; Honda, Yoshihiro; Shono, Mariko; Miyake, Hiroshi; Oguri, Suguru; Sakamoto, Hikaru; Momonoki, Yoshie S 2015-09-25 Acetylcholine (ACh), a known neurotransmitter in animals and acetylcholinesterase (AChE) exists widely in plants, although its role in plant signal transduction is unclear. We previously reported AChE in Zea mays L. might be related to gravitropism based on pharmacological study using an AChE inhibitor. Here we clearly demonstrate plant AChE play an important role as a positive regulator in the gravity response of plants based on a genetic study. First, the gene encoding a second component of the ACh-mediated signal transduction system, AChE was cloned from rice, Oryza sativa L. ssp. Japonica cv. Nipponbare. The rice AChE shared high homology with maize, siratro and Salicornia AChEs. Similar to animal and other plant AChEs, the rice AChE hydrolyzed acetylthiocholine and propionylthiocholine, but not butyrylthiocholine. Thus, the rice AChE might be characterized as an AChE (E.C.3.1.1.7). Similar to maize and siratro AChEs, the rice AChE exhibited low sensitivity to the AChE inhibitor, neostigmine bromide, compared with the electric eel AChE. Next, the functionality of rice AChE was proved by overexpression in rice plants. The rice AChE was localized in extracellular spaces of rice plants. Further, the rice AChE mRNA and its activity were mainly detected during early developmental stages (2 d-10 d after sowing). Finally, by comparing AChE up-regulated plants with wild-type, we found that AChE overexpression causes an enhanced gravitropic response. This result clearly suggests that the function of the rice AChE relate to positive regulation of gravitropic response in rice seedlings. PMID:26277389 2. Natural AChE Inhibitors from Plants and their Contribution to Alzheimer’s Disease Therapy PubMed Central Murray, Ana Paula; Faraoni, María Belén; Castro, María Julia; Alza, Natalia Paola; Cavallaro, Valeria 2013-01-01 As acetylcholinesterase (AChE) inhibitors are an important therapeutic strategy in Alzheimer’s disease, efforts are being made in search of new molecules with anti-AChE activity. The fact that naturally-occurring compounds from plants are considered to be a potential source of new inhibitors has led to the discovery of an important number of secondary metabolites and plant extracts with the ability of inhibiting the enzyme AChE, which, according to the cholinergic hypothesis, increases the levels of the neurotransmitter acetylcholine in the brain, thus improving cholinergic functions in patients with Alzheimer’s disease and alleviating the symptoms of this neurological disorder. This review summarizes a total of 128 studies which correspond to the most relevant research work published during 2006-2012 (1st semester) on plant-derived compounds, plant extracts and essential oils found to elicit AChE inhibition. PMID:24381530 3. AChE biosensor based on zinc oxide sol-gel for the detection of pesticides. PubMed Sinha, Ravi; Ganesana, Mallikarjunarao; Andreescu, Silvana; Stanciu, Lia 2010-02-28 Zinc oxide has been used as a matrix for immobilization of acetylcholinesterase (AChE) and detection of the pesticide paraoxon. The immobilized enzyme retained its enzymatic activity up to three months when stored in phosphate buffered saline (pH 7.4) at 4 degrees C. An amperometric biosensor for the detection of paraoxon was designed. The biosensor detected paraoxon in the range 0.035-1.38 ppm and can be used to detect other AChE inhibiting organophosphate pesticides. PMID:20113735 4. Disulfide bonds of acetylcholinesterase SciTech Connect MacPhee-Quigley, K.; Vedvick, T.; Taylor, P.; Taylor, S. 1986-05-01 The positions of the inter- and intrasubunit disulfide bridges were established for the 11S form of acetylcholinesterase (AChE) isolated from Torpedo californica. A major form of AChE localized within the basal lamina of the synapse is a dimensionally asymmetric molecule which contains either two (13S) or three (17S) sets of catalytic subunits linked to collagenous and non-collagenous structural subunits. Limited proteolysis yields a tetramer of catalytic subunits which sediments at 11S. Each catalytic subunit contains 8 cysteine residues. Initially, these Cys residues were identified following trypsin digestion of the reduced protein alkylated with (/sup 14/C)-iodoacetate. Peptides were resolved by gel filtration followed by reverse phase HPLC. To determine the disulfide bonding profile, native non-reduced 11S AChE was treated with a fluorescent, sulfhydryl-specific reagent, monobromobimane, prior to proteolytic digestion. One fluorescent Cys peptide was identified indicating that a single sulfhydryl residue was present in its reduced form. Three pairs of disulfide bonded peptides were identified, sequenced, and localized in the polypeptide chain. The Cys residue that is located in the C-terminal tryptic peptide was disulfide bonded to an identical peptide and thus forms the intersubunit crosslink. Finally, the cysteine positions have been compared with the sequence of the homologous protein, thyroglobulin. Both likely share a common pattern of folding. 5. Altered Levels of Acetylcholinesterase in Alzheimer Plasma PubMed Central García-Ayllón, María-Salud; Riba-Llena, Iolanda; Serra-Basante, Carol; Alom, Jordi; Boopathy, Rathnam; Sáez-Valero, Javier 2010-01-01 Background Many studies have been conducted in an extensive effort to identify alterations in blood cholinesterase levels as a consequence of disease, including the analysis of acetylcholinesterase (AChE) in plasma. Conventional assays using selective cholinesterase inhibitors have not been particularly successful as excess amounts of butyrylcholinesterase (BuChE) pose a major problem. Principal Findings Here we have estimated the levels of AChE activity in human plasma by first immunoprecipitating BuChE and measuring AChE activity in the immunodepleted plasma. Human plasma AChE activity levels were ∼20 nmol/min/mL, about 160 times lower than BuChE. The majority of AChE species are the light G1+G2 forms and not G4 tetramers. The levels and pattern of the molecular forms are similar to that observed in individuals with silent BuChE. We have also compared plasma AChE with the enzyme pattern obtained from human liver, red blood cells, cerebrospinal fluid (CSF) and brain, by sedimentation analysis, Western blotting and lectin-binding analysis. Finally, a selective increase of AChE activity was detected in plasma from Alzheimer's disease (AD) patients compared to age and gender-matched controls. This increase correlates with an increase in the G1+G2 forms, the subset of AChE species which are increased in Alzheimer's brain. Western blot analysis demonstrated that a 78 kDa immunoreactive AChE protein band was also increased in Alzheimer's plasma, attributed in part to AChE-T subunits common in brain and CSF. Conclusion Plasma AChE might have potential as an indicator of disease progress and prognosis in AD and warrants further investigation. PMID:20090844 6. Morphogenic role for acetylcholinesterase in axonal outgrowth during neural development. PubMed Central Bigbee, J W; Sharma, K V; Gupta, J J; Dupree, J L 1999-01-01 Acetylcholinesterase (AChE) is the enzyme that hydrolyzes the neurotransmitter acetylcholine at cholinergic synapses and neuromuscular junctions. However, results from our laboratory and others indicate that AChE has an extrasynaptic, noncholinergic role during neural development. This article is a review of our findings demonstrating the morphogenic role of AChE, using a neuronal cell culture model. We also discuss how these data suggest that AChE has a cell adhesive function during neural development. These results could have additional significance as AChE is the target enzyme of agricultural organophosphate and carbamate pesticides as well as the commonly used household organophosphate chlorpyrifos (Dursban). Prenatal exposure to these agents could have adverse effects on neural development by interfering with the morphogenic function of AChE. Images Figure 1 Figure 2 Figure 4 Figure 5 Figure 6 Figure 7 PMID:10229710 7. Acetylcholinesterase inhibitory properties of some benzoic acid derivatives Yildiz, Melike; Kiliç, Deryanur; Ünver, Yaǧmur; Şentürk, Murat; Askin, Hakan; Küfrevioǧlu, Ömer Irfan 2016-04-01 Acetylcholinesterase (AChE) hydrolyses the neurotransmitter acetylcholine to acetic acid and choline. AChE inhibitors are used in treatment of several neurodegeneartive disorder and Alzheimer's disease. In the present study, inhibition of AChE with some benzoic acid derivatives were investigated. 3-Chloro-benzoic acid (1), 2-hydroxy-5-sulfobenzoic acid (2), 2-(sulfooxy) benzoic acid (3), 2-hydroxybenzoic acid (4), 2,3-dimethoxybenzoic (5), and 3,4,5-trimethoxybenzoic (6) were calculated IC50 values AChE enzyme. Kinetic investigations showed that similarly to AChE inhibitors. Benzoic acid derivatives (1-6) investigated are encouraging agents which may be used as lead molecules in order to derivative novel AChE inhibitors that might be useful in medical applications. 8. Control levels of acetylcholinesterase expression in the mammalian skeletal muscle. PubMed Grubic, Z; Zajc-Kreft, K; Brank, M; Mars, T; Komel, R; Miranda, A F 1999-05-14 Protein expression can be controled at different levels. Understanding acetylcholinesterase (EC. 3.1.1.7, AChE) expression in the living organisms therefore necessitates: (1) determination and mapping of control levels of AChE metabolism; (2) identification of the regulatory factors acting at these levels; and (3) detailed insight into the mechanisms of action of these factors. Here we summarize the results of our studies on the regulation of AChE expression in the mammalian skeletal muscle. Three experimental models were employed: in vitro innervated human muscle, mechanically denervated adult fast rat muscle, and the glucocorticoid treated fast rat muscle. In situ hybridization of AChE mRNA, combined with AChE histochemistry, revealed that different distribution patterns of AChE, observed during in vitro ontogenesis and synaptogenesis of human skeletal muscle, reflect alterations in the distribution of AChE mRNA (Z. Grubic, R. Komel, W.F. Walker, A.F. Miranda, Myoblast fusion and innervation with rat motor nerve alter the distribution of acetylcholinesterase and its mRNA in human muscle cultures, Neuron 14 (1995) 317-327). To study the mechanisms of AChE mRNA loss in denervated adult rat skeletal muscle, we exposed deproteinated AChE mRNA to various subcellular fractions in vitro. Fractions were isolated from the normal and denervated rat sternomastoideus muscle. We found significantly increased, but non-specific AChE mRNA degradation capacities in the three fractions studied, suggesting that increased susceptibility of muscle mRNA to degradation might be at least partly responsible for the decreased AChE mRNA observed under such conditions (K. Zajc-Kreft, S. Kreft, Z. Grubic, Degradation of AChE mRNA in the normal and denervated rat skeletal muscle, Book of Abstracts, The Sixth International Meeting on Cholinesterases, La Jolla, CA, March 20-24, 1998, p. A3.). In adult fast rat muscle, treated chronically with glucocorticoids, we found the fraction of early 9. An in vitro AChE inhibition assay combined with UF-HPLC-ESI-Q-TOF/MS approach for screening and characterizing of AChE inhibitors from roots of Coptis chinensis Franch. PubMed Zhao, Hengqiang; Zhou, Siduo; Zhang, Minmin; Feng, Jinhong; Wang, Shanshan; Wang, Daijie; Geng, Yanling; Wang, Xiao 2016-02-20 In this study, an in vitro acetylcholinesterase (AChE) inhibition assay based on microplate reader combined with ultrafiltration high performance liquid chromatography-electrospray quadrupole time of flight mass (UF-HPLC-ESI-Q-TOF/MS) was developed for the rapid screening and identification of acetylcholinesterase inhibitors (AChEI) from roots of Coptis chinensis Franch. Incubation conditions such as enzyme concentration, incubation time, incubation temperature and co-solvent was optimized so as to get better screening results. Five alkaloids including columbamine, jatrorrhizine, coptisine, palmatine and berberine were found with AChE inhibition activity in the 80% ethanol extract of C. chinensis Franch. The screened compounds were identified by HPLC-DAD-ESI-Q-TOF/MS compared with the reference stands and literatures. The screened results were verified by in vitro AChE inhibition assays, palmatine showed the best AChE inhibitory activities with IC50 values of 36.6μM among the five compounds. Results of the present study indicated that the combinative method using in vitro AChE inhibition assay and UF-HPLC-ESI-Q-TOF/MS could be widely applied for rapid screening and identification of AChEI from complex TCM extract. 10. Analysis of AchE and LDH in mollusc, Lamellidens marginalis after exposure to chlorpyrifos. PubMed Amanullah, B; Stalin, A; Prabu, P; Dhanapal, S 2010-07-01 The enzymes Acetylcholinesterase (AchE) and Lactatedehydrogenase (LDH) are used as biological markers in the present study. Enzymes are highly sensitive and used to evaluate the biological effects of organophosphate pesticide chlorpyrifos in freshwater mussel Lamellidens marginalis. The test organisms were exposed to sub-lethal concentration (5 ppm) of chlorpyrifos for 30 days and allowed to recover for seven days. A distinct reduction of the enzyme AchE (34 +/- 3.3 U l(-1)) was found in the treated hepatopancreas. A significant increase in LDH activity in gill, hepatopancreas and muscle was observed. There was a significant recovery in AchE and LDH in the different tissues, after seven days recovery period.. Hence, the changes in the enzymes are found as the best biomarkering tool to evaluate the effect of organophosphate pesticide chlorpyrifos on the aquatic biota. 11. Esterase detoxification of acetylcholinesterase inhibitors by human or rat liver in vitro EPA Science Inventory Organophosphate (OP) and N-methylcarbamate pesticides inhibit acetylcholinesterase (AChE), but differences in metabolism and detoxification can influence potency of these pesticides across and within species. Carboxylesterase (CaE) and A-esterase (paraoxonase, PON) are considered... 12. Tissue localization of maize acetylcholinesterase associated with heat tolerance in plants PubMed Central Yamamoto, Kosuke; Momonoki, Yoshie S. 2012-01-01 Our recent study reported that maize acetylcholinesterase (AChE) activity in the coleoptile node is enhanced through a post-translational modification response to heat stress and transgenic plants overexpressing maize AChE gene had an elevated heat tolerance, which strongly suggests that maize AChE plays a positive, important role in maize heat tolerance. Here we present (1) maize AChE activity in the mesocotyl also enhances during heat stress and (2) maize AChE mainly localizes in vascular bundles including endodermis and epidermis in coleoptile nodes and mesocotyls of maize seedlings. PMID:22476469 13. Characterisation of acetylcholinesterase release from neuronal cells. PubMed Hicks, David A; Makova, Natalia Z; Nalivaeva, Natalia N; Turner, Anthony J 2013-03-25 Although acetylcholinesterase (AChE) is primarily a hydrolytic enzyme, metabolising the neurotransmitter acetylcholine in cholinergic synapses, it also has some non-catalytic functions in the brain which are far less well characterised. AChE was shown to be secreted or shed from the neuronal cell surface like several other membrane proteins, such as the amyloid precursor protein (APP). Since AChE does not possess a transmembrane domain, its anchorage in the membrane is established via the Proline Rich Membrane Anchor (PRiMA), a transmembrane protein. Both the subunit oligomerisation and membrane anchor of AChE are shared by a related enzyme, butyrylcholinesterase (BChE), the physiological function of which in the brain is unclear. In this work, we have assayed the relative activities of AChE and BChE in membrane fractions and culture medium of three different neuronal cell lines, namely the neuroblastoma cell lines SH-SY5Y and NB7 and the mouse basal forebrain cell line SN56. In an effort to understand the shedding process of AChE, we have used several pharmacological treatments, which showed that it is likely to be mediated in part by an EDTA- and batimastat-sensitive, but GM6001-insensitive metalloprotease, with the possible additional involvement of a thiol isomerase. Cellular release of AChE by SH-SY5Y is significantly enhanced by the muscarinic acetylcholine receptor (mAChR) agonists carbachol or muscarine, with the effect of carbachol blocked by the mAChR antagonist atropine. AChE has been implicated in the pathogenesis of Alzheimer's disease and it has been shown that it accelerates formation and increases toxicity of amyloid fibrils, which have been closely linked to the pathology of AD. In light of this, greater understanding of AChE and BChE physiology may also benefit AD research. 14. Cholinesterases in development: AChE as a firewall to inhibit cell proliferation and support differentiation. PubMed Layer, Paul G; Klaczinski, Janine; Salfelder, Anika; Sperling, Laura E; Thangaraj, Gopenath; Tuschl, Corina; Vogel-Höpker, Astrid 2013-03-25 Acetylcholinesterase (AChE) is a most remarkable protein, not only because it is one of the fastest enzymes in nature, but also since it appears in many molecular forms and is regulated by elaborate genetic networks. AChE is expressed in many tissues during development and in mature organisms, as well as in healthy and diseased states. In search for alternative, "non-classical" functions of cholinesterases (ChEs), AChE could either work within the frame of classic cholinergic systems, but in non-neural tissues ("non-synaptic function"), or act non-enzymatically. Here, we review briefly some of the major ideas and advances of this field, and report on some recent progress from our own experimental work, e.g. that (i) non-neural ChEs have pronounced, predominantly enzymatic effects on early embryonic (limb) development in chick and mouse, that (ii) retinal R28 cells of the rat overexpressing synaptic AChE present a significantly decreased cell proliferation, and that (iii) in developing chick retina ACh-synthesizing and ACh-degrading cells originate from the same postmitotic precursor cells, which later form two locally opposing cell populations. We suggest that such distinct distributions of ChAT(+) vs. AChE(+) cells in the inner half retina provide graded distributions of ACh, which can direct cell differentiation and network formation. Thus, as corroborated by works from many labs, AChE can be considered a highly co-opting protein, which can combine enzymatic and non-enzymatic functions within one molecule. PMID:23047026 15. Synthetic conversion of ACAT inhibitor to acetylcholinesterase inhibitor. PubMed Obata, R; Sunazuka, T; Otoguro, K; Tomoda, H; Harigaya, Y; Omura, S 2000-06-19 Natural product acyl-CoA:cholesterol acyltransferase (ACAT) inhibitor pyripyropene A was synthetically converted to acetylcholinesterase (AChE) inhibitor via heterolitic cleavage of the 2-pyrone ring, followed by gamma-acylation/cyclization with several aroyl chlorides. The 4-pyridyl analogue selectively showed AChE inhibitory activity (IC50 7.9 microM) and no ACAT inhibitory activity IC50 = >1000 microM. PMID:10890154 16. A novel role for synaptic acetylcholinesterase as an apoptotic deoxyribonuclease PubMed Central Du, Aiying; Xie, Jing; Guo, Kaijie; Yang, Lei; Wan, Yihan; OuYang, Qi; Zhang, Xuejin; Niu, Xin; Lu, Lu; Wu, Jun; Zhang, Xuejun 2015-01-01 In addition to terminating neurotransmission by hydrolyzing acetylcholine, synaptic acetylcholinesterase (AChES) has been found to have a pro-apoptotic role. However, the underlying mechanism has rarely been investigated. Here, we report a nuclear translocation-dependent role for AChES as an apoptotic deoxyribonuclease (DNase). AChES polypeptide binds to and cleaves naked DNA at physiological pH in a Ca2+–Mg2+-dependent manner. It also cleaves chromosomal DNA both in pre-fixed and in apoptotic cells. In the presence of a pan-caspase inhibitor, the cleavage still occurred after nuclear translocation of AChES, implying that AChES-DNase acts in a CAD- and EndoG-independent manner. AChE gene knockout impairs apoptotic DNA cleavage; this impairment is rescued by overexpression of the wild-type but not (aa 32–138)-deleted AChES. Furthermore, in comparison with the nuclear-localized wild-type AChES, (aa 32–138)-deleted AChES loses the capacity to initiate apoptosis. These observations confirm that AChES mediates apoptosis via its DNase activity. PMID:27462404 17. Synthesis and in vitro reactivation study of isonicotinamide derivatives of 2-(hydroxyimino)-N-(pyridin-3-yl)acetamide as reactivators of Sarin and VX inhibited human acetylcholinesterase (hAChE). PubMed Karade, Hitendra N; Raviraju, G; Acharya, B N; Valiveti, Aditya Kapil; Bhalerao, Uma; Acharya, Jyotiranjan 2016-09-15 Previously (Karade et al., 2014), we have reported the synthesis and in vitro evaluation of bis-pyridinium derivatives of pyridine-3-yl-(2-hydroxyimino acetamide), as reactivators of sarin and VX inhibited hAChE. Few of the molecules showed superior in vivo protection efficacy (mice model) (Kumar et al., 2014; Swami et al., 2016) in comparison to 2-PAM against DFP and sarin poisoning. Encouraged by these results, herein we report the synthesis and in vitro evaluation of isonicotinamide derivatives of pyridine-3-yl-(2-hydroxyimino acetamide) (4a-4d) against sarin and VX inhibited erythrocyte ghost hAChE. Reactivation kinetics of these compounds was studied and the determined kinetic parameters were compared with that of commercial reactivators viz. 2-PAM and obidoxime. In comparison to 2-PAM and obidoxime, oxime 4a and 4b exhibited enhanced reactivation efficacy toward sarin inhibited hAChE while oxime 4c showed far greater reactivation efficacy toward VX inhibited hAChE. The acid dissociation constant and IC50 values of these oximes were determined and correlated with the observed reactivation potential. PMID:27450532 18. Copper, aluminum, iron and calcium inhibit human acetylcholinesterase in vitro. PubMed Pohanka, Miroslav 2014-01-01 Acetylcholinesterase (AChE) is an important part of cholinergic nerves where it participates in termination of neurotransmission. AChE can be inhibited by e.g. some Alzheimer disease drugs, nerve agents, and secondary metabolites. In this work, metal salts aluminum chloride, calcium chloride, cupric chloride, ferric chloride, potassium chloride, magnesium chloride and sodium chloride were tested for their ability to inhibit AChE. Standard Ellman assay based on human recombinant AChE was done and inhibition was measured using Dixon plot. No inhibition was proved for sodium, potassium and magnesium ions. However, aluminum, cupric, ferric and calcium ions were able to inhibit AChE via noncompetitive mechanism of inhibition. Though the inhibition is much weaker when compared to e.g. drugs with noncompetitive mechanism of action, biological relevance of the findings can be anticipated. PMID:24473150 19. The spectrum of mutations causing end-plate acetylcholinesterase deficiency. PubMed Ohno, K; Engel, A G; Brengman, J M; Shen, X M; Heidenreich, F; Vincent, A; Milone, M; Tan, E; Demirci, M; Walsh, P; Nakano, S; Akiguchi, I 2000-02-01 The end-plate species of acetylcholinesterase (AChE) is an asymmetric enzyme consisting of a collagenic tail subunit composed of three collagenic strands (ColQ), each attached to a tetramer of the T isoform of the catalytic subunit (AChE(T)) via a proline-rich attachment domain. The principal function of the tail subunit is to anchor asymmetric AChE in the synaptic basal lamina. Human end-plate AChE deficiency was recently shown to be caused by mutations in COLQ. We here report nine novel COLQ mutations in 7 patients with end-plate AChE deficiency. We examine the effects of the mutations on the assembly of asymmetric AChE by coexpressing each genetically engineered COLQ mutant with ACHE(T) in COS cells. We classify the newly recognized and previously reported COLQ mutations into four classes according to their position in ColQ and their effect on AChE expression. We find that missense mutations in the proline-rich attachment domain abrogate attachment of catalytic subunits, that truncation mutations in the ColQ collagen domain prevent the assembly of asymmetric AChE, that hydrophobic missense residues in the C-terminal domain prevent triple helical assembly of the ColQ collagen domain, and that other mutations in the C-terminal region produce asymmetric species of AChE that are likely insertion incompetent. PMID:10665486 20. Altered expression of acetylcholinesterase gene in rice results in enhancement or suppression of shoot gravitropism PubMed Central Yamamoto, Kosuke; Sakamoto, Hikaru; Momonoki, Yoshie S. 2016-01-01 ABSTRACT Acetylcholinesterase (AChE), an acetylcholine-hydrolyzing enzyme, exists widely in plants, although its role in plant signal transduction is still unclear. We have hypothesized that the plant AChE regulates asymmetric distribution of hormones and substrates due to gravity stimulus, based on indirect pharmacological experiments using an AChE inhibitor. As a direct evidence for this hypothesis, our recent study has shown that AChE overexpression causes an enhanced gravitropic response in rice seedlings and suggested that the function of the rice AChE relates to the promotion of shoot gravitropism in the seedlings. Here, we report that AChE suppression inhibited shoot gravitropism in rice seedlings, as supportive evidence demonstrating the role of AChE as a positive regulator of shoot gravitropic response in plants. PMID:26979939 1. Acute toxicity and anti acetylcholinesterase potential of some biphenyl derivatives to non target species. PubMed Rahman, M F; Siddiqui, M K; Anjum, F; Qadri, S S; Sidky, M M; Osman, F H 1989-02-01 Five newly synthesised biphenyl derivatives were evaluated for their acute contact toxicity (LC50) against rice weevil and honey bee and anti acetylcholinesterase potential (I50) against honey bee, fish, pigeon and rat. Amongst, O,O-dimethyl-O, p-Nitro-biphenyl phosphate was most potent against rice weevil, whereas p-(4-Nitrophenyl) phenyl-N-methyl carbamate against honey bee. Based on I50 values the biphenyl derivatives of phosphoric acid esters were more potent anti acetylcholinesterase (AChE) agents against rat and fish brain AChE while derivative of carbamic esters towards pigeon brain AChE. The anti AChE potency of both groups appear to be of the same order towards bee head AChE. 2. Complexity of acetylcholinesterases in biting flies and ticks Technology Transfer Automated Retrieval System (TEKTRAN) Acetylcholinesterase (AChE) inhibitors function as pesticides for invertebrates, vertebrate nerve agents, and medicine to reduce cognitive effects of Alzheimer’s disease. Organophosphate (OP) pesticides have been widely used to control biting flies and ticks, however, OP-resistance has compromised c... 3. Protection from the toxicity of diisopropylfluorophosphate by adeno-associated virus expressing acetylcholinesterase SciTech Connect Li Bin; Duysen, Ellen G.; Poluektova, Larisa Y.; Murrin, L. Charles . E-mail: cmurrin@unmc.edu; Lockridge, Oksana . E-mail: olockrid@unmc.edu 2006-07-15 Organophosphorus esters (OP) are highly toxic chemicals used as pesticides and nerve agents. Their acute toxicity is attributed to inhibition of acetylcholinesterase (AChE, EC 3.1.1.7) in nerve synapses. Our goal was to find a new therapeutic for protection against OP toxicity. We used a gene therapy vector, adeno-associated virus serotype 2 (AAV-2), to deliver murine AChE to AChE-/- mice that have no endogenous AChE activity. The vector encoded the most abundant form of AChE: exons 2, 3, 4, and 6. Two-day old animals, with an immature immune system, were injected. AChE delivered intravenously was expressed up to 5 months in plasma, liver, heart, and lung, at 5-15% of the level in untreated wild-type mice. A few mice formed antibodies, but antibodies did not block AChE activity. The plasma AChE was a mixture of dimers and tetramers. AChE delivered intramuscularly had 40-fold higher activity levels than in wild-type muscle. None of the AChE was collagen-tailed. No retrograde transport through the motor neurons to the central nervous system was detected. AChE delivered intrastriatally assembled into tetramers. In brain, the AAV-2 vector transduced neurons, but not astrocytes and microglia. Vector-treated AChE-/- mice lived longer than saline-treated controls. AChE-/- mice were protected from diisopropylfluorophosphate-induced respiratory failure when the vector was delivered intravenously, but not intrastriatally. Since vector-treated animals had no AChE activity in diaphragm muscle, protection from respiratory failure came from AChE in other tissues. We conclude that AChE scavenged OP and in this way protected the activity of butyrylcholinesterase (BChE, EC 3.1.1.8) in motor endplates. 4. Are soluble and membrane-bound rat brain acetylcholinesterase different SciTech Connect Andres, C.; el Mourabit, M.; Stutz, C.; Mark, J.; Waksman, A. ) 1990-11-01 Salt-soluble and detergent-soluble acetylcholinesterases (AChE) from adult rat brain were purified to homogeneity and studied with the aim to establish the differences existing between these two forms. It was found that the enzymatic activities of the purified salt-soluble AChE as well as the detergent-soluble AChE were dependent on the Triton X-100 concentration. Moreover, the interaction of salt-soluble AChE with liposomes suggests amphiphilic behaviour of this enzyme. Serum cholinesterase (ChE) did not bind to liposomes but its activity was also detergent-dependent. Detergent-soluble AChE remained in solution below critical micellar concentrations of Triton X-100. SDS polyacrylamide gel electrophoresis of purified, Biobeads-treated and iodinated detergent-soluble 11 S AChE showed, under non reducing conditions, bands of 69 kD, 130 kD and greater than 250 kD corresponding, respectively, to monomers, dimers and probably tetramers of the same polypeptide chain. Under reducing conditions, only a 69 kD band was detected. It is proposed that an amphiphilic environment stabilizes the salt-soluble forms of AChE in the brain in vivo and that detergent-soluble Biobeads-treated 11 S AChE possess hydrophobic domain(s) different from the 20 kD peptide already described. 5. Active Acetylcholinesterase Immobilization on a Functionalized Silicon Surface. PubMed Khaldi, K; Sam, S; Gouget-Laemmel, A C; Henry de Villeneuve, C; Moraillon, A; Ozanam, F; Yang, J; Kermad, A; Ghellai, N; Gabouze, N 2015-08-01 In this work, we studied the attachment of active acetylcholinesterase (AChE) enzyme on a silicon substrate as a potential biomarker for the detection of organophosphorous (OP) pesticides. A multistep functionalization strategy was developed on a crystalline silicon surface: a carboxylic acid-terminated monolayer was grafted onto a hydrogen-terminated silicon surface by photochemical hydrosilylation, and then AChE was covalently attached through amide bonds using an activation EDC/NHS process. Each step of the modification was quantitatively characterized by ex-situ Fourier transform infrared spectroscopy in attenuated-total-reflection geometry (ATR-FTIR) and atomic force microscopy (AFM). The kinetics of enzyme immobilization was investigated using in situ real-time infrared spectroscopy. The enzymatic activity of immobilized acetylcholinesterase enzymes was determined with a colorimetric test. The surface concentration of active AChE was estimated to be Γ = 1.72 × 10(10) cm(-2). 6. Primary Investigation for the Mechanism of Biatractylolide from Atractylodis Macrocephalae Rhizoma as an Acetylcholinesterase Inhibitor. PubMed Xie, Yong-Chao; Ning, Ning; Zhu, Li; Li, Dan-Ning; Feng, Xing; Yang, Xiao-Ping 2016-01-01 Biatractylolide was isolated from ethyl acetate extract of dried Atractylodis Macrocephalae Rhizoma root by multistep chromatographic processing. Structure of biatractylolide was confirmed by (1)H-NMR and (13)C-NMR. The IC50 on acetylcholinesterase (AChE) activity was 6.5458 μg/mL when the control IC50 value of huperzine A was 0.0192 μg/mL. Molecular Docking Software (MOE) was used to discover molecular sites of action between biatractylolide and AChE protein by regular molecular docking approaches. Moreover, biatractylolide downregulated the expression of AChE of MEF and 293T cells in a dose-dependent manner. These results demonstrated that the molecular mechanisms of inhibitory activities of biatractylolide on AChE are not only through binding to AChE, but also via reducing AChE expression by inhibiting the activity of GSK3β. PMID:27642355 7. Primary Investigation for the Mechanism of Biatractylolide from Atractylodis Macrocephalae Rhizoma as an Acetylcholinesterase Inhibitor PubMed Central Xie, Yong-Chao; Ning, Ning; Zhu, Li; Li, Dan-Ning 2016-01-01 Biatractylolide was isolated from ethyl acetate extract of dried Atractylodis Macrocephalae Rhizoma root by multistep chromatographic processing. Structure of biatractylolide was confirmed by 1H-NMR and 13C-NMR. The IC50 on acetylcholinesterase (AChE) activity was 6.5458 μg/mL when the control IC50 value of huperzine A was 0.0192 μg/mL. Molecular Docking Software (MOE) was used to discover molecular sites of action between biatractylolide and AChE protein by regular molecular docking approaches. Moreover, biatractylolide downregulated the expression of AChE of MEF and 293T cells in a dose-dependent manner. These results demonstrated that the molecular mechanisms of inhibitory activities of biatractylolide on AChE are not only through binding to AChE, but also via reducing AChE expression by inhibiting the activity of GSK3β. 8. Purification and characterization of acetylcholinesterase from desert cobra (Walterinnesia aegyptia) venom. PubMed Duhaiman, A S; Alhomida, A S; Rabbani, N; Kamal, M A; al-Jafari, A A 1996-01-01 Acetylcholinesterase (AChE) has been identified and purified from the venom of desert cobra (W aegyptia) to apparent homogeneity using a TSK G 3000 SW gel filtration column and a Mono Q anion-exchange column. AChE was purified to homogeneity as established by sodium dodecylsulfate/polyacrylamide gel electrophoresis. The specific activity of AChE was 357 IU/mg with acetylthiocholine iodide as substrate. The denatured W aegyptia venom AChE displayed a molecular mass of 67000 +/- 3000 Da suggesting it was a single polypeptide. Isoelectric focusing of AChE revealed that the enzyme exists in different isoforms, with isoelectric points ranging between pH 7.4-7.9. The kinetic parameters (Km and Vmax) and IC50 of AChE inhibition by procaine, tetracaine and physostigmine were investigated in the present study. 9. Oximes: inhibitors of human recombinant acetylcholinesterase. A structure-activity relationship (SAR) study. PubMed Sepsova, Vendula; Karasova, Jana Zdarova; Korabecny, Jan; Dolezal, Rafael; Zemek, Filip; Bennion, Brian J; Kuca, Kamil 2013-08-16 Acetylcholinesterase (AChE) reactivators were developed for the treatment of organophosphate intoxication. Standard care involves the use of anticonvulsants (e.g., diazepam), parasympatolytics (e.g., atropine) and oximes that restore AChE activity. However, oximes also bind to the active site of AChE, simultaneously acting as reversible inhibitors. The goal of the present study is to determine how oxime structure influences the inhibition of human recombinant AChE (hrAChE). Therefore, 24 structurally different oximes were tested and the results compared to the previous eel AChE (EeAChE) experiments. Structural factors that were tested included the number of pyridinium rings, the length and structural features of the linker, and the number and position of the oxime group on the pyridinium ring. 10. Nature: A Substantial Source of Auspicious Substances with Acetylcholinesterase Inhibitory Action PubMed Central Orhan, Ilkay Erdogan 2013-01-01 Acetylcholinesterase (AChE) (EC 3.1.1.7) is an important enzyme that breaks down of acetylcholine in synaptic cleft in neuronal junctions. Inhibition of AChE is associated with treatment of several diseases such as Alzheimer’s disease (AD), myasthenia gravis, and glaucoma as well as the mechanisms of insecticide and anthelmintic drugs. Several AChE inhibitors are available in clinical use currently for the treatment of AD; however, none of them has ability, yet, to seize progress of the disease. Consequently, an extensive research has been going on finding new AChE inhibitors. In this sense, natural inhibitors have gained great attention due to their encouraging effects toward AChE. In this review, promising candidate molecules with marked AChE inhibition from both plant and animal sources will be underlined. PMID:24381529 11. Primary Investigation for the Mechanism of Biatractylolide from Atractylodis Macrocephalae Rhizoma as an Acetylcholinesterase Inhibitor PubMed Central Xie, Yong-Chao; Ning, Ning; Zhu, Li; Li, Dan-Ning 2016-01-01 Biatractylolide was isolated from ethyl acetate extract of dried Atractylodis Macrocephalae Rhizoma root by multistep chromatographic processing. Structure of biatractylolide was confirmed by 1H-NMR and 13C-NMR. The IC50 on acetylcholinesterase (AChE) activity was 6.5458 μg/mL when the control IC50 value of huperzine A was 0.0192 μg/mL. Molecular Docking Software (MOE) was used to discover molecular sites of action between biatractylolide and AChE protein by regular molecular docking approaches. Moreover, biatractylolide downregulated the expression of AChE of MEF and 293T cells in a dose-dependent manner. These results demonstrated that the molecular mechanisms of inhibitory activities of biatractylolide on AChE are not only through binding to AChE, but also via reducing AChE expression by inhibiting the activity of GSK3β. PMID:27642355 12. Altered GPI modification of insect AChE improves tolerance to organophosphate insecticides. PubMed Kakani, Evdoxia G; Bon, Suzanne; Massoulié, Jean; Mathiopoulos, Kostas D 2011-03-01 The olive fruit fly Bactrocera oleae is the most destructive and intractable pest of olives. The management of B. oleae has been based on the use of organophosphate (OP) insecticides, a practice that induced resistance. OP-resistance in the olive fly was previously shown to be associated with two mutations in the acetylcholinesterase (AChE) enzyme that, apparently, hinder the entrance of the OP into the active site. The search for additional mutations in the ace gene that encodes AChE revealed a short deletion of three glutamines (Δ3Q) from a stretch of five glutamines, in the C-terminal peptide that is normally cleaved and substituted by a GPI anchor. We verified that AChEs from B. oleae and other Dipterans are actually GPI-anchored, although this is not predicted by the "big-PI" algorithm. The Δ3Q mutation shortens the unusually long hydrophilic spacer that follows the predicted GPI attachment site and may thus improve the efficiency of GPI anchor addition. We expressed the wild type B. oleae AChE, the natural mutant Δ3Q and a constructed mutant lacking all 5 consecutive glutamines (Δ5Q) in COS cells and compared their kinetic properties. All constructs presented identical K(m) and k(cat) values, in agreement with the fact that the mutations did not affect the catalytic domain of the enzyme. In contrast, the mutants produced higher AChE activity, suggesting that a higher proportion of the precursor protein becomes GPI-anchored. An increase in the number of GPI-anchored molecules in the synaptic cleft may reduce the sensitivity to insecticides. 13. Avarol derivatives as competitive AChE inhibitors, non hepatotoxic and neuroprotective agents for Alzheimer's disease. PubMed Tommonaro, Giuseppina; García-Font, Nuria; Vitale, Rosa Maria; Pejin, Boris; Iodice, Carmine; Cañadas, Sixta; Marco-Contelles, José; Oset-Gasque, María Jesús 2016-10-21 Avarol is a marine sesquiterpenoid hydroquinone, previously isolated from the marine sponge Dysidea avara Schmidt (Dictyoceratida), with antiinflammatory, antitumor, antioxidant, antiplatelet, anti-HIV, and antipsoriatic effects. Recent findings indicate that some thio-avarol derivatives exhibit acetylcholinesterase (AChE) inhibitory activity. The multiple pharmacological properties of avarol, thio-avarol and/or their derivatives prompted us to continue the in vitro screening, focusing on their AChE inhibitory and neuroprotective effects. Due to the complex nature of Alzheimer's disease (AD), there is a renewed search for new, non hepatotoxic anticholinesterasic compounds. This paper describes the synthesis and in vitro biological evaluation of avarol-3'-thiosalicylate (TAVA) and thiosalycil-prenyl-hydroquinones (TPHs), as non hepatotoxic anticholinesterasic agents, showing a good neuroprotective effect on the decreased viability of SHSY5Y human neuroblastoma cells induced by oligomycin A/rotenone and okadaic acid. A molecular modeling study was also undertaken on the most promising molecules within the series to elucidate their AChE binding modes and in particular the role played by the carboxylate group in enzyme inhibition. Among them, TPH4, bearing a geranylgeraniol substituent, is the most significant Electrophorus electricus AChE (EeAChE) inhibitor (IC50 = 6.77 ± 0.24 μM), also endowed with a moderate serum horse butyrylcholinesterase (eqBuChE) inhibitory activity, being also the least hepatotoxic and the best neuroprotective compound of the series. Thus, TPHs represents a new family of synthetic compounds, chemically related to the natural compound avarol, which has been discovered for the potential treatment of AD. Findings prove the relevance of TPHs as a new possible generation of competitive AChE inhibitors pointing out the importance of the salycilic substituents on the hydroquinone ring. Since these compounds do not belong to the class of 14. Avarol derivatives as competitive AChE inhibitors, non hepatotoxic and neuroprotective agents for Alzheimer's disease. PubMed Tommonaro, Giuseppina; García-Font, Nuria; Vitale, Rosa Maria; Pejin, Boris; Iodice, Carmine; Cañadas, Sixta; Marco-Contelles, José; Oset-Gasque, María Jesús 2016-10-21 Avarol is a marine sesquiterpenoid hydroquinone, previously isolated from the marine sponge Dysidea avara Schmidt (Dictyoceratida), with antiinflammatory, antitumor, antioxidant, antiplatelet, anti-HIV, and antipsoriatic effects. Recent findings indicate that some thio-avarol derivatives exhibit acetylcholinesterase (AChE) inhibitory activity. The multiple pharmacological properties of avarol, thio-avarol and/or their derivatives prompted us to continue the in vitro screening, focusing on their AChE inhibitory and neuroprotective effects. Due to the complex nature of Alzheimer's disease (AD), there is a renewed search for new, non hepatotoxic anticholinesterasic compounds. This paper describes the synthesis and in vitro biological evaluation of avarol-3'-thiosalicylate (TAVA) and thiosalycil-prenyl-hydroquinones (TPHs), as non hepatotoxic anticholinesterasic agents, showing a good neuroprotective effect on the decreased viability of SHSY5Y human neuroblastoma cells induced by oligomycin A/rotenone and okadaic acid. A molecular modeling study was also undertaken on the most promising molecules within the series to elucidate their AChE binding modes and in particular the role played by the carboxylate group in enzyme inhibition. Among them, TPH4, bearing a geranylgeraniol substituent, is the most significant Electrophorus electricus AChE (EeAChE) inhibitor (IC50 = 6.77 ± 0.24 μM), also endowed with a moderate serum horse butyrylcholinesterase (eqBuChE) inhibitory activity, being also the least hepatotoxic and the best neuroprotective compound of the series. Thus, TPHs represents a new family of synthetic compounds, chemically related to the natural compound avarol, which has been discovered for the potential treatment of AD. Findings prove the relevance of TPHs as a new possible generation of competitive AChE inhibitors pointing out the importance of the salycilic substituents on the hydroquinone ring. Since these compounds do not belong to the class of 15. Acetylcholinesterase inhibitors and Gulf War illnesses PubMed Central Golomb, Beatrice Alexandra 2008-01-01 Increasing evidence suggests excess illness in Persian Gulf War veterans (GWV) can be explained in part by exposure of GWV to organophosphate and carbamate acetylcholinesterase inhibitors (AChEis), including pyridostigmine bromide (PB), pesticides, and nerve agents. Evidence germane to the relation of AChEis to illness in GWV was assessed. Many epidemiological studies reported a link between AChEi exposure and chronic symptoms in GWV. The link is buttressed by a dose–response relation of PB pill number to chronic symptoms in GWV and by a relation between avidity of AChEi clearance and illness, based on genotypes, concentrations, and activity levels of enzymes that detoxify AChEis. Triangulating evidence derives from studies linking occupational exposure to AChEis to chronic health symptoms that mirror those of ill GWV. Illness is again linked to lower activity of AChEi detoxifying enzymes and genotypes conferring less-avid AChEi detoxification. AChEi exposure satisfies Hill's presumptive criteria for causality, suggesting this exposure may be causally linked to excess health problems in GWV. PMID:18332428 16. Rat brain acetylcholinesterase visualized with [11C]physostigmine. PubMed Planas, A M; Crouzel, C; Hinnen, F; Jobert, A; Né, F; DiGiamberardino, L; Tavitian, B 1994-06-01 Physostigmine, a powerful cholinesterase inhibitor, has recently been labelled with 11C in view of its potential application for in vivo imaging of cerebral acetylcholinesterase (AChE) using positron emission tomography. Here we carried out autoradiography of the rat brain using [11C]physostigmine in order to characterize the cerebral targets of this ligand. Autoradiograms were obtained using phosphor storage plates which, compared to autoradiographic films, greatly improved the quality of 11C images. Following autoradiography, brain sections were stained for AChE activity, allowing a direct comparison of autoradiographic and histoenzymatic localizations. The distributions of 11C label and of AChE activity were found to be essentially super-imposable, both after in vivo injection of and after in vitro incubation with [11C]physostigmine. Densitometric analysis showed that radioactivity and enzymatic activity distributions were regionally correlated. The fixation of [11C]physostigmine to cerebral tissue was abolished after incubation of the rat brain sections with BW 284C51, a specific AChE inhibitor, but not after incubation with iso-OMPA, a specific inhibitor of butyrylcholinesterase. Unilateral excitotoxic lesions of the striatum that eliminated local AChE expression concomitantly reduced the binding of the ligand in the lesioned area. These results indicate that autoradiographic images of the rat brain obtained with [11C]physostigmine reflect AChE distribution, thus supporting the use of this radioligand to trace cerebral AChE activity in humans with positron emission tomography. 17. Molecular Cloning and Characterization of an Acetylcholinesterase cDNA in the Brown Planthopper, Nilaparvata lugens PubMed Central Yang, Zhifan; Chen, Jun; Chen, Yongqin; Jiang, Sijing 2010-01-01 A full cDNA encoding an acetylcholinesterase (AChE, EC 3.1.1.7) was cloned and characterized from the brown planthopper, Nilaparvata lugens Stål (Hemiptera: Delphacidae). The complete cDNA (2467 bp) contains a 1938-bp open reading frame encoding 646 amino acid residues. The amino acid sequence of the AChE deduced from the cDNA consists of 30 residues for a putative signal peptide and 616 residues for the mature protein with a predicted molecular weight of 69,418. The three residues (Ser242, Glu371, and His485) that putatively form the catalytic triad and the six Cys that form intra-subunit disulfide bonds are completely conserved, and 10 out of the 14 aromatic residues lining the active site gorge of the AChE are also conserved. Northern blot analysis of poly(A)+ RNA showed an approximately 2.6-kb transcript, and Southern blot analysis revealed there likely was just a single copy of this gene in N. lugens. The deduced protein sequence is most similar to AChE of Nephotettix cincticeps with 83% amino acid identity. Phylogenetic analysis constructed with 45 AChEs from 30 species showed that the deduced N. lugens AChE formed a cluster with the other 8 insect AChE2s. Additionally, the hypervariable region and amino acids specific to insect AChE2 also existed in the AChE of N. lugens. The results revealed that the AChE cDNA cloned in this work belongs to insect AChE2 subgroup, which is orthologous to Drosophila AChE. Comparison of the AChEs between the susceptible and resistant strains revealed a point mutation, Gly185Ser, is likely responsible for the insensitivity of the AChE to methamidopho in the resistant strain. PMID:20874389 18. Study of Inhibition, Reactivation and Aging Processes of Pesticides Using Graphene Nanosheets/Gold Nanoparticles-Based Acetylcholinesterase Biosensor SciTech Connect Zhang, Lin; Long, Linjuan; Zhang, Weiying; Du, Dan; Lin, Yuehe 2012-09-10 Organophosphate (OP) and carbamate pesticides exert their toxicity via attacking the hydroxyl moiety of serine in the 'active site' of acetylcholinesterase (AChE). In this paper we developed a stable AChE biosensor based on self-assembling AChE to graphene nanosheet (GN)-gold nanoparticles (AuNPs) nanocomposite electrode for investigation of inhibition, reactivation and aging processes of different pesticides. It is confirmed that pesticides can inhibit AChE in a short time. OPs poisoning is treatable with oximes while carbarmates exposure is insensitive to oximes. The proposed electrochemical approach thus provides a new simple tool for comparison of pesticide sensitivity and guide of therapeutic intervention. 19. In silico methods to assist drug developers in acetylcholinesterase inhibitor design. PubMed Bermúdez-Lugo, J A; Rosales-Hernández, M C; Deeb, O; Trujillo-Ferrara, J; Correa-Basurto, J 2011-01-01 Alzheimer's disease (AD) is a neurodegenerative disease characterized by a low acetylcholine (ACh) concentration in the hippocampus and cortex. ACh is a neurotransmitter hydrolyzed by acetylcholinesterase (AChE). Therefore, it is not surprising that AChE inhibitors (AChEIs) have shown better results in the treatment of AD than any other strategy. To improve the effects of AD, many researchers have focused on designing and testing new AChEIs. One of the principal strategies has been the use of computational methods (structural bioinformatics or in silico methods). In this review, we summarize the in silico methods used to enhance the understanding of AChE, particularly at the binding site, to design new AChEIs. Several computational methods have been used, such as docking approaches, molecular dynamics studies, quantum mechanical studies, electronic properties, hindrance effects, partition coefficients (Log P) and molecular electrostatic potentials surfaces, among other physicochemical methods that exhibit quantitative structure-activity relationships. 20. Development of 3D-QSAR model for acetylcholinesterase inhibitors using a combination of fingerprint, molecular docking, and structure-based pharmacophore approaches EPA Science Inventory Acetylcholinesterase (AChE), a serine hydrolase vital for regulating the neurotransmitter acetylcholine in animals, has been used as a target for drugs and pesticides. With the increasing availability of AChE crystal structures, with or without ligands bound, structure-based appr... 1. Development of a 3D-QSAR model for acetylcholinesterase inhibitors using a combination of fingerprint, docking, and structure-based pharmacophore approaches - Conference Abstract EPA Science Inventory Acetylcholinesterase (AChE), a serine hydrolase vital for regulating the neurotransmitter acetylcholine in animals, has been used as a target for drugs and pesticides. With the increasing availability of AChE crystal structures, with or without ligands bound, structure-based appr... 2. [Relation between neural structures possessing acetylcholinesterase activity and the hemomicrocirculatory bed of the fascia of the rat]. PubMed Vshivtseva, V V; Lesova, L D 1986-05-01 By means of Karnovsky--Roots method the nervous apparatus of the hemomicrocirculatory bed has been revealed in the subcutaneous muscle fascia possessing acetylcholinesterase (AChE) activity. Innervational peculiarities in some microvascular branches, bushy pattern of AChE-positive nervous structures have been stated, as well as their uneven distribution along the vessels. 3. Toxicological and Biochemical Characterizations of AChE in Phosalone-Susceptible and Resistant Populations of the Common Pistachio Psyllid, Agonoscena pistaciae PubMed Central 2014-01-01 The toxicological and biochemical characteristics of acetylcholinesterases (AChE) in nine populations of the common pistachio psyllid, Agonoscena pistaciae Burckhardt and Lauterer (Hemiptera: Psyllidae), were investigated in Kerman Province, Iran. Nine A. pistaciae populations were collected from pistachio orchards, Pistacia vera L. (Sapindales: Anacardiaceae), located in Rafsanjan, Anar, Bam, Kerman, Shahrbabak, Herat, Sirjan, Pariz, and Paghaleh regions of Kerman province. The previous bioassay results showed these populations were susceptible or resistant to phosalone, and the Rafsanjan population was most resistant, with a resistance ratio of 11.3. The specific activity of AChE in the Rafsanjan population was significantly higher than in the susceptible population (Bam). The affinity (KM) and hydrolyzing efficiency (Vmax) of AChE on acetylthiocholine iodide, butyrylthiocholine iodide, and propionylthiocholine odide as artificial substrates were clearly lower in the Bam population than that in the Rafsanjan population. These results indicated that the AChE of the Rafsanjan population had lower affinity to these substrates than that of the susceptible population. The higher Vmax value in the Rafsanjan population compared to the susceptible population suggests a possible over expression of AChE in the Rafsanjan population. The in vitro inhibitory effect of several organophosphates and carbamates on AChE of the Rafsanjan and Bam populations was determined. Based on I50, the results showed that the ratios of AChE insensitivity of the resistant to susceptible populations were 23 and 21.7-fold to monocrotophos and phosphamidon, respectively. Whereas, the insensitivity ratios for Rafsanjan population were 0.86, 0.8, 0.78, 0.46, and 0.43 for carbaryl, eserine, propoxur, m-tolyl methyl carbamate, and carbofuran, respectively, suggesting negatively correlated sensitivity to organophosphate-insensitive AChE. Therefore, AChE from the Rafsanjan population showed negatively 4. Toxicological and biochemical characterizations of AChE in phosalone-susceptible and resistant populations of the common pistachio psyllid, Agonoscena pistaciae. PubMed 2014-01-01 The toxicological and biochemical characteristics of acetylcholinesterases (AChE) in nine populations of the common pistachio psyllid, Agonoscena pistaciae Burckhardt and Lauterer (Hemiptera: Psyllidae), were investigated in Kerman Province, Iran. Nine A. pistaciae populations were collected from pistachio orchards, Pistacia vera L. (Sapindales: Anacardiaceae), located in Rafsanjan, Anar, Bam, Kerman, Shahrbabak, Herat, Sirjan, Pariz, and Paghaleh regions of Kerman province. The previous bioassay results showed these populations were susceptible or resistant to phosalone, and the Rafsanjan population was most resistant, with a resistance ratio of 11.3. The specific activity of AChE in the Rafsanjan population was significantly higher than in the susceptible population (Bam). The affinity (K(M)) and hydrolyzing efficiency (Vmax) of AChE on acetylthiocholine iodide, butyrylthiocholine iodide, and propionylthiocholine odide as artificial substrates were clearly lower in the Bam population than that in the Rafsanjan population. These results indicated that the AChE of the Rafsanjan population had lower affinity to these substrates than that of the susceptible population. The higher Vmax value in the Rafsanjan population compared to the susceptible population suggests a possible over expression of AChE in the Rafsanjan population. The in vitro inhibitory effect of several organophosphates and carbamates on AChE of the Rafsanjan and Bam populations was determined. Based on I50, the results showed that the ratios of AChE insensitivity of the resistant to susceptible populations were 23 and 21.7-fold to monocrotophos and phosphamidon, respectively. Whereas, the insensitivity ratios for Rafsanjan population were 0.86, 0.8, 0.78, 0.46, and 0.43 for carbaryl, eserine, propoxur, m-tolyl methyl carbamate, and carbofuran, respectively, suggesting negatively correlated sensitivity to organophosphate-insensitive AChE. Therefore, AChE from the Rafsanjan population showed negatively 5. The Ace locus of Drosophila melanogaster: structural gene for acetylcholinesterase with an unusual 5' leader. PubMed Central Hall, L M; Spierer, P 1986-01-01 The Ace locus of Drosophila melanogaster has been mapped at the molecular level. cDNA clones from the locus have been isolated and their sequence determined, confirming that Ace forms the structural gene for acetylcholinesterase (AChE). The cDNAs have a 1950 nucleotide open reading frame from which the complete amino acid sequence of AChE has been deduced. The Drosophila enzyme is found to have extensive homology to the known sequence of Torpedo AChE. Ace cDNAs have an unusual structure with a long 5' leader and several short upstream open reading frames. Images Fig. 2. PMID:3024971 6. Nanomaterials-based optical techniques for the detection of acetylcholinesterase and pesticides. PubMed Xia, Ning; Wang, Qinglong; Liu, Lin 2015-01-01 The large amount of pesticide residues in the environment is a threat to global health by inhibition of acetylcholinesterase (AChE). Biosensors for inhibition of AChE have been thus developed for the detection of pesticides. In line with the rapid development of nanotechnology, nanomaterials have attracted great attention and have been intensively studied in biological analysis due to their unique chemical, physical and size properties. The aim of this review is to provide insight into nanomaterial-based optical techniques for the determination of AChE and pesticides, including colorimetric and fluorescent assays and surface plasmon resonance. 7. Nanomaterials-Based Optical Techniques for the Detection of Acetylcholinesterase and Pesticides PubMed Central Xia, Ning; Wang, Qinglong; Liu, Lin 2015-01-01 The large amount of pesticide residues in the environment is a threat to global health by inhibition of acetylcholinesterase (AChE). Biosensors for inhibition of AChE have been thus developed for the detection of pesticides. In line with the rapid development of nanotechnology, nanomaterials have attracted great attention and have been intensively studied in biological analysis due to their unique chemical, physical and size properties. The aim of this review is to provide insight into nanomaterial-based optical techniques for the determination of AChE and pesticides, including colorimetric and fluorescent assays and surface plasmon resonance. PMID:25558991 8. Tacrine derivatives-acetylcholinesterase interaction: 1H NMR relaxation study. PubMed Delfini, Maurizio; Di Cocco, Maria Enrica; Piccioni, Fabiana; Porcelli, Fernando; Borioni, Anna; Rodomonte, Andrea; Del Giudice, Maria Rosaria 2007-06-01 Two acetylcholinesterase (AChE) inhibitors structurally related to Tacrine, 6-methoxytacrine (1a) and 9-heptylamino-6-methoxytacrine (1b), and their interaction with Electrophorus Electricus AChE were investigated. The complete assignment of the 1H and 13C NMR spectra of 1a and 1b was performed by mono-dimensional and homo- and hetero-correlated two-dimensional NMR experiments. This study was undertaken to elucidate the interaction modes between AChE and 1a and 1b in solution, using NMR. The interaction between the two inhibitors and AChE was studied by the analysis of the motional parameters non-selective and selective spin-lattice relaxation times, thereby allowing the motional state of 1a and 1b, both free and bound with AChE, to be defined. The relaxation data pointed out the ligands molecular moiety most involved in the binding with AChE. The relevant ligand/enzyme interaction constants were also evaluated for both compounds and resulted to be 859 and 5412M(-1) for 1a and1b, respectively. 9. Evolutionary origin and status of two insect acetylcholinesterases and their structural conservation and differentiation. PubMed Cha, Deok Jea; Lee, Si Hyeock 2015-01-01 Acetylcholinesterase (AChE) plays a pivotal role in synaptic transmission in the cholinergic nervous system of most animals, including insects. Insects possess duplicated AChE gene loci (ace1 vs. ace2) encoding two distinct AChEs (AChE1 and AChE2). A phylogenetic analysis suggested that the last common ancestor of two aces shared its origin with Platyhelminthes. In addition, the ace duplication event likely occurred after the divergence of Protostomian but before the split of Ecdysozoa. The ace1 lineage exhibited a significantly lower evolutionary rate (d and dN/dS ratio) than the ace2 lineage, suggesting that the ace1 lineage has retained the essential function of synaptic transmission following its duplication. Therefore, the putative functional transition from ace1 to ace2 observed in some Hymenopteran insects appears to be a local and relatively recent event. The amino acid sequence comparison and three-dimensional modeling of insect AChEs identified a few consistent differences in the amino acid residues in functionally crucial domains between two AChEs, which are likely responsible for the functional differentiation between two AChEs. A unique amino acid substitution causing a dramatic reduction in the catalytic activity of AChE1 in some Hymenopteran insects was suggested to be responsible for the aforementioned functional transition of ace. 10. Effect of local acetylcholinesterase inhibition on sweat rate in humans NASA Technical Reports Server (NTRS) Shibasaki, M.; Crandall, C. G. 2001-01-01 ACh is the neurotransmitter responsible for increasing sweat rate (SR) in humans. Because ACh is rapidly hydrolyzed by acetylcholinesterase (AChE), it is possible that AChE contributes to the modulation of SR. Thus the primary purpose of this project was to identify whether AChE around human sweat glands is capable of modulating SR during local application of various concentrations of ACh in vivo, as well as during a heat stress. In seven subjects, two microdialysis probes were placed in the intradermal space of the forearm. One probe was perfused with the AChE inhibitor neostigmine (10 microM); the adjacent membrane was perfused with the vehicle (Ringer solution). SR over both membranes was monitored via capacitance hygrometry during microdialysis administration of various concentrations of ACh (1 x 10(-7)-2 M) and during whole body heating. SR was significantly greater at the neostigmine-treated site than at the control site during administration of lower concentrations of ACh (1 x 10(-7)-1 x 10(-3) M, P < 0.05), but not during administration of higher concentrations of ACh (1 x 10(-2)-2 M, P > 0.05). Moreover, the core temperature threshold for the onset of sweating at the neostigmine-treated site was significantly reduced relative to that at the control site. However, no differences in SR were observed between sites after 35 min of whole body heating. These results suggest that AChE is capable of modulating SR when ACh concentrations are low to moderate (i.e., when sudomotor activity is low) but is less effective in governing SR after SR has increased substantially. 11. Surface display and bioactivity of Bombyx mori acetylcholinesterase on Pichia pastoris Technology Transfer Automated Retrieval System (TEKTRAN) To construct the Pichia pastoris (P. pastoris) cell surface display system of Bombyx mori acetylcholinesterase (BmAChE), the gene for the anchor protein (AGa1) was obtained from Saccharomyces cerevisiae and was fused with the modified Bombyx mori acetylcholinesterase gene (bmace) and transformed int... 12. Induction of plasma acetylcholinesterase activity in mice challenged with organophosphorus poisons SciTech Connect Duysen, Ellen G.; Lockridge, Oksana 2011-09-01 The restoration of plasma acetylcholinesterase activity in mice following inhibition by organophosphorus pesticides and nerve agents has been attributed to synthesis of new enzyme. It is generally assumed that activity levels return to normal, are stable and do not exceed the normal level. We have observed over the past 10 years that recovery of acetylcholinesterase activity levels in mice treated with organophosphorus agents (OP) exceeds pretreatment levels and remains elevated for up to 2 months. The most dramatic case was in mice treated with tri-cresyl phosphate and tri-ortho-cresyl phosphate, where plasma acetylcholinesterase activity rebounded to a level 250% higher than the pretreatment activity. The present report summarizes our observations on plasma acetylcholinesterase activity in mice treated with chlorpyrifos, chlorpyrifos oxon, diazinon, tri-ortho-cresyl phosphate, tri-cresyl phosphate, tabun thiocholine, parathion, dichlorvos, and diisopropylfluorophosphate. We have developed a hypothesis to explain the excess acetylcholinesterase activity, based on published observations. We hypothesize that acetylcholinesterase activity is induced when cells undergo apoptosis and that consequently there is a rise in the level of plasma acetylcholinesterase. - Highlights: > Acetylcholinesterase activity is induced by organophosphorus agents. > AChE induction is related to apoptosis. > Induction of AChE activity by OP is independent of BChE. 13. Identification and Biochemical Properties of Two New Acetylcholinesterases in the Pond Wolf Spider (Pardosa pseudoannulata). PubMed Meng, Xiangkun; Li, Chunrui; Xiu, Chunli; Zhang, Jianhua; Li, Jingjing; Huang, Lixin; Zhang, Yixi; Liu, Zewen 2016-01-01 Acetylcholinesterase (AChE), an important neurotransmitter hydrolase in both invertebrates and vertebrates, is targeted by organophosphorus and carbamate insecticides. In this study, two new AChEs were identified in the pond wolf spider Pardosa pseudoannulata, an important predatory natural enemy of several insect pests. In total, four AChEs were found in P. pseudoannulata (including two AChEs previously identified in our laboratory). The new putative AChEs PpAChE3 and PpAChE4 contain most of the common features of the AChE family, including cysteine residues, choline binding sites, the conserved sequence 'FGESAG' and conserved aromatic residues but with a catalytic triad of 'SDH' rather than 'SEH'. Recombinant enzymes expressed in Sf9 cells showed significant differences in biochemical properties compared to other AChEs, such as the optimal pH, substrate specificity, and catalytic efficiency. Among three test substrates, PpAChE1, PpAChE3 and PpAChE4 showed the highest catalytic efficiency (Vmax/KM) for ATC (acetylthiocholine iodide), with PpAChE3 exhibiting a clear preference for ATC based on the VmaxATC/VmaxBTC ratio. In addition, the four PpAChEs were more sensitive to the AChE-specific inhibitor BW284C51, which acts against ATC hydrolysis, than to the BChE-specific inhibitor ISO-OMPA, which acts against BTC hydrolysis, with at least a 8.5-fold difference in IC50 values for each PpAChE. PpAChE3, PpAChE4, and PpAChE1 were more sensitive than PpAChE2 to the tested Carb insecticides, and PpAChE3 was more sensitive than the other three AChEs to the tested OP insecticides. Based on all the results, two new functional AChEs were identified from P. pseudoannulata. The differences in AChE sequence between this spider and insects enrich our knowledge of invertebrate AChE diversity, and our findings will be helpful for understanding the selectivity of insecticides between insects and natural enemy spiders. 14. Identification and Biochemical Properties of Two New Acetylcholinesterases in the Pond Wolf Spider (Pardosa pseudoannulata) PubMed Central Meng, Xiangkun; Li, Chunrui; Xiu, Chunli; Zhang, Jianhua; Li, Jingjing; Huang, Lixin; Zhang, Yixi; Liu, Zewen 2016-01-01 Acetylcholinesterase (AChE), an important neurotransmitter hydrolase in both invertebrates and vertebrates, is targeted by organophosphorus and carbamate insecticides. In this study, two new AChEs were identified in the pond wolf spider Pardosa pseudoannulata, an important predatory natural enemy of several insect pests. In total, four AChEs were found in P. pseudoannulata (including two AChEs previously identified in our laboratory). The new putative AChEs PpAChE3 and PpAChE4 contain most of the common features of the AChE family, including cysteine residues, choline binding sites, the conserved sequence ‘FGESAG’ and conserved aromatic residues but with a catalytic triad of ‘SDH’ rather than ‘SEH’. Recombinant enzymes expressed in Sf9 cells showed significant differences in biochemical properties compared to other AChEs, such as the optimal pH, substrate specificity, and catalytic efficiency. Among three test substrates, PpAChE1, PpAChE3 and PpAChE4 showed the highest catalytic efficiency (Vmax/KM) for ATC (acetylthiocholine iodide), with PpAChE3 exhibiting a clear preference for ATC based on the VmaxATC/VmaxBTC ratio. In addition, the four PpAChEs were more sensitive to the AChE-specific inhibitor BW284C51, which acts against ATC hydrolysis, than to the BChE-specific inhibitor ISO-OMPA, which acts against BTC hydrolysis, with at least a 8.5-fold difference in IC50 values for each PpAChE. PpAChE3, PpAChE4, and PpAChE1 were more sensitive than PpAChE2 to the tested Carb insecticides, and PpAChE3 was more sensitive than the other three AChEs to the tested OP insecticides. Based on all the results, two new functional AChEs were identified from P. pseudoannulata. The differences in AChE sequence between this spider and insects enrich our knowledge of invertebrate AChE diversity, and our findings will be helpful for understanding the selectivity of insecticides between insects and natural enemy spiders. PMID:27337188 15. Identification and Biochemical Properties of Two New Acetylcholinesterases in the Pond Wolf Spider (Pardosa pseudoannulata). PubMed Meng, Xiangkun; Li, Chunrui; Xiu, Chunli; Zhang, Jianhua; Li, Jingjing; Huang, Lixin; Zhang, Yixi; Liu, Zewen 2016-01-01 Acetylcholinesterase (AChE), an important neurotransmitter hydrolase in both invertebrates and vertebrates, is targeted by organophosphorus and carbamate insecticides. In this study, two new AChEs were identified in the pond wolf spider Pardosa pseudoannulata, an important predatory natural enemy of several insect pests. In total, four AChEs were found in P. pseudoannulata (including two AChEs previously identified in our laboratory). The new putative AChEs PpAChE3 and PpAChE4 contain most of the common features of the AChE family, including cysteine residues, choline binding sites, the conserved sequence 'FGESAG' and conserved aromatic residues but with a catalytic triad of 'SDH' rather than 'SEH'. Recombinant enzymes expressed in Sf9 cells showed significant differences in biochemical properties compared to other AChEs, such as the optimal pH, substrate specificity, and catalytic efficiency. Among three test substrates, PpAChE1, PpAChE3 and PpAChE4 showed the highest catalytic efficiency (Vmax/KM) for ATC (acetylthiocholine iodide), with PpAChE3 exhibiting a clear preference for ATC based on the VmaxATC/VmaxBTC ratio. In addition, the four PpAChEs were more sensitive to the AChE-specific inhibitor BW284C51, which acts against ATC hydrolysis, than to the BChE-specific inhibitor ISO-OMPA, which acts against BTC hydrolysis, with at least a 8.5-fold difference in IC50 values for each PpAChE. PpAChE3, PpAChE4, and PpAChE1 were more sensitive than PpAChE2 to the tested Carb insecticides, and PpAChE3 was more sensitive than the other three AChEs to the tested OP insecticides. Based on all the results, two new functional AChEs were identified from P. pseudoannulata. The differences in AChE sequence between this spider and insects enrich our knowledge of invertebrate AChE diversity, and our findings will be helpful for understanding the selectivity of insecticides between insects and natural enemy spiders. PMID:27337188 16. Caffeine inhibits acetylcholinesterase, but not butyrylcholinesterase. PubMed Pohanka, Miroslav; Dobes, Petr 2013-05-08 Caffeine is an alkaloid with a stimulant effect in the body. It can interfere in transmissions based on acetylcholine, epinephrine, norepinephrine, serotonin, dopamine and glutamate. Clinical studies indicate that it can be involved in the slowing of Alzheimer disease pathology and some other effects. The effects are not well understood. In the present work, we focused on the question whether caffeine can inhibit acetylcholinesterase (AChE) and/or, butyrylcholinesterase (BChE), the two enzymes participating in cholinergic neurotransmission. A standard Ellman test with human AChE and BChE was done for altering concentrations of caffeine. The test was supported by an in silico examination as well. Donepezil and tacrine were used as standards. In compliance with Dixon's plot, caffeine was proved to be a non-competitive inhibitor of AChE and BChE. However, inhibition of BChE was quite weak, as the inhibition constant, Ki, was 13.9 ± 7.4 mol/L. Inhibition of AChE was more relevant, as Ki was found to be 175 ± 9 µmol/L. The predicted free energy of binding was -6.7 kcal/mol. The proposed binding orientation of caffeine can interact with Trp86, and it can be stabilize by Tyr337 in comparison to the smaller Ala328 in the case of human BChE; thus, it can explain the lower binding affinity of caffeine for BChE with reference to AChE. The biological relevance of the findings is discussed. 17. Evaluation of the Toxicity, AChE Activity and DNA Damage Caused by Imidacloprid on Earthworms, Eisenia fetida. PubMed Wang, Kai; Qi, Suzhen; Mu, Xiyan; Chai, Tingting; Yang, Yang; Wang, Dandan; Li, Dongzhi; Che, Wunan; Wang, Chengju 2015-10-01 Imidacloprid is a well-known pesticide and it is timely to evaluate its toxicity to earthworms (Eisenia fetida). In the present study, the effect of imidacloprid on reproduction, growth, acetylcholinesterase (AChE) and DNA damage in earthworms was assessed using an artificial soil medium. The median lethal concentration (LC50) and the median number of hatched cocoons (EC50) of imidacloprid to earthworms was 3.05 and 0.92 mg/kg respectively, the lowest observed effect concentration of imidacloprid about hatchability, growth, AChE activity and DNA damage was 0.02, 0.5, 0.1 and 0.5 mg/kg, respectively. 18. Synthesis of aminoalkyl-substituted aurone derivatives as acetylcholinesterase inhibitors. PubMed Lee, Young Hun; Shin, Min Cheol; Yun, Yong Don; Shin, Seo Young; Kim, Jong Min; Seo, Jeong Moo; Kim, Nam-Jung; Ryu, Jong Hoon; Lee, Yong Sup 2015-01-01 Alzheimer's disease (AD), a progressive and neurodegenerative disorder of the brain, is the most common cause of dementia among elderly people. To date, the successful therapeutic strategy to treat AD is maintaining the levels of acetylcholine by inhibiting acetylcholinesterase (AChE). In the present study, aurone derivatives were designed and synthesized as AChE inhibitors based on the lead structure of sulfuretin. Of those synthesized, compound 10d showed ca. 1700-fold and 6-fold higher AChE inhibitory activity than sulfuretin and galantamine, respectively. This compound also ameliorated scopolamine-induced memory deficit in mice when administered orally at the dose of 1 and 2mg/kg. PMID:25468034 19. Effects of acetylcholinesterase gene silencing on its activity in cultured human skeletal muscle. PubMed Mis, Katarina; Mars, Tomaz; Golicnik, Marko; Jevsek, Marko; Grubic, Zoran 2006-01-01 In spite of several reports demonstrating that acetylcholinesterase (AChE [EC 3.1.1.7]) expression is importantly regulated at the level of its mRNA, we still know little about the relationship between AChE mRNA level and the level of mature, catalytically active enzyme in the cell. Better insight into this relationship is, however, essential for our understanding of the molecular pathways underlying AChE synthesis in living cells. We have approached this problem previously (Grubic et al., 1995; Brank et al., 1998; Mis et al., 2003; Jevsek et al., 2004); however, recently introduced small interfering RNA (siRNA) methodology, which allows blockade of gene expression at the mRNA level, opens new possibilities in approaching the AChE mRNA-AChE activity relationship. With this technique one can eliminate AChE mRNA in the cell, specifically and at selected times, and follow the effects of such treatment at the mature enzyme level. In this study we followed AChE activity in siRNA-treated cultured human myoblasts. Our aim was to find out how the temporal profile of the AChE mRNA decrease is reflected at the level of AChE activity under normal conditions and after inhibition of preexisting AChE by diisopropyl phosphorofluoridate (DFP).AChE activity was determined at selected time intervals after siRNA treatment in both myoblast homogenates and in culture medium to follow the effects of siRNA treatment at the level of intracellular AChE synthesis and at the level of AChE secreted from the cell. 20. Acetylcholinesterase triggers the aggregation of PrP 106-126 SciTech Connect Pera, M.; Roman, S.; Ratia, M.; Camps, P.; Munoz-Torrero, D.; Colombo, L.; Manzoni, C.; Salmona, M.; Badia, A.; Clos, M.V. . E-mail: Victoria.Clos@uab.es 2006-07-21 Acetylcholinesterase (AChE), a senile plaque component, promotes amyloid-{beta}-protein (A{beta}) fibril formation in vitro. The presence of prion protein (PrP) in Alzheimer's disease (AD) senile plaques prompted us to assess if AChE could trigger the PrP peptides aggregation as well. Consequently, the efficacy of AChE on the PrP peptide spanning-residues 106-126 aggregation containing a coumarin fluorescence probe (coumarin-PrP 106-126) was studied. Kinetics of coumarin-PrP 106-126 aggregation showed a significant increase of maximum size of aggregates (MSA), which was dependent on AChE concentration. AChE-PrP 106-126 aggregates showed the tinctorial and optical amyloid properties as determined by polarized light and electronic microscopy analysis. A remarkable inhibition of MSA was obtained with propidium iodide, suggesting that AChE triggers PrP 106-126 and A{beta} aggregation through a similar mechanism. Huprines (AChE inhibitors) also significantly decreased MSA induced by AChE as well, unveiling the potential interest for some AChE inhibitors as a novel class of potential anti-prion drugs. 1. Necator americanus secretory acetylcholinesterase and its purification from excretory-secretory products by affinity chromatography. PubMed Pritchard, D I; Leggett, K V; Rogan, M T; McKean, P G; Brown, A 1991-03-01 Acetylcholinesterase (AChE) secretion by adult N. americanus was enhanced in vitro by incorporating insoluble collagen rafts into culture dishes. Enzyme produced in this way had preferential substrate specificity for acetylthiocholine iodide (ATC), and its activity was inhibited by eserine (1.1 x 10(-8) M). Ancylostoma ceylanicum, another hookworm species, failed to produce comparable amounts of AChE in culture. AChE was efficiently purified from culture medium by affinity chromatography on edrophonium sepharose; 81% of the AChE activity was retained by the affinity matrix, although this fraction contained only 4.3% of the protein loaded. Antisera raised against purified AChE in rabbits immunohistochemically stained the oesophageal glands of the parasite, and reacted with molecules of 32, 60, 80, 140 and 220 kDa in reduced adult ES products on Western blotting, although differential activity was observed against worm homogenates and earlier developmental stages. On IEF, purified AChE resolved predominantly with a pl of 3.55; proteins with a similar pl were recognized by rabbit anti-AChE. IgG preparations of this antiserum inhibited AChE activity in ES products, and inhibited AChE secretion by adult worms in culture. The availability of this immunological probe will allow definitive experiments to be conducted on the role of this enigmatic enzyme in the host-parasite relationship. PMID:2052405 2. An acetylcholinesterase biosensor based on graphene-gold nanocomposite and calcined layered double hydroxide. PubMed Zhai, Chen; Guo, Yemin; Sun, Xia; Zheng, Yuhe; Wang, Xiangyou 2014-05-10 In this study, a novel acetylcholinesterase-based biosensor was fabricated. Acetylcholinesterase (AChE) was immobilized onto a glassy carbon electrode (GCE) with the aid of Cu-Mg-Al calcined layered double hydroxide (CLDH). CLDH can provide a bigger effective surface area for AChE loading, which could improve the precision and stability of AChE biosensor. However, the poor electroconductibility of CLDHs could lead to the low sensitivity of AChE biosensor. In order to effectively compensate the disadvantages of CLDHs, graphene-gold nanocomposites were used for improving the electron transfer rate. Thus, the graphene-gold nanocomposite (GN-AuNPs) was firstly modified onto the GCE, and then the prepared CLDH-AChE composite was immobilized onto the modified GCE to construct a sensitive AChE biosensor for pesticides detection. Relevant parameters were studied in detail and optimized, including the pH of the acetylthiocholine chloride (ATCl) solution, the amount of AChE immobilized on the biosensor and the inhibition time governing the analytical performance of the biosensor. The biosensor detected chlorpyrifos at concentrations ranging from 0.05 to 150μg/L. The detection limit for chlorpyrifos was 0.05μg/L. 3. Comparative study on short- and long-term behavioral consequences of organophosphate exposure: relationship to AChE mRNA expression. PubMed López-Granero, Caridad; Cardona, Diana; Giménez, Estela; Lozano, Rafael; Barril, José; Aschner, Michael; Sánchez-Santed, Fernando; Cañadas, Fernando 2014-01-01 Organophosphates (OPs) affect behavior by inhibiting acetylcholinesterase (AChE). While the cognitive short-term effects may be directly attributed to this inhibition, the mechanisms that underlie OP's long-term cognitive effects remain controversial and poorly understood. Accordingly, two experiments were designed to assess the effects of OPs on cognition, and to ascertain whether both the short- and long-term effects of are AChE-dependent. A single subcutaneous dose of 250 mg/kg chlorpyrifos (CPF), 1.5mg/kg diisopropylphosphorofluoridate (DFP) or 15 mg/kg parathion (PTN) was administered to male Wistar rats. Spatial learning was evaluated 72 h or 23 weeks after exposure, and impulsive choice was tested at 10 and 30 weeks following OPs administration (experiment 1 and 2, respectively). Brain soluble and membrane-bound AChE activity, synaptic AChE-S mRNA, read-through AChE-R mRNA and brain acylpeptide hydrolase (APH) activity (as alternative non-cholinergic target) were analyzed upon completion of the behavioral testing (17 and 37 weeks after OPs exposure). Both short- and long-term CPF treatment caused statistically significant effects on spatial learning, while PTN treatment led only to statistically significant short-term effects. Neither CPF, DFP nor PTN affected the long-term impulsivity response. Long-term exposure to CPF and DFP significantly decreased AChE-S and AChE-R mRNA, while in the PTN treated group only AChE-S mRNA levels were decreased. However, after long-term OP exposure, soluble and membrane-bound AChE activity was indistinguishable from controls. Finally, no changes were noted in brain APH activity in response to OP treatment. Taken together, this study demonstrates long-term effects of OPs on AChE-S and AChE-R mRNA in the absence of changes in AChE soluble and membrane-bound activity. Thus, changes in AChE mRNA expression imply non-catalytic properties of the AChE enzyme. 4. Inhibition of acetylcholinesterase in CSF versus brain assessed by 11C-PMP PET in AD patients treated with galantamine. PubMed Darreh-Shori, T; Kadir, A; Almkvist, O; Grut, M; Wall, A; Blomquist, G; Eriksson, B; Långström, B; Nordberg, A 2008-02-01 The relationship between acetylcholinesterase (AChE) activity in the CSF and brain of patients with Alzheimer's disease (AD) was investigated in 18 mild AD patients following galantamine treatment. The first 3 months of the study had a randomized double-blind placebo-controlled design, during which 12 patients received galantamine (16-24 mg/day) and six patients placebo. This was followed by 9 months galantamine treatment in all patients. Activities and protein levels of both the "read-through" AChE (AChE-R) and the synaptic (AChE-S) variants in CSF were assessed in parallel together with the regional brain AChE activity by (11)C-PMP and PET. The AChE-S inhibition was 30-36% in CSF, which correlated well with the in vivo AChE inhibition in the brain. No significant AChE inhibition was observed in the placebo group. The increased level of the AChE-R protein was 16% higher than that of AChE-S. Both the AChE inhibition and the increased level of AChE-R protein positively correlated with the patient's performance in cognitive tests associated with visuospatial ability and attention. In conclusion, AChE levels in CSF closely mirror in vivo brain AChE levels prior to and after treatment with the cholinesterase inhibitors. A positive cognitive response seems to dependent on the AChE inhibition level, which is balanced by an increased protein level of the AChE-R variant in the patients. 5. Acetylcholinesterase is associated with apoptosis in β cells and contributes to insulin-dependent diabetes mellitus pathogenesis. PubMed Zhang, Bao; Yang, Lei; Yu, Luyang; Lin, Bo; Hou, Yanan; Wu, Jun; Huang, Qin; Han, Yifan; Guo, Lihe; Ouyang, Qi; Zhang, Bo; Lu, Lu; Zhang, Xuejun 2012-03-01 Acetylcholinesterase (AChE) expression is pivotal during apoptosis. Indeed, AChE inhibitors partially protect cells from apoptosis. Insulin-dependent diabetes mellitus (IDDM) is characterized in part by pancreatic β-cell apoptosis. Here, we investigated the role of AChE in the development of IDDM and analyzed protective effects of AChE inhibitors. Multiple low-dose streptozotocin (MLD-STZ) administration resulted in IDDM in a mouse model. Western blot analysis, cytochemical staining, and immunofluorescence staining were used to detect AChE expression in MIN6 cells, primary β cells, and apoptotic pancreatic β cells of MLD-STZ-treated mice. AChE inhibitors were administered intraperitoneally to the MLD-STZ mice for 30 days. Blood glucose, plasma insulin, and creatine levels were measured, and glucose tolerance tests were performed. The effects of AChE inhibitors on MIN6 cells were also evaluated. AChE expression was induced in the apoptotic MIN6 cells and primary β cells in vitro and pancreatic islets in vivo when treated with STZ. Induction and progressive accumulation of AChE in the pancreatic islets were associated with apoptotic β cells during IDDM development. The administration of AChE inhibitors effectively decreased hyperglycemia and incidence of diabetes, and restored plasma insulin levels and plasma creatine clearance in the MLD-STZ mice. AChE inhibitors partially protected MIN6 cells from the damage caused by STZ treatment. Induction and accumulation of AChE in pancreatic islets and the protective effects of AChE inhibitors on the onset and development of IDDM indicate a close relationship between AChE and IDDM. 6. Acetylcholinesterase liquid crystal biosensor based on modulated growth of gold nanoparticles for amplified detection of acetylcholine and inhibitor. PubMed Liao, Shuzhen; Qiao, Yanan; Han, Wenting; Xie, Zhaoxia; Wu, Zhaoyang; Shen, Guoli; Yu, Ruqin 2012-01-01 A novel acetylcholinesterase (AChE) liquid crystal (LC) biosensor based on enzymatic growth of gold nanoparticles (Au NPs) has been developed for amplified detection of acetylcholine (ACh) and AChE inhibitor. In this method, AChE mediates the hydrolysis of acetylthiocholine (ATCl) to form thiocholine, and the latter further reduces AuCl(4)(-) to Au NPs without Au nanoseeds. This process, termed biometallization, leads to a great enhancement in the optical signal of the LC biosensor due to the large size of Au NPs, which can greatly disrupt the orientational arrangement of LCs. On the other hand, the hydrolysis of ATCl is inhibited in the presence of ACh or organophosphate pesticides (OPs, a AChE inhibitor), which will decrease the catalytic growth of Au NPs and, as a result, reduce the orientational response of LCs. On the basis of such an inhibition mechanism, the AChE LC biosensor can be used as an effective way to realize the detection of ACh and AChE inhibitors. The results showed that the AChE LC biosensor was highly sensitive to ACh with a detection limit of 15 μmol/L and OPs with a detection limit of 0.3 nmol/L. This study provides a simple and sensitive AChE LC biosensing approach and offers effective signal enhanced strategies for the development of enzyme LC biosensors. PMID:22148672 7. Chlorpyrifos and Chlorpyrifos-Oxon Inhibit Axonal Growth by Interfering with the Morphogenic Activity of Acetylcholinesterase PubMed Central Yang, Dongren; Howard, Angela; Bruun, Donald; Ajua-Alemanj, Mispa; Pickart, Cecile; Lein, Pamela J. 2008-01-01 A primary role of acetylcholinesterase (AChE) is regulation of cholinergic neurotransmission by hydrolysis of synaptic acetylcholine. In the developing nervous system, however, AChE also functions as a morphogenic factor to promote axonal growth. This raises the question of whether organophosphorus pesticides (OPs) that are known to selectively bind to and inactivate the enzymatic function of AChE also interfere with its morphogenic function to perturb axonogenesis. To test this hypothesis, we exposed primary cultures of sensory neurons derived from embryonic rat dorsal root ganglia (DRG) to chlorpyrifos (CPF) or its oxon metabolite (CPFO). Both OPs significantly decreased axonal length at concentrations that had no effect on cell viability, protein synthesis or the enzymatic activity of AChE. Comparative analyses of the effects of CPF and CPFO on axonal growth in DRG neurons cultured from AChE nullizygous (AChE−/−) versus wildtype (AChE+/+) mice indicated that while these OPs inhibited axonal growth in AChE+/+ DRG neurons, they had no effect on axonal growth in AChE−/− DRG neurons. However, transfection of AChE−/− DRG neurons with cDNA encoding full-length AChE restored the wildtype response to the axon inhibitory effects of OPs. These data indicate that inhibition of axonal growth by OPs requires AChE, but the mechanism involves inhibition of the morphogenic rather than enzymatic activity of AChE. These findings suggest a novel mechanism for explaining not only the functional deficits observed in children and animals following developmental exposure to OPs, but also the increased vulnerability of the developing nervous system to OPs. PMID:18076960 8. Esterase detoxification of acetylcholinesterase inhibitors using human liver samples in vitro EPA Science Inventory Organophosphate (OP) and N-methylcarbamate pesticides inhibit acetylcholinesterase (AChE), but differences in metabolism and detoxification can influence potency of these pesticides across and within species. Carboxylesterase (CaE) and A-esterase (paraoxonase, PON1) are consider... 9. Acetylcholinesterase of Haematobia irritans (Diptera: Muscidae): Baculovirus expression, biochemical properties and organophosphate insensitivity Technology Transfer Automated Retrieval System (TEKTRAN) This study reports the baculovirus expression and biochemical characterization of recombinant acetylcholinesterase from Haematobia irritans (L) (rHiAChE) and the effect of the previously described G262A mutation on enzyme activity and sensitivity to selected organophosphates. The rHiAChE was confirm... 10. Inhibition of erythrocyte acetylcholinesterase by n-butanol at high concentrations. PubMed Arsov, Zoran; Zorko, Matjaz; Schara, Milan 2005-05-01 Erythrocyte acetylcholinesterase (AChE) is bound to the membrane by a complex glycosylphosphatidylinositol anchor, so the effect of alcohol on AChE activity may reflect direct and/or membrane-mediated effects. The indication of a direct interaction between n-butanol and AChE molecules is the activation/inhibition of AChE by occupation of the enzyme's active and/or regulatory sites by alcohol. The activation of AChE can occur only at low concentrations of alcohols, while at high concentrations AChE is inhibited. In this work the mechanism of inhibition of erythrocyte AChE by n-butanol at high concentrations was studied. The values of activity, calculated assuming parabolic competitive inhibition, which implies that one or two molecules of inhibitor bind to the enzyme, fit well to the experimental values. From the values of the inhibition constants it was concluded that at high n-butanol concentrations two alcohol molecules usually interact with AChE. PMID:15820219 11. Methionine-choline deprivation alters liver and brain acetylcholinesterase activity in C57BL6 mice. PubMed Vučević, Danijela B; Cerović, Ivana B; Mladenović, Dušan R; Vesković, Milena N; Stevanović, Ivana; Jorgačević, Bojan Z; Ješić Vukićević, Rada; Radosavljević, Tatjana S 2016-07-01 Choline and methionine are precursors of acetylcholine, whose hydrolysis is catalyzed by acetylcholinesterase (AChE). Considering the possibility of their common deficiency, we investigated the influence of methionine-choline deprivation on AChE activity in liver and various brain regions (hypothalamus, hippocampus, cerebral cortex and striatum) in mice fed with methionine-choline deficient (MCD) diet. Male C57BL/6 mice (n = 28) were randomly and equally divided into following groups: control group fed with standard diet for 6 weeks (C) and groups fed with MCD diet for 2 weeks (MCD2), 4 weeks (MCD4) and for 6 weeks (MCD6). After the diet, mice were sacrificied and AChE activity in liver and brain was determined spectrophotometrically. Hepatic AChE activity was higher in MCD2, MCD4 and MCD6 compared to control (p < 0.01), with most prominent increase in MCD6. AChE activity in hypothalamus was higher in MCD4 and MCD6 vs. control (p < 0.05 and p < 0.01, respectively), as well as in MCD6 compared to MCD4 (p < 0.01). In hippocampus, increase in AChE activity was shown in MCD6 compared to control (p < 0.01). In cortex and striatum, increase in AChE activity was noted in MCD6 compared to control (p < 0.05). Our findings indicate the increase of hepatic and brain AChE activity in mice caused by methionine-choline deprivation. 12. Influence of differential expression of acetylcholinesterase in brain and muscle on respiration PubMed Central Boudinot, Eliane; Bernard, Véronique; Camp, Shelley; Taylor, Palmer; Champagnat, Jean; Krejci, Eric; Foutz, Arthur S. 2009-01-01 A mouse strain with a deleted acetylcholinesterase (AChE) gene (AChE knockout) shows a decreased inspiration time and increased tidal volume and ventilation. To investigate the respective roles of AChE in brain and muscle, we recorded respiration by means of whole-body plethysmography in knockout mice with tissue selective deletions in AChE expression. A mouse strain with the anchoring domains of AChE deleted (del E5+6 knockout mice) has very low activity in the brain and neuromuscular junction, but increased monomeric AChE in serum. A mouse strain with deletion of the muscle specific region of AChE (del i1RR knockout mice) exhibits no expression in muscle, but unaltered expression in the central nervous system. Neither strain exhibits the pronounced phenotypic traits observed in the complete AChE knockout strain. A third strain lacking the anchor molecule PRiMA, has no functional AChE and butyrylcholinesterase (BChE) in brain and an unaltered respiratory function. BChE inhibition by bambuterol decreases tidal volume and body temperature in del E5+6 and i1RR knockout strains, but not in PRiMA deletion or wild-type controls. We find that: (1) deletion of the full AChE gene is required for a pronounced alteration in respiratory phenotype, (2) BChE is involved in respiratory muscles contraction and temperature control in del E5+6 and i1RR knockout mice, and (3) AChE expression requiring a gene product splice to either exons 5 and 6 or regulated by intron1 influences temperature control. PMID:18977317 13. Dual inhibition of acetylcholinesterase and butyrylcholinesterase enzymes by allicin PubMed Central Kumar, Suresh 2015-01-01 Objectives: The brain of mammals contains two major form of cholinesterase enzymes, acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE). The dual inhibition of these enzymes is considered as a promising strategy for the treatment of neurological disorder such as Alzheimer's disease (AD), senile dementia, ataxia, and myasthenia gravis. The present study was undertaken to explore the anticholinesterase inhibition property of allicin. Materials and Methods: An assessment of cholinesterase inhibition was carried out by Ellman's assay. Results: The present study demonstrates allicin, a major ingredient of crushed garlic (Allium sativum L.) inhibited both AChE and BuChE enzymes in a concentration-dependent manner. For allicin, the IC50 concentration was 0.01 mg/mL (61.62 μM) for AChE and 0.05 ± 0.018 mg/mL (308.12 μM) for BuChE enzymes. Conclusions: Allicin shows a potential to ameliorate the decline of cognitive function and memory loss associated with AD by inhibiting cholinesterase enzymes and upregulate the levels of acetylcholine (ACh) in the brain. It can be used as a new lead to target AChE and BuChE to upregulate the level of ACh which will be useful in alleviating the symptoms associated with AD. PMID:26288480 14. Perspectives for the structure-based design of acetylcholinesterase reactivators. PubMed Ochoa, Rodrigo; Rodriguez, Carlos A; Zuluaga, Andres F 2016-07-01 Rational design of active molecules through structure-based methods has been gaining adepts during the last decades due to the wider availability of protein structures, most of them conjugated with relevant ligands. Acetylcholinesterase (AChE) is a molecular target with a considerable amount of data related to its sequence and 3-dimensional structure. In addition, there are structural insights about the mechanism of action of the natural substrate and drugs used in Alzheimer's disease, organophosphorus compounds, among others. We looked for AChE structural data useful for in silico design of potential interacting molecules. In particular, we focused on information regarding the design of ligands aimed to reactivate AChE catalytic activity. The structures of 178 AChE were annotated and categorized on different subsets according to the nature of the ligand, source organisms and experimental details. We compared sequence homology among the active site from Torpedo californica, Mus musculus and Homo sapiens with the latter two species having the closest relationship (88.9% identity). In addition, the mechanism of organophosphorus binding and the design of effective reactivators are reviewed. A curated data collection obtained with information from several sources was included for researchers working on the field. Finally, a molecular dynamics simulation with human AChE indicated that the catalytic pocket volume stabilizes around 600 Å(3), providing additional clues for drug design. PMID:27450771 15. Polyproline Tetramer Organizing Peptides in Fetal Bovine Serum Acetylcholinesterase PubMed Central Biberoglu, Kevser; Schopfer, Lawrence M.; Saxena, Ashima; Tacal, Ozden; Lockridge, Oksana 2013-01-01 Acetylcholinesterase (AChE) in the serum of fetal cow is a tetramer. The related enzyme, butyrylcholinesterase (BChE), in the sera of humans and horse requires polyproline peptides for assembly into tetramers. Our goal was to determine whether soluble tetrameric AChE includes tetramer organizing peptides in its structure. Fetal bovine serum AChE was denatured by boiling to release non-covalently bound peptides. Bulk protein was separated from peptides by filtration and by high performance liquid chromatography. Peptide mass and amino acid sequence of the released peptides were determined by MALDI-TOF-TOF and LTQ-Orbitrap mass spectrometry. Twenty polyproline peptides, divided into 5 families, were identified. The longest peptide contained 25 consecutive prolines and no other amino acid. Other polyproline peptides included one non-proline amino acid, for example serine at the C-terminus of 20 prolines. A search of the mammalian proteome database suggested that this assortment of polyproline peptides originated from at least 5 different precursor proteins, none of which were the ColQ or PRiMA of membrane-anchored AChE. To date, AChE and BChE are the only proteins known that include polyproline tetramer organizing peptides in their tetrameric structure. PMID:23352838 16. Acetylcholinesterase of the sand fly, Phlebotomus papatasi (Scopoli): construction, expression and biochemical properties of the G119S orthologous mutant Technology Transfer Automated Retrieval System (TEKTRAN) Phlebotomus papatasi vectors zoonotic cutaneous leishmaniasis, widespread in intertropical and temperate regions of the world. Previous cloning, expression, and biochemical characterization of recombinant P. papatasi acetylcholinesterase 1 (PpAChE1) revealed 85% amino acid sequence identity to mosq... 17. Extracts from Traditional Chinese Medicinal Plants Inhibit Acetylcholinesterase, a Known Alzheimer's Disease Target. PubMed Kaufmann, Dorothea; Kaur Dogra, Anudeep; Tahrani, Ahmad; Herrmann, Florian; Wink, Michael 2016-01-01 Inhibition of acetylcholinesterase (AChE) is a common treatment for early stages of the most general form of dementia, Alzheimer's Disease (AD). In this study, methanol, dichloromethane and aqueous crude extracts from 80 Traditional Chinese Medical (TCM) plants were tested for their in vitro anti-acetylcholinesterase activity based on Ellman's colorimetric assay. All three extracts of Berberis bealei (formerly Mahonia bealei), Coptis chinensis and Phellodendron chinense, which contain numerous isoquinoline alkaloids, substantially inhibited AChE. The methanol and aqueous extracts of Coptis chinensis showed IC50 values of 0.031 µg/mL and 2.5 µg/mL, therefore having an up to 100-fold stronger AChE inhibitory activity than the already known AChE inhibitor galantamine (IC50 = 4.33 µg/mL). Combinations of individual alkaloids berberine, coptisine and palmatine resulted in a synergistic enhancement of ACh inhibition. Therefore, the mode of AChE inhibition of crude extracts of Coptis chinensis, Berberis bealei and Phellodendron chinense is probably due to of this synergism of isoquinoline alkaloids. All extracts were also tested for their cytotoxicity in COS7 cells and none of the most active extracts was cytotoxic at the concentrations which inhibit AChE. Based on these results it can be stated that some TCM plants inhibit AChE via synergistic interaction of their secondary metabolites. The possibility to isolate pure lead compounds from the crude extracts or to administer these as nutraceuticals or as cheap alternative to drugs in third world countries make TCM plants a versatile source of natural inhibitors of AChE. PMID:27589716 18. Functional Analysis and Molecular Docking studies of Medicinal Compounds for AChE and BChE in Alzheimer’s Disease and Type 2 Diabetes Mellitus PubMed Central Kaladhar, Dowluru SVGK; Yarla, Nagendra Sastry; Anusha, N. 2013-01-01 Acetylcholinesterase and Butyrylcholinesterase share unravelling link with components of metabolic syndromes that’s characterised by low levels of HDL cholesterol, obesity, high fast aldohexose levels, hyper-trigliceridaemia and high blood pressure, by regulation of cholinergic transmission and therefore the enzyme activity within a living system. The phosphomotifs associated with amino acid and tyrosine binding motifs in AChE and BChE were known to be common. Phylogenetic tree was constructed to these proteins usinf UPGMA and Maximum Likelihood methods in MEGA software has shown interaction of AChE and BChE with ageing diseases like Alzheimer’s disease and Diabetes. AChE has shown closely related to BChE, retinol dehydrogenase and β-polypeptide. The present studies is also accomplished that AChE, BChE, COLQ, HAND1, APP, NLGN2 and NGF proteins has interactions with diseases such as Alzheimer’s and D2M using Pathwaylinker and STRING. Medicinal compounds like Ortho-7, Dibucaine and HI-6 are predicted as good targets for modeled AChE and BChE proteins based on docking studies. Hence perceptive studies of cholinesterase structure and the biological mechanisms of inhibition are necessary for effective drug development. PMID:23936743 19. Preliminary studies of acetylcholinesterase activity in the rat brain using N-phenylferrocenecarboxamide labelled by the technetium-99m. PubMed Mejri, Najoua; Said, Nadia Malek; Guizani, Sihem; Essouissi, Imen; Saidi, Mouldi 2013-05-01 There is currently great interest in developing radiolabeled substrates for acetylcholinesterase that would be useful in the in vivo imaging of patients with Alzheimer's disease. The reduction of acetylcholinesterase (AChE) activity in the brain has been measured in dementia disorders such as Alzheimer's disease and dementia with Lewy bodies using (11)C and (18)F-labeled acetylcholine analogues. Our aim was to develop a new 99mTc-labeled acetylcholine analogue: N-phenylferrocenecarboxamide labelled with technetium-99m (99mTc-TPCC) to study acetylcholinesterase activity. In vivo and in vitro studies demonstrated that the labelled compound was a substrate for acetylcholinesterase. The hydrolytic rate of this substrate was measured and the specificity was evaluated using the inhibitor BW 284 C51. In rat experiments, the 99mTc-TPCC showed desirable properties for studying the acetylcholinesterase in the rat brain: high hydrolytic rate and a moderate specificity of the substrate for acetylcholinesterase. 20. Status of acetylcholinesterase and butyrylcholinesterase in Alzheimer's disease and type 2 diabetes mellitus. PubMed Mushtaq, Gohar; Greig, Nigel H; Khan, Jalaluddin A; Kamal, Mohammad A 2014-01-01 Both Alzheimer's disease (AD) and Type 2 diabetes mellitus (T2DM) share the presence of systemic and neuro-inflammation, enhanced production and accumulation of β -amyloid peptide and abnormal levels of the enzymes acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE). Altered levels of AChE and BuChE both in AD as well as in T2DM imply that those two enzymes may be playing a pivotal role in the pathogenesis of the two disorders. AD and T2DM are both characterized by elevated levels of AChE and BuChE in the plasma. On the other hand, in AD the brain levels of AChE go down while those of BuChE go up, resulting in deregulation in balance between AChE and BuChE. This imbalance and change in the AChE/BuChE ratio causes cholinergic deficit in the brain, i.e. deficiency in the brain neurotransmitter acetylcholine. With better understanding of the inter-relationship of AChE and BuChE levels in normality as well as abnormality, AD and T2DM can be effectively treated. Thus, general cholinesterase inhibitors that inhibit both AChE and BuChE as well as highly selective BuChE inhibitors may have potential therapeutic benefits in the treatment of AD and other related dementias. 1. [Effect of acetylcholine and acetylcholinesterase on the activity of contractile vacuole of Amoeba proteus]. PubMed Bagrov, Ia Iu; Manusova, N B 2011-01-01 Acetylcholine (ACh, 1 microM) stimulates activity of the contractile vacuole of proteus. The effect of ACh is not mimicked by its analogs which are not hydrolyzed by acetylcholinesterase (AChE), i. e., carbacholine and 5-methylfurmethide. The effect of ACh is not sensitive to the blocking action of M-cholinolytics, atropine and mytolone, but is suppressed by N-cholinolytic, tubocurarine. The inhibitors of AChE, eserine (0.01 microM) and armine (0.1 microM), suppress the effect of ACh on amoeba contractile vacuole. ACh does not affect activation of contractile vacuole induced by arginine-vasopressin (1 microM), but it blocks such effect of opiate receptors agonist, dynorphin A1-13 (0.01 microM). This effect of ACh is also suppressed by the inhibitors of AChE. These results suggest that, in the above-described effects of ACh, AChE acts not as an antagonist, but rather as a synergist. 2. Inhibitory effect of ebselen on cerebral acetylcholinesterase activity in vitro: kinetics and reversibility of inhibition. PubMed Martini, Franciele; Bruning, César Augusto; Soares, Suelen Mendonca; Nogueira, Cristina Wayne; Zeni, Gilson 2015-01-01 Ebselen is a synthetic organoselenium compound that has been considered a potential pharmacological agent with low toxicity, showing antioxidant, anti-inflammatory and neuroprotective effects. It is bioavailable, blood-brain barrier permeant and safe based on cellular toxicity and Phase I-III clinical trials. There is evidence that ebselen inhibits acetylcholinesterase (AChE) activity, an enzyme that plays a key role in the cholinergic system by hydrolyzing acetylcholine (ACh), in vitro and ex vivo. This system has a well-known relationship with cognitive process, and AChE inhibitors, such as donepezil and galantamine, have been used to treat cognitive deficits, mainly in the Alzheimer's Disease (AD). However, these drugs have poor bioavailability and a number of side effects, including gastrointestinal upsets and hepatotoxicity. In this way, this study aimed to evaluate the effect of ebselen on cerebral AChE activity in vitro and to determine the kinetic profile and the reversibility of inhibition by dialysis. Ebselen inhibited the cerebral AChE activity with an IC50 of 29 µM, similar to IC50 found with pure AChE from electric eel, demonstrating a mixed and reversible inhibition of AChE, since it increased Km and decreased Vmax. The AChE activity was recovered within 60 min of dialysis. Therefore, the use of ebselen as a therapeutic agent for treatment of AD should be considered, although memory behavior tasks are needed to support such hypothesis. PMID:25312723 3. Acetylcholinesterase accelerates assembly of amyloid-beta-peptides into Alzheimer's fibrils: possible role of the peripheral site of the enzyme. PubMed Inestrosa, N C; Alvarez, A; Pérez, C A; Moreno, R D; Vicente, M; Linker, C; Casanueva, O I; Soto, C; Garrido, J 1996-04-01 Acetylcholinesterase (AChE), an important component of cholinergic synapses, colocalizes with amyloid-beta peptide (A beta) deposits of Alzheimer's brain. We report here that bovine brain AChE, as well as the human and mouse recombinant enzyme, accelerates amyloid formation from wild-type A beta and a mutant A beta peptide, which alone produces few amyloid-like fibrils. The action of AChE was independent of the subunit array of the enzyme, was not affected by edrophonium, an active site inhibitor, but it was affected by propidium, a peripheral anionic binding site ligand. Butyrylcholinesterase, an enzyme that lacks the peripheral site, did not affect amyloid formation. Furthermore, AChE is a potent amyloid-promoting factor when compared with other A beta-associated proteins. Thus, in addition to its role in cholinergic synapses, AChE may function by accelerating A beta formation and could play a role during amyloid deposition in Alzheimer's brain. 4. Chlorpyrifos and chlorpyrifos-oxon inhibit axonal growth by interfering with the morphogenic activity of acetylcholinesterase SciTech Connect Yang Dongren; Howard, Angela; Bruun, Donald; Ajua-Alemanj, Mispa; Pickart, Cecile; Lein, Pamela J. 2008-04-01 A primary role of acetylcholinesterase (AChE) is regulation of cholinergic neurotransmission by hydrolysis of synaptic acetylcholine. In the developing nervous system, however, AChE also functions as a morphogenic factor to promote axonal growth. This raises the question of whether organophosphorus pesticides (OPs) that are known to selectively bind to and inactivate the enzymatic function of AChE also interfere with its morphogenic function to perturb axonogenesis. To test this hypothesis, we exposed primary cultures of sensory neurons derived from embryonic rat dorsal root ganglia (DRG) to chlorpyrifos (CPF) or its oxon metabolite (CPFO). Both OPs significantly decreased axonal length at concentrations that had no effect on cell viability, protein synthesis or the enzymatic activity of AChE. Comparative analyses of the effects of CPF and CPFO on axonal growth in DRG neurons cultured from AChE nullizygous (AChE{sup -/-}) versus wild type (AChE{sup +/+}) mice indicated that while these OPs inhibited axonal growth in AChE{sup +/+} DRG neurons, they had no effect on axonal growth in AChE{sup -/-} DRG neurons. However, transfection of AChE{sup -/-} DRG neurons with cDNA encoding full-length AChE restored the wild type response to the axon inhibitory effects of OPs. These data indicate that inhibition of axonal growth by OPs requires AChE, but the mechanism involves inhibition of the morphogenic rather than enzymatic activity of AChE. These findings suggest a novel mechanism for explaining not only the functional deficits observed in children and animals following developmental exposure to OPs, but also the increased vulnerability of the developing nervous system to OPs. 5. Selective and Irreversible Inhibitors of Aphid Acetylcholinesterases: Steps Toward Human-Safe Insecticides PubMed Central Pang, Yuan-Ping; Singh, Sanjay K.; Gao, Yang; Lassiter, T. Leon; Mishra, Rajesh K.; Zhu, Kun Yan; Brimijoin, Stephen 2009-01-01 Aphids, among the most destructive insects to world agriculture, are mainly controlled by organophosphate insecticides that disable the catalytic serine residue of acetylcholinesterase (AChE). Because these agents also affect vertebrate AChEs, they are toxic to non-target species including humans and birds. We previously reported that a cysteine residue (Cys), found at the AChE active site in aphids and other insects but not mammals, might serve as a target for insect-selective pesticides. However, aphids have two different AChEs (termed AP and AO), and only AP-AChE carries the unique Cys. The absence of the active-site Cys in AO-AChE might raise concerns about the utility of targeting that residue. Herein we report the development of a methanethiosulfonate-containing small molecule that, at 6.0 µM, irreversibly inhibits 99% of all AChE activity extracted from the greenbug aphid (Schizaphis graminum) without any measurable inhibition of the human AChE. Reactivation studies using β-mercaptoethanol confirm that the irreversible inhibition resulted from the conjugation of the inhibitor to the unique Cys. These results suggest that AO-AChE does not contribute significantly to the overall AChE activity in aphids, thus offering new insight into the relative functional importance of the two insect AChEs. More importantly, by demonstrating that the Cys-targeting inhibitor can abolish AChE activity in aphids, we can conclude that the unique Cys may be a viable target for species-selective agents to control aphids without causing human toxicity and resistance problems. PMID:19194505 6. Highly sensitive electrochemiluminescenc assay of acetylcholinesterase activity based on dual biomarkers using Pd-Au nanowires as immobilization platform. PubMed Ye, Cui; Wang, Min-Qiang; Zhong, Xia; Chen, Shihong; Chai, Yaqin; Yuan, Ruo 2016-05-15 One-dimensional Pd-Au nanowires (Pd-Au NWs) were prepared and applied to fabricate an electrochemiluminescence (ECL) biosensor for the detection of acetylcholinesterase (AChE) activity. Compared with single-component of Pd or Au, the bimetallic nanocomposite of Pd-Au NWs offers a larger surface area for the immobilization of enzyme, and displays superior electrocatalytic activity and efficient electron transport capacity. In the presence of AChE and choline oxidase (ChOx), acetylcholine (ATCl) is hydrolyzed by AChE to generate thiocholine, then thiocholine is catalyzed by ChOx to produce H2O2 in situ, which serves as the coreactant to effectively enhance the ECL intensity in luminol-ECL system. The detection principle is based on the inhibited AChE and reactivated AChE as dual biomarkers, in which AChE was inhibited by organophosphorus (OP) agents, and then reactivated by obidoxime. Such dual biomarkers method can achieve credible evaluation for AChE activity via providing AChE activity before and after reactivation. The liner range for AChE activity detection was from 0.025 U L(-1) to 25 KU L(-1) with a low detection limit down to 0.0083 U L(-1). PMID:26686921 7. A comparative study on the relationship between acetylcholinesterase activity and acute toxicity in Daphnia magna exposed to anticholinesterase insecticides. PubMed Printes, Liane Biehl; Callaghan, Amanda 2004-05-01 Acetylcholinesterase (AChE) activity was measured in Daphnia magna that had been exposed to four organophosphates (OPs; parathion, chlorpyrifos, malathion, and acephate) and one carbamate (propoxur) for 48 h. These results were related to acute toxicity (median effective concentration [EC50] for immobility). For the four OPs, the EC50s were 7.03 pM, 3.17 pM, 10.56 pM, and 309.82 microM, respectively. The EC50 for propoxur was 449.90 pM. Reduction in AChE activity was directly related to an increase in immobility in all chemicals tested. However, the ratio between the EC50 and the AChE median inhibiting concentration ranged from 0.31 to 0.90. A 50% reduction in AChE activity generally was associated with detrimental effects on mobility. However, for acephate, high levels of AChE inhibition (70%) were observed in very low concentrations and were not associated with immobility. In addition, increasing the concentration of acephate further had a slight negative effect on AChE activity but a strong detrimental effect on mobility. Binding sites other than AChE possibly are involved in acephate toxicity to D. magna. Our findings demonstrate different associations between AChE inhibition and toxicity when different chemicals are compared. Therefore, the value of using AChE activity as a biomarker in D. magna will be dependent on the chemical tested. 8. Highly sensitive electrochemiluminescenc assay of acetylcholinesterase activity based on dual biomarkers using Pd-Au nanowires as immobilization platform. PubMed Ye, Cui; Wang, Min-Qiang; Zhong, Xia; Chen, Shihong; Chai, Yaqin; Yuan, Ruo 2016-05-15 One-dimensional Pd-Au nanowires (Pd-Au NWs) were prepared and applied to fabricate an electrochemiluminescence (ECL) biosensor for the detection of acetylcholinesterase (AChE) activity. Compared with single-component of Pd or Au, the bimetallic nanocomposite of Pd-Au NWs offers a larger surface area for the immobilization of enzyme, and displays superior electrocatalytic activity and efficient electron transport capacity. In the presence of AChE and choline oxidase (ChOx), acetylcholine (ATCl) is hydrolyzed by AChE to generate thiocholine, then thiocholine is catalyzed by ChOx to produce H2O2 in situ, which serves as the coreactant to effectively enhance the ECL intensity in luminol-ECL system. The detection principle is based on the inhibited AChE and reactivated AChE as dual biomarkers, in which AChE was inhibited by organophosphorus (OP) agents, and then reactivated by obidoxime. Such dual biomarkers method can achieve credible evaluation for AChE activity via providing AChE activity before and after reactivation. The liner range for AChE activity detection was from 0.025 U L(-1) to 25 KU L(-1) with a low detection limit down to 0.0083 U L(-1). 9. Discovery of New Classes of Compounds that Reactivate Acetylcholinesterase Inhibited by Organophosphates PubMed Central Schneider, Laura; Zhu, Zhengxiang; Ton-That, Long; Luzac, Michal; Zlatanic, Viktor; Damera, Shivani; Macdonald, Joanne; Landry, Donald W.; Tong, Liang; Stojanovic, Milan N. 2015-01-01 Acetylcholinesterase (AChE) that has been covalently inhibited by organophosphate compounds (OPCs), such as nerve agents and pesticides, has traditionally been reactivated by using nucleophilic oximes. There is, however, a clearly recognized need for new classes of compounds with the ability to reactivate inhibited AChE with improved in vivo efficacy. Here we describe our discovery of new functional groups—Mannich phenols and general bases—that are capable of reactivating OPC-inhibited AChE more efficiently than standard oximes and we describe the cooperative mechanism by which these functionalities are delivered to the active site. These discoveries, supported by preliminary in vivo results and crystallographic data, significantly broaden the available approaches for reactivation of AChE. PMID:26350723 10. The herbicide glyphosate is a weak inhibitor of acetylcholinesterase in rats. PubMed Larsen, Karen E; Lifschitz, Adrián L; Lanusse, Carlos E; Virkel, Guillermo L 2016-07-01 The current work evaluated the inhibitory potency of the herbicide glyphosate (GLP) on acetylcholinesterase (AChE) activity in male and female rat tissues. The AChE activity in brain was higher (p<0.05) than those observed in kidney (females: 2.2-fold; males: 1.9-fold), liver (females: 6-fold; males: 6.9-fold) and plasma (females: 14.7-fold; males: 25.3-fold). Enzyme activities were higher in presence of 10mM GLP compared to those measured at an equimolar concentration of the potent AChE inhibitor dichlorvos (DDVP). Moreover, IC50s for GLP resulted between 6×10(4)- and 6.8×10(5)-fold higher than those observed for DDVP. In conclusion, GLP is a weak inhibitor of AChE in rats. PMID:27258137 11. Discovery of Potent Carbonic Anhydrase and Acetylcholinesterase Inhibitors: 2-Aminoindan β-Lactam Derivatives PubMed Central Genç, Hayriye; Kalin, Ramazan; Köksal, Zeynep; Sadeghian, Nastaran; Kocyigit, Umit M.; Zengin, Mustafa; Gülçin, İlhami; Özdemir, Hasan 2016-01-01 β-Lactams are pharmacologically important compounds because of their various biological uses, including antibiotic and so on. β-Lactams were synthesized from benzylidene-inden derivatives and acetoxyacetyl chloride. The inhibitory effect of these compounds was examined for human carbonic anhydrase I and II (hCA I, and II) and acetylcholinesterase (AChE). The results reveal that β-lactams are inhibitors of hCA I, II and AChE. The Ki values of β-lactams (2a–k) were 0.44–6.29 nM against hCA I, 0.93–8.34 nM against hCA II, and 0.25–1.13 nM against AChE. Our findings indicate that β-lactams (2a–k) inhibit both carbonic anhydrases (CA) isoenzymes and AChE at low nanomolar concentrations. PMID:27775608 12. Screening of POP pollution by AChE and EROD activities in Zebra mussels from the Italian Great Lakes. PubMed Binelli, A; Ricciardi, Francesco; Riva, Consuelo; Provini, Alfredo 2005-12-01 The increase of ethoxyresorufin dealkylation (EROD) and the inhibition of acetylcholinesterase (AChE) as biomarkers have been commonly used in vertebrates for the persistent organic pollutants (POPs) biomonitoring of aquatic environments, but very few studies have been performed for invertebrates. Previous researches demonstrated the interference due to some chemicals on EROD and AChE activities of the freshwater bivalve Zebra mussel (Dreissena polymorpha) in laboratory and field studies, showing its possible use for the screening of POP effects. We investigated the contamination of the Italian sub-alpine great lakes (Maggiore, Lugano, Como, Iseo, Garda) by the biomarker approach on Zebra mussel specimens collected at 17 sampling sites with different morphometric characteristics and anthropization levels. Results showed a homogeneous contamination of AChE inhibitors in Lake Garda, Maggiore, Como and Iseo with values ranging from 0.5 to 3 nmol/min/mg proteins and with an average inhibition of about 66% to controls. The planar compounds pollution, able to activate the EROD activity, seems higher in some sampling stations of Lake Garda, Como and Iseo (2-4 pmol/min/mg proteins) than that measured in Lake Lugano (1.5-3 pmol/min/mg proteins). On the contrary, the enzyme activity in Lake Maggiore showed an interesting opposite effect of AhR-binding compounds and trace metals. Finally, the possible use of Zebra mussel specimens maintained at laboratory conditions as controls against the selection of the less polluted sampling site is discussed. 13. Comparison of acetylcholinesterase, pyridostigmine, and HI-6 as antidotes against organophosphorus compounds SciTech Connect Maxwell, D.M.; Brecht, K.M.; Saxena, A.; Taylor, P.; Doctor, B.P. 1995-12-31 Conventional medical treatment against the toxicity of organophosphorus (OP) compounds consists of a regimen of anticholinergic drugs to counteract the accumulation of acetylcholine and oximes to reactivate OP-inhibited acetylcholinesterase (AChE) (Taylor, 1985). Reactivation ofOP-inhibited AChE by oximes can generate enough active AChE in the peripheral nervous system, especially in the diaphragm, to restore normal cholinergic neurotransmission after exposure to many OP compounds. However, some OP compounds, such as soman (pinacolylmdhylphos phonofluofldate), inhibit AChE and rapidly age into a form that cannot be reactivated by oximes (De Jong and Wolring, 1984), thereby reducing the ability of oximes to provide protection (Maxwell and Brecht, 1991). The inability of oximes to provide adequate protection against the toxicity of rapidly aging OP compounds stimulated the development of carbamate pretreatment in which carbamylation of AChE effectively protects it against inhibition by OP compounds (Leadbeater et al., 1985). Spontaneous decarbamylation of AChE after the OP compound has been detoxified then generates enough active AChE to allow normal cholinergic neurotransmission. Behavioral side effects from carbamate pretreatment in the absence of exposure to OP compounds have been avoided by the use of cationic pretreatment carbamates, such as pyridostigmine, which do not enter the central nervous system. 14. Protein-anchoring strategy for delivering acetylcholinesterase to the neuromuscular junction. PubMed Ito, Mikako; Suzuki, Yumi; Okada, Takashi; Fukudome, Takayasu; Yoshimura, Toshiro; Masuda, Akio; Takeda, Shin'ichi; Krejci, Eric; Ohno, Kinji 2012-07-01 Acetylcholinesterase (AChE) at the neuromuscular junction (NMJ) is anchored to the synaptic basal lamina via a triple helical collagen Q (ColQ). Congenital defects of ColQ cause endplate AChE deficiency and myasthenic syndrome. A single intravenous administration of adeno-associated virus serotype 8 (AAV8)-COLQ to Colq(-/-) mice recovered motor functions, synaptic transmission, as well as the morphology of the NMJ. ColQ-tailed AChE was specifically anchored to NMJ and its amount was restored to 89% of the wild type. We next characterized the molecular basis of this efficient recovery. We first confirmed that ColQ-tailed AChE can be specifically targeted to NMJ by an in vitro overlay assay in Colq(-/-) mice muscle sections. We then injected AAV1-COLQ-IRES-EGFP into the left tibialis anterior and detected AChE in noninjected limbs. Furthermore, the in vivo injection of recombinant ColQ-tailed AChE protein complex into the gluteus maximus muscle of Colq(-/-) mice led to accumulation of AChE in noninjected forelimbs. We demonstrated for the first time in vivo that the ColQ protein contains a tissue-targeting signal that is sufficient for anchoring itself to the NMJ. We propose that the protein-anchoring strategy is potentially applicable to a broad spectrum of diseases affecting extracellular matrix molecules. 15. Novel Triazole-Quinoline Derivatives as Selective Dual Binding Site Acetylcholinesterase Inhibitors. PubMed Mantoani, Susimaire P; Chierrito, Talita P C; Vilela, Adriana F L; Cardoso, Carmen L; Martínez, Ana; Carvalho, Ivone 2016-02-05 Alzheimer's disease (AD) is the most prevalent neurodegenerative disorder worldwide. Currently, the only strategy for palliative treatment of AD is to inhibit acetylcholinesterase (AChE) in order to increase the concentration of acetylcholine in the synaptic cleft. Evidence indicates that AChE also interacts with the β-amyloid (Aβ) protein, acting as a chaperone and increasing the number and neurotoxicity of Aβ fibrils. It is known that AChE has two binding sites: the peripheral site, responsible for the interactions with Aβ, and the catalytic site, related with acetylcholine hydrolysis. In this work, we reported the synthesis and biological evaluation of a library of new tacrine-donepezil hybrids, as a potential dual binding site AChE inhibitor, containing a triazole-quinoline system. The synthesis of hybrids was performed in four steps using the click chemistry strategy. These compounds were evaluated as hAChE and hBChE inhibitors, and some derivatives showed IC50 values in the micro-molar range and were remarkably selective towards hAChE. Kinetic assays and molecular modeling studies confirm that these compounds block both catalytic and peripheral AChE sites. These results are quite interesting since the triazole-quinoline system is a new structural scaffold for AChE inhibitors. Furthermore, the synthetic approach is very efficient for the preparation of target compounds, allowing a further fruitful new chemical library optimization. 16. Characterization of acetylcholinesterase in Hong Kong oyster (Crassostrea hongkongensis) from South China Sea. PubMed Zha, Guangcai; Chen, Vicky P; Luk, Wilson K W; Zou, Xianghui; Choi, Roy C Y; Tsim, Karl W K 2013-03-25 Acetylcholinesterase (AChE) activity has been used to evaluate the exposure of mollusk bivalves to organophosphates, carbamate pesticides, and heavy metals. Crassostrea hongkongensis is a Hong Kong endemic oyster, and has a high commercial value along the coastal area of South China. The use of this species as a bio-indicator of the marine environment, and the use of AChE activity measurements in tissues of C. hongkongensis require prior characterization of AChE in this species. Here, we report that gill tissue contains the highest AChE activity in C. hongkongensis, and that the molecular form of AChE is most likely to be a dimeric form. In addition, the effect of the pesticide acephate on AChE activity in the gill of C. hongkongensis was analyzed, and the mean inhibition concentration (IC50) value was determined. This study suggests that AChE activity in the gill tissue of C. hongkongensis might be used as a biomarker in monitoring organophosphate contamination in the marine fauna of South China. 17. Flavoring extracts of Hemidesmus indicus roots and Vanilla planifolia pods exhibit in vitro acetylcholinesterase inhibitory activities. PubMed 2013-09-01 Acetylcholinesterase inhibitors (AChEIs) are important for treatment of Alzheimer's disease and other neurological disorders. Search for potent and safe AChEIs from plant sources still continues. In the present work, we explored fragrant plant extracts that are traditionally used in flavoring foods, namely, Hemidesmus indicus and Vanilla planifolia, as possible sources for AChEI. Root and pod extracts of H. indicus and V. planifolia, respectively, produce fragrant phenolic compounds, 2-hydroxy-4-methoxybenzaldehyde (MBALD) and 4-hydroxy-3-methoxybenzaldehyde (vanillin). These methoxybenzaldehydes were shown to have inhibitory potential against acetylcholinesterase (AChE). Vanillin (IC50 = 0.037 mM) was detected as more efficient inhibitor than MBALD (IC50 = 0.047 mM). This finding was supported by kinetic analysis. Thus, plant-based food flavoring agents showed capacity in curing Alzheimer's disease and other neurological dysfunctions. 18. Intensified vmPFC surveillance over PTSS under perturbed microRNA-608/AChE interaction PubMed Central Lin, T; Simchovitz, A; Shenhar-Tsarfaty, S; Vaisvaser, S; Admon, R; Hanin, G; Hanan, M; Kliper, E; Bar-Haim, Y; Shomron, N; Fernandez, G; Lubin, G; Fruchter, E; Hendler, T; Soreq, H 2016-01-01 Trauma causes variable risk of posttraumatic stress symptoms (PTSS) owing to yet-unknown genome–neuronal interactions. Here, we report co-intensified amygdala and ventromedial prefrontal cortex (vmPFC) emotional responses that may overcome PTSS in individuals with the single-nucleotide polymorphism (SNP) rs17228616 in the acetylcholinesterase (AChE) gene. We have recently shown that in individuals with the minor rs17228616 allele, this SNP interrupts AChE suppression by microRNA (miRNA)-608, leading to cortical elevation of brain AChE and reduced cortisol and the miRNA-608 target GABAergic modulator CDC42, all stress-associated. To examine whether this SNP has effects on PTSS and threat-related brain circuits, we exposed 76 healthy Israel Defense Forces soldiers who experienced chronic military stress to a functional magnetic resonance imaging task of emotional and neutral visual stimuli. Minor allele individuals predictably reacted to emotional stimuli by hyperactivated amygdala, a hallmark of PTSS and a predisposing factor of posttraumatic stress disorder (PTSD). Despite this, minor allele individuals showed no difference in PTSS levels. Mediation analyses indicated that the potentiated amygdala reactivity in minor allele soldiers promoted enhanced vmPFC recruitment that was associated with their limited PTSS. Furthermore, we found interrelated expression levels of several miRNA-608 targets including CD44, CDC42 and interleukin 6 in human amygdala samples (N=7). Our findings suggest that miRNA-608/AChE interaction is involved in the threat circuitry and PTSS and support a model where greater vmPFC regulatory activity compensates for amygdala hyperactivation in minor allele individuals to neutralize their PTSS susceptibility. PMID:27138800 19. Acetylcholinesterase-inhibiting activity of salicylanilide N-alkylcarbamates and their molecular docking. PubMed Imramovsky, Ales; Stepankova, Sarka; Vanco, Jan; Pauk, Karel; Monreal-Ferriz, Juana; Vinsova, Jarmila; Jampilek, Josef 2012-08-24 A series of twenty-five novel salicylanilide N-alkylcarbamates were investigated as potential acetylcholinesterase inhibitors. The compounds were tested for their ability to inhibit acetylcholinesterase (AChE) from electric eel (Electrophorus electricus L.). Experimental lipophilicity was determined, and the structure-activity relationships are discussed. The mode of binding in the active site of AChE was investigated by molecular docking. All the discussed compounds expressed significantly higher AChE inhibitory activity than rivastigmine and slightly lower than galanthamine. Disubstitution by chlorine in C'(₃,₄) of the aniline ring and the optimal length of hexyl-undecyl alkyl chains in the carbamate moiety provided the most active AChE inhibitors. Monochlorination in C'(₄) exhibited slightly more effective AChE inhibitors than in C'(₃). Generally it can be stated that compounds with higher lipophilicity showed higher inhibition, and the activity of the compounds is strongly dependent on the length of the N-alkyl chain. 20. Biochemical and toxicological properties of two acetylcholinesterases from the common bed bug, Cimex lectularius. PubMed Hwang, Chae Eun; Kim, Young Ho; Kwon, Deok Ho; Seong, Keon Mook; Choi, Jae Young; Je, Yeon Ho; Lee, Si Hyeock 2014-03-01 We examined the molecular and enzymatic properties of two acetylcholinesterases (AChEs; ClAChE1 and ClAChE2) from the common bed bug, Cimex lectularius. Native polyacrylamide gel electrophoresis followed by activity staining and Western blotting revealed that ClAChE1 is the main catalytic enzyme and is abundantly expressed in various tissues. Both ClAChEs existed in dimeric form connected by a disulfide bridge and were attached to the membrane via a glycophosphatidylinositol anchor. To determine their kinetic and inhibitory properties, both ClAChE1 and ClAChE2 were in vitro expressed in Sf9 cells using a baculovirus expression system. ClAChE1 showed higher catalytic efficiency toward acetylcholine, supporting the hypothesis that ClAChE1 plays a major role in postsynaptic transmission. An inhibition assay revealed that ClAChE1 is generally more sensitive to organophosphates and carbamates examined although ClAChE2 was >4000-fold more sensitive to malaoxon than ClAChE1. The relatively higher correlation between the in vitro ClAChE1 inhibition and the in vivo toxicity suggested that ClAChE1 is the more relevant toxicological target for organophosphates and carbamates. Although the physiological function of ClAChE2 remains to be elucidated, ClAChE2 also appears to have neuronal functions, as judged by its tissue distribution and molecular and kinetic properties. Our findings help expand our knowledge on insect AChEs and their toxicological properties. PMID:24759047 1. Acetylcholinesterase Activity and Neurodevelopment in Boys and Girls PubMed Central Himes, John H.; Jacobs, David R.; Alexander, Bruce H.; Gunnar, Megan R. 2013-01-01 BACKGROUND: Organophosphate exposures can affect children’s neurodevelopment, possibly due to neurotoxicity induced by acetylcholinesterase (AChE) inhibition, and may affect boys more than girls. We tested the hypothesis that lower AChE activity is associated with lower neurobehavioral development among children living in Ecuadorian floricultural communities. METHODS: In 2008, we examined 307 children (age: 4–9 years; 52% male) and quantified AChE activity and neurodevelopment in 5 domains: attention/executive functioning, language, memory/learning, visuospatial processing, and sensorimotor (NEPSY-II test). Associations were adjusted for demographic and socioeconomic characteristics and height-for-age, flower worker cohabitation, and hemoglobin concentration. RESULTS: Mean ± standard deviation AChE activity was 3.14 ± 0.49 U/mL (similar for both genders). The range of scores among neurodevelopment subtests was 5.9 to 10.7 U (standard deviation: 2.6–4.9 U). Girls had a greater mean attention/executive functioning domain score than boys. In boys only, there were increased odds ratios of low (<9th percentile) neurodevelopment among those in the lowest tertile versus the highest tertile of AChE activity (odds ratios: total neurodevelopment: 5.14 [95% confidence interval (CI): 0.84 to 31.48]; attention/executive functioning domain: 4.55 [95% CI: 1.19 to 17.38], memory/learning domain: 6.03 [95% CI: 1.17 to 31.05]) after adjustment for socioeconomic and demographic factors, height-for-age, and hemoglobin. Within these domains, attention, inhibition and long-term memory subtests were most affected. CONCLUSIONS: Low AChE activity was associated with deficits in neurodevelopment, particularly in attention, inhibition, and memory in boys but not in girls. These critical cognitive skills affect learning and academic performance. Added precautions regarding secondary occupational pesticide exposure would be prudent. PMID:24249815 2. Comparative effect of pesticides on brain acetylcholinesterase in tropical fish. PubMed Assis, Caio Rodrigo Dias; Linhares, Amanda Guedes; Oliveira, Vagne Melo; França, Renata Cristina Penha; Carvalho, Elba Veronica Matoso Maciel; Bezerra, Ranilson Souza; de Carvalho, Luiz Bezerra 2012-12-15 Monitoring of pesticides based on acetylcholinesterase (AChE; EC 3.1.1.7) inhibition in vitro avoids interference of detoxification defenses and bioactivation of some of those compounds in non-target tissues. Moreover, environmental temperature, age and stress are able to affect specific enzyme activities when performing in vivo studies. Few comparative studies have investigated the inter-specific differences in AChE activity in fish. Screening studies allow choosing the suitable species as source of AChE to detect pesticides in a given situation. Brain AChE from the tropical fish: pirarucu (Arapaima gigas), cobia (Rachycentron canadum) and Nile tilapia (Oreochromis niloticus) were characterized and their activities were assayed in the presence of pesticides (the organophosphates: dichlorvos, diazinon, chlorpyrifos, temephos, tetraethyl pyrophosphate- TEPP and the carbamates: carbaryl and carbofuran). Inhibition parameters (IC₅₀ and Ki) for each species were found and compared with commercial AChE from electric eel (Electrophorus electricus). Optimal pH and temperature were found to be 8.0 and 35-45 °C, respectively. A. gigas AChE retained 81% of the activity after incubation at 50 °C for 30 min. The electric eel enzyme was more sensitive to the compounds (mainly carbofuran, IC₅₀ of 5 nM), excepting the one from A. gigas (IC₅₀ of 9 nM) under TEPP inhibition. These results show comparable sensitivity between purified and non-purified enzymes suggesting them as biomarkers for organophosphorus and carbamate detection in routine environmental and food monitoring programs for pesticides. 3. Acetylcholinesterase staining differentiates functionally distinct auditory pathways in the barn owl. PubMed 1993-03-15 The aim of this study was to examine how the functional specialization of the barn owl's auditory brainstem might correlate with histochemical compartmentalization. The barn owl uses interaural intensity and time differences to encode, respectively, the vertical and azimuthal positions of sound sources in space. These two auditory cues are processed in parallel ascending pathways that separate from each other at the level of the cochlear nuclei. Sections through the auditory brainstem were stained for acetylcholinesterase (AChE) to examine whether nuclei that process different auditory cues stain differentially for this enzyme. Of the two cochlear nuclei, angularis showed more intense staining than nucleus magnocellularis. Nucleus angularis projects to all of the nuclei and subdivisions of nuclei that belong to the intensity processing pathway. Acetylcholinesterase stained all regions that contain terminal fields of nucleus angularis and thus provided discrimination between the time and intensity pathways. Moreover, staining patterns with acetylcholinesterase were complementary to those previously reported with an anti-calbindin antibody, which stains terminal fields of nucleus laminaris, and thus stains all the nuclei and subdivisions of nuclei that belong to the time pathway. Some of the gross staining patterns observed with AChE were similar to those reported with antibodies to glutamate decarboxylase. However, AChE is a more convenient and definitive marker in discriminating between these pathways than is calbindin or glutamate decarboxylase. Acetylcholinesterase staining of the intensity pathway in the owl may be related to encoding of sound intensity by spike rate over large dynamic ranges. PMID:7681456 4. Acetylcholinesterase 1 in populations of organophosphate resistant North American strains of the cattle tick, Rhipicephalus microplus (Acari: Ixodidae) Technology Transfer Automated Retrieval System (TEKTRAN) In a collaboration with Purdue University researchers, we sequenced a 143,606 base pair Rhipicephalus microplus BAC library clone that contained the coding region for acetylcholinesterase 1 (AChE1). Sequencing was by Sanger protocols and the final assembly resulted in 15 contigs of varying length, e... 5. Inhibitor Profile of bis(n)-tacrines and N-methylcarbamates on Acetylcholinesterase from Rhipicephalus (Boophilus) microplus and Phlebotomus papatasi Technology Transfer Automated Retrieval System (TEKTRAN) The cattle tick, Rhipicephalus (Boophilus) microplus (Bm), and the sand fly, Phlebotomus papatasi (Pp), are disease vectors to cattle and humans, respectively. The purpose of this study was to characterize the inhibitor profile of acetylcholinesterases from Bm (BmAChE1) and Pp (PpAchE) compared to h... 6. Inhibitors of acetylcholinesterase and butyrylcholinesterase meet immunity. PubMed Pohanka, Miroslav 2014-06-02 Acetylcholinesterase (AChE) inhibitors are widely used for the symptomatic treatment of Alzheimer's disease and other dementias. More recent use is for myasthenia gravis. Many of these inhibitors interact with the second known cholinesterase, butyrylcholinesterase (BChE). Further, evidence shows that acetylcholine plays a role in suppression of cytokine release through a "cholinergic anti-inflammatory pathway" which raises questions about the role of these inhibitors in the immune system. This review covers research and discussion of the role of the inhibitors in modulating the immune response using as examples the commonly available drugs, donepezil, galantamine, huperzine, neostigmine and pyridostigmine. Major attention is given to the cholinergic anti-inflammatory pathway, a well-described link between the central nervous system and terminal effector cells in the immune system. 7. Inhibitors of Acetylcholinesterase and Butyrylcholinesterase Meet Immunity PubMed Central Pohanka, Miroslav 2014-01-01 Acetylcholinesterase (AChE) inhibitors are widely used for the symptomatic treatment of Alzheimer’s disease and other dementias. More recent use is for myasthenia gravis. Many of these inhibitors interact with the second known cholinesterase, butyrylcholinesterase (BChE). Further, evidence shows that acetylcholine plays a role in suppression of cytokine release through a “cholinergic anti-inflammatory pathway” which raises questions about the role of these inhibitors in the immune system. This review covers research and discussion of the role of the inhibitors in modulating the immune response using as examples the commonly available drugs, donepezil, galantamine, huperzine, neostigmine and pyridostigmine. Major attention is given to the cholinergic anti-inflammatory pathway, a well-described link between the central nervous system and terminal effector cells in the immune system. PMID:24893223 8. Inhibitors of acetylcholinesterase and butyrylcholinesterase meet immunity. PubMed Pohanka, Miroslav 2014-01-01 Acetylcholinesterase (AChE) inhibitors are widely used for the symptomatic treatment of Alzheimer's disease and other dementias. More recent use is for myasthenia gravis. Many of these inhibitors interact with the second known cholinesterase, butyrylcholinesterase (BChE). Further, evidence shows that acetylcholine plays a role in suppression of cytokine release through a "cholinergic anti-inflammatory pathway" which raises questions about the role of these inhibitors in the immune system. This review covers research and discussion of the role of the inhibitors in modulating the immune response using as examples the commonly available drugs, donepezil, galantamine, huperzine, neostigmine and pyridostigmine. Major attention is given to the cholinergic anti-inflammatory pathway, a well-described link between the central nervous system and terminal effector cells in the immune system. PMID:24893223 9. Asymmetric distribution of acetylcholinesterase in gravistimulated maize seedlings. PubMed Momonoki, Y S 1997-05-01 Acetylcholinesterase (AChE) activity has previously been studied by this laboratory and shown to occur at the interface between the stele and cortex of the mesocotyl of maize (Zea mays L.) seedlings. In this work we studied the distribution of AChE activity in 5-d-old maize seedlings following a gravity stimulus. After the stimulus, we found an asymmetric distribution of the enzyme in the coleoptile, the coleoptile node, and the mesocotyl of the stimulated seedlings using both histochemical and colorimetric methods for measuring the hydrolysis of acetylthiocholine. The hydrolytic capability of the esterase was greater on the lower side of the horizontally placed seedlings. Using the histochemical method, we localized the hydrolytic capability in the cortical cells around the vascular stele of the tissues. The hydrolytic activity was inhibited 80 to 90% by neostigmine, an inhibitor of AChE. When neostigmine was applied to the corn kernel, the gravity response of the seedling was inhibited and no enzyme-positive spots appeared in the gravity-stimulated seedlings. We believe these results indicate a role for AChE in the gravity response of maize seedlings. PMID:11536808 10. Choline-induced selective fluorescence quenching of acetylcholinesterase conjugated Au@BSA clusters. PubMed Mathew, Meegle S; Baksi, Ananya; Pradeep, T; Joseph, Kuruvilla 2016-07-15 We have developed a highly selective sensitive fluorescent detection of acetylcholine (ACh) using bovine serum albumin (BSA) protected atomically precise clusters of gold. The gold quantum clusters (AuQC@BSA) synthesized using bovine serum albumin and conjugated with acetylcholinesterase (AChE), an enzyme specific for acetylcholine, resulting in AuQC@BSA-AChE. The enzyme, AChE hydrolyzes acetylcholine (ACh) to choline (Ch) which in turn interacts with AuQC@BSA-AChE and quenches its fluorescence, enabling sensing. We have carried out the real time monitoring of the hydrolysis of ACh using electrospray ionization mass spectrometry (ESI MS) to find out the mechanism of fluorescent quenching. The validity of present method for determination of concentration of acetylcholine in real system such as blood was demonstrated. Further, the sensor, AuQC@BSA-AChE can be easily coated on paper and an efficient and cheap sensor can be developed and detection limit for ACh is found to be 10nM. The fluorescent intensity of AuQC@BSA-AChE is sensitive towards acetylcholine in range of 10nM to 6.4µM. This suggests that AuQC@BSA-AChE has an excellent potential to be used for diagnosis of various neuropsychological and neuropsychiatric disorders. 11. Identification and Molecular Characterization of Two Acetylcholinesterases from the Salmon Louse, Lepeophtheirus salmonis PubMed Central Kaur, Kiranpreet; Bakke, Marit Jørgensen; Nilsen, Frank; Horsberg, Tor Einar 2015-01-01 Acetylcholinesterase (AChE) is an important enzyme in cholinergic synapses. Most arthropods have two genes (ace1 and ace2), but only one encodes the predominant synaptic AChE, the main target for organophosphates. Resistance towards organophosphates is widespread in the marine arthropod Lepeophtheirus salmonis. To understand this trait, it is essential to characterize the gene(s) coding for AChE(s). The full length cDNA sequences encoding two AChEs in L. salmonis were molecularly characterized in this study. The two ace genes were highly similar (83.5% similarity at protein level). Alignment to the L. salmonis genome revealed that both genes were located close to each other (separated by just 26.4 kbp on the L. salmonis genome), resulting from a recent gene duplication. Both proteins had all the typical features of functional AChE and clustered together with AChE-type 1 proteins in other species, an observation that has not been described in other arthropods. We therefore concluded the presence of two versions of ace1 gene in L. salmonis, named ace1a and ace1b. Ace1a was predominantly expressed in different developmental stages compared to ace1b and was possibly active in the cephalothorax, indicating that ace1a is more likely to play the major role in cholinergic synaptic transmission. The study is essential to understand the role of AChEs in resistance against organophosphates in L. salmonis. PMID:25938836 12. Rubus coreanus Miquel Inhibits Acetylcholinesterase Activity and Prevents Cognitive Impairment in a Mouse Model of Dementia PubMed Central Kim, Cho Rong; Choi, Soo Jung; Oh, Seung Sang; Kwon, Yoon Kyung; Lee, Na Young; Park, Gwi Gun; Kim, Youn-Jung; Heo, Ho Jin; Jun, Woo Jin; Park, Cheung-Seog; Shin, Dong-Hoon 2013-01-01 Abstract To find acetylcholinesterase (AChE) inhibitors for the prevention of neurological disorders, such as Alzheimer's disease, ethanol extracts of promising traditional edible Korean plants were tested. Among them, Rubus coreanus Miquel extract exhibited the most significant AChE inhibitory activity. The effect of R. coreanus extract on trimethyltin-induced memory impairment in mice was investigated using Y-maze and passive avoidance tests. Our results showed that administration of R. coreanus extract significantly improved alternation behavior and step-through latency. In addition, R. coreanus extract was sequentially fractionated, and the purified constituent was determined to be 3,4,5-trihydroxybenzoic acid. PMID:24044488 13. Neurophysiological predictors of long term response to AChE inhibitors in AD patients PubMed Central Di, L; Oliviero, A; Pilato, F; Saturno, E; Dileone, M; Marra, C; Ghirlanda, S; Ranieri, F; Gainotti, G; Tonali, P 2005-01-01 Background: In vivo evaluation of cholinergic circuits of the human brain has recently been introduced using a transcranial magnetic stimulation (TMS) protocol based on coupling peripheral nerve stimulation with motor cortex TMS (short latency afferent inhibition, SAI). SAI is reduced in Alzheimer's disease (AD) and drugs enhancing cholinergic transmission increase SAI. Methods: We evaluated whether SAI testing, together with SAI test-retest, after a single dose of the acetylcholinesterase (AChE) inhibitor rivastigmine, might be useful in predicting the response after 1 year treatment with rivastigmine in 16 AD patients. Results: Fourteen AD patients had pathologically reduced SAI. SAI was increased after administration of a single oral dose of rivastigmine in AD patients with abnormal baseline SAI, but individual responses to rivastigmine varied widely, with SAI change ranging from an increase in inhibition of ∼50% of test size to no change. Baseline SAI and the increase in SAI after a single dose of rivastigmine were correlated with response to long term treatment. A normal SAI in baseline conditions, or an abnormal SAI in baseline conditions that was not greatly increased by a single oral dose of rivastigmine, were invariably associated with poor response to long term treatment, while an abnormal SAI in baseline conditions in conjunction with a large increase in SAI after a single dose of rivastigmine was associated with good response to long term treatment in most of the patients. Conclusions: Evaluation of SAI may be useful for identifying AD patients likely to respond to treatment with AChE inhibitors. PMID:16024879 14. Screening of selected Indian medicinal plants for acetylcholinesterase inhibitory activity. PubMed Vinutha, B; Prashanth, D; Salma, K; Sreeja, S L; Pratiti, D; Padmaja, R; Radhika, S; Amit, A; Venkateshwarlu, K; Deepak, M 2007-01-19 Seventy-six plant extracts including methanolic and successive water extracts from 37 Indian medicinal plants were investigated for acetylcholinesterase (AChE) inhibitory activity (in vitro). Results indicated that methanolic extracts to be more active than water extracts. The potent AChE inhibiting methanolic plant extracts included Withania somnifera (root), Semecarpus anacardium (stem bark), Embelia ribes (Root), Tinospora cordifolia (stem), Ficus religiosa (stem bark) and Nardostachys jatamansi (rhizome). The IC(50) values obtained for these extracts were 33.38, 16.74, 23.04, 38.36, 73.69 and 47.21mug/ml, respectively. These results partly substantiate the traditional use of these herbs for improvement of cognition. PMID:16950584 15. Interpretation of honeybees contact toxicity associated to acetylcholinesterase inhibitors. PubMed Dulin, Fabienne; Halm-Lemeille, Marie-Pierre; Lozano, Sylvain; Lepailleur, Alban; Santos, Jana Sopkova-de Oliveira; Rault, Sylvain; Bureau, Ronan 2012-05-01 The widespread use of different pesticides generates adverse effects on non target organisms like honeybees. Organophosphorous and carbamates kill honeybees through the inactivation of acetylcholinesterase (AChE), thereby interfering with nerve signaling and function. For this class of pesticides, it is fundamental to understand the relationship between their structures and the contact toxicity for honeybees. A Quantitative Structure-Activity Relationship (QSAR) study was carried out on 45 derivatives by a genetic algorithm approach starting from more than 2500 descriptors. In parallel, a new 3D model of AChE associated to honeybees was defined. Physicochemical properties of the receptor and docking studies of the derivatives allow understanding the meaningful of three descriptors and the implication of several amino acids in the overall toxicity of the pesticides. 16. Quantitative studies on acetylcholinesterase in seven species of digenetic trematodes. PubMed Nizami, W A; Siddiqi, A H; Islam, M W 1977-07-29 Quantitative estimation of absolute levels and in vitro release of acetylcholinesterase (AChE) in seven species of digenetic trematodes: Isoparorchis hypselobagri from the swim bladder of catfish, Wallago attu; Srivastavaia indica and Gastrothylax crumenifer from the rumen, and Gigantocotyle explanatum from the liver of the water buffalo, Bubalus bubalis; Fasciolopsis buski, Echinostoma malayanum from the small intestine and Gastrodiscoides hominis from the caecum of the pig, Sus scrofa revealed that the enzyme is present in remarkably high quantities in species which inhibit gastrointestinal tract compared with those that parasitize liver and swim bladder. The rate of in vitro release of AChE also varies with the species which supports the view that such differential secretion probably takes place in situ as well to counteract peristalsis and it is a biochemical adaptation on the part of these trematodes. 17. Nonenzymatic role of acetylcholinesterase in neuritic sprouting: regional changes in acetylcholinesterase and choline acetyltransferase after neonatal 6-hydroxydopamine lesions. PubMed Slotkin, Theodore A; Ryde, Ian T; Wrench, Nicola; Card, Jennifer A; Seidler, Frederic J 2009-01-01 Acetylcholinesterase (AChE) is postulated to play a nonenzymatic role in the development of neuritic projections. We gave the specific neurotoxin, 6-OHDA to rats on postnatal day (PN) 1, a treatment that destroys noradrenergic nerve terminals in the forebrain while producing reactive sprouting in the brainstem. AChE showed profound decreases in the forebrain that persisted in males over the entire phase of major synaptogenesis, from PN4 through PN21; in the brainstem, AChE was increased. Parallel examinations of choline acetyltransferase, an enzymatic marker for cholinergic nerve terminals, showed a different pattern of 6-OHDA-induced alterations, with initial decreases in both forebrain and brainstem in males and regression toward normal by PN21; females were far less affected. The sex differences are in accord with the greater plasticity of the female brain and its more rapid recovery from neurotoxic injury; our findings indicate that these differences are present well before puberty. These results support the view that AChE is involved in neurite formation, unrelated to its enzymatic role in cholinergic neurotransmission. Further, the results for choline acetyltransferase indicate that early depletion of norepinephrine compromises development of acetylcholine systems, consistent with a trophic role for this neurotransmitter. 18. Nonenzymatic role of acetylcholinesterase in neuritic sprouting: regional changes in acetylcholinesterase and choline acetyltransferase after neonatal 6-hydroxydopamine lesions. PubMed Slotkin, Theodore A; Ryde, Ian T; Wrench, Nicola; Card, Jennifer A; Seidler, Frederic J 2009-01-01 Acetylcholinesterase (AChE) is postulated to play a nonenzymatic role in the development of neuritic projections. We gave the specific neurotoxin, 6-OHDA to rats on postnatal day (PN) 1, a treatment that destroys noradrenergic nerve terminals in the forebrain while producing reactive sprouting in the brainstem. AChE showed profound decreases in the forebrain that persisted in males over the entire phase of major synaptogenesis, from PN4 through PN21; in the brainstem, AChE was increased. Parallel examinations of choline acetyltransferase, an enzymatic marker for cholinergic nerve terminals, showed a different pattern of 6-OHDA-induced alterations, with initial decreases in both forebrain and brainstem in males and regression toward normal by PN21; females were far less affected. The sex differences are in accord with the greater plasticity of the female brain and its more rapid recovery from neurotoxic injury; our findings indicate that these differences are present well before puberty. These results support the view that AChE is involved in neurite formation, unrelated to its enzymatic role in cholinergic neurotransmission. Further, the results for choline acetyltransferase indicate that early depletion of norepinephrine compromises development of acetylcholine systems, consistent with a trophic role for this neurotransmitter. PMID:19452616 19. Evaluation of acetylcholinesterase in an animal model of maple syrup urine disease. PubMed Scaini, Giselli; de Rochi, Natália; Jeremias, Isabela C; Deroza, Pedro F; Zugno, Alexandra I; Pereira, Talita C B; Oliveira, Giovanna M T; Kist, Luiza W; Bogo, Maurício R; Schuck, Patrícia F; Ferreira, Gustavo C; Streck, Emilio L 2012-04-01 Maple syrup urine disease is an inherited metabolic disease predominantly characterized by neurological dysfunction. However, the mechanisms underlying the neuropathology of this disease are still not defined. Therefore, the aim of this study was to investigate the effect of acute and chronic administration of a branched-chain amino acids (BCAA) pool (leucine, isoleucine, and valine) on acetylcholinesterase (AChE) activity and gene expression in the brain and serum of rats and to assess if antioxidant treatment prevented the alterations induced by BCAA administration. Our results show that the acute administration of a BCAA pool in 10- and 30-day-old rats increases AChE activity in the cerebral cortex, striatum, hippocampus, and serum. Moreover, chronic administration of the BCAA pool also increases AChE activity in the structures studied, and antioxidant treatment prevents this increase. In addition, we show a significant decrease in the mRNA expression of AChE in the hippocampus following acute administration in 10- and 30-day-old rats. On the other hand, AChE expression increased significantly after chronic administration of the BCAA pool. Interestingly, the antioxidant treatment was able to prevent the increased AChE activity without altering AChE expression. In conclusion, the results from the present study demonstrate a marked increase in AChE activity in all brain structures following the administration of a BCAA pool. Moreover, the increased AChE activity is prevented by the coadministration of N-acetylcysteine and deferoxamine as antioxidants. PMID:22328136 20. Drosophila acetylcholinesterase: demonstration of a glycoinositol phospholipid anchor and an endogenous proteolytic cleavage SciTech Connect Haas, R.; Marshall, T.L.; Rosenberry, T.L. 1988-08-23 The presence of a glycoinositol phospholipid anchor Drosophila acetylcholinesterase (AChE) was shown by several criteria. Chemical analysis of highly purified Drosophila AChE demonstrated approximately one residue of inositol per enzyme subunit. Selective cleavage by Staphylococcus aureus phosphatidylinositol-specific phospholipase C (PI-PLC) was tested with Drosophila AChE radiolabeled by the photoactivatable affinity probe 3-(trifluoromethyl)-3-(m-(/sup 125/I)iodophenyl)diazirine ((/sup 125/I)TID), a reagent that specifically labels the lipid moiety of glycoinositol phospholipid-anchored proteins. Digestion with PI-PLC released 75% of this radiolabel from the protein. Gel electrophoresis of Drosophila AChE in sodium dodecyl sulfate indicated prominent 55- and 16-kDa bands and a faint 70-kDa band. The (/sup 125/)I)TID label was localized on the 55-kDa fragment, suggesting that this fragment is the C-terminal portion of the protein. In support of this conclusion, a sensitive microsequencing procedure that involved manual Edman degradation combined with radiomethylation was used to determine residues 2-5 of the 16-kDa fragment. Comparison with the Drosophila AChE cDNA sequence confirmed that the 16-kDa fragment includes the N-terminus of AChE. Furthermore, the position of the N-terminal amino acid of the mature Drosophila AChE is closely homologous to that of Torpedo AChE. The presence of radiomethylatable ethanolamine in both 16- and 55-kDa fragments was also confirmed. Thus, Drosophila AChE may include a second posttranslational modification involving ethanolamine. 1. Gastrointestinal acetylcholinesterase activity following endotracheal microinstillation inhalation exposure to sarin in guinea pigs. PubMed Chanda, Soma; Song, Jian; Rezk, Peter; Sabnekar, Praveena; Doctor, Bhupendra P; Sciuto, Alfred M; Nambiar, Madhusoodana P 2010-09-01 The goal of this study was to assess acetylcholinesterase (AChE) inhibition at different regions of the gastrointestinal (GI) tract following inhalation exposure to nerve agent sarin. Seven major regions of the GI tract were removed from saline control animals (n=3) and 677.4 mg/m(3) sarin-exposed animals at 4h (n=4) and 24h (n=4) post-exposure. AChE activity was determined in blood and homogenized tissue supernatant by specific Ellman's assay using Iso-OMPA, a BChE inhibitor, and expressed as activity/optical density of hemoglobin for blood and activity/mg protein for tissues. Our data showed that the AChE activity was significantly decreased for groups both 4h and 24h post-sarin exposure. Among the seven chosen regions of the guinea pig GI tract, duodenum showed the highest AChE activity in control animals. The AChE activity was significantly decreased in the stomach (p=0.03), duodenum (p=0.029), jejunum (p=0.006), and ileum (p=0.006) 4h following sarin exposure. At 24h post-sarin exposure the AChE activity of duodenum (p=0.029) and ileum (p=0.006) was significantly inhibited. Esophagus showed no inhibition following sarin exposure at both 4h and 24h groups. These results suggest that the AChE activity is different in different regions of the GI tract and highest levels of AChE inhibition following sarin exposure were seen in regions exhibiting higher overall AChE activity and cholinergic function. 2. In silico analysis of binding of neurotoxic venom ligands with acetylcholinesterase for therapeutic use in treatment of Alzheimer's disease. PubMed Waqar, Maleeha; Batool, Sidra 2015-05-01 Acetylcholinesterases (AChE) are enzymes that function in hydrolyzing the neurotransmitter acetylcholine. Diminished levels of acetylcholine have been reported for various neurodegenerative diseases, especially Alzheimer's. Therefore, acetylcholinesterase inhibitors are being considered quite effective in treating these diseases. Fasciculin 2 is a toxin isolated from Eastern green mamba that had been reported as a reversible acetylcholinesterase inhibitor. In this study, we have reported the in silico analysis of venom toxins via various computational tools used for drug designing, to find out the protein-protein interaction of these toxins in complex with acetylcholinesterase enzyme. In total 15 toxins have been selected from the venoms of various species as ligand dataset, to study their binding interactions with the acetylcholinesterase enzyme. PMID:25747777 3. Chlorpyrifos and Malathion have opposite effects on behaviors and brain size that are not correlated to changes in AChE activity PubMed Central Richendrfer, Holly; Creton, Robbert 2015-01-01 Organophosphates, a type of neurotoxicant pesticide, are used globally for the treatment of pests on croplands and are therefore found in a large number of conventional foods. These pesticides are harmful and potentially deadly if ingested or inhaled in large quantities by causing a significant reduction in acetylcholinesterase (AChE) activity in the central and peripheral nervous system. However, much less is known about the effects of exposure to small quantities of the pesticides on neural systems and behavior during development. In the current study we used zebrafish larvae in order to determine the effects of two of the most widely used organophosphates, chlorpyrifos and malathion, on zebrafish behavior and AChE activity. Embryos and larvae were exposed to the organophosphates during different time points in development and then tested at 5 days post-fertilization for behavioral, neurodevelopmental and AChE abnormalities. The results of the study indicate that chlorpyrifos and malathion cause opposing behaviors in the larvae such as swim speed (hypoactivity vs. hyperactivity) and rest. Additionally, the pesticides affect only certain behaviors, such as thigmotaxis, during specific time points in development that are unrelated to changes in AChE activity. Larvae treated with malathion but not chlorpyrifos also had significantly smaller forebrain and hindbrain regions compared to controls by 5 days post-fertilization. We conclude that exposure to very low concentrations of organophosphate pesticides during development cause abnormalities in behavior and brain size. PMID:25983063 4. Highly sensitive and selective immuno-capture/electrochemical assay of acetylcholinesterase activity in red blood cells: a biomarker of exposure to organophosphorus pesticides and nerve agents. PubMed Chen, Aiqiong; Du, Dan; Lin, Yuehe 2012-02-01 Acetylcholinesterase (AChE) enzyme activity in red blood cells (RBCs) is a useful biomarker for biomonitoring of exposures to organophosphorus (OP) pesticides and chemical nerve agents. In this paper, we reported a new method for AChE activity assay based on selective immuno-capture of AChE from biological samples followed by enzyme activity assay of captured AChE using a disposable electrochemical sensor. The electrochemical sensor is based on multiwalled carbon nanotubes-gold (MWCNTs-Au) nanocomposites modified screen printed carbon electrode (SPCE), which is used for the immobilization of AChE specific antibody. Upon the completion of immunoreaction, the target AChE (including active and inhibited) is captured onto the electrode surface and followed by an electrochemical detection of enzymatic activity in the presence of acetylthiocholine. A linear response is obtained over standard AChE concentration range from 0.1 to 10 nM. To demonstrate the capability of this new biomonitoring method, AChE solutions dosed with different concentrations of paraoxon were used to validate the new AChE assay method. AChE inhibition in OP dosed solutions was proportional to OP concentration from 0.2 to 50 nM. The new AChE activity assay method for biomonitoring of OP exposure was further validated with in vitro paraoxon-dosed RBC samples. The established electrochemical sensing platform for AChE activity assay not only avoids the problem of overlapping substrate specificity with esterases by using selective antibody, but also eliminates potential interference from other electroactive species in biological samples. It offers a new approach for sensitive, selective, and rapid AChE activity assay for biomonitoring of exposure to OPs. 5. Inactivation of acetylcholinesterase by various fluorophores PubMed Central Guo, Lilu; Suarez, Alirica I.; Thompson, Charles M. 2012-01-01 The inhibition of recombinant mouse acetylcholinesterase (rMAChE) and electric eel acetylcholinesterase (EEAChE) by seven, structurally different chromophore-based (dansyl, pyrene, dabsyl, diethylamino- and methoxycoumarin, Lissamine rhodamine B, and Texas Red) propargyl carboxamides or sulfonamides was studied. Diethylaminocoumarin, Lissamine, and Texas Red amides inhibited rMAChE with IC50 values of 1.00 µM, 0.05 µM, and 0.70 µM, respectively. Lissamine and Texas Red amides inhibited EEAChE with IC50 values of 3.57 and 10.4 µM, respectively. The other chromophore amides did not inhibit either AChE. The surprising inhibitory potency of Lissamine was examined in further detail against EEAChE and revealed a mixed-type inhibition with Ki = 11.7 µM (competitive) and Ki′ = 24.9 µM (noncompetitive), suggesting that Lissamine binds to free enzyme and enzyme–substrate complex. PMID:19842944 6. Novel bis-(−)-nor-meptazinol derivatives act as dual binding site AChE inhibitors with metal-complexing property SciTech Connect Zheng, Wei; Li, Juan; Qiu, Zhuibai; Xia, Zheng; Li, Wei; Yu, Lining; Chen, Hailin; Chen, Jianxing; Chen, Yan; Hu, Zhuqin; Zhou, Wei; Shao, Biyun; Cui, Yongyao; Xie, Qiong; Chen, Hongzhuan 2012-10-01 The strategy of dual binding site acetylcholinesterase (AChE) inhibition along with metal chelation may represent a promising direction for multi-targeted interventions in the pathophysiological processes of Alzheimer's disease (AD). In the present study, two derivatives (ZLA and ZLB) of a potent dual binding site AChE inhibitor bis-(−)-nor-meptazinol (bis-MEP) were designed and synthesized by introducing metal chelating pharmacophores into the middle chain of bis-MEP. They could inhibit human AChE activity with IC{sub 50} values of 9.63 μM (for ZLA) and 8.64 μM (for ZLB), and prevent AChE-induced amyloid-β (Aβ) aggregation with IC{sub 50} values of 49.1 μM (for ZLA) and 55.3 μM (for ZLB). In parallel, molecular docking analysis showed that they are capable of interacting with both the catalytic and peripheral anionic sites of AChE. Furthermore, they exhibited abilities to complex metal ions such as Cu(II) and Zn(II), and inhibit Aβ aggregation triggered by these metals. Collectively, these results suggest that ZLA and ZLB may act as dual binding site AChEIs with metal-chelating potency, and may be potential leads of value for further study on disease-modifying treatment of AD. -- Highlights: ► Two novel bis-(−)-nor-meptazinol derivatives are designed and synthesized. ► ZLA and ZLB may act as dual binding site AChEIs with metal-chelating potency. ► They are potential leads for disease-modifying treatment of Alzheimer's disease. 7. Nanomaterials - Acetylcholinesterase Enzyme Matrices for Organophosphorus Pesticides Electrochemical Sensors: A Review PubMed Central Periasamy, Arun Prakash; Umasankar, Yogeswaran; Chen, Shen-Ming 2009-01-01 Acetylcholinesterase (AChE) is an important cholinesterase enzyme present in the synaptic clefts of living organisms. It maintains the levels of the neurotransmitter acetylcholine by catalyzing the hydrolysis reaction of acetylcholine to thiocholine. This catalytic activity of AChE is drastically inhibited by trace amounts of organophosphorus (OP) pesticides present in the environment. As a result, effective monitoring of OP pesticides in the environment is very desirable and has been done successfully in recent years with the use of nanomaterial-based AChE sensors. In such sensors, the enzyme AChE has been immobilized onto nanomaterials like multiwalled carbon nanotubes, gold nanoparticles, zirconia nanoparticles, cadmium sulphide nano particles or quantum dots. These nanomaterial matrices promote significant enhancements of OP pesticide determinations, with the thiocholine oxidation occurring at much lower oxidation potentials. Moreover, nanomaterial-based AChE sensors with rapid response, increased operational and long storage stability are extremely well suited for OP pesticide determination over a wide concentration range. In this review, the unique advantages of using nanomaterials as AChE immobilization matrices are discussed. Further, detection limits, sensitivities and correlation coefficients obtained using various electroanalytical techniques have also been compared with chromatographic techniques. PMID:22408512 8. Acetylcholinesterase in Biofouling Species: Characterization and Mode of Action of Cyanobacteria-Derived Antifouling Agents. PubMed Almeida, Joana R; Freitas, Micaela; Cruz, Susana; Leão, Pedro N; Vasconcelos, Vitor; Cunha, Isabel 2015-07-24 Effective and ecofriendly antifouling (AF) compounds have been arising from naturally produced chemicals. The objective of this study is to use cyanobacteria-derived agents to investigate the role of acetylcholinesterase (AChE) activity as an effect and/or mode of action of promising AF compounds, since AChE inhibitors were found to inhibit invertebrate larval settlement. To pursue this objective, in vitro quantification of AChE activity under the effect of several cyanobacterial strain extracts as potential AF agents was performed along with in vivo AF (anti-settlement) screening tests. Pre-characterization of different cholinesterases (ChEs) forms present in selected tissues of important biofouling species was performed to confirm the predominance of AChE, and an in vitro AF test using pure AChE activity was developed. Eighteen cyanobacteria strains were tested as source of potential AF and AChE inhibitor agents. Results showed effectiveness in selecting promising eco-friendly AF agents, allowing the understanding of the AF biochemical mode of action induced by different compounds. This study also highlights the potential of cyanobacteria as source of AF agents towards invertebrate macrofouling species. 9. Novel nonquaternary reactivators showing reactivation efficiency for soman-inhibited human acetylcholinesterase. PubMed Wei, Zhao; Liu, Yan-Qin; Wang, Yong-An; Li, Wan-Hua; Zhou, Xin-Bo; Zhao, Jian; Huang, Chun-Qian; Li, Xing-Zhou; Liu, Jia; Zheng, Zhi-Bing; Li, Song 2016-03-30 Soman is a highly toxic nerve agent with strong inhibition of acetylcholinesterase (AChE), but of the few reactivators showing antidotal efficiency for soman-inhibited AChE presently are all permanently charged cationic oximes with poor penetration of the blood-brain barrier. To overcome this problem, uncharged reactivators have been designed and synthesized, but few of them were efficient for treating soman poisoning. Herein, we used a dual site biding strategy to develop more efficient uncharged reactivators. The ortho-hydroxylbenzaldoximes were chosen as reactivation ligands of AChE to prevent the secondary poisoning of AChE, and simple aromatic groups were used as peripheral site ligands of AChE, which were linked to the oximes in a similar way as that found in the reactivator HI-6. The in vitro experiment demonstrated that some of the resulting conjugates have robust activity against soman-inhibited AChE, and oxime 8b was highlighted as the most efficient one. Although not good as HI-6 in vitro, these new compounds hold promise for development of more efficient centrally acting reactivators for soman poisoning due to their novel nonquaternary structures, which are predicted to be able to cross the blood-brain barrier. PMID:26809136 10. Carbon-11 labeling of CP-126,998: A radiotracer for in vivo studies of acetylcholinesterase SciTech Connect Musachio, J.L.; Flesher, J.E.; Scheffel, U. 1996-05-01 The study of acetylcholinesterase (AChE) via PET is of interest as reduced activity of this enzyme has been observed in Alzheimer`s disease. Our efforts to develop a radiotracer for mapping of AChE have focused on the N-benzylpiperidine benzisoxazole, CP-126,998, a highly potent (IC{sub 50}=0.48 nm) and selective inhibitor of AChE. High specific activity [C-11] CP-126,998 was synthesized (14 - 24% radiochemical yield, non-decay corrected) by treatment of the desmethyl precursor, CP-118,954, with [C-11] methyl iodide and tetrabutylammonium hydroxide in DMF. In vivo studies with [C-11] CP-126,998 in mice show that this radiotracer displays highest uptake in striatum (6.2 %ID/g), a brain region known to be rich in AChE. The (striatum-cerebellum)/cerebellar radioactivity ratio reached a maximum of 4.3 at 30 min postinjection, and this ratio decreased to 2.4 at 120 min. .Radiotracer binding was saturable in vivo by pretreatment with CP-118,954. Pretreatment of mice with diisopropylfluorophosphate (4 mg/kg i.p.), a known AChE inhibitor, significantly inhibited binding in striatum in a dose-dependent manner. Initial results suggest that [C-11] CP-126,998 may prove useful as a marker for the study of AChE in humans via PET. 11. Acetylcholinesterase in Biofouling Species: Characterization and Mode of Action of Cyanobacteria-Derived Antifouling Agents. PubMed Almeida, Joana R; Freitas, Micaela; Cruz, Susana; Leão, Pedro N; Vasconcelos, Vitor; Cunha, Isabel 2015-08-01 Effective and ecofriendly antifouling (AF) compounds have been arising from naturally produced chemicals. The objective of this study is to use cyanobacteria-derived agents to investigate the role of acetylcholinesterase (AChE) activity as an effect and/or mode of action of promising AF compounds, since AChE inhibitors were found to inhibit invertebrate larval settlement. To pursue this objective, in vitro quantification of AChE activity under the effect of several cyanobacterial strain extracts as potential AF agents was performed along with in vivo AF (anti-settlement) screening tests. Pre-characterization of different cholinesterases (ChEs) forms present in selected tissues of important biofouling species was performed to confirm the predominance of AChE, and an in vitro AF test using pure AChE activity was developed. Eighteen cyanobacteria strains were tested as source of potential AF and AChE inhibitor agents. Results showed effectiveness in selecting promising eco-friendly AF agents, allowing the understanding of the AF biochemical mode of action induced by different compounds. This study also highlights the potential of cyanobacteria as source of AF agents towards invertebrate macrofouling species. PMID:26213967 12. Acetylcholinesterase in Biofouling Species: Characterization and Mode of Action of Cyanobacteria-Derived Antifouling Agents PubMed Central Almeida, Joana R.; Freitas, Micaela; Cruz, Susana; Leão, Pedro N.; Vasconcelos, Vitor; Cunha, Isabel 2015-01-01 Effective and ecofriendly antifouling (AF) compounds have been arising from naturally produced chemicals. The objective of this study is to use cyanobacteria-derived agents to investigate the role of acetylcholinesterase (AChE) activity as an effect and/or mode of action of promising AF compounds, since AChE inhibitors were found to inhibit invertebrate larval settlement. To pursue this objective, in vitro quantification of AChE activity under the effect of several cyanobacterial strain extracts as potential AF agents was performed along with in vivo AF (anti-settlement) screening tests. Pre-characterization of different cholinesterases (ChEs) forms present in selected tissues of important biofouling species was performed to confirm the predominance of AChE, and an in vitro AF test using pure AChE activity was developed. Eighteen cyanobacteria strains were tested as source of potential AF and AChE inhibitor agents. Results showed effectiveness in selecting promising eco-friendly AF agents, allowing the understanding of the AF biochemical mode of action induced by different compounds. This study also highlights the potential of cyanobacteria as source of AF agents towards invertebrate macrofouling species. PMID:26213967 13. The protective role of tacrine and donepezil in the retina of acetylcholinesterase knockout mice PubMed Central Yi, Yun-Min; Cai, Li; Shao, Yi; Xu, Man; Yi, Jing-Lin 2015-01-01 AIM To determine the effect of different concentrations of the acetylcholinesterase (AChE) inhibitors tacrine and donepezil on retinal protection in AChE+/− mice (AChE knockout mice) of various ages. METHODS Cultured ARPE-19 cells were treated with hydrogen peroxide (H2O2) at concentrations of 0, 250, 500, 1000 and 2000 µmol/L and protein levels were measured using Western blot. Intraperitoneal injections of tacrine and donepezil (0.1 mg/mL, 0.2 mg/mL and 0.4 mg/mL) were respectively given to AChE+/− mice aged 2mo and 4mo and wild-type S129 mice for 7d; phosphate buffered saline (PBS) was administered to the control group. The mice were sacrificed after 30d by in vitro cardiac perfusion and retinal samples were taken. AChE-deficient mice were identified by polymerase chain reaction (PCR) analysis using specific genotyping protocols obtained from the Jackson Laboratory website. H&E staining, immunofluorescence and Western blot were performed to observe AChE protein expression changes in the retinal pigment epithelial (RPE) cell layer. RESULTS Different concentrations of H2O2 induced AChE expression during RPE cell apoptosis. AChE+/− mice retina were thinner than those in wild-type mice (P<0.05); the retinal structure was still intact at 2mo but became thinner with increasing age (P<0.05); furthermore, AChE+/− mice developed more slowly than wild-type mice (P<0.05). Increased concentrations of tacrine and donepezil did not significantly improve the protection of the retina function and morphology (P>0.05). CONCLUSION In vivo, tacrine and donepezil can inhibit the expression of AChE; the decrease of AChE expression in the retina is beneficial for the development of the retina. PMID:26558196 14. Effect of thermal stress and water deprivation on the acetylcholinesterase activity of the pig brain and hypophyses Adejumo, D. O.; Egbunike, G. N. 1988-06-01 The effects of direct exposure of boars to thermal stress for 1 h daily for 5 days and to acute water deprivation for 24 or 48 h were studied on the acetylcholinesterase (AChE) activity of porcine brain and hypophysial regions. Mean ambient temperatures, respiratory rates and rectal temperatures in the open were significantly higher than inside the pen. Heat stress induced a rise in AChE activities in the pons, cerebellum, amygdala, hippocampus, hypothalamus, mid-brain and medulla oblongata. However, no significant changes were observed in the cerebral cortex, adenohypophysis and neurohypophysis. Water deprivation significantly ( P<0.05) depressed AChE activity to varying extents depending on the duration of water restriction. Thus AChE activity in the amygdala was depressed by water deprivation for 24 h but partially restored at 48 h. The pons and medulla oblongata were comparable to the amygdala in this respect. The adenohypophysis and neurohypophysis were relatively unaffected. 15. Inhibition of Acetylcholinesterase in Different Structures of the Rat Brain Following Soman Intoxication Pretreated with Huperzine A PubMed Central Bajgar, Jiri; Hajek, Petr; Karasova, Jana; Slizova, Dasa; Krs, Otakar; Kuca, Kamil; Jun, Daniel; Fusek, Josef; Capek, Lukas 2007-01-01 Acetylcholinesterase (AChE) activities in different brain parts were determined quantitatively in rats treated with huperzine A, soman, and huperzine A followed by soman, using histochemical and biochemical methods. Following soman intoxication (1.2 × LD50, i.m.), AChE activity was decreased to 30–80% of control values depending on the brain structure. The most sensitive area was the frontal cortex and the most relatively resistant was ncl. ruber. Huperzine A treatment only caused a change in AChE activity varying from 70 to 100 % of control values. In rats pretreated with huperzine A and intoxicated with soman, AChE activity was significantly higher than that observed after soman. In these animals, survival of rats pretreated with huperzine was observed while the mortality of unpretreated animals was near to 80 %. The results suggest that huperzine A is good candidate for further study for clinical use as a prophylactic drug against nerve agent poisoning. 16. Use and disuse and the control of acetylcholinesterase activity in fast and slow twitch muscle of rat NASA Technical Reports Server (NTRS) Dettbarn, W. D.; Groswald, D.; Gupta, R. C.; Misulis, K. E. 1985-01-01 The role of acetylcholinesterase (AChE) in neuromuscular transmission is relatively well established, little is known, however, of the mechanisms that regulate its synthesis and control its specific distribution in fast and slow muscle. Innervation plays an important role in the regulation of AChE and elimination of the influence of the nerve by surgical denervation results in a loss of AChE. The influences of the nerve and how they are mediated was investigated. It is suggested that muscle usage and other factors such as materials carried by axonal transport may participate in the regulation of this enzyme. The mechanisms that regulate AChE and its molecular forms in two functionally different forms are studied. 17. Lower Acetylcholinesterase Activity among Children Living with Flower Plantation Workers PubMed Central Suarez-Lopez, Jose R.; Jacobs, David R.; Himes, John H.; Alexander, Bruce H.; Lazovich, DeAnn; Gunnar, Megan 2012-01-01 BACKGROUND Children of workers exposed to pesticides are at risk of secondary pesticide exposure. We evaluated the potential for lower acetylcholinesterase activity in children cohabiting with fresh-cut flower plantation workers, which would be expected from organophosphate and carbamate insecticide exposure. Parental home surveys were performed and acetylcholinesterase activity was measured in 277 children aged 4–9 years in the study of Secondary Exposure to Pesticides among Infants, Children and Adolescents (ESPINA). Participants lived in a rural county in Ecuador with substantial flower plantation activity. RESULTS Mean acetylcholinesterase activity was 3.14 U/ml, standard deviation (SD): 0.49. It was lower by 0.09 U/ml (95% confidence interval (CI) −0.19, −0.001) in children of flower workers (57% of participants) than non-flower workers’ children, after adjustment for gender, age, height-for-age, hemoglobin concentration, income, pesticide use within household lot, pesticide use by contiguous neighbors, examination date and residence distance to nearest flower plantation. Using a 4 level polychotomous acetylcholinesterase activity dependent variable, flower worker cohabitation (vs. not) had odds ratio 3.39 (95% CI 1.19, 9.64) for being <15th percentile compared to the highest tertile. Children cohabitating for ≥5 years (vs. never) had OR of 4.11 (95% CI: 1.17, 14.38) of AChE activity within <15th percentile compared to the highest tertile. CONCLUSIONS Cohabitation with a flower worker was related to lower acetylcholinesterase activity in children. This supports the hypothesis that the amount of take-home pesticides from flower workers suffices to decrease acetylcholinesterase activity, with lower activity associated with longer exposure. PMID:22405996 18. Glycine effects on glutamate-receptor elicited acetylcholinesterase release from slices and synaptosomes of the spinal ventral horn. PubMed Rodríguez-Ithurralde, D; Olivera, S; La Paz, A; Vincent, O; Rondeau, A 1996-08-01 To study the mechanisms by which glutamate-elicited acetylcholinesterase release (GEAR) might play a part in the pathogenesis of excitotoxically triggered motor neurone disease, and to investigate the interaction of GEAR with spinal glycinergic mechanisms, we measured acetylcholinesterase (AChE) and cholinergic markers, after stimulating ventral horn slices and synaptosomes from the mouse spinal cord, with both glutamate- and glycine-receptor agonists. Glutamate (GLU), kainate and AMPA, as well as glycine (GLY) evoked dose-related, calcium-dependent liberation of soluble forms of AChE from both slices and synaptosomes. GLY-evoked AChE release showed remarkable age-related postnatal changes. In the immature slice of the ventral horn. GLY potentiated the GEAR response in the presence of strychnine, suggesting N-methyl-D-aspartate (NMDA) receptor involvement, and was also able to evoke a strychnine-sensitive AChE release in the absence of exogenous GLU. After the 28th postnatal day, nearly all the AChE secreted was released either after the activation of non-NMDA glutamate receptors or by strychnine-sensitive GLY-evoked AChE release mechanisms. Both GEAR and GLY-evoked AChE release might impair the negative feedback loop which modulates the overactivation of motor neurones, and cause prolonged extracellular rises of soluble AChE. These effects might augment the vulnerability of motor neurones to excitotoxic stress, promote fiber outgrowth, and eventually accelerate the metabolic exhaustion of lower motor neurones. It is possible that the mechanisms described are operative at the spinal cord of ALS/MND patients. 19. Biochemical properties, expression profiles, and tissue localization of orthologous acetylcholinesterase-2 in the mosquito, Anopheles gambiae. PubMed Zhao, Picheng; Wang, Yang; Jiang, Haobo 2013-03-01 Acetylcholinesterases (AChEs) catalyze the hydrolysis of acetylcholine, a neurotransmitter for cholinergic neurotransmission in animals. Most insects studied so far possess two AChE genes: ace-1 paralogous and ace-2 orthologous to Drosophila melanogaster ace. We characterized the catalytic domain of Anopheles gambiae AChE1 in a previous study (Jiang et al., 2009) and report here biochemical properties of A. gambiae AChE2 expressed in Sf9 cells. An unknown protease in the expression system cleaved the recombinant AChE2 next to Arg(110), yielding two non-covalently associated polypeptides. A mixture of the intact and cleaved AChE2 had a specific activity of 72.3 U/mg, much lower than that of A. gambiae AChE1 (523 U/mg). The order of V(max)/K(M) values for the model substrates was acetylthiocholine > propionylthiocholine ≈ acetyl-(β-methyl)thiocholine > butyrylthiocholine. The IC(50)'s for eserine, carbaryl, BW284C51, paraoxon and malaoxon were 1.32, 13.6, 26.8, 192 and 294 nM, respectively. A. gambiae AChE2 bound eserine and carbaryl stronger than paraoxon and malaoxon, whereas eserine and malaoxon modified the active site Ser(232) faster than carbaryl or paraoxon did. Consequently, the k(i)'s were 1.173, 0.245, 0.029 and 0.018 μM(-1)min(-1) for eserine, carbaryl, paraoxon and malaoxon, respectively. Quantitative polymerase chain reactions showed a similar pattern of ace-1 and ace-2 expression. Their mRNAs were abundant in early embryos, greatly decreased in late embryos, larvae, pupae, and pharate adult, and became abundant again in adults. Both transcripts were higher in head and abdomen than thorax of adults and higher in male than female mosquitoes. Transcript levels of ace-1 were 1.9- to 361.8-fold higher than those of ace-2, depending on developmental stages and body parts. Cross-reacting polyclonal antibodies detected AChEs in adult brains, thoracic ganglia, and genital/rectal area. Activity assays, immunoblotting, and tandem mass spectrometric 20. Response and recovery of acetylcholinesterase activity in freshwater shrimp, Paratya australiensis (Decapoda: Atyidae) exposed to selected anti-cholinesterase insecticides. PubMed Kumar, A; Doan, H; Barnes, Mary; Chapman, J C; Kookana, R S 2010-10-01 The toxicity of carbaryl, chlorpyrifos, dimethoate and profenofos to the freshwater shrimp, Paratya australiensis was assessed by measuring acetylcholinesterase (AChE) inhibition after 96h exposures. Shrimp exposed to these pesticides exhibited significant AChE inhibition, with mortality in shrimp corresponding to 70-90% AChE inhibition. The sensitivity of P. australiensis to the four pesticides based on AChE inhibition can be given as chlorpyrifos > profenofos > carbaryl > dimethoate. Recovery of AChE activity was followed in shrimp after 96 h exposures to carbaryl, chlorpyrifos and dimethoate. Recovery after exposure to the carbamate pesticide carbaryl was more rapid than for the two organophosphorus pesticides, chlorpyrifos and dimethoate. The slow recovery of depressed AChE activity may mean that affected organisms in the natural system are unable to sustain physical activities such as searching for food or eluding predators. To investigate the ecological significance of AChE inhibition, chemotaxis behaviour was assessed in shrimp exposed to profenofos for 24h. Abnormal chemotaxis behaviour in the exposed shrimp was observed at concentrations representing 30-50% AChE inhibition. A clear relationship existed between the depression of AChE activity and observed chemotaxis responses, such as approaching and grasping the chemoattractant source. These results suggest that in vivo toxicity tests based on this specific biomarker are sensitive and present advantages over conventional acute tests based on mortality. Behavioural studies of test organisms conducted in conjunction with measurement of AChE inhibition will provide data to clarify the toxic effects caused by sublethal chemical concentrations of anti-cholinesterase compounds. PMID:20701973 1. Screening for antimalarial and acetylcholinesterase inhibitory activities of some Iranian seaweeds. PubMed Ghannadi, A; Plubrukarn, A; Zandi, K; Sartavi, K; Yegdaneh, A 2013-04-01 Alcoholic extracts of 8 different types of seaweeds from Iran's Persian Gulf were tested for their antimalarial and acetylcholinesterase enzyme (AChE) inhibitory activities for the first time. A modified Ellman and Ingkaninan method was used for measuring AChE inhibitory activity in which galanthamine was used as the reference. The antimalarial assay was performed using microculture radioisotope technique. Mefloquine and dihydroartemisinin were uased as the standards. The extract of Sargassum boveanum (Sargasseae family) showed the highest AChE inhibitory activity (IC50 equals to 1 mg ml(-1)) while Cystoseira indica (Cystoseiraceae family) exhibited the least activity (IC50 of 11 mg ml(-1)). The species from Rhodophyta (Gracilaria corticata and Gracilaria salicornia) also showed moderate activities (IC509.5, 8.7 mg ml(-1), respectively). All extracts were inactive in antimalarial assay. PMID:24019820 2. Screening for acetylcholinesterase inhibition and antioxidant activity of selected plants from Croatia. PubMed Jukic, Mila; Burcul, Franko; Carev, Ivana; Politeo, Olivera; Milos, Mladen 2012-01-01 The methanol, ethyl acetate and chloroform extracts of selected Croatian plants were tested for their acetylcholinesterase (AChE) inhibition and antioxidant activity. Assessment of AChE inhibition was carried out using microplate reader at 1 mg mL⁻¹. Antioxidant capacities were determined by 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging test and ferric reducing/antioxidant power assay (FRAP). Total phenol content (TPC) of extracts were determined using Folin-Ciocalteu colorimetric method. Out of 48 extracts, only methanolic extract of the Salix alba L. cortex exerted modest activity towards AChE, reaching 50.80% inhibition at concentration of 1 mg mL⁻¹. All the other samples tested had activity below 20%. The same extract performed the best antioxidative activity using DPPH and FRAP method, too. In essence, among all extracts used in the screening, methanolic extracts showed the best antioxidative activity as well as highest TPC. 3. Solanocapsine derivatives as potential inhibitors of acetylcholinesterase: Synthesis, molecular docking and biological studies. PubMed García, Manuela E; Borioni, José L; Cavallaro, Valeria; Puiatti, Marcelo; Pierini, Adriana B; Murray, Ana P; Peñéñory, Alicia B 2015-12-01 The investigation of natural products in medicinal chemistry is essential today. In this context, acetylcholinesterase (AChE) inhibitors comprise one type of the compounds most actively studied in the search for an effective treatment of symptoms of Alzheimer's disease. This work describes the isolation of a natural compound, solanocapsine, the preparation of its chemical derivatives, the evaluation of AChE inhibitory activity, and the structure-activity analysis of relevant cases. The influence of structural variations on the inhibitory potency was carefully investigated by modifying different reactive parts of the parent molecule. A theoretical study was also carried out into the binding mode of representative compounds to the enzyme through molecular modeling. The biological properties of the series were investigated. Through this study valuable information was obtained of steroidal alkaloid-type compounds as a starting point for the synthesis of AChE inhibitors. PMID:26362598 4. Purification and characterization of acetylcholinesterase from the Lake Van fish (Chalcalburnus tarichii Pallas, 1811). PubMed Aliriz, Serpil; Turkoglu, Vedat 2003-05-01 In this study, acetylcholinesterase (AChE; EC 3.1.1.7) was purified from plasma and erythrocytes in the Lake Van fish (Chalcalburnus tarichii P.1811) by affinity chromatography. Enzymatic activity was spectrophotometrically measured according to Ellman's method, at 412 nm. Then, the optimal pH and temperature of the enzyme was determined. According to the results, the optimal pH and the optimum temperature were 8.0 and 25 degrees C, respectively. In order to control the purification of the enzyme, sodium dodecyl-sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) was done. SDS-PAGE showed a single band for enzyme. The purification rates for plasma AChE and erythrocyte AChE are 3251.6 and 8500, respectively. 5. Evaluation of acetylcholinesterase source from fish, Tor tambroides for detection of carbamate. PubMed Ahmad, Siti Aqlima; Sabullah, Mohd Khalizan; Shamaan, Nor Aripin; Abd Shukor, Mohd Yunus; Jirangon, Hussain; Khalid, Ariff; Syed, Mohd Arif 2016-07-01 Acetylcholinesterase (AChE) from the brain tissue of local freshwater fish, Tor tambroides was isolated through affinity purification. Acetylthiocholine iodide (ATCi) was preferable synthetic substrate to purified AChE with highest maximal velocity (V(max)) and lowest biomolecular constant (K(m)) at 113.60 Umg(-1) and 0.0689 mM, respectively, with highest catalytic efficiency ratio (V(max)/K(m)) of 1648.77. The optimum pH was 7.5 with sodium phosphate buffer as medium, while optimal temperature was in the range of 25 to 35 degrees C. Bendiocarp, carbofuran, carbaryl, methomyl and propoxur significantly lowered the AChE activity greater than 50%, and the IC50 value was estimated at inhibitor concentration of 0.0758, 0.0643, 0.0555, 0.0817 and 0.0538 ppm, respectively. PMID:27498490 6. Acetylcholinesterase, a senile plaque component, affects the fibrillogenesis of amyloid-beta-peptides. PubMed Alvarez, A; Bronfman, F; Pérez, C A; Vicente, M; Garrido, J; Inestrosa, N C 1995-12-01 Acetylcholinesterase (AChE) colocalizes with amyloid-beta peptide (A beta) deposits present in the brain of Alzheimer's patients. Recent studies showed that A beta 1-40 can adopt two different conformational states in solution (an amyloidogenic conformer, A beta ac, and a non-amyloidogenic conformer, A beta nac) which have distinct abilities to form amyloid fibrils. We report here that AChE binds A beta nac and accelerates amyloid formation by the same peptide. No such effect was observed with A beta ac, the amyloidogenic conformer, suggesting that AChE acts as a 'pathological chaperone' inducing a conformational transition from A beta nac into A beta ac in vitro. 7. Differential acetylcholinesterase inhibition of chlorpyrifos, diazinon and parathion in larval zebrafish PubMed Central Yen, Jerry; Donerly, Sue; Levin, Edward D.; Linney, Elwood A. 2011-01-01 Zebrafish are increasingly used for developmental neurotoxicity testing because early embryonic events are easy to visualize, exposures are done without affecting the mother and the rapid development of zebrafish allows for high throughput testing. We used zebrafish to examine how exposures to three different organophosphorus pesticides (chlorpyrifos, diazinon and parathion) over the first five days of embryonic and larval development of zebrafish affected their survival, acetylcholinesterase (AChE) activity and behavior. We show that at non-lethal, equimolar concentrations, chlorpyrifos (CPF) is more effective at equimolar concentrations than diazinon (DZN) and parathion (PA) in producing AChE inhibition. As concentrations of DZN and PA are raised, lethality occurs before they can produce the degree of AChE inhibition observed with CPF at 300nM. Because of its availability outside the mother at the time of fertilization, zebrafish provides a complementary model for studying the neurotoxicity of very early developmental exposures. PMID:22036888 8. Highly Sensitive and Selective Immuno-capture/Electrochemical Assay of Acetylcholinesterase Activity in Red Blood Cells: A Biomarker of Exposure to Organophosphorus Pesticides and Nerve Agents SciTech Connect Chen, Aiqiong; Du, Dan; Lin, Yuehe 2012-02-09 Acetylcholinesterase (AChE) enzyme activity in red blood cells (RBCs) is a useful biomarker for biomonitoring of exposures to organophosphorus (OP) pesticides and chemical nerve agents. In this paper, we reported a new method for AChE activity assay based on selective immuno-capture of AChE from biological samples followed by enzyme activity assay of captured AChE using a disposable electrochemical sensor. The electrochemical sensor is based on multiwalled carbon nanotubes-gold nanocomposites (MWCNTs-Au) modified screen printed carbon electrode (SPCE). Upon the completion of immunoreaction, the target AChE (including active and inhibited) is captured onto the electrode surface and followed by an electrochemical detection of enzymatic activity in the presence of acetylthiocholine. A linear response is obtained over standard AChE concentration range from 0.1 to 10 nM. To demonstrate the capability of this new biomonitoring method, AChE solutions dosed with different concentration of paraoxon were used to validate the new AChE assay method. AChE inhibition in OP dosed solutions was proportional to its concentration from 0.2 to 50 nM. The new AChE activity assay method for biomonitoring of OP exposure was further validated with in-vitro paraoxon-dosed RBC samples. The established electrochemical sensing platform for AChE activity assay not only avoids the problem of overlapping substrate specificity with esterases by using selective antibody, but also eliminates potential interference from other electroactive species in biological samples. It offers a new approach for sensitive, selective, and rapid AChE activity assay for biomonitoring of exposures to OPs. 9. Cardanol-derived AChE inhibitors: Towards the development of dual binding derivatives for Alzheimer's disease. PubMed Lemes, Laís Flávia Nunes; de Andrade Ramos, Giselle; de Oliveira, Andressa Souza; da Silva, Fernanda Motta R; de Castro Couto, Gina; da Silva Boni, Marina; Guimarães, Marcos Jorge R; Souza, Isis Nem O; Bartolini, Manuela; Andrisano, Vincenza; do Nascimento Nogueira, Patrícia Coelho; Silveira, Edilberto Rocha; Brand, Guilherme D; Soukup, Ondřej; Korábečný, Jan; Romeiro, Nelilma C; Castro, Newton G; Bolognesi, Maria Laura; Romeiro, Luiz Antonio Soares 2016-01-27 Cardanol is a phenolic lipid component of cashew nut shell liquid (CNSL), obtained as the byproduct of cashew nut food processing. Being a waste product, it has attracted much attention as a precursor for the production of high-value chemicals, including drugs. On the basis of these findings and in connection with our previous studies on cardanol derivatives as acetylcholinesterase (AChE) inhibitors, we designed a novel series of analogues by including a protonable amino moiety belonging to different systems. Properly addressed docking studies suggested that the proposed structural modifications would allow the new molecules to interact with both the catalytic active site (CAS) and the peripheral anionic site (PAS) of AChE, thus being able to act as dual binding inhibitors. To disclose whether the new molecules showed the desired profile, they were first tested for their cholinesterase inhibitory activity towards EeAChE and eqBuChE. Compound 26, bearing an N-ethyl-N-(2-methoxybenzyl)amine moiety, showed the highest inhibitory activity against EeAChE, with a promising IC50 of 6.6 μM, and a similar inhibition profile of the human isoform (IC50 = 5.7 μM). As another positive feature, most of the derivatives did not show appreciable toxicity against HT-29 cells, up to a concentration of 100 μM, which indicates drug-conform behavior. Also, compound 26 is capable of crossing the blood-brain barrier (BBB), as predicted by a PAMPA-BBB assay. Collectively, the data suggest that the approach to obtain potential anti-Alzheimer drugs from CNSL is worth of further pursuit and development. PMID:26735910 10. Natural factors to consider when using acetylcholinesterase activity as neurotoxicity biomarker in Young-Of-Year striped bass (Morone saxatilis). PubMed Durieux, Eric D H; Farver, Thomas B; Fitzgerald, Patrick S; Eder, Kai J; Ostrach, David J 2011-03-01 Acetylcholinesterase (AChE) activity is one of the most common biomarkers of neurotoxicity used in aquatic organisms. However, compared to its extensive use as biomarker, the effects of natural factors on AChE activity remain unclear especially in estuarine fishes. The aim of this study was to evaluate the effects of natural factors on AChE activity of striped bass (Morone saxatilis) juveniles. Brain AChE activity was measured in YOY (Young-Of-Year) individuals collected monthly from August 2007 to January 2008 at 12 different sites in the San Francisco Estuary system. The spatio-temporal variability of AChE was analyzed relative to water temperature and salinity as well as fish size. AChE activity was highly positively correlated with water temperature and to a lesser extent negatively with fish size while no relationship was detected with salinity. Taking into account these natural factors when using AChE as a biomarker will help to determine and understand the effects of neurotoxic contaminants on fish in estuarine systems. 11. Upregulation of Acetylcholinesterase Mediated by p53 Contributes to Cisplatin-Induced Apoptosis in Human Breast Cancer Cell PubMed Central Ye, Xiaolei; Zhang, Changsong; Chen, Yichen; Zhou, Tianbao 2015-01-01 Background: The expression of acetylcholinesterase (AChE) could be induced during apoptosis in various cell types. And reduced AChE expression either by siRNA could prevent apoptosis. However, the detailed mechanisms underlying the AChE regulation are largely unknown in human breast cancer cell. Material and methods: MCF-7 cells were cultured and treated by cisplatin in the absence or presence of p53 siRNA. Results: In this study, the regulation of AChE expression during apoptosis induced by cisplatin, a current used anticancer drug, was investigated in human breast cancer cell line MCF-7. Exposure of MCF-7 cells to cisplatin resulted in apoptosis in a time- and concentration-dependent manner. Meanwhile, the upregulated AChE and p53 were also observed during apoptosis. Silencing interfering RNA directed against p53 blocked the expression of AChE. Conclusion: Taken together, these results suggested that AChE expression could be upregulated by the activation of p53 during apoptosis induced by cisplatin in MCF-7 cells. PMID:25553088 12. SC35 promotes sustainable stress-induced alternative splicing of neuronal acetylcholinesterase mRNA. PubMed Meshorer, E; Bryk, B; Toiber, D; Cohen, J; Podoly, E; Dori, A; Soreq, H 2005-11-01 Long-lasting alternative splicing of neuronal acetylcholinesterase (AChE) pre-mRNA occurs during neuronal development and following stress, altering synaptic properties. To explore the corresponding molecular events, we sought to identify mRNAs encoding for abundant splicing factors in the prefrontal cortex (PFC) following stress. Here we show elevated levels of the splicing factor SC35 in stressed as compared with naïve mice. In cotransfections of COS-1 and HEK293 cells with an AChE minigene allowing 3' splice variations, SC35 facilitated a shift from the primary AChE-S to the stress-induced AChE-R variant, while ASF/SF2 caused the opposite effect. Transfection with chimeric constructs comprising of SC35 and ASF/SF2 RRM/RS domains identified the SC35 RRM as responsible for AChE mRNA's alternative splicing. In poststress PFC neurons, increased SC35 mRNA and protein levels coincided with selective increase in AChE-R mRNA. In the developing mouse embryo, cortical progenitor cells in the ventricular zone displayed transient SC35 elevation concomitant with dominance of AChE-R over AChE-S mRNA. Finally, transgenic mice overexpressing human AChE-R, but not those overexpressing AChE-S, showed significant elevation in neuronal SC35 levels, suggesting a reciprocal reinforcement process. Together, these findings point to an interactive relationship of SC35 with cholinergic signals in the long-lasting consequences of stress on nervous system plasticity and development. 13. Inhibitory effects of sodium arsenite and acacia honey on acetylcholinesterase in rats. PubMed Muhammad, Aliyu; Odunola, Oyeronke A; Gbadegesin, Michael A; Sallau, Abdullahi B; Ndidi, Uche S; Ibrahim, Mohammed A 2015-01-01 This study was conducted to investigate the effect of sodium arsenite and Acacia honey on acetylcholinesterase (AChE) activity and electrolytes in the brain and serum of Wistar rats. Male Wistar albino rats in four groups of five rats each were treated with distilled water, sodium arsenite (5 mg/kg body weight), Acacia honey (20% v/v), and sodium arsenite and Acacia honey, daily for one week. The sodium arsenite and Acacia honey significantly (P < 0.05) decreased AChE activity in the brain with the combined treatment being more potent. Furthermore, sodium arsenite and Acacia honey significantly (P < 0.05) decreased AChE activity in the serum. Strong correlation was observed between the sodium and calcium ion levels with acetylcholinesterase activity in the brain and serum. The gas chromatography mass spectrometry analysis of Acacia honey revealed the presence of a number of bioactive compounds such as phenolics, sugar derivatives, and fatty acids. These findings suggest that sodium arsenite and/or Acacia honey modulates acetylcholinesterase activities which may be explored in the management of Alzheimer's diseases but this might be counteracted by the hepatotoxicity induced by arsenics. PMID:25821630 14. Inhibitory Effects of Sodium Arsenite and Acacia Honey on Acetylcholinesterase in Rats PubMed Central Odunola, Oyeronke A.; Gbadegesin, Michael A.; Sallau, Abdullahi B.; Ndidi, Uche S.; Ibrahim, Mohammed A. 2015-01-01 This study was conducted to investigate the effect of sodium arsenite and Acacia honey on acetylcholinesterase (AChE) activity and electrolytes in the brain and serum of Wistar rats. Male Wistar albino rats in four groups of five rats each were treated with distilled water, sodium arsenite (5 mg/kg body weight), Acacia honey (20% v/v), and sodium arsenite and Acacia honey, daily for one week. The sodium arsenite and Acacia honey significantly (P < 0.05) decreased AChE activity in the brain with the combined treatment being more potent. Furthermore, sodium arsenite and Acacia honey significantly (P < 0.05) decreased AChE activity in the serum. Strong correlation was observed between the sodium and calcium ion levels with acetylcholinesterase activity in the brain and serum. The gas chromatography mass spectrometry analysis of Acacia honey revealed the presence of a number of bioactive compounds such as phenolics, sugar derivatives, and fatty acids. These findings suggest that sodium arsenite and/or Acacia honey modulates acetylcholinesterase activities which may be explored in the management of Alzheimer's diseases but this might be counteracted by the hepatotoxicity induced by arsenics. PMID:25821630 15. Is acetylcholinesterase a biomarker of susceptibility in Daphnia magna (Crustacea, Cladocera) after deltamethrin exposure? PubMed Toumi, Héla; Boumaiza, Moncef; Millet, Maurice; Radetski, Claudemir Marcos; Felten, Vincent; Férard, Jean François 2015-02-01 In the present study, we explored the possibility of using the acetylcholinesterase (AChE) as a biomarker after deltamethrin (pyrethroid insecticide) exposure with three strains of the cladoceran Daphnia magna. Four calculated time-weighted deltamethrin concentrations (20.1, 40.3, 80.6 and 161.3 ng L(-1)) were compared against control acetylcholinesterase activity. Our results showed that after 48 h of deltamethrin exposure, all treatments induced a significant decrease of AChE activities whatever the three considered strains. However, diverse responses were registered in terms of lowest observed effect concentrations (LOEC: 80.6 ng L(-1) for strain 1 and 20.1 ng L(-1) for strains 2 and 3) revealing differences in sensitivity among the three tested strains of D. magna. Our results suggest that after deltamethrin exposure, the AChE activity responses can be also used as a biomarker of susceptibility (i.e., variation of strain specific response). Moreover, our results show that strain 1 is the less sensitive in terms of IC50-48 h of AChE, whereas it became the most sensitive when considering the EC50-48 h estimated in the standard ecotoxicity test. 16. Virtual Screening of Acetylcholinesterase Inhibitors Using the Lipinski's Rule of Five and ZINC Databank PubMed Central Nogara, Pablo Andrei; Saraiva, Rogério de Aquino; Caeran Bueno, Diones; Lissner, Lílian Juliana; Lenz Dalla Corte, Cristiane; Braga, Marcos M.; Rosemberg, Denis Broock; Rocha, João Batista Teixeira 2015-01-01 Alzheimer's disease (AD) is a progressive and neurodegenerative pathology that can affect people over 65 years of age. It causes several complications, such as behavioral changes, language deficits, depression, and memory impairments. One of the methods used to treat AD is the increase of acetylcholine (ACh) in the brain by using acetylcholinesterase inhibitors (AChEIs). In this study, we used the ZINC databank and the Lipinski's rule of five to perform a virtual screening and a molecular docking (using Auto Dock Vina 1.1.1) aiming to select possible compounds that have quaternary ammonium atom able to inhibit acetylcholinesterase (AChE) activity. The molecules were obtained by screening and further in vitro assays were performed to analyze the most potent inhibitors through the IC50 value and also to describe the interaction models between inhibitors and enzyme by molecular docking. The results showed that compound D inhibited AChE activity from different vertebrate sources and butyrylcholinesterase (BChE) from Equus ferus (EfBChE), with IC50 ranging from 1.69 ± 0.46 to 5.64 ± 2.47 µM. Compound D interacted with the peripheral anionic subsite in both enzymes, blocking substrate entrance to the active site. In contrast, compound C had higher specificity as inhibitor of EfBChE. In conclusion, the screening was effective in finding inhibitors of AChE and BuChE from different organisms. PMID:25685814 17. 2,3-Dihydro-1H-cyclopenta[b]quinoline Derivatives as Acetylcholinesterase Inhibitors—Synthesis, Radiolabeling and Biodistribution PubMed Central Szymański, Paweł; Lázničková, Alice; Lázniček, Milan; Bajda, Marek; Malawska, Barbara; Markowicz, Magdalena; Mikiciuk-Olasik, Elżbieta 2012-01-01 In the present study we describe the synthesis and biological assessment of new tacrine analogs in the course of inhibition of acetylcholinesterase. The obtained molecules were synthesized in a condensation reaction between activated 6-BOC-hydrazinopyridine-3-carboxylic acid and 8-aminoalkyl derivatives of 2,3-dihydro-1H-cyclopenta[b]quinoline. Activities of the newly synthesized compounds were estimated by means of Ellman’s method. Compound 6h (IC50 = 3.65 nM) was found to be most active. All obtained novel compounds present comparable activity to that of tacrine towards acetylcholinesterase (AChE) and, simultaneously, lower activity towards butyrylcholinesterase (BChE). Apart from 6a, all synthesized compounds are characterized by a higher affinity for AChE and a lower affinity for BChE in comparison with tacrine. Among all obtained molecules, compound 6h presented the highest selectivity towards inhibition of acetylcholinesterase. Molecular modeling showed that all compounds demonstrated a similar binding mode with AChE and interacted with catalytic and peripheral sites of AChE. Also, a biodistribution study of compound 6a radiolabeled with 99mTc was performed. PMID:22949848 18. Rational modification of donepezil as multifunctional acetylcholinesterase inhibitors for the treatment of Alzheimer's disease. PubMed Wang, Zhi-Min; Cai, Pei; Liu, Qiao-Hong; Xu, Ding-Qiao; Yang, Xue-Lian; Wu, Jia-Jia; Kong, Ling-Yi; Wang, Xiao-Bing 2016-11-10 A series of novel donepezil derivatives was designed, synthesized and evaluated as multifunctional acetylcholinesterase (AChE) inhibitors for the treatment of Alzheimer's disease (AD). The screening results indicated that most of the compounds exhibited potent inhibition of AChE with IC50 values in the nanomolar range. Moreover, these derivatives displayed good antioxidant, Aβ interaction, blood-brain barrier penetration (PAMPA-BBB+) and ADMET properties (in silico). Among them, 5c demonstrated excellent AChE inhibition (IC50: 85 nM for eeAChE, 73 nM for hAChE), metal chelation, and inhibitory effects on self-induced, hAChE-induced and Cu(2+)-induced Aβ1-42 aggregation (18.5%, 72.4% and 46.3%, at 20 μM). Kinetic analysis and molecular modeling studies suggested that 5c could bind simultaneously to the catalytic active site (CAS) and peripheral anionic site (PAS) of AChE. More importantly, 5c exhibited significant neuroprotective potency against Aβ1-42-induced PC12 cell injury. Furthermore, the step-through passive avoidance test showed 5c significantly reversed scopolamine-induced memory deficit and no hepatotoxicity in mice. These results indicated that 5c might be a promising drug candidate for AD therapy. PMID:27484514 19. Calretinin immunohistochemistry versus acetylcholinesterase histochemistry in the evaluation of suction rectal biopsies for Hirschsprung Disease. PubMed Kapur, Raj P; Reed, Robyn C; Finn, Laura S; Patterson, Kathleen; Johanson, Judy; Rutledge, Joe C 2009-01-01 Diagnosis of Hirschsprung disease (HSCR) relies on histologic and/or histochemical staining of sections from suction rectal biopsies. Acetylcholinesterase histochemistry (AChE) facilitates diagnosis but is not universally employed, in part because it requires special tissue handling. Calretinin immunohistochemistry (IHC) may be a useful alternative, because loss of calretinin immunoreactive nerves reportedly correlates spatially with aganglionosis. We investigated the patterns of calretinin IHC in suction rectal biopsies from HSCR and non-HSCR patients and compared the diagnostic value of calretinin IHC with a widely used rapid AChE method. In suction rectal biopsies that contain ganglion cells, small nerves in the lamina propria, muscularis mucosae, and superficial submucosa contain granular aggregates of calretinin immunoreactivity. Immunolabeling of these nerves is completely absent in the aganglionic biopsies of HSCR patients. Multiple observers independently reviewed calretinin IHC and AChE sections of suction rectal biopsies from 14 HSCR patients and 17 non-HSCR controls. Five observers, blinded to the correct diagnosis, scored each patient's calretinin IHC and AChE slides as HSCR, not HSCR, or equivocal. The frequencies of major and minor discrepant diagnoses were compared. Calretinin IHC yielded no misdiagnoses or major discrepancies between observers. In contrast, 2 misdiagnoses and significantly more interobserver disagreement resulted from the AChE-stained sections. Calretinin IHC appears to be a reasonable, and potentially superior, alternative to AChE as an adjunctive diagnostic method for evaluating suction rectal biopsies for HSCR. 20. Molecular and Kinetic Properties of Two Acetylcholinesterases from the Western Honey Bee, Apis mellifera PubMed Central Kim, Young Ho; Cha, Deok Jea; Jung, Je Won; Kwon, Hyung Wook; Lee, Si Hyeock 2012-01-01 We investigated the molecular and kinetic properties of two acetylcholinesterases (AmAChE1 and AmAChE2) from the Western honey bee, Apis mellifera. Western blot analysis revealed that AmAChE2 has most of catalytic activity rather than AmAChE1, further suggesting that AmAChE2 is responsible for synaptic transmission in A. mellifera, in contrast to most other insects. AmAChE2 was predominately expressed in the ganglia and head containing the central nervous system (CNS), while AmAChE1 was abundantly observed not only in the CNS but also in the peripheral nervous system/non-neuronal tissues. Both AmAChEs exist as homodimers; the monomers are covalently connected via a disulfide bond under native conditions. However, AmAChE2 was associated with the cell membrane via the glycophosphatidylinositol anchor, while AmAChE1 was present as a soluble form. The two AmAChEs were functionally expressed with a baculovirus system. Kinetic analysis revealed that AmAChE2 has approximately 2,500-fold greater catalytic efficiency toward acetylthiocholine and butyrylthiocholine than AmAChE1, supporting the synaptic function of AmAChE2. In addition, AmAChE2 likely serves as the main target of the organophosphate (OP) and carbamate (CB) insecticides as judged by the lower IC50 values against AmAChE2 than against AmAChE1. When OP and CB insecticides were pre-incubated with a mixture of AmAChE1 and AmAChE2, a significant reduction in the inhibition of AmAChE2 was observed, suggesting a protective role of AmAChE1 against xenobiotics. Taken together, based on their tissue distribution pattern, molecular and kinetic properties, AmAChE2 plays a major role in synaptic transmission, while AmAChE1 has non-neuronal functions, including chemical defense. PMID:23144990 1. A Mechanism-based 3D-QSAR Approach for Classification and Prediction of Acetylcholinesterase Inhibitory Potency of Organophosphate and Carbamate Analogs EPA Science Inventory Organophosphate (OP) and carbamate esters can inhibit acetylcholinesterase (AChE) by binding covalently to a serine residue in the enzyme active site, and their inhibitory potency depends largely on affinity for the enzyme and the reactivity of the ester. Despite this understandi... 2. Extracts and constituents of Leontopodium alpinum enhance cholinergic transmission: Brain ACh increasing and memory improving properties PubMed Central Hornick, Ariane; Schwaiger, Stefan; Rollinger, Judith M.; Vo, Nguyen Phung; Prast, Helmut; Stuppner, Hermann 2012-01-01 Leontopodium alpinum (‘Edelweiss’) was phytochemically investigated for constituents that might enhance cholinergic neurotransmission. The potency to increase synaptic availability of acetylcholine (ACh) in rat brain served as key property for the bioguided isolation of cholinergically active compounds using different chromatographic techniques. The dichlormethane (DCM) extract of the root, fractions and isolated constituents were injected i.c.v. and the effect on brain ACh was detected via the push–pull technique. The DCM extract enhanced extracellular ACh concentration in rat brain and inhibited acetylcholinesterase (AChE) in vitro. The extracellular level of brain ACh was significantly increased by the isolated sesquiterpenes, isocomene and 14-acetoxyisocomene, while silphiperfolene acetate and silphinene caused a small increasing tendency. Only silphiperfolene acetate showed in vitro AChE inhibitory activity, thus suggesting the other sesquiterpenes to stimulate cholinergic transmission by an alternative mechanism of action. Isocomene was further investigated with behavioural tasks in mice. It restored object recognition in scopolamine-impaired mice and showed nootropic effects in the T-maze alternation task in normal and scopolamine-treated mice. Additionally, this sesquiterpene reduced locomotor activity of untreated mice in the open field task, while the activity induced by scopolamine was abolished. The enhancement of synaptic availability of ACh, the promotion of alternation, and the amelioration of scopolamine-induced deficit are in accordance with a substance that amplifies cholinergic transmission. Whether the mechanism of action is inhibition of AChE or another pro-cholinergic property remains to be elucidated. Taken together, isocomene and related constituents of L. alpinum deserve further interest as potential antidementia agents in brain diseases associated with cholinergic deficits. PMID:18541221 3. Targeting Acetylcholinesterase: Identification of Chemical Leads by High Throughput Screening, Structure Determination and Molecular Modeling PubMed Central Berg, Lotta; Andersson, C. David; Artursson, Elisabet; Hörnberg, Andreas; Tunemalm, Anna-Karin; Linusson, Anna; Ekström, Fredrik 2011-01-01 Acetylcholinesterase (AChE) is an essential enzyme that terminates cholinergic transmission by rapid hydrolysis of the neurotransmitter acetylcholine. Compounds inhibiting this enzyme can be used (inter alia) to treat cholinergic deficiencies (e.g. in Alzheimer's disease), but may also act as dangerous toxins (e.g. nerve agents such as sarin). Treatment of nerve agent poisoning involves use of antidotes, small molecules capable of reactivating AChE. We have screened a collection of organic molecules to assess their ability to inhibit the enzymatic activity of AChE, aiming to find lead compounds for further optimization leading to drugs with increased efficacy and/or decreased side effects. 124 inhibitors were discovered, with considerable chemical diversity regarding size, polarity, flexibility and charge distribution. An extensive structure determination campaign resulted in a set of crystal structures of protein-ligand complexes. Overall, the ligands have substantial interactions with the peripheral anionic site of AChE, and the majority form additional interactions with the catalytic site (CAS). Reproduction of the bioactive conformation of six of the ligands using molecular docking simulations required modification of the default parameter settings of the docking software. The results show that docking-assisted structure-based design of AChE inhibitors is challenging and requires crystallographic support to obtain reliable results, at least with currently available software. The complex formed between C5685 and Mus musculus AChE (C5685•mAChE) is a representative structure for the general binding mode of the determined structures. The CAS binding part of C5685 could not be structurally determined due to a disordered electron density map and the developed docking protocol was used to predict the binding modes of this part of the molecule. We believe that chemical modifications of our discovered inhibitors, biochemical and biophysical characterization 4. Electroanalysis of amino acid substitutions in bioengineered acetylcholinesterase. PubMed Somji, Mehdi; Dounin, Vladimir; Muench, Susanne B; Schulze, Holger; Bachmann, Till T; Kerman, Kagan 2012-12-01 This study reports the electrochemical profiling of Nippostrongylus brasiliensis acetylcholinesterase (AChE) wild-type and mutant proteins. An irreversible oxidation signal of electro-active tyrosine (Y), tryptophan (W) and cysteine (C) residues in five mutant proteins along with the wild-type AChE were detected using square-wave voltammetry (SWV) on screen-printed carbon electrodes. Significant differences were observed in the W303L, T65Y and M301W substituted proteins showing a 25-35% higher peak current intensity compared to the Y349Y and F345Y mutants. It was predicted that AChE substituted with electrochemically active residues would produce the greatest signals and this trend was observed in the T65Y, M301W and Y349L mutants. However, conformational changes in the proteins structure as a result of the substitutions appeared to be most influential on peak current intensities. This was demonstrated by the W303L and F345Y mutant enzymes. The current intensity of W303L was greatest despite the removal of its electro-active W residue whereas the F345Y mutant had the lowest peak value despite the addition of an electro-active Y residue. The preliminary results of this study demonstrate that SWV provides a promising tool to probe the presence of electro-active amino acid residues on the surface of a protein produced through bioengineering. 5. Cortical metabolism, acetylcholinesterase staining and pathological changes in Alzheimer's disease. PubMed McGeer, E G; McGeer, P L; Kamo, H; Tago, H; Harrop, R 1986-11-01 The local cerebral metabolic rate for glucose (LCMRgl) was determined by positron emission tomography (PET) using the 18F-fluorodeoxyglucose method in a series of Alzheimer patients and normal controls. The LCMRgl declined in the cerebral cortex with age, but the decrement was significantly greater in the clinically diagnosed Alzheimer's cases. Comparison of PET and psychological data indicated that, as the disease progressed clinically, the reduction in cortical LCMRgl and the number of cortical regions involved also increased. Variable regions of cortex were involved in the early stages but the temporal, parietal and frontal regions were most typically affected. One case coming to autopsy showed that the severity of the LCMRgl decline paralleled loss of neurons in the cortex and their replacement with astroglia. A case of Pick's disease coming to autopsy had shown a different and highly characteristic pattern of cortical metabolic defect. In this case also a poor metabolic rate was associated with extensive gliosis. Acetylcholinesterase (AChE) staining of the cerebral cortex in elderly normals and Alzheimer's disease cases with a new, highly sensitive method showed that in Alzheimer's disease there was an extensive loss of AChE-positive fibers with senile plaques frequently incorporating AChE-positive fiber debris. AChE staining of the substantia innominata area, where the cells giving rise to these neocortical fibers are presumably located, also showed evidence of degenerating cells and fibers. 6. Acetylcholinesterase Biosensors for Electrochemical Detection of Organophosphorus Compounds: A Review PubMed Central Dhull, Vikas; Gahlaut, Anjum; Dilbaghi, Neeraj 2013-01-01 The exponentially growing population, with limited resources, has exerted an intense pressure on the agriculture sector. In order to achieve high productivity the use of pesticide has increased up to many folds. These pesticides contain organophosphorus (OP) toxic compounds which interfere with the proper functioning of enzyme acetylcholinesterase (AChE) and finally affect the central nervous system (CNS). So, there is a need for routine, continuous, on spot detection of OP compounds which are the main limitations associated with conventional analytical methods. AChE based enzymatic biosensors have been reported by researchers as the most promising tool for analysis of pesticide level to control toxicity and for environment conservation. The present review summarises AChE based biosensors by discussing their characteristic features in terms of fabrication, detection limit, linearity range, time of incubation, and storage stability. Use of nanoparticles in recently reported fabrication strategies has improved the efficiency of biosensors to a great extent making them more reliable and robust. PMID:24383001 7. Alkaloid metabolite profiles by GC/MS and acetylcholinesterase inhibitory activities with binding-mode predictions of five Amaryllidaceae plants. PubMed Cortes, Natalie; Alvarez, Rafael; Osorio, Edison H; Alzate, Fernando; Berkov, Strahil; Osorio, Edison 2015-01-01 Acetylcholinesterase (AChE) enzymatic inhibition is an important target for the management of Alzheimer disease (AD) and AChE inhibitors are the mainstay drugs for its treatment. In order to discover new sources of potent AChE inhibitors, a combined strategy is presented based on AChE-inhibitory activity and chemical profiles by GC/MS, together with in silico studies. The combined strategy was applied on alkaloid extracts of five Amaryllidaceae species that grow in Colombia. Fifty-seven alkaloids were detected using GC/MS, and 21 of them were identified by comparing their mass-spectral fragmentation patterns with standard reference spectra in commercial and private library databases. The alkaloid extracts of Zephyranthes carinata exhibited a high level of inhibitory activity (IC50 = 5.97 ± 0.24 μg/mL). Molecular modeling, which was performed using the structures of some of the alkaloids present in this extract and the three-dimensional crystal structures of AChE derived from Torpedo californica, disclosed their binding configuration in the active site of this AChE. The results suggested that the alkaloids 3-epimacronine and lycoramine might be of interest for AChE inhibition. Although the galanthamine group is known for its potential utility in treating AD, the tazettine-type alkaloids should be evaluated to find more selective compounds of potential benefit for AD. PMID:25305596 8. A novel biosensor method for surfactant determination based on acetylcholinesterase inhibition Kucherenko, I. S.; Soldatkin, O. O.; Arkhypova, V. M.; Dzyadevych, S. V.; Soldatkin, A. P. 2012-06-01 A novel enzyme biosensor based on acetylcholinesterase inhibition for the determination of surfactants in aqueous solutions is described. Acetylcholinesterase-based bioselective element was deposited via glutaraldehyde on the surface of conductometric transducers. Different variants of inhibitory analysis of surfactants were tested, and finally surfactant's concentration was evaluated by measuring initial rate of acetylcholinesterase inhibition. Besides, we studied the effect of solution characteristics on working parameters of the biosensor for direct measurement of acetylcholine and for inhibitory determination of surfactants. The biosensor's sensitivity to anionic and cationic surfactants (0.35 mg l-1) was tested. The high operational stability of the biosensor during determination of acetylcholine (RSD 2%) and surfactants (RSD 11%) was shown. Finally, we discussed the selectivity of the biosensor toward surfactants and other AChE inhibitors. The proposed biosensor can be used as a component of the multibiosensor for ecological monitoring of toxicants. 9. Seasonal exposure of fish to neurotoxic pesticides in an intensive agricultural catchment, Uma-oya, Sri Lanka: linking contamination and acetylcholinesterase inhibition. PubMed Sumith, Jayakody A; Hansani, P L Chamila; Weeraratne, Thilini C; Munkittrick, Kelly R 2012-07-01 The annual cultivation pattern in the Uma-oya catchment in Sri Lanka is characterized by Yala and Maha rainfall periods and associated cropping. Two cultivation seasons were compared for pesticide residues: base flow, field drainage, and the runoff and supplementary sediment data for three sites in the catchment. Organophosphate and N-methyl carbamate pesticide analysis confirmed a higher concentration in the Yala season with low-flow conditions. Acetylcholinesterase (AChE) activity was measured by standard spectrometry in the brain, muscle, and eye tissues of three freshwater cyprinid fishes, Garra ceylonensis, Devario malabaricus, and Rasbora daniconius from three study sites during months overlapping two seasons in 2010 (December) and 2011 (July). Baseline AChE data were measured from fish samples from a forested reserve in the Knuckles. A 73% inhibition in muscle AChE activity in G. ceylonensis was associated with intense pesticide exposure months in the Yala season. The AChE inhibition more than 70% in G. ceylonensis eyes in both Yala (76%) and Maha (72.5%) seasons indicates particular sensitivity of eye tissue to inhibitors. The less dramatic AChE inhibition in the eye tissues in D. malabaricus and R. daniconius in both seasons indicates exemplary protective capacity of muscle AChE in fish. The highest inhibition of AChE (up to 60% in brain and up to 56% in muscle AChE activity in R. daniconius and up to 47.8% in brain and up to 64.6% in muscle AChE activity in D. malabaricus) occurred during the Yala season. Tissue AChE activity and physiological activity in fish were correlated. The results collectively indicate that AChE is a consistent biomarker for diffused contaminant exposure in agricultural catchments. 10. Acetylcholinesterase secreted by Anisakis simplex larvae (Nematoda: Anisakidae) parasitizing herring, Clupea harengus: an inverse relationship of enzyme activity in the host-parasite system. PubMed 2014-06-01 Acetylcholinesterase (AChE) is a key enzyme involved in nerve impulse transmission in both vertebrates and invertebrates. In addition to neuromuscular AChE, many parasitic nematodes synthesize AChE in secretory glands and release the enzyme into their external environment. In this study, we evaluate the activities of both somatic and secreted AChE from larvae (L3) of the parasitic nematode Anisakis simplex, and compare these to the AChE activity in its host, herring, Clupea harengus. A. simplex larvae were obtained from a herring sampled in three areas of the southern Baltic. Enzyme kinetics were determined for excretory/secretory (E/S) products and somatic extracts of larvae as well as for herring muscle tissue. The results reveal that mean AChE activity is approximately fourfold higher in E/S products and eightfold higher in somatic extracts of post-secretory A. simplex larvae than in host muscle tissue. The level of AChE activity in nematodes is inversely related to the enzyme activity in their hosts, i.e. reduced AChE activity in herring was accompanied by increased enzyme activity in its parasites. The physiological function of AChE secreted by parasitic nematodes has been widely discussed in the literature, and numerous roles for this form of enzyme have been suggested. The results of our investigation indicate that AChE secretion by A. simplex larvae may constitute an adaptive mechanism that promotes survival under adverse environmental conditions. Larvae probably increase secretion of AChE in response to a direct and/or indirect effect of neurotoxic compounds. This is the first report of such a phenomenon in A. simplex. 11. Effects of Anticholinesterases on Catalysis and Induced Conformational Change of the Peripheral Anionic Site of Murine Acetylcholinesterase PubMed Central Tong, Fan; Islam, Rafique M.; Carlier, Paul R.; Ma, Ming; Ekström, Fredrik; Bloomquist, Jeffrey R. 2013-01-01 Conventional insecticides targeting acetylcholinesterase (AChE) typically show high mammalian toxicities and because there is resistance to these compounds in many insect species, alternatives to established AChE inhibitors used for pest control are needed. Here we used a fluorescence method to monitor interactions between various AChE inhibitors and the AChE peripheral anionic site, which is a novel target for new insecticides acting on this enzyme. The assay uses thioflavin-T as a probe, which binds to the peripheral anionic site of AChE and yields an increase in fluorescent signal. Three types of AChE inhibitors were studied: catalytic site inhibitors (carbamate insecticides, edrophonium, and benzylpiperidine), peripheral site inhibitors (tubocurarine, ethidium bromide, and propidium iodide), and bivalent inhibitors (donepezil, BW284C51, and a series of bis(n)-tacrines). All were screened on murine AChE to compare and contrast changes of peripheral site conformation in the TFT assay with catalytic inhibition. All the inhibitors reduced thioflavin-T fluorescence in a concentration-dependent manner with potencies (IC50) ranging from 8 nM for bis(6)-tacrine to 159 μM for benzylpiperidine. Potencies in the fluorescence assay were correlated well with their potencies for enzyme inhibition (R2 = 0.884). Efficacies for reducing thioflavin-T fluorescence ranged from 23–36% for catalytic site inhibitors and tubocurarine to near 100% for ethidium bromide and propidium iodide. Maximal efficacies could be reconciled with known mechanisms of interaction of the inhibitors with AChE. When extended to pest species, we anticipate these findings will assist in the discovery and development of novel, selective bivalent insecticides acting on AChE. PMID:24003261 12. Design of multi-target compounds as AChE, BACE1, and amyloid-β(1-42) oligomerization inhibitors: in silico and in vitro studies. PubMed Hernández-Rodríguez, Maricarmen; Correa-Basurto, José; Martínez-Ramos, Federico; Padilla-Martínez, Itzia Irene; Benítez-Cardoza, Claudia G; Mera-Jiménez, Elvia; Rosales-Hernández, Martha Cecilia 2014-01-01 Despite great efforts to develop new therapeutic strategies against Alzheimer's disease (AD), the acetylcholinesterase inhibitors (AChEIs): donepezil, rivastigmine, and galantamine, have been used only as a palliative therapeutic approach. However, the pathogenesis of AD includes several factors such as cholinergic hypothesis, amyloid-β (Aβ) aggregation, and oxidative stress. For this reason, the design of compounds that target the genesis and progression of AD could offer a therapeutic benefit. We have designed a set of compounds (M-1 to M-5) with pharmacophore moieties to inhibit the release, aggregation, or toxicity of Aβ, act as AChEIs and have antioxidant properties. Once the compounds were designed, we analyzed their physicochemical parameters and performed docking studies to determine their affinity values for AChE, β-site amyloid-protein precursor cleaving enzyme 1 (BACE1), and the Aβ monomer. The best ligands, M-1 and M-4, were then synthesized, chemically characterized, and evaluated in vitro. The in vitro studies showed that these compounds inhibit AChE (M-1 Ki = 0.12 and M-4 Ki = 0.17 μM) and BACE1 (M-1 IC50 = 15.1 and M-4 IC50 = 15.4 nM). They also inhibit Aβ oligomerization and exhibit antioxidant activity. In addition, these compounds showed low cytotoxicity in microglial cells. For these reasons, they are promising for future use as drugs in AD mice transgenic models. 13. Design of multi-target compounds as AChE, BACE1, and amyloid-β(1-42) oligomerization inhibitors: in silico and in vitro studies. PubMed Hernández-Rodríguez, Maricarmen; Correa-Basurto, José; Martínez-Ramos, Federico; Padilla-Martínez, Itzia Irene; Benítez-Cardoza, Claudia G; Mera-Jiménez, Elvia; Rosales-Hernández, Martha Cecilia 2014-01-01 Despite great efforts to develop new therapeutic strategies against Alzheimer's disease (AD), the acetylcholinesterase inhibitors (AChEIs): donepezil, rivastigmine, and galantamine, have been used only as a palliative therapeutic approach. However, the pathogenesis of AD includes several factors such as cholinergic hypothesis, amyloid-β (Aβ) aggregation, and oxidative stress. For this reason, the design of compounds that target the genesis and progression of AD could offer a therapeutic benefit. We have designed a set of compounds (M-1 to M-5) with pharmacophore moieties to inhibit the release, aggregation, or toxicity of Aβ, act as AChEIs and have antioxidant properties. Once the compounds were designed, we analyzed their physicochemical parameters and performed docking studies to determine their affinity values for AChE, β-site amyloid-protein precursor cleaving enzyme 1 (BACE1), and the Aβ monomer. The best ligands, M-1 and M-4, were then synthesized, chemically characterized, and evaluated in vitro. The in vitro studies showed that these compounds inhibit AChE (M-1 Ki = 0.12 and M-4 Ki = 0.17 μM) and BACE1 (M-1 IC50 = 15.1 and M-4 IC50 = 15.4 nM). They also inhibit Aβ oligomerization and exhibit antioxidant activity. In addition, these compounds showed low cytotoxicity in microglial cells. For these reasons, they are promising for future use as drugs in AD mice transgenic models. PMID:24762947 14. Effect of carbaryl (carbamate insecticide) on acetylcholinesterase activity of two strains of Daphnia magna (Crustacea, Cladocera). PubMed Toumi, Hela; Bejaoui, Mustapha; Touaylia, Samir; Burga Perez, Karen F; Ferard, Jean François 2016-11-01 The present study was designed to investigate the effect of carbaryl (carbamate insecticide) on the acetylcholinesterase activity in two strains (same clone A) of the crustacean cladoceran Daphnia magna. Four carbaryl concentrations (0.4, 0.9, 1.8 and 3.7 µg L(-1)) were compared against control AChE activity. Our results showed that after 48 h of carbaryl exposure, all treatments induced a significant decrease of AChE activities whatever the two considered strains. However, different responses were registered in terms of lowest observed effect concentrations (LOEC: 0.4 µg L(-1) for strain 1 and 0.9 µg L(-1) for strains 2) revealing differences in sensitivity among the two tested strains of D. magna. These results suggest that after carbaryl exposure, the AChE activity responses can be also used as a biomarker of susceptibility. Moreover, our results show that strain1 is less sensitive than strain 2 in terms of IC50-48 h of AChE activity. Comparing the EC50-48 h of standard ecotoxicity test and IC50-48 h of AChE inhibition, there is the same order of sensitivity with both strains. 15. Identification of non-alkaloid acetylcholinesterase inhibitors from Ferulago campestris (Besser) Grecescu (Apiaceae). PubMed Dall'Acqua, Stefano; Maggi, Filippo; Minesso, Paola; Salvagno, Marina; Papa, Fabrizio; Vittori, Sauro; Innocenti, Gabbriella 2010-12-01 Inhibition of Acetylcholinesterase (AChE) is still considered as a strategy for the treatment of neurological disorders such as Alzheimer's disease. Many plant derived alkaloids (such as galantamine and rivastigmine) are known for their AChE inhibitory activity. Recently, other classes of natural compounds such as terpenoids, sesquiterpene glycosides and coumarins have been studied as new AChE inhibitors, with the aim to discover less toxic compounds compared to alkaloidal ones. The Ferulago campestris roots dichloromethane extract was used for a bioassay-guided fractionation for the search of AChE inhibitors. Three coumarin derivatives (umbelliprenin 1, coladonin 2 and coladin 3), three daucane ester derivatives (siol anisate 4, ferutinin 5 and 1-acetyl-5-angeloyl lapiferol 6), two phenol derivatives (2-epilaserine 7 and epielmanticine 8) and one polyacetylene (9-epoxyfalcarindiol 9) were isolated by the bioassay-guided approach. Their structures were characterized on the basis of spectral methods (1D and 2D NMR, and MS spectroscopy). All the isolated compounds were able to inhibit the AChE (IC(50) 1.2-0.1mM) although at higher doses if compared to galantamine (6.7 μM) measured in the same conditions. The most active compounds were the daucane derivative siol anisate 4 and the epielmanticine 8, with IC(50) of 0.172 and 0.175 mM respectively. 16. Oxidized low density lipoprotein increases acetylcholinesterase activity correlating with reactive oxygen species production. PubMed Yamchuen, Panit; Aimjongjun, Sathid; Limpeanchob, Nanteetip 2014-12-01 Hyperlipidemia, low density lipoproteins (LDL) and their oxidized forms, and oxidative stress are suspected to be a key combination in the onset of AD and acetylcholinesterase (AChE) plays a part in this pathology. The present study aimed to link these parameters using differentiated SH-SY5Y human neuroblastoma cells in culture. Both mildly and fully oxidized human LDL (mox- and fox-LDL), but not native (non-oxidized) LDL were cytotoxic in dose- and time-dependent patterns and this was accompanied by an increased production of intracellular reactive oxygen species (ROS). Oxidized LDL (10-200 μg/mL) augmented AChE activity after 4 and 24h treatments, respectively while the native LDL was without effect. The increased AChE with oxidized LDLs was accompanied by a proportionate increase in intracellular ROS formation (R=0.904). These findings support the notion that oxidized LDLs are cytotoxic and that their action on AChE may reduce central cholinergic transmission in AD and affirm AChE as a continued rational for anticholinesterase therapy but in conjunction with antioxidant/antihyperlipidemic cotreatments. 17. Brain acetylcholinesterase diurnal variations during the rapid development of tolerance to the hypothermic effect of ethanol SciTech Connect Wang, O.; Soliman, K.F.A. ) 1991-03-11 Male Sprague-Dawley rats maintained under controlled environmental conditions were used. Acetylcholinesterase (AChE) activity was determined in the cerebral cortex, midbrain, hypothalamus, hippocampus, cerebellum, pons and medulla oblongata of saline control and ethanol-treated rats, either after a single dose at 06:0 or 18:00h, or after a second dose administered 24 hrs later at the same time scheduled. Results of this experiment indicate that repeated administration with ethanol was associated with the rapid development of tolerance to the hypothermic action of ethanol. A single injection of ethanol at 0600h resulted in a significant decrease in AChE activity in the hypothalamus, medulla, cerebellum, hippocampus and the cortex. However, ethanol administration at 18.00h was associated with significant increases in AChE activity in the same brain regions. The repeated administration of ethanol at 06.00h was associated with tolerance in AChE response to ethanol in the hypothalamus and hippocampus. However, there was no tolerance development in AChE activity in brain regions when ethanol was administered at 18.00h. The results indicate that chronotolerance to ethanol might be related to the brain cholinergic system. 18. Motor neurone acetylcholinesterase release precedes neurotoxicity caused by systemic administration of excitatory amino acids and strychnine. PubMed Rodríguez-Ithurralde, D; Maruri, A; Rodríguez, X 1998-10-01 We have proposed that neuronal overactivation by either stimulation of excitatory receptors or hypofunction of inhibitory circuits is a cause of excessive acetylcholinesterase (AChE) release, which, in turn, can contribute to ALS/MND pathogenesis. We investigated histochemical and histopathological changes in cell populations of the mouse spinal ventral horn upon in vivo stimulation of glutamate receptors with L-aspartate (ASP, 10-50 mg/kg, intraperitoneal: i.p.), or blockade of glycine receptors with strychnine (STRY, 2 mg/kg, i.p.). ASP in P4-P13 (postnatal age in days) but not in older mice, and STRY irrespective of age, provoked rapid, striking depletions of motor neurone AChE, and appearance of AChE activity in astrocytes. This was followed by recovery of the enzyme in most motor neurones, astrocyte activation and statistically significant changes in: brain macrophage infiltration, loss of interneurones and motor neurones and neuronophagic images including rosettes of glial cells surrounding a central 'ghost-like' motor neurone. Although AChE release preceded the neuropathology found, it is not known if its uptake is a cause of glial activation. However, it has been shown that the enzyme potentiates non-N-metyl-D-aspartate receptors identical to those that mediate astrocyte activation. AChE activity produces protons and choline, possible microglial activators. These are putative routes towards long-lasting neuropathology. 19. Novel Selective and Irreversible Mosquito Acetylcholinesterase Inhibitors for Controlling Malaria and Other Mosquito-Borne Diseases Dou, Dengfeng; Park, Jewn Giew; Rana, Sandeep; Madden, Benjamin J.; Jiang, Haobo; Pang, Yuan-Ping 2013-01-01 We reported previously that insect acetylcholinesterases (AChEs) could be selectively and irreversibly inhibited by methanethiosulfonates presumably through conjugation to an insect-specific cysteine in these enzymes. However, no direct proof for the conjugation has been published to date, and doubts remain about whether such cysteine-targeting inhibitors have desirable kinetic properties for insecticide use. Here we report mass spectrometric proof of the conjugation and new chemicals that irreversibly inhibited African malaria mosquito AChE with bimolecular inhibition rate constants (kinact/KI) of 3,604-458,597 M-1sec-1 but spared human AChE. In comparison, the insecticide paraoxon irreversibly inhibited mosquito and human AChEs with kinact/KI values of 1,915 and 1,507 M-1sec-1, respectively, under the same assay conditions. These results further support our hypothesis that the insect-specific AChE cysteine is a unique and unexplored target to develop new insecticides with reduced insecticide resistance and low toxicity to mammals, fish, and birds for the control of mosquito-borne diseases. 20. Chemical composition of the bark of Tetrapterys mucronata and identification of acetylcholinesterase inhibitory constituents. PubMed Queiroz, Marcos Marçal Ferreira; Queiroz, Emerson Ferreira; Zeraik, Maria Luiza; Ebrahimi, Samad Nejad; Marcourt, Laurence; Cuendet, Muriel; Castro-Gamboa, Ian; Hamburger, Matthias; da Silva Bolzani, Vanderlan; Wolfender, Jean-Luc 2014-03-28 The secondary metabolite content of Tetrapterys mucronata, a poorly studied plant that is used occasionally in Brazil for the preparation of a psychotropic plant decoction called "Ayahuasca", was determined to establish its chemical composition and to search for acetylcholinesterase (AChE) inhibitors. The ethanolic extract of the bark of T. mucronata exhibited in vitro AChE inhibition in a TLC bioautography assay. To localize the active compounds, biological profiling for AChE inhibition was performed using at-line HPLC-microfractionation in 96-well plates and subsequent AChE inhibition bioautography. The analytical HPLC-PDA conditions were transferred geometrically to a preparative medium-pressure liquid chromatography column using chromatographic calculations for the efficient isolation of the active compounds at the milligram scale. Twenty-two compounds were isolated, of which six are new natural products. The structures of the new compounds (9, 10, 16-18, and 20) were elucidated by spectroscopic data interpretation. Compounds 1, 5, 6, 9, and 10 inhibited AChE with IC50 values below 15 μM. 1. How Is Acetylcholinesterase Phosphonylated by Soman? An Ab Initio QM/MM Molecular Dynamics Study PubMed Central 2015-01-01 Acetylcholinesterase (AChE) is a crucial enzyme in the cholinergic nerve system that hydrolyzes acetylcholine (ACh) and terminates synaptic signals by reducing the effective concentration of ACh in the synaptic clefts. Organophosphate compounds irreversibly inhibit AChEs, leading to irreparable damage to nerve cells. By employing Born–Oppenheimer ab initio QM/MM molecular dynamics simulations with umbrella sampling, a state-of-the-art approach to simulate enzyme reactions, we have characterized the covalent inhibition mechanism between AChE and the nerve toxin soman and determined its free energy profile for the first time. Our results indicate that phosphonylation of the catalytic serine by soman employs an addition–elimination mechanism, which is highly associative and stepwise: in the initial addition step, which is also rate-limiting, His440 acts as a general base to facilitate the nucleophilic attack of Ser200 on the soman’s phosphorus atom to form a trigonal bipyrimidal pentacovalent intermediate; in the subsequent elimination step, Try121 of the catalytic gorge stabilizes the leaving fluorine atom prior to its dissociation from the active site. Together with our previous characterization of the aging mechanism of soman inhibited AChE, our simulations have revealed detailed molecular mechanistic insights into the damaging function of the nerve agent soman. PMID:24786171 2. Screening of acetylcholinesterase inhibitors by CE after enzymatic reaction at capillary inlet. PubMed Martín-Biosca, Yolanda; Asensi-Bernardi, Lucia; Villanueva-Camañas, Rosa M; Sagrado, Salvador; Medina-Hernández, Maria J 2009-05-01 In this study the development of a procedure based on capillary electrophoresis after enzymatic reaction at capillary inlet methodology for the screening and in vitro evaluation of the biological activity of acetylcholinesterase (AChE) inhibitors is presented. The progress of the enzymatic reaction of the hydrolysis of acetylthiocholine at pH 8 in the presence of AChE and the inhibitor studied is determined by measuring at 230 nm the peak area of the reaction product thiocholine (TCh). In the method employed the capillary was first filled with 30 mM borate-phosphate buffer (pH 8.0) and subsequently, plugs of: (i) water, (ii) AChE solution, (iii) substrate solution with or without inhibitor, (iv) AChE solution, and (v) water, were hydrodynamically injected into the capillary, and were allowed to stand (and react) during a waiting period of 2 min. The applicability of the proposed methodology to estimate different kinetic parameters of interest such as inhibition constants K(i), identification of inhibitory action mechanism and IC(50), is evaluated using compounds with known activity, tacrine edrophonium, and neostigmine. The results obtained are compared with bibliographic values and confirm the effectiveness of the methodology proposed. Finally a method for AChE Inhibitor screening is proposed. 3. Identification and characterization of mutations in housefly (Musca domestica) acetylcholinesterase involved in insecticide resistance. PubMed Walsh, S B; Dolden, T A; Moores, G D; Kristensen, M; Lewis, T; Devonshire, A L; Williamson, M S 2001-10-01 Acetylcholinesterase (AChE) insensitive to organophosphate and carbamate insecticides has been identified as a major resistance mechanism in numerous arthropod species. However, the associated genetic changes have been reported in the AChE genes from only three insect species; their role in conferring insecticide insensitivity has been confirmed, using functional expression, only for those in Drosophila melanogaster. The housefly, Musca domestica, was one of the first insects shown to have this mechanism; here we report the occurrence of five mutations (Val-180-->Leu, Gly-262-->Ala, Gly-262-->Val, Phe-327-->Tyr and Gly-365-->Ala) in the AChE gene of this species that, either singly or in combination, confer different spectra of insecticide resistance. The baculovirus expression of wild-type and mutated housefly AChE proteins has confirmed that the mutations each confer relatively modest levels of insecticide insensitivity except the novel Gly-262-->Val mutation, which results in much stronger resistance (up to 100-fold) to certain compounds. In all cases the effects of mutation combinations are additive. The mutations introduce amino acid substitutions that are larger than the corresponding wild-type residues and are located within the active site of the enzyme, close to the catalytic triad. The likely influence of these substitutions on the accessibility of the different types of inhibitor and the orientation of key catalytic residues are discussed in the light of the three-dimensional structures of the AChE protein from Torpedo californica and D. melanogaster. PMID:11563981 4. Nature of stress: differential effects on brain acetylcholinesterase activity and memory in rats. PubMed Das, Amitava; Rai, Deepak; Dikshit, Madhu; Palit, Gautam; Nath, Chandishwar 2005-09-16 Effect of acute, chronic-predictable and chronic-unpredictable stress on memory and acetylcholinesterase (AChE) was investigated in rats. The animals were subjected to 3 type of stressors--(1) acute immobilization stress, (2) chronic-predictable stress i.e., immobilization daily for 5 consecutive days and (3) chronic-unpredictable stress that included reversal of light/dark cycle, over-night fasting, forced-swimming, immobilization and forced exercise in random unpredictable manner daily for 5 consecutive days. Learning and memory function was studied by single trial Passive avoidance test. AChE activity was assayed spectrophotometrically in the detergent (DS) and salt (SS) soluble fractions in different brain regions. Learning was obtained in acute and chronic-predictable stress groups but not in chronic-unpredictable group. Acute, chronic-predictable and chronic-unpredictable stress caused significant decrease in AChE activity in the DS fraction of cortex, hippocampus and hypothalamus as compared to control. Results indicate that AChE in DS fraction is predominantly affected in stressed and stressed-trained group but cognition is affected only by chronic-unpredictable stress. In acute and chronic-predictable groups the decreased AChE activity in the hippocampal DS fraction during learning may be responsible to maintain cognitive function by enhancing the cholinergic activity. 5. Acetylcholinesterase inhibitory, antioxidant and phytochemical properties of selected medicinal plants of the Lamiaceae family. PubMed 2014-01-09 The present study aimed to evaluate acetylcholinesterase (AChE) inhibitory and antioxidant activities of Lamiaceae medicinal plants growing wild in Croatia. Using Ellman's colorimetric assay all tested ethanolic extracts and their hydroxycinnamic acid constituents demonstrated in vitro AChE inhibitory properties in a dose dependent manner. The extracts of Mentha x piperita, M. longifolia, Salvia officinalis, Satureja montana, Teucrium arduini, T. chamaedrys, T. montanum, T. polium and Thymus vulgaris at 1 mg/mL showed strong inhibitory activity against AChE. The antioxidant potential of the investigated Lamiaceae species was assessed by DPPH• scavenging activity and total antioxidant capacity assays, in comparison with hydroxycinnamic acids and trolox. The extracts differed greatly in their total hydroxycinnamic derivatives content, determined spectrophotometrically. Rosmarinic acid was found to be the predominant constituent in most of the investigated medicinal plants (by RP-HPLC) and had a substantial influence on their AChE inhibitory and antioxidant properties, with the exception of Teucrium species. These findings indicate that Lamiaceae species are a rich source of various natural AChE inhibitors and antioxidants that could be useful in the prevention and treatment of Alzheimer's and other related diseases. 6. Effect of carbaryl (carbamate insecticide) on acetylcholinesterase activity of two strains of Daphnia magna (Crustacea, Cladocera). PubMed Toumi, Hela; Bejaoui, Mustapha; Touaylia, Samir; Burga Perez, Karen F; Ferard, Jean François 2016-11-01 The present study was designed to investigate the effect of carbaryl (carbamate insecticide) on the acetylcholinesterase activity in two strains (same clone A) of the crustacean cladoceran Daphnia magna. Four carbaryl concentrations (0.4, 0.9, 1.8 and 3.7 µg L(-1)) were compared against control AChE activity. Our results showed that after 48 h of carbaryl exposure, all treatments induced a significant decrease of AChE activities whatever the two considered strains. However, different responses were registered in terms of lowest observed effect concentrations (LOEC: 0.4 µg L(-1) for strain 1 and 0.9 µg L(-1) for strains 2) revealing differences in sensitivity among the two tested strains of D. magna. These results suggest that after carbaryl exposure, the AChE activity responses can be also used as a biomarker of susceptibility. Moreover, our results show that strain1 is less sensitive than strain 2 in terms of IC50-48 h of AChE activity. Comparing the EC50-48 h of standard ecotoxicity test and IC50-48 h of AChE inhibition, there is the same order of sensitivity with both strains. PMID:27428655 7. Surface Display and Bioactivity of Bombyx mori Acetylcholinesterase on Pichia pastoris PubMed Central He, Yong-Sheng; Beier, Ross C.; Sun, Yuan-Ming; Xu, Zhen-Lin; Wu, Wei-Jian; Shen, Yu-Dong; Xiao, Zhi-Li; Lai, Li-Na; Wang, Hong; Yang, Jin-Yi 2013-01-01 A Pichia pastoris (P. pastoris) cell surface display system of Bombyx mori acetylcholinesterase (BmAChE) was constructed and its bioactivity was studied. The modified Bombyx mori acetylcholinesterase gene (bmace) was fused with the anchor protein (AGα1) from Saccharomyces cerevisiae and transformed into P. pastoris strain GS115. The recombinant strain harboring the fusion gene bmace-AGα1 was induced to display BmAChE on the P. pastoris cell surface. Fluorescence microscopy and flow cytometry assays revealed that the BmAChE was successfully displayed on the cell surface of P. pastoris GS115. The enzyme activity of the displayed BmAChE was detected by the Ellman method at 787.7 U/g (wet cell weight). In addition, bioactivity of the displayed BmAChE was verified by inhibition tests conducted with eserine, and with carbamate and organophosphorus pesticides. The displayed BmAChE had an IC50 of 4.17×10−8 M and was highly sensitive to eserine and five carbamate pesticides, as well as seven organophosphorus pesticides. Results suggest that the displayed BmAChE had good bioactivity. PMID:23940577 8. Wild Argentinian Amaryllidaceae, a new renewable source of the acetylcholinesterase inhibitor galanthamine and other alkaloids. PubMed Ortiz, Javier E; Berkov, Strahil; Pigni, Natalia B; Theoduloz, Cristina; Roitman, German; Tapia, Alejandro; Bastida, Jaume; Feresin, Gabriela E 2012-11-13 The Amaryllidaceae family is well known for its pharmacologically active alkaloids. An important approach to treat Alzheimer’s disease involves the inhibition of the enzyme acetylcholinesterase (AChE). Galanthamine, an Amaryllidaceae alkaloid, is an effective, selective, reversible, and competitive AchE inhibitor. This work was aimed at studying the alkaloid composition of four wild Argentinian Amarillydaceae species for the first time, as well as analyzing their inhibitory activity on acetylcholinesterase. Alkaloid content was characterized by means of GC-MS analysis. Chloroform basic extracts from Habranthus jamesonii, Phycella herbertiana, Rhodophiala mendocina and Zephyranthes filifolia collected in the Argentinian Andean region all contained galanthamine, and showed a strong AChE inhibitory activity (IC50 between 1.2 and 2 µg/mL). To our knowledge, no previous reports on alkaloid profiles and AChEIs activity of wild Argentinian Amarillydaceae species have been publisihed. The demand for renewable sources of industrial products like galanthamine and the need to protect plant biodiversity creates an opportunity for Argentinian farmers to produce such crops. 9. Selective and irreversible inhibitors of mosquito acetylcholinesterases for controlling malaria and other mosquito-borne diseases. PubMed Pang, Yuan-Ping; Ekström, Fredrik; Polsinelli, Gregory A; Gao, Yang; Rana, Sandeep; Hua, Duy H; Andersson, Björn; Andersson, Per Ola; Peng, Lei; Singh, Sanjay K; Mishra, Rajesh K; Zhu, Kun Yan; Fallon, Ann M; Ragsdale, David W; Brimijoin, Stephen 2009-01-01 New insecticides are urgently needed because resistance to current insecticides allows resurgence of disease-transmitting mosquitoes while concerns for human toxicity from current compounds are growing. We previously reported the finding of a free cysteine (Cys) residue at the entrance of the active site of acetylcholinesterase (AChE) in some insects but not in mammals, birds, and fish. These insects have two AChE genes (AP and AO), and only AP-AChE carries the Cys residue. Most of these insects are disease vectors such as the African malaria mosquito (Anopheles gambiae sensu stricto) or crop pests such as aphids. Recently we reported a Cys-targeting small molecule that irreversibly inhibited all AChE activity extracted from aphids while an identical exposure caused no effect on the human AChE. Full inhibition of AChE in aphids indicates that AP-AChE contributes most of the enzymatic activity and suggests that the Cys residue might serve as a target for developing better aphicides. It is therefore worth investigating whether the Cys-targeting strategy is applicable to mosquitocides. Herein, we report that, under conditions that spare the human AChE, a methanethiosulfonate-containing molecule at 6 microM irreversibly inhibited 95% of the AChE activity extracted from An. gambiae s. str. and >80% of the activity from the yellow fever mosquito (Aedes aegypti L.) or the northern house mosquito (Culex pipiens L.) that is a vector of St. Louis encephalitis. This type of inhibition is fast ( approximately 30 min) and due to conjugation of the inhibitor to the active-site Cys of mosquito AP-AChE, according to our observed reactivation of the methanethiosulfonate-inhibited AChE by 2-mercaptoethanol. We also note that our sulfhydryl agents partially and irreversibly inhibited the human AChE after prolonged exposure (>4 hr). This slow inhibition is due to partial enzyme denaturation by the inhibitor and/or micelles of the inhibitor, according to our studies using atomic force 10. Steric and Dynamic Parameters Influencing In Situ Cycloadditions to Form Triazole Inhibitors with Crystalline Acetylcholinesterase. PubMed Bourne, Yves; Sharpless, K Barry; Taylor, Palmer; Marchot, Pascale 2016-02-10 Ligand binding sites on acetylcholinesterase (AChE) comprise an active center, at the base of a deep and narrow gorge lined by aromatic residues, and a peripheral site at the gorge entry. These features launched AChE as a reaction vessel for in situ click-chemistry synthesis of high-affinity TZ2PA6 and TZ2PA5 inhibitors, forming a syn-triazole upon cycloaddition within the gorge from alkyne and azide reactants bound at the two sites, respectively. Subsequent crystallographic analyses of AChE complexes with the TZ2PA6 regioisomers demonstrated that syn product association is accompanied by side chain reorganization within the gorge, freezing-in-frame a conformation distinct from an unbound state or anti complex. To correlate inhibitor dimensions with reactivity and explore whether in situ cycloaddition could be accelerated in a concentrated, crystalline template, we developed crystal-soaking procedures and solved structures of AChE complexes with the TZ2PA5 regioisomers and their TZ2/PA5 precursors (2.1-2.7 Å resolution). The structures reveal motions of residue His447 in the active site and, unprecedentedly, residue Tyr341 at the gorge mouth, associated with TZ2 binding and coordinated with other side chain motions in the gorge that may guide AChE toward a transient state favoring syn-triazole formation. Despite precursor binding to crystalline AChE, coupling of rapid electric field fluctuations in the gorge with proper alignments of the azide and alkyne reactants to form the triazole remains a likely limiting step. These observations point to a prime requirement for AChE to interconvert dynamically between sequential conformations to promote favorable electrostatic factors enabling a productive apposition of the reactants for reactivity. PMID:26731630 11. Acetylcholinesterase inhibition in the threeridge mussel (Amblema plicata) by chlorpyrifos: implications for biomonitoring USGS Publications Warehouse Doran, W.J.; Cope, W.G.; Rada, R.G.; Sandheinrich, M.B. 2001-01-01 The effects of chlorpyrifos, an organophosphorus insecticide, were examined on the activity of the nervous system enzyme acetylcholinesterase (AChE) in the threeridge mussel Amblema plicata in a 24-day laboratory test. Thirty-six mussels in each of seven treatments (18 mussels per duplicate) were exposed to chlorpyrifos (0.1, 0.2, 0.3, 0.6, and 1.2 mg/L), a solvent (acetone), and a solvent-free (well water) control for 12, 24, or 96 h. The activity of AChE was measured in the anterior adductor muscle of eight mussels from each treatment after exposure. To assess potential latent effects, six mussels from each treatment were removed after 24 h of exposure and transferred to untreated water for a 21-day holding period; AChE activity was measured on three mussels from each treatment at 7 and 21 days of the holding period. The activity of AChE in chlorpyrifos-exposed mussels did not differ from controls after 12 or 24 h of exposure (t- test, P>0.05), but was significantly less than controls after 96 h (t- test, P=0.01). AChE activity did not vary among mussels at 24 h of exposure (i.e., Day 0 of holding period) and those at Day 7 and Day 21 of the holding period. Overall changes in AChE activity of mussels during the test were unrelated to individual chlorpyrifos concentrations and exposure times (repeated measure ANOVA; (P=0.06). A power analysis revealed that the sample size must be increased from 2 to 5 replicates (8 to 20 mussels per time interval and test concentration) to increase the probability of detecting significant differences in AChE activity. This calculated increase in sample size has potential implications for future biomonitoring studies with chlorpyrifos and unionid mussels. 12. Freeze-frame inhibitor captures acetylcholinesterase in a unique conformation. PubMed Bourne, Yves; Kolb, Hartmuth C; Radić, Zoran; Sharpless, K Barry; Taylor, Palmer; Marchot, Pascale 2004-02-10 The 1,3-dipolar cycloaddition reaction between unactivated azides and acetylenes proceeds exceedingly slowly at room temperature. However, considerable rate acceleration is observed when this reaction occurs inside the active center gorge of acetylcholinesterase (AChE) between certain azide and acetylene reactants, attached via methylene chains to specific inhibitor moieties selective for the active center and peripheral site of the enzyme. AChE catalyzes the formation of its own inhibitor in a highly selective fashion: only a single syn1-triazole regioisomer with defined substitution positions and linker distances is generated from a series of reagent combinations. Inhibition measurements revealed this syn1-triazole isomer to be the highest affinity reversible organic inhibitor of AChE with association rate constants near the diffusion limit. The corresponding anti1 isomer, not formed by the enzyme, proved to be a respectable but weaker inhibitor. The crystal structures of the syn1- and anti1-mouse AChE complexes at 2.45- to 2.65-A resolution reveal not only substantial binding contributions from the triazole moieties, but also that binding of the syn1 isomer induces large and unprecedented enzyme conformational changes not observed in the anti1 complex nor predicted from structures of the apoenzyme and complexes with the precursor reactants. Hence, the freeze-frame reaction offers both a strategically original approach for drug discovery and a means for kinetically controlled capture, as a high-affinity complex between the enzyme and its self-created inhibitor, of a highly reactive minor abundance conformer of a fluctuating protein template. 13. Freeze-frame inhibitor captures acetylcholinesterase in a unique conformation PubMed Central Bourne, Yves; Kolb, Hartmuth C.; Radić, Zoran; Sharpless, K. Barry; Taylor, Palmer; Marchot, Pascale 2004-01-01 The 1,3-dipolar cycloaddition reaction between unactivated azides and acetylenes proceeds exceedingly slowly at room temperature. However, considerable rate acceleration is observed when this reaction occurs inside the active center gorge of acetylcholinesterase (AChE) between certain azide and acetylene reactants, attached via methylene chains to specific inhibitor moieties selective for the active center and peripheral site of the enzyme. AChE catalyzes the formation of its own inhibitor in a highly selective fashion: only a single syn1-triazole regioisomer with defined substitution positions and linker distances is generated from a series of reagent combinations. Inhibition measurements revealed this syn1-triazole isomer to be the highest affinity reversible organic inhibitor of AChE with association rate constants near the diffusion limit. The corresponding anti1 isomer, not formed by the enzyme, proved to be a respectable but weaker inhibitor. The crystal structures of the syn1- and anti1-mouse AChE complexes at 2.45- to 2.65-Å resolution reveal not only substantial binding contributions from the triazole moieties, but also that binding of the syn1 isomer induces large and unprecedented enzyme conformational changes not observed in the anti1 complex nor predicted from structures of the apoenzyme and complexes with the precursor reactants. Hence, the freeze-frame reaction offers both a strategically original approach for drug discovery and a means for kinetically controlled capture, as a high-affinity complex between the enzyme and its self-created inhibitor, of a highly reactive minor abundance conformer of a fluctuating protein template. PMID:14757816 14. Isolation of human erythrocyte acetylcholinesterase using phase separation with Triton X-114 and monoclonal immunosorbent chromatography. PubMed Bjerrum, O J; Selmer, J; Hangaard, J; Larsen, F 1985-01-01 A generally applicable approach to the preparative isolation of amphiphilic membrane proteins that follow the Triton X-114 phase during a temperature-dependent phase separation is described. The phase separations were performed direct on whole blood and a 650-fold purification of human erythrocyte membrane acetylcholinesterase (AchE) was obtained. Thus, 0.2 mg enzyme was isolated per 1 liter of blood, with a specific activity of 13 IU/mg, the major contaminants being glycophorin and hemoglobin. The protein material was isolated from the detergent phase by Cu2+ chelate chromatography. This material was used to raise monoclonal anti-AchE antibodies which, when applied to immunosorbent chromatography of washed Triton X-100-lysed erythrocytes in one step, allowed a 246,000-fold purification of AchE with a yield of 88% and a specific activity of 3800 IU/mg. 15. Nutritional and Physicochemical Characteristics of the Antidementia Acetylcholinesterase-Inhibiting Methanol Extracts from Umbilicaria esculenta PubMed Central Lee, Ji-Su; Min, Gyung-Hun 2009-01-01 To develop new antidementia nutraceuticals, a potent acetylcholinesterase (AChE)-inhibiting extract was screened from various extracts of nutritional mushrooms and lichens nutritional and its physicochemical properties were investigated. Among the several extracts tested, methanol extracts of Umbilicaria esculenta fruiting body showed the highest AChE inhibitory activity of 22.4%. U. esculenta AChE inhibitor was maximally extracted when fruiting bodies were treated with 80% methanol at 40℃ for 18 h. The methanol extracts contained 18.9% crude lipid, 18.8% crude protein, and 11.6% total sugar. In addition, they contained 444 mg/g glutamic acid, 44 mg/g histidine, and 41 mg/g aspartic acid. The methanol extracts were soluble in a solution of methanol and 20% dimethylsulfoxide, insoluble in n-hexane, chloroform, and water, and were stable at 20~60℃ and pH 1.0~5.0 for 1 h. PMID:23983533 16. Three-dimensional ordered macroporous (3DOM) composite for electrochemical study on acetylcholinesterase inhibition induced by endogenous neurotoxin. PubMed Teng, Yingqiao; Fu, Ying; Xu, Lili; Lin, Bin; Wang, Zhongchuan; Xu, Zhiai; Jin, Litong; Zhang, Wen 2012-09-13 In this paper, an electrochemical acetylcholinesterase (AChE) inhibition assay based on three-dimensional ordered macroporous (3DOM) composite was conducted. The 3DOM composite was first fabricated on the glassy carbon electrode by electropolymerization of aniline in the presence of ionic liquid (IL) on a sacrificial silica nanospheres template. After the silica nanospheres were etched, an IL-doped polyaniline (IL-PANI) film with 3DOM morphology was formed. Then, gold nanoparticles (AuNPs) were decorated on the IL-PANI film by electrodeposition. The immobilized AChE on the 3DOM composite displayed favorable affinity to substrate acetylthiocholine chloride (ATCh), and the 3DOM composite showed excellent electrocatalytic effect on thiocholine, the hydrolysis product of ATCh. The presence of IL and AuNPs could improve the sensitivity by accelerating the electron transfer. The designed AChE biosensor was successfully applied to evaluate the AChE inhibition induced by endogenous neurotoxin 1(R),2N-dimethyl-6,7-dihydroxy-1,2,3,4-tetrahydroisoquinoline [(R)-NMSal]. The results demonstrate that (R)-NMSal exerts a considerable effect on AChE activity, and the inhibition is reversible. The developed method offers a new approach for AChE inhibition assay, which is of great benefit in understanding the mechanism behind neurotoxin-induced neurodegenerative disorders. 17. Fucoxanthin, a Marine Carotenoid, Reverses Scopolamine-Induced Cognitive Impairments in Mice and Inhibits Acetylcholinesterase in Vitro PubMed Central Lin, Jiajia; Huang, Ling; Yu, Jie; Xiang, Siying; Wang, Jialing; Zhang, Jinrong; Yan, Xiaojun; Cui, Wei; He, Shan; Wang, Qinwen 2016-01-01 Fucoxanthin, a natural carotenoid abundant in edible brown seaweeds, has been shown to possess anti-cancer, anti-oxidant, anti-obesity and anti-diabetic effects. In this study, we report for the first time that fucoxanthin effectively protects against scopolamine-induced cognitive impairments in mice. In addition, fucoxanthin significantly reversed the scopolamine-induced increase of acetylcholinesterase (AChE) activity and decreased both choline acetyltransferase activity and brain-derived neurotrophic factor (BDNF) expression. Using an in vitro AChE activity assay, we discovered that fucoxanthin directly inhibits AChE with an IC50 value of 81.2 μM. Molecular docking analysis suggests that fucoxanthin likely interacts with the peripheral anionic site within AChE, which is in accordance with enzymatic activity results showing that fucoxanthin inhibits AChE in a non-competitive manner. Based on our current findings, we anticipate that fucoxanthin might exhibit great therapeutic efficacy for the treatment of Alzheimer’s disease by acting on multiple targets, including inhibiting AChE and increasing BDNF expression. PMID:27023569 18. Pre- and post-treatment effect of physostigmine on soman-inhibited human erythrocyte and muscle acetylcholinesterase in vitro SciTech Connect Herkert, N.M.; Schulz, S.; Wille, T.; Thiermann, H.; Hatz, R.A.; Worek, F. 2011-05-15 Standard treatment of organophosphorus (OP) poisoning includes administration of an antimuscarinic (e.g., atropine) and of an oxime-based reactivator. However, successful oxime treatment in soman poisoning is limited due to rapid aging of phosphylated acetylcholinesterase (AChE). Hence, the inability of standard treatment procedures to counteract the effects of soman poisoning resulted in the search for alternative strategies. Recently, results of an in vivo guinea pig study indicated a therapeutic effect of physostigmine given after soman. The present study was performed to investigate a possible pre- and post-treatment effect of physostigmine on soman-inhibited human AChE given at different time intervals before or after perfusion with soman by using a well-established dynamically working in vitro model for real-time analysis of erythrocyte and muscle AChE. The major findings were that prophylactic physostigmine prevented complete inhibition of AChE by soman and resulted in partial spontaneous recovery of the enzyme by decarbamylation. Physostigmine given as post-treatment resulted in a time-dependent reduction of the protection from soman inhibition and recovery of AChE. Hence, these date indicate that physostigmine given after soman does not protect AChE from irreversible inhibition by the OP and that the observed therapeutic effect of physostigmine in nerve agent poisoning in vivo is probably due to other factors. 19. Effect of different buffers on kinetic properties of human acetylcholinesterase and the interaction with organophosphates and oximes. PubMed Wille, T; Thiermann, H; Worek, F 2011-03-01 Acetylcholinesterase (AChE) is the primary target of organophosphorus compounds (OP). The investigation into interactions between AChE, OP and oximes in vitro may be affected by the experimental conditions, e.g. by the buffer system. Hence, it was tempting to investigate the Michaelis-Menten kinetics and the inhibition and reactivation kinetics of paraoxon-ethyl, sarin, soman and VX in the presence of phosphate, MOPS, Tyrode and TRIS buffer with human AChE. Compared to phosphate buffer, the inhibition and reactivation kinetics of human erythrocyte AChE were markedly changed by TRIS and in part by MOPS, whereas Tyrode showed similar results to phosphate buffer. These results indicate an effect of the tested buffers on the properties of AChE, and an interaction between OP and oximes has to be considered for the design of in vitro studies and may impair the comparison of data from different laboratories. In view of the comparability of human in vitro kinetic data determined with phosphate buffer with data from human OP poisoning, it seems to be a suitable buffer for the investigation into interactions between AChE, OP and oximes. 20. IN VITRO ACETYLCHOLINESTERASE AND BUTYRYLCHOLINESTERASE INHIBITORY POTENTIALS OF JATROPHA GOSSYPIFOLIA PLANT EXTRACTS. PubMed 2016-01-01 Inhibition of acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE), which breakdown acetylcholine and butyrylcholine, are considered as a promising strategy in the management of Alzheimer's disease (AD). Traditional accounts of indigenous plant Jatopha gossypyfolia suggest presence of important medicinal activities including improvement of memory functioning. To establish correlation of its use as anti-Alzheimer, AChE and BuChE inhibitory activity of extracts obtained from different parts of plant Jatropha gossypyfolia belonging to the family Euphorbiaceae were tested. Extracts from leaves, stem bark and roots were prepared by maceration. Enzyme inhibitory activity was carried out by using standard in vitro AChE and BuChE inhibition assays (Ellman's assay method) and the percentage inhibition was calculated. The results showed that roots dichloromethane fraction (65.43 ± 0.11), roots methanol fraction (62.79 ± 0.34) and leaves dichloromethane fraction (57.71 ± 0.15) showed significant acetylcholinesterase inhibitory activity compared to other fractions when compared with standard serine (91.29 ± 1.17). Similarly, butyrylcholinesterase enzyme inhibitory results showed that roots dichloromethane fraction (80.46 ± 0.44), JGLE (77.34 ± 0.34) showed significant BuChE enzyme inhibitory activity as compared to other fractions when compared with standard eserine (82.82 ± 1.09). Dichloromethane extracts showed higher enzyme inhibition comparatively. Highest AChE and BuChE inhibition was observed with leaf extracts of ethyl acetate fraction. In conclusion, the plant extracts exhibited presence of bioactive compounds with significant AChE and BuChE inhibition supporting traditional use of this herb in the management of AD. However, further investigation of the plant is required. PMID:27180434 1. Solubilization, molecular forms, purification and substrate specificity of two acetylcholinesterases in the medicinal leech (Hirudo medicinalis). PubMed Central Talesa, V; Grauso, M; Giovannini, E; Rosi, G; Toutant, J P 1995-01-01 Two acetylcholinesterases (AChE) differing in substrate and inhibitor specificities have been characterized in the medical leech (Hirudo medicinalis). A 'spontaneously-soluble' portion of AChE activity (SS-AChE) was recovered from haemolymph and from tissues dilacerated in low-salt buffer. A second portion of AChE activity was obtained after extraction of tissues in low-salt buffer alone or containing 1% Triton X-100 [detergent-soluble (DS-) AChE). Both enzymes were purified to homogeneity by affinity chromatography on edrophonium- and concanavalin A-Sepharose columns. Denaturing SDS/PAGE under reducing conditions gave one band at 30 kDa for purified SS-AChE and 66 kDa for DS-AChE. Sephadex G-200 chromatography indicated a molecular mass of 66 kDa for native SS-AChE and of 130 kDa for DS-AChE. SS-AChE showed a single peak sedimenting at 5.0 S in sucrose gradients with or without Triton X-100, suggesting that it was a hydrophylic monomer (G1). DS-AChE sedimented as a single 6.1-6.5 S peak in the presence of Triton X-100 and aggregated in the absence of detergent. A treatment with phosphatidylinositol-specific phospholipase C suppressed aggregation and gave a 7 S peak. DS-AChE was thus an amphiphilic glycolipid-anchored dimer. Substrate specificities were studied using p-nitrophenyl esters (acetate, propionate and butyrate) and corresponding thiocholine esters as substrates. SS-AChE displayed only limited variations in Km values with charged and uncharged substrates, suggesting a reduced influence of electrostatic interactions in the enzyme substrate affinity. By contrast, DS-AChE displayed higher Km values with uncharged than with charged substrates. SS-AChE was more sensitive to eserine and di-isopropyl fluorophosphate (IC50 5 x 10(-8) and 10(-8) M respectively) than DS-AChE (5 x 10(-7) and 5 x 10(-5) M. Images Figure 2 Figure 3 Figure 4 PMID:7702560 2. Syntheses of coumarin-tacrine hybrids as dual-site acetylcholinesterase inhibitors and their activity against butylcholinesterase, Aβ aggregation, and β-secretase. PubMed Sun, Qi; Peng, Da-Yong; Yang, Sheng-Gang; Zhu, Xiao-Lei; Yang, Wen-Chao; Yang, Guang-Fu 2014-09-01 Exploring small-molecule acetylcholinesterase (AChE) inhibitors to slow the breakdown of acetylcholine (Ach) represents the mainstream direction for Alzheimer's disease (AD) therapy. As the first acetylcholinesterase inhibitor approved for the clinical treatment of AD, tacrine has been widely used as a pharmacophore to design hybrid compounds in order to combine its potent AChE inhibition with other multi-target profiles. In present study, a series of novel tacrine-coumarin hybrids were designed, synthesized and evaluated as potent dual-site AChE inhibitors. Moreover, compound 1g was identified as the most potent candidate with about 2-fold higher potency (Ki=16.7nM) against human AChE and about 2-fold lower potency (Ki=16.1nM) against BChE than tacrine (Ki=35.7nM for AChE, Ki=8.7nM for BChE), respectively. In addition, some of the tacrine-coumarin hybrids showed simultaneous inhibitory effects against both Aβ aggregation and β-secretase. We therefore conclude that tacrine-coumarin hybrid is an interesting multifunctional lead for the AD drug discovery. 3. Coextracted dissolved organic carbon has a suppressive effect on the acetylcholinesterase inhibition assay. PubMed Neale, Peta A; Escher, Beate I 2013-07-01 The acetylcholinesterase (AChE) inhibition assay is frequently applied to detect organophosphates and carbamate pesticides in different water types, including dissolved organic carbon (DOC)-rich wastewater and surface water. The aim of the present study was to quantify the effect of coextracted DOC from different water samples on the commonly used enzyme-based AChE inhibition assay. Approximately 40% to 70% of DOC is typically recovered by solid-phase extraction, and this comprises not only organic micropollutants but also natural organic matter. The inhibition of the water extracts in the assay differed greatly from the expected mixture effects based on chemical analysis of organophosphates and carbamates. Binary mixture experiments with the known AChE inhibitor parathion and the water extracts showed reduced toxicity in comparison with predictions using the mixture models of concentration addition and independent action. In addition, the extracts and reference organic matter had a suppressive effect on a constant concentration of parathion. The present study thus indicated that concentrations of DOC as low as 2 mg carbon/L can impair the AChE inhibition assay and, consequently, that only samples with a final DOC concentration of less than 2 mgC /L are suitable for this assay. To check for potential suppression in environmental samples, standard addition experiments using an AChE-inhibiting reference compound are recommended. PMID:23424099 4. Nanoparticle-based immunosensor with apoferritin templated metallic phosphate label for quantification of phosphorylated acetylcholinesterase SciTech Connect Du, Dan; Chen, Aiqiong; Xie, Yunying; Zhang, Aidong; Lin, Yuehe 2011-05-15 A new sandwich-like electrochemical immunosensor has been developed for quantification of organophosphorylated acetylcholinesterase (OP-AChE), an exposure biomarker of organophosphate pesticides and nerve agents. Zirconia nanoparticles (ZrO2 NPs) were anchored on a screen printed electrode (SPE) to preferably capture OP-AChE adducts by metal chelation with phospho-moieties, which was selectively recognized by lead phosphate-apoferritin labeled anti-AChE antibody (LPA-anti-AChE). The sandwich-like immunoreactions were performed among ZrO2 NPs, OP-AChE and LPA-anti-AChE to form ZrO2/OP-AChE/LPA-anti-AChE complex and the released lead ions were detected on a disposable SPE. The binding affinity was investigated by both square wave voltammetry (SWV) and quartz crystal microbalance (QCM) measurements. The proposed immunosensor yielded a linear response current over a broad OP-AChE concentrations range from 0.05 nM to 10 nM, with detection limit of 0.02 nM, which has enough sensitivity for monitoring of low-dose exposure to OPs. This method avoids the drawback of unavailability of commercial OP-specific antibody as well as amplifies detection signal by using apoferritin encoded metallic phosphate nanoparticle tags. This nanoparticle-based immunosensor offers a new method for rapid, sensitive, selective and inexpensive quantification of phosphorylated adducts for monitoring of OP pesticides and nerve agents exposures. 5. A fluorescence assay for measuring acetylcholinesterase activity in rat blood and a human neuroblastoma cell line (SH-SY5Y). PubMed Santillo, Michael F; Liu, Yitong 2015-01-01 Acetylcholinesterase (AChE) is an enzyme responsible for metabolism of the neurotransmitter acetylcholine, and inhibition of AChE can have therapeutic applications (e.g., drugs for Alzheimer's disease) or neurotoxic consequences (e.g., pesticides). A common absorbance-based AChE activity assay that uses 5,5'-dithiobis(2-nitrobenzoic acid) (DTNB) can have limited sensitivity and be prone to interference. Therefore, an alternative assay was developed, in which AChE activity was determined by measuring fluorescence of resorufin produced from coupled enzyme reactions involving acetylcholine and Amplex Red (10-acetyl-3,7-dihydroxyphenoxazine). The Amplex Red assay was used for two separate applications. First, AChE activity was measured in rat whole blood, which is a biomarker for exposure to AChE inhibitor pesticides. Activity was quantified from a 10(5)-fold dilution of whole blood, and there was a linear correlation between Amplex Red and DTNB assays. For the second application, Amplex Red assay was used to measure AChE inhibition potency in a human neuroblastoma cell line (SH-SY5Y), which is important for assessing pharmacological and toxicological potential of AChE inhibitors including drugs, phytochemicals, and pesticides. Five known reversible inhibitors were evaluated (IC50, 7-225 nM), along with irreversible inhibitors chlorpyrifos-oxon (ki=1.01 nM(-1)h(-1)) and paraoxon (ki=0.16 nM(-1)h(-1)). Lastly, in addition to inhibition, AChE reactivation was measured in SH-SY5Y cells incubated with pralidoxime chloride (2-PAM). The Amplex Red assay is a sensitive, specific, and reliable fluorescence method for measuring AChE activity in both rat whole blood and cultured SH-SY5Y cells. PMID:26165232 6. Inhibition of acetylcholinesterase activity in the terrestrial isopod Porcellio scaber as a biomarker of organophosphorus compounds in food. PubMed Stanek, Katja; Gabrijelcic, Elizabeta; Drobne, Damjana; Trebse, Polonca 2003-09-01 This paper describes the toxicity of organophosphorus pesticide diazinon in juvenile and adult terrestrial isopods Porcellio scaber (Isopoda, Crustacea). The woodlice were exposed to different concentrations of diazinon added to food (5, 10, 50, and 100 or 150 micrograms/g dry food). Weight change and food assimilation efficiency were determined two and four weeks after the exposure. The activity of acetylcholinesterase (AChE) in surviving animals was measured at the end of the experiment. The results show that woodlice exposed to diazinon do not significantly differ from controls in growth and feeding rate. The reduction of AChE activity was observed at the lowest diazinon exposure (5 and 10 micrograms/g dry food). These results suggest that AChE activity might prove a useful biomarker, indicating low levels of organophosphates in food. 7. mAChRs activation induces epithelial-mesenchymal transition on lung epithelial cells PubMed Central 2014-01-01 Background Epithelial-mesenchymal transition (EMT) has been proposed as a mechanism in the progression of airway diseases and cancer. Here, we explored the role of acetylcholine (ACh) and the pathway involved in the process of EMT, as well as the effects of mAChRs antagonist. Methods Human lung epithelial cells were stimulated with carbachol, an analogue of ACh, and epithelial and mesenchymal marker proteins were evaluated using western blot and immunofluorescence analyses. Results Decreased E-cadherin expression and increased vimentin and α-SMA expression induced by TGF-β1 in alveolar epithelial cell (A549) were significantly abrogated by the non-selective mAChR antagonist atropine and enhanced by the acetylcholinesterase inhibitor physostigmine. An EMT event also occurred in response to physostigmine alone. Furthermore, ChAT express and ACh release by A549 cells were enhanced by TGF-β1. Interestingly, ACh analogue carbachol also induced EMT in A549 cells as well as in bronchial epithelial cells (16HBE) in a time- and concentration-dependent manner, the induction of carbachol was abrogated by selective antagonist of M1 (pirenzepine) and M3 (4-DAMP) mAChRs, but not by M2 (methoctramine) antagonist. Moreover, carbachol induced TGF-β1 production from A549 cells concomitantly with the EMT process. Carbachol-induced EMT occurred through phosphorylation of Smad2/3 and ERK, which was inhibited by pirenzepine and 4-DAMP. Conclusions Our findings for the first time indicated that mAChR activation, perhaps via M1 and M3 mAChR, induced lung epithelial cells to undergo EMT and provided insights into novel therapeutic strategies for airway diseases in which lung remodeling occurs. PMID:24678619 8. Affinity binding-guided fluorescent nanobiosensor for acetylcholinesterase inhibitors via distance modulation between the fluorophore and metallic nanoparticle. PubMed Zhang, Yaodong; Hei, Tingting; Cai, Yanan; Gao, Qunqun; Zhang, Qi 2012-03-20 The magnitude of fluorescence enhancement was found to depend strongly on the distance between fluorophores and metal nanostructures in metal-enhanced fluorescence (MEF). However, the precise placement of the particle in front of the molecule with nanometer accuracy and distance control is a great challenge. We describe a method using acetylcholinesterase (AChE) to modulate the distance between a gold nanoparticle (AuNP) and the fluorophore 7-hydroxy-9H-(1,3-dichloro-9,9-dimethylacridin-2-one) (DDAO). We found that DDAO is a reversible mixed type-I AChE inhibitor. DDAO binds to the peripheral anionic site and penetrates into the active gorge site of AChE via inhibition kinetics test and molecular docking study. The affinity ligand DDAO bound to AChE which was immobilized onto AuNPs, and its fluorescence was sharply enhanced due to MEF. The fluorescence was reduced by distance variations between the AuNP and DDAO, which resulted from other inhibitors competitively binding with AChE and partly or completely displacing DDAO. Experimental results show that changes in fluorescence intensity are related to the concentration of inhibitors present in the solution. In addition, the nanobiosensor has high sensitivity, with detection limits as low as 0.4 μM for paraoxon and 10 nM for tacrine, and also exhibits different reduction efficiencies for the two types of inhibitor. Thus, instead of an inhibition test, a new type of affinity binding-guided fluorescent nanobiosensor was fabricated to detect AChE inhibitors, determine AChE inhibitor binding mode, and screen more potent AChE inhibitors. The proposed strategy may be applied to other proteins or protein domains via changes in the affinity ligand. 9. Functional study on the mutations in the silkworm (Bombyx mori) acetylcholinesterase type 1 gene (ace1) and its recombinant proteins. PubMed Wang, Ju-mei; Wang, Bin-bin; Xie, Yi; Sun, Shan-shan; Gu, Zhi-ya; Ma, Lie; Li, Fan-chi; Zhao, Yi-fan; Yang, Bin; Shen, Wei-de; Li, Bing 2014-01-01 The acetylcholinesterase of Lepidoptera insects is encoded by two genes, ace1 and ace2. The expression of the ace1 gene is significantly higher than that of the ace2 gene, and mutations in ace1 are one of the major reasons for pesticide resistance in insects. In order to investigate the effects of the mutations in ace1's characteristic sites on pesticide resistance, we generated mutations for three amino acids using site-directed mutagenesis, which were Ala(GCG)303Ser(TCG), Gly(GGA)329Ala(GCA) and Leu (TCT)554Ser(TTC). The Baculovirus expression system was used for the eukaryotic expression of the wild type ace1 (wace1) and the mutant ace1 (mace1). SDS-PAGE and Western blotting were used to detect the targeting proteins with expected sizeof about 76 kDa. The expression products were purified for the determination of AChE activity and the inhibitory effects of physostigmine and phoxim. We observed no significant differences in the overall activity of the wild type and mutant AChEs. However, with 10 min of physostigmine (10 μM) inhibition, the remaining activity of the wild type AChE was significantly lower than that of the mutant AChE. Ten min inhibition with 33.4 μM phoxim also resulted in significantly lower remaining activity of the wild type AChE than that of the mutant AChE. These results indicated that mutations for the three amino acids reduced the sensitivity of AChE to physostigmine and phoxim, which laid the foundation for future in vivo studies on AChE's roles in pesticide resistance. 10. Oxidative stress biomarkers and acetylcholinesterase activity in human erythrocytes exposed to clomazone (in vitro). PubMed Santi, Adriana; Menezes, Charlene; Duarte, Marta Maria F; Leitemperger, Jossiele; Lópes, Thais; Loro, Vania L 2011-09-01 The aim of this study was to investigate the effect of clomazone herbicide on oxidative stress biomarkers and acetylcholinesterase activity in human erythrocytes in in vitro conditions. The activity of catalase (CAT), superoxide dismutase (SOD) and acetylcholinesterase (AChE), as well as the levels of thiobarbituric acid reactive substances (TBARS) and reduced glutathione (GSH) were measured in human erythrocytes exposed (in vitro) to clomazone at varying concentrations in the range of 0, 100, 250 and 500 µg/L for 1 h at 37 °C.TBARS levels were significantly higher in erythrocytes incubated with clomazone at 100, 250 and 500 µg/L. However, erythrocyte CAT and AChE activities were decreased at all concentrations tested. SOD activity was increased only at 100 µg/L of clomazone. GSH levels did not change with clomazone exposure. These results clearly showed clomazone to induce oxidative stress and AChE inhibition in human erythrocytes (in vitro). We, thus, suggest a possible role of ROS on toxicity mechanism induced by clomazone in humans. 11. Oxidative stress biomarkers and acetylcholinesterase activity in human erythrocytes exposed to clomazone (in vitro) PubMed Central Santi, Adriana; Menezes, Charlene; Duarte, Marta Maria F.; Leitemperger, Jossiele; Lópes, Thais; Loro, Vania L. 2011-01-01 The aim of this study was to investigate the effect of clomazone herbicide on oxidative stress biomarkers and acetylcholinesterase activity in human erythrocytes in in vitro conditions. The activity of catalase (CAT), superoxide dismutase (SOD) and acetylcholinesterase (AChE), as well as the levels of thiobarbituric acid reactive substances (TBARS) and reduced glutathione (GSH) were measured in human erythrocytes exposed (in vitro) to clomazone at varying concentrations in the range of 0, 100, 250 and 500 µg/L for 1 h at 37 °C.TBARS levels were significantly higher in erythrocytes incubated with clomazone at 100, 250 and 500 µg/L. However, erythrocyte CAT and AChE activities were decreased at all concentrations tested. SOD activity was increased only at 100 µg/L of clomazone. GSH levels did not change with clomazone exposure. These results clearly showed clomazone to induce oxidative stress and AChE inhibition in human erythrocytes (in vitro). We, thus, suggest a possible role of ROS on toxicity mechanism induced by clomazone in humans. PMID:22058656 12. In vivo and in vitro effects of fructose on rat brain acetylcholinesterase activity: an ontogenetic study. PubMed Guimarães, Carine A; Biella, Mairis S; Lopes, Abigail; Deroza, Pedro F; Oliveira, Mariana B; Macan, Tamires P; Streck, Emilio L; Ferreira, Gustavo C; Zugno, Alexandra I; Schuck, Patrícia F 2014-12-01 Increased fructose concentrations are the biochemical hallmark of fructosemia, a group of inherited disorders on the metabolic pathway of this sugar. The main clinical findings observed in patients affected by fructosemia include neurological abnormalities with developmental delay, whose pathophysiology is still undefined. In the present work we investigated the in vitro and in vivo effects of fructose on acetylcholinesterase (AchE) activity in brain structures of developing rats. For the in vitro experiments, fructose was added at increasing concentrations to the incubation medium. It was observed that fructose provoked an inhibition of acetylcholinesterase activity in cerebral cortex of 30-day-old-rats, even at low concentrations (0.1 mM). For the in vivo experiments, rats were killed 1 h after a single fructose administration (5 µmol/g). Control group received the same volume of saline solution. We found that AchE activity was increased in cerebral cortex of 30- and 60-day-old rats receiving fructose administration. Finally, we observed that AchE activity was unaffected by acute fructose administration in cerebral cortex, striatum or hippocampus of 15- and 90-day-old rats. The present data suggest that a disruption in cholinergic homeostasis may be involved in the pathophysiology of brain damage observed in young patients affected by fructosemia. PMID:25590728 13. Acetylcholinesterase from Human Erythrocytes as a Surrogate Biomarker of Lead Induced Neurotoxicity PubMed Central Gupta, Vivek Kumar; Pal, Rajnish; Siddiqi, Nikhat Jamal; Sharma, Bechan 2015-01-01 Lead induced neurotoxicity in the people engaged in different occupations has received wide attention but very little studies have been carried out to monitor occupational neurotoxicity directly due to lead exposure using biochemical methods. In the present paper an endeavour has been made in order to assess the lead mediated neurotoxicity by in vitro assay of the activity of acetylcholinesterase (AChE) from human erythrocytes in presence of different concentrations of lead. The results suggested that the activity of this enzyme was localized in membrane bound fraction and it was found to be highly stable up to 30 days when stored at −20°C in phosphate buffer (50 mM, pH 7.4) containing 0.2% Triton X-100. The erythrocyte's AChE exhibited Km for acetylcholinesterase to be 0.1 mM. Lead caused sharp inhibition of the enzyme and its IC50 value was computed to be 1.34 mM. The inhibition of the enzyme by lead was found to be of uncompetitive type (Ki value, 3.6 mM) which negatively influenced both the Vmax and the enzyme-substrate binding affinity. Taken together, these results indicate that AChE from human erythrocytes could be exploited as a surrogate biomarker of lead induced neurotoxicity particularly in the people occupationally exposed to lead. PMID:26600946 14. Evaluation of aflatoxin B1--acetylcholinesterase dissociation kinetic using the amperometric biosensor technology: prospect for toxicity mechanism. PubMed Pohanka, Miroslav; Musilek, Kamil; Kuca, Kamil 2010-03-01 Aflatoxins are group of secondary metabolites from moulds. The main toxic effect of aflatoxins on body is based on metabolic activation on cytochrome P450 system. Recently, some studies appointed at anticholinergic properties of aflatoxins and inhibition of acetylcholinesterases (AChE) was described. Inhibition is reversible; however, some questions arose. Is the interaction firmly enough to prevent distribution of aflatoxins in body? Could be AChE considered as a scavenger of aflatoxins? Amperometric biosensor with immobilized acetylcholinesterase was used for evaluation of aflatoxin B1 (AFB1) - AChE complex spontaneous dissociation, where AFB1 acts as an inhibitor. Displacement of solution with substrate and AFB1 by the intact one enabled estimation of dissociation kinetics. The dissociation rate constant k(dis) was found 0.0047 +/- 0.0005 s(-1). The half time (t(1/2)) of complex dissociation was 146 s. The achieved data appoint at fact that AChE could allow to distribute aflatoxins in body instead acting as a scavenger. Analytical impact of study is discussed, too. 15. A first principle study on the interaction between acetylcholinesterase and acetylcholine, and also rivastigmine in alzheimer's disease case Khoirunisa, V.; Rusydi, F.; Kasai, H.; Gandaryus, A. G.; Dipojono, H. K. 2016-08-01 The catalytic activity of acetylcholinesterase enzyme (AChE) relates to the symptom progress in Alzheimer's disease. Interaction of AChE with rivastigmine (from the medicine) can reduce its catalytic activity toward acetylcholine to decelerate the progression of Alzheimer's disease. This research attempts to study the interaction between AChE and rivastigmine, and also acetylcholine (without the presence of rivastigmine) using density functional theory by simplifying the reaction occurs in the active site, which is assumed to be C2H5OH, C3N2H3(Ch3), and CH3COO-. The results suggest that AChE interacts easier with acetylcholine than with rivastigmine, which implies that the medicine does not effectively reduce the catalytic activity of AChE. At this stage, no experimental data is available to be compared with the calculation results. Nonetheless, this study has shown a good prospect to understand the AChE-substrate interaction using a first-principles calculation. 16. Acetylcholinesterase as a Biomarker in Environmental and Occupational Medicine: New Insights and Future Perspectives PubMed Central Caricato, Roberto; Calisi, Antonio; Giordano, Maria Elena; Schettino, Trifone 2013-01-01 Acetylcholinesterase (AChE) is a key enzyme in the nervous system. It terminates nerve impulses by catalysing the hydrolysis of neurotransmitter acetylcholine. As a specific molecular target of organophosphate and carbamate pesticides, acetylcholinesterase activity and its inhibition has been early recognized to be a human biological marker of pesticide poisoning. Measurement of AChE inhibition has been increasingly used in the last two decades as a biomarker of effect on nervous system following exposure to organophosphate and carbamate pesticides in occupational and environmental medicine. The success of this biomarker arises from the fact that it meets a number of characteristics necessary for the successful application of a biological response as biomarker in human biomonitoring: the response is easy to measure, it shows a dose-dependent behavior to pollutant exposure, it is sensitive, and it exhibits a link to health adverse effects. The aim of this work is to review and discuss the recent findings about acetylcholinesterase, including its sensitivity to other pollutants and the expression of different splice variants. These insights open new perspective for the future use of this biomarker in environmental and occupational human health monitoring. PMID:23936791 17. Exposure to Acetylcholinesterase Inhibitors Alters the Physiology and Motor Function of Honeybees PubMed Central Williamson, Sally M.; Moffat, Christopher; Gomersall, Martha A. E.; Saranzewa, Nastja; Connolly, Christopher N.; Wright, Geraldine A. 2013-01-01 Cholinergic signaling is fundamental to neuromuscular function in most organisms. Sub-lethal doses of neurotoxic pesticides that target cholinergic signaling can alter the behavior of insects in subtle ways; their influence on non-target organisms may not be readily apparent in simple mortality studies. Beneficial arthropods such as honeybees perform sophisticated behavioral sequences during foraging that, if influenced by pesticides, could impair foraging success and reduce colony health. Here, we investigate the behavioral effects on honeybees of exposure to a selection of pesticides that target cholinergic signaling by inhibiting acetylcholinesterase (AChE). To examine how continued exposure to AChE inhibitors affected motor function, we fed adult foraging worker honeybees sub-lethal concentrations of these compounds in sucrose solution for 24 h. Using an assay for locomotion in bees, we scored walking, stopped, grooming, and upside down behavior continuously for 15 min. At a 10 nM concentration, all the AChE inhibitors caused similar effects on behavior, notably increased grooming activity and changes in the frequency of bouts of behavior such as head grooming. Coumaphos caused dose-dependent effects on locomotion as well as grooming behavior, and a 1 μM concentration of coumaphos induced symptoms of malaise such as abdomen grooming and defecation. Biochemical assays confirmed that the four compounds we assayed (coumaphos, aldicarb, chlorpyrifos, and donepezil) or their metabolites acted as AChE inhibitors in bees. Furthermore, we show that transcript expression levels of two honeybee AChE inhibitors were selectively upregulated in the brain and in gut tissues in response to AChE inhibitor exposure. The results of our study imply that the effects of pesticides that rely on this mode of action have subtle yet profound effects on physiological effects on behavior that could lead to reduced survival. PMID:23386834 18. Exposure to acetylcholinesterase inhibitors alters the physiology and motor function of honeybees. PubMed Williamson, Sally M; Moffat, Christopher; Gomersall, Martha A E; Saranzewa, Nastja; Connolly, Christopher N; Wright, Geraldine A 2013-01-01 Cholinergic signaling is fundamental to neuromuscular function in most organisms. Sub-lethal doses of neurotoxic pesticides that target cholinergic signaling can alter the behavior of insects in subtle ways; their influence on non-target organisms may not be readily apparent in simple mortality studies. Beneficial arthropods such as honeybees perform sophisticated behavioral sequences during foraging that, if influenced by pesticides, could impair foraging success and reduce colony health. Here, we investigate the behavioral effects on honeybees of exposure to a selection of pesticides that target cholinergic signaling by inhibiting acetylcholinesterase (AChE). To examine how continued exposure to AChE inhibitors affected motor function, we fed adult foraging worker honeybees sub-lethal concentrations of these compounds in sucrose solution for 24 h. Using an assay for locomotion in bees, we scored walking, stopped, grooming, and upside down behavior continuously for 15 min. At a 10 nM concentration, all the AChE inhibitors caused similar effects on behavior, notably increased grooming activity and changes in the frequency of bouts of behavior such as head grooming. Coumaphos caused dose-dependent effects on locomotion as well as grooming behavior, and a 1 μM concentration of coumaphos induced symptoms of malaise such as abdomen grooming and defecation. Biochemical assays confirmed that the four compounds we assayed (coumaphos, aldicarb, chlorpyrifos, and donepezil) or their metabolites acted as AChE inhibitors in bees. Furthermore, we show that transcript expression levels of two honeybee AChE inhibitors were selectively upregulated in the brain and in gut tissues in response to AChE inhibitor exposure. The results of our study imply that the effects of pesticides that rely on this mode of action have subtle yet profound effects on physiological effects on behavior that could lead to reduced survival. 19. Inhibition of acetylcholinesterase by two genistein derivatives: kinetic analysis, molecular docking and molecular dynamics simulation. PubMed Fang, Jiansong; Wu, Ping; Yang, Ranyao; Gao, Li; Li, Chao; Wang, Dongmei; Wu, Song; Liu, Ai-Lin; Du, Guan-Hua 2014-12-01 In this study two genistein derivatives (G1 and G2) are reported as inhibitors of acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE), and differences in the inhibition of AChE are described. Although they differ in structure by a single methyl group, the inhibitory effect of G1 (IC50=264 nmol/L) on AChE was 80 times stronger than that of G2 (IC50=21,210 nmol/L). Enzyme-kinetic analysis, molecular docking and molecular dynamics (MD) simulations were conducted to better understand the molecular basis for this difference. The results obtained by kinetic analysis demonstrated that G1 can interact with both the catalytic active site and peripheral anionic site of AChE. The predicted binding free energies of two complexes calculated by the molecular mechanics/generalized born surface area (MM/GBSA) method were consistent with the experimental data. The analysis of the individual energy terms suggested that a difference between the net electrostatic contributions (ΔE ele+ΔG GB) was responsible for the binding affinities of these two inhibitors. Additionally, analysis of the molecular mechanics and MM/GBSA free energy decomposition revealed that the difference between G1 and G2 originated from interactions with Tyr124, Glu292, Val294 and Phe338 of AChE. In conclusion, the results reveal significant differences at the molecular level in the mechanism of inhibition of AChE by these structurally related compounds. PMID:26579414 20. Molecular Characterization of Monoclonal Antibodies that Inhibit Acetylcholinesterase by Targeting the Peripheral Site and Backdoor Region PubMed Central Essono, Sosthène; Mondielli, Grégoire; Lamourette, Patricia; Boquet, Didier; Grassi, Jacques; Marchot, Pascale 2013-01-01 The inhibition properties and target sites of monoclonal antibodies (mAbs) Elec403, Elec408 and Elec410, generated against Electrophorus electricus acetylcholinesterase (AChE), have been defined previously using biochemical and mutagenesis approaches. Elec403 and Elec410, which bind competitively with each other and with the peptidic toxin inhibitor fasciculin, are directed toward distinctive albeit overlapping epitopes located at the AChE peripheral anionic site, which surrounds the entrance of the active site gorge. Elec408, which is not competitive with the other two mAbs nor fasciculin, targets a second epitope located in the backdoor region, distant from the gorge entrance. To characterize the molecular determinants dictating their binding site specificity, we cloned and sequenced the mAbs; generated antigen-binding fragments (Fab) retaining the parental inhibition properties; and explored their structure-function relationships using complementary x-ray crystallography, homology modeling and flexible docking approaches. Hypermutation of one Elec403 complementarity-determining region suggests occurrence of antigen-driven selection towards recognition of the AChE peripheral site. Comparative analysis of the 1.9Å-resolution structure of Fab408 and of theoretical models of its Fab403 and Fab410 congeners evidences distinctive surface topographies and anisotropic repartitions of charges, consistent with their respective target sites and inhibition properties. Finally, a validated, data-driven docking model of the Fab403-AChE complex suggests a mode of binding at the PAS that fully correlates with the functional data. This comprehensive study documents the molecular peculiarities of Fab403 and Fab410, as the largest peptidic inhibitors directed towards the peripheral site, and those of Fab408, as the first inhibitor directed toward the backdoor region of an AChE and a unique template for the design of new, specific modulators of AChE catalysis. PMID:24146971 1. Contribution of Ldace1 gene to acetylcholinesterase activity in Colorado potato beetle. PubMed Revuelta, L; Ortego, F; Díaz-Ruíz, J R; Castañera, P; Tenllado, F; Hernández-Crespo, P 2011-10-01 The Colorado potato beetle (CPB), Leptinotarsa decemlineata is an important economic pest of potato worldwide. Resistance to organophosphates and carbamates in CPB has been associated in some cases to point mutations in the acetylcholinesterase (AChE) gene Ldace2, an orthologue of Drosophila melanogaster Dmace2. In this paper we report cloning and sequencing of Ldace1, an orthologue of Anopheles gambiae Agace1 that was previously unknown in CPB. The Ldace1 coding enzyme contains all residues conserved in a functionally active AChE. Ldace1 is expressed at higher levels (between 2- and 11-fold) than Ldace2 in embryos, in the four larval instars and in adults. Specific interference of Ldace1 by means of dsRNA injection resulted in a reduction of AChE activity to an approximate 50% compared to control, whilst interference of Ldace2 reduced AChE activity to an approximate 85%. Analysis of zymograms of AChE activity after interference indicates that LdAChE1 is the enzyme predominantly responsible for the activity visualised. Interference of Ldace1 in CPB adults caused a significant increase in mortality (43%) as early as three days post-injection (p.i.), suggesting the essential role of Ldace1. Interference of Ldace2 also caused a significant increase in mortality (29%) compared to control, although at seven days p.i. The effect of the interference of Ldace1 on susceptibility to the organophosphate chlorpyrifos points out that LdAChE1 could be a main target for this insecticide. In the light of our results, studies associating resistance in CPB to mutations in Ldace2 should be reviewed, taking into consideration analysis of the Ldace1 gene. 2. Influence of dimethoate on acetylcholinesterase activity and locomotor function in terrestrial isopods. PubMed Engenheiro, Elizabeth L; Hankard, Peter K; Sousa, José P; Lemos, Marco F; Weeks, Jason M; Soares, Amadeu M V M 2005-03-01 Locomotor behavior in terrestrial organisms is crucial for burrowing, avoiding predators, food seeking, migration, and reproduction; therefore, it is a parameter with ecological relevance. Acetylcholinesterase (AChE) is a nervous system enzyme inhibited by several compounds and widely used as an exposure biomarker in several organisms. Moreover, changes in energy reserves also may indicate an exposure to a stress situation. The aim of this study is to link biomarkers of different levels of biological organization in isopods exposed to increasing doses of dimethoate in semifield conditions. Locomotor parameters, AChE activity, and energy reserves (lipid, glycogen, and protein contents) were evaluated in the isopod Porcellio dilatatus after 48-h and 10-d exposure to dimethoate-contaminated soil. Results showed a clear impairment of both locomotor and AChE activity during the entire study, although effects were more pronounced after 48 h. Most locomotor parameters and AChE activity showed a clear dose-response relationship. By contrast, no clear trend was observed on energetic components. A positive and significant relationship was found between AChE activity and those locomotor parameters indicating activity, and the opposite was observed with those locomotor parameters indicating confusion and disorientation. The results obtained in this study enhance the importance of linking biochemical responses to parameters with ecological relevance at individual level, the value of locomotor behavior as an important marker to assess effects of toxicants, and also the usefulness and the acquisition of ecological relevance by AChE as a biomarker, by linking it with ecologically relevant behavioral parameters. 3. Evaluation of a Brain Acetylcholinesterase Extraction Method and Kinetic Constants after Methyl-Paraoxon Inhibition in Three Brazilian Fish Species PubMed Central Freitas, A. P.; Santos, C. R.; Sarcinelli, P. N.; Hauser-Davis, R. A.; Lopes, R. M. 2016-01-01 Acetylcholinesterase (AChE) is an important enzyme in the control of the neuronal action potential and sensitive to organophosphate inhibition. Brain fish AChE is less sensitive to organophosphate inhibition than AChE from terrestrial animals, although this sensitivity is variable among species and has not yet been fully evaluated in fish species. In this setting, inhibition kinetic constants for progressive irreversible inhibition of brain acetylcholinesterase due to methyl-paraoxon exposure were determined in three fish species (Mugil liza, Genidens genidens and Lagocephalus laevigatus) and hen (Gallus domesticus). Enzyme extraction using a detergent was shown to be adequate, and samples presented activity inhibition in high substrate concentrations and suppression of inhibition by methyl-paraoxon in the presence of the substrate, similar to kinetic patterns from purified enzyme preparations. Catfish (G. genidens) AChE presented the highest sensitivity among the evaluated fish species (IC50 = 1031.20 nM ± 63.17) in comparison to M. liza and L. laevigatus (IC50: 2878.83 ± 421.94 and 2842.5 ± 144.63 nM respectively). The lower dissociation constant (Kd = 20.3 ± 2.95 μM) of catfish AChE showed greater enzyme affinity for methyl-paraoxon, explaining this species higher sensitivity to organophosphates. Hen AChE presented higher ki (900.57 ± 65.3 mM-1min-1) and, consequently, greater sensitivity to methyl-paraoxon, explained by a lower Kd (0.6 ± 0.13 μM). Furthermore, hen AChE did not differentiate between the propionylthiocholine and acetylthiocholine substrates, indicating easier access of methyl-paraoxon to the hen enzyme activity site. The results obtained herein indicate a suitable extraction of AChE and, despite different inhibition kinetic constants, demonstrate that fish AChE is less sensitive to methyl-paraoxon, probably due to reduced access to the catalytic center which provides greater enzyme substrate selectivity. PMID:27655611 4. Inhibitor profile of bis(n)-tacrines and N-methylcarbamates on acetylcholinesterase from Rhipicephalus (Boophilus) microplus and Phlebotomus papatasi PubMed Central Swale, Daniel R.; Tong, Fan; Temeyer, Kevin B.; Li, Andrew; Lam, Polo C-H.; Totrov, Maxim M.; Carlier, Paul R.; Pérez de León, Adalberto A.; Bloomquist, Jeffrey R. 2013-01-01 The cattle tick, Rhipicephalus (Boophilus) microplus (Bm), and the sand fly, Phlebotomus papatasi (Pp), are disease vectors to cattle and humans, respectively. The purpose of this study was to characterize the inhibitor profile of acetylcholinesterases from Bm (BmAChE1) and Pp (PpAChE) compared to human and bovine AChE, in order to identify divergent pharmacology that might lead to selective inhibitors. Results indicate that BmAChE has low sensitivity (IC50 = 200 μM) toward tacrine, a monovalent catalytic site inhibitor with sub micromolar blocking potency in all previous species tested. Similarly, a series of bis(n)-tacrine dimer series, bivalent inhibitors and peripheral site AChE inhibitors possess poor potency toward BmAChE. Molecular homology models suggest the rBmAChE enzyme possesses a W384F orthologous substitution near the catalytic site, where the larger tryptophan side chain obstructs the access of larger ligands to the active site, but functional analysis of this mutation suggests it only partially explains the low sensitivity to tacrine. In addition, BmAChE1 and PpAChE have low nanomolar sensitivity to some experimental carbamate anticholinesterases originally designed for control of the malaria mosquito, Anopheles gambiae. One experimental compound, 2-((2-ethylbutyl)thio)phenyl methylcarbamate, possesses >300-fold selectivity for BmAChE1 and PpAChE over human AChE, and a mouse oral LD50 of >1500 mg/kg, thus providing an excellent new lead for vector control. PMID:24187393 5. Electronic structure calculations toward new potentially AChE inhibitors de Paula, A. A. N.; Martins, J. B. L.; Gargano, R.; dos Santos, M. L.; Romeiro, L. A. S. 2007-10-01 The main purpose of this study was the use of natural non-isoprenoid phenolic lipid of cashew nut shell liquid from Anacardium occidentale as lead material for generating new potentially candidates of acetylcholinesterase inhibitors. Therefore, we studied the electronic structure of 15 molecules derivatives from the cardanol using the following groups: methyl, acetyl, N, N-dimethylcarbamoyl, N, N-dimethylamine, N, N-diethylamine, piperidine, pyrrolidine, and N-benzylamine. The calculations were performed at RHF level using 6-31G, 6-31G(d), 6-31+G(d) and 6-311G(d,p) basis functions. Among the proposed compounds we found that the structures with substitution by acetyl, N, N-dimethylcarbamoyl, N, N-dimethylamine, and pyrrolidine groups were better correlated to rivastigmine indicating possible activity. 6. Chemical composition, aroma evaluation, and inhibitory activity towards acetylcholinesterase of essential oils from Gynura bicolor DC. PubMed Miyazawa, Mitsuo; Nakahashi, Hiroshi; Usami, Atsushi; Matsuda, Naoki 2016-04-01 The compositions of the essential oils obtained from leaves and stems of Gynura bicolor DC. were analyzed by GC-MS. One hundred eight components of these oils were identified. (E)-β-caryophyllene (31.42 %), α-pinene (17.11 %), and bicyclogermacrene (8.09 %) were found to be the main components of the leaf oil, while α-pinene (61.42 %), β-pinene (14.39 %), and myrcene (5.10 %) were the major constituents of the stem oil. We found 73 previously unidentified components in these oils from G. bicolor. The oils were also subjected to odor evaluation. Eleven and 12 aroma-active compounds were detected in the leaf and stem oils, respectively. The abilities of these oils to inhibit acetylcholinesterase (AChE) activity were determined. The sesquiterpenoids in the oils were found to inhibit AChE activity more strongly than the monoterpenoids in the oils did. It was suggested that the three main components in each essential oil act synergistically against AChE activity. These results show that the essential oils obtained from G. bicolor are a good dietary source of AChE activity inhibition. 7. Influence of water temperature on acetylcholinesterase activity in the pacific tree frog (Hyla regilla) USGS Publications Warehouse Johnson, Catherine S.; Schwarzbach, Steven E.; Henderson, John D.; Wilson, Barry W.; Tjeerdema, Ronald S. 2005-01-01 This investigation evaluated whether acetylcholinesterase (AChE) in Pacific tree frogs (Hyla regilla) from different geographical locations was influenced by different temperatures during early aquatic life stages, independent of pesticide exposure. Tadpoles were collected from both a California coastal pond and a Sierra Nevada mountain range pond, USA. Groups of frogs from each location were raised in temperatures representative of either the Sierra Nevada (8°C) or the coastal (19°C) location. Metamorphs from both locations raised as tadpoles at 19°C had AChE activities of 42.3 and 38.7 nm/min/mg protein, while those raised as tadpoles at 8°C had activities of 26.9 and 28.2 nm/min/mg protein. A two-way analysis of variance revealed temperature to be the significant factor in determining AChE activity (F = 22.3, p < 0.001), although origin was not important (F = 0.09, p = 0.75). Interpretations regarding the influence of pesticides upon AChE activity in Pacific tree frogs must consider the influence of environmental temperature to enable cross-population comparisons. 8. Sub-chronic effect of neem based pesticide (Vepacide) on acetylcholinesterase and ATPases in rat. PubMed Rahman, M F; Siddiqui, M K; Jamil, K 1999-09-01 Acetylcholinesterases (AChE), Na(+)-K+, Mg2+ and Ca(2+)-ATPases were monitored in rat brain when treated orally with 80, 160 and 320 mg/kg of Vepacide, an active ingredient from neem seed oil, daily for 90 days. Brain AChE, Na(+)-K+ and Ca(2+)-ATPases were inhibited whereas Mg(2+)-ATPase levels were enhanced in both the sexes after 45 and 90 days of treatment. The relative sensitivities of these ATPases to Vepacide indicated that Ca(2+)-ATPase being more sensitive than Na(+)-K(+)-ATPase in both the sexes. The magnitude of Ca(2+)-ATPase inhibited by this compound was higher than that of brain AChE. It appears to be sexual dimorphism in the alterations of brain AChE, Na(+)-K+ and Mg(2+)-ATPases by Vepacide with females being significant when compared with males. After 28 days of post treatment the alterations observed were approached to those of controls both in male and female rats showing reversal of the toxicity. These results indicated that the ATPases were potently inhibited by Vepacide and seemed to be its precise target among the enzyme studied. This can be used as biochemical marker of exposure to this neem derived product. PMID:10466107 9. Assessment of acetylcholinesterase activity using indoxylacetate and comparison with the standard Ellman's method. PubMed Pohanka, Miroslav; Hrabinova, Martina; Kuca, Kamil; Simonato, Jean-Pierre 2011-01-01 Assay of acetylcholinesterase (AChE) activity plays an important role in diagnostic, detection of pesticides and nerve agents, in vitro characterization of toxins and drugs including potential treatments for Alzheimer's disease. These experiments were done in order to determine whether indoxylacetate could be an adequate chromogenic reactant for AChE assay evaluation. Moreover, the results were compared to the standard Ellman's method. We calculated Michaelis constant Km (2.06 × 10(-4) mol/L for acetylthiocholine and 3.21 × 10(-3) mol/L for indoxylacetate) maximum reaction velocity V(max) (4.97 × 10(-7) kat for acetylcholine and 7.71 × 10(-8) kat for indoxylacetate) for electric eel AChE. In a second part, inhibition values were plotted for paraoxon, and reactivation efficacy was measured for some standard oxime reactivators: obidoxime, pralidoxime (2-PAM) and HI-6. Though indoxylacetate is split with lower turnover rate, this compound appears as a very attractive reactant since it does not show any chemical reactivity with oxime antidots and thiol used for the Ellman's method. Thus it can be advantageously used for accurate measurement of AChE activity. Suitability of assay for butyrylcholinesterase activity assessment is also discussed. 10. Acetylcholinesterase inhibitory activity of Thai traditional nootropic remedy and its herbal ingredients. PubMed Tappayuthpijarn, Pimolvan; Itharat, Arunporn; Makchuchit, Sunita 2011-12-01 The incidence of Alzheimer disease (AD) is increasing every year in accordance with the increasing of elderly population and could pose significant health problems in the future. The use of medicinal plants as an alternative prevention or even for a possible treatment of the AD is, therefore, becoming an interesting research issue. Acetylcholinesterase (AChE) inhibitors are well-known drugs commonly used in the treatment of AD. The aim of the present study was to screen for AChE inhibitory activity of the Thai traditional nootropic recipe and its herbal ingredients. The results showed that ethanolic extracts of four out of twenty-five herbs i.e. Stephania pierrei Diels. Kaempfera parviflora Wall. ex Baker, Stephania venosa (Blume) Spreng, Piper nigrum L at 0.1 mg/mL showed % AChE inhibition of 89, 64, 59, 50; the IC50 were 6, 21, 29, 30 microg/mL respectively. The other herbs as well as combination of the whole recipe had no synergistic inhibitory effect on AChE activity. However some plants revealed antioxidant activity. More research should have be performed on this local wisdom remedy to verify the uses in scientific term. PMID:22619927 11. Effects of carbofuran and deltamethrin on acetylcholinesterase activity in brain and muscle of the common carp. PubMed Ensibi, Cherif; Hernández-Moreno, David; Míguez Santiyán, M Prado; Daly Yahya, Mohamed Néjib; Rodríguez, Francisco Soler; Pérez-López, Marcos 2014-04-01 This work investigated the effect from exposure to insecticides carbofuran and deltamethrin on acetylcholinesterase (AChE) activity in the brain and muscle of common carp (Cyprinus carpio). Both pesticides were evaluated through two separate experiments, and carp were exposed in a semi-static system to three different concentrations of carbofuran (10, 50, and 100 μg/L) and deltamethrin (0.08, 0.4, and 0.8 μg/L) during a month with sampling times at 0, 4, 15, and 30 days (n = 7 from each aquarium). AChE activity was significantly inhibited in both organs of carps exposed to carbofuran at all sampling times depending on dose and time, reaching inhibition values of 73.5 and 67.1%, in brain and muscle tissues respectively, after 30 days with the highest concentration. On the contrary, AChE activity was not significantly affected after deltamethrin exposure at all concentrations and times of the assay. This study shows that the measurement of brain and muscle AChE activity in Cyprinus carpio is a useful biomarker of carbamates exposure and/or effects, but has no application with pyrethroids. 12. Discovery of dual binding site acetylcholinesterase inhibitors identified by pharmacophore modeling and sequential virtual screening techniques. PubMed Gupta, Shikhar; Fallarero, Adyary; Järvinen, Päivi; Karlsson, Daniela; Johnson, Mark S; Vuorela, Pia M; Mohan, C Gopi 2011-02-15 Dual binding site acetylcholinesterase (AChE) inhibitors are promising for the treatment of Alzheimer's disease (AD). They alleviate the cognitive deficits and AD-modifying agents, by inhibiting the β-amyloid (Aβ) peptide aggregation, through binding to both the catalytic and peripheral anionic sites, the so called dual binding site of the AChE enzyme. In this Letter, chemical features based 3D-pharmacophore models were developed based on the eight potent and structurally diverse AChE inhibitors (I-VIII) obtained from high-throughput in vitro screening technique. The best 3D-pharmacophore model, Hypo1, consists of two hydrogen-bond acceptor lipid, one hydrophobe, and two hydrophobic aliphatic features obtained by Catalyst/HIPHOP algorithm adopted in Discovery studio program. Hypo1 was used as a 3D query in sequential virtual screening study to filter three small compound databases. Further, a total of nine compounds were selected and followed on in vitro analysis. Finally, we identified two leads--Specs1 (IC(50)=3.279 μM) and Spec2 (IC(50)=5.986 μM) dual binding site compounds from Specs database, having good AChE enzyme inhibitory activity. PMID:21273074 13. β-glucan attenuated scopolamine induced cognitive impairment via hippocampal acetylcholinesterase inhibition in rats. PubMed Haider, Ali; Inam, Wali; Khan, Shahab Ali; Hifza; Mahmood, Wajahat; Abbas, Ghulam 2016-08-01 β-glucan (polysaccharide) rich diet has been reported to enhance cognition in humans but the mechanism remained elusive. Keeping this in mind, the present study was designed to investigate the interaction of β-glucan with central cholinergic system. Briefly, in-silico analysis revealed promising interactions of β-glucan with the catalytic residues of acetylcholinesterase (AChE) enzyme. In line with this outcome, the in vitro assay (Ellman's method) also exhibited inhibition of AChE by β-glucan (IC50=0.68±0.08μg/µl). Furthermore, the in vivo study (Morris water maze) showed significant dose dependent reversal of the amnesic effect of scopolamine (2mg/kg i.p.) by β-glucan treatment (5, 25, 50 and 100mg/kg, i.p.). Finally, the hippocampi of aforementioned treated animals also revealed dose dependent inhibition of AChE enzyme. Hence, it can be deduced that β-glucan possesses potential to enhance central cholinergic tone via inhibiting AChE enzyme. In conclusion, the present study provides mechanistic insight to the cognition enhancing potential of β-glucan. Keeping in mind its dietary use and abundance in nature, it can be considered as economic therapeutic option against cognitive ailments associated with decline in cholinergic neurotransmission. 14. Acetylcholinesterase Inhibitory Activity of Pigment Echinochrome A from Sea Urchin Scaphechinus mirabilis PubMed Central Lee, Sung Ryul; Pronto, Julius Ryan D.; Sarankhuu, Bolor-Erdene; Ko, Kyung Soo; Rhee, Byoung Doo; Kim, Nari; Mishchenko, Natalia P.; Fedoreyev, Sergey A.; Stonik, Valentin A.; Han, Jin 2014-01-01 Echinochrome A (EchA) is a dark-red pigment of the polyhydroxynaphthoquinone class isolated from sea urchin Scaphechinus mirabilis. Acetylcholinesterase (AChE) inhibitors are used in the treatment of various neuromuscular disorders, and are considered as strong therapeutic agents for the treatment of Alzheimer’s disease (AD). Although EchA is clinically used to treat ophthalmic diseases and limit infarct formation during ischemia/reperfusion injury, anti-AChE effect of EchA is still unknown. In this study, we investigated the anti-AChE effect of EchA in vitro. EchA and its exhausted form which lost anti-oxidant capacity did not show any significant cytotoxicy on the H9c2 and A7r5 cells. EchA inhibited AChE with an irreversible and uncompetitive mode. In addition, EchA showed reactive oxygen species scavenging activity, particularly with nitric oxide. These findings indicate new therapeutic potential for EchA in treating reduced acetylcholine-related diseases including AD and provide an insight into developing new AChE inhibitors. PMID:24918454 15. Discovery of dual binding site acetylcholinesterase inhibitors identified by pharmacophore modeling and sequential virtual screening techniques. PubMed Gupta, Shikhar; Fallarero, Adyary; Järvinen, Päivi; Karlsson, Daniela; Johnson, Mark S; Vuorela, Pia M; Mohan, C Gopi 2011-02-15 Dual binding site acetylcholinesterase (AChE) inhibitors are promising for the treatment of Alzheimer's disease (AD). They alleviate the cognitive deficits and AD-modifying agents, by inhibiting the β-amyloid (Aβ) peptide aggregation, through binding to both the catalytic and peripheral anionic sites, the so called dual binding site of the AChE enzyme. In this Letter, chemical features based 3D-pharmacophore models were developed based on the eight potent and structurally diverse AChE inhibitors (I-VIII) obtained from high-throughput in vitro screening technique. The best 3D-pharmacophore model, Hypo1, consists of two hydrogen-bond acceptor lipid, one hydrophobe, and two hydrophobic aliphatic features obtained by Catalyst/HIPHOP algorithm adopted in Discovery studio program. Hypo1 was used as a 3D query in sequential virtual screening study to filter three small compound databases. Further, a total of nine compounds were selected and followed on in vitro analysis. Finally, we identified two leads--Specs1 (IC(50)=3.279 μM) and Spec2 (IC(50)=5.986 μM) dual binding site compounds from Specs database, having good AChE enzyme inhibitory activity. 16. Role of acetylcholinesterase inhibitors in the metabolism of amyloid precursor protein. PubMed 2003-06-01 Potentiation of central cholinergic activity has been proposed as a therapeutic approach for improving the cognitive function in patients with Alzheimer's disease (AD). Increasing the acetylcholine concentration in the brain by modulating acetylcholine-sterase (AChE) activity is among the most promising therapeutic strategies. Efforts to treat the underlying pathology based on the modulation of amyloid precursor protein (APP) processing in order to decrease the accumulation of beta-amyloid are also very important. Alterations in APP metabolism have recently been proposed to play a key role in the long-lasting effects of AChE inhibitors. This review surveys recent data from in vivo and in vitro studies that have contributed to our understanding of the role of AChE inhibitors in APP processing. The regulatory mechanisms relating to the muscarinic agonist effect, protein kinase C activation and mitogen-activated protein kinase phosphorylation, involving the alpha-secretase or the 5 -UTR region of the APP gene, are also discussed. Further work is warranted to elucidate the exact roles in APP metabolism of the AChE inhibitors used in AD therapy at present. PMID:12769797 17. Acrylonitrile has Distinct Hormetic Effects on Acetyl-Cholinesterase Activity in Mouse Brain and Blood that are Modulated by Ethanol. PubMed Yuanqing, He; Suhua, Wang; Guangwei, Xing; Chunlan, Ren; Hai, Qian; Wenrong, Xu; Rongzhu, Lu; Aschner, Michael; Milatovic, Dejan 2013-01-01 Acrylonitrile(AN) is a neurotoxin both in animals and humans, but its effects on acetylcholinesterase (AChE) activity remain controversial. This study aimed to determine the dose-response effects of AN on AChE activity and the modulatory role of ethanol pre-treatment. A total of 144 Kunming mice were randomly divided into 18 groups: nine groups received 5% ethanol in their drinking water, and the remaining nine groups received regular tap water. One week later, both the ethanol and tap water only groups were given an intraperitoneal injection of AN at the following doses: 0 (control), 0.156, 0.3125, 0.625, 1.25, 2.5, 5, 10 or 20 mg AN/kg body weight. AChE activity was determined on whole blood and brain 24 h later. Blood AChE activity was higher in AN-injected mice than in controls at all doses. AChE activity in blood increased in a dose-dependent manner, peaking at 0.156 mg/kg, after which a gradual decrease ensued, displaying a β-typed dose-response relationship. In contrast, brain AChE activity, following a single AN injection, was consistently lower than in control mice, and continued to fall up to a dose of 0.313 mg/kg, and thereafter increased gradually with higher doses. Mice receiving a 20 mg/kg dose of AN exhibited AChE brain activity indistinguishable from that of control mice, demonstrating a typical U-typed dose-response relationship. The activity of AChE in the blood and brain of the AN + ethanol-treated groups displayed a shift to the right, and the magnitude of the decrease in AChE activity induced by AN was attenuated relative to the AN-only group. These results suggest that AN affects AChE activity in both mouse blood and brain in a hormetic manner. Pretreatment with ethanol modifies the effect of AN on AChE, indicating that parent AN has a more prominent role than its metabolites in modulating enzyme activity. PMID:23550232 18. Computational studies of acetylcholinesterase complexed with fullerene derivatives: a new insight for Alzheimer disease treatment. PubMed da Silva Gonçalves, Arlan; França, Tanos Celmar Costa; Vital de Oliveira, Osmair 2016-06-01 Here, we propose five fullerene (C60) derivatives as new drugs against Alzheimer's disease (AD). These compounds were designed to act as new human acetylcholinesterase (HssAChE) inhibitors by blocking its fasciculin II (FASII) binding site. Docking and molecular dynamic results show that our proposals bind to the HssAChE tunnel entrance, forming stable complex, and further binding free energy calculations suggest that three of the derivatives proposed here could be potent HssAChE inhibitors. We found a region formed by a set of residues (Tyr72, Asp74, Trp286, Gln291, Tyr341, and Pro344) which can be further exploited in the drug design of new inhibitors of HssAChE based on C60 derivatives. Results presented here report for the first time by a new class of molecules that can become effective drugs against AD. 19. Acetylcholinesterase-reduced graphene oxide hybrid films for organophosphorus neurotoxin sensing via quartz crystal microbalance Tang, Shi; Ma, Wenying; Xie, Guangzhong; Su, Yuanjie; Jiang, Yadong 2016-09-01 An acetylcholinesterase (AChE)-reduced graphene oxide (RGO) hybrid films based biosensor enabled by quartz crystal microbalance (QCM) has been developed for the detection of organophosphorus neurotoxin in gas phase at room temperature. To improve the sensing performance, RGO was used to immobilize large quantities of enzyme and provide a favorable microenvironment to maintain the enzyme activity. The experimental results reveal that the response of AChE-RGO/glutaraldehyde based sensors is about 8 times larger than that of the AChE with the sensitivity of 1.583 Hz/mg/m3. 1.0 mg amount of RGO, 5% concentration of glutaraldehyde and pH 6.8 is the optimal condition of this biosensor. 20. Key active site residues in the inhibition of acetylcholinesterases by soman. PubMed Qian, N; Kovach, I M 1993-12-27 Molecular modeling (GEMM 7.3) and molecular mechanics calculations (YETI V 5.3) using the X-ray coordinates for acetylcholinesterase (AChE) from Torpedo californica indicate electrostatic stabilization by the active site, Glu-199, of the developing positive charge on the incipient carbonium ion in the dealkylation in the adducts of AChE with PSCR and PSCS diastereomers of 2-(3,3-dimethylbutyl) methylphosphonofluoridate (soman). His-440 is indispensable as a general acid catalyst of C-O bond breaking in the dealkylation reaction and that of bond breaking to the Ser gamma-O in reactivation. This demand for catalysis seems to be satisfied for the reactivation of enzyme from the PSCS diastereomer of soman, but not from the P(S)C(R) diastereomer. 1. 1H NMR Relaxation Investigation of Inhibitors Interacting with Torpedo californica Acetylcholinesterase Delfini, Maurizio; Gianferri, Raffaella; Dubbini, Veronica; Manetti, Cesare; Gaggelli, Elena; Valensin, Gianni 2000-05-01 Two naphthyridines interacting with Torpedo californica acetylcholinesterase (AChE) were investigated. 1H NMR spectra were recorded and nonselective, selective, and double-selective spin-lattice relaxation rates were measured. The enhancement of selective relaxation rates could be titrated by different ligand concentrations at constant AChE (yielding 0.22 and 1.53 mM for the dissociation constants) and was providing evidence of a diverse mode of interaction. The double-selective relaxation rates were used to evaluate the motional correlation times of bound ligands at 34.9 and 36.5 ns at 300 K. Selective relaxation rates of bound inhibitors could be interpreted also in terms of dipole-dipole interactions with protons in the enzyme active site. 2. Graphene quantum dots for ultrasensitive detection of acetylcholinesterase and its inhibitors Li, Nan; Wang, Xuewan; Chen, Jie; Sun, Lei; Chen, Peng 2015-09-01 Graphene quantum dots (GQDs) are emerging zero-dimensional materials promising a wide spectrum of novel applications including development of optical sensors. Herein, a GQD-based fluorometric sensor is devised to detect acetylcholinesterase (AChE, a critical enzyme in central nervous system and neuromuscular junctions) with an ultralow detection limit (0.58 pM with S/N of 5.0), using a photoluminescence ‘turn-off’ mechanism. This simple ‘mix-and-detect’ platform can also be employed to sense a variety of compounds that can directly or indirectly inhibit the enzymatic activities of AChE, such as nerve gases, pesticides, and therapeutic drugs. As the proof-of-concept demonstrations, we show the sensitive detection of paraoxon (a pesticide), tacrine (a drug to treat Alzheimer’s disease), and dopamine (an important neurotransmitter). 3. Inhibition of acetylcholinesterase by extracts and constituents from Angelica archangelica and Geranium sylvaticum. PubMed Sigurdsson, Steinthor; Gudbjarnason, Sigmundur 2007-01-01 The aim of this study was to explore the acetylcholinesterase (AChE) inhibition of several Icelandic medicinal herbs. Ethanolic extracts of Angelica archangelica seeds and the aerial parts of Geranium sylvaticum proved effective, with IC50 values of 2.20 mg/ml and 3.56 mg/ml, respectively. The activity of imperatorin and xanthotoxin from A. archangelica was measured. Xanthotoxin proved much more potent than imperatorin, with an IC50 value of 155 microg/ml (0.72 mM) but that for imperatorin was above 274 microg/ml (1.01 mM). However, furanocoumarins seem to have a minor part in the total activity of this extract. Synergistic interaction was observed between the extracts of A. archangelica and G. sylvaticum. Several medicinal herbs (Achillea millefolium, Filipendula ulmaria, Thymus praecox and Matricaria maritima) did not show AChE inhibitory activity. PMID:18069242 4. Antioxidative Properties and Effect of Quercetin and Its Glycosylated Form (Rutin) on Acetylcholinesterase and Butyrylcholinesterase Activities. PubMed Ademosun, Ayokunle O; Oboh, Ganiyu; Bello, Fatai; Ayeni, Peluola O 2016-10-01 This study sought to investigate the anticholinesterase and antioxidative properties of quercetin and its glycosylated conjugate, rutin. The in vitro inhibition of acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) activities, inhibition of Fe(2+)-induced lipid peroxidation in rat's brain homogenates, radicals scavenging, and Fe(2+)-chelating abilities of the flavonoids were investigated in vitro with concentrations of the samples ranging from 0.06 to 0.6 mM. Quercetin had significantly higher AChE and BChE inhibitory abilities than rutin. Quercetin also had stronger inhibition of Fe(2+)-induced lipid peroxidation in rat's brain homogenates. Similarly, quercetin had higher radical scavenging abilities than rutin. Quercetin also had stronger Fe(2+)-chelating ability than rutin. The inhibition of cholinesterases and antioxidative properties are possible mechanisms by which the flavonoids can be used in the management of oxidative stress-induced neurodegeneration. 5. Ligand exclusion on acetylcholinesterase. PubMed Berman, H A; Leonard, K 1990-11-27 This paper examines covalent reactivity of AchE with respect to cationic and uncharged methylphosphonates and substrates in the absence and presence of cationic ligands selective for the active center and the peripheral anionic site. The organophosphorus inhibitors are enantiomeric alkyl methylphosphonothioates (1-5) containing cycloheptyl and isopropyl phosphono ester groups and S-methyl, S-n-pentyl, and S-[beta-(trimethylammonio)ethyl] leaving groups; these agents differ in their configuration about phosphorus and their steric, hydrophobic, and electrostatic characteristics. The synthetic substrates examined are acetylthiocholine, p-nitrophenyl acetate, and 7-acetoxy-4-methylcoumarin (7AMC). Antagonism of the methylphosphonothioate reaction by cationic ligands is strongly dependent on the nature of both the cation and the methylphosphonate but independent of the configuration about phosphorus. While all cations cause linear mixed inhibition of acetylthiocholine hydrolysis, there are observed a variety of inhibition patterns of 7AMC and p-nitrophenyl acetate hydrolysis that are distinctly nonlinear, as well as patterns in which the reciprocal plots intersect in the upper right quadrant. Strong antagonism of cationic (methylphosphonyl)thiocholines correlates very well with linear inhibition of acetylthiocholine. Ligands that cause only negligible antagonism of the uncharged methylphosphonates display nonlinear inhibition of uncharged substrates. These relationships, since they are most pronounced for peripheral site ligands and are strongly dependent on the charge carried by the reactant, suggest that the peripheral anionic site alters enzyme reactivity through an electrostatic interaction with the net negative active center. Such behavior indicates a potential role for the peripheral anionic site in conserving AchE catalytic efficiency within a narrow range of values. PMID:2271673 6. Lanostanoids with acetylcholinesterase inhibitory activity from the mushroom Haddowia longipes. PubMed Zhang, Shuang-Shuang; Ma, Qing-Yun; Huang, Sheng-Zhuo; Dai, Hao-Fu; Guo, Zhi-Kai; Yu, Zhi-Fang; Zhao, You-Xing 2015-02-01 Nine lanostanoids, together with nine known ones, were isolated from the ethyl acetate extract of the fruiting bodies of the mushroom Haddowia longipes. Their structures were elucidated as 11-oxo-ganoderiol D, lanosta-8-en-7,11-dioxo-3β-acetyloxy-24,25,26-trihydroxy, lanosta-8-en-7-oxo-3β-acetyloxy-11β,24,25,26-tetrahydroxy, lanosta-7,9(11)-dien-3β-acetyloxy-24,25,26-trihydroxy, lanosta-7,9(11)-dien-3β-acetyloxy-24,26-dihydroxy-25-methoxy, 11-oxo-lucidadiol, 11β-hydroxy-lucidadiol, lucidone H and lanosta-7,9(11),24E-trien-3β-acetyloxy-26,27-dihydroxy by analysing their 1D/2D NMR and MS spectra. In addition, bioassays of inhibitory activity against acetylcholinesterase (AChE) of all compounds showed that thirteen compounds possessed inhibitory activity against AChE with the percentage inhibition ranging from 10.3% to 42.1% when tested at 100 μM. 7. In vivo and in vitro studies of glycine- and glutamate-evoked acetylcholinesterase release from spinal motor neurones: implications for amyotrophic lateral sclerosis/motor neurone disease pathogenesis. PubMed Rodríguez-Ithurralde, D; Olivera, S; Vincent, O; Maruri, A 1997-10-01 To investigate the spinal cellular structures and molecular mechanisms involved in acetylcholinesterase (AChE) release evoked by both glycine (GLY) and glutamate (GLU)--responses that might play a role in chronic neurotoxicity--we analysed AChE histochemistry and histology upon systemic administration of aspartate (ASP), and conducted in vitro experiments in synaptosomes and slices prepared from mouse spinal ventral horns. Upon superfusion and incubation exposure of these preparations to GLY- and GLU-receptor agonists, we assayed both tissue content and release of AChE, butyrylcholinesterase and lactic dehydrogenase. Histochemical reduction of motor neurone (MN) AChE, calcium dependency, decreases in intracellular AChE and the ratio amongst molecular forms released, suggest that both synaptosomal GLY-evoked AChE release (GLY-EAR) and GLU-receptor-elicited AChE release (GEAR) have release sites located at MN presynaptic terminals. These responses exhibited remarkable postnatal regulation. GEAR seems to be mediated through alpha-amino-3-hydroxy-5-methylisoxazole-4-propionic acid/kainate receptors after the fourth postnatal week and through both NMDA and non-NMDA receptors at earlier stages. Sustained rises of extracellular AChE might link acute excitotoxic injury with several long-lasting pathways leading to chronic neurotoxicity, since AChE molecular properties include: (1) the ability to block cholinergic mechanisms that protect MN against overactivity; (2) activation of ATP-dependent potassium channels; (3) promotion of neurite and axon outgrowth; and possibly (4) stimulation of brain macrophage migration and activation. 8. COOH-terminal collagen Q (COLQ) mutants causing human deficiency of endplate acetylcholinesterase impair the interaction of ColQ with proteins of the basal lamina. PubMed Arredondo, Juan; Lara, Marian; Ng, Fiona; Gochez, Danielle A; Lee, Diana C; Logia, Stephanie P; Nguyen, Joanna; Maselli, Ricardo A 2014-05-01 Collagen Q (ColQ) is a key multidomain functional protein of the neuromuscular junction (NMJ), crucial for anchoring acetylcholinesterase (AChE) to the basal lamina (BL) and accumulating AChE at the NMJ. The attachment of AChE to the BL is primarily accomplished by the binding of the ColQ collagen domain to the heparan sulfate proteoglycan perlecan and the COOH-terminus to the muscle-specific receptor tyrosine kinase (MuSK), which in turn plays a fundamental role in the development and maintenance of the NMJ. Yet, the precise mechanism by which ColQ anchors AChE at the NMJ remains unknown. We identified five novel mutations at the COOH-terminus of ColQ in seven patients from five families affected with endplate (EP) AChE deficiency. We found that the mutations do not affect the assembly of ColQ with AChE to form asymmetric forms of AChE or impair the interaction of ColQ with perlecan. By contrast, all mutations impair in varied degree the interaction of ColQ with MuSK as well as basement membrane extract (BME) that have no detectable MuSK. Our data confirm that the interaction of ColQ to perlecan and MuSK is crucial for anchoring AChE to the NMJ. In addition, the identified COOH-terminal mutants not only reduce the interaction of ColQ with MuSK, but also diminish the interaction of ColQ with BME. These findings suggest that the impaired attachment of COOH-terminal mutants causing EP AChE deficiency is in part independent of MuSK, and that the COOH-terminus of ColQ may interact with other proteins at the BL. 9. Age-dependent modulation of fasting and long-term dietary restriction on acetylcholinesterase in non-neuronal tissues of mice. PubMed Suchiang, Kitlangki; Sharma, Ramesh 2016-08-01 Dietary restriction (DR) without malnutrition is a robust intervention that extends lifespan and slows the onset of nervous system deficit and age-related diseases in diverse organisms. Acetylcholinesterase (AChE), a thoroughly studied enzyme better known for hydrolyzing acetylcholine (ACh) in neuronal tissues, has recently been linked with multiple unrelated biological functions in different non-neuronal tissues. In the present study, the activity and protein expression level of AChE in liver, heart, and kidney of young (1 month), adult (6 month), and aged (18 month) mice were investigated. We also studied age- and tissue-specific changes in AChE activity and protein expression level after the mice were subjected to 24-h fasting and long-term DR. Our results showed that AChE activity and protein expression in kidney and heart of aged mice decreased significantly in comparison with young mice. On the contrary, long-term DR decreases the AChE activity and the protein expression level in all tissues irrespective of ages studied. We summarized that changes in AChE with age in different tissues studied reflects its different roles at different phases of an organism's life. Conversely, the cumulative modulation manifested in the form of lowering AChE by long-term DR may prevent the futile synthesis and accumulation of unwanted AChE besides the added compensatory benefit of enhanced ACh availability needed during the period of starvation. This, in turn, may help in preventing the declining homeostatic roles of this important neurotransmitter in different tissues. 10. Phe362Tyr in AChE: A Major Factor Responsible for Azamethiphos Resistance in Lepeophtheirus salmonis in Norway PubMed Central Kaur, Kiranpreet; Jansen, Peder Andreas; Aspehaug, Vidar Teis; Horsberg, Tor Einar 2016-01-01 Organophosphates (OP) are one of the major treatments used against the salmon louse (Lepeophtherius salmonis) in Norwegian salmonid aquaculture. The use of OP since the late 1970s has resulted in widespread resistant parasites. Recently, we reported a single mutation (Phe362Tyr) in acetylcholinesterase (AChE) as the major mechanism behind resistance in salmon louse towards OP. The present study was carried out to validate this mechanism at the field level. A total of 6658 salmon louse samples were enrolled from 56 different fish farms across the Norwegian coast, from Vest Agder in the south to Finnmark in the north. All the samples were genotyped using a TaqMan probe assay for the Phe362Tyr mutation. A strong association was observed between areas with frequent use of the OP (azamethiphos) and the Phe362Tyr mutation. This was confirmed at 15 sites where results from independently conducted bioassays and genotyping of parasites correlated well. Furthermore, genotyping of surviving and moribund parasites from six bioassay experiments demonstrated a highly significant negative correlation between the frequency of resistance alleles and the probability of dying when exposed to azamethiphos in a bioassay. Based on these observations, we could strongly conclude that the Phe362Tyr mutation is a major factor responsible for OP resistance in salmon louse on Norwegian fish farms. PMID:26882536 11. Phe362Tyr in AChE: A Major Factor Responsible for Azamethiphos Resistance in Lepeophtheirus salmonis in Norway. PubMed Kaur, Kiranpreet; Jansen, Peder Andreas; Aspehaug, Vidar Teis; Horsberg, Tor Einar 2016-01-01 Organophosphates (OP) are one of the major treatments used against the salmon louse (Lepeophtherius salmonis) in Norwegian salmonid aquaculture. The use of OP since the late 1970s has resulted in widespread resistant parasites. Recently, we reported a single mutation (Phe362Tyr) in acetylcholinesterase (AChE) as the major mechanism behind resistance in salmon louse towards OP. The present study was carried out to validate this mechanism at the field level. A total of 6658 salmon louse samples were enrolled from 56 different fish farms across the Norwegian coast, from Vest Agder in the south to Finnmark in the north. All the samples were genotyped using a TaqMan probe assay for the Phe362Tyr mutation. A strong association was observed between areas with frequent use of the OP (azamethiphos) and the Phe362Tyr mutation. This was confirmed at 15 sites where results from independently conducted bioassays and genotyping of parasites correlated well. Furthermore, genotyping of surviving and moribund parasites from six bioassay experiments demonstrated a highly significant negative correlation between the frequency of resistance alleles and the probability of dying when exposed to azamethiphos in a bioassay. Based on these observations, we could strongly conclude that the Phe362Tyr mutation is a major factor responsible for OP resistance in salmon louse on Norwegian fish farms. PMID:26882536 12. A 1-methyl-4-piperidinyl cytectrene carboxylate labeled by the technetium 99m, a radiotracer for rat brain acetylcholinesterase activity. PubMed Mejri, Najoua; Barhoumi, Chokri; Trabelsi, Moez; Mekni, Abdelkader; Said, Nadia Malek; Saidi, Mouldi 2010-02-01 Alzheimer's disease (AD) is a degenerative neurological disorder that causes progressive and irreversible loss of connections between brain cells and loss of mental functions. Clinical and postmortem studies show that the biochemical changes in brains of AD patients include decrease in acetylcholinesterase (AChE) activity. Our aim was to study AChE activity using piperidinyl ester labelled with technetium-99m. In vivo and in vitro studies demonstrated that labelled piperidinyl ester was a substrate for AChE. The hydrolytic rate of this substrate was measured and the specificity was evaluated using the inhibitor BW284c51. The rhenium analogues of the technetium-labelled substrate were used to determine the affinity constant (K(m)) and the maximum reaction velocity (V(max)) because of the high specific activity of technetium. The high hydrolytic rate and high specificity of the substrate for AChE make it suitable as an in vivo radiotracer for studying AChE activity in the brain. 13. Designing Second Generation Anti-Alzheimer Compounds as Inhibitors of Human Acetylcholinesterase: Computational Screening of Synthetic Molecules and Dietary Phytochemicals PubMed Central Amat-ur-Rasool, Hafsa; Ahmed, Mehboob 2015-01-01 14. Designing Second Generation Anti-Alzheimer Compounds as Inhibitors of Human Acetylcholinesterase: Computational Screening of Synthetic Molecules and Dietary Phytochemicals. PubMed Amat-Ur-Rasool, Hafsa; Ahmed, Mehboob 2015-01-01 15. Preparation and performance of a colorimetric biosensor using acetylcholinesterase and indoxylacetate for assay of nerve agents and drugs PubMed Central Vlcek, Vitezslav 2014-01-01 Different toxic compounds can target the cholinergic nervous system. Acetylcholinesterase (AChE; EC 3.1.1.7) is one of the most crucial components of the cholinergic nervous system and thus many of the toxins interact with this enzyme. As to inhibitors, nerve agents used as chemical warfare, some insecticides, and drugs influencing the cholinergic system are common examples of AChE inhibitors. Once inhibited by a neurotoxic compound, a serious cholinergic crisis can occur. On the other hand, sensitivity of AChE to the inhibition can be used for analytical purposes. In this study, a simple disposable biosensor with AChE as a recognition element was devised. AChE was immobilized onto a cellulose matrix and indoxylacetate was used as a chromogenic substrate. The enzyme reaction was assessed by the naked eye using arbitrary units and pyridostigmine, tacrine, paraoxon, carbofuran, soman and VX were assayed as selected inhibitors. A good stability of the biosensors was found, with no aging over a quarter of a year and minimal sensitivity to the interference of organic solvents. The limit of detection ranged from 10 to 100 nmol/L for the compounds tested with a sample volume of 40 µL. PMID:26109903 16. The effect of glyphosate, its metabolites and impurities on erythrocyte acetylcholinesterase activity. PubMed Kwiatkowska, Marta; Nowacka-Krukowska, Hanna; Bukowska, Bożena 2014-05-01 Glyphosate [N-(phosphonomethyl)glycine] is used all over the world to protect agricultural and horticultural crops. According to initial reports, glyphosate has been considered to be safe for humans and animals; nevertheless, recent investigations had proven its toxicity. Extensive use of glyphosate and the conviction of its low toxicity leads to a situation in which it is used in excessive amounts in agriculture. That is why, we have investigated the effect of the most commonly used pesticide: glyphosate, its metabolites and impurities on acetylcholinesterase (AChE) activity (in vitro) in human erythrocytes, which is biochemically similar to acetylcholinesterase present in neural synapses. The analysis of noxious effects of metabolites and impurities of pesticides seems to be very important to evaluate toxicological risk that is associated with the effect of pesticide formulations (requirement of the EU regulations 1107/200/EC). The erythrocytes were incubated with xenobiotics at concentrations range from 0.01 to 5 mM for 1 and 4 h. Statistically significant decrease in AChE activity (about 20%) was observed only at high concentrations of the compounds (0.25-5 mM), which enter body only as a result of acute poisoning. There were no statistically significant differences in the effect of the investigated compounds, while the changes caused by them were similar after 1 and 4 h incubation. The investigated metabolites and impurities did not cause stronger changes in AChE activity than glyphosate itself. It may be concluded that the compounds studied (used in the concentrations that are usually determined in the environment) do not disturb function of human erythrocyte acetylcholinesterase. PMID:24780534 17. Screening the methanol extracts of some Iranian plants for acetylcholinesterase inhibitory activity PubMed Central Gholamhoseinian, A.; Moradi, M.N.; Sharifi-far, F. 2009-01-01 Acetylcholinesterase (AChE) is the main enzyme for the breakdown of acetylcholine. Nowadays, usage of the inhibitors of this enzyme is one of the most important types of treatment of mild to moderate neurodegenerative diseases such as Alzheimer’s disease. Herbal medicines can be a new source of inhibitors of this enzyme. In this study we examined around 100 different plants to evaluate their inhibitory properties for AChE enzyme. Plants were scientifically identified and their extracts were prepared by methanol percolation. Acetylcholinesterase activity was measured using a colorimetric method in the presence or absence of the extracts. Eserine was used as a positive control. Methanol extracts of the Levisticum officinale, Bergeris integrima and Rheum ribes showed more than 50% AChE inhibitory activity. The inhibition kinetics were studied in the presence of the most effective extracts. L. officinale and B. integrima inhibited AChE activity in a non-competitive manner, while R. ribes competitively inhibitied the enzyme as revealed by double-reciprocal Linweaver-Burk plot analysis. Under controlled condition, Km and Vmax values of the enzyme were found to be 9.4 mM and 0.238 mM/min, respectively. However, in the presence of L. officinale, B. integrima, and R. ribes extracts, Vmax values were 0.192, 0.074 and 0.238 mM/min, respectively. Due to the competitive inhibition of the enzyme by R. ribes extract, the Km value of 21.2 mM was obtained. The concentration required for 50% enzyme inhibition (IC50 value) was 0.5, 0.9, and 0.95 mg/ml for the L. officinale, B. integrima and R. ribes extracts, respectively. The IC50 of the eserine was determined to be 0.8 mg/ml. PMID:21589805 18. Acetylcholine as a signaling system to environmental stimuli in plants. III. Asymmetric solute distribution controlled by ACh in gravistimulated maize seedlings. PubMed Momonoki, Y S; Hineno, C; Noguchi, K 1998-01-01 Asymmetric distribution of acetylcholinesterase (AChE) activity has previously been demonstrated to occur in the lower side of the gravity-stimulated maize shoot. The localization of immunoreacted IAA-inositol synthase, AChE and safranin was detected in selected organs of gravistimulated dark grown maize seedlings using a light microscope. Immunoreacted IAA-inositol synthase was asymmetrically distributed in the lower side of the stele of coleoptile node and mesocotyl in maize seedlings placed horizontally. The positive AChE spots in the coleoptile node and mesocotyl were apparently localized in the lower half of the gravistimulated seedlings. Safranin was also asymmetrically distributed in the lower half of the endodermis and stele cells of coleoptile node and mesocotyl. Namely, transport of safranin in the upper half of the coleoptile node and mesocotyl was blocked by gravistimulation. Furthermore, the asymmetric distribution of immunoreacted IAA-inositol synthase was inhibited by neostigmine bromide, AChE inhibitor. These results show that an asymmetric environmental stimulus induces changes in AChE activity, affecting IAA-inositol synthase localization and safranin transport. PMID:12162322 19. The discovery of potential acetylcholinesterase inhibitors: A combination of pharmacophore modeling, virtual screening, and molecular docking studies PubMed Central 2011-01-01 Background Alzheimer's disease (AD) is the most common cause of dementia characterized by progressive cognitive impairment in the elderly people. The most dramatic abnormalities are those of the cholinergic system. Acetylcholinesterase (AChE) plays a key role in the regulation of the cholinergic system, and hence, inhibition of AChE has emerged as one of the most promising strategies for the treatment of AD. Methods In this study, we suggest a workflow for the identification and prioritization of potential compounds targeted against AChE. In order to elucidate the essential structural features for AChE, three-dimensional pharmacophore models were constructed using Discovery Studio 2.5.5 (DS 2.5.5) program based on a set of known AChE inhibitors. Results The best five-features pharmacophore model, which includes one hydrogen bond donor and four hydrophobic features, was generated from a training set of 62 compounds that yielded a correlation coefficient of R = 0.851 and a high prediction of fit values for a set of 26 test molecules with a correlation of R2 = 0.830. Our pharmacophore model also has a high Güner-Henry score and enrichment factor. Virtual screening performed on the NCI database obtained new inhibitors which have the potential to inhibit AChE and to protect neurons from Aβ toxicity. The hit compounds were subsequently subjected to molecular docking and evaluated by consensus scoring function, which resulted in 9 compounds with high pharmacophore fit values and predicted biological activity scores. These compounds showed interactions with important residues at the active site. Conclusions The information gained from this study may assist in the discovery of potential AChE inhibitors that are highly selective for its dual binding sites. PMID:21251245 20. GC-MS investigation and acetylcholinesterase inhibitory activity of Galanthus rizehensis. PubMed Sarikaya, Buket Bozkurt; Somer, Nehir Unver; Kaya, Gulen Irem; Onur, Mustafa Ali; Bastida, Jaume; Berkov, Strahil 2013-01-01 GC-MS (gas chromatography-mass spectrometry) analyses of alkaloids in the aerial parts and bulbs of Galanthus rizehensis Stern (Amaryllidaceae), collected during two different vegetation periods, was performed. Twenty three alkaloids were identified in four different alkaloid extracts. Acetylcholinesterase (AChE) inhibitory activities of the alkaloid extracts were tested. Both the highest alkaloid diversity and the most potent inhibitory activity (IC50 12.94 microg/ml) were obtained in extracts from the bulbs of G. rizehensis collected during the fruiting period. 1. Acetylcholinesterase inhibitory dimeric indole derivatives from the marine actinomycetes Rubrobacter radiotolerans. PubMed Li, Jian Lin; Huang, Lei; Liu, Juan; Song, Yan; Gao, Jie; Jung, Jee H; Liu, Yonghong; Chen, Guangtong 2015-04-01 Investigation of the bioactive secondary metabolites of the marine actinomycetes Rubrobacter radiotolerans led to the isolation and characterization of two naturally rare dimeric indole derivatives (1 and 2). The structures of these new compounds were elucidated by spectroscopic data interpretation, and the absolute configurations were assigned by CD calculations. The acetylcholinesterase (AchE) inhibitory activity of compounds 1 and 2 was evaluated, both of which showed moderate activity with IC50 values of 11.8 and 13.5μM, respectively. 2. An expedient synthesis, acetylcholinesterase inhibitory activity, and molecular modeling study of highly functionalized hexahydro-1,6-naphthyridines. PubMed Almansour, Abdulrahman I; Kumar, Raju Suresh; Arumugam, Natarajan; Basiri, Alireza; Kia, Yalda; Ali, Mohamed Ashraf 2015-01-01 A series of hexahydro-1,6-naphthyridines were synthesized in good yields by the reaction of 3,5-bis[(E)-arylmethylidene]tetrahydro-4(1H)-pyridinones with cyanoacetamide in the presence of sodium ethoxide under simple mixing at ambient temperature for 6-10 minutes and were assayed for their acetylcholinesterase (AChE) inhibitory activity using colorimetric Ellman's method. Compound 4e with methoxy substituent at ortho-position of the phenyl rings displayed the maximum inhibitory activity with IC50 value of 2.12 μM. Molecular modeling simulation of 4e was performed using three-dimensional structure of Torpedo californica AChE (TcAChE) enzyme to disclose binding interaction and orientation of this molecule into the active site gorge of the receptor. PMID:25710037 3. An Expedient Synthesis, Acetylcholinesterase Inhibitory Activity, and Molecular Modeling Study of Highly Functionalized Hexahydro-1,6-naphthyridines PubMed Central Almansour, Abdulrahman I.; Suresh Kumar, Raju; Arumugam, Natarajan; Basiri, Alireza; Kia, Yalda; Ashraf Ali, Mohamed 2015-01-01 A series of hexahydro-1,6-naphthyridines were synthesized in good yields by the reaction of 3,5-bis[(E)-arylmethylidene]tetrahydro-4(1H)-pyridinones with cyanoacetamide in the presence of sodium ethoxide under simple mixing at ambient temperature for 6–10 minutes and were assayed for their acetylcholinesterase (AChE) inhibitory activity using colorimetric Ellman's method. Compound 4e with methoxy substituent at ortho-position of the phenyl rings displayed the maximum inhibitory activity with IC50 value of 2.12 μM. Molecular modeling simulation of 4e was performed using three-dimensional structure of Torpedo californica AChE (TcAChE) enzyme to disclose binding interaction and orientation of this molecule into the active site gorge of the receptor. PMID:25710037 4. Probing the origins of human acetylcholinesterase inhibition via QSAR modeling and molecular docking. PubMed Simeon, Saw; Anuwongcharoen, Nuttapat; Shoombuatong, Watshara; Malik, Aijaz Ahmad; Prachayasittikul, Virapong; Wikberg, Jarl E S; Nantasenamat, Chanin 2016-01-01 Alzheimer's disease (AD) is a chronic neurodegenerative disease which leads to the gradual loss of neuronal cells. Several hypotheses for AD exists (e.g., cholinergic, amyloid, tau hypotheses, etc.). As per the cholinergic hypothesis, the deficiency of choline is responsible for AD; therefore, the inhibition of AChE is a lucrative therapeutic strategy for the treatment of AD. Acetylcholinesterase (AChE) is an enzyme that catalyzes the breakdown of the neurotransmitter acetylcholine that is essential for cognition and memory. A large non-redundant data set of 2,570 compounds with reported IC50 values against AChE was obtained from ChEMBL and employed in quantitative structure-activity relationship (QSAR) study so as to gain insights on their origin of bioactivity. AChE inhibitors were described by a set of 12 fingerprint descriptors and predictive models were constructed from 100 different data splits using random forest. Generated models afforded R (2), [Formula: see text] and [Formula: see text] values in ranges of 0.66-0.93, 0.55-0.79 and 0.56-0.81 for the training set, 10-fold cross-validated set and external set, respectively. The best model built using the substructure count was selected according to the OECD guidelines and it afforded R (2), [Formula: see text] and [Formula: see text] values of 0.92 ± 0.01, 0.78 ± 0.06 and 0.78 ± 0.05, respectively. Furthermore, Y-scrambling was applied to evaluate the possibility of chance correlation of the predictive model. Subsequently, a thorough analysis of the substructure fingerprint count was conducted to provide informative insights on the inhibitory activity of AChE inhibitors. Moreover, Kennard-Stone sampling of the actives were applied to select 30 diverse compounds for further molecular docking studies in order to gain structural insights on the origin of AChE inhibition. Site-moiety mapping of compounds from the diversity set revealed three binding anchors encompassing both hydrogen bonding and van der Waals 5. The interactions of azure B, a metabolite of methylene blue, with acetylcholinesterase and butyrylcholinesterase SciTech Connect Petzer, Anél; Harvey, Brian H.; Petzer, Jacobus P. 2014-02-01 Methylene blue (MB) is reported to possess diverse pharmacological actions and is attracting increasing attention for the treatment of neurodegenerative disorders such as Alzheimer's disease. Among the pharmacological actions of MB, is the significant inhibition of acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE). These activities may, at least in part, underlie MB's beneficial effects in Alzheimer's disease. MB is metabolized to yield N-demethylated products of which azure B, the monodemethyl metabolite, is the predominant species. Azure B has been shown to be pharmacologically active and also possesses a variety of biological actions. Azure B therefore may contribute to the pharmacological profile of MB. Based on these considerations, the present study investigates the possibility that azure B may, similar to MB, act as an inhibitor of human AChE and BuChE. The results document that azure B inhibits AChE and BuChE with IC{sub 50} values of 0.486 μM and 1.99 μM, respectively. The results further show that azure B inhibits AChE and BuChE reversibly, and that the modes of inhibition are most likely competitive. Although the AChE and BuChE inhibitory activities of azure B are twofold and fivefold, respectively, less potent than those recorded for MB [IC{sub 50}(AChE) = 0.214 μM; IC{sub 50}(BuChE) = 0.389 μM] under identical conditions, azure B may be a contributor to MB's in vivo activation of the cholinergic system and beneficial effects in Alzheimer's disease. - Highlights: • Methylene blue (MB) is a known inhibitor of AChE and BuChE. • Azure B, the major metabolite of MB, also is an inhibitor of AChE and BuChE. • Azure B may be a contributor to MB's in vivo activation of the cholinergic system. • Azure B may contribute to MB's potential in Alzheimer's disease therapy. 6. Probing the origins of human acetylcholinesterase inhibition via QSAR modeling and molecular docking. PubMed Simeon, Saw; Anuwongcharoen, Nuttapat; Shoombuatong, Watshara; Malik, Aijaz Ahmad; Prachayasittikul, Virapong; Wikberg, Jarl E S; Nantasenamat, Chanin 2016-01-01 Alzheimer's disease (AD) is a chronic neurodegenerative disease which leads to the gradual loss of neuronal cells. Several hypotheses for AD exists (e.g., cholinergic, amyloid, tau hypotheses, etc.). As per the cholinergic hypothesis, the deficiency of choline is responsible for AD; therefore, the inhibition of AChE is a lucrative therapeutic strategy for the treatment of AD. Acetylcholinesterase (AChE) is an enzyme that catalyzes the breakdown of the neurotransmitter acetylcholine that is essential for cognition and memory. A large non-redundant data set of 2,570 compounds with reported IC50 values against AChE was obtained from ChEMBL and employed in quantitative structure-activity relationship (QSAR) study so as to gain insights on their origin of bioactivity. AChE inhibitors were described by a set of 12 fingerprint descriptors and predictive models were constructed from 100 different data splits using random forest. Generated models afforded R (2), [Formula: see text] and [Formula: see text] values in ranges of 0.66-0.93, 0.55-0.79 and 0.56-0.81 for the training set, 10-fold cross-validated set and external set, respectively. The best model built using the substructure count was selected according to the OECD guidelines and it afforded R (2), [Formula: see text] and [Formula: see text] values of 0.92 ± 0.01, 0.78 ± 0.06 and 0.78 ± 0.05, respectively. Furthermore, Y-scrambling was applied to evaluate the possibility of chance correlation of the predictive model. Subsequently, a thorough analysis of the substructure fingerprint count was conducted to provide informative insights on the inhibitory activity of AChE inhibitors. Moreover, Kennard-Stone sampling of the actives were applied to select 30 diverse compounds for further molecular docking studies in order to gain structural insights on the origin of AChE inhibition. Site-moiety mapping of compounds from the diversity set revealed three binding anchors encompassing both hydrogen bonding and van der Waals 7. Distribution of Intravenously Administered Acetylcholinesterase Inhibitor and Acetylcholinesterase Activity in the Adrenal Gland: 11C-Donepezil PET Study in the Normal Rat PubMed Central Watabe, Tadashi; Naka, Sadahiro; Ikeda, Hayato; Horitsugi, Genki; Kanai, Yasukazu; Isohashi, Kayako; Ishibashi, Mana; Kato, Hiroki; Shimosegawa, Eku; Watabe, Hiroshi; Hatazawa, Jun 2014-01-01 Purpose Acetylcholinesterase (AChE) inhibitors have been used for patients with Alzheimer's disease. However, its pharmacokinetics in non-target organs other than the brain has not been clarified yet. The purpose of this study was to evaluate the relationship between the whole-body distribution of intravenously administered 11C-Donepezil (DNP) and the AChE activity in the normal rat, with special focus on the adrenal glands. Methods The distribution of 11C-DNP was investigated by PET/CT in 6 normal male Wistar rats (8 weeks old, body weight = 220±8.9 g). A 30-min dynamic scan was started simultaneously with an intravenous bolus injection of 11C-DNP (45.0±10.7 MBq). The whole-body distribution of the 11C-DNP PET was evaluated based on the Vt (total distribution volume) by Logan-plot analysis. A fluorometric assay was performed to quantify the AChE activity in homogenized tissue solutions of the major organs. Results The PET analysis using Vt showed that the adrenal glands had the 2nd highest level of 11C-DNP in the body (following the liver) (13.33±1.08 and 19.43±1.29 ml/cm3, respectively), indicating that the distribution of 11C-DNP was the highest in the adrenal glands, except for that in the excretory organs. The AChE activity was the third highest in the adrenal glands (following the small intestine and the stomach) (24.9±1.6, 83.1±3.0, and 38.5±8.1 mU/mg, respectively), indicating high activity of AChE in the adrenal glands. Conclusions We demonstrated the whole-body distribution of 11C-DNP by PET and the AChE activity in the major organs by fluorometric assay in the normal rat. High accumulation of 11C-DNP was observed in the adrenal glands, which suggested the risk of enhanced cholinergic synaptic transmission by the use of AChE inhibitors. PMID:25225806 8. The stabilization of Au NP-AChE nanocomposites by biosilica encapsulation for the development of a thiocholine biosensor. PubMed Buiculescu, Raluca; Chaniotakis, Nikos A 2012-08-01 We report on the construction of an amperometric biosensor based on the immobilization of the enzyme acetylcholinesterase (AChE) onto gold nanoparticles (Au NPs). The active enzyme is covalently bound directly onto the surface of the Au NPs via a thiol bond. This immobilization provides increased stability and high electron-transfer between the colloidal Au NPs, the catalyst and the transducer surface. To further increase the biosensor stability by protecting the enzyme from denaturation and protease attack, a layer of biosilica was grown around the Au NP enzyme nanocomposite. All steps, i.e., the conjugation of the enzyme to the gold nanoparticles and the encapsulation into biosilica, are monitored and confirmed by ATR-FT-IR spectroscopy. The stabilizing effect of the entrapment was evaluated amperometrically, while the operation of the biosensor was monitored over a period of 4 months. The initial sensitivity of the biosensor was calculated to be 27.58 nA mM(-1) with a linear response to the concentration of the substrate in the range from 0.04 to 0.4 mM. It is thus shown that the biosilica nanocomposites doped with Au NPs-AChE conjugates create a system that provides both signal mediation and significant enzyme stabilization over the existing AChE biosensor. The biosensor had retained all its activity at the end of the 4 months, compared with the normal AChE biosensor whose activity reached 50% after only 42 days of operation. 9. Acetylcholinesterase activity in the host-parasite system of the cod Gadus morhua and acanthocephalan Echinorhynchus gadi from the southern Baltic Sea. PubMed Podolska, M; Nadolna, K; Szostakowska, B 2014-02-15 Acetylcholinesterase (AChE) activity measurement is widely used as a specific biomarker of neurotoxic effects. The aim of this study was to evaluate AChE activity in a host fish (the cod) and its acanthocephalan parasite Echinorhynchus gadi from the southern Baltic. AChE activity in hosts and parasites was inversely related: the highest cod AChE activity corresponded to the lowest E. gadi enzymatic activity and vice versa ("mirror effect"). This is the first report on the simultaneous application of this biomarker in cod and its acanthocephalan parasites. Results obtained for the host-parasite system are complementary and provide comprehensive information about the response of this biomarker. Analysis of the system allows for detection of a greater number of factors influencing AChE activity in the marine environment than separate analysis of the host and parasites. Thus, AChE activity measurement in a host-parasite system may be considered to be a promising tool for biomonitoring. PMID:24393378 10. Comparison of inhibition kinetics of several organophosphates, including some nerve agent surrogates, using human erythrocyte and rat and mouse brain acetylcholinesterase. PubMed Coban, Alper; Carr, Russell L; Chambers, Howard W; Willeford, Kenneth O; Chambers, Janice E 2016-04-25 Because testing of nerve agents is limited to only authorized facilities, our laboratory developed several surrogates that resemble nerve agents because they phosphylate the acetylcholinesterase (AChE) with the same moiety as the actual nerve agents. The inhibition kinetic parameters were determined for AChE by surrogates of cyclosarin (NCMP), sarin (NIMP, PIMP and TIMP) and VX (NEMP and TEMP) and other organophosphorus compounds derived from insecticides. All compounds were tested with rat brain and a subset was tested with mouse brain and purified human erythrocyte AChE. Within the compounds tested on all AChE sources, chlorpyrifos-oxon had the highest molecular rate constant followed by NCMP and NEMP. This was followed by NIMP then paraoxon and DFP with rat and mouse brain AChE but DFP was a more potent inhibitor than NIMP and paraoxon with human AChE. With the additional compounds tested only in rat brain, TEMP was slightly less potent than NEMP but more potent than PIMP which was more potent than NIMP. Methyl paraoxon was slightly less potent than paraoxon but more potent than TIMP which was more potent than DFP. Overall, this study validates that the pattern of inhibitory potencies of our surrogates is comparable to the pattern of inhibitory potencies of actual nerve agents (i.e., cyclosarin>VX>sarin), and that these are more potent than insecticidal organophosphates. 11. Insect-specific irreversible inhibitors of acetylcholinesterase in pests including the bed bug, the eastern yellowjacket, German and American cockroaches, and the confused flour beetle. PubMed Polsinelli, Gregory A; Singh, Sanjay K; Mishra, Rajesh K; Suranyi, Robert; Ragsdale, David W; Pang, Yuan-Ping; Brimijoin, Stephen 2010-09-01 Insecticides directed against acetylcholinesterase (AChE) are facing increased resistance among target species as well as increasing concerns for human toxicity. The result has been a resurgence of disease vectors, insects destructive to agriculture, and residential pests. We previously reported a free cysteine (Cys) residue at the entrance to the AChE active site in some insects but not higher vertebrates. We also reported Cys-targeting methanethiosulfonate molecules (AMTSn), which, under conditions that spared human AChE, caused total irreversible inhibition of aphid AChE, 95% inhibition of AChE from the malaria vector mosquito (Anopheles gambia), and >80% inhibition of activity from the yellow fever mosquito (Aedes aegypti) and northern house mosquito (Culex pipiens). We now find the same compounds inhibit AChE from cockroaches (Blattella germanica and Periplaneta americana), the flour beetle (Tribolium confusum), the multi-colored Asian ladybird beetle (Harmonia axyridis), the bed bug (Cimex lectularius), and a wasp (Vespula maculifrons), with IC(50) values of approximately 1-11muM. Our results support further study of Cys-targeting inhibitors as conceptually novel insecticides that may be free of resistance in a range of insect pests and disease vectors and, compared with current compounds, should demonstrate much lower toxicity to mammals, birds, and fish. PMID:20109441 12. Isolation, diversity and acetylcholinesterase inhibitory activity of the culturable endophytic fungi harboured in Huperzia serrata from Jinggang Mountain, China. PubMed Wang, Ya; Lai, Zheng; Li, Xi-Xi; Yan, Ri-Ming; Zhang, Zhi-Bin; Yang, Hui-Lin; Zhu, Du 2016-02-01 Huperzia serrata has many important medicinal properties with proven pharmacological potential. Some of these properties may be mediated by its endophytic fungi. To test this hypothesis, in the present study, we provided a first insights into evaluating the species composition and acetylcholinesterase (AChE) inhibitory activity of the culturable endophytic fungi of H. serrata from the regional at Jinggang Mountain in southeastern China. A total number of 885 fungal isolates distributed across 44 genera and 118 putative species were obtained from 1422 fragments of fine H. serrata roots, stems and leaves base on ITS-rDNA sequences BLAST analysis. The endophytic fungi were phylogenetically diverse and species-rich, with high rate of colonization and isolation. The assemble of endophytic fungi consisted mainly of Ascomycota (97.15%), followed by Basidiomycota (1.92%) and unknown fungal species (0.90%). Colletotrichum (64.29%), Phyllosticta (3.39%), Hypoxylon (2.81%), Xylaria (2.25%) and Nigrospora (2.04%) were the most abundant genera, whereas the remaining genera were infrequent groups. Although, roots yielded low abundance strains, the diverse and species-rich were both higher than that of stems and leaves. In addition, out of the 247 endophytic fungi strains determinated, 221 fungal extracts showed AChE inhibition activities in vitro. Among them, 22 endophytic fungi strains achieved high inhibitory activity (≥50%) on AChE which belongs to 13 genera and five incertae sedis strains. Four endophytic fungi designated as JS4 (Colletotrichum spp.), FL14 (Ascomycota spp.), FL9 (Sarcosomataceae spp.) and FL7 (Dothideomycetes spp.) were displayed highly active (≥80%) against AChE, which the inhibition effects were even more intense than the positive control. Our findings highlight that H. serrata grown in Jinggang Mountain harbors a rich and fascinating endophytic fungus community with potential AChE inhibitory activity, which could further broaden the natural 13. Screen-printed electrode modified with carbon black and chitosan: a novel platform for acetylcholinesterase biosensor development. PubMed Talarico, Daria; Arduini, Fabiana; Amine, Aziz; Cacciotti, Ilaria; Moscone, Danila; Palleschi, Giuseppe 2016-10-01 We report a screen-printed electrode (SPE) modified with a dispersion of carbon black (CB) and chitosan by drop casting. A cyclic voltammetry technique towards ferricyanide, caffeic acid, hydroquinone, and thiocholine was performed and an improvement of the electrochemical response with respect to bare SPE as well as SPE modified only with chitosan was observed. The possibility to detect thiocholine at a low applied potential with high sensitivity was exploited and an acetylcholinesterase (AChE) biosensor was developed. A dispersion of CB, chitosan, and AChE was used to fabricate this biosensor in one step by drop casting. The enzymatic activity of the immobilized AChE was determined measuring the enzymatic product thiocholine at +300 mV. Owing to the capability of organophosphorus pesticides to inhibit AChE, this biosensor was used to detect these pollutants, and paraoxon was taken as model compound. The enzyme inhibition was linearly related to the concentration of paraoxon up to 0.5 μg L(-1), and a low detection limit equal to 0.05 μg L(-1) (calculated as 10% of inhibition) was achieved. This biosensor was challenged for paraoxon detection in drinking waters with satisfactory recovery values. The use of AChE embedded in a dispersion of CB and chitosan allowed an easy and fast production of a sensitive biosensor suitable for paraoxon detection in drinking waters at legal limit levels. Graphical Abstract Biosensors based on screen-printed electrodes modified with Acetylcholinesterase, Carbon Black, and Chitosan for organophosphorus pesticide detection. 14. Multiple Mutations on the Second Acetylcholinesterase Gene Associated With Dimethoate Resistance in the Melon Aphid, Aphis gossypii (Hemiptera: Aphididae). PubMed Lokeshwari, D; Krishna Kumar, N K; Manjunatha, H 2016-04-01 The melon aphid, Aphis gossypii Glover (Hemiptera: Aphididae), is an important cosmopolitan and extremely polyphagous species capable of causing direct and indirect damage to various crops. Insecticide resistance in melon aphids is of particular concern. To determine the basis of resistance, organophosphate (OP)-resistant strains of A. gossypii were obtained by continuous selection with dimethoate in the laboratory, and resistance mechanisms were investigated along with susceptible strains. Three resistant strains LKR-1, LKR-2, and LKR-3 exhibiting 270-, 243-, and 210-fold resistance obtained after 30 generations of selection with dimethoate, respectively, were utilized in this study. The role of acetylcholinesterase (AChE), a target enzyme for OPs and carbamates (CMs), was investigated. AChE enzyme assay revealed that there was no significant change in the activities of AChE in resistant and susceptible strains. However, AChE inhibitory assay showed that 50% of the enzyme activity in resistant strains was inhibited at significantly higher concentration of dimethoate (131.87, 158.65, and 99.29 µmolL(−1)) as compared with susceptible strains (1.75 and 2.01 µmolL(−1)), indicating AChE insensitivity owing to altered AChE. Molecular diagnostic tool polymerase chain reaction-restriction fragment length polymorphism revealed the existence of two consistent non-synonymous point mutations, single-nucleotide polymorphism, viz., A302S (equivalent to A201 in Torpedo californica Ayres) and S431F (equivalent to F331 in T. californica), in the AChE gene Ace2 of resistant strains. Further, cloning and sequencing of a partial fragment of Ace2 (897 bp) gene from susceptible and resistant strains revealed an additional novel mutation G221A in resistant strains, LKR-1 and LKR-2. Susceptible Ace2 genes shared 99.6 and 98.9% identity at the nucleic acid and amino acid levels with resistant ones, respectively. Functional analysis of these point mutations was assessed by in 15. Immobilization of Acetylcholinesterase on Screen-Printed Electrodes. Application to the Determination of Arsenic(III) PubMed Central Sanllorente-Méndez, Silvia; Domínguez-Renedo, Olga; Arcos-Martínez, M. Julia 2010-01-01 Enzymatic amperometric procedures for measuring arsenic, based on the inhibitive action of this metal on acetylcholinesterase enzyme activity, have been developed. Screen-printed carbon electrodes (SPCEs) were used with acetylcholinesterase covalently bonded directly to its surface. The amperometric response of acetylcholinesterase was affected by the presence of arsenic ions, which caused a decrease in the current intensity. The experimental optimum working conditions of pH, substrate concentration and potential applied, were established. Under these conditions, repeatability and reproducibility of biosensors were determined, reaching values below 4% in terms of relative standard deviation. The detection limit obtained for arsenic was 1.1 × 10−8 M for Ach/SPCE biosensor. Analysis of the possible effect of the presence of foreign ions in the solution was performed. The method was applied to determine levels of arsenic in spiked tap water samples. PMID:22294918 16. Cinnamomum loureirii Extract Inhibits Acetylcholinesterase Activity and Ameliorates Trimethyltin-Induced Cognitive Dysfunction in Mice. PubMed Kim, Cho Rong; Choi, Soo Jung; Kwon, Yoon Kyung; Kim, Jae Kyeom; Kim, Youn-Jung; Park, Gwi Gun; Shin, Dong-Hoon 2016-01-01 The pathogenesis of Alzheimer's disease (AD) has been linked to the deficiency of neurotransmitter acetylcholine (ACh) in the brain, and the main treatment strategy for improving AD symptoms is the inhibition of acetylcholinesterase (AChE) activity. In the present study, we aimed to identify potent AChE inhibitors from Cinnamomum loureirii extract via bioassay-guided fractionation. We demonstrated that the most potent AChE inhibitor present in the C. loureirii extract was 2,4-bis(1,1-dimethylethyl)phenol. To confirm the antiamnesic effects of the ethanol extract of C. loureirii, mice were intraperitoneally injected with the neurotoxin trimethyltin (2.5 mg/kg) to induce cognitive dysfunction, and performance in the Y-maze and passive avoidance tests was assessed. Treatment with C. loureirii extract significantly improved performance in both behavioral tests, suggesting that this extract may be neuroprotective and therefore beneficial in preventing or ameliorating the degenerative processes of AD, potentially by restoring cholinergic function. PMID:27374288 17. 6-Methyluracil Derivatives as Bifunctional Acetylcholinesterase Inhibitors for the Treatment of Alzheimer's Disease. PubMed Semenov, Vyacheslav E; Zueva, Irina V; Mukhamedyarov, Marat A; Lushchekina, Sofya V; Kharlamova, Alexandra D; Petukhova, Elena O; Mikhailov, Anatoly S; Podyachev, Sergey N; Saifina, Lilya F; Petrov, Konstantin A; Minnekhanova, Oksana A; Zobov, Vladimir V; Nikolsky, Evgeny E; Masson, Patrick; Reznik, Vladimir S 2015-11-01 Novel 6-methyluracil derivatives with ω-(substituted benzylethylamino)alkyl chains at the nitrogen atoms of the pyrimidine ring were designed and synthesized. The numbers of methylene groups in the alkyl chains were varied along with the electron-withdrawing substituents on the benzyl rings. The compounds are mixed-type reversible inhibitors of cholinesterases, and some of them show remarkable selectivity for human acetylcholinesterase (hAChE), with inhibitory potency in the nanomolar range, more than 10,000-fold higher than that for human butyrylcholinesterase (hBuChE). Molecular modeling studies indicate that these compounds are bifunctional AChE inhibitors, spanning the enzyme active site gorge and binding to its peripheral anionic site (PAS). In vivo experiments show that the 6-methyluracil derivatives are able to penetrate the blood-brain barrier (BBB), inhibiting brain-tissue AChE. The most potent AChE inhibitor, 3 d (1,3-bis[5-(o-nitrobenzylethylamino)pentyl]-6-methyluracil), was found to improve working memory in scopolamine and transgenic APP/PS1 murine models of Alzheimer's disease, and to significantly decrease the number and area of β-amyloid peptide plaques in the brain. PMID:26412714 18. Acetylcholinesterase Activity, Cohabitation with Floricultural Workers, and Blood Pressure in Ecuadorian Children PubMed Central Jacobs, David R.; Himes, John H.; Alexander, Bruce H. 2013-01-01 Background: Acetylcholinesterase (AChE) inhibitors are commonly used pesticides that can effect hemodynamic changes through increased cholinergic stimulation. Children of agricultural workers are likely to have paraoccupational exposures to pesticides, but the potential physiological impact of such exposures is unclear. Objectives: We investigated whether secondary pesticide exposures were associated with blood pressure and heart rate among children living in agricultural Ecuadorian communities. Methods: This cross-sectional study included 271 children 4–9 years of age [51% cohabited with one or more flower plantation workers (mean duration, 5.2 years)]. Erythrocyte AChE activity was measured using the EQM Test-mate system. Linear regression models were used to estimate associations of systolic blood pressure (SBP), diastolic blood pressure (DBP), and heart rate with AChE activity, living with flower workers, duration of cohabitation with a flower worker, number of flower workers in the child’s home, and number of practices that might increase children’s exposure to pesticides. Results: Mean (± SD) AChE activity was 3.14 ± 0.49 U/mL. A 1-U/mL decrease in AChE activity was associated with a 2.86-mmHg decrease in SBP (95% CI: –5.20, –0.53) and a 2.89-mmHg decrease in DBP (95% CI: –5.00, –0.78), after adjustment for potential confounders. Children living with flower workers had lower SBP (–1.72 mmHg; 95% CI: –3.53, 0.08) than other children, and practices that might increase exposure also were associated with lower SBP. No significant associations were found between exposures and heart rate. Conclusions: Our findings suggest that subclinical secondary exposures to pesticides may affect vascular reactivity in children. Additional research is needed to confirm these findings. PMID:23359481 19. Effect of Chlorpyrifos Ethyl on Acetylcholinesterase Activity in Climbing Perch (Anabas testudineus, Bloch, 1972). PubMed Tam, Nguyen Thanh; Berg, Håkan; Tuyen, Phan Thi Bich; Van Cong, Nguyen 2015-11-01 The high use of pesticides in intensive rice farming in the Mekong Delta constitutes a potential hazard to the environment and to people's health. Chlorpyrifos ethyl (CPF) is a commonly used organophosphate (OP) insecticide, but information about its potential negative impacts on the aquatic environment in the Mekong Delta is scarce. Both acute and subacute toxicity tests were performed in a static nonrenewable system to investigate the effects of CPF on brain acetylcholinesterase (AChE) activity in native climbing perch fingerlings (Anabas testudineus, Bloch, 1972). Environmental parameters, such as dissolved oxygen, water temperature, and pH, were similar to field conditions in the Mekong Delta. In a 96-h lethal concentration (LC50) test, fingerlings of climbing perch were randomly exposed to five levels of CPF ranging from 0.8 to 4.5 ppm. Five sublethal levels of CPF (1, 5, 10, 15, and 20 % of the 96-h LC50 value) were tested to assess the sensitivity and recovery of the brain AChE activity in climbing perch fingerlings exposed to CPF. The results showed that CPF were moderately toxic to climbing perch with a 96-h median LC50 of 1.73 ppm. CPF also caused long-term AChE inhibition with 70 % inhibition remaining after 96 h for the four highest test concentrations. The recovery of brain AChE activity in fish placed in CPF-free water was very slow, and after 7 days the brain AChE activity was still significant lower in fish from the four highest concentrations compared with the control. The results from this study indicate that OP insecticides, such as CPF, can have long-lasting sublethal effects on aquatic species in the Mekong Delta. PMID:26135300 20. The effect of aspartame metabolites on human erythrocyte membrane acetylcholinesterase activity. PubMed Tsakiris, Stylianos; Giannoulia-Karantana, Aglaia; Simintzi, Irene; Schulpis, Kleopatra H 2006-01-01 Studies have implicated aspartame (ASP) with neurological problems. The aim of this study was to evaluate acetylcholinesterase (AChE) activity in human erythrocyte membranes after incubation with the sum of ASP metabolites, phenylalanine (Phe), methanol (met) and aspartic acid (aspt), or with each one separately. Erythrocyte membranes were obtained from 12 healthy individuals and were incubated with ASP hydrolysis products for 1 h at 37 degrees C. AChE was measured spectrophotometrically. Incubation of membranes with ASP metabolites corresponding with 34 mg/kg, 150 mg/kg or 200 mg/kg of ASP consumption resulted in an enzyme activity reduction by -33%, -41%, and -57%, respectively. Met concentrations 0.14 mM, 0.60 mM, and 0.80 mM decreased the enzyme activity by -20%, -32% or -40%, respectively. Aspt concentrations 2.80 mM, 7.60 mM or 10.0 mM inhibited membrane AChE activity by -20%, -35%, and -47%, respectively. Phe concentrations 0.14 mM, 0.35 mM or 0.50mM reduced the enzyme activity by -11%, -33%, and -35%, respectively. Aspt or Phe concentrations 0.82 mM or 0.07 mM, respectively, did not alter the membrane AChE activity. It is concluded that low concentrations of ASP metabolites had no effect on the membrane enzyme activity, whereas high or toxic concentrations partially or remarkably decreased the membrane AChE activity, respectively. Additionally, neurological symptoms, including learning and memory processes, may be related to the high or toxic concentrations of the sweetener metabolites. 1. Proline-induced changes in acetylcholinesterase activity and gene expression in zebrafish brain: reversal by antipsychotic drugs. PubMed Savio, L E B; Vuaden, F C; Kist, L W; Pereira, T C; Rosemberg, D B; Bogo, M R; Bonan, C D; Wyse, A T S 2013-10-10 Hyperprolinemia is an inherited disorder of proline metabolism and hyperprolinemic patients can present neurological manifestations, such as seizures, cognitive dysfunctions, and schizoaffective disorders. However, the mechanisms related to these symptoms are still unclear. In the present study, we evaluated the in vivo and in vitro effects of proline on acetylcholinesterase (AChE) activity and gene expression in the zebrafish brain. For the in vivo studies, animals were exposed at two proline concentrations (1.5 and 3.0mM) during 1h or 7 days (short- or long-term treatments, respectively). For the in vitro assays, different proline concentrations (ranging from 3.0 to 1000 μM) were tested. Long-term proline exposures significantly increased AChE activity for both treated groups when compared to the control (34% and 39%). Moreover, the proline-induced increase on AChE activity was completely reverted by acute administration of antipsychotic drugs (haloperidol and sulpiride), as well as the changes induced in ache expression. When assessed in vitro, proline did not promote significant changes in AChE activity. Altogether, these data indicate that the enzyme responsible for the control of acetylcholine levels might be altered after proline exposure in the adult zebrafish. These findings contribute for better understanding of the pathophysiology of hyperprolinemia and might reinforce the use of the zebrafish as a complementary vertebrate model for studying inborn errors of amino acid metabolism. PMID:23867765 2. Biological evaluation of synthetic α,β-unsaturated carbonyl based cyclohexanone derivatives as neuroprotective novel inhibitors of acetylcholinesterase, butyrylcholinesterase and amyloid-β aggregation. PubMed 2016-05-15 A series of new α,β-unsaturated carbonyl-based cyclohexanone derivatives was synthesized by simple condensation method and all compounds were characterized by using various spectroscopic techniques. New compounds were evaluated for their effects on acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE). These compounds were also screened for in vitro cytotoxicity and for inhibitory activity for self-induced Aβ1-42 aggregation. The effect of these compounds against amyloid β-induced cytotoxicity was also investigated. The findings of in vitro experiment revealed that most of these compounds exhibited potent inhibitory activity against AChE and self-induced Aβ1-42 aggregation. The compound 3o exhibited best AChE (IC50=0.037μM) inhibitory potential. Furthermore, compound 3o disassembled the Aβ fibrils produced by self-induced Aβ aggregation by 76.6%. Compounds containing N-methyl-4-piperidone linker, showed high acetylcholinesterase and self-induced Aβ aggregation inhibitory activities as compared to reference drug donepezil. The pre-treatment of cells with synthetic compounds protected them against Aβ-induced cell death by up to 92%. Collectively, these findings suggest that some compounds from this series have potential to be promising multifunctional agents for AD treatment and our study suggest the cyclohexanone derivatives as promising new inhibitors for AChE and BuChE, potentially useful to treat neurodegenerative diseases. 3. 1,2,3,4-Tetrahydrobenzo[h][1,6]naphthyridines as a new family of potent peripheral-to-midgorge-site inhibitors of acetylcholinesterase: synthesis, pharmacological evaluation and mechanistic studies. PubMed Di Pietro, Ornella; Viayna, Elisabet; Vicente-García, Esther; Bartolini, Manuela; Ramón, Rosario; Juárez-Jiménez, Jordi; Clos, M Victòria; Pérez, Belén; Andrisano, Vincenza; Luque, F Javier; Lavilla, Rodolfo; Muñoz-Torrero, Diego 2014-02-12 A series of 1,2,3,4-tetrahydrobenzo[h][1,6]naphthyridines differently substituted at positions 1, 5, and 9 have been designed from the pyrano[3,2-c]quinoline derivative 1, a weak inhibitor of acetylcholinesterase (AChE) with predicted ability to bind to the AChE peripheral anionic site (PAS), at the entrance of the catalytic gorge. Fourteen novel benzonaphthyridines have been synthesized through synthetic sequences involving as the key step a multicomponent Povarov reaction between an aldehyde, an aniline and an enamine or an enamide as the activated alkene. The novel compounds have been tested against Electrophorus electricus AChE (EeAChE), human recombinant AChE (hAChE), and human serum butyrylcholinesterase (hBChE), and their brain penetration has been assessed using the PAMPA-BBB assay. Also, the mechanism of AChE inhibition of the most potent compounds has been thoroughly studied by kinetic studies, a propidium displacement assay, and molecular modelling. We have found that a seemingly small structural change such as a double O → NH bioisosteric replacement from the hit 1 to 16a results in a dramatic increase of EeAChE and hAChE inhibitory activities (>217- and >154-fold, respectively), and in a notable increase in hBChE inhibitory activity (>11-fold), as well. An optimized binding at the PAS besides additional interactions with AChE midgorge residues seem to account for the high hAChE inhibitory potency of 16a (IC50 = 65 nM), which emerges as an interesting anti-Alzheimer lead compound with potent dual AChE and BChE inhibitory activities. PMID:24389509 4. Identification of Potential Herbal Inhibitor of Acetylcholinesterase Associated Alzheimer's Disorders Using Molecular Docking and Molecular Dynamics Simulation PubMed Central Seniya, Chandrabhan; Khan, Ghulam Jilani; Uchadia, Kuldeep 2014-01-01 Cholinesterase inhibitors (ChE-Is) are the standard for the therapy of AD associated disorders and are the only class of approved drugs by the Food and Drug Administration (FDA). Additionally, acetylcholinesterase (AChE) is the target for many Alzheimer's dementia drugs which block the function of AChE but have some side effects. Therefore, in this paper, an attempt was made to elucidate cholinesterase inhibition potential of secondary metabolite from Cannabis plant which has negligible or no side effect. Molecular docking of 500 herbal compounds, against AChE, was performed using Autodock 4.2 as per the standard protocols. Molecular dynamics simulations have also been carried out to check stability of binding complex in water for 1000 ps. Our molecular docking and simulation have predicted high binding affinity of secondary metabolite (C28H34N2O6) to AChE. Further, molecular dynamics simulations for 1000 ps suggest that ligand interaction with the residues Asp72, Tyr70-121-334, and Phe288 of AChE, all of which fall under active site/subsite or binding pocket, might be critical for the inhibitory activity of AChE. This approach might be helpful to understand the selectivity of the given drug molecule in the treatment of Alzheimer's disease. The study provides evidence for consideration of C28H34N2O6 as a valuable small ligand molecule in treatment and prevention of AD associated disorders and further in vitro and in vivo investigations may prove its therapeutic potential. PMID:25054066 5. Acetylcholinesterase inhibition in the basolateral amygdala plays a key role in the induction of status epilepticus after soman exposure. PubMed Prager, Eric M; Aroniadou-Anderjaska, Vassiliki; Almeida-Suhett, Camila P; Figueiredo, Taiza H; Apland, James P; Braga, Maria F M 2013-09-01 Exposure to nerve agents induces intense seizures (status epilepticus, SE), which cause brain damage or death. Identification of the brain regions that are critical for seizure initiation after nerve agent exposure, along with knowledge of the physiology of these regions, can facilitate the development of pretreatments and treatments that will successfully prevent or limit the development of seizures and brain damage. It is well-established that seizure initiation is due to excessive cholinergic activity triggered by the nerve agent-induced irreversible inhibition of acetylcholinesterase (AChE). Therefore, the reason that when animals are exposed to lethal doses of a nerve agent, a small proportion of these animals do not develop seizures, may have to do with failure of the nerve agent to inhibit AChE in brain areas that play a key role in seizure initiation and propagation. In the present study, we compared AChE activity in the basolateral amygdala (BLA), hippocampus, and piriform cortex of rats that developed SE (SE rats) after administration of the nerve agent soman (154μg/kg) to AChE activity in these brain regions of rats that received the same dose of soman but did not develop SE (no-SE rats). The levels of AChE activity were measured at the onset of SE in SE rats, 30min after soman administration in no-SE rats, as well as in controls which received saline in place of soman. In the control group, AChE activity was significantly higher in the BLA compared to the hippocampus and piriform cortex. Compared to controls, AChE activity was dramatically lower in the hippocampus and the piriform cortex of both the SE rats and the no-SE rats, but AChE activity in the BLA was reduced only in the SE rats. Consistent with the notion that soman-induced neuropathology is due to intense seizures, rather than due to a direct neurotoxic effect of soman, no-SE rats did not present any neuronal loss or degeneration, 7 days after exposure. The results suggest that inhibition of 6. Comparison of Chlorpyrifos-Oxon and Paraoxon Acetylcholinesterase Inhibition Dynamics: Potential role of a peripheral binding site SciTech Connect Kousba, Ahmed A.; Sultatos, L G.; Poet, Torka S.; Timchalk, Chuck 2004-08-02 The primary mechanism of action for organophosphorus (OP) insecticides involves the inhibition of acetylcholinesterase (AChE) by oxygenated metabolites (oxons). This inhibition has been attributed to the phosphorylation of the serine hydroxyl group located in the active site of the AChE molecule. The rate of phosphorylation is described by the bimolecular inhibitory rate constant (ki), which has been utilized for quantification of OP inhibitory capacity. It has been previously proposed that a peripheral binding site exists on the AChE molecule, which when occupied, reduces the capacity of additional oxon molecules to phosphorylate the active site. The objective of the current study was to evaluate the interaction of chlorpyrifos oxon (CPO) and paraoxon (PO) with rat brain AChE using a modified Ellman assay in conjunction with a pharmacodynamic model to further assess the dynamics of AChE inhibition and the potential role of a peripheral binding site. The ki for AChE inhibition determined at oxon concentrations of 5 x 10{sup -4} 100 nM were 0.212 and 0.0216 nM-1h-1 for CPO and PO, respectively. The spontaneous reactivation rates of the inhibited AChE for CPO and PO were 0.087 and 0.078 h-1, respectively. In contrast, the ki estimated at a low oxon concentration (1 pM) were {approx} 1,000 and 10,000 -fold higher than those determined at high CPO and PO concentrations, respectively. At these low concentrations, the ki estimates were approximately similar for both CPO and PO (180 and 250 nM-1h-1, respectively). This implies that at low exposure concentrations, both oxons exhibited similar inhibitory potency in contrast to the marked difference exhibited at higher concentrations, which is consistent with the presence of a peripheral binding site on the AChE enzyme. These results support the potential importance of a secondary binding site associated with AChE kinetics, particularly at low environmentally relevant concentrations. 7. Comparative investigation between acetylcholinesterase obtained from commercial sources and genetically modified Drosophila melanogaster: application in amperometric biosensors for methamidophos pesticide detection. PubMed de Oliveira Marques, Paulo Roberto Brasil; Nunes, Gilvanda Silva; dos Santos, Teresa Cristina Rodrigues; Andreescu, Silvana; Marty, Jean-Louis 2004-11-01 Genetically modified acetylcholinesterase (AChE) from Drosophila melanogaster (dm) and from commercial sources, Electric eel (ee), Bovine erythrocites (be) and Human erythrocites (he), were investigated as biological receptors for the detection of methamidophos pesticide based on inhibition studies. Most engineered variant of AChE from dm showed enhanced sensitivity toward methamidophos pesticide. Among 24 dmAChE variants tested, 12 presented a sensitivity comparable to the commercially available eeAChE, but higher than AChEs from be and he. Four were found more sensitive and six others were insensitive to methamidophos insecticide. The D375G,Y370F,Y374A,F376L mutant was the most sensitive, with a ki value of 2.2 X 10(6) mol(-1) L min(-1), three orders of magnitude higher than eeAChE (1.1 X 10(3) mol(-1) L min(-1)). The sensor constructed with genetically modified enzyme showed better characteristics with respect to detection limit and sensitivity compared with those using commercial eeAChE. Differential pulse polarography and chronoamperometry were used as electrochemical techniques to characterize the AChE biosensors. The lower detection limit of 1 ppb was obtained with D375G,Y370F,Y374A,F376L mutant of dmAChE, compared to 90 ppb for the commercial eeAChE. This study may stimulate scientists to develop more sensitive and selective procedures for organophosphorus insecticides detection by using engineered variant of dmAChE. PMID:15522598 8. Nanoparticle-Based Electrochemical Immunosensor for the Detection of Phosphorylated Acetylcholinesterase: An Exposure Biomarker of Organophosphate Pesticides and Nerve AgentsOrganophosphate Pesticides and Nerve Agents SciTech Connect Liu, Guodong; Wang, Jun; Barry, Richard C.; Petersen, Catherine E.; Timchalk, Charles; Gassman, Paul L.; Lin, Yuehe 2008-11-01 A nanoparticle-based electrochemical immunosensor has been developed for the detection of phosphorylated acetylcholinesterase (AChE) adducts, which is a potential exposure biomarker for organophosphate pesticides (OP) and chemical warfare nerve agent exposures. Zirconia nanoparticles (ZrO2 NPs) were used as selective sorbents to capture the phosphorylated AChE adduct, and quantum dots (ZnS@CdS, QDs) were used as tags to label monoclonal anti-AChE antibody to track the immunorecognition events. The sandwich-like immunoreactions were performed among the ZrO2 NPs, which were pre-coated on a screen printed electrode (SPE) by electrodeposition, phosphorylated AChE and QD-anti-AChE. The captured QD tags were determined on the SPE by electrochemical stripping analysis of its metallic component (cadmium) after an acid-dissolution step. Paraoxon was used as a model OP insecticide to prepare the phosphorylated AChE adduct to demonstrate the proof of principle for this sensor technology. The paraoxon-AChE adduct was characterized by Fourier Transform Infrared Spectrum, and the binding affinity of anti-AChE to the paraoxon-AChE was validated with an enzyme-linked immunosorbent assay. The parameters (e.g., amount of ZrO2 NP, QD-anti-AChE concentration,) that govern the electrochemical response of immunosensors were optimized. The voltammetric response of the immunosensor is highly linear over the range of 10 pM to 4 nM paraoxon-AChE, and the limit of detection is estimated to be 8 pM. This new nanoparticle-based electrochemical immunosensor thus provides a sensitive and quantitative tool for biomonitoring exposure to OP pesticides and nerve agents. 9. Increased Acetylcholinesterase Expression in Bumble Bees During Neonicotinoid-Coated Corn Sowing. PubMed Samson-Robert, Olivier; Labrie, Geneviève; Mercier, Pierre-Luc; Chagnon, Madeleine; Derome, Nicolas; Fournier, Valérie 2015-01-01 While honey bee exposure to systemic insecticides has received much attention, impacts on wild pollinators have not been as widely studied. Neonicotinoids have been shown to increase acetylcholinesterase (AChE) activity in honey bees at sublethal doses. High AChE levels may therefore act as a biomarker of exposure to neonicotinoids. This two-year study focused on establishing whether bumble bees living and foraging in agricultural areas using neonicotinoid crop protection show early biochemical signs of intoxication. Bumble bee colonies (Bombus impatiens) were placed in two different agricultural cropping areas: 1) control (≥ 3 km from fields planted with neonicotinoid-treated seeds) or 2) exposed (within 500 m of fields planted with neonicotinoid-treated seeds), and maintained for the duration of corn sowing. As determined by Real Time qPCR, AChE mRNA expression was initially significantly higher in bumble bees from exposed sites, then decreased throughout the planting season to reach a similar endpoint to that of bumble bees from control sites. These findings suggest that exposure to neonicotinoid seed coating particles during the planting season can alter bumble bee neuronal activity. To our knowledge, this is the first study to report in situ that bumble bees living in agricultural areas exhibit signs of neonicotinoid intoxication. PMID:26223214 10. Maternal caffeine exposure alters neuromotor development and hippocampus acetylcholinesterase activity in rat offspring. PubMed Souza, Ana Claudia; Souza, Andressa; Medeiros, Liciane Fernandes; De Oliveira, Carla; Scarabelot, Vanessa Leal; Da Silva, Rosane Souza; Bogo, Mauricio Reis; Capiotti, Katiucia Marques; Kist, Luiza Wilges; Bonan, Carla D; Caumo, Wolnei; Torres, Iraci L S 2015-01-21 The objective of this study was to evaluate the effects of maternal caffeine intake on the neuromotor development of rat offspring and on acetylcholine degradation and acetylcholinesterase (AChE) expression in the hippocampus of 14-day-old infant rats. Rat dams were treated with caffeine (0.3g/L) throughout gestation and lactation until the pups were 14 days old. The pups were divided into three groups: (1) control, (2) caffeine, and (3) washout caffeine. The washout group received a caffeine solution until the seventh postnatal day (P7). Righting reflex (RR) and negative geotaxis (NG) were assessed to evaluate postural parameters as an index of neuromotor reflexes. An open-field (OF) test was conducted to assess locomotor and exploratory activities as well as anxiety-like behaviors. Caffeine treatment increased both RR and NG latency times. In the OF test, the caffeine group had fewer outer crossings and reduced locomotion compared to control, while the washout group showed increased inner crossings in relation to the other groups and fewer rearings only in comparison to the control group. We found decreased AChE activity in the caffeine group compared to the other groups, with no alteration in AChE transcriptional regulation. Chronic maternal exposure to caffeine promotes important alterations in neuromotor development. These results highlight the ability of maternal caffeine intake to interfere with cholinergic neurotransmission during brain development. 11. Increased Acetylcholinesterase Expression in Bumble Bees During Neonicotinoid-Coated Corn Sowing. PubMed Samson-Robert, Olivier; Labrie, Geneviève; Mercier, Pierre-Luc; Chagnon, Madeleine; Derome, Nicolas; Fournier, Valérie 2015-07-30 While honey bee exposure to systemic insecticides has received much attention, impacts on wild pollinators have not been as widely studied. Neonicotinoids have been shown to increase acetylcholinesterase (AChE) activity in honey bees at sublethal doses. High AChE levels may therefore act as a biomarker of exposure to neonicotinoids. This two-year study focused on establishing whether bumble bees living and foraging in agricultural areas using neonicotinoid crop protection show early biochemical signs of intoxication. Bumble bee colonies (Bombus impatiens) were placed in two different agricultural cropping areas: 1) control (≥ 3 km from fields planted with neonicotinoid-treated seeds) or 2) exposed (within 500 m of fields planted with neonicotinoid-treated seeds), and maintained for the duration of corn sowing. As determined by Real Time qPCR, AChE mRNA expression was initially significantly higher in bumble bees from exposed sites, then decreased throughout the planting season to reach a similar endpoint to that of bumble bees from control sites. These findings suggest that exposure to neonicotinoid seed coating particles during the planting season can alter bumble bee neuronal activity. To our knowledge, this is the first study to report in situ that bumble bees living in agricultural areas exhibit signs of neonicotinoid intoxication. 12. A novel and highly sensitive acetyl-cholinesterase biosensor modified with hollow gold nanospheres. PubMed Sun, Xia; Zhai, Chen; Wang, Xiangyou 2013-03-01 In this work, a highly sensitive acetylcholinesterase (AChE) inhibition-based amperometric biosensor has been developed. Firstly, a glassy carbon electrode (GCE) was modified with chitosan (Chits). Then, hollow gold nanospheres (HGNs) were absorbed onto the surface of chitosan based on the strong affinity through electrostatic adsorption. After that, L-cysteine (L-cys) was assembled on HGNs through Au-S bond. The hollow gold nanospheres were prepared by using Co nanoparticles as sacrificial templates and characterized by scanning electron microscopy, transmission electron microscopy and ultraviolet spectra, respectively. Finally, AChE was immobilized with covalent binding via -COOH groups of L-cysteine onto the modified GCE. The AChE biosensor fabrication process was characterized by cyclic voltammetry and electrochemical impedance spectroscopy methods with the use of ferricyanide as an electrochemical redox indicator. Under optimum conditions, the inhibition rates of pesticides were proportional to their concentrations in the range of 0.1-150 and 0.1-200 μg L(-1) for chlorpyrifos and carbofuran, respectively, the detection limits were 0.06 μg L(-1) for chlorpyrifos and 0.08 μg L(-1) for carbofuran. Moreover, the biosensor exhibited a good stability and reproducibility and was suitable for trace detection of pesticide residues in vegetables and fruits. 13. Investigation of kinetic interactions between approved oximes and human acetylcholinesterase inhibited by pesticide carbamates. PubMed Wille, Timo; Kaltenbach, Lisa; Thiermann, Horst; Worek, Franz 2013-12-01 Carbamates are widely used for pest control and act primarily by inhibition of insect and mammalian acetylcholinesterase (AChE). Accidental or intentional uptake of carbamates may result in typical signs and symptoms of cholinergic overstimulation which cannot be discriminated from those of organophosphorus pesticide poisoning. There is an ongoing debate whether standard treatment with atropine and oximes should be recommended for human carbamate poisoning as well, since in vitro and in vivo animal data indicate a deleterious effect of oximes when used in combination with the N-methyl carbamate carbaryl. Therefore, we performed an in vitro kinetic study to investigate the effect of clinically used oximes on carbamoylation and decarbamoylation of human AChE. It became evident that pralidoxime and obidoxime in therapeutic concentrations aggravate the inhibition of AChE by carbaryl and propoxur, with obidoxime being substantially more potent compared to 2-PAM. However, obidoxime had no impact on the decarbamoylation kinetics. Hence, the administration of 2-PAM and especially of obidoxime to severely propoxur and carbaryl poisoned humans cannot be recommended. 14. Luminescent silica nanoparticles for sensing acetylcholinesterase-catalyzed hydrolysis of acetylcholine. PubMed Mukhametshina, Alsu R; Fedorenko, Svetlana V; Zueva, Irina V; Petrov, Konstantin A; Masson, Patrick; Nizameev, Irek R; Mustafina, Asiya R; Sinyashin, Oleg G 2016-03-15 This work highlights the H-function of Tb(III)-doped silica nanoparticles in aqueous solutions of acetic acid as a route to sense acetylcholinesterase-catalyzed hydrolysis of acetylcholine (ACh). The H-function results from H(+)-induced quenching of Tb(III)-centered luminescence due to protonation of Tb(III) complexes located close to silica/water interface. The H-function can be turned on/switched off by the concentration of complexes within core or nanoparticle shell zones, by the silica surface decoration and adsorption of both organic and inorganic cations on silica surface. Results indicate the optimal synthetic procedure for making nanoparticles capable of sensing acetic acid produced by enzymatic hydrolysis of acetylcholine. The H-function of nanoparticles was determined at various concentrations of ACh and AChE. The measurements show experimental conditions for fitting the H-function to Michaelis-Menten kinetics. Results confirm that reliable fluorescent monitoring AChE-catalyzed hydrolysis of ACh is possible through the H-function properties of Tb(III)-doped silica nanoparticles. 15. Screening of siddha medicinal plants for its in-vitro acetylcholinesterase and butyrylcholinesterase inhibitory activity PubMed Central 2014-01-01 Background: The plants selected for the study were traditionally used in siddha system of medicine in neurological disorders. Aim: The aim of the following study isto screen the plant species for both acetylcholinesterase (AchE) and butyrylcholinesterase (BuchE) inhibition by in-vitro Ellman's method and a thin layer chromatography bioautographic assay for newer drug candidates for the treatment of Alzheimer's disease. Materials and Methods: Ellman's colorimetric method was performed in a 96 well micro plate for cholinesterases inhibition using galantamine as standard drug. Results: Present studies confirmed that out of all the tested extracts Hemidesmus indicus R.Br (HI) showed considerable IC50 values for AchE (28.40 ± 0.92 μg/mL) and BuchE (43.47 ± 0.64 μg/mL) inhibition which indicates that HI extract has considerable specificity toward AchE and BuchE compared with all the tested extracts and the activity was followed by Vernonia anthelmintica (VA) Willd and Saussurea lappa Clarke (SL). The bioautograms also confirmed the activity potent extracts. Conclusion: Besides various bioactivities HI, VA and SL exhibited considerable cholinesterases inhibition making it to consider these species for further investigation of new compounds. PMID:24991106 16. Molecular evaluation of herbal compounds as potent inhibitors of acetylcholinesterase for the treatment of Alzheimer's disease. PubMed Chen, Yan-Xiu; Li, Guan-Zeng; Zhang, Bin; Xia, Zhang-Yong; Zhang, Mei 2016-07-01 Alzheimer's disease (AD) is a progressive disease and the predominant cause of dementia. Common symptoms include short-term memory loss, and confusion with time and place. Individuals with AD depend on their caregivers for assistance, and may pose a burden to them. The acetylcholinesterase (AChE) enzyme is a key target in AD and inhibition of this enzyme may be a promising strategy in the drug discovery process. In the present study, an inhibitory assay was carried out against AChE using total alkaloidal plants and herbal extracts commonly available in vegetable markets. Subsequently, molecular docking simulation analyses of the bioactive compounds present in the plants were conducted, as well as a protein‑ligand interaction analysis. The stability of the docked protein‑ligand complex was assessed by 20 ns molecular dynamics simulation. The inhibitory assay demonstrated that Uncaria rhynchophylla and Portulaca oleracea were able to inhibit AChE. In addition, molecular docking simulation analyses indicated that catechin present in Uncaria rhynchophylla, and dopamine and norepinephrine present in Portulaca oleracea, had the best docking scores and interaction energy. In conclusion, catechin in Uncaria rhynchophylla, and dopamine and norepinephrine in Portulaca oleracea may be used to treat AD. 17. Luminescent silica nanoparticles for sensing acetylcholinesterase-catalyzed hydrolysis of acetylcholine. PubMed Mukhametshina, Alsu R; Fedorenko, Svetlana V; Zueva, Irina V; Petrov, Konstantin A; Masson, Patrick; Nizameev, Irek R; Mustafina, Asiya R; Sinyashin, Oleg G 2016-03-15 This work highlights the H-function of Tb(III)-doped silica nanoparticles in aqueous solutions of acetic acid as a route to sense acetylcholinesterase-catalyzed hydrolysis of acetylcholine (ACh). The H-function results from H(+)-induced quenching of Tb(III)-centered luminescence due to protonation of Tb(III) complexes located close to silica/water interface. The H-function can be turned on/switched off by the concentration of complexes within core or nanoparticle shell zones, by the silica surface decoration and adsorption of both organic and inorganic cations on silica surface. Results indicate the optimal synthetic procedure for making nanoparticles capable of sensing acetic acid produced by enzymatic hydrolysis of acetylcholine. The H-function of nanoparticles was determined at various concentrations of ACh and AChE. The measurements show experimental conditions for fitting the H-function to Michaelis-Menten kinetics. Results confirm that reliable fluorescent monitoring AChE-catalyzed hydrolysis of ACh is possible through the H-function properties of Tb(III)-doped silica nanoparticles. PMID:26516688 18. Increased Acetylcholinesterase Expression in Bumble Bees During Neonicotinoid-Coated Corn Sowing PubMed Central Samson-Robert, Olivier; Labrie, Geneviève; Mercier, Pierre-Luc; Chagnon, Madeleine; Derome, Nicolas; Fournier, Valérie 2015-01-01 While honey bee exposure to systemic insecticides has received much attention, impacts on wild pollinators have not been as widely studied. Neonicotinoids have been shown to increase acetylcholinesterase (AChE) activity in honey bees at sublethal doses. High AChE levels may therefore act as a biomarker of exposure to neonicotinoids. This two-year study focused on establishing whether bumble bees living and foraging in agricultural areas using neonicotinoid crop protection show early biochemical signs of intoxication. Bumble bee colonies (Bombus impatiens) were placed in two different agricultural cropping areas: 1) control (≥3 km from fields planted with neonicotinoid-treated seeds) or 2) exposed (within 500 m of fields planted with neonicotinoid-treated seeds), and maintained for the duration of corn sowing. As determined by Real Time qPCR, AChE mRNA expression was initially significantly higher in bumble bees from exposed sites, then decreased throughout the planting season to reach a similar endpoint to that of bumble bees from control sites. These findings suggest that exposure to neonicotinoid seed coating particles during the planting season can alter bumble bee neuronal activity. To our knowledge, this is the first study to report in situ that bumble bees living in agricultural areas exhibit signs of neonicotinoid intoxication. PMID:26223214 19. Screening of β-secretase and acetylcholinesterase inhibitors from plant resources. PubMed Murata, Kazuya; Matsumura, Shinichi; Yoshioka, Yuri; Ueno, Yoshihiro; Matsuda, Hideaki 2015-01-01 The therapeutic agents for dementia are limited due to the complex system underlying the mechanisms. Taking a preventive point of view, we focused on the inhibition of β-secretase and acetylcholinesterase (AChE). In addition, plant resources including herbs and spices have been widely consumed, and further, may be consumed for a long period over a lifetime. Considering this background, we screened β-secretase and AChE inhibitors from curry spices. Amongst them, curry leaf, black pepper, and turmeric extracts were effective to inhibit β-secretase. Furthermore, black pepper and turmeric extracts were also effective to inhibit AChE. Having these results in hand, we focused on the investigation of β-secretase inhibitors since the inhibitor of this enzyme has not previously been well investigated. As a result, α- and β-caryophyllene, β-caryophyllene oxide (from curry leaf), piperine (from black pepper), curcumin, demethoxycurcumin, and bisdemethoxycurcumin (from turmeric) were successfully identified as low molecular inhibitors. This is the first report to determine α- and β-caryophyllene, β-caryophyllene oxide, and piperine as β-secretase inhibitors. These compounds may pass through the blood brain barrier since their molecular weights are relatively low. PMID:25119528 20. Maternal caffeine exposure alters neuromotor development and hippocampus acetylcholinesterase activity in rat offspring. PubMed Souza, Ana Claudia; Souza, Andressa; Medeiros, Liciane Fernandes; De Oliveira, Carla; Scarabelot, Vanessa Leal; Da Silva, Rosane Souza; Bogo, Mauricio Reis; Capiotti, Katiucia Marques; Kist, Luiza Wilges; Bonan, Carla D; Caumo, Wolnei; Torres, Iraci L S 2015-01-21 The objective of this study was to evaluate the effects of maternal caffeine intake on the neuromotor development of rat offspring and on acetylcholine degradation and acetylcholinesterase (AChE) expression in the hippocampus of 14-day-old infant rats. Rat dams were treated with caffeine (0.3g/L) throughout gestation and lactation until the pups were 14 days old. The pups were divided into three groups: (1) control, (2) caffeine, and (3) washout caffeine. The washout group received a caffeine solution until the seventh postnatal day (P7). Righting reflex (RR) and negative geotaxis (NG) were assessed to evaluate postural parameters as an index of neuromotor reflexes. An open-field (OF) test was conducted to assess locomotor and exploratory activities as well as anxiety-like behaviors. Caffeine treatment increased both RR and NG latency times. In the OF test, the caffeine group had fewer outer crossings and reduced locomotion compared to control, while the washout group showed increased inner crossings in relation to the other groups and fewer rearings only in comparison to the control group. We found decreased AChE activity in the caffeine group compared to the other groups, with no alteration in AChE transcriptional regulation. Chronic maternal exposure to caffeine promotes important alterations in neuromotor development. These results highlight the ability of maternal caffeine intake to interfere with cholinergic neurotransmission during brain development. PMID:25451122 1. Bromotyrosine Alkaloids with Acetylcholinesterase Inhibitory Activity from the Thai Sponge Acanthodendrilla sp. PubMed Sirimangkalakitti, Natchanun; Olatunji, Opeyemi J; Changwichit, Kanokwan; Saesong, Tongchai; Chamni, Supakarn; Chanvorachote, Pithi; Ingkaninan, Kornkanok; Plubrukarn, Anuchit; Suwanborirux, Khanit 2015-11-01 Twenty bromotyrosine alkaloids, including a new compound, 13-oxosubereamolline D (5), were isolated from the Thai sponge Acanthodendrilla sp. Their structures were determined by analyses of 1D- and 2D-NMR, high-resolution mass, and circular dichroism data. The complete 1H and 13C NMR assignments of 5,7β-dichlorocavernicolin (19) and 5,7α-dichlorocavernicolin (20) are described herein for the first time. The acetylcholinesterase (AChE) inhibitory activity of all isolated compounds was evaluated. Only homoaerothionin (7) and fistularin 1 (10) exhibited inhibitory activity against human recombinant AChE (hrAChE) with IC50s of 4.5 and 47.5 µM, respectively. The hrAChE inhibition kinetics of 7, the most potent alkaloid, showed increased Km and unchanged Vmaxvalues, suggesting its competitive mode of inhibition. The spirocyclohexadienylisoxazole and the length of the alkyl diamine linkage were proposed as the crucial parts for its strong inhibitory activity. This finding indicates a therapeutic potential for 7 in acetylcholine-related diseases, most importantly Alzheimer's disease. PMID:26749833 2. Bioactive Paper Sensor Based on the Acetylcholinesterase for the Rapid Detection of Organophosphate and Carbamate Pesticides PubMed Central 2014-01-01 In many countries, people are becoming more concerned about pesticide residues which are present in or on food and feed products. For this reason, several methods have been developed to monitor the pesticide residue levels in food samples. In this study, a bioactive paper-based sensor was developed for detection of acetylcholinesterase (AChE) inhibitors including organophosphate and carbamate pesticides. Based on the Ellman colorimetric assay, the assay strip is composed of a paper support (1 × 10 cm), onto which a biopolymer chitosan gel immobilized in crosslinking by glutaraldehyde with AChE and 5,5′-dithiobis(2-nitrobenzoic) acid (DTNB) and uses acetylthiocholine iodide (ATChI) as an outside reagent. The assay protocol involves introducing the sample to sensing zone via dipping of a pesticide-containing solution. Following an incubation period, the paper is placed into ATChI solution to initiate enzyme catalyzed hydrolysis of the substrate, causing a yellow color change. The absence or decrease of the yellow color indicates the levels of the AChE inhibitors. The biosensor is able to detect organophosphate and carbamate pesticides with good detection limits (methomyl = 6.16 × 10−4 mM and profenofos = 0.27 mM) and rapid response times (~5 min). The results show that the paper-based biosensor is rapid, sensitive, inexpensive, portable, disposable, and easy-to-use. PMID:25484901 3. Acetylcholinesterases from the Disease Vectors Aedes aegypti and Anopheles gambiae: Functional Characterization and Comparisons with Vertebrate Orthologues PubMed Central Engdahl, Cecilia; Knutsson, Sofie; Fredriksson, Sten-Åke; Linusson, Anna; Bucht, Göran; Ekström, Fredrik 2015-01-01 Mosquitoes of the Anopheles (An.) and Aedes (Ae.) genus are principal vectors of human diseases including malaria, dengue and yellow fever. Insecticide-based vector control is an established and important way of preventing transmission of such infections. Currently used insecticides can efficiently control mosquito populations, but there are growing concerns about emerging resistance, off-target toxicity and their ability to alter ecosystems. A potential target for the development of insecticides with reduced off-target toxicity is the cholinergic enzyme acetylcholinesterase (AChE). Herein, we report cloning, baculoviral expression and functional characterization of the wild-type AChE genes (ace-1) from An. gambiae and Ae. aegypti, including a naturally occurring insecticide-resistant (G119S) mutant of An. gambiae. Using enzymatic digestion and liquid chromatography-tandem mass spectrometry we found that the secreted proteins were post-translationally modified. The Michaelis-Menten constants and turnover numbers of the mosquito enzymes were lower than those of the orthologous AChEs from Mus musculus and Homo sapiens. We also found that the G119S substitution reduced the turnover rate of substrates and the potency of selected covalent inhibitors. Furthermore, non-covalent inhibitors were less sensitive to the G119S substitution and differentiate the mosquito enzymes from corresponding vertebrate enzymes. Our findings indicate that it may be possible to develop selective non-covalent inhibitors that effectively target both the wild-type and insecticide resistant mutants of mosquito AChE. PMID:26447952 4. Acetylcholinesterase biosensor for inhibitor measurements based on glassy carbon electrode modified with carbon black and pillar[5]arene. PubMed Shamagsumova, Rezeda V; Shurpik, Dmitry N; Padnya, Pavel L; Stoikov, Ivan I; Evtugyn, Gennady A 2015-11-01 New acetylcholinesterase (AChE) biosensor based on unsubstituted pillar[5]arene (P[5]A) as electron mediator was developed and successfully used for highly sensitive detection of organophosphate and carbamate pesticides. The AChE from electric eel was immobilized by carbodiimide binding on carbon black (CB) placed on glassy carbon electrode. The working potential of 200mV was obtained in chronoamperometric mode with the measurement time of 180 s providing best inter-biosensors precision of the results. The AChE biosensor developed made it possible to detect 1×10(-11)-1×10(-6) M of malaoxon, 1×10(-8)-7×10(-6) M of methyl-paraoxon, 1×10(-10)-2×10(-6) M of carbofuran and 7×10(-9)-1×10(-5) M of aldicarb with 10 min incubation. The limits of detection were 4×10(-12), 5×10(-9), 2×10(-11) and 6×10(-10) M, respectively. The AChE biosensor was tested in the analysis of pesticide residuals in spiked samples of peanut and beetroot. The protecting effect of P[5]A derivative bearing quaternary ammonia groups on malaoxon inhibition was shown. PMID:26452862 5. Effects of the herbicides clomazone, quinclorac, and metsulfuron methyl on acetylcholinesterase activity in the silver catfish (Rhamdia quelen) (Heptapteridae). PubMed dos Santos Miron, Denise; Crestani, Márcia; Rosa Shettinger, Maria; Maria Morsch, Vera; Baldisserotto, Bernardo; Angel Tierno, Miguel; Moraes, Gilberto; Vieira, Vania Lucia Pimentel 2005-07-01 Fingerlings of the silver catfish (Rhamdia quelen) were exposed to three herbicides widely used in rice culture in south Brazil: clomazone, quinclorac, and metsulfuron methyl. LC50 was determined and acetylcholinesterase (AChE) activity was evaluated in brain and muscle tissue of fish exposed to different herbicide concentrations after 96h (short term). The LC50 value (nominal concentration) was 7.32 mg/L for clomazone and 395 mg/L for quinclorac, but was not obtained for metsulfuron-methyl since all fingerlings survived the highest concentration of 1200 mg/L. Brain and muscle AChE activity in unexposed fish were 17.9 and 9.08 micromol/min/g protein, respectively. Clomazone significantly inhibited AChE activity in both tissues, achieving maximal inhibition of about 83% in brain and 89% in muscle tissue. In contrast, quinclorac and metsulfuron methyl caused increases in enzyme activity in the brain (98 and 179%, respectively) and inhibitions in muscle tissue (88 and 56%, respectively). This study demonstrated short-term effects of exposure to environmentally relevant concentrations of rice field herbicides on AChE activity in brain and muscle tissue of silver catfish. 6. Age-related changes of the noradrenergic and acetylcholinesterase reactive nerve fibres innervating the pigeon bursa of Fabricius. PubMed Ciriaco, E; Ricci, A; Bronzetti, E; Mammola, C L; Germanà, G; Vega, J A 1995-05-01 Age-dependent changes in the innervation of the pigeon (Columba livia, L.) bursa of Fabricius, from hatching to 120 days of age, were studied by fluorescence-histochemical and neurochemical methods for demonstrating noradrenergic and acetylcholinesterase (AChE)-reactive nerve fibres respectively. The distribution of both nerve fibre types was largely perivascular. Furthermore, a few isolated nerve fiber profiles were observed beneath the bursal epithelium, in the interfollicular septa and in the follicular cortex. No nerve fibre profiles reaching the medulla of the lymphoid follicles were observed. In addition to nerve fibres, AChE reactive neuron-like cells were encountered within the capsule and interfollicular septa. AChE reactivity was also found in dendritic-like cells localized in the cortical and cortico-medullary border. No changes in the density of perivascular noradrenergic innervation were noticeable during the ages studied, whereas the density of AChE-reactive fibres supplying vessels reached the adult pattern at 30 days, and then remained unvaried. The density of non-perivascular nerve fiber profiles, specially the AChE reactive type, increased until 30 days, remained unchanged until 75 days and then increased with aging (90-120 days). The interrelationship between the autonomic nervous system and the immune system is discussed. 7. Acetylcholinesterases from the Disease Vectors Aedes aegypti and Anopheles gambiae: Functional Characterization and Comparisons with Vertebrate Orthologues. PubMed Engdahl, Cecilia; Knutsson, Sofie; Fredriksson, Sten-Åke; Linusson, Anna; Bucht, Göran; Ekström, Fredrik 2015-01-01 Mosquitoes of the Anopheles (An.) and Aedes (Ae.) genus are principal vectors of human diseases including malaria, dengue and yellow fever. Insecticide-based vector control is an established and important way of preventing transmission of such infections. Currently used insecticides can efficiently control mosquito populations, but there are growing concerns about emerging resistance, off-target toxicity and their ability to alter ecosystems. A potential target for the development of insecticides with reduced off-target toxicity is the cholinergic enzyme acetylcholinesterase (AChE). Herein, we report cloning, baculoviral expression and functional characterization of the wild-type AChE genes (ace-1) from An. gambiae and Ae. aegypti, including a naturally occurring insecticide-resistant (G119S) mutant of An. gambiae. Using enzymatic digestion and liquid chromatography-tandem mass spectrometry we found that the secreted proteins were post-translationally modified. The Michaelis-Menten constants and turnover numbers of the mosquito enzymes were lower than those of the orthologous AChEs from Mus musculus and Homo sapiens. We also found that the G119S substitution reduced the turnover rate of substrates and the potency of selected covalent inhibitors. Furthermore, non-covalent inhibitors were less sensitive to the G119S substitution and differentiate the mosquito enzymes from corresponding vertebrate enzymes. Our findings indicate that it may be possible to develop selective non-covalent inhibitors that effectively target both the wild-type and insecticide resistant mutants of mosquito AChE. PMID:26447952 8. Effect of a glyphosate-based herbicide in Cyprinus carpio: assessment of acetylcholinesterase activity, hematological responses and serum biochemical parameters. PubMed Gholami-Seyedkolaei, Seyed Jalil; Mirvaghefi, Alireza; Farahmand, Hamid; Kosari, Ali Asghar 2013-12-01 The objective of this study was to investigate the toxicity effects of acute and sublethal of Roundup® as a glyphosate-based herbicide on acetylcholinesterase (AChE) activity and several hematological and biochemical parameters of Cyprinus carpio. The LC₅₀-96 h of Roundup® to C. carpio was found to be 22.19 ppm. Common carp was subjected to Roundup® at 0 (control), 3.5, 7 and 14 ppm for 16 days, and the AChE activity is verified in tissues of gill, muscle, brain and liver. After 5 days, a significant decrease was observed in the AChE activity of muscle, brain and liver tissues. Besides, a time- and dose-dependent increase in mean cell hemoglobin (MCH) and mean cell volume (MCV) was observed. In contrast, a significant decrease was found in the quantities of hemoglobin (Hb), hematocrit (HCT) and, red (RBC) and white (WBC) blood cell count. Also, the activities of aspartate aminotransferase (AST), alanine aminotransferase (ALT) and lactate dehydrogenase (LDH) in Roundup® treated groups were significantly higher than the controlled group at experimental periods. However, the level of alkaline phosphatase (ALP) had a significant reduction behavior during the sampling days. It seems that the changes in hematological and biochemical parameters as well as AChE activity could be used as efficient biomarkers in order to determine Roundup® toxicity in aquatic environment. 9. A cationic surfactant-decorated liquid crystal sensing platform for simple and sensitive detection of acetylcholinesterase and its inhibitor. PubMed Wang, Yi; Hu, Qiongzheng; Guo, Yongxian; Yu, Li 2015-10-15 In this paper, construction of the liquid crystal (LC)-based sensing platform for simple and sensitive detection of acetylcholinesterase (AChE) and its inhibitor using a cationic surfactant-decorated LC interface was demonstrated. A change of the optical images of LCs from bright to dark appearance was observed when the cationic surfactant, myristoylcholine chloride (Myr), was transferred onto the aqueous/LC interface, due to the formation of a stable surfactant monolayer at the interface. A dark-to-bright change of the optical appearance was then observed when AChE was transferred onto the Myr-decorated LC interface. The sensitivity of this new type of LC-based sensor is 3 orders of magnitude higher in the serum albumin solution than that only in the buffer solution. Noteworthy is that the AChE LC sensor shows a very high sensitivity for the detection of the enzyme inhibitor, which is around 1 fM. The constructed low-cost LC-based sensor is quite simple and convenient, showing high promise for label-free detection of AChE and its inhibitors. PMID:25957073 10. Acetylcholinesterase biosensor for inhibitor measurements based on glassy carbon electrode modified with carbon black and pillar[5]arene. PubMed Shamagsumova, Rezeda V; Shurpik, Dmitry N; Padnya, Pavel L; Stoikov, Ivan I; Evtugyn, Gennady A 2015-11-01 New acetylcholinesterase (AChE) biosensor based on unsubstituted pillar[5]arene (P[5]A) as electron mediator was developed and successfully used for highly sensitive detection of organophosphate and carbamate pesticides. The AChE from electric eel was immobilized by carbodiimide binding on carbon black (CB) placed on glassy carbon electrode. The working potential of 200mV was obtained in chronoamperometric mode with the measurement time of 180 s providing best inter-biosensors precision of the results. The AChE biosensor developed made it possible to detect 1×10(-11)-1×10(-6) M of malaoxon, 1×10(-8)-7×10(-6) M of methyl-paraoxon, 1×10(-10)-2×10(-6) M of carbofuran and 7×10(-9)-1×10(-5) M of aldicarb with 10 min incubation. The limits of detection were 4×10(-12), 5×10(-9), 2×10(-11) and 6×10(-10) M, respectively. The AChE biosensor was tested in the analysis of pesticide residuals in spiked samples of peanut and beetroot. The protecting effect of P[5]A derivative bearing quaternary ammonia groups on malaoxon inhibition was shown. 11. High yield production of a mutant Nippostrongylus brasiliensis acetylcholinesterase in Pichia pastoris and its purification. PubMed Richter, Sven; Nieveler, Jens; Schulze, Holger; Bachmann, Till T; Schmid, Rolf D 2006-04-01 The mutant M301A of the acetylcholinesterase B from Nippostrongylus brasiliensis (NbAChE) was produced in a high-cell-density fermentation of a recombinant methylotrophic yeast Pichia pastoris. Dissolved oxygen (DO) spikes were used as an indicator for feeding the carbon source. Wet cell weight (WCW) reached after 8 days a maximum value of 316 g/L and the OD600 at this time was 280. The acetylcholinesterase activity increased up to 6,600 U/mL corresponding to an expression rate of 2 g of NbAChE per liter supernatant. The specific activity of the mutant NbAChE was determined after purification as 3,300 U/mg. Active site titration with chlorpyrifos, a strong AChE inhibitor, yielded in a specific activity of 3,400 U/mg. The enzyme was secreted by Pichia pastoris. Therefore, it could be concentrated from culture broth by cross-flow-filtration (50 kDa cut-off membrane). It was further purified in one-step anion-exchange chromatography, using a XK 50/20 column filled with 125 mL Q Sepharose HP. Mutant NbAChE was purified 1.9-fold up to a purity of 97% and a yield of 87%. The isolated enzyme was nearly homogenous, as seen on the silver stained SDS-PAGE as well as by a single peak after gel filtration. This extraordinary high expression rate and the ease of purification is an important prerequisite for their practical application, for example in biosensors for the detection of neurotoxic insecticides. 12. Acetylcholinesterase inhibition, antioxidant activity and toxicity of Peumus boldus water extracts on HeLa and Caco-2 cell lines. PubMed Falé, P L; Amaral, F; Amorim Madeira, P J; Sousa Silva, M; Florêncio, M H; Frazão, F N; Serralheiro, M L M 2012-08-01 This work aimed to study the inhibition on acetylcholinesterase activity (AChE), the antioxidant activity and the toxicity towards Caco-2 and HeLa cells of aqueous extracts of Peumus Boldus. An IC(50) value of 0.93 mg/mL, for AChE inhibition, and EC(50) of 18.7 μg/mL, for the antioxidant activity, was determined. This activity can be attributed to glycosylated flavonoid derivatives detected, which were the main compounds, although boldine and other aporphine derivatives were also present. No changes in the chemical composition or the biochemical activities were found after gastrointestinal digestion. Toxicity of P. boldus decoction gave an IC(50) value 0.66 mg/mL for HeLa cells, which caused significant changes in the cell proteome profile. PMID:22617353 13. Plasma protein thiols, ceruloplasmin, C-reactive protein and red blood cell acetylcholinesterase in patients undergoing intrauterine insemination PubMed Central Prabhu, Krishnananda; Kumar, Pratap; Adiga, Satish Kumar; Rao, Anjali; Lanka, Anupama; Singh, Jaipal 2009-01-01 OBJECTIVE: To estimate acetylcholinesterase (AChE), protein thiols (PT), ceruloplasmin (CP) and C-reactive proteins (CRPs) to assess any change in their levels following intrauterine insemination (IUI). MATERIALS AND METHODS: Forty-two patients aged 31 ± 4.65 years (mean ± SD) with primary infertility selected for IUI. All of them had induced ovulation with clomiphene citrate 50 mg from day 2 to day 6. After taking the consent, 2 ml of blood was withdrawn before and after 24 h of IUI for biochemical estimations. RESULTS: We observed a significant decrease in plasma CP, PT and RBC AChE (P < 0.001) following IUI compared with the respective pre-procedure levels. Highly sensitive CRP showed a marginal increase after IUI. CONCLUSION: Fluctuations in levels of the above parameters point to their role in the female reproductive system and in the outcome of the IUI. PMID:19562071 14. [Distribution of acetylcholinesterase activity in the digestive system of the gastropod molluscs Littorina littorea and Achatina fulica]. PubMed Zaĭtseva, O V; Kuznetsova, T V 2008-01-01 With the use of the histochemical procedure for the demonstration of acetylcholinesterase (AchE) activity, the distribution cholinergic regulatory elements was studied in the esophagus, the pharynx, the stomach, the liver (the digestive gland) and the intestine in sea and terrestrial gastropod molluscs that differed in their general organization level, lifestyle, habitat and feeding type. In both molluscs, all the parts of the digestive tract contained the significant amount of intraepithelial AchE-positive cells of the open type, single subepithelial neurons and the nervous fibers localized among the muscle cells of the wall of the organs. The basal processes of the AchE-positive intraepithelial cells were shown to form the intraepithelial nerve plexus and to pass under the epithelium. The peculiarities and common principles in the distribution of the nervous elements detected, their possible function and the regulatory role in the digestion in gastropod molluscs and other animals are discussed. PMID:19069417 15. 3-Oxoisoxazole-2(3H)-carboxamides and isoxazol-3-yl carbamates: Resistance-breaking acetylcholinesterase inhibitors targeting the malaria mosquito, Anopheles gambiae PubMed Central Verma, Astha; Wong, Dawn M.; Islam, Rafique; Tong, Fan; Ghavami, Maryam; Mutunga, James M.; Slebodnick, Carla; Li, Jianyong; Viayna, Elisabet; Lam, Polo C.-H.; Totrov, Maxim M.; Bloomquist, Jeffrey R.; Carlier, Paul R. 2015-01-01 To identify potential selective and resistance-breaking mosquitocides against the African malaria vector Anopheles gambiae, we investigated the acetylcholinesterase (AChE) inhibitory and mosquitocidal properties of isoxazol-3-yl dimethylcarbamates (15), and the corresponding 3-oxoisoxazole-2(3H)-dimethylcarboxamide isomers (14). In both series, compounds were found with excellent contact toxicity to wild-type susceptible (G3) strain and multiply resistant (Akron) strain mosquitoes that carry the G119S resistance mutation of AChE. Compounds possessing good to excellent toxicity to Akron strain mosquitoes inhibit the G119S mutant of An. gambiae AChE (AgAChE) with ki values at least 10- to 600-fold higher than that of propoxur, a compound that does not kill Akron mosquitoes at the highest concentration tested. On average, inactivation of WT AgAChE by dimethylcarboxamides 14 was 10-20 fold faster than that of the corresponding isoxazol-3-yl dimethylcarbamates 15. X-ray crystallography of dimethylcarboxamide 14d provided insight into that reactivity, a finding that may explain the inhibitory power of structurally-related inhibitors of hormone-sensitive lipase. Finally, human/An. gambiae AChE inhibition selectivities of these compounds were low, suggesting the need for additional structural modification. PMID:25684426 16. Activation of phosphorothionate pesticides based on a cytochrome P450 BM-3 (CYP102 A1) mutant for expanded neurotoxin detection in food using acetylcholinesterase biosensors. PubMed Schulze, Holger; Schmid, Rolf D; Bachmann, Till T 2004-03-15 A novel enzymatic in vitro activation method for phosphorothionates has been developed to allow their detection with acetylcholinesterase (AChE) biosensors. Activation is necessary because this group of insecticides shows nearly no inhibitory effect toward AChE in their pure nonmetabolized form. In contrast, they exert a strong inhibitory effect on AChE after oxidation as it takes place by metabolic activation in higher organisms. Standard chemical methods to oxidize phosphorothionates showed inherent disadvantages that impede their direct use in food analysis. In contrast, a genetically engineered triple mutant of P450 BM-3 (CYP102 A1) could convert the two frequently used insecticides parathion and chlorpyrifos into their oxo variants as was confirmed by GC/MS measurements. The wild-type protein was unable to do so. In the case of chlorpyrifos, the enzymatic activation was as good as the chemical oxidation. In the case of parathion, the P450 activation was more efficient than the oxidation by NBS but neither activation method yielded an AChE inhibition that was as high as with paraoxon. The application of the method to infant food in combination with a disposable AChE biosensor enabled detection of chlorpyrifos and parathion at concentrations down to 20 microg/kg within an overall assay time of 95 min. PMID:15018574 17. Structural and functional characterization of the interaction of the photosensitizing probe methylene blue with Torpedo californica acetylcholinesterase PubMed Central Paz, Aviv; Roth, Esther; Ashani, Yacov; Xu, Yechun; Shnyrov, Valery L; Sussman, Joel L; Silman, Israel; Weiner, Lev 2012-01-01 The photosensitizer, methylene blue (MB), generates singlet oxygen that irreversibly inhibits Torpedo californica acetylcholinesterase (TcAChE). In the dark, it inhibits reversibly. Binding is accompanied by a bathochromic absorption shift, used to demonstrate displacement by other acetylcholinesterase inhibitors interacting with the catalytic “anionic” subsite (CAS), the peripheral “anionic” subsite (PAS), or bridging them. MB is a noncompetitive inhibitor of TcAChE, competing with reversible inhibitors directed at both “anionic” subsites, but a single site is involved in inhibition. MB also quenches TcAChE's intrinsic fluorescence. It binds to TcAChE covalently inhibited by a small organophosphate (OP), but not an OP containing a bulky pyrene. Differential scanning calorimetry shows an ∼8° increase in the denaturation temperature of the MB/TcAChE complex relative to native TcAChE, and a less than twofold increase in cooperativity of the transition. The crystal structure reveals a single MB stacked against Trp279 in the PAS, oriented down the gorge toward the CAS; it is plausible that irreversible inhibition is associated with photooxidation of this residue and others within the active-site gorge. The kinetic and spectroscopic data showing that inhibitors binding at the CAS can impede binding of MB are reconciled by docking studies showing that the conformation adopted by Phe330, midway down the gorge, in the MB/TcAChE crystal structure, precludes simultaneous binding of a second MB at the CAS. Conversely, binding of ligands at the CAS dislodges MB from its preferred locus at the PAS. The data presented demonstrate that TcAChE is a valuable model for understanding the molecular basis of local photooxidative damage. PMID:22674800 18. Nanoparticles Ease Aching Joints in Mice MedlinePlus ... page: https://medlineplus.gov/news/fullstory_161188.html Nanoparticles Ease Aching Joints in Mice Treatment might one ... News) -- New research in mice suggests that tiny nanoparticles might one day be a better way to ... 19. Acetylcholinesterase Inhibitors: Pharmacology and Toxicology PubMed Central Čolović, Mirjana B; Krstić, Danijela Z; Lazarević-Pašti, Tamara D; Bondžić, Aleksandra M; Vasić, Vesna M 2013-01-01 Acetylcholinesterase is involved in the termination of impulse transmission by rapid hydrolysis of the neurotransmitter acetylcholine in numerous cholinergic pathways in the central and peripheral nervous systems. The enzyme inactivation, induced by various inhibitors, leads to acetylcholine accumulation, hyperstimulation of nicotinic and muscarinic receptors, and disrupted neurotransmission. Hence, acetylcholinesterase inhibitors, interacting with the enzyme as their primary target, are applied as relevant drugs and toxins. This review presents an overview of toxicology and pharmacology of reversible and irreversible acetylcholinesterase inactivating compounds. In the case of reversible inhibitors being commonly applied in neurodegenerative disorders treatment, special attention is paid to currently approved drugs (donepezil, rivastigmine and galantamine) in the pharmacotherapy of Alzheimer’s disease, and toxic carbamates used as pesticides. Subsequently, mechanism of irreversible acetylcholinesterase inhibition induced by organophosphorus compounds (insecticides and nerve agents), and their specific and nonspecific toxic effects are described, as well as irreversible inhibitors having pharmacological implementation. In addition, the pharmacological treatment of intoxication caused by organophosphates is presented, with emphasis on oxime reactivators of the inhibited enzyme activity administering as causal drugs after the poisoning. Besides, organophosphorus and carbamate insecticides can be detoxified in mammals through enzymatic hydrolysis before they reach targets in the nervous system. Carboxylesterases most effectively decompose carbamates, whereas the most successful route of organophosphates detoxification is their degradation by corresponding phosphotriesterases. PMID:24179466 20. Catalytic-site conformational equilibrium in nerve-agent adducts of acetylcholinesterase: possible implications for the HI-6 antidote substrate specificity. PubMed Artursson, Elisabet; Andersson, Per Ola; Akfur, Christine; Linusson, Anna; Börjegren, Susanne; Ekström, Fredrik 2013-05-01 Nerve agents such as tabun, cyclosarin and Russian VX inhibit the essential enzyme acetylcholinesterase (AChE) by organophosphorylating the catalytic serine residue. Nucleophiles, such as oximes, are used as antidotes as they can reactivate and restore the function of the inhibited enzyme. The oxime HI-6 shows a notably low activity on tabun adducts but can effectively reactivate adducts of cyclosarin and Russian VX. To examine the structural basis for the pronounced substrate specificity of HI-6, we determined the binary crystal structures of Mus musculus AChE (mAChE) conjugated by cyclosarin and Russian VX and found a conformational mobility of the side chains of Phe338 and His447. The interaction between HI-6 and tabun-adducts of AChE were subsequently investigated using a combination of time resolved fluorescence spectroscopy and X-ray crystallography. Our findings show that HI-6 binds to tabun inhibited Homo sapiens AChE (hAChE) with an IC50 value of 300μM and suggest that the reactive nucleophilic moiety of HI-6 is excluded from the phosphorus atom of tabun. We propose that a conformational mobility of the side-chains of Phe338 and His447 is a common feature in nerve-agent adducts of AChE. We also suggest that the conformational mobility allow HI-6 to reactivate conjugates of cyclosarin and Russian VX while a reduced mobility in tabun conjugated AChE results in steric hindrance that prevents efficient reactivation. 1. Paper-based fluorescent sensor for rapid naked-eye detection of acetylcholinesterase activity and organophosphorus pesticides with high sensitivity and selectivity. PubMed Chang, Jiafu; Li, Haiyin; Hou, Ting; Li, Feng 2016-12-15 Various strategies have been proposed for the sensing of acetylcholinesterase (AChE) activity and organophosphorus pesticides (OPs). However, the practical application of most methods is restricted by their intrinsic drawbacks such as complexity, long analysis time, and high cost. Thus, it is highly desirable to develop simple, fast and sensitive approaches for AChE activity and OPs detection. Herein, we reported a simple paper-based fluorescent sensor (PFS) based on the aggregation induced emission (AIE) effect of tetraphenylethylene (TPE) and the addition reaction capability of maleimide, which has been used as a powerful tool for rapid naked-eye detection of AChE activity and OPs. The introduction of TPE provides the probe with unique fluorescence property in solid state and is of great importance for improving the sensitivity of PFS. The hydrolysis product of acetylthiocholine catalyzed by AChE induced the maleimide ring destruction and activated the fluorescence performance of TPE. Given that AChE activity can be specifically inhibited by OPs, the as-proposed PFS can also be utilized for sensitive detection of OPs. Meanwhile, the variation of fluorescence signal can be readily detected by naked eyes, and low detection limits of 2.5mUmL(-1) and 0.5ngmL(-1) for AChE activity and OPs are obtained, respectively. Moreover, it has been successfully applied for AChE activity and OPs detection in diluted human serum samples, showing its great potential to be applied in real samples. Thus, this strategy possesses considerable advantages of simplicity, rapid detection, portability, cost efficiency and visualization. PMID:27498323 2. Paper-based fluorescent sensor for rapid naked-eye detection of acetylcholinesterase activity and organophosphorus pesticides with high sensitivity and selectivity. PubMed Chang, Jiafu; Li, Haiyin; Hou, Ting; Li, Feng 2016-12-15 Various strategies have been proposed for the sensing of acetylcholinesterase (AChE) activity and organophosphorus pesticides (OPs). However, the practical application of most methods is restricted by their intrinsic drawbacks such as complexity, long analysis time, and high cost. Thus, it is highly desirable to develop simple, fast and sensitive approaches for AChE activity and OPs detection. Herein, we reported a simple paper-based fluorescent sensor (PFS) based on the aggregation induced emission (AIE) effect of tetraphenylethylene (TPE) and the addition reaction capability of maleimide, which has been used as a powerful tool for rapid naked-eye detection of AChE activity and OPs. The introduction of TPE provides the probe with unique fluorescence property in solid state and is of great importance for improving the sensitivity of PFS. The hydrolysis product of acetylthiocholine catalyzed by AChE induced the maleimide ring destruction and activated the fluorescence performance of TPE. Given that AChE activity can be specifically inhibited by OPs, the as-proposed PFS can also be utilized for sensitive detection of OPs. Meanwhile, the variation of fluorescence signal can be readily detected by naked eyes, and low detection limits of 2.5mUmL(-1) and 0.5ngmL(-1) for AChE activity and OPs are obtained, respectively. Moreover, it has been successfully applied for AChE activity and OPs detection in diluted human serum samples, showing its great potential to be applied in real samples. Thus, this strategy possesses considerable advantages of simplicity, rapid detection, portability, cost efficiency and visualization. 3. Naturally Occurring Genetic Variants of Human Acetylcholinesterase and Butyrylcholinesterase and Their Potential Impact on the Risk of Toxicity from Cholinesterase Inhibitors PubMed Central 2016-01-01 Acetylcholinesterase (AChE) is the physiologically important target for organophosphorus toxicants (OP) including nerve agents and pesticides. Butyrylcholinesterase (BChE) in blood serves as a bioscavenger that protects AChE in nerve synapses from inhibition by OP. Mass spectrometry methods can detect exposure to OP by measuring adducts on the active site serine of plasma BChE. Genetic variants of human AChE and BChE do exist, but loss of function mutations have been identified only in the BCHE gene. The most common AChE variant, His353Asn (H322N), also known as the Yt blood group antigen, has normal AChE activity. The most common BChE variant, Ala567Thr (A539T) or the K-variant in honor of Werner Kalow, has 33% reduced plasma BChE activity. The genetic variant most frequently associated with prolonged response to muscle relaxants, Asp98Gly (D70G) or atypical BChE, has reduced activity and reduced enzyme concentration. Early studies in young, healthy males, performed at a time when it was legal to test nerve agents in humans, showed that individuals responded differently to the same low dose of sarin with toxic symptoms ranging in severity from minimal to moderate. Additionally, animal studies indicated that BChE protects from toxicants that have a higher reactivity with AChE than with BChE (e.g., nerve agents) but not from toxicants that have a higher reactivity with BChE than with AChE (e.g., OP pesticides). As a corollary, we hypothesize that individuals with genetic variants of BChE may be at increased risk of toxicity from nerve agents but not from OP pesticides. PMID:27551784 4. The natural product dihydrotanshinone I provides a prototype for uncharged inhibitors that bind specifically to the acetylcholinesterase peripheral site with nanomolar affinity. PubMed Beri, Veena; Wildman, Scott A; Shiomi, Kazuro; Al-Rashid, Ziyad F; Cheung, Jonah; Rosenberry, Terrone L 2013-10-22 Cholinergic synaptic transmission often requires extremely rapid hydrolysis of acetylcholine by acetylcholinesterase (AChE). AChE is inactivated by organophosphates (OPs) in chemical warfare nerve agents. The resulting accumulation of acetylcholine disrupts cholinergic synaptic transmission and can lead to death. A potential long-term strategy for preventing AChE inactivation by OPs is based on evidence that OPs must pass through a peripheral site or P-site near the mouth of the AChE active site gorge before reacting with a catalytic serine in an acylation site or A-site at the base of the gorge. An ultimate goal of this strategy is to design compounds that bind tightly at or near the P-site and exclude OPs from the active site while interfering minimally with the passage of acetylcholine. However, to target the AChE P-site with ligands and potential drugs that selectively restrict access, much more information must be gathered about the structure-activity relationships of ligands that bind specifically to the P-site. We apply here an inhibitor competition assay that can correctly determine whether an AChE inhibitor binds to the P-site, the A-site, or both sites. We have used this assay to examine three uncharged, natural product inhibitors of AChE, including aflatoxin B1, dihydrotanshinone I, and territrem B. The first two of these inhibitors are predicted by the competition assay to bind selectively to the P-site, while territrem B is predicted to span both the P- and A-sites. These predictions have recently been confirmed by X-ray crystallography. Dihydrotanshinone I, with an observed binding constant (KI) of 750 nM, provides a good lead compound for the development of high-affinity, uncharged inhibitors with specificity for the P-site. PMID:24040835 5. Naturally Occurring Genetic Variants of Human Acetylcholinesterase and Butyrylcholinesterase and Their Potential Impact on the Risk of Toxicity from Cholinesterase Inhibitors. PubMed Lockridge, Oksana; Norgren, Robert B; Johnson, Rudolph C; Blake, Thomas A 2016-09-19 Acetylcholinesterase (AChE) is the physiologically important target for organophosphorus toxicants (OP) including nerve agents and pesticides. Butyrylcholinesterase (BChE) in blood serves as a bioscavenger that protects AChE in nerve synapses from inhibition by OP. Mass spectrometry methods can detect exposure to OP by measuring adducts on the active site serine of plasma BChE. Genetic variants of human AChE and BChE do exist, but loss of function mutations have been identified only in the BCHE gene. The most common AChE variant, His353Asn (H322N), also known as the Yt blood group antigen, has normal AChE activity. The most common BChE variant, Ala567Thr (A539T) or the K-variant in honor of Werner Kalow, has 33% reduced plasma BChE activity. The genetic variant most frequently associated with prolonged response to muscle relaxants, Asp98Gly (D70G) or atypical BChE, has reduced activity and reduced enzyme concentration. Early studies in young, healthy males, performed at a time when it was legal to test nerve agents in humans, showed that individuals responded differently to the same low dose of sarin with toxic symptoms ranging in severity from minimal to moderate. Additionally, animal studies indicated that BChE protects from toxicants that have a higher reactivity with AChE than with BChE (e.g., nerve agents) but not from toxicants that have a higher reactivity with BChE than with AChE (e.g., OP pesticides). As a corollary, we hypothesize that individuals with genetic variants of BChE may be at increased risk of toxicity from nerve agents but not from OP pesticides. PMID:27551784 6. Gold nanoclusters-Cu(2+) ensemble-based fluorescence turn-on and real-time assay for acetylcholinesterase activity and inhibitor screening. PubMed Sun, Jian; Yang, Xiurong 2015-12-15 Based on the specific binding of Cu(2+) ions to the 11-mercaptoundecanoic acid (11-MUA)-protected AuNCs with intense orange-red emission, we have proposed and constructed a novel fluorescent nanomaterials-metal ions ensemble at a nonfluorescence off-state. Subsequently, an AuNCs@11-MUA-Cu(2+) ensemble-based fluorescent chemosensor, which is amenable to convenient, sensitive, selective, turn-on and real-time assay of acetylcholinesterase (AChE), could be developed by using acetylthiocholine (ATCh) as the substrate. Herein, the sensing ensemble solution exhibits a marvelous fluorescent enhancement in the presence of AChE and ATCh, where AChE hydrolyzes its active substrate ATCh into thiocholine (TCh), and then TCh captures Cu(2+) from the ensemble, accompanied by the conversion from fluorescence off-state to on-state of the AuNCs. The AChE activity could be detected less than 0.05 mU/mL within a good linear range from 0.05 to 2.5 mU/mL. Our proposed fluorescence assay can be utilized to evaluate the AChE activity quantitatively in real biological sample, and furthermore to screen the inhibitor of AChE. As far as we know, the present study has reported the first analytical proposal for sensing AChE activity in real time by using a fluorescent nanomaterials-Cu(2+) ensemble or focusing on the Cu(2+)-triggered fluorescence quenching/recovery. This strategy paves a new avenue for exploring the biosensing applications of fluorescent AuNCs, and presents the prospect of AuNCs@11-MUA-Cu(2+) ensemble as versatile enzyme activity assay platforms by means of other appropriate substrates/analytes. PMID:26141104 7. Acetylcholinesterase Reactivators (HI-6, Obidoxime, Trimedoxime, K027, K075, K127, K203, K282): Structural Evaluation of Human Serum Albumin Binding and Absorption Kinetics PubMed Central Zemek, Filip; Zdarova, Jana Karasova; Sepsova, Vendula; Kuca, Kamil 2013-01-01 Acetylcholinesterase (AChE) reactivators (oximes) are compounds predominantly targeting the active site of the enzyme. Toxic effects of organophosphates nerve agents (OPNAs) are primarily related to their covalent binding to AChE and butyrylcholinesterase (BChE), critical detoxification enzymes in the blood and in the central nervous system (CNS). After exposure to OPNAs, accumulation of acetylcholine (ACh) overstimulates receptors and blocks neuromuscular junction transmission resulting in CNS toxicity. Current efforts at treatments for OPNA exposure are focused on non-quaternary reactivators, monoisonitrosoacetone oximes (MINA), and diacylmonoxime reactivators (DAM). However, so far only quaternary oximes have been approved for use in cases of OPNA intoxication. Five acetylcholinesterase reactivator candidates (K027, K075, K127, K203, K282) are presented here, together with pharmacokinetic data (plasma concentration, human serum albumin binding potency). Pharmacokinetic curves based on intramuscular application of the tested compounds are given, with binding information and an evaluation of structural relationships. Human Serum Albumin (HSA) binding studies have not yet been performed on any acetylcholinesterase reactivators, and correlations between structure, concentration curves and binding are vital for further development. HSA bindings of the tested compounds were 1% (HI-6), 7% (obidoxime), 6% (trimedoxime), and 5%, 10%, 4%, 15%, and 12% for K027, K075, K127, K203, and K282, respectively. PMID:23917882 8. Validating the importance of two acetylcholinesterases in insecticide sensitivities by RNAi in Pardosa pseudoannulata, an important predatory enemy against several insect pests. PubMed Meng, Xiangkun; Li, Chunrui; Bao, Haibo; Fang, Jichao; Liu, Zewen; Zhang, Yixi 2015-11-01 The pond wolf spider (Pardosa pseudoannulata) is an important predatory enemy against several insect pests and showed relative different sensitivities to organophosphate and carbamate insecticides compared to insect pests. In our previous studies, two acetylcholinesterases were identified in P. pseudoannulata and played important roles in insecticide sensitivities. In order to understand the contributions of the two acetylcholinesterases to insecticide sensitivities, we firstly employed the RNAi technology in the spider. For a suitable microinjection RNAi method, the injection site, injection volume and interference time were optimized, which then demonstrated that the injection RNAi method was applicable in this spider. With the new RNAi method, it was revealed that both Pp-AChE1 and Pp-AChE2, encoded by genes Ppace1 and Ppace2, were the targets of organophosphate insecticides, but Pp-AChE1 would be more important. In contrast, the carbamate acted selectively on Pp-AChE1. The results showed that Pp-AChE1 was the major catalytic enzyme in P. pseudoannulata and the major target of organophosphate and carbamate insecticides. In a word, an RNAi method was established in the pond wolf spider, which further validated the importance of two acetylcholinesterases in insecticide sensitivities in this spider. 9. Copper acutely impairs behavioral function and muscle acetylcholinesterase activity in zebrafish (Danio rerio). PubMed Haverroth, Gabriela M B; Welang, Chariane; Mocelin, Riciéri N; Postay, Daniela; Bertoncello, Kanandra T; Franscescon, Francini; Rosemberg, Denis B; Dal Magro, Jacir; Dalla Corte, Cristiane L 2015-12-01 Copper is a heavy metal found at relatively high concentrations in surface waters around the world. Copper is a micronutrient at low concentrations and is essential to several organisms. At higher concentrations copper can become toxic, which reveal the importance of studying the toxic effects of this metal on the aquatic life. Thus, the objective of this study was to evaluate the toxic effects of copper on the behavior and biochemical parameters of zebrafish (Danio rerio). Zebrafish were exposed for 24h at a concentration of 0.006 mg/L Cu. After the exposure period, behavioral profile of animals was recorded through 6 min using two different apparatuses tests: the Novel Tank and the Light-Dark test. After behavioral testing, animals were euthanized with a solution of 250 mg/L of tricaine (MS-222). Brain, muscle, liver and gills were extracted for analysis of parameters related to oxidative stress and accumulation of copper in these tissues. Acetylcholinesterase (AChE) activity was determined in brain and muscle. Results showed acute exposure to copper induces significant changes in behavioral profile of zebrafish by changing locomotion and natural tendency to avoid brightly lit area. On the other hand, there were no significant effects on parameters related to oxidative stress. AChE activity decreased significantly in zebrafish muscle, but there were no significant changes in cerebral AChE activity. Copper levels in tissues did not increase significantly compared to the controls. Taken together, these results indicate that a low concentration of copper can acutely affect behavioral profile of adult zebrafish which could be partially related to an inhibition on muscle AChE activity. These results reinforce the need of additional tests to establishment of safe copper concentrations to aquatic organisms and the importance of behavioral parameters in ecotoxicological studies. 10. Isolation and characterisation of acetylcholinesterase inhibitors from Aquilaria subintegra for the treatment of Alzheimer's disease (AD). PubMed 2014-02-01 Aquilaria subintegra, locally known as "Gaharu", belongs to the Thymelaeceae family. This plant's leaves have been claimed to be effective for the treatment of Alzheimer's disease (AD) by Malay traditional practitioner in Malaysia. In this research, the chloroform extracts of the leaves and stem of A. subintegra were tested for acetylcholinesterase (AChE) inhibitory activity. The Thin Layer Chromatography (TLC) results indicated the presence of phenols, flavonoids, terpenoids, and alkaloids compounds in the extracts. Analysis of the stem chloroform extracts with LCMS/MS displayed that it contains kaempferol 3,4,7-trimethyl ether. The AChE inhibitory activity of leaves and stem chloroform extracts and kaempferol were 80%, 93% and 85.8%, respectively. The Brine Shrimp Lethality Assay (BSLA) exhibited low to moderate toxicity of the chloroform extract from leaves (LC50=531.18 ± 49.53 μg/ml), the stem chloroform extract (LC50=407.34 ± 68.05 μg/ml) and kaempferol (LC50=762.41 ± 45.09 μg/ml). The extracts and kaempferol were not cytotoxic to human umbilical vein endothelial cells (HUVEC), human normal gastric epithelial cell line (GES-1) and human normal hepatic cell line (WRL-68). The effect of leaf and stem chloroform extracts and kaempferol were determined in the Radial Arm Maze (RAM) after administration by oral gavage to ICR male and female mice with valium-impaired memory. Administration of kaempferol to the mice significantly reduced the number of repeated entries into the arms of maze in males and females. In conclusion, the inhibition of AChE by leaf and stem chloroform extracts of A. subintegra could be due to the presence of kaempferol. This extract is safe for use as a natural AChE inhibitor as an alternative to berberine for the treatment of AD. PMID:24479629 11. Copper acutely impairs behavioral function and muscle acetylcholinesterase activity in zebrafish (Danio rerio). PubMed Haverroth, Gabriela M B; Welang, Chariane; Mocelin, Riciéri N; Postay, Daniela; Bertoncello, Kanandra T; Franscescon, Francini; Rosemberg, Denis B; Dal Magro, Jacir; Dalla Corte, Cristiane L 2015-12-01 Copper is a heavy metal found at relatively high concentrations in surface waters around the world. Copper is a micronutrient at low concentrations and is essential to several organisms. At higher concentrations copper can become toxic, which reveal the importance of studying the toxic effects of this metal on the aquatic life. Thus, the objective of this study was to evaluate the toxic effects of copper on the behavior and biochemical parameters of zebrafish (Danio rerio). Zebrafish were exposed for 24h at a concentration of 0.006 mg/L Cu. After the exposure period, behavioral profile of animals was recorded through 6 min using two different apparatuses tests: the Novel Tank and the Light-Dark test. After behavioral testing, animals were euthanized with a solution of 250 mg/L of tricaine (MS-222). Brain, muscle, liver and gills were extracted for analysis of parameters related to oxidative stress and accumulation of copper in these tissues. Acetylcholinesterase (AChE) activity was determined in brain and muscle. Results showed acute exposure to copper induces significant changes in behavioral profile of zebrafish by changing locomotion and natural tendency to avoid brightly lit area. On the other hand, there were no significant effects on parameters related to oxidative stress. AChE activity decreased significantly in zebrafish muscle, but there were no significant changes in cerebral AChE activity. Copper levels in tissues did not increase significantly compared to the controls. Taken together, these results indicate that a low concentration of copper can acutely affect behavioral profile of adult zebrafish which could be partially related to an inhibition on muscle AChE activity. These results reinforce the need of additional tests to establishment of safe copper concentrations to aquatic organisms and the importance of behavioral parameters in ecotoxicological studies. PMID:26386335 12. Design and prediction of new acetylcholinesterase inhibitor via quantitative structure activity relationship of huprines derivatives. PubMed Zhang, Shuqun; Hou, Bo; Yang, Huaiyu; Zuo, Zhili 2016-05-01 Acetylcholinesterase (AChE) is an important enzyme in the pathogenesis of Alzheimer's disease (AD). Comparative quantitative structure-activity relationship (QSAR) analyses on some huprines inhibitors against AChE were carried out using comparative molecular field analysis (CoMFA), comparative molecular similarity indices analysis (CoMSIA), and hologram QSAR (HQSAR) methods. Three highly predictive QSAR models were constructed successfully based on the training set. The CoMFA, CoMSIA, and HQSAR models have values of r (2) = 0.988, q (2) = 0.757, ONC = 6; r (2) = 0.966, q (2) = 0.645, ONC = 5; and r (2) = 0.957, q (2) = 0.736, ONC = 6. The predictabilities were validated using an external test sets, and the predictive r (2) values obtained by the three models were 0.984, 0.973, and 0.783, respectively. The analysis was performed by combining the CoMFA and CoMSIA field distributions with the active sites of the AChE to further understand the vital interactions between huprines and the protease. On the basis of the QSAR study, 14 new potent molecules have been designed and six of them are predicted to be more active than the best active compound 24 described in the literature. The final QSAR models could be helpful in design and development of novel active AChE inhibitors. 13. Paper-based acetylcholinesterase inhibition assay combining a wet system for organophosphate and carbamate pesticides detection PubMed Central Apilux, Amara; Isarankura-Na-Ayudhya, Chartchalerm; Tantimongcolwat, Tanawut; Prachayasittikul, Virapong 2015-01-01 A dramatic increase in pesticide usage in agriculture highlights the need for on-site monitoring for public health and safety. Here, a paper-based sensor combined with a wet system was developed for the simple and rapid screening of organophosphate (OP) and carbamate (CM) pesticides based on the inhibition of acetylcholinesterase (AChE). The paper-based sensor was designed as a foldable device consisting of a cover and detection sheets pre-prepared with indoxyl acetate and AChE, respectively. The paper-based sensor requires only the incubation of a sample on the test zone for 10 minutes, followed by closing of the foldable sheet to initiate the enzymatic reaction. Importantly, the buffer loading hole was additionally designed on the cover sheet to facilitate the interaction of the coated substrate and the immobilized enzyme. This subsequently facilitates the mixing of indoxyl acetate with AChE, resulting in the improved analytical performance of the sensor. The absence or decrease in blue color produced by the AChE hydrolysis of indoxyl acetate can be observed in the presence of OPs and CMs. Under optimized conditions and using image analysis, the limit of detection (LOD) of carbofuran, dichlorvos, carbaryl, paraoxon, and pirimicarb are 0.003, 0.3, 0.5, 0.6, and 0.6 ppm, respectively. The assay could be applied to determine OP and CM residues in spiked food samples. Visual interpretation of the color signal was clearly observed at the concentration of 5 mg/kg. Furthermore, a self-contained sample pre-concentration approach greatly enhanced the detection sensitivity. The paper-based device developed here is low-cost, requires minimal reagents and is easy to handle. As such, it would be practically useful for pesticide screening by non-professional end-users. PMID:26417364 14. Paper-based acetylcholinesterase inhibition assay combining a wet system for organophosphate and carbamate pesticides detection. PubMed Apilux, Amara; Isarankura-Na-Ayudhya, Chartchalerm; Tantimongcolwat, Tanawut; Prachayasittikul, Virapong 2015-01-01 A dramatic increase in pesticide usage in agriculture highlights the need for on-site monitoring for public health and safety. Here, a paper-based sensor combined with a wet system was developed for the simple and rapid screening of organophosphate (OP) and carbamate (CM) pesticides based on the inhibition of acetylcholinesterase (AChE). The paper-based sensor was designed as a foldable device consisting of a cover and detection sheets pre-prepared with indoxyl acetate and AChE, respectively. The paper-based sensor requires only the incubation of a sample on the test zone for 10 minutes, followed by closing of the foldable sheet to initiate the enzymatic reaction. Importantly, the buffer loading hole was additionally designed on the cover sheet to facilitate the interaction of the coated substrate and the immobilized enzyme. This subsequently facilitates the mixing of indoxyl acetate with AChE, resulting in the improved analytical performance of the sensor. The absence or decrease in blue color produced by the AChE hydrolysis of indoxyl acetate can be observed in the presence of OPs and CMs. Under optimized conditions and using image analysis, the limit of detection (LOD) of carbofuran, dichlorvos, carbaryl, paraoxon, and pirimicarb are 0.003, 0.3, 0.5, 0.6, and 0.6 ppm, respectively. The assay could be applied to determine OP and CM residues in spiked food samples. Visual interpretation of the color signal was clearly observed at the concentration of 5 mg/kg. Furthermore, a self-contained sample pre-concentration approach greatly enhanced the detection sensitivity. The paper-based device developed here is low-cost, requires minimal reagents and is easy to handle. As such, it would be practically useful for pesticide screening by non-professional end-users. PMID:26417364 15. Isolation and characterisation of acetylcholinesterase inhibitors from Aquilaria subintegra for the treatment of Alzheimer's disease (AD). PubMed 2014-02-01 Aquilaria subintegra, locally known as "Gaharu", belongs to the Thymelaeceae family. This plant's leaves have been claimed to be effective for the treatment of Alzheimer's disease (AD) by Malay traditional practitioner in Malaysia. In this research, the chloroform extracts of the leaves and stem of A. subintegra were tested for acetylcholinesterase (AChE) inhibitory activity. The Thin Layer Chromatography (TLC) results indicated the presence of phenols, flavonoids, terpenoids, and alkaloids compounds in the extracts. Analysis of the stem chloroform extracts with LCMS/MS displayed that it contains kaempferol 3,4,7-trimethyl ether. The AChE inhibitory activity of leaves and stem chloroform extracts and kaempferol were 80%, 93% and 85.8%, respectively. The Brine Shrimp Lethality Assay (BSLA) exhibited low to moderate toxicity of the chloroform extract from leaves (LC50=531.18 ± 49.53 μg/ml), the stem chloroform extract (LC50=407.34 ± 68.05 μg/ml) and kaempferol (LC50=762.41 ± 45.09 μg/ml). The extracts and kaempferol were not cytotoxic to human umbilical vein endothelial cells (HUVEC), human normal gastric epithelial cell line (GES-1) and human normal hepatic cell line (WRL-68). The effect of leaf and stem chloroform extracts and kaempferol were determined in the Radial Arm Maze (RAM) after administration by oral gavage to ICR male and female mice with valium-impaired memory. Administration of kaempferol to the mice significantly reduced the number of repeated entries into the arms of maze in males and females. In conclusion, the inhibition of AChE by leaf and stem chloroform extracts of A. subintegra could be due to the presence of kaempferol. This extract is safe for use as a natural AChE inhibitor as an alternative to berberine for the treatment of AD. 16. Expression of APP, BACE1, AChE and ChAT in an AD model in rats and the effect of donepezil hydrochloride treatment. PubMed Li, Qiang; Chen, Min; Liu, Hongmin; Yang, Liqun; Yang, Guiying 2012-12-01 The aim of this study was to investigate the pathological changes in a rat model of Alzheimer's disease (AD) and the effect of donepezil hydrochloride (HCl) treatment. The rat model of AD was established by the bilateral injection of amyloid β₁₋₄₀ (Aβ₁₋₄₀) into the hippocampus. Changes in spatial learning and memory functions were examined using the Morris water maze test and changes in catalase (CAT) and glutathione peroxidase (GSH-Px) activities were determined using chemical colorimetry. Moreover, the changes in acetylcholinesterase (AChE) and choline acetyltransferase (ChAT) expression were analyzed using immunohistochemical staining. The mRNA expression levels of the amyloid precursor protein (APP) and β-secreted enzyme 1 (BACE1) were evaluated using RT-PCR. The effects of donepezil HCl on the aforementioned indices were also observed. The rat memories of the platform quadrants in the blank, sham and donepezil HCl groups were improved compared with those of the rats in the model group. The ratio of swim distance in the fourth platform quadrant (l₄) to the total swim distance (l total) for the model group rats (l₄/l total) was significantly decreased compared with that for the blank and sham group rats. Following donepezil HCl treatment, the ratio of l₄/l total significantly increased. AD modeling caused a significant decrease in the CAT and GSH-Px activities in the brain tissues of the rats. The CAT and GSH-Px activities in the AD model rats significantly increased following donepezil HCl treatment. Moreover, donepezil HCl treatment significantly decreased the AChE, APP and BACE1 mRNA expression levels and increased the ChAT expression levels. Therefore, donepezil HCl was able to significantly decrease learning and memory damage in a rat model of AD. 17. Cyperus rotundus extract inhibits acetylcholinesterase activity from animal and plants as well as inhibits germination and seedling growth in wheat and tomato. PubMed Sharma, Rashmi; Gupta, Rajendra 2007-05-30 Cyperus rotundus (nutgrass) is the world's worst invasive weed through tubers. Its success in dominating natural habitats depends on its ability to prevent herbivory, and to kill or suppress other plants growing in its vicinity. The present study was done to investigate whether chemicals in nutgrass target neuronal and non-neuronal acetylcholinesterases to affect surrounding animals and plants respectively. Methanolic extract of tubers of nutgrass strongly inhibited activity of AChE from electric eel, wheat and tomato. It also inhibited seed germination and seedling growth in wheat and tomato. Our results suggest that inhibitor of AChE in nutgrass possibly acts as agent of plant's war against (a) herbivore animals, and (b) other plants trying to grow in the same habitat. An antiAChE from nutgrass has been purified by employing chromatography and crystallization. The structural determination of the purified inhibitor is in progress. 18. Acetylcholinesterase 1 in populations of organophosphate-resistant North American strains of the cattle tick, Rhipicephalus microplus (Acari: Ixodidae). PubMed Bendele, Kylie G; Guerrero, Felix D; Miller, Robert J; Li, Andrew Y; Barrero, Roberto A; Moolhuijzen, Paula M; Black, Michael; McCooke, John K; Meyer, Jason; Hill, Catherine A; Bellgard, Matthew I 2015-08-01 Rhipicephalus microplus, the cattle fever tick, is a global economic problem to the cattle industry due to direct infestation of cattle and pathogens transmitted during feeding. Cattle fever tick outbreaks continue to occur along the Mexico-US border even though the tick has been eradicated from the USA. The organophosphate (OP) coumaphos targets acetylcholinesterase (AChE) and is the approved acaricide for eradicating cattle fever tick outbreaks. There is evidence for coumaphos resistance developing in cattle ticks in Mexico, and OP-resistant R. microplus ticks were discovered in outbreak populations of Texas in 2005. The molecular basis of coumaphos resistance is not known, and our study was established to gather further information on whether AChE1 is involved in the resistance mechanism. We also sought information on allele diversity in tick populations with different levels of coumaphos resistance. The overarching project goal was to define OP resistance-associated gene mutations such that a DNA-based diagnostic assay could be developed to assist the management of resistance. Three different AChE transcripts have been reported in R. microplus, and supporting genomic and transcriptomic data are available at CattleTickBase. Here, we report the complete R. microplus AChE1 gene ascertained by sequencing a bacterial artificial chromosome clone containing the entire coding region and the flanking 5' and 3' regions. We also report AChE1 sequences of larval ticks from R. microplus strains having different sensitivities to OP. To accomplish this, we sequenced a 669-bp region of the AChE1 gene corresponding to a 223 amino acid region of exon 2 to assess alleles in seven strains of R. microplus with varying OP resistance phenotypes. We identified 72 AChE1 sequence variants, 2 of which are strongly associated with OP-resistant phenotypes. Esterase-like sequences from the R. microplus transcriptome RmiTr Version 1.0 were compared to the available sequence databases to 19. Acetylcholinesterase inhibition by biofumigant (Coumaran) from leaves of Lantana camara in stored grain and household insect pests. PubMed Rajashekar, Yallappa; Raghavendra, Anjanappa; Bakthavatsalam, Nandagopal 2014-01-01 Recent studies proved that the biofumigants could be an alternative to chemical fumigants against stored grain insect pests. For this reason, it is necessary to understand the mode of action of biofumigants. In the present study the prospectus of utilising Lantana camara as a potent fumigant insecticide is being discussed. Inhibition of acetylcholinesterase (AChE) by Coumaran, an active ingredient extracted from the plant L. camara, was studied. The biofumigant was used as an enzyme inhibitor and acetylthiocholine iodide as a substrate along with Ellman's reagent to carry out the reactions. The in vivo inhibition was observed in both dose dependent and time dependent in case of housefly, and the nervous tissue (ganglion) and the whole insect homogenate of stored grain insect exposed to Coumaran. The possible mode of action of Coumaran as an acetylcholinesterase inhibitor is discussed. 20. Antioxidant and anti-acetylcholinesterase activities of extracts and secondary metabolites from Acacia cyanophylla PubMed Central Ghribia, Lotfi; Ghouilaa, Hatem; Omrib, Amel; Besbesb, Malek; Janneta, Hichem Ben 2014-01-01 Objective To investigate the antioxidant potential and anti-acetycholinesterase activity of compounds and extracts from Acacia cyanophylla (A. cyanophylla). Methods Three polyphenolic compounds were isolated from ethyl acetate extract of A. cyanophylla flowers. They have been identified as isosalipurposide 1, quercetin 2 and naringenin 3. Their structures were elucidated by extensive spectroscopic methods including 1D and 2D NMR experiments as well as ES-MS. The prepared extracts and the isolated compounds 1-3 were tested for their antioxidant activity using 1′-1′-diphenylpicrylhydrazyl (DPPH) and 2,2′-azinobis(3-ethylbenzothiazoline-6-sulfonic acid) scavenging assays and reducing power. They have been also investigated for inhibitory effect against acetylcholinesterase using the microplate assay. Results In the DPPH test, the EtOAc extract of flowers exhibited the highest antioxidant effect (67.26 µg/mL). Isosalipurposide 1 showed a significant antiradical power against DPPH (81.9 µg/mL). All extracts showed a dose-dependent acetylcholinesterase inhibition. In terms of the IC50 value, the butanolic extract (16.03 µg/mL) was the most potent sample. Isosalipurposide 1 was found to be active against AChE with an IC50 value of 52.04 µg/mL. Conclusions The results demonstrated the important antioxidant and anti-acetylcholinesterase activity of pure compounds and extracts from A. cyanophylla. PMID:25183120 1. Interaction of human brain acetylcholinesterase with cyclophosphamide: a molecular modeling and docking study. PubMed Shakil, Shazi; Khan, Rosina; Tabrez, Shams; Alam, Qamre; Jabir, Nasimudeen R; Sulaiman, Mansour I; Greig, Nigel H; Kamal, Mohammad A 2011-11-01 This study describes the interaction between human acetylcholinesterase (AChE), a key regulator of central and peripheral cholinergic function, and the widely used nitrogen mustard alkylating agent, cyclophosphamide (CP). Modeling of the AChE sequence (NCBI Accession No: AAI05061.1) was performed using 'Swiss Model Workspace'. The protein-model was submitted to the Protein Model Database and was assigned accession number PM0077393. A plot showing normalized QMEAN scores versus protein size was made to compare the model with a non-redundant set of Protein Data Bank structures, which gave a Z-score QMEAN as -0.58. The predicted local error for the modeled structure was found to be well within tolerable limits. Z-score values for Cβ interaction, all atom interaction, solvation and torsion were found to be -1.10, -0.90, -0.06 and -0.40, respectively. Docking between CP and AChE was performed using 'Autodock4.2'. Apart from other interaction-types, six carbon atoms of CP (C1, C2, C3, C4, C6 and C7) were determined to be involved in hydrophobic interactions with amino acid residues Y121, W233, L323, F331, F335 and Y338 of the 'acyl pocket' within AChE. Five carbon atoms of CP (C2, C4, C5, C6 and C7) were involved in hydrophobic interactions with 3 amino acid residues within the enzyme's 'catalytic site'. In conclusion, hydrophobic interactions play a major role in the appropriate positioning of CP within the 'acyl pocket' as well as 'catalytic site' of AChE to permit suitable orientation and allow docking. This information may aid the design of more potent and versatile AChE-inhibitors as pharmacologic tools and drugs to characterize and treat neurological disorders, and additionally provides a model whose value can be quantitatively assessed by X-ray crystallographic analysis of the AChECP three-dimensional structure. 2. Dose-limiting inhibition of acetylcholinesterase by ladostigil results from the rapid formation and fast hydrolysis of the drug-enzyme complex formed by its major metabolite, R-MCPAI. PubMed Moradov, Dorit; Finkin-Groner, Efrat; Bejar, Corina; Sunita, Priyashree; Schorer-Apelbaum, Donna; Barasch, Dinorah; Nemirovski, Alina; Cohen, Marganit; Weinstock, Marta 2015-03-15 3. Can hydroxylamine be a more potent nucleophile for the reactivation of tabun-inhibited AChE than prototype oxime drugs? An answer derived from quantum chemical and steered molecular dynamics studies. PubMed Lo, Rabindranath; Ganguly, Bishwajit 2014-07-29 Organophosphorus nerve agents are highly toxic compounds which strongly inhibit acetylcholinesterase (AChE) in the blood and in the central nervous system (CNS). Tabun is one of the highly toxic organophosphorus (OP) compounds and is resistant to many oxime drugs formulated for the reactivation of AChE. The reactivation mechanism of tabun-conjugated AChE with various drugs has been examined with density functional theory and ab initio quantum chemical calculations. The presence of a lone-pair located on the amidic group resists the nucleophilic attack at the phosphorus center of the tabun-conjugated AChE. We have shown that the newly designed drug candidate N-(pyridin-2-yl)hydroxylamine, at the MP2/6-31+G//M05-2X/6-31G* level in the aqueous phase with the polarizable continuum solvation model (PCM), is more effective in reactivating the tabun-conjugated AChE than typical oxime drugs. The rate determining activation barrier with N-(pyridin-2-yl)hydroxylamine was found to be ∼1.7 kcal mol(-1), which is 7.2 kcal mol(-1) lower than the charged oxime trimedoxime (one of the most efficient reactivators in tabun poisonings). The greater nucleophilicity index (ω(-)) and higher CHelpG charge of pyridinylhydroxylamine compared to TMB4 support this observation. Furthermore, we have also examined the reactivation process of tabun-inhibited AChE with some other bis-quaternary oxime drug candidates such as methoxime (MMB4) and obidoxime. The docking analysis suggests that charged bis-quaternary pyridinium oximes have greater binding affinity inside the active-site gorge of AChE compared to the neutral pyridinylhydroxylamine. The peripheral ligand attached to the neutral pyridinylhydroxylamine enhanced the binding with the aromatic residues in the active-site gorge of AChE through effective π-π interactions. Steered molecular dynamics (SMD) simulations have also been performed with the charged oxime (TMB4) and the neutral hydroxylamine. From protein-drug interaction 4. Association between acetylcholinesterase inhibitors and risk of stroke in patients with dementia PubMed Central Lin, Yi-Ting; Wu, Ping-Hsun; Chen, Cheng-Sheng; Yang, Yi-Hsin; Yang, Yuan-Han 2016-01-01 Patients with dementia are at increased risk of stroke. Acetylcholinesterase inhibitors (AChEIs) have endothelial function protection effects and anti-inflammatory properties. We investigated the ischemic stroke risk in AChEIs use in dementia patients without stroke history. Using Taiwan National Health Insurance Database from 1999 to 2008, 37,352 dementia patients over 50 years old without stroke history were eligible. The results were analyzed by propensity score–matched Cox proportional hazard models with competing risk adjustment. AChEIs users had lower incidence of ischemic stroke (160.3/10,000 person-years), compared to the propensity score–matched reference (240.8/10,000 person-years). The adjusted hazard ratio for ischemic stroke based on propensity score–matched Cox proportional hazard model was 0.508 (95% confidence interval, 0.434–0.594; P < 0.001). There was no significant difference in all-cause mortality between AChEIs users and nonusers. In conclusion, among dementia patients without previous ischemic stroke history, AChEIs treatment was associated with a decreased risk of ischemic stroke but not greater survival. PMID:27377212 5. Differences between male and female rhesus monkey erythrocyte acetylcholinesterase and plasma cholinesterase activity before and after exposure to sarin SciTech Connect Woodard, C.L.; Calamaio, C.A.; Kaminskis, A.; Anderson, D.R.; Harris, L.W. 1993-05-13 The female rhesus monkey has a menstrual cycle like the human. Additionally, several differences in enzyme levels between males and females and in the female during the menstrual cycle are present. Therefore we quantitated plasma cholinesterase (ChE/BuChE) and erythrocyte (RBC) acetylcholinesterase (AChE) activity before and after exposure to sarin (GB)(1 5 ug/kg, iv; a 0.75 LD50), in male and female rhesus (Macaca mulatta) monkeys. Twenty-eight-day preexposure baseline plasma ChE and RBC AChE values for six male and six female rhesus monkeys were compared for intra-animal, within sex and between sex differences. After these baseline values were obtained, the organophosphorus (OP) compound/Isopropyl methylphosphono-fluoridate (GB) was administered to atropinized monkeys to determine if there was a significant in vivo difference between the sexes in their response to this intoxication in regard to the rate of BuChE /AChE inhibition, pyridine-2-aldoxime methyl chloride (2-PAM) reactivation of the phosphonylated BuChE and the rate of aging of the phosphonylated:BuChE/AChE. In the pre-exposure portion of the protocol; the intra-animal and intra-group BuChE/AChE variations were found to be minimal; but there were significant differences between the male and female monkeys in both plasma BuChE and RBC AChE levels; although probably clinically insignificant in respect to an OP intoxication. No significant cyclic fluctuations were seen during the 28-day study in either sex. 6. Study of acetylcholinesterase activity in rectal suction biopsy for diagnosis of intestinal dysganglionoses: 17-year experience of a single center. PubMed Santos, Maria Mercês; Tannuri, Uenis; Coelho, Maria Cecília M 2008-06-01 Although the utility of the acetylcholinesterase (AChE) histochemistry on rectal suction biopsy in diagnosing Hirschsprung's disease (HD) has been documented, few reports address a great number of biopsies and patients. Our aim is to present a 17-year experience on the method of rectal suction biopsy and AChE histochemical staining for diagnosis of intestinal dysganglionoses. Between August 1989 and July 2006, 297 children suspected of having HD were submitted to rectal suction biopsies that were evaluated by the same two surgeons. There were 18 complications (6.0%), namely one self-limited rectal bleeding and 17 (5.7%) inadequate procedures that were repeated. A total of 157 patients (52.8%) showed no increased AChE activity and the remaining patients (140-47.2.0%) presented patterns of increased AChE activity confirming the diagnosis of HD or neuronal intestinal dysplasia. Among the 140 cases suspected as having HD, in 131 children the diagnosis of HD was confirmed and they were operated on. The histological studies showed that 111 children presented the classic form of HD or a long spastic segment. Sixteen children presented total colonic aganglionosis and four children proved to have intestinal neuronal dysplasia, according to histological and radiological criteria. Nine (6.6%) newborns were identified as false-positives and no false-negative results were verified. The rectal suction biopsy combined with AChE staining is advantageous for the differentiation between normal bowel and intestinal dysganglionoses. The rectal suction method is simple and can easily be performed by experienced surgeons. The histological evaluation is very objective and can be performed by a non-pathologist. 7. Enhanced pesticide sensitivity of novel housefly acetylcholinesterases: a new tool for the detection of residual pesticide contamination. PubMed Tan, Furong; Wang, Ligang; Wang, Jinbin; Wu, Xiao; Zhu, Hong; Jiang, Lingxi; Tao, Shiru; Zhao, Kai; Yang, Yan; Tang, Xueming 2011-03-01 The full-length cDNA encoding an acetylcholinesterase (AChE) was cloned and sequenced from the housefly, Musca domestica, by reverse transcriptase-polymerase chain reaction (RT-PCR). Sequence analysis revealed that this 2,076 bp sequence encodes a mature protein of 612 amino acids (67 kDa) and a 79 residue signal peptide. The amino acid sequence shared 52.8-81.4% identity with the AChE proteins of other insects. The cDNA sequence, which lacked the signal peptide was inserted into the vector pPIC9K and then introduced into strain GS115 of the yeast Pichia pastoris. The recombinant AChE protein was then expressed in P. pastoris strain GS115 by methanol induction. Site-directed mutagenesis of the A262G, Y327F, Y327D and I374D residues, either singly or in combination, was performed by reverse PCR. These mutants improved the catalytic activity and sensitivity to the organophosphate and carbamate insecticides. Although the sensitivity of other mutants was slightly increased, the results still showed that the sensitivity of triple mutant, GDD (A262G/Y327D/I374D), enhanced remarkably as much as 16 times for methomyl, 14 times for both carbofuran and chlorpyrifos, and ten times for parathion-methyl, compared to that of the wild-type. The results strongly suggested that these residues are the key structural elements controlling AChE enzyme catalytic activity and sensitivity to inhibition by insecticides. The AChE enzyme obtained by this method could be used to detect the organophosphate and carbamate insecticide residues in fruits and vegetables, a characteristic of great potential research and industrial application. 8. Brain regional acetylcholinesterase activity and muscarinic acetylcholine receptors in rats after repeated administration of cholinesterase inhibitors and its withdrawal SciTech Connect Kobayashi, Haruo . E-mail: hk1664@iwate-u.ac.jp; Suzuki, Tadahiko; Sakamoto, Maki; Hashimoto, Wataru; Kashiwada, Keiko; Sato, Itaru; Akahori, Fumiaki; Satoh, Tetsuo 2007-03-15 Activity of acetylcholinesterase (AChE) and specific binding of [{sup 3}H]quinuclidinyl benzilate (QNB), [{sup 3}H]pirenzepine (PZP) and [{sup 3}H]AF-DX 384 to muscarinic acetylcholine receptor (mAChR) preparations in the striatum, hippocampus and cortex of rats were determined 1, 6 and 11 days after the last treatment with an organophosphate DDVP, a carbamate propoxur or a muscarinic agonist oxotremorine as a reference for 7 and 14 days. AChE activity was markedly decreased in the three regions 1 day after the treatment with DDVP for 7 and 14 days with a gradual recovery 6 to 11 days, and much less decreased 1, 6 and 11 days after the treatment with propoxur for 7 days but not for 14 days in the hippocampus and cortex. The binding of [{sup 3}H]-QNB, PZP and AF-DX 384 in the three regions was generally decreased by the treatment with DDVP for 7 and 14 days. Such down-regulations were generally restored 6 or 11 days after the treatment for 7 but not for 14 days. The down-regulation or up-regulation as measured by [{sup 3}H]-QNB, PZP and AF-DX 384 was observed 1, 6 or 11 days after treatment with propoxur for 7 days and/or 14 days. Repeated treatment with oxotremorine produced similar effects except AChE activity to DDVP. These results suggest that repeated inhibition of AChE activity may usually cause down-regulation of mAChRs with some exception in the hippocampus when a reversible antiChE propoxur is injected. 9. AMPA receptor potentiation by acetylcholinesterase is age-dependently upregulated at synaptogenesis sites of the rat brain PubMed Central Olivera, Silvia; Henley, Jeremy M.; Rodriguez-Ithurralde, Daniel 2012-01-01 We have used radioligand binding to synaptic membranes from distinct rat brain regions and quantitative autoradiography to investigate the postnatal evolution of acetylcholinesterase (AChE)-evoked up-regulation of α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid (AMPA) receptors in CNS areas undergoing synaptogenesis. Incubation of synaptosomal membranes or brain sections with purified AChE caused a developmentally modulated enhancement in the binding of [3H]-(S)–AMPA and the specific AMPA receptor ligand [3H]-(S)-5–fluorowillardiine, but did not modify binding to kainate neither N-methyl-D-aspartate receptors. In all postnatal ages investigated (4, 7, 14, 20, 27, 40 days-old and adult rats), AChE effect on binding was concentration-dependent and blocked by propidium, BW 284c51, diisopropylfluorophosphonate and eserine, therefore requiring indemnity of both peripheral and active sites of the enzyme. AChE-mediated enhancement of [3H]-fluorowillardiine binding was measurable in all major CNS areas, but displayed remarkable anatomical selectivity and developmental regulation. Autoradiograph densitometry exhibited distinct temporal profiles and peaks of treated/control binding ratios for different cortices, cortical layers, and nuclei. Within the parietal, occipital and temporal neocortices, hippocampal CA1 field and cerebellum, AChE-potentiated binding ratios peaked in chronological correspondence with synaptogenesis periods of the respective AMPA-receptor containing targets. This modulation of AMPA receptors by AChE is a molecular mechanism able to transduce localized neural activity into durable modifications of synaptic molecular structure and function. It might also contribute to AChE-mediated neurotoxicity, as postulated in Alzheimer’s disease and other CNS disorders. PMID:12565696 10. Postnatal growth hormone deficiency in growing rats causes marked decline in the activity of spinal cord acetylcholinesterase but not butyrylcholinesterase. PubMed Koohestani, Faezeh; Brown, Chester M; Meisami, Esmail 2012-11-01 The effects of growth hormone (GH) deficiency on the developmental changes in the abundance and activity of cholinesterase enzymes were studied in the developing spinal cord (SC) of postnatal rats by measuring the specific activity of acetylcholinesterase (AChE), a marker for cholinergic neurons and their synaptic compartments, and butyrylcholinesterase (BuChE), a marker for glial cells and neurovascular cells. Specific activities of these two enzymes were measured in SC tissue of 21- and 90 day-old (P21, weaning age; P90, young adulthood) GH deficient spontaneous dwarf (SpDwf) mutant rats which lack anterior pituitary and circulating plasma GH, and were compared with SC tissue of normal age-matched control animals. Assays were carried out for AChE and BuChE activity in the presence of their specific chemical inhibitors, BW284C51 and iso-OMPA, respectively. Results revealed that mean AChE activity was markedly and significantly reduced [28% at P21, 49% at P90, (p<0.01)] in the SC of GH deficient rats compared to age-matched controls. GH deficiency had a higher and more significant effect on AChE activity of the older (P90) rats than the younger ones (P21) ones. In contrast, BuChE activity in SC showed no significant changes in GH deficient rats at either of the two ages studied. Results imply that, in the absence of pituitary GH, the postnatal proliferation of cholinergic synapses in the rat SC, a CNS structure, where AChE activity is abundant, is markedly reduced during both the pre- and postweaning periods; more so in the postweaning than preweaning ages. In contrast, the absence of any effects on BuChE activity implies that GH does not affect the development of non-neuronal elements, e.g., glia, as much as the neuronal and synaptic compartments of the developing rat SC. PMID:22922167 11. Local salt substitutes "Obu-otoyo" activate acetylcholinesterase and butyrylcholinesterase and induce lipid peroxidation in rat brain. PubMed 2015-09-01 Evidence has shown that ingestion of heavy metals can lead to neurodegenerative diseases. This study aimed to investigate the neurotoxic potential of salt substitutes (Obu-Otoyo); salt A (made by burning palm kernel shaft then soaked in water overnight and the extract from the resulting residue is used as the salt substitute) and salt B (an unrefined salt mined from a local site at Ilobu town, Osun-State, Nigeria) by assessing their effect on some key enzymes linked with neurodegenerative disease [acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) activities] as well as on malondialdehyde (MDA) content of the rat brain. Salt substitutes were fed to normal rats as dietary inclusion at doses of 0.5 and 1.0% for 30 days. Thereafter, the effect of the salt substitutes on AChE and BChE activities as well as on MDA level in the rat brain was determined. The results revealed that the salt substitutes caused a significant (p<0.05) increase in both AChE and BChE activity and also induced lipid peroxidation in the brain of rats in vivo as well as under in vitro condition in a dose-dependent manner. The effect of the salt substitutes on AChE and BChE activities could be attributed to the presence of some toxic heavy metals. Therefore, the ability of the salt substitutes to induce lipid peroxidation and activate AChE and BChE activities could provide some possible mechanism for their neurotoxic effect. PMID:27486373 12. Role of aqueous extract of Cynodon dactylon in prevention of carbofuran- induced oxidative stress and acetylcholinesterase inhibition in rat brain. PubMed Rai, D K; Sharma, R K; Rai, P K; Watal, G; Sharma, B 2011-02-12 The present study was designed to investigate the ameliorating effect of aqueous extract of C. dactylon on carbofuran induced oxidative stress (OS) and alterations in the activity of acetylcholinesterase (AChE) in the brain of rats. Vitamin C was used as a positive control. Wistar rats were administered with single sub-acute oral dose (1.6 mgkg-1 b.wt.) of carbofuran for 24 h. The OS parameters such as lipid peroxidation (LPO) and the activities of antioxidant enzymes including super oxide dismutase (SOD), catalase (CAT) and glutathione-S-transferase (GST), and that of AChE were studied in brain. Carbofuran treatment significantly increased the activities of SOD and CAT by 75 and 60%, respectively. It also induced the level of LPO by 113%. In contrast, the activities of GST and AChE were recorded to be diminished by 25 and 33%, respectively. Pretreatment of the rats with aqueous extract of C. dactylon (oral; 500mgkg-1) restored SOD activity completely but CAT activity only partially (7%). Carbofuran induced LPO was moderated by 95% in the brain of C. dactylon treated rats. The observed changes in OS parameters in C. dactylon treated group were comparable to that observed in vitamin C (200 mg-kg-1 b. wt.) treated group. Surprisingly, C. dactylon treatment significantly recovered the activity of AChE to a similar level as observed in the brain of control group. In contrast vitamin C treatment did not cause significant change in the activity of AChE in carbofuran treated group. There were no noticeable changes in the aforementioned study parameters in the brain of rats receiving C. dactylon and vitamin C, only. The results suggest that the study is extremely important in the context of development of new anticholinestesterase and antioxidant antidotes against carbofuran from C. dactylon. 13. Catalytic soman scavenging by Y337A/F338A acetylcholinesterase mutant assisted with novel site-directed aldoximes PubMed Central Kovarik, Zrinka; Hrvat, Nikolina Maček; Katalinić, Maja; Sit, Rakesh K.; Paradyse, Alexander; Žunec, Suzana; Musilek, Kamil; Fokin, Valery V.; Taylor, Palmer; Radić, Zoran 2016-01-01 Exposure to the nerve agent soman is difficult to treat due to the rapid dealkylation of soman-acetylcholinesterase (AChE) conjugate known as aging. Oxime antidotes commonly used to reactivate organophosphate inhibited AChE are ineffective against soman, while the efficacy of the recommended nerve agent bioscavenger butyrylcholinesterase is limited by strictly stoichiometric scavenging. To overcome this limitation, we tested ex vivo, in human blood, and in vivo, in soman exposed mice, the capacity of aging-resistant human AChE mutant Y337A/F338A in combination with oxime HI-6 to act as a catalytic bioscavenger of soman. HI-6 was previously shown in vitro to efficiently reactivate this mutant upon soman, as well as VX, cyclosarin, sarin and paraoxon inhibition. We here demonstrate that ex vivo, in whole human blood, 1 μM soman was detoxified within 30 minutes when supplemented with 0.5 μM Y337A/F338A AChE and 100 μM HI-6. This combination was further tested in vivo. Catalytic scavenging of soman in mice improved the therapeutic outcome and resulted in the delayed onset of toxicity symptoms. Furthermore, in a preliminary in vitro screen we identified an even more efficacious oxime than HI-6, in a series of forty-two pyridinium aldoximes, and five imidazole 2-aldoxime N-propyl pyridinium derivatives. One of the later imidazole aldoximes, RS-170B, was a 2–3 –fold more effective reactivator of Y337A/F338A AChE than HI-6 due to the smaller imidazole ring, as indicated by computational molecular models, that affords a more productive angle of nucleophilic attack. PMID:25835984 14. Postnatal growth hormone deficiency in growing rats causes marked decline in the activity of spinal cord acetylcholinesterase but not butyrylcholinesterase. PubMed Koohestani, Faezeh; Brown, Chester M; Meisami, Esmail 2012-11-01 The effects of growth hormone (GH) deficiency on the developmental changes in the abundance and activity of cholinesterase enzymes were studied in the developing spinal cord (SC) of postnatal rats by measuring the specific activity of acetylcholinesterase (AChE), a marker for cholinergic neurons and their synaptic compartments, and butyrylcholinesterase (BuChE), a marker for glial cells and neurovascular cells. Specific activities of these two enzymes were measured in SC tissue of 21- and 90 day-old (P21, weaning age; P90, young adulthood) GH deficient spontaneous dwarf (SpDwf) mutant rats which lack anterior pituitary and circulating plasma GH, and were compared with SC tissue of normal age-matched control animals. Assays were carried out for AChE and BuChE activity in the presence of their specific chemical inhibitors, BW284C51 and iso-OMPA, respectively. Results revealed that mean AChE activity was markedly and significantly reduced [28% at P21, 49% at P90, (p<0.01)] in the SC of GH deficient rats compared to age-matched controls. GH deficiency had a higher and more significant effect on AChE activity of the older (P90) rats than the younger ones (P21) ones. In contrast, BuChE activity in SC showed no significant changes in GH deficient rats at either of the two ages studied. Results imply that, in the absence of pituitary GH, the postnatal proliferation of cholinergic synapses in the rat SC, a CNS structure, where AChE activity is abundant, is markedly reduced during both the pre- and postweaning periods; more so in the postweaning than preweaning ages. In contrast, the absence of any effects on BuChE activity implies that GH does not affect the development of non-neuronal elements, e.g., glia, as much as the neuronal and synaptic compartments of the developing rat SC. 15. Local salt substitutes “Obu-otoyo” activate acetylcholinesterase and butyrylcholinesterase and induce lipid peroxidation in rat brain PubMed Central 2015-01-01 Evidence has shown that ingestion of heavy metals can lead to neurodegenerative diseases. This study aimed to investigate the neurotoxic potential of salt substitutes (Obu-Otoyo); salt A (made by burning palm kernel shaft then soaked in water overnight and the extract from the resulting residue is used as the salt substitute) and salt B (an unrefined salt mined from a local site at Ilobu town, Osun-State, Nigeria) by assessing their effect on some key enzymes linked with neurodegenerative disease [acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) activities] as well as on malondialdehyde (MDA) content of the rat brain. Salt substitutes were fed to normal rats as dietary inclusion at doses of 0.5 and 1.0% for 30 days. Thereafter, the effect of the salt substitutes on AChE and BChE activities as well as on MDA level in the rat brain was determined. The results revealed that the salt substitutes caused a significant (p<0.05) increase in both AChE and BChE activity and also induced lipid peroxidation in the brain of rats in vivo as well as under in vitro condition in a dose-dependent manner. The effect of the salt substitutes on AChE and BChE activities could be attributed to the presence of some toxic heavy metals. Therefore, the ability of the salt substitutes to induce lipid peroxidation and activate AChE and BChE activities could provide some possible mechanism for their neurotoxic effect. PMID:27486373 16. Effects of thyroxine and donepezil on hippocampal acetylcholine content, acetylcholinesterase activity, synaptotagmin-1 and SNAP-25 expression in hypothyroid adult rats. PubMed Wang, Fen; Zeng, Xianzhong; Zhu, Yangbo; Ning, Dan; Liu, Junxia; Liu, Chunlei; Jia, Xuemei; Zhu, Defa 2015-02-01 A growing number of studies have revealed that neurocognitive impairment, induced by adult-onset hypothyroidism, may not be fully restored by traditional hormone substitution therapies, including thyroxine (T4). The present study has investigated the effect of T4 and donepezil (DON; an acetylcholinesterase (AChE) inhibitor) treatment on the hypothyroidism-induced alterations of acetylcholine (ACh) content and AChE activity. Furthermore, we examined synaptotagmin-1 (syt-1) and SNAP-25 expression in the hippocampus of adult rats. Adding 0.05% propylthiouracil to their drinking water for five weeks induced hypothyroidism in the rat models. From the fourth week, the rats were treated with T4, DON or a combination of both. Concentration of ACh and the activity of AChE was determined colorimetrically. The results demonstrated that hypothyroidism induced a signiﬁcant decrease of Ach content and AChE activity (by 17 and 34%, respectively), which were restored to control values by T4 administration. DON treatment also restored Ach to the normal level. Protein levels of syt-1 and SNAP-25 were determined by immunohistochemistry. The results demonstrated that syt-1 was expressed at significantly lower levels in hypothyroid rats, while SNAP-25 levels were notably higher compared with the controls. Two-week treatment with T4 alone failed to normalize the expression levels of these two proteins, while co-administration of T4 and DON was able to induce this effect. These data suggested that the thyroid hormone, T4, may have a direct effect on the metabolism of hippocampal ACh in adult rats, and that the DON treatment may facilitate the recovery of synaptic protein impairments induced by hypothyroidism. 17. In vitro inhibition of acetylcholinesterase from four marine species by organophosphates and carbamates SciTech Connect Galgani, F.; Bocquene, G. ) 1990-08-01 The literature on the biological, physical, and pharmaceutical chemistry of cholinesterase is considerable and includes data on activators and inhibitors. Most of the work on specific anticholinesterasic agents has been concerned with carbamates and organophosphates. Because of the sensitivity of acetylcholinesterase to carbamates and organophosphates, the enzyme has been used as a biochemical indicator of pollution by these agents. However, the chemical reactivity of such chemicals has not been correlated with their effect on Ache and it is impossible to accurately predict biological effects based only on structure. The objectives of this study were to investigate the sensitivity of various marine animals to both organo-phosphates and carbamates. The study was conducted by assessing the in vitro effect of five organophosphates and three carbamates on acetylcholinesterase activity from the muscle of the shrimp Palaemon serratus, the fishes Scomber and Pleuronectes platessa, and from the whole mussels Mytilus edulis. All these species could be used for the monitoring of effect of pollutants. 18. Magnetic Electrochemical Immunoassays with Quantum Dot Labels for Detection of Phosphorylated Acetylcholinesterase in Plasma SciTech Connect Wang, Hua; Wang, Jun; Timchalk, Charles; Lin, Yuehe 2008-11-01 A new magnetic electrochemical immunoassay has been developed as a tool for biomonitoring exposures to organophosphate (OP) compounds, e.g., insecticides and chemical nerve agents, by directly detecting organophosphorylated acetylcholinesterase (OP-AChE). This immunoassay uniquely incorporates highly efficient magnetic separation with ultrasensitive square wave voltammetry (SWV) analysis with quantum dots (QDs) as labels. A pair of antibodies was used to achieve the specific recognition of OP-AChE that was prepared with paraoxon as an OP model agent. Antiphosphoserine polyclonal antibodies were anchored on amorphous magnetic particles preferably chosen to capture OP-AChE from the sample matrixes by binding their phosphoserine moieties that were exposed through unfolding the protein adducts. This was validated by electrochemical examinations and enzyme-linked immunosorbent assays. Furthermore, antihuman AChE monoclonal antibodies were labeled with cadmium-source QDs to selectively recognize the captured OP-AChE, as characterized by transmission electron microscopy. The subsequent electrochemical SWV analysis of the cadmium component released by acid from the coupled QDs was conducted on disposable screen-printed electrodes. Experimental results indicated that the SWV-based immunoassays could yield a linear response over a broad concentration range of 0.3-300 ng/mL OP-AChE in human plasma with a detection limit of 0.15 ng/mL. Such a novel electrochemical immunoassay holds great promise as a simple, selective, sensitive, and field-deployable tool for the effective biomonitoring and diagnosis of potential exposures to nerve agents and pesticides. 19. Differential binding of bispyridinium oxime drugs with acetylcholinesterase PubMed Central Kesharwani, Manoj K; Ganguly, Bishwajit; Das, Amit; Bandyopadhyay, Tusar 2010-01-01 Aim: To performe a time-dependent topographical delineation of protein-drug interactions to gain molecular insight into the supremacy of Ortho-7 over HI-6 in reactivating tabun-conjugated mouse acetylcholinesterase (mAChE). Methods: We conducted all-atom steered molecular dynamics simulations of the two protein-drug complexes. Through a host of protein-drug interaction parameters (rupture force profiles, hydrogen bonds, water bridges, hydrophobic interactions), geometrical, and orientation ordering of the drugs, we monitored the enzyme's response during the release of the drugs from its active-site. Results: The results show the preferential binding of the drugs with the enzyme. The pyridinium ring of HI-6 shows excellent complementary binding with the peripheral anionic site, whereas one of two identical pyridinium rings of Ortho-7 has excellent binding compatibility in the enzyme active-site where it can orchestrate the reactivation process. We found that the active pyridinium ring of HI-6 undergoes a complete turn along the active site axis, directed away from the active-site region during the course of the simulation. Conclusion: Due to excellent cooperative binding of Ortho-7, as rendered by several cation-π interactions with the active-site gorge of the enzyme, Ortho-7 may be a more efficient reactivator than HI-6. Our work supports the growing body of evidence that the efficacy of the drugs is due to the differential bindings of the oximes with AChE and can aid to the rational design of oxime drugs. PMID:20140002 20. Acetylcholinesterase-Inhibition and Antibacterial Activity of Mondia whitei Adventitious Roots and Ex vitro-Grown Somatic Embryogenic-Biomass PubMed Central 2016-01-01 Mondia whitei (Hook.f.) Skeels is an important endangered medicinal and commercial plant in South Africa. In vitro propagation systems are required for biomass production and bioactivity analysis to supplement wild resources/stocks. Adventitious roots from somatic embryogenic explants using suspension culture and ex vitro-grown plants produced via somatic embryogenesis were established using different plant growth regulator treatments. The adventitious root biomass and different parts of ex vitro-grown and mother plants were used to investigate the potential for acetylcholinesterase (AChE) and antibacterial activities. Adventitious roots derived from 2.5 μM indole-3-acetic acid (IAA) treatments and ex vitro-grown plants derived from meta-topolin riboside and IAA treatments gave the best AChE and antibacterial activities. The in vitro-established M. whitei and ex vitro biomass have comparable ability to function as inhibitors of acetylcholinesterase and antibacterial agents, and can be used as potent bioresources in traditional medicine. PMID:27752244 1. Dihydroquinoline Carbamate Derivatives as "Bio-oxidizable" Prodrugs for Brain Delivery of Acetylcholinesterase Inhibitors: [¹¹C] Radiosynthesis and Biological Evaluation. PubMed Bohn, Pierre; Gourand, Fabienne; Papamicaël, Cyril; Ibazizène, Méziane; Dhilly, Martine; Gembus, Vincent; Alix, Florent; Ţînţaş, Mihaela-Liliana; Marsais, Francis; Barré, Louisa; Levacher, Vincent 2015-05-20 With the aim of improving the efficiency of marketed acetylcholinesterase (AChE) inhibitors in the symptomatic treatment of Alzheimer's disease, plagued by adverse effects arising from peripheral cholinergic activation, this work reports a biological evaluation of new central AChE inhibitors based on an original "bio-oxidizable" prodrug strategy. After peripheral injection of the prodrug 1a [IC50 > 1 mM (hAChE)] in mice, monitoring markers of central and peripheral cholinergic activation provided in vivo proof-of-concept for brain delivery of the drug 2a [IC50 = 20 nM (hAChE)] through central redox activation of 1a. Interestingly, peripheral cholinergic activation has been shown to be limited in time, likely due to the presence of a permanent positive charge in 2a promoting rapid elimination of the AChE inhibitor from the circulation of mice. To support these assumptions, the radiosynthesis with carbon-11 of prodrug 1a was developed for additional ex vivo studies in rats. Whole-body biodistribution of radioactivity revealed high accumulation in excretory organs along with moderate but rapid brain uptake. Radio-HPLC analyses of brain samples confirm rapid CNS penetration of [(11)C]1a, while identification of [(11)C]2a and [(11)C]3a both accounts for central redox activation of 1a and pseudoirreversible inhibition of AChE, respectively. Finally, Caco-2 permeability assays predicted metabolite 3a as a substrate for efflux transporters (P-gp inter alia), suggesting that metabolite 3a might possibly be actively transported out of the brain. Overall, a large body of evidence from in vivo and ex vivo studies on small animals has been collected to validate this "bio-oxidizable" prodrug approach, emerging as a very promising strategy in the rational design of selective central AChE inhibitors. PMID:25695305 2. Mechanism of interaction of novel uncharged, centrally active reactivators with OP-hAChE conjugates. PubMed Radić, Zoran; Sit, Rakesh K; Garcia, Edzna; Zhang, Limin; Berend, Suzana; Kovarik, Zrinka; Amitai, Gabriel; Fokin, Valery V; Barry Sharpless, K; Taylor, Palmer 2013-03-25 A library of more than 200 novel uncharged oxime reactivators was used to select and refine lead reactivators of human acetylcholinesterase (hAChE) covalently conjugated with sarin, cyclosarin, VX, paraoxon and tabun. N-substituted 2-hydroxyiminoacetamido alkylamines were identified as best reactivators and reactivation kinetics of the lead oximes, RS41A and RS194B, were analyzed in detail. Compared to reference pyridinium reactivators, 2PAM and MMB4, molecular recognition of RS41A reflected in its Kox constant was compromised by an order of magnitude on average for different OP-hAChE conjugates, without significant differences in the first order maximal phosphorylation rate constant k(2). Systematic structural modifications of the RS41A lead resulted in several-fold improvement with reactivator, RS194B. Kinetic analysis indicated K(ox) reduction for RS194B as the main kinetic constant leading to efficient reactivation. Subtle structural modifications of RS194B were used to identify essential determinants for efficient reactivation. Computational molecular modeling of RS41A and RS194B interactions with VX inhibited hAChE, bound reversibly in Michaelis type complex and covalently in the pentacoordinate reaction intermediate suggests that the faster reactivation reaction is a consequence of a tighter RS194B interactions with hAChE peripheral site (PAS) residues, in particular with D74, resulting in lower interaction energies for formation of both the binding and reactivation states. Desirable in vitro reactivation properties of RS194B, when coupled with its in vivo pharmacokinetics and disposition in the body, reveal the potential of this oxime design as promising centrally and peripherally active antidotes for OP toxicity. 3. Influence of triiodothyronine (L-T3) on the morphological and biochemical development of fetal brain acetylcholinesterase-positive neurons cultured in a chemically defined medium. PubMed Garza, R; Dussault, J H; Puymirat, J 1988-10-01 In cerebral hemisphere cultures initiated from 15-day-old rat embryos, the number of acetylcholinesterase-positive (AChE+) cells increased from 6.8 +/- 1.6 cells/well on day 3 to 112 +/- 16 cells/well on day 15. With time in culture, AChE+ cells increased both in size of the perikarya and neurite length. The addition of L-triiodothyronine (L-T3) at a concentration of 3 x 10(-8) M at the initiation of the culture had no effect on the number of AChE+ cells but significantly increased the size and neurite length of AChE+ neurons after 5 days in vitro. These morphological effects are associated with biochemical effects. L-T3 increased AChE activity in both a dose- and time-dependent manner (the stimulatory effect of L-T3 becomes significant between day 8 and day 15). Since a major part of AChE+ cells may be cholinergic neurons, we have also measured the effect of L-T3 on ChAT activity. L-T3 also increased ChAT activity in a dose and time dependent manner. Furthermore, treatment of cultures with L-T3 at different times in culture demonstrated the presence of a critical period which occurs in vitro around day 20, since the stimulatory effect of L-T3 on ChAT activity is lost after 20 days in vitro. Studies of the time necessary for L-T3 to increase both ChAT and AChE activities show that 2 days and 15 days, respectively, are required for L-T3 to significantly stimulate both enzyme activities. This in vitro analysis demonstrated the morphological effect of L-T3 on the size and the neurite length of AChE+ cells. These effects are associated with biochemical effects on ChAT and AChE activities. Thus, it appears that thyroid hormones regulate several steps of neuronal maturation. 4. Possibility of Acetylcholinesterase Overexpression in Alzheimer Disease Patients after Therapy with Acetylcholinesterase Inhibitors. PubMed Kračmarová, Alžběta; Drtinová, Lucie; Pohanka, Miroslav 2015-01-01 Acetylcholinesterase is an enzyme responsible for termination of excitatory transmission at cholinergic synapses by the hydrolyzing of a neurotransmitter acetylcholine. Nowadays, other functions of acetylcholinesterase in the organism are considered, for example its role in regulation of apoptosis. Cholinergic nervous system as well as acetylcholinesterase activity is closely related to pathogenesis of Alzheimer disease. The mostly used therapy of Alzheimer disease is based on enhancing cholinergic function using inhibitors of acetylcholinesterase like rivastigmine, donepezil or galantamine. These drugs can influence not only the acetylcholinesterase activity but also other processes in treated organism. The paper is aimed mainly on possibility of increased expression and protein level of acetylcholinesterase caused by the therapy with acetylcholinesterase inhibitors. 5. Possibility of Acetylcholinesterase Overexpression in Alzheimer Disease Patients after Therapy with Acetylcholinesterase Inhibitors. PubMed Kračmarová, Alžběta; Drtinová, Lucie; Pohanka, Miroslav 2015-01-01 Acetylcholinesterase is an enzyme responsible for termination of excitatory transmission at cholinergic synapses by the hydrolyzing of a neurotransmitter acetylcholine. Nowadays, other functions of acetylcholinesterase in the organism are considered, for example its role in regulation of apoptosis. Cholinergic nervous system as well as acetylcholinesterase activity is closely related to pathogenesis of Alzheimer disease. The mostly used therapy of Alzheimer disease is based on enhancing cholinergic function using inhibitors of acetylcholinesterase like rivastigmine, donepezil or galantamine. These drugs can influence not only the acetylcholinesterase activity but also other processes in treated organism. The paper is aimed mainly on possibility of increased expression and protein level of acetylcholinesterase caused by the therapy with acetylcholinesterase inhibitors. PMID:26455564 6. Difluoromethyl ketones: Potent inhibitors of wild type and carbamate-insensitive G119S mutant Anopheles gambiae acetylcholinesterase. PubMed Camerino, Eugene; Wong, Dawn M; Tong, Fan; Körber, Florian; Gross, Aaron D; Islam, Rafique; Viayna, Elisabet; Mutunga, James M; Li, Jianyong; Totrov, Maxim M; Bloomquist, Jeffrey R; Carlier, Paul R 2015-10-15 Malaria is a devastating disease in sub-Saharan Africa, and current vector control measures are threatened by emerging resistance mechanisms. With the goal of developing new, selective, resistance-breaking insecticides we explored α-fluorinated methyl ketones as reversible covalent inhibitors of Anopheles gambiae acetylcholinesterase (AgAChE). Trifluoromethyl ketones 5 demonstrated remarkable volatility in microtiter plate assays, but 5c,e-h exhibited potent (1-100 nM) inhibition of wild type (WT) AgAChE and weak inhibition of resistant mutant G119S mutant AgAChE. Fluoromethyl ketones 10c-i exhibited submicromolar to micromolar inhibition of WT AgAChE, but again only weakly inhibited G119S AgAChE. Interestingly, difluoromethyl ketone inhibitors 9c and 9g had single digit nanomolar inhibition of WT AgAChE, and 9g had excellent potency against G119S AgAChE. Approach to steady-state inhibition was quite slow, but after 23 h incubation an IC50 value of 25.1 ± 1.2 nM was measured. We attribute the slow, tight-binding G119S AgAChE inhibition of 9g to a balance of steric size and electrophilicity. However, toxicities of 5g, 9g, and 10g to adult A. gambiae in tarsal contact, fumigation, and injection assays were lower than expected based on WT AgAChE inhibition potency and volatility. Potential toxicity-limiting factors are discussed. PMID:26386602 7. Interactions in vitro of some organophosphoramidates with neuropathy target esterase and acetylcholinesterase of hen brain. PubMed Jokanovic, M; Johnson, M K 1993-03-01 For organophosphates or phosphonates to initiate delayed neuropathy two steps are necessary: (1) progressive covalent reaction with neuropathy target esterase (NTE) to produce a form of inhibited NTE which can be reactivated by incubation with aqueous potassium fluoride (KF) and (2) progressive "aging" of inhibited NTE to a form which can no longer be reactivated by KF. However, it has been shown recently that certain N-unsubstituted organophosphoro-monoamidates (analogues of methamidophos) cause delayed neuropathy even though the inhibited NTE appeared not to have aged (Johnson et al. (1991). Arch. Toxicol., 65, 618-624). In order to study the generality of this phenomenon, we have examined some N-substituted compounds. We report in vitro studies of inhibition and reactivation and aging of both NTE and acetylcholinesterase (AChE) prior to toxicological tests. All the compounds studied were less inhibitory to both NTE and AChE in concentrated rather than in dilute suspensions of EDTA-washed brain particles without added cofactors. There was an apparent disposal of up to 100 mumoles of test compound by particles from 95 mg hen brain, which is far greater than can be explained by covalent binding. The activity is distinct from calcium-dependent "A" esterase. Several N-alkyl phosphoromonoamidates were found to be potent and selective inhibitors of NTE: second-order rate constant for O-n-pentyl N-benzylphosphoramido-fluoridate (Cmpd 6) = 5.6 x 10(7) M-1 min-1 at 37 degrees, which is about 100x higher than for acetylcholinesterase (AChE). Inhibited NTE and AChE from several chiral phosphoromono-amidates did not reactivate spontaneously (21 hours at 37 degrees). Virtually 100% reactivation by KF of AChE inhibited by phosphoromonoamidates was achieved at all times tested. Acetylcholinesterase inhibited by 2,5-dichlorophenyl N,N'-di-n-butylphosphorodiamidate was 42-56% reactivated by incubation with KF (192 mM in pH 5.2 buffer for 30 minutes at 37 degrees). We believe this 8. Theoretical modeling study for the phosphonylation mechanisms of the catalytic triad of acetylcholinesterase by sarin. PubMed Wang, Jing; Gu, Jiande; Leszczynski, Jerzy 2008-03-20 Potential energy surfaces for the process of phosphonylation of the catalytic triad of acetylcholinesterase by sarin have been explored at the B3LYP/6-311G(d,p) level of theory through a computational study. It is concluded that the phosphonylation process involves a critical addition-elimination mechanism. The first nucleophilic addition process is the rate-determining step. The following elimination process of the fluoride ion comprises a composite reaction that includes several steps, and it occurs rapidly by comparison with the rate-determining step. The mobility characteristics of histidine play an important role in the reaction. A double proton-transfer mechanism is proposed for the catalytic triad during the phosphonylation process of sarin on AChE. The effect of aqueous solvation has been considered via the polarizable continuum model (PCM). One concludes that the energy barriers are generally lowered in solvent, compared to the gas-phase reactions. 9. Potential use of acetylcholinesterase, glutathione-S-transferase and metallothionein for assessment of contaminated sediment in tropical chironomid, Chironomus javanus. PubMed Somparn, A; Iwai, C B; Noller, B 2015-11-01 Heavy metals and organophosphorus insecticide is known to act as disruptors for the enzyme system, leading to physiologic disorders. The present study was conducted to investigate the potential use of these enzymes as biomarkers in assessment of contaminated sediments on tropical chironomid species. Acetylcholinesterase (AChE), glutathione-S-transferase (GST) and metallothionein (MT) activity was measured in the fourth-instar chironomid larvae, Chironomus javanus, Kieffer, after either 48-hr or 96-hr exposure to organophosphorus insecticide, chlorpyrifos (0.01- 0.25 mg kg(-1)) or heavy metal cadmium (0.1-25 mg kg(-1)). Exposure to chlorpyrifos (0.01 mg kg(-1)) at 48 and 96 hr significantly of AChE activity (64.2%-85.9%) and induced GST activity (33.9-63.8%) when compared with control (P < 0.05). Moreover, exposure to cadmium (0.1 mg kg(-1)) at 48 and 96 hr also showed significant increas GST activity (11.7-40%) and MT level (9.0%-70.5%) when compared with control (P < 0.05). The results indicated the impact of enzyme activity on chlorpyrifos and cadmium contamination. Activity of AChE, GST and MT could serve as potential biomarkers for assessment and biomonitoring the effects of insecticide and heavy metal contamination in tropical aquatic ecosystems. PMID:26688973 10. Effect of adult onset hypothyroidism on behavioral parameters and acetylcholinesterase isoforms activity in specific brain regions of male mice. PubMed Vasilopoulou, Catherine G; Constantinou, Caterina; Giannakopoulou, Dimitra; Giompres, Panagiotis; Margarity, Marigoula 2016-10-01 Thyroid hormones (TH) are essential for normal development and function of mammalian central nervous system (CNS); TH dysregulation has been implicated in several cognitive and behavioral deficits related to dysfunctions of neurotransmitter systems. In the present study, we investigated the effects of adult onset hypothyroidism on the activity of acetylcholinesterase (AChE) and on related behavioral parameters. For this purpose we used adult male Balb/cJ mice that were divided randomly into euthyroid and hypothyroid animal groups. Animals were rendered hypothyroid through administration of 1% w/v KClO4 in their drinking water for 8weeks. At the end of the treatment, learning/memory procedures were examined through step-through passive avoidance task while fear/anxiety was assessed using elevated plus-maze (EPM) and open-field (OF) tests. AChE activity was determined colorimetrically in two different fractions, salt-soluble fraction (SS) (containing mainly the G1 isoform) and detergent-soluble fraction (DS) (containing mainly the G4 isoform) in cerebral cortex, cerebellum, midbrain, hippocampus and striatum. Our results indicate that adult onset hypothyroidism caused significant memory impairment and increased fear/anxiety. Moreover, the activity of both isoforms of AChE was reduced in all brain regions examined in a brain region- and isoform-specific manner. PMID:27317840 11. Taspine: Bioactivity-Guided Isolation and Molecular Ligand–Target Insight of a Potent Acetylcholinesterase Inhibitor from Magnolia x soulangiana PubMed Central Rollinger, Judith M.; Schuster, Daniela; Baier, Elisabeth; Ellmerer, Ernst P.; Langer, Thierry; Stuppner, Hermann 2012-01-01 A bioactivity-guided approach was taken to identify the acetylcholinesterase (AChE, EC 3.1.1.7) inhibitory agent in a Magnolia x soulangiana extract using a microplate enzyme assay with Ellman’s reagent. This permitted the isolation of the alkaloids taspine (1) and (−)-asimilobine (2), which were detected for the first time in this species. Compound 1 showed a significantly higher effect on AChE than the positive control galanthamine and selectively inhibited the enzyme in a long-lasting and concentration-dependent fashion with an IC50 value of 0.33 ± 0.07 μM. Extensive molecular docking studies were performed with human and Torpedo californica-AChE employing Gold software to rationalize the binding interaction. The results suggested ligand 1 to bind in an alternative binding orientation when compared to galanthamine. While this is located in close vicinity to the catalytic amino acid triad, the 1–AChE complex was found to be stabilized by (i) sandwich-like π-stacking interactions between the planar aromatic ligand (1) and the Trp84 and Phe330 of the enzyme, (ii) an esteratic site anchoring with the amino side chain, and (iii) a hydrogen-bonding network. PMID:16989531 12. Effect of adult onset hypothyroidism on behavioral parameters and acetylcholinesterase isoforms activity in specific brain regions of male mice. PubMed Vasilopoulou, Catherine G; Constantinou, Caterina; Giannakopoulou, Dimitra; Giompres, Panagiotis; Margarity, Marigoula 2016-10-01 Thyroid hormones (TH) are essential for normal development and function of mammalian central nervous system (CNS); TH dysregulation has been implicated in several cognitive and behavioral deficits related to dysfunctions of neurotransmitter systems. In the present study, we investigated the effects of adult onset hypothyroidism on the activity of acetylcholinesterase (AChE) and on related behavioral parameters. For this purpose we used adult male Balb/cJ mice that were divided randomly into euthyroid and hypothyroid animal groups. Animals were rendered hypothyroid through administration of 1% w/v KClO4 in their drinking water for 8weeks. At the end of the treatment, learning/memory procedures were examined through step-through passive avoidance task while fear/anxiety was assessed using elevated plus-maze (EPM) and open-field (OF) tests. AChE activity was determined colorimetrically in two different fractions, salt-soluble fraction (SS) (containing mainly the G1 isoform) and detergent-soluble fraction (DS) (containing mainly the G4 isoform) in cerebral cortex, cerebellum, midbrain, hippocampus and striatum. Our results indicate that adult onset hypothyroidism caused significant memory impairment and increased fear/anxiety. Moreover, the activity of both isoforms of AChE was reduced in all brain regions examined in a brain region- and isoform-specific manner. 13. Structure of a prereaction complex between the nerve agent sarin, its biological target acetylcholinesterase, and the antidote HI-6 PubMed Central Allgardsson, Anders; Berg, Lotta; Akfur, Christine; Hörnberg, Andreas; Linusson, Anna; Ekström, Fredrik J. 2016-01-01 Organophosphorus nerve agents interfere with cholinergic signaling by covalently binding to the active site of the enzyme acetylcholinesterase (AChE). This inhibition causes an accumulation of the neurotransmitter acetylcholine, potentially leading to overstimulation of the nervous system and death. Current treatments include the use of antidotes that promote the release of functional AChE by an unknown reactivation mechanism. We have used diffusion trap cryocrystallography and density functional theory (DFT) calculations to determine and analyze prereaction conformers of the nerve agent antidote HI-6 in complex with Mus musculus AChE covalently inhibited by the nerve agent sarin. These analyses reveal previously unknown conformations of the system and suggest that the cleavage of the covalent enzyme–sarin bond is preceded by a conformational change in the sarin adduct itself. Together with data from the reactivation kinetics, this alternate conformation suggests a key interaction between Glu202 and the O-isopropyl moiety of sarin. Moreover, solvent kinetic isotope effect experiments using deuterium oxide reveal that the reactivation mechanism features an isotope-sensitive step. These findings provide insights into the reactivation mechanism and provide a starting point for the development of improved antidotes. The work also illustrates how DFT calculations can guide the interpretation, analysis, and validation of crystallographic data for challenging reactive systems with complex conformational dynamics. PMID:27140636 14. Double layer structure-based virtual screening reveals 3'-Hydroxy-A-Naphthoflavone as novel inhibitor candidate of human acetylcholinesterase 2016-03-01 One of the most effective target for Alzheimer's disease's (AD) treatment is the inhibition of human acetylcholinesterase (hAChE) eventhough it has many side effects. So that, this study was aimed to discover a new candidate of hAChE's inhibitor that has more negative binding affinity than existing drugs. hAChE's 3D model used in this study has a good quality according to its number of residues in most favoured regions (92%), three bad contacts, >50 ERRAT's score (85,870) and successfully passed the VERIFY 3D threshold (>80%). Based on the first layer of SBVS againts more than 12.180.630 ligands, we discovered 11.806 hits and then we found 359 hits from the second layer of SBVS. Based on our previous steps, we found that 3'-Hydroxy-a-Naphthoflavone was the only one candidate, that directly interacted with Trp286 via hydrogen bond and hydrophobic interactions and also has the most negative binding affinity (-10,6 kcal/mol) and also has more negative than existing hAChE's inhibitors, such as tacrine, donepezil, etc. 3'-Hydroxy-a-Naphthoflavone is the best candidate of hAChE's inhibitor based on its binding affinity (-10,6 kcal/mol) that is more negative than existing hAChE's inhibitors, such as tacrine, donepezil, etc. 15. Discovery of non-oxime reactivators using an in silico pharmacophore model of oxime reactivators of OP-inhibited acetylcholinesterase. PubMed Bhattacharjee, Apurba K; Marek, Elizabeth; Le, Ha Thu; Gordon, Richard K 2012-03-01 We earlier reported an in silico pharmacophore model for reactivation of oximes to tabun-inhibited AChE. Since DFP (diisopropylfluorophosphate) like tabun is a G-agent simulator, we utilized the model as a rational strategy to discover non-oxime reactivators of DFP-inhibited AChE in this study. The phramacophore was used for virtual screening of two commercial databases, Maybridge and ChemNavigator, to identify reactivators which lack the oxime functions. The procedure led us to identify several potent non-oxime compounds that reactivate DFP-inhibited AChE. These non-oxime reactivators contain a nucleophile group in lieu of the oxime moiety in the compound. Five of these novel non-oximes showed Kr values within ten-fold of 2-PAM in an in vitro assay. The pharmacophore model contained a hydrogen bond acceptor, a hydrogen bond donor, and an aromatic ring features distributed in a 3D space. Calculated stereoelectronic properties reported earlier with respect to the location of molecular orbitals and electrostatic potentials were consistent with the model and the newly identified compounds. Down selection of compounds after virtual screening was performed on the basis of fit score to the model, conformational energy, and in silico evaluations for favorable blood-brain barrier (BBB) penetrability, octanol-water partition (log P), and toxicity (rat oral LD(50)) assessments. In vitro reactivation efficacy of the compounds was evaluated in a DFP-inhibited eel acetylcholinesterase assay. PMID:22309910 16. Flow-through enzyme immobilized amperometric detector for the rapid screening of acetylcholinesterase inhibitors by flow injection analysis. PubMed Vandeput, Marie; Parsajoo, Cobra; Vanheuverzwijn, Jérôme; Patris, Stéphanie; Yardim, Yavuz; le Jeune, Alexandre; Sarakbi, Ahmad; Mertens, Dominique; Kauffmann, Jean-Michel 2015-01-01 A commercially available thin-layer flow-through amperometric detector, with the sensing block customized in an original design, was applied to the screening of drug compounds known as acetylcholinesterase (AChE) inhibitors. AChE from electric eel was covalently immobilized onto a cysteamine modified gold disk adjacent to a silver disk working electrode. On-line studies were performed by flow injection analysis (FIA) in PBS buffer pH 7.4. Seven commercially available AChE inhibitors used in the medical field, namely neostigmine, eserine, tacrine, donepezil, rivastigmine, pyridostigmine and galantamine as well as two natural compounds, quercetin and berberine, were investigated. The same trend of inhibitory potency as described in the literature was observed. Of particular interest and in addition to the determination of the IC50 values, this flow-through system allowed the study of both, the stability of the enzyme-inhibitor complex and the kinetic of the enzyme activity recovery. PMID:25459923 17. Bilateral injection of fasciculin into the amygdala of rats: effects on two avoidance tasks, acetylcholinesterase activity, and cholinergic muscarinic receptors. PubMed Quillfeldt, J; Raskovsky, S; Dalmaz, C; Dias, M; Huang, C; Netto, C A; Schneider, F; Izquierdo, I; Medina, J H; Silveira, R 1990-11-01 These experiments examined the effects of the bilateral injection of fasciculin-2 (FAS), a natural acetylcholinesterase (AChE) inhibitory peptide, into the amygdala of rats on acquisition and retention of two avoidance behaviors. Intraamygdala injection of FAS (150 ng/amygdala) produced a pronounced and long-lasting inhibition of AChE activity: 85% and 74% on day 2 and day 5, respectively. After 48 hr, FAS-treated animals showed no changes in training or test session performance in a step-down inhibitory avoidance task (training-test interval was 24 hr). In a 2-way shuttle avoidance task, intraamygdala FAS slightly reduced retention test performance without modifying training session scores. Two and five days after FAS injections into the amygdala, the density of muscarinic receptor decreased about 50% as measured by the specific bindings of 3H-quinuclidinyl benzilate and 3H-oxotremorine. No alterations were observed in the apparent dissociation constants. On the other hand, the central-type benzodiazepine receptor population of the amygdala remained unchanged, suggesting that FAS microinjection did not produce damage to neuronal components of these nuclei. In conclusion, the results presented have indicated that a clear-cut and long-lasting inhibition of AChE activity in the amygdala is not accompanied by a facilitation of learning and memory of two different avoidance tasks. Compensation of the increased cholinergic activity by a down-regulation of muscarinic receptors could account for these findings. 18. The effect of basketball training on the players' erythrocyte membrane acetylcholinesterase, (Na+,K+)-ATPase and Mg2+-ATPase activities. PubMed Parthimos, T; Tsopanakis, C; Angelogianni, P; Schulpis, K H; Parthimos, N; Tsakiris, S 2007-08-01 The aim of this study was to investigate whether the activities of erythrocyte membrane acetylcholinesterase (AChE), (Na (+),K (+))-ATPase and Mg (2+)-ATPase are modulated by a basketball training. Blood was obtained from 10 basketball players pre- and postexercise. Total antioxidant status (TAS), lactate and pyruvate concentrations were determined with kits, while the enzyme activities were determined spectrophotometrically. Post-training blood lactate and pyruvate concentrations as well as AChE (2.90 +/- 0.05 vs. 3.98 +/- 0.09 Delta OD/min . mg protein, p < 0.01) and Na (+),K (+)-ATPase (0.58 +/- 0.04 vs. 1.27 +/- 0.12 micromol Pi/h . mg protein, p < 0.001) activities were remarkably increased, whereas TAS was significantly decreased. Mg (2+)-ATPase activity remained unaltered at the end of the training. In conclusion, the stimulation of AChE and Na (+),K (+)-ATPase by the training may be due to the rise of blood catecholamine oxidation contributing to TAS decrease and/or the increase of serotonin levels. This stress condition may modulate cholinergic and catecholaminergic/serotoninergic functions in players. 19. Exploration of a Library of 3,4-(Methylenedioxy)aniline-Derived Semicarbazones as Dual Inhibitors of Monoamine Oxidase and Acetylcholinesterase: Design, Synthesis, and Evaluation. PubMed Tripathi, Rati K P; Rai, Gopal K; Ayyannan, Senthil R 2016-06-01 A library of 3,4-(methylenedioxy)aniline-derived semicarbazones was designed, synthesized, and evaluated as monoamine oxidase (MAO) and acetylcholinesterase (AChE) inhibitors for the treatment of neurodegenerative diseases. Most of the new compounds selectively inhibited MAO-B and AChE, with IC50 values in the micro- or nanomolar ranges. Compound 16, 1-(2,6-dichlorobenzylidene)-4-(benzo[1,3]dioxol-5-yl)semicarbazide presented a balanced multifunctional profile of MAO-A (IC50 =4.52±0.032 μm), MAO-B (IC50 =0.059±0.002 μm), and AChE (IC50 =0.0087±0.0002 μm) inhibition without neurotoxicity. Kinetic studies revealed that compound 16 exhibits competitive and reversible inhibition against MAO-A and MAO-B, and mixed-type inhibition against AChE. Molecular docking studies further revealed insight into the possible interactions within the enzyme-inhibitor complexes. The most active compounds were found to interact with the enzymes through hydrogen bonding and hydrophobic interactions. Additionally, in silico molecular properties and ADME properties of the synthesized compounds were calculated to explore their drug-like characteristics. 20. DEVELOPMENT OF REFERENCE RANGES FOR PLASMA TOTAL CHOLINESTERASE AND BRAIN ACETYLCHOLINESTERASE ACTIVITY IN FREE-RANGING CARNABY'S BLACK-COCKATOOS (CALYPTORHYNCHUS LATIROSTRIS). PubMed Vaughan-Higgins, Rebecca; Vitali, Simone; Reiss, Andrea; Besier, Shane; Hollingsworth, Tom; Smith, Gerard 2016-07-01 Published avian reference ranges for plasma cholinesterase (ChE) and brain acetylcholinesterase (AChE) are numerous. However, a consistently reported recommendation is the need for species- and laboratory-specific reference ranges because of variables, including assay methods, sample storage conditions, season, and bird sex, age, and physiologic status. We developed normal reference ranges for brain AChE and plasma total ChE (tChE) activity for Carnaby's Black-Cockatoos (Calyptorhynchus latirostris) using a standardized protocol (substrate acetylthiocholine at 25 C). We report reference ranges for brain AChE (19-41 μmol/min per g, mean 21±6.38) and plasma tChE (0.41-0.53 μmol/min per mL, mean 0.47±0.11) (n=15). This information will be of use in the ongoing field investigation of a paresis-paralysis syndrome in the endangered Carnaby's Black-Cockatoos, suspected to be associated with exposure to anticholinesterase compounds and add to the paucity of reference ranges for plasma tChE and brain AChE in Australian psittacine birds. 1. Exploration of a Library of 3,4-(Methylenedioxy)aniline-Derived Semicarbazones as Dual Inhibitors of Monoamine Oxidase and Acetylcholinesterase: Design, Synthesis, and Evaluation. PubMed Tripathi, Rati K P; Rai, Gopal K; Ayyannan, Senthil R 2016-06-01 A library of 3,4-(methylenedioxy)aniline-derived semicarbazones was designed, synthesized, and evaluated as monoamine oxidase (MAO) and acetylcholinesterase (AChE) inhibitors for the treatment of neurodegenerative diseases. Most of the new compounds selectively inhibited MAO-B and AChE, with IC50 values in the micro- or nanomolar ranges. Compound 16, 1-(2,6-dichlorobenzylidene)-4-(benzo[1,3]dioxol-5-yl)semicarbazide presented a balanced multifunctional profile of MAO-A (IC50 =4.52±0.032 μm), MAO-B (IC50 =0.059±0.002 μm), and AChE (IC50 =0.0087±0.0002 μm) inhibition without neurotoxicity. Kinetic studies revealed that compound 16 exhibits competitive and reversible inhibition against MAO-A and MAO-B, and mixed-type inhibition against AChE. Molecular docking studies further revealed insight into the possible interactions within the enzyme-inhibitor complexes. The most active compounds were found to interact with the enzymes through hydrogen bonding and hydrophobic interactions. Additionally, in silico molecular properties and ADME properties of the synthesized compounds were calculated to explore their drug-like characteristics. PMID:27135466 2. Probing the origins of human acetylcholinesterase inhibition via QSAR modeling and molecular docking PubMed Central Shoombuatong, Watshara; Malik, Aijaz Ahmad; Prachayasittikul, Virapong; Wikberg, Jarl E.S. 2016-01-01 Alzheimer’s disease (AD) is a chronic neurodegenerative disease which leads to the gradual loss of neuronal cells. Several hypotheses for AD exists (e.g., cholinergic, amyloid, tau hypotheses, etc.). As per the cholinergic hypothesis, the deficiency of choline is responsible for AD; therefore, the inhibition of AChE is a lucrative therapeutic strategy for the treatment of AD. Acetylcholinesterase (AChE) is an enzyme that catalyzes the breakdown of the neurotransmitter acetylcholine that is essential for cognition and memory. A large non-redundant data set of 2,570 compounds with reported IC50 values against AChE was obtained from ChEMBL and employed in quantitative structure-activity relationship (QSAR) study so as to gain insights on their origin of bioactivity. AChE inhibitors were described by a set of 12 fingerprint descriptors and predictive models were constructed from 100 different data splits using random forest. Generated models afforded R2, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} }{}${Q}_{\\mathrm{CV }}^{2}$\\end{document}QCV2 and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} }{}${Q}_{\\mathrm{Ext}}^{2}$\\end{document}QExt2 values in ranges of 0.66–0.93, 0.55–0.79 and 0.56–0.81 for the training set, 10-fold cross-validated set and external set, respectively. The best model built using the substructure count was selected according to the OECD guidelines and it afforded R2, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage 3. Probing the origins of human acetylcholinesterase inhibition via QSAR modeling and molecular docking PubMed Central Shoombuatong, Watshara; Malik, Aijaz Ahmad; Prachayasittikul, Virapong; Wikberg, Jarl E.S. 2016-01-01 Alzheimer’s disease (AD) is a chronic neurodegenerative disease which leads to the gradual loss of neuronal cells. Several hypotheses for AD exists (e.g., cholinergic, amyloid, tau hypotheses, etc.). As per the cholinergic hypothesis, the deficiency of choline is responsible for AD; therefore, the inhibition of AChE is a lucrative therapeutic strategy for the treatment of AD. Acetylcholinesterase (AChE) is an enzyme that catalyzes the breakdown of the neurotransmitter acetylcholine that is essential for cognition and memory. A large non-redundant data set of 2,570 compounds with reported IC50 values against AChE was obtained from ChEMBL and employed in quantitative structure-activity relationship (QSAR) study so as to gain insights on their origin of bioactivity. AChE inhibitors were described by a set of 12 fingerprint descriptors and predictive models were constructed from 100 different data splits using random forest. Generated models afforded R2, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} }{}${Q}_{\\mathrm{CV }}^{2}$\\end{document}QCV2 and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} }{}${Q}_{\\mathrm{Ext}}^{2}$\\end{document}QExt2 values in ranges of 0.66–0.93, 0.55–0.79 and 0.56–0.81 for the training set, 10-fold cross-validated set and external set, respectively. The best model built using the substructure count was selected according to the OECD guidelines and it afforded R2, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage 4. Inhibition and Larvicidal Activity of Phenylpropanoids from Piper sarmentosum on Acetylcholinesterase against Mosquito Vectors and Their Binding Mode of Interaction PubMed Central Hematpoor, Arshia; Liew, Sook Yee; Chong, Wei Lim; Azirun, Mohd Sofian; Lee, Vannajan Sanghiran; Awang, Khalijah 2016-01-01 Aedes aegypti, Aedes albopictus and Culex quinquefasciatus are vectors of dengue fever and West Nile virus diseases. This study was conducted to determine the toxicity, mechanism of action and the binding interaction of three active phenylpropanoids from Piper sarmentosum (Piperaceae) toward late 3rd or early 4th larvae of above vectors. A bioassay guided-fractionation on the hexane extract from the roots of Piper sarmentosum led to the isolation and identification of three active phenylpropanoids; asaricin 1, isoasarone 2 and trans-asarone 3. The current study involved evaluation of the toxicity and acetylcholinesterase (AChE) inhibition of these compounds against Aedes aegypti, Aedes albopictus and Culex quinquefasciatus larvae. Asaricin 1 and isoasarone 2 were highly potent against Aedes aegypti, Aedes albopictus and Culex quinquefasciatus larvae causing up to 100% mortality at ≤ 15 μg/mL concentration. The ovicidal activity of asaricin 1, isoasarone 2 and trans-asarone 3 were evaluated through egg hatching. Asaricin 1 and isoasarone 2 showed potent ovicidal activity. Ovicidal activity for both compounds was up to 95% at 25μg/mL. Asaricin 1 and isoasarone 2 showed strong inhibition on acetylcholinesterase with relative IC50 values of 0.73 to 1.87 μg/mL respectively. These findings coupled with the high AChE inhibition may suggest that asaricin 1 and isoasarone 2 are neuron toxic compounds toward Aedes aegypti, Aedes albopictus and Culex quinquefasciatus. Further computational docking with Autodock Vina elaborates the possible interaction of asaricin 1 and isoasarone 2 with three possible binding sites of AChE which includes catalytic triads (CAS: S238, E367, H480), the peripheral sites (PAS: E72, W271) and anionic binding site (W83). The binding affinity of asaricin 1 and isoasarone 2 were relatively strong with asaricin 1 showed a higher binding affinity in the anionic pocket. PMID:27152416 5. Bioaccumulation of PCB-153 and effects on molecular biomarkers acetylcholinesterase, glutathione-S-transferase and glutathione peroxidase in Mytilus galloprovincialis mussels. PubMed Vidal-Liñán, Leticia; Bellas, Juan; Soriano, José Antonio; Concha-Graña, Estefanía; Muniategui, Soledad; Beiras, Ricardo 2016-07-01 In this study, PCB-153 bioaccumulation kinetics and concentration-response experiments were performed employing wild Mytilus galloprovincialis mussels. In addition, the activity of three enzymatic biomarkers: glutathione S-transferase (GST), glutathione peroxidase (GPx) and acetylcholinesterase (AChE), were measured in the mussel gills. The experimental data fitted well to an asymptotic accumulation model with a high bioconcentration factor (BCF) of 9324 L kg(-1) and a very limited depuration capacity, described by a low excretion rate coefficient (Kd = 0.083 d(-1)). This study reports by first time in mussels significant inhibition of GST activity and significant induction of GPx activity as a result of exposure to dissolved PCB-153. In contrast, AChE activity was unaffected at all concentrations and exposure times tested. The effects on both enzymes are time-dependent, which stresses the difficulties inherent to the use of these biomarkers in chemical pollution monitoring programs. 6. Bioaccumulation of PCB-153 and effects on molecular biomarkers acetylcholinesterase, glutathione-S-transferase and glutathione peroxidase in Mytilus galloprovincialis mussels. PubMed Vidal-Liñán, Leticia; Bellas, Juan; Soriano, José Antonio; Concha-Graña, Estefanía; Muniategui, Soledad; Beiras, Ricardo 2016-07-01 In this study, PCB-153 bioaccumulation kinetics and concentration-response experiments were performed employing wild Mytilus galloprovincialis mussels. In addition, the activity of three enzymatic biomarkers: glutathione S-transferase (GST), glutathione peroxidase (GPx) and acetylcholinesterase (AChE), were measured in the mussel gills. The experimental data fitted well to an asymptotic accumulation model with a high bioconcentration factor (BCF) of 9324 L kg(-1) and a very limited depuration capacity, described by a low excretion rate coefficient (Kd = 0.083 d(-1)). This study reports by first time in mussels significant inhibition of GST activity and significant induction of GPx activity as a result of exposure to dissolved PCB-153. In contrast, AChE activity was unaffected at all concentrations and exposure times tested. The effects on both enzymes are time-dependent, which stresses the difficulties inherent to the use of these biomarkers in chemical pollution monitoring programs. PMID:27176625 7. Zephycandidine A, the First Naturally Occurring Imidazo[1,2-f]phenanthridine Alkaloid from Zephyranthes candida, Exhibits Significant Anti-tumor and Anti-acetylcholinesterase Activities PubMed Central Zhan, Guanqun; Qu, Xiaolan; Liu, Junjun; Tong, Qingyi; Zhou, Junfei; Sun, Bin; Yao, Guangmin 2016-01-01 Zephycandidine A (1), the first naturally occurring imidazo[1,2-f]phenanthridine alkaloid, was isolated from Zephyranthes candida (Amaryllidaceae). The structure of 1 was elucidated by spectroscopic analyses and NMR calculation, and a plausible biogenetic pathway for zephycandidine A (1) was proposed. Zephycandidine A (1) exhibited significant cytotoxicity against five cancer cell lines with IC50 values ranging from 1.98 to 7.03 μM with selectivity indices as high as 10 when compared to the normal Beas-2B cell. Further studies suggested that zephycandidine A (1) induces apoptosis in leukemia cells by the activation of caspase-3, upregulation of Bax, downregulation of Bcl-2, and degradation of PARP expression. In addition, zephycandidine A (1) showed acetylcholinesterase (AChE) inhibitory activity, and the docking studies of zephycandidine A (1) and galanthamine (2) with AChE revealed that interactions with W286 and Y337 are necessary. PMID:27658482 8. Self assembly of acetylcholinesterase on a gold nanoparticles–graphene nanosheet hybrid for organophosphate pesticide detection using polyelectrolyte as a linker SciTech Connect Wang, Ying; Zhang, Sheng; Du, Dan; Shao, Yuyan; Li, Zhaohui; Wang, Jun; Engelhard, Mark H.; Li, Jinghong; Lin, Yuehe 2011-04-14 A nanohybrid of gold nanoparticles (Au NPs) and chemically reduced graphene oxide nanosheets (cr-Gs) was synthesized by in situ growth of Au NPs on the surface of graphene nanosheets in the presence of poly(diallyldimethylammonium chloride) (PDDA), which not only improved the dispersion of Au NPs but also stabilized cholinesterase with high activity and loading efficiency. The obtained nanohybrid was characterized by TEM, XRD, XPS, and electrochemistry. Then an enzyme nanoassembly (AChE/Au NPs/cr-Gs) was prepared by self-assembling acetylcholinesterase (AChE) on Au NP/cr-Gs nanohybrid. An electrochemical sensor based on AChE/Au NPs/cr-Gs was further developed for ultrasensitive detection of organophosphate pesticide. The results demonstrate that the developed approach provides a promising strategy to improve the sensitivity and enzyme activity of electrochemical biosensors. 9. Bioaccumulation of 4-nonylphenol and effects on biomarkers, acetylcholinesterase, glutathione-S-transferase and glutathione peroxidase, in Mytilus galloprovincialis mussel gilla. PubMed Vidal-Liñán, Leticia; Bellas, Juan; Salgueiro-González, Noelia; Muniategui, Soledad; Beiras, Ricardo 2015-05-01 Wild marine mussels, Mytilus galloprovincialis showed a moderate bioaccumulation ability when exposed to waterborne 4-nonylphenol (4-NP), with a bioconcentration factor (BCF) of 6850 L Kg(-1) (dry weight). Kinetic and concentration-response experiments were performed and three enzymatic biomarkers in mussel gills were measured: Glutathione S-transferase (GST), glutathione peroxidase (GPx) and acetylcholinesterase (AChE). Exposure of mussels to environmentally relevant concentrations (25-100 μg L(-1)) of 4-nonylphenol significantly inhibited the AChE activity and induced the GST and GPx activities. GST induction was dose dependent whilst GPx activity showed a less consistent pattern, but in both cases the induction remained after a 10 d depuration period. Mussels seem capable of eliminating 4-NP from their tissues through a mechanism involving GST induction. 10. Bioaccumulation of BDE-47 and effects on molecular biomarkers acetylcholinesterase, glutathione-S-transferase and glutathione peroxidase in Mytilus galloprovincialis mussels. PubMed Vidal-Liñán, Leticia; Bellas, Juan; Fumega, José; Beiras, Ricardo 2015-03-01 Mussels, Mytilus galloprovincialis, showed a high bioaccumulation ability when exposed to waterborne tetrabromodiphenyl ether (BDE-47), with a bioconcentration factor of 10,900 L Kg(-1) wet weight, and slow depuration rates in clean seawater. Kinetic and concentration-response experiments were performed measuring in the exposed mussel the activities of three molecular biomarkers: glutathione S-transferase (GST), glutathione peroxidase (GPx) and acetylcholinesterase (AChE). The long term (30 days) exposure of mussels to all concentrations (2-15 µg L(-1)) of BDE-47 significantly inhibited the AChE and GST activities, a result that supports the suitability of these biomarkers in marine pollution monitoring programs. However, GPx activity showed a less consistent pattern of response depending on the concentration and the duration of exposure. 11. Zephycandidine A, the First Naturally Occurring Imidazo[1,2-f]phenanthridine Alkaloid from Zephyranthes candida, Exhibits Significant Anti-tumor and Anti-acetylcholinesterase Activities Zhan, Guanqun; Qu, Xiaolan; Liu, Junjun; Tong, Qingyi; Zhou, Junfei; Sun, Bin; Yao, Guangmin 2016-09-01 Zephycandidine A (1), the first naturally occurring imidazo[1,2-f]phenanthridine alkaloid, was isolated from Zephyranthes candida (Amaryllidaceae). The structure of 1 was elucidated by spectroscopic analyses and NMR calculation, and a plausible biogenetic pathway for zephycandidine A (1) was proposed. Zephycandidine A (1) exhibited significant cytotoxicity against five cancer cell lines with IC50 values ranging from 1.98 to 7.03 μM with selectivity indices as high as 10 when compared to the normal Beas-2B cell. Further studies suggested that zephycandidine A (1) induces apoptosis in leukemia cells by the activation of caspase-3, upregulation of Bax, downregulation of Bcl-2, and degradation of PARP expression. In addition, zephycandidine A (1) showed acetylcholinesterase (AChE) inhibitory activity, and the docking studies of zephycandidine A (1) and galanthamine (2) with AChE revealed that interactions with W286 and Y337 are necessary. 12. Calcium-activated butyrylcholinesterase in human skin protects acetylcholinesterase against suicide inhibition by neurotoxic organophosphates SciTech Connect Schallreuter, Karin U.; University of Bradford ). E-mail: K.Schallreuter@bradford.ac.uk; Gibbons, Nicholas C.J.; Elwary, Souna M.; Parkin, Susan M.; Wood, John M. 2007-04-20 The human epidermis holds an autocrine acetylcholine production and degradation including functioning membrane integrated and cytosolic butyrylcholinesterase (BuchE). Here we show that BuchE activities increase 9-fold in the presence of calcium (0.5 x 10{sup -3}M) via a specific EF-hand calcium binding site, whereas acetylcholinesterase (AchE) is not affected. {sup 45}Calcium labelling and computer simulation confirmed the presence of one EF-hand binding site per subunit which is disrupted by H{sub 2}O{sub 2}-mediated oxidation. Moreover, we confirmed the faster hydrolysis by calcium-activated BuchE using the neurotoxic organophosphate O-ethyl-O-(4-nitrophenyl)-phenylphosphonothioate (EPN). Considering the large size of the human skin with 1.8 m{sup 2} surface area with its calcium gradient in the 10{sup -3}M range, our results implicate calcium-activated BuchE as a major protective mechanism against suicide inhibition of AchE by organophosphates in this non-neuronal tissue. 13. Scapaundulin C, a novel labdane diterpenoid isolated from Chinese liverwort Scapania undulate, inhibits acetylcholinesterase activity. PubMed Kang, Ya-Qi; Zhou, Jin-Chuan; Fan, Pei-Hong; Wang, Shu-Qi; Lou, Hong-Xiang 2015-12-01 In the present study, scapaundulin C (1), a new labdane diterpenoid, and four related known compounds scapaundulin A (2), 5α, 8α, 9α-trihydroxy-13E-labden-12-one (3), 5α, 8α-dihydroxy-13E-labden-12-one (4), and (13S)-15-hydroxylabd-8 (17)-en-19-oic acid (5), were isolated from the Chinese liverwort Scapania undulate (L.) Dum., using column chromatography. The structures of these compounds were determined on the basis of 1D- and 2D-NMR analyses. The acetylcholinesterase (AchE) inhibitory activity was evaluated using a bioautographic TLC assay and the cytotoxic activity was evaluated by the MTT method. All the compounds were reported for the first time to exhibit moderate AchE inhibitory activity with minimal inhibitory quantities ranging from 250 to 500 ng. All the compounds were tested for their cytotoxicity against five human tumor cell lines, A549, K562, A2780, Hela, and HT29, and compounds 3 and 4 exhibited moderate inhibitory effects on the growth of A2780 cells. PMID:26721712 14. acetylcholinesterase inhibitory potential and insecticidal activity of an endophytic Alternaria sp. from Ricinus communis. PubMed 2012-11-01 Keeping in view the vast potential of endophytic fungi to produce bioactive molecules, this study aimed at isolating and screening endophytes for the production of acetylcholinesterase inhibitors. Fifty-four endophytic fungi were isolated from Ricinus communis and screened for their AChE inhibitory activity using Ellman's colorimetric assay method. Six isolates were found to possess AChE inhibitory activity with maximum inhibition of 78 % being evinced by culture Cas1 which was identified to be Alternaria sp. on the basis of molecular as well as microscopic methods. Optimization of inhibitor production was carried out using one factor at a time approach. Maximum production of inhibitor was obtained on potato dextrose broth after 10 days incubation. The IC(50) of the chloroform extract was observed to be 40 μg/ml. The extract was purified on silica gel and eluted stepwise with a gradient of chloroform/methanol. The insecticidal potential of the extract was evaluated by feeding the larvae of Spodoptera litura on diet containing varying concentrations of the extract. It was observed that with increase in the concentration of the extract, mortality of the larvae increased. The culture has the potential of being exploited in medicine as well as a biocontrol agent. 15. Inhibition of acetylcholinesterase and cytochrome oxidase activity in Fasciola gigantica cercaria by phytoconstituents. PubMed Sunita, Kumari; Habib, Maria; Kumar, P; Singh, Vinay Kumar; Husain, Syed Akhtar; Singh, D K 2016-02-01 Fasciolosis is an important cattle and human disease caused by Fasciola hepatica and Fasciola gigantica. One of the possible methods to control this problem is to interrupt the life cycle of Fasciola by killing its larva (redia and cercaria) in host snail. Molecular identification of cercaria larva of F. gigantica was done by comparing the nucleotide sequencing with adult F. gigantica. It was noted that nucleotide sequencing of cercaria larva and adult F. gigantica were 99% same. Every month during the year 2011-2012, in vivo treatment with 60% of 4 h LC50 of phyto cercaricides citral, ferulic acid, umbelliferone, azadirachtin and allicin caused significant inhibition of acetylcholinesterase (AChE) and cytochrome oxidase activity in the treated cercaria larva of F. gigantica. Whereas, activity of both enzymes were not significantly altered in the nervous tissues of vector snail Lymnaea acuminata exposed to same treatments. Maximum reduction in AChE (1.35% of control in month of June) and cytochrome oxidase (3.71% of control in the month of July) activity were noted in the cercaria exposed to 60% of 4 h LC50 of azadirachtin and allicin, respectively. PMID:26536397 16. Isolating a cell maximally secreting acetylcholinesterase. Annual report, 31 January 1984-30 January 1985 SciTech Connect Rose, S.; Von Wedel, R.J.; Dorian, R.; Scott, M.C.; Mighetto, P.I. 1985-04-01 Basic methods were developed for the isolation of subpopulations of cells which are high producers of a desired secreted cell protein. The ultimate goal of this research is to isolate a cell line maximally secreting human acetylcholinesterase (AChE, acetylcholine hydrolase). This positive selection system, termed the Cell Isolation Technique (CIT), has evolved in two different directions to screen individual cells trapped within agarose beads. Both approaches rely on a specific ligand-receptor antigen-antibody interaction to capture the desired secreted protein and immobilize it within the beads. In both cases, the cells secrete product, product binds to immobilized specific reagents and thus accumulates within the beads. Beads with high densities of desired product are identified and physically isolated so as to enrich for subpopulations of high producer cells. The two approaches differ with respect to how they identify and sort the beads with desired cells. In the original method, simple density gradient centrifugation is sufficient to separate beads with lysed red blood cells from the vast majority of beads with intact cells. The second approach uses a fluorescence activated cell sorter to screen beads which have accumulated captured secreted cell product now identified with fluorescently labeled antibodies. Although a cell line secreting high levels of AChE has not yet been developed by these methods, model studies have been encouraging. This report will therefore focus on the basic research behind this technology and its application for screening cells transfected with total genomic human DNA. 17. Sublethal Effects of Insecticide Exposure on Megacopta cribraria (Fabricius) Nymphs: Key Biological Traits and Acetylcholinesterase Activity PubMed Central Miao, Jin; Reisig, Dominic D.; Li, Guoping; Wu, Yuqing 2016-01-01 Megacopta cribraria F. (Hemiptera: Plataspidae), the kudzu bug, is an invasive insect pest of U.S. soybean. At present, insecticide application is the primary and most effective control option for M. cribraria. In this study, the potential effects of sublethal and low-lethal concentrations (LC10 and LC40) of three common insecticides on key biological traits and acetylcholinesterase (AChE) activity of the treated nymphal stage of insect were assessed. The results show that the sublethal concentration of imidacloprid significantly reduced adult emergence rate of M. cribraria. A low-lethal concentration of imidacloprid significantly increased nymphal development time, but significantly decreased adult emergence rate and adult longevity. Both sublethal and low-lethal concentrations of acephate caused an increase in nymphal development time and a reduction in adult emergence rate and adult longevity. Fecundity of females was significantly reduced only by exposure to low-lethal concentrations of acephate. Sublethal and low-lethal concentrations of bifenthrin increased nymphal development time, but significantly decreased adult emergence rate. In addition, we found that the AChE activity of M. cribraria was significantly increased only by LC40 imidacloprid, but strongly inhibited by acephate. PMID:27638957 18. Acetylcholinesterase secretion--a parameter for the interpretation of in vitro anthelmintic screens. PubMed Rapson, E B; Chilwan, A S; Jenkins, D C 1986-04-01 Interpretation of anthelmintic activity using in vitro screens has, until now, relied on the detection of drug-induced effects on nematode development, viability and motility. A novel biochemical parameter dependent upon the spectrophotometric assay of acetylcholinesterase (AChE), an enzyme secreted in large quantities by certain trichostrongylid nematodes, has been developed to replace these often subjective indices of activity. Using Nippostrongylus brasiliensis, a worm frequently employed for primary screening, the secretion of this enzyme in the presence or absence of a large number of drugs in vitro was determined. During a 4-day incubation period in a complex undefined medium without serum. AChE was secreted by normal 4th larval and immature adult stages of the worm in a linear fashion. All modern broad-spectrum veterinary anthelmintics, regardless of their mode of action, dramatically reduced the amount of enzyme secreted. Correlation between the biochemical and observational parameters was excellent and the selectivity of the assay when based solely on enzyme secretion was not lost. Other advantages were that the time required for the activity of certain slow-acting compounds to be detected was reduced from 7 to 4 days and that close microscopical examination of the worms was not necessary. 19. Ocimum sanctum Linn. leaf extracts inhibit acetylcholinesterase and improve cognition in rats with experimentally induced dementia. PubMed Giridharan, Vijayasree Vayalanellore; Thandavarayan, Rajarajan Amirthalingam; Mani, Vasudevan; Ashok Dundapa, Taranalli; Watanabe, Kenichi; Konishi, Tetsuya 2011-09-01 Cognitive disorders such as dementia, attention deficits, and Alzheimer's disease (AD) have been well investigated. However, effective interventions for the promotion and progression of AD are unavailable to date. The present work was undertaken to investigate the effects of the aqueous (300 and 500 mg/kg) and alcoholic (300 and 500 mg/kg) extracts of Ocimum sanctum Linn. leaves as an antidementic and anticholinesterase agent and also as an immunostimulant in rats. Maximal electroshock, atropine, and cyclosporine were used to induce dementia. The passive avoidance task was used for assessing memory. Acetylcholinesterase (AChE) activity was estimated in different parts of the brain, and immune status was studied using dinitrochlorobenzene (DNCB) skin sensitivity tests. In all the three models both aqueous and alcoholic O. sanctum extracts decreased the time taken to reach the shock-free zone and the number of mistakes and significantly decreased the AChE activity in rats. O. sanctum treatment significantly increased the induration in the DNCB skin test. Therefore, O. sanctum was shown to be useful for the management of experimentally induced cognitive dysfunctions in rats. 20. Sublethal Effects of Insecticide Exposure on Megacopta cribraria (Fabricius) Nymphs: Key Biological Traits and Acetylcholinesterase Activity. PubMed Miao, Jin; Reisig, Dominic D; Li, Guoping; Wu, Yuqing 2016-01-01 Megacopta cribraria F. (Hemiptera: Plataspidae), the kudzu bug, is an invasive insect pest of U.S. soybean. At present, insecticide application is the primary and most effective control option for M. cribraria In this study, the potential effects of sublethal and low-lethal concentrations (LC10 and LC40) of three common insecticides on key biological traits and acetylcholinesterase (AChE) activity of the treated nymphal stage of insect were assessed. The results show that the sublethal concentration of imidacloprid significantly reduced adult emergence rate of M. cribraria A low-lethal concentration of imidacloprid significantly increased nymphal development time, but significantly decreased adult emergence rate and adult longevity. Both sublethal and low-lethal concentrations of acephate caused an increase in nymphal development time and a reduction in adult emergence rate and adult longevity. Fecundity of females was significantly reduced only by exposure to low-lethal concentrations of acephate. Sublethal and low-lethal concentrations of bifenthrin increased nymphal development time, but significantly decreased adult emergence rate. In addition, we found that the AChE activity of M. cribraria was significantly increased only by LC40 imidacloprid, but strongly inhibited by acephate. PMID:27638957 1. Sublethal Effects of Insecticide Exposure on Megacopta cribraria (Fabricius) Nymphs: Key Biological Traits and Acetylcholinesterase Activity. PubMed Miao, Jin; Reisig, Dominic D; Li, Guoping; Wu, Yuqing 2016-01-01 Megacopta cribraria F. (Hemiptera: Plataspidae), the kudzu bug, is an invasive insect pest of U.S. soybean. At present, insecticide application is the primary and most effective control option for M. cribraria In this study, the potential effects of sublethal and low-lethal concentrations (LC10 and LC40) of three common insecticides on key biological traits and acetylcholinesterase (AChE) activity of the treated nymphal stage of insect were assessed. The results show that the sublethal concentration of imidacloprid significantly reduced adult emergence rate of M. cribraria A low-lethal concentration of imidacloprid significantly increased nymphal development time, but significantly decreased adult emergence rate and adult longevity. Both sublethal and low-lethal concentrations of acephate caused an increase in nymphal development time and a reduction in adult emergence rate and adult longevity. Fecundity of females was significantly reduced only by exposure to low-lethal concentrations of acephate. Sublethal and low-lethal concentrations of bifenthrin increased nymphal development time, but significantly decreased adult emergence rate. In addition, we found that the AChE activity of M. cribraria was significantly increased only by LC40 imidacloprid, but strongly inhibited by acephate. 2. Inhibition of acetylcholinesterase and cytochrome oxidase activity in Fasciola gigantica cercaria by phytoconstituents. PubMed Sunita, Kumari; Habib, Maria; Kumar, P; Singh, Vinay Kumar; Husain, Syed Akhtar; Singh, D K 2016-02-01 Fasciolosis is an important cattle and human disease caused by Fasciola hepatica and Fasciola gigantica. One of the possible methods to control this problem is to interrupt the life cycle of Fasciola by killing its larva (redia and cercaria) in host snail. Molecular identification of cercaria larva of F. gigantica was done by comparing the nucleotide sequencing with adult F. gigantica. It was noted that nucleotide sequencing of cercaria larva and adult F. gigantica were 99% same. Every month during the year 2011-2012, in vivo treatment with 60% of 4 h LC50 of phyto cercaricides citral, ferulic acid, umbelliferone, azadirachtin and allicin caused significant inhibition of acetylcholinesterase (AChE) and cytochrome oxidase activity in the treated cercaria larva of F. gigantica. Whereas, activity of both enzymes were not significantly altered in the nervous tissues of vector snail Lymnaea acuminata exposed to same treatments. Maximum reduction in AChE (1.35% of control in month of June) and cytochrome oxidase (3.71% of control in the month of July) activity were noted in the cercaria exposed to 60% of 4 h LC50 of azadirachtin and allicin, respectively. 3. Zebrafish as a model for acetylcholinesterase-inhibiting organophosphorus agent exposure and oxime reactivation. PubMed Koenig, Jeffrey A; Dao, Thuy L; Kan, Robert K; Shih, Tsung-Ming 2016-06-01 The current research progression efforts for investigating novel treatments for exposure to organophosphorus (OP) compounds that inhibit acetylcholinesterase (AChE), including pesticides and chemical warfare nerve agents (CWNAs), rely solely on in vitro cell assays and in vivo rodent models. The zebrafish (Danio rerio) is a popular, well-established vertebrate model in biomedical research that offers high-throughput capabilities and genetic manipulation not readily available with rodents. A number of research studies have investigated the effects of subacute developmental exposure to OP pesticides in zebrafish, observing detrimental effects on gross morphology, neuronal development, and behavior. Few studies, however, have utilized this model to evaluate treatments, such as oxime reactivators, anticholinergics, or anticonvulsants, following acute exposure. Preliminary work has investigated the effects of CWNA exposure. The results clearly demonstrated relative toxicity and oxime efficacy similar to that reported for the rodent model. This review surveys the current literature utilizing zebrafish as a model for OP exposure and highlights its potential use as a high-throughput system for evaluating AChE reactivator antidotal treatments to acute pesticide and CWNA exposure. PMID:27123828 4. Potent acetylcholinesterase inhibitors: Synthesis, biological assay and docking study of nitro acridone derivatives. PubMed Parveen, Mehtab; Aslam, Afroz; Nami, Shahab A A; Malla, Ali Mohammed; Alam, Mahboob; Lee, Dong-Ung; Rehman, Sumbul; Silva, P S Pereira; Silva, M Ramos 2016-08-01 The reaction of o-halobenzoic acid with aniline derivatives and their subsequent cyclization reaction yielded the acridone derivatives. The series of nitro acridone derivatives were prepared by Ullmann condensation in presence of copper as catalyst and were characterized by FTIR, (1)H, (13)C NMR and mass spectra. The structure of 5-nitro-(2-phenyl amino) benzoic acid (4) was confirmed by X-ray crystallography and was found to crystallize in P21/c space group. The in vitro efficacy of the compounds for their acetylcholinesterase (AChE) and antimicrobial inhibitory activities have been evaluated against the standard drugs Ampicillin and Gentamicin against Gram positive and Gram negative bacteria. 1,7-Dinitroacridone was found to be the most potent AChE inhibitor (IC50=0.22μM). Moreover, the compounds have been screened for their antioxidant activity using the DPPH assay. Also, docking study results were found to be in good agreement with the results obtained through in vitro experiments. The docking study further predicted possible binding conformation. PMID:27295412 5. An Acetylcholinesterase-Based Chronoamperometric Biosensor for Fast and Reliable Assay of Nerve Agents PubMed Central Pohanka, Miroslav; Adam, Vojtech; Kizek, Rene 2013-01-01 The enzyme acetylcholinesterase (AChE) is an important part of cholinergic nervous system, where it stops neurotransmission by hydrolysis of the neurotransmitter acetylcholine. It is sensitive to inhibition by organophosphate and carbamate insecticides, some Alzheimer disease drugs, secondary metabolites such as aflatoxins and nerve agents used in chemical warfare. When immobilized on a sensor (physico-chemical transducer), it can be used for assay of these inhibitors. In the experiments described herein, an AChE- based electrochemical biosensor using screen printed electrode systems was prepared. The biosensor was used for assay of nerve agents such as sarin, soman, tabun and VX. The limits of detection achieved in a measuring protocol lasting ten minutes were 7.41 × 10−12 mol/L for sarin, 6.31 × 10−12 mol/L for soman, 6.17 × 10−11 mol/L for tabun, and 2.19 × 10−11 mol/L for VX, respectively. The assay was reliable, with minor interferences caused by the organic solvents ethanol, methanol, isopropanol and acetonitrile. Isopropanol was chosen as suitable medium for processing lipophilic samples. PMID:23999806 6. Conformational remodeling of femtomolar inhibitor-acetylcholinesterase complexes in the crystalline state PubMed Central Bourne, Yves; Radic, Zoran; Taylor, Palmer; Marchot, Pascale 2010-01-01 The active center of acetylcholinesterase (AChE), a target site for competitive inhibitors, resides centrosymmetric to the subunit at the base of a deep, narrow gorge lined by aromatic residues. At the gorge entry, a peripheral site encompasses overlapping binding loci for non-competitive inhibitors, which alter substrate access to the gorge. The click-chemistry inhibitor TZ2PA6 links the active center ligand, tacrine, to the peripheral site ligand, propidium, through a biorthogonal reaction of an acetylene and an azide that forms either a syn1 or an anti1 triazole. Compared with wild-type mouse AChE, a Tyr337Ala mutant displays full catalytic activity, albeit with two to three orders of magnitude higher affinities for the TZ2PA6 syn1 and anti1 regioisomers, reflected in low femtomolar Kd values, diffusion-limited association and dissociation half-times greater than one month and one week, respectively. Three structures of each of the co-crystallized syn1 and anti1 complexes of the Tyr337Ala mutant were solved at three distinct times of crystal maturation, consistent with or exceeding the half-lives of the complexes in solution, while crystalline complexes obtained from soaked Tyr337Ala crystals led to picturing “freshly formed” complexes. The structures, at 2.55-2.75Å resolution, reveal a range of unprecedented conformations of the bound regioisomers, not observed in the wild-type AChE complexes, associated with concerted positional rearrangements of side chains in the enzyme gorge. Moreover, time-dependent conformational remodeling of the crystalline complexes appears to correlate with the dissociation half-times of the solution complexes. Hence for the tight-binding TZ2PA6 inhibitors, the initial complexes kinetically driven in solution slowly form more stable complexes governed by thermodynamic equilibrium and observable in mature crystals. PMID:21090615 7. Acetylcholinesterase inhibition and locomotor function after motor-sensory cortex impact injury. PubMed Holschneider, Daniel P; Guo, Yumei; Roch, Margareth; Norman, Keith M; Scremin, Oscar U 2011-09-01 Traumatic brain injury (TBI) induces transient or persistent dysfunction of gait and balance. Enhancement of cholinergic transmission has been reported to accelerate recovery of cognitive function after TBI, but the effects of this intervention on locomotor activity remain largely unexplored. The hypothesis that enhancement of cholinergic function by inhibition of acetylcholinesterase (AChE) improves locomotion following TBI was tested in Sprague-Dawley male rats after a unilateral controlled cortical impact (CCI) injury of the motor-sensory cortex. Locomotion was tested by time to fall on the constant speed and accelerating Rotarod, placement errors and time to cross while walking through a horizontal ladder, activity monitoring in the home cages, and rearing behavior. Assessments were performed the 1st and 2nd day and the 1st, 2nd, and 3rd week after TBI. The AChE inhibitor physostigmine hemisulfate (PHY) was administered continuously via osmotic minipumps implanted subcutaneously at the rates of 1.6-12.8 μmol/kg/day. All measures of locomotion were impaired by TBI and recovered to initial levels between 1 and 3 weeks post-TBI, with the exception of the maximum speed achievable on the accelerating Rotarod, as well as rearing in the open field. PHY improved performance in the accelerating Rotarod at 1.6 and 3.2 μmol/kg/day (AChE activity 95 and 78% of control, respectively), however, higher doses induced progressive deterioration. No effect or worsening of outcomes was observed at all PHY doses for home cage activity, rearing, and horizontal ladder walking. Potential benefits of cholinesterase inhibition on locomotor function have to be weighed against the evidence of the narrow range of useful doses. PMID:21787180 8. A sensitive magnetic nanoparticle-based immunoassay of phosphorylated acetylcholinesterase using protein cage templated lead phosphate for signal amplification with graphite furnace atomic absorption spectrometry detection. PubMed Liang, Pei; Kang, Caiyan; Yang, Enjian; Ge, Xiaoxiao; Du, Dan; Lin, Yuehe 2016-04-01 We developed a new magnetic nanoparticle sandwich-like immunoassay using protein cage nanoparticles (PCN) for signal amplification together with graphite furnace atomic absorption spectrometry (GFAAS) for the quantification of an organophosphorylated acetylcholinesterase adduct (OP-AChE), the biomarker of exposure to organophosphate pesticides (OPs) and nerve agents. OP-AChE adducts were firstly captured by titanium dioxide coated magnetic nanoparticles (TiO2-MNPs) from the sample matrixes through metal chelation with phospho-moieties, and then selectively recognized by anti-AChE antibody labeled on PCN which was packed with lead phosphate in its cavity (PCN-anti-AChE). The sandwich-like immunoreaction was performed among TiO2-MNPs, OP-AChE and PCN-anti-AChE to form a TiO2-MNP/OP-AChE/PCN-anti-AChE immunocomplex. The complex could be easily isolated from the sample solution with the help of magnet, and the released lead ions from PCN were detected by GFAAS for the quantification of OP-AChE. Greatly enhanced sensitivity was achieved because PCN increased the amount of metal ions in the cavity of each apoferritin. The proposed immunoassay yielded a linear response over a broad range of OP-AChE concentrations from 0.01 nM to 2 nM, with a detection limit of 2 pM, which has enough sensitivity for monitoring of low-dose exposure to OPs. This new method showed an acceptable stability and reproducibility and was validated with OP-AChE spiked human plasma. 9. Sensitive magnetic nanoparticle-based immunoassay of phosphorylated acetylcholinesterase using protein cage templated lead phosphate for signal amplification with graphite furnace atomic absorption spectrometry detection PubMed Central Liang, Pei; Kang, Caiyan; Yang, Enjian; Ge, Xiaoxiao; Du, Dan; Lin, Yuehe 2016-01-01 We developed a new magnetic nanoparticles sandwich-like immunoassay using protein cage nanoparticles (PCN) for signal amplification together with graphite furnace atomic absorption spectrometry (GFAAS) for quantification of organophosphorylated acetylcholinesterase adduct (OP-AChE), the biomarker of exposure to organophosphate pesticides (OPs) and nerve agents. OP-AChE adducts were firstly captured by titanium dioxide coated magnetic nanoparticles (TiO2-MNPs) from the sample matrixes through metal chelation with phospho-moieties, and then selectively recognized by anti-AChE antibody labeled on PCN which was packed with lead phosphate in its cavity (PCN-anti-AChE). The sandwich-like immunoreaction was performed among TiO2-MNPs, OP-AChE and PCN-anti-AChE to form TiO2-MNPs/OP-AChE/PCN-anti-AChE immunocomplex. The complex could be easily isolated from the sample solution with the help of magnet, and the released lead ions from PCN were detected by GFAAS for the quantification of OP-AChE. Greatly enhanced sensitivity was achieved because PCN increased the amount of metal ions in the cavity of each apoferritin. The proposed immunoassay yielded a linear response over a broad OP-AChE concentrations from 0.01 nM to 2 nM, with a detection limit of 2 pM, which has enough sensitivity for monitoring of low-dose exposure to OPs. This new method showed an acceptable stability and reproducibility and was validated with OP-AChE spiked human plasma. PMID:26953358 10. A sensitive magnetic nanoparticle-based immunoassay of phosphorylated acetylcholinesterase using protein cage templated lead phosphate for signal amplification with graphite furnace atomic absorption spectrometry detection. PubMed Liang, Pei; Kang, Caiyan; Yang, Enjian; Ge, Xiaoxiao; Du, Dan; Lin, Yuehe 2016-04-01 We developed a new magnetic nanoparticle sandwich-like immunoassay using protein cage nanoparticles (PCN) for signal amplification together with graphite furnace atomic absorption spectrometry (GFAAS) for the quantification of an organophosphorylated acetylcholinesterase adduct (OP-AChE), the biomarker of exposure to organophosphate pesticides (OPs) and nerve agents. OP-AChE adducts were firstly captured by titanium dioxide coated magnetic nanoparticles (TiO2-MNPs) from the sample matrixes through metal chelation with phospho-moieties, and then selectively recognized by anti-AChE antibody labeled on PCN which was packed with lead phosphate in its cavity (PCN-anti-AChE). The sandwich-like immunoreaction was performed among TiO2-MNPs, OP-AChE and PCN-anti-AChE to form a TiO2-MNP/OP-AChE/PCN-anti-AChE immunocomplex. The complex could be easily isolated from the sample solution with the help of magnet, and the released lead ions from PCN were detected by GFAAS for the quantification of OP-AChE. Greatly enhanced sensitivity was achieved because PCN increased the amount of metal ions in the cavity of each apoferritin. The proposed immunoassay yielded a linear response over a broad range of OP-AChE concentrations from 0.01 nM to 2 nM, with a detection limit of 2 pM, which has enough sensitivity for monitoring of low-dose exposure to OPs. This new method showed an acceptable stability and reproducibility and was validated with OP-AChE spiked human plasma. PMID:26953358 11. Reanalysis with optimized power of red blood cell acetylcholinesterase activity from a 1-year dietary treatment of dogs to chlorpyrifos. PubMed Mattsson, J L; Holden, L; Eisenbrandt, D L; Gibson, J E 2001-03-01 A no-observed-effect level (NOEL) of 0.1 mg/kg/day was reported for inhibition of red blood cell (RBC) acetylcholinesterase (AChE) in two groups of Beagle dogs fed chlorpyrifos (0, 0.01, 0.03, 0.1, 1 or 3 mg/kg/day) in the diet for 1 or 2 years (McCollister et al., Food Cosmet. Toxicol. 12 (1974) 45-61). The statistical analyses were by t-test that had low statistical power due to small sample sizes. Common time points for blood samples in both phases allowed a reanalysis of the grouped data over a 1-year time period. The reanalysis increased statistical power by increasing the sample size to n=14 from n=3 or 4, and decreasing the variance, by statistical step-by-step aggregation of the data from both phases, both sexes, and four sample periods. Factors retained in the ANOVA were dose, sex, and phase (sex-by-dose was not significant). Contrasts with one-sided t-tests indicated the 1 and 3 mg/kg/day groups had significantly inhibited RBC AChE (P<0.0001). At alpha=0.05, the uncorrected one-sided model had 80% power to detect a 12% decrease, 93% power for a 15% decrease, and 99.5% power for a 20% decrease in AChE activity. Overall, the reanalysis had high power to detect a clinically significant decrease in RBC AChE activity, and substantiated the original NOEL for chronic treatment of dogs to dietary chlorpyrifos at 0.1 mg/kg/day. PMID:11246135 12. Pesticide Mixture Toxicity in Surface Water Extracts in Snails (Lymnaea stagnalis) by an in Vitro Acetylcholinesterase Inhibition Assay and Metabolomics. PubMed Tufi, Sara; Wassenaar, Pim N H; Osorio, Victoria; de Boer, Jacob; Leonards, Pim E G; Lamoree, Marja H 2016-04-01 Many chemicals in use end up in the aquatic environment. The toxicity of water samples can be tested with bioassays, but a metabolomic approach has the advantage that multiple end points can be measured simultaneously and the affected metabolic pathways can be revealed. A current challenge in metabolomics is the study of mixture effects. This study aims at investigating the toxicity of an environmental extract and its most abundant chemicals identified by target chemical analysis of >100 organic micropollutants and effect-directed analysis (EDA) using the acetylcholinesterase (AChE) bioassay and metabolomics. Surface water from an agricultural area was sampled with a large volume solid phase extraction (LVSPE) device using three cartridges containing neutral, anionic, and cationic sorbents able to trap several pollutants classes like pharmaceuticals, pesticides, PAHs, PCBs, and perfluorinated surfactants. Targeted chemical analysis and AChE bioassay were performed on the cartridge extracts. The extract of the neutral sorbent cartridge contained most of the targeted chemicals, mainly imidacloprid, thiacloprid, and pirimicarb, and was the most potent AChE inhibitor. Using an EDA approach, other AChE inhibiting candidates were identified in the neutral extract, such as carbendazim and esprocarb. Additionally, a metabolomics experiment on the central nervous system (CNS) of the freshwater snail Lymnaea stagnalis was conducted. The snails were exposed to the extract, the three most abundant chemicals individually, and a mixture of these. The extract disturbed more metabolic pathways than the three most abundant chemicals individually, indicating the contribution of other chemicals. Most pathways perturbed by the extract exposure overlapped with those related to exposure to neonicotinoids, like the polyamine metabolism involved in CNS injuries. Metabolomics for the straightforward comparison between a complex mixture and single compound toxicity is still challenging but 13. Brain acetylcholinesterase, malondialdehyde and reduced glutathione as biomarkers of continuous exposure of tench, Tinca tinca, to carbofuran or deltamethrin. PubMed Hernández-Moreno, D; Soler, F; Míguez, M P; Pérez-López, M 2010-10-01 In this study, the chronic effect of the insecticides carbofuran and deltamethrin on acetylcholinesterase (AChE) activity and malondialdehyde (MDA) and reduced glutathione (GSH) levels were examined in the brain of tench. Both pesticides were evaluated in two separate experiments, and animals were exposed in a continuous flow-system to three different concentrations of carbofuran (0, 10 and 100 microg/L) and deltamethrin (0, 0.0039 and 0.039 microg/L) for 60 days. After that period, animals were kept into pesticide-free water for other 30 days. In all cases, animals were sampled every 10 days all along the experience. AChE activity was significantly inhibited in fish exposed to 100 microg/L of carbofuran, during the first 30 days of exposition, returning to basal levels after this initial period. With respect to deltamethrin exposure, AChE activity was not significantly affected. When considering MDA levels, significant changes could only be detected during the recovery period for both pesticides, with a maximum of induction at 70 and 80 days, respectively associated to the highest dose of carbofuran and deltamethrin. Similarly, GSH levels varied all along the experience, with a maximum of significant increase at day 80 of exposition to the highest dose of both pesticides. This study shows that changes in AChE brain activity in tench can be used as a biomarker of early pesticide exposition in environmental monitoring programs, whereas MDA and GSH levels could be more associated to long-term expositions. The above results confirm and broaden former observations, suggesting that more investigations are needed before these biochemical parameters can be used as biomarkers. 14. Synthesis and evaluation of (-)- and (+)-[¹¹C]galanthamine as PET tracers for cerebral acetylcholinesterase imaging. PubMed Kimura, Hiroyuki; Kawai, Tomoki; Hamashima, Yoshio; Kawashima, Hidekazu; Miura, Kenji; Nakaya, Yuta; Hirasawa, Makoto; Arimitsu, Kenji; Kajimoto, Tetsuya; Ohmomo, Yoshiro; Ono, Masahiro; Node, Manabu; Saji, Hideo 2014-01-01 Improved radiopharmaceuticals for imaging cerebral acetylcholinesterase (AChE) are needed for the diagnosis of Alzheimer's disease (AD). Thus, (11)C-labeled (-)-galanthamine and its enantiomers were synthesized as novel agents for imaging the localization and activity of AChE by positron emission tomography (PET). C-11 was incorporated into (-)- and (+)-[(11)C]galanthamine by N-methylation of norgalanthamines with [(11)C]methyl triflate. Simple accumulation of (11)C in the brain was measured in an in vivo biodistribution study using mice, whilst donepezil was used as a blocking agent in analogous in vivo blocking studies. In vitro autoradiography of rat brain tissue was performed to investigate the distribution of (-)-[(11)C]galanthamine, and confirmed the results of PET studies in mice. The radiochemical yields of N-methylation of (-)- and (+)-norgalanthamines were 13.7% and 14.4%, respectively. The highest level of accumulation of (11)C in the brains of mice was observed at 10 min after administration (2.1% ID/g). Intravenous pretreatment with donepezil resulted in a 30% decrease in accumulation of (-)-[(11)C]galanthamine in the striatum; however, levels in the cerebellum were unchanged. In contrast, use of (+)-[(11)C]galanthamine led to accumulation of radioactivity in the striatum equal to that in the cerebellum, and these levels were unaffected by pretreatment with donepezil. In in vitro autoradiography of regional radioactive signals of brain sections showed that pretreatment with either (-)-galanthamine or donepezil blocked the binding of (-)-[(11)C]galanthamine to the striatum, while sagittal PET imaging revealed accumulation of (-)-[(11)C]galanthamine in the brain. These results indicate that (-)-[(11)C]galanthamine showed specific binding to AChE, whereas (+)-[(11)C]-galanthamine accumulated in brain tissue by non-specific binding. Thus, optically pure (-)-[(11)C]galanthamine could be a useful PET tracer for imaging cerebral AChE. 15. Molecular characterization of two acetylcholinesterase genes from the oriental tobacco budworm, Helicoverpa assulta (Guenée). PubMed Lee, Dae-Weon; Kim, Sung-Su; Shin, Seung Won; Kim, Won Tae; Boo, Kyung Saeng 2006-02-01 Acetylcholinesterase (AChE) has been known to be the target of organophosphorous and carbamate insecticides. Only a single AChE, however, existed in insects and was involved in insecticide resistance, recently another AChE is reported in mosquitoes and aphids. We have cloned cDNAs encoding two ace genes, designated as Ha-ace1 and Ha-ace2 by a combined degenerate PCR and RACE strategy from adult heads of the oriental tobacco budworm, Helicoverpa assulta. The Ha-ace1 and Ha-ace2 genes encode 664 and 647 amino acids, respectively and have conserved motifs including a catalytic triad, a choline-binding site and an acyl pocket. Both Ha-AChEs were determined to be secretory proteins based on the existence of a signal peptide. The Ha-ace1 gene, the first reported ace1 in lepidopterans, belongs to the ace1 subfamily whereas the Ha-ace2 gene showed high similarity to those in the ace2 subfamily. Phylogenetic analysis showed that the Ha-ace1 gene was completely diverged from the Ha-ace2, suggesting that the Ha-ace genes are duplicated. Quantitative real time-PCR revealed that expression level of the Ha-ace1 gene was much higher than that of the Ha-ace2 in all body parts examined. The biochemical properties of purified proteins by affinity chromatography showed substrate specificity for acetylthiocholine iodide, and inhibitor specificity for BW284C51 and eserine and their peptide sequences partially identified by a MALDI-TOF mass spectrometer demonstrated that two Ha-AChEs were expressed in vivo. PMID:16352398 16. A combined molecular docking and charge density analysis is a new approach for medicinal research to understand drug-receptor interaction: curcumin-AChE model. PubMed Renuga Parameswari, A; Rajalakshmi, G; Kumaradhas, P 2015-01-01 In the present study, a molecular docking analysis has been performed on diketone form of curcumin molecule with acetylcholinesterase (AChE). The calculated lowest docked energy of curcumin molecule in the active site of AChE is -11.21 kcal/mol; this high negative value indicates that the molecule exhibits large binding affinity towards AChE. When the curcumin molecule present in the active site of AChE, subsequently, its conformation has altered significantly and the molecule adopts a U-shape geometry as it is linear in gas phase (before entering into the active site). This conformational transition facilitates curcumin to form strong interaction with Phe330 of acyl-binding pocket and the choline binding site with indole ring of Trp84 and Asp72. The gas phase and the active site analysis of curcumin allows to understand the conformational geometry, nature of molecular flexibility, charge density redistribution and the variation of electrostatic properties of curcumin in the active site. To obtain the gas phase structure, the curcumin molecule was optimized using Hartree-Fock and density functional methods (B3LYP) with the basis set 6-311G(∗∗). A charge density analysis on both gas phase as well as the molecule lifted from the active site was carried out using Bader's theory of atoms in molecules (AIM). The difference in molecular electrostatic potential between the two forms of curcumin displays the difference in charge distribution. The large dipole moment of curcumin (7.54 D) in the active site reflects the charge redistribution as it is much less in the gas phase (4.34 D). 17. Anti-acetylcholinesterase and antioxidant activities and HPLC-MS analysis of polyphenol from extracts of Nelsonia canescens (Lam.) Spreng. PubMed Central Ouattara, Nabèrè; Meda, Roland Nâg-Tiero; Hilou, Adama; Guenné, Samson; Konaté, Kiessoum; Coulibaly, Ahmed Y; Kiendrébeogo, Martin; Millogo, Jeanne F; Nacoulma, Odile G 2013-01-01 Objective To investigate the anti-acetylcholinesterase and antioxidant activities and to evaluate the major polyphenolic compounds of Nelsonia canescens extracts. Methods The anti-acetylcholinesterase activity was assessed using a kinetic inhibition standard method. Two methods, ABTS and lipid peroxidation, were used to estimate the antioxidant capacity. Polyphenols profile of the plant extract has been determined with a HPLC-MS method. Results The results showed that butanol extract exhibited the best anti-acetylcholinesterase activity with inhibition percentage of (55.62±1.49)%. The best 3 ethylbenzothiazoline-6-sulphonate radical cation scavenging capacity was found for ethyl acetate extract with a value of (56.20±0.77) mg equivalent trolox/g while the crude extract showed the highest inhibition of the rat liver lipid peroxidation (52.57±1.20)%. Polyphenols profile revealed the presence of five phenol acids (p-coumaric acid, caffeic acid, chlorogenic acid, ferulic acid and gentisic acid) and three flavonoids (apigenin, luteolin, quercetin). Conclusions All the extracts of Nelsonia canescens exhibited antioxidant and AChE inhibition capacities. The active compounds identified and quantified in this species are mainly responsible for these in vitro biological activities and allow to justify its widely use in Burkina Faso traditional medicine. 18. Mutations of acetylcholinesterase which confer insecticide resistance in Drosophila melanogaster populations PubMed Central Menozzi, Philippe; Shi, Ming An; Lougarre, Andrée; Tang, Zhen Hua; Fournier, Didier 2004-01-01 Background Organophosphate and carbamate insecticides irreversibly inhibit acetylcholinesterase causing death of insects. Resistance-modified acetylcholinesterases(AChEs) have been described in many insect species and sequencing of their genes allowed several point mutations to be described. However, their relative frequency and their cartography had not yet been addressed. Results To analyze the most frequent mutations providing insecticide resistance in Drosophila melanogaster acetylcholinesterase, the Ace gene was cloned and sequenced in several strains harvested from different parts of the world. Sequence comparison revealed four widespread mutations, I161V, G265A, F330Y and G368A. We confirm here that mutations are found either isolated or in combination in the same protein and we show that most natural populations are heterogeneous, composed of a mixture of different alleles. In vitro expression of mutated proteins showed that combining mutations in the same protein has two consequences: it increases resistance level and provides a wide spectrum of resistance. Conclusion The presence of several alleles in natural populations, offering various resistance to carbamate and organophosphate compounds will complicate the establishment of resistance management programs. PMID:15018651 19. Multiple animal studies for medical chemical defense program in soldier/patient decontamination and drug development on task order 85-13: Advanced screening system for evaluating barrier compounds for protection from organophosphate chemical surety material using a nonlethal end point, acetylcholinesterase inhibition. Final report, 1 January 1985-1 September 1988 SciTech Connect Joiner, R.L.; Dill, S.; Olson, T.; Kiser, C.; Feder, I. 1988-09-01 This task was initiated at the Medical Research and Evaluation Facility to develop a protocol for advanced screening of candidate barrier compounds for protection from nerve agents using a quantifiable nonlethal end point as a measure of effectiveness. Soman (GD), thickened GD (TGD), and VX were used to generate a family of curves for erythrocyte (RBC) acetylcholinesterase (AChE) inhibition as a function these data, a single dose was selected for each agent to challenge barrier-protected and unprotected animals. Blood samples were drawn at three times after exposure from each group of agent-challenged animals to validate the model by comparing AChE depression and rate of inhibition in unprotected and barrier-protected animals. Screen, organophosphate, chemical surety materiel, TGD, GD, VX, acetylcholinesterase inhibition, barrier compounds, nonlethal end point, PEG 540, rabbits. 20. Musical Hallucinations Treated with Acetylcholinesterase Inhibitors PubMed Central Blom, Jan Dirk; Coebergh, Jan Adriaan F.; Lauw, René; Sommer, Iris E. C. 2015-01-01 Musical hallucinations are relatively rare auditory percepts which, due to their intrusive nature and the accompanying fear of impending mental decline, tend to cause significant distress and impairment. Although their etiology and pathophysiology appear to be heterogeneous and no evidence-based treatment methods are available, case reports indicate that acetylcholinesterase inhibitors may yield positive results in patients with comorbid hearing loss. We present two female patients (aged 76 and 78 years) both of whom suffered from hearing impairment and practically incessant musical hallucinations. Both patients were successfully treated with the acetylcholinesterase inhibitor rivastigmine. Based on these two case descriptions and an overview of studies describing the use of acetylcholinesterase inhibitors in similar patients, we discuss possible mechanisms and propose further research on the use of acetylcholinesterase inhibitors for musical hallucinations experienced in concordance with hearing loss. PMID:25904872 1. EQCM Immunoassay for Phosphorylated Acetylcholinesterase as a Biomarker for Organophosphate Exposures Based on Selective Zirconia Adsorption and Enzyme-Catalytic Precipitation SciTech Connect Wang, Hua; Wang, Jun; Choi, Daiwon; Tang, Zhiwen; Wu, Hong; Lin, Yuehe 2009-03-01 A zirconia (ZrO2) adsorption-based immunoassay by electrochemical quartz crystal microbalance (EQCM) has been initially developed, aiming at the detection of phosphorylated acetylcholinesterase (AChE) as a potential biomarker for bio-monitoring exposures to organophosphate (OP) pesticides and chemical warfare agents. Hydroxyl-derivatized monolayer was preferably chosen to modify the crystal serving as the template for directing the electro-deposition of ZrO2 film with uniform nanostructures. The resulting ZrO2 film was utilized to selectively capture phosphorylated AChE from the sample media. Horseradish peroxidase (HRP)-labeled anti-AChE antibodies were further employed to recognize the captured phosphorylated protein. Enzyme-catalytic oxidation of the benzidine substrate resulted in the accumulation of insoluble product on the functionalized crystal. Ultrasensitive EQCM quantification by mass-amplified frequency responses as well as rapid qualification by visual color changes of product could be thus achieved. Moreover, 4-chloro-1-naphthol (CN) was comparably studied as an ideal chromogenic substrate for the enzyme-catalytic precipitation. Experimental results show that the developed EQCM technique can allow for the detection of phosphorylated AChE in human plasma. Such an EQCM immunosensing format opens a new door towards the development of simple, sensitive, and field-applicable biosensor for biologically monitoring low-level OP exposures. 2. Preclinical and first-in-human evaluation of PRX-105, a PEGylated, plant-derived, recombinant human acetylcholinesterase-R SciTech Connect Atsmon, Jacob; Brill-Almon, Einat; Nadri-Shay, Carmit; Chertkoff, Raul; Alon, Sari; Shaikevich, Dimitri; Volokhov, Inna; Haim, Kirsten Y.; Bartfeld, Daniel; Shulman, Avidor; Ruderfer, Ilya; Ben-Moshe, Tehila; Shilovitzky, Orit; Soreq, Hermona; Shaaltiel, Yoseph 2015-09-15 PRX-105 is a plant-derived recombinant version of the human ‘read-through’ acetylcholinesterase splice variant (AChE-R). Its active site structure is similar to that of the synaptic variant, and it displays the same affinity towards organophosphorus (OP) compounds. As such, PRX-105 may serve as a bio-scavenger for OP pesticides and chemical warfare agents. To assess its potential use in prophylaxis and treatment of OP poisoning we conducted several preliminary tests, reported in this paper. Intravenous (IV) PRX-105 was administered to mice either before or after exposure to an OP toxin. All mice who received an IV dose of 50 nmol/kg PRX-105, 2 min before being exposed to 1.33 × LD{sub 50} and 1.5 × LD{sub 50} of toxin and 10 min after exposure to 1.5 × LD{sub 50} survived. The pharmacokinetic and toxicity profiles of PRX-105 were evaluated in mice and mini-pigs. Following single and multiple IV doses (50 to 200 mg/kg) no deaths occurred and no significant laboratory and histopathological changes were observed. The overall elimination half-life (t{sub ½}) in mice was 994 (± 173) min. Additionally, a first-in-human study, to assess the safety, tolerability and pharmacokinetics of the compound, was conducted in healthy volunteers. The t{sub ½} in humans was substantially longer than in mice (average 26.7 h). Despite the small number of animals and human subjects who were assessed, the fact that PRX-105 exerts a protective and therapeutic effect following exposure to lethal doses of OP, its favorable safety profile and its relatively long half-life, renders it a promising candidate for treatment and prophylaxis against OP poisoning and warrants further investigation. - Highlights: • PRX-105 is a PEGylated plant-derived recombinant human acetylcholinesterase-R. • PRX-105 is a promising bio-scavenger for organophosphorous toxins at lethal doses. • PRX-105 was shown to protect animals both prophylactically and post-poisoning. • First-in-human study 3. Biosensor based on acetylcholinesterase immobilized onto layered double hydroxides for flow injection/amperometric detection of organophosphate pesticides. PubMed Gong, Jingming; Guan, Zhangqiong; Song, Dandan 2013-01-15 We developed a highly sensitive flow injection/amperometric biosensor for the detection of organophosphate pesticides (OPs) using layered double hydroxides (LDHs) as the immobilization matrix of acetylcholinesterase (AChE). LDHs provided a biocompatible microenvironment to keep the bioactivity of AChE, due to the intrinsic properties of LDHs (such as a regular structure, good mechanical, chemical and thermal stabilities, and swelling properties). By integrating the flow injection analysis (FIA) with amperometric detection, the resulting AChE-LDHs modified electrode greatly catalyzed the oxidation of the enzymatically generated thiocholine product, and facilitated the detection automation, thus increasing the detection sensitivity. The analytical conditions for the FIA/amperometric detection of OPs were optimized by using methyl parathion (MP) as a model. The inhibition of MP was proportional to its concentration ranging from 0.005 to 0.3μg mL(-1) and 0.3 to 4.0μg mL(-1) with a detection limit 0.6ng mL(-1) (S/N=3). The developed biosensor exhibited good reproducibility and acceptable stability. 4. Development of 3D-QSAR Model for Acetylcholinesterase Inhibitors Using a Combination of Fingerprint, Molecular Docking, and Structure-Based Pharmacophore Approaches. PubMed Lee, Sehan; Barron, Mace G 2015-11-01 Acetylcholinesterase (AChE), a serine hydrolase vital for regulating the neurotransmitter acetylcholine in animals, has been used as a target for drugs and pesticides. With the increasing availability of AChE crystal structures, with or without ligands bound, structure-based approaches have been successfully applied to AChE inhibitors (AChEIs). The major limitation of these approaches has been the small applicability domain due to the lack of structural diversity in the training set. In this study, we developed a 3 dimensional quantitative structure-activity relationship (3D-QSAR) for inhibitory activity of 89 reversible and irreversible AChEIs including drugs and insecticides. A 3D-fingerprint descriptor encoding protein-ligand interactions was developed using molecular docking and structure-based pharmacophore to rationalize the structural requirements responsible for the activity of these compounds. The obtained 3D-QSAR model exhibited high correlation value (R(2) = 0.93) and low mean absolute error (MAE = 0.32 log units) for the training set (n = 63). The model was predictive across a range of structures as shown by the leave-one-out cross-validated correlation coefficient (Q(2) = 0.89) and external validation results (n = 26, R(2) = 0.89, and MAE = 0.38 log units). The model revealed that the compounds with high inhibition potency had proper conformation in the active site gorge and interacted with key amino acid residues, in particular Trp84 and Phe330 at the catalytic anionic site, Trp279 at the peripheral anionic site, and Gly118, Gly119, and Ala201 at the oxyanion hole. The resulting universal 3D-QSAR model provides insight into the multiple molecular interactions determining AChEI potency that may guide future chemical design and regulation of toxic AChEIs. 5. Effects of exposure to oxamyl, carbofuran, dichlorvos, and lindane on acetylcholinesterase activity in the gills of the Pacific oyster Crassostrea gigas. PubMed Anguiano, Gerardo A; Amador, Alejandro; Moreno-Legorreta, Manuel; Arcos-Ortega, Fabiola; Vazquez-Boucard, Celia 2010-08-01 Acetylcholinesterase (AChE) activity has been used to test the exposure of mollusk bivalves to pesticides and other pollutants. The Pacific oyster Crassostrea gigas is a species with a worldwide distribution, and it has a high commercial value. The use of this species as a bioindicator in the marine environment, and the use of measurements of AChE activity in tissues of C. gigas require prior evaluation of organisms exposed to several toxic compounds in the laboratory. In our study, the effects of pesticides on AChE activity in the gills and mantle tissues of C. gigas were analyzed by exposing animals to organophosphate (dichlorvos), carbamate (carbofuran and oxamyl), and organochlorine (lindane) pesticides. Adult Pacific oysters were exposed to several concentrations (0.1-200 microM) of dichlorvos, carbofuran, and oxamyl for 96 h, and lindane (1.0 and 2.5 microM) was applied for 12 days. In gill tissues, all pesticides analyzed caused a decrease in AChE activity when compared to the control unexposed group. The mean inhibition concentration (IC(50)) values were determined for dichlorvos, carbofuran, and oxamyl pesticides. Dichlorvos had the highest toxic effect, with an IC(50) of 1.08 microM; lesser effects were caused by oxamyl and carbofuran, with IC(50)s of 1.67 and 3.03 microM, respectively. This study reports the effects of pesticides with several chemical structures and validates measurement of AChE activity in the gill tissues of C. gigas for use in environmental evaluations or food quality tests. 6. Biosensor Based on Self-Assembling Acetylcholinesterase on Carbon Nanotubes for Flow injection/Amperometric Detection of Organophosphate Pesticides and Nerve Agents SciTech Connect Liu, Guodong; Lin, Yuehe 2006-02-01 A highly sensitive flow-injection amperometric biosensor for organophosphate pesticides and nerve agents based on self-assembly of acet	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6089863181114197, "perplexity": 18829.99068636493}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608617.6/warc/CC-MAIN-20170525214603-20170525234603-00278.warc.gz"}
https://terrytao.wordpress.com/category/mathematics/mathlo/	You are currently browsing the category archive for the ‘math.LO’ category. Rachel Greenfeld and I have just uploaded to the arXiv our preprint “Undecidable translational tilings with only two tiles, or one nonabelian tile“. This paper studies the following question: given a finitely generated group ${G}$, a (periodic) subset ${E}$ of ${G}$, and finite sets ${F_1,\dots,F_J}$ in ${G}$, is it possible to tile ${E}$ by translations ${a_j+F_j}$ of the tiles ${F_1,\dots,F_J}$? That is to say, is there a solution ${\mathrm{X}_1 = A_1, \dots, \mathrm{X}_J = A_J}$ to the (translational) tiling equation $\displaystyle (\mathrm{X}_1 \oplus F_1) \uplus \dots \uplus (\mathrm{X}_J \oplus F_J) = E \ \ \ \ \ (1)$ for some subsets ${A_1,\dots,A_J}$ of ${G}$, where ${A \oplus F}$ denotes the set of sums ${\{a+f: a \in A, f \in F \}}$ if the sums ${a+f}$ are all disjoint (and is undefined otherwise), and ${\uplus}$ denotes disjoint union. (One can also write the tiling equation in the language of convolutions as ${1_{\mathrm{X}_1} * 1_{F_1} + \dots + 1_{\mathrm{X}_J} * 1_{F_J} = 1_E}$.) A bit more specifically, the paper studies the decidability of the above question. There are two slightly different types of decidability one could consider here: • Logical decidability. For a given ${G, E, J, F_1,\dots,F_J}$, one can ask whether the solvability of the tiling equation (1) is provable or disprovable in ZFC (where we encode all the data ${G, E, F_1,\dots,F_J}$ by appropriate constructions in ZFC). If this is the case we say that the tiling equation (1) (or more precisely, the solvability of this equation) is logically decidable, otherwise it is logically undecidable. • Algorithmic decidability. For data ${G,E,J, F_1,\dots,F_J}$ in some specified class (and encoded somehow as binary strings), one can ask whether the solvability of the tiling equation (1) can be correctly determined for all choices of data in this class by the output of some Turing machine that takes the data as input (encoded as a binary string) and halts in finite time, returning either YES if the equation can be solved or NO otherwise. If this is the case, we say the tiling problem of solving (1) for data in the given class is algorithmically decidable, otherwise it is algorithmically undecidable. Note that the notion of logical decidability is “pointwise” in the sense that it pertains to a single choice of data ${G,E,J,F_1,\dots,F_J}$, whereas the notion of algorithmic decidability pertains instead to classes of data, and is only interesting when this class is infinite. Indeed, any tiling problem with a finite class of data is trivially decidable because one could simply code a Turing machine that is basically a lookup table that returns the correct answer for each choice of data in the class. (This is akin to how a student with a good memory could pass any exam if the questions are drawn from a finite list, merely by memorising an answer key for that list of questions.) The two notions are related as follows: if a tiling problem (1) is algorithmically undecidable for some class of data, then the tiling equation must be logically undecidable for at least one choice of data for this class. For if this is not the case, one could algorithmically decide the tiling problem by searching for proofs or disproofs that the equation (1) is solvable for a given choice of data; the logical decidability of all such solvability questions will ensure that this algorithm always terminates in finite time. One can use the Gödel completeness theorem to interpret logical decidability in terms of universes (also known as structures or models) of ZFC. In addition to the “standard” universe ${{\mathfrak U}}$ of sets that we believe satisfies the axioms of ZFC, there are also other “nonstandard” universes ${{\mathfrak U}^}$ that also obey the axioms of ZFC. If the solvability of a tiling equation (1) is logically undecidable, this means that such a tiling exists in some universes of ZFC, but not in others. (To continue the exam analogy, we thus see that a yes-no exam question is logically undecidable if the answer to the question is yes in some parallel universes, but not in others. A course syllabus is algorithmically undecidable if there is no way to prepare for the final exam for the course in a way that guarantees a perfect score (in the standard universe).) Questions of decidability are also related to the notion of aperiodicity. For a given ${G, E, J, F_1,\dots,F_J}$, a tiling equation (1) is said to be aperiodic if the equation (1) is solvable (in the standard universe ${{\mathfrak U}}$ of ZFC), but none of the solutions (in that universe) are completely periodic (i.e., there are no solutions ${\mathrm{X}_1 = A_1,\dots, \mathrm{X}_J = A_J}$ where all of the ${A_1,\dots,A_J}$ are periodic). Perhaps the most well-known example of an aperiodic tiling (in the context of ${{\bf R}^2}$, and using rotations as well as translations) come from the Penrose tilings, but there are many others besides. It was (essentially) observed by Hao Wang in the 1960s that if a tiling equation is logically undecidable, then it must necessarily be aperiodic. Indeed, if a tiling equation fails to be aperiodic, then (in the standard universe) either there is a periodic tiling, or there are no tilings whatsoever. In the former case, the periodic tiling can be used to give a finite proof that the tiling equation is solvable; in the latter case, the compactness theorem implies that there is some finite fragment of ${E}$ that is not compatible with being tiled by ${F_1,\dots,F_J}$, and this provides a finite proof that the tiling equation is unsolvable. Thus in either case the tiling equation is logically decidable. This observation of Wang clarifies somewhat how logically undecidable tiling equations behave in the various universes of ZFC. In the standard universe, tilings exist, but none of them will be periodic. In nonstandard universes, tilings may or may not exist, and the tilings that do exist may be periodic (albeit with a nonstandard period); but there must be at least one universe in which no tiling exists at all. In one dimension when ${G={\bf Z}}$ (or more generally ${G = {\bf Z} \times G_0}$ with ${G_0}$ a finite group), a simple pigeonholing argument shows that no tiling equations are aperiodic, and hence all tiling equations are decidable. However the situation changes in two dimensions. In 1966, Berger (a student of Wang) famously showed that there exist tiling equations (1) in the discrete plane ${E = G = {\bf Z}^2}$ that are aperiodic, or even logically undecidable; in fact he showed that the tiling problem in this case (with arbitrary choices of data ${J, F_1,\dots,F_J}$) was algorithmically undecidable. (Strictly speaking, Berger established this for a variant of the tiling problem known as the domino problem, but later work of Golomb showed that the domino problem could be easily encoded within the tiling problem.) This was accomplished by encoding the halting problem for Turing machines into the tiling problem (or domino problem); the latter is well known to be algorithmically undecidable (and thus have logically undecidable instances), and so the latter does also. However, the number of tiles ${J}$ required for Berger’s construction was quite large: his construction of an aperiodic tiling required ${J = 20426}$ tiles, and his construction of a logically undecidable tiling required an even larger (and not explicitly specified) collection of tiles. Subsequent work by many authors did reduce the number of tiles required; in the ${E=G={\bf Z}^2}$ setting, the current world record for the fewest number of tiles in an aperiodic tiling is ${J=8}$ (due to Amman, Grunbaum, and Shephard) and for a logically undecidable tiling is ${J=11}$ (due to Ollinger). On the other hand, it is conjectured (see Grunbaum-Shephard and Lagarias-Wang) that one cannot lower ${J}$ all the way to ${1}$: Conjecture 1 (Periodic tiling conjecture) If ${E}$ is a periodic subset of a finitely generated abelian group ${G}$, and ${F}$ is a finite subset of ${G}$, then the tiling equation ${\mathrm{X} \oplus F = E}$ is not aperiodic. This conjecture is known to be true in two dimensions (by work of Bhattacharya when ${G=E={\bf Z}^2}$, and more recently by us when ${E \subset G = {\bf Z}^2}$), but remains open in higher dimensions. By the preceding discussion, the conjecture implies that every tiling equation with a single tile is logically decidable, and the problem of whether a given periodic set can be tiled by a single tile is algorithmically decidable. In this paper we show on the other hand that aperiodic and undecidable tilings exist when ${J=2}$, at least if one is permitted to enlarge the group ${G}$ a bit: Theorem 2 (Logically undecidable tilings) • (i) There exists a group ${G}$ of the form ${G = {\bf Z}^2 \times G_0}$ for some finite abelian ${G_0}$, a subset ${E_0}$ of ${G_0}$, and finite sets ${F_1, F_2 \subset G}$ such that the tiling equation ${(\mathbf{X}_1 \oplus F_1) \uplus (\mathbf{X}_2 \oplus F_2) = {\bf Z}^2 \times E_0}$ is logically undecidable (and hence also aperiodic). • (ii) There exists a dimension ${d}$, a periodic subset ${E}$ of ${{\bf Z}^d}$, and finite sets ${F_1, F_2 \subset G}$ such that tiling equation ${(\mathbf{X}_1 \oplus F_1) \uplus (\mathbf{X}_2 \oplus F_2) = E}$ is logically undecidable (and hence also aperiodic). • (iii) There exists a non-abelian finite group ${G_0}$ (with the group law still written additively), a subset ${E_0}$ of ${G_0}$, and a finite set ${F \subset {\bf Z}^2 \times G_0}$ such that the nonabelian tiling equation ${\mathbf{X} \oplus F = {\bf Z}^2 \times E_0}$ is logically undecidable (and hence also aperiodic). We also have algorithmic versions of this theorem. For instance, the algorithmic version of (i) is that the problem of determining solvability of the tiling equation ${(\mathbf{X}_1 \oplus F_1) \uplus (\mathbf{X}_2 \oplus F_2) = {\bf Z}^2 \times E_0}$ for a given choice of finite abelian group ${G_0}$, subset ${E_0}$ of ${G_0}$, and finite sets ${F_1, F_2 \subset {\bf Z}^2 \times G_0}$ is algorithmically undecidable. Similarly for (ii), (iii). This result (together with a negative result discussed below) suggest to us that there is a significant qualitative difference in the ${J=1}$ theory of tiling by a single (abelian) tile, and the ${J \geq 2}$ theory of tiling with multiple tiles (or one non-abelian tile). (The positive results on the periodic tiling conjecture certainly rely heavily on the fact that there is only one tile, in particular there is a “dilation lemma” that is only available in this setting that is of key importance in the two dimensional theory.) It would be nice to eliminate the group ${G_0}$ from (i) (or to set ${d=2}$ in (ii)), but I think this would require a fairly significant modification of our methods. Like many other undecidability results, the proof of Theorem 2 proceeds by a sequence of reductions, in which the undecidability of one problem is shown to follow from the undecidability of another, more “expressive” problem that can be encoded inside the original problem, until one reaches a problem that is so expressive that it encodes a problem already known to be undecidable. Indeed, all three undecidability results are ultimately obtained from Berger’s undecidability result on the domino problem. The first step in increasing expressiveness is to observe that the undecidability of a single tiling equation follows from the undecidability of a system of tiling equations. More precisely, suppose we have non-empty finite subsets ${F_j^{(m)}}$ of a finitely generated group ${G}$ for ${j=1,\dots,J}$ and ${m=1,\dots,M}$, as well as periodic sets ${E^{(m)}}$ of ${G}$ for ${m=1,\dots,M}$, such that it is logically undecidable whether the system of tiling equations $\displaystyle (\mathrm{X}_1 \oplus F_1^{(m)}) \uplus \dots \uplus (\mathrm{X}_J \oplus F_J^{(m)}) = E^{(m)} \ \ \ \ \ (2)$ for ${m=1,\dots,M}$ has no solution ${\mathrm{X}_1 = A_1,\dots, \mathrm{X}_J = A_J}$ in ${G}$. Then, for any ${N>M}$, we can “stack” these equations into a single tiling equation in the larger group ${G \times {\bf Z}/N{\bf Z}}$, and specifically to the equation $\displaystyle (\mathrm{X}_1 \oplus F_1) \uplus \dots \uplus (\mathrm{X}_J \oplus F_J) = E \ \ \ \ \ (3)$ where $\displaystyle F_j := \biguplus_{m=1}^M F_j^{(m)} \times \{m\}$ and $\displaystyle E := \biguplus_{m=1}^M E^{(m)} \times \{m\}.$ It is a routine exercise to check that the system of equations (2) admits a solution in ${G}$ if and only if the single equation (3) admits a equation in ${G \times {\bf Z}/N{\bf Z}}$. Thus, to prove the undecidability of a single equation of the form (3) it suffices to establish undecidability of a system of the form (2); note here how the freedom to select the auxiliary group ${G_0}$ is important here. We view systems of the form (2) as belonging to a kind of “language” in which each equation in the system is a “sentence” in the language imposing additional constraints on a tiling. One can now pick and choose various sentences in this language to try to encode various interesting problems. For instance, one can encode the concept of a function ${f: {\bf Z}^2 \rightarrow G_0}$ taking values in a finite group ${G_0}$ as a single tiling equation $\displaystyle \mathrm{X} \oplus (\{0\} \times G_0) = {\bf Z}^2 \times G_0 \ \ \ \ \ (4)$ since the solutions to this equation are precisely the graphs $\displaystyle \mathrm{X} = \{ (n, f(n)): n \in {\bf Z}^2 \}$ of a function ${f: {\bf Z}^2 \rightarrow G_0}$. By adding more tiling equations to this equation to form a larger system, we can start imposing additional constraints on this function ${f}$. For instance, if ${x+H}$ is a coset of some subgroup ${H}$ of ${G_0}$, we can impose the additional equation $\displaystyle \mathrm{X} \oplus (\{0\} \times H) = {\bf Z}^2 \times (x+H) \ \ \ \ \ (5)$ to impose the additional constraint that ${f(n) \in x+H}$ for all ${n \in {\bf Z}^2}$, if we desire. If ${G_0}$ happens to contain two distinct elements ${1, -1}$, and ${h \in {\bf Z}^2}$, then the additional equation $\displaystyle \mathrm{X} \oplus (\{0,h\} \times \{0\}) = {\bf Z}^2 \times \{-1,1\} \ \ \ \ \ (6)$ imposes the additional constraints that ${f(n) \in \{-1,1\}}$ for all ${n \in {\bf Z}^2}$, and additionally that $\displaystyle f(n+h) = -f(n)$ for all ${n \in {\bf Z}^2}$. This begins to resemble the equations that come up in the domino problem. Here one has a finite set of Wang tiles – unit squares ${T}$ where each of the four sides is colored with a color ${c_N(T), c_S(T), c_E(T), c_W(T)}$ (corresponding to the four cardinal directions North, South, East, and West) from some finite set ${{\mathcal C}}$ of colors. The domino problem is then to tile the plane with copies of these tiles in such a way that adjacent sides match. In terms of equations, one is seeking to find functions ${c_N, c_S, c_E, c_W: {\bf Z}^2 \rightarrow {\mathcal C}}$ obeying the pointwise constraint $\displaystyle (c_N(n), c_S(n), c_E(n), c_W(n)) \in {\mathcal W} \ \ \ \ \ (7)$ for all ${n \in {\bf Z}^2}$ where ${{\mathcal W}}$ is the set of colors associated to the set of Wang tiles being used, and the matching constraints $\displaystyle c_S(n+(0,1)) = c_N(n); \quad c_W(n+(1,0)) = c_E(n) \ \ \ \ \ (8)$ for all ${{\bf Z}^2}$. As it turns out, the pointwise constraint (7) can be encoded by tiling equations that are fancier versions of (4), (5), (6) that involve only one unknown tiling set ${{\mathrm X}}$, but in order to encode the matching constraints (8) we were forced to introduce a second tile (or work with nonabelian tiling equations). This appears to be an inherent feature of the method, since we found a partial rigidity result for tilings of one tile in one dimension that obstructs this encoding strategy from working when one only has one tile available. The result is as follows: Proposition 3 (Swapping property) Consider the solutions to a tiling equation $\displaystyle \mathrm{X} \oplus F = E \ \ \ \ \ (9)$ in a one-dimensional group ${G = {\bf Z} \times G_0}$ (with ${G_0}$ a finite abelian group, ${F}$ finite, and ${E}$ periodic). Suppose there are two solutions ${\mathrm{X} = A_0, \mathrm{X} = A_1}$ to this equation that agree on the left in the sense that $\displaystyle A_0 \cap (\{0, -1, -2, \dots\} \times G_0) = A_1 \cap (\{0, -1, -2, \dots\} \times G_0).$ For any function ${\omega: {\bf Z} \rightarrow \{0,1\}}$, define the “swap” ${A_\omega}$ of ${A_0}$ and ${A_1}$ to be the set $\displaystyle A_\omega := \{ (n, g): n \in {\bf Z}, (n,g) \in A_{\omega(n)} \}$ Then ${A_\omega}$ also solves the equation (9). One can think of ${A_0}$ and ${A_1}$ as “genes” with “nucleotides” ${\{ g \in G_0: (n,g) \in A_0\}}$, ${\{ g \in G_0: (n,g) \in A_1\}}$ at each position ${n \in {\bf Z}}$, and ${A_\omega}$ is a new gene formed by choosing one of the nucleotides from the “parent” genes ${A_0}$, ${A_1}$ at each position. The above proposition then says that the solutions to the equation (9) must be closed under “genetic transfer” among any pair of genes that agree on the left. This seems to present an obstruction to trying to encode equation such as $\displaystyle c(n+1) = c'(n)$ for two functions ${c, c': {\bf Z} \rightarrow \{-1,1\}}$ (say), which is a toy version of the matching constraint (8), since the class of solutions to this equation turns out not to obey this swapping property. On the other hand, it is easy to encode such equations using two tiles instead of one, and an elaboration of this construction is used to prove our main theorem. Abdul Basit, Artem Chernikov, Sergei Starchenko, Chiu-Minh Tran and I have uploaded to the arXiv our paper Zarankiewicz’s problem for semilinear hypergraphs. This paper is in the spirit of a number of results in extremal graph theory in which the bounds for various graph-theoretic problems or results can be greatly improved if one makes some additional hypotheses regarding the structure of the graph, for instance by requiring that the graph be “definable” with respect to some theory with good model-theoretic properties. A basic motivating example is the question of counting the number of incidences between points and lines (or between points and other geometric objects). Suppose one has ${n}$ points and ${n}$ lines in a space. How many incidences can there be between these points and lines? The utterly trivial bound is ${n^2}$, but by using the basic fact that two points determine a line (or two lines intersect in at most one point), a simple application of Cauchy-Schwarz improves this bound to ${n^{3/2}}$. In graph theoretic terms, the point is that the bipartite incidence graph between points and lines does not contain a copy of ${K_{2,2}}$ (there does not exist two points and two lines that are all incident to each other). Without any other further hypotheses, this bound is basically sharp: consider for instance the collection of ${p^2}$ points and ${p^2+p}$ lines in a finite plane ${{\bf F}_p^2}$, that has ${p^3+p^2}$ incidences (one can make the situation more symmetric by working with a projective plane rather than an affine plane). If however one considers lines in the real plane ${{\bf R}^2}$, the famous Szemerédi-Trotter theorem improves the incidence bound further from ${n^{3/2}}$ to ${O(n^{4/3})}$. Thus the incidence graph between real points and lines contains more structure than merely the absence of ${K_{2,2}}$. More generally, bounding on the size of bipartite graphs (or multipartite hypergraphs) not containing a copy of some complete bipartite subgraph ${K_{k,k}}$ (or ${K_{k,\dots,k}}$ in the hypergraph case) is known as Zarankiewicz’s problem. We have results for all ${k}$ and all orders of hypergraph, but for sake of this post I will focus on the bipartite ${k=2}$ case. In our paper we improve the ${n^{3/2}}$ bound to a near-linear bound in the case that the incidence graph is “semilinear”. A model case occurs when one considers incidences between points and axis-parallel rectangles in the plane. Now the ${K_{2,2}}$ condition is not automatic (it is of course possible for two distinct points to both lie in two distinct rectangles), so we impose this condition by fiat: Theorem 1 Suppose one has ${n}$ points and ${n}$ axis-parallel rectangles in the plane, whose incidence graph contains no ${K_{2,2}}$‘s, for some large ${n}$. • (i) The total number of incidences is ${O(n \log^4 n)}$. • (ii) If all the rectangles are dyadic, the bound can be improved to ${O( n \frac{\log n}{\log\log n} )}$. • (iii) The bound in (ii) is best possible (up to the choice of implied constant). We don’t know whether the bound in (i) is similarly tight for non-dyadic boxes; the usual tricks for reducing the non-dyadic case to the dyadic case strangely fail to apply here. One can generalise to higher dimensions, replacing rectangles by polytopes with faces in some fixed finite set of orientations, at the cost of adding several more logarithmic factors; also, one can replace the reals by other ordered division rings, and replace polytopes by other sets of bounded “semilinear descriptive complexity”, e.g., unions of boundedly many polytopes, or which are cut out by boundedly many functions that enjoy coordinatewise monotonicity properties. For certain specific graphs we can remove the logarithmic factors entirely. We refer to the preprint for precise details. The proof techniques are combinatorial. The proof of (i) relies primarily on the order structure of ${{\bf R}}$ to implement a “divide and conquer” strategy in which one can efficiently control incidences between ${n}$ points and rectangles by incidences between approximately ${n/2}$ points and boxes. For (ii) there is additional order-theoretic structure one can work with: first there is an easy pruning device to reduce to the case when no rectangle is completely contained inside another, and then one can impose the “tile partial order” in which one dyadic rectangle ${I \times J}$ is less than another ${I' \times J'}$ if ${I \subset I'}$ and ${J' \subset J}$. The point is that this order is “locally linear” in the sense that for any two dyadic rectangles ${R_-, R_+}$, the set ${[R_-,R_+] := \{ R: R_- \leq R \leq R_+\}}$ is linearly ordered, and this can be exploited by elementary double counting arguments to obtain a bound which eventually becomes ${O( n \frac{\log n}{\log\log n})}$ after optimising certain parameters in the argument. The proof also suggests how to construct the counterexample in (iii), which is achieved by an elementary iterative construction. Asgar Jamneshan and I have just uploaded to the arXiv our paper “An uncountable Moore-Schmidt theorem“. This paper revisits a classical theorem of Moore and Schmidt in measurable cohomology of measure-preserving systems. To state the theorem, let ${X = (X,{\mathcal X},\mu)}$ be a probability space, and ${\mathrm{Aut}(X, {\mathcal X}, \mu)}$ be the group of measure-preserving automorphisms of this space, that is to say the invertible bimeasurable maps ${T: X \rightarrow X}$ that preserve the measure ${\mu}$: ${T_ \mu = \mu}$. To avoid some ambiguity later in this post when we introduce abstract analogues of measure theory, we will refer to measurable maps as concrete measurable maps, and measurable spaces as concrete measurable spaces. (One could also call ${X = (X,{\mathcal X}, \mu)}$ a concrete probability space, but we will not need to do so here as we will not be working explicitly with abstract probability spaces.) Let ${\Gamma = (\Gamma,\cdot)}$ be a discrete group. A (concrete) measure-preserving action of ${\Gamma}$ on ${X}$ is a group homomorphism ${\gamma \mapsto T^\gamma}$ from ${\Gamma}$ to ${\mathrm{Aut}(X, {\mathcal X}, \mu)}$, thus ${T^1}$ is the identity map and ${T^{\gamma_1} \circ T^{\gamma_2} = T^{\gamma_1 \gamma_2}}$ for all ${\gamma_1,\gamma_2 \in \Gamma}$. A large portion of ergodic theory is concerned with the study of such measure-preserving actions, especially in the classical case when ${\Gamma}$ is the integers (with the additive group law). Let ${K = (K,+)}$ be a compact Hausdorff abelian group, which we can endow with the Borel ${\sigma}$-algebra ${{\mathcal B}(K)}$. A (concrete measurable) ${K}$cocycle is a collection ${\rho = (\rho_\gamma)_{\gamma \in \Gamma}}$ of concrete measurable maps ${\rho_\gamma: X \rightarrow K}$ obeying the cocycle equation $\displaystyle \rho_{\gamma_1 \gamma_2}(x) = \rho_{\gamma_1} \circ T^{\gamma_2}(x) + \rho_{\gamma_2}(x) \ \ \ \ \ (1)$ for ${\mu}$-almost every ${x \in X}$. (Here we are glossing over a measure-theoretic subtlety that we will return to later in this post – see if you can spot it before then!) Cocycles arise naturally in the theory of group extensions of dynamical systems; in particular (and ignoring the aforementioned subtlety), each cocycle induces a measure-preserving action ${\gamma \mapsto S^\gamma}$ on ${X \times K}$ (which we endow with the product of ${\mu}$ with Haar probability measure on ${K}$), defined by $\displaystyle S^\gamma( x, k ) := (T^\gamma x, k + \rho_\gamma(x) ).$ This connection with group extensions was the original motivation for our study of measurable cohomology, but is not the focus of the current paper. A special case of a ${K}$-valued cocycle is a (concrete measurable) ${K}$-valued coboundary, in which ${\rho_\gamma}$ for each ${\gamma \in \Gamma}$ takes the special form $\displaystyle \rho_\gamma(x) = F \circ T^\gamma(x) - F(x)$ for ${\mu}$-almost every ${x \in X}$, where ${F: X \rightarrow K}$ is some measurable function; note that (ignoring the aforementioned subtlety), every function of this form is automatically a concrete measurable ${K}$-valued cocycle. One of the first basic questions in measurable cohomology is to try to characterize which ${K}$-valued cocycles are in fact ${K}$-valued coboundaries. This is a difficult question in general. However, there is a general result of Moore and Schmidt that at least allows one to reduce to the model case when ${K}$ is the unit circle ${\mathbf{T} = {\bf R}/{\bf Z}}$, by taking advantage of the Pontryagin dual group ${\hat K}$ of characters ${\hat k: K \rightarrow \mathbf{T}}$, that is to say the collection of continuous homomorphisms ${\hat k: k \mapsto \langle \hat k, k \rangle}$ to the unit circle. More precisely, we have Theorem 1 (Countable Moore-Schmidt theorem) Let ${\Gamma}$ be a discrete group acting in a concrete measure-preserving fashion on a probability space ${X}$. Let ${K}$ be a compact Hausdorff abelian group. Assume the following additional hypotheses: • (i) ${\Gamma}$ is at most countable. • (ii) ${X}$ is a standard Borel space. • (iii) ${K}$ is metrisable. Then a ${K}$-valued concrete measurable cocycle ${\rho = (\rho_\gamma)_{\gamma \in \Gamma}}$ is a concrete coboundary if and only if for each character ${\hat k \in \hat K}$, the ${\mathbf{T}}$-valued cocycles ${\langle \hat k, \rho \rangle = ( \langle \hat k, \rho_\gamma \rangle )_{\gamma \in \Gamma}}$ are concrete coboundaries. The hypotheses (i), (ii), (iii) are saying in some sense that the data ${\Gamma, X, K}$ are not too “large”; in all three cases they are saying in some sense that the data are only “countably complicated”. For instance, (iii) is equivalent to ${K}$ being second countable, and (ii) is equivalent to ${X}$ being modeled by a complete separable metric space. It is because of this restriction that we refer to this result as a “countable” Moore-Schmidt theorem. This theorem is a useful tool in several other applications, such as the Host-Kra structure theorem for ergodic systems; I hope to return to these subsequent applications in a future post. Let us very briefly sketch the main ideas of the proof of Theorem 1. Ignore for now issues of measurability, and pretend that something that holds almost everywhere in fact holds everywhere. The hard direction is to show that if each ${\langle \hat k, \rho \rangle}$ is a coboundary, then so is ${\rho}$. By hypothesis, we then have an equation of the form $\displaystyle \langle \hat k, \rho_\gamma(x) \rangle = \alpha_{\hat k} \circ T^\gamma(x) - \alpha_{\hat k}(x) \ \ \ \ \ (2)$ for all ${\hat k, \gamma, x}$ and some functions ${\alpha_{\hat k}: X \rightarrow {\mathbf T}}$, and our task is then to produce a function ${F: X \rightarrow K}$ for which $\displaystyle \rho_\gamma(x) = F \circ T^\gamma(x) - F(x)$ for all ${\gamma,x}$. Comparing the two equations, the task would be easy if we could find an ${F: X \rightarrow K}$ for which $\displaystyle \langle \hat k, F(x) \rangle = \alpha_{\hat k}(x) \ \ \ \ \ (3)$ for all ${\hat k, x}$. However there is an obstruction to this: the left-hand side of (3) is additive in ${\hat k}$, so the right-hand side would have to be also in order to obtain such a representation. In other words, for this strategy to work, one would have to first establish the identity $\displaystyle \alpha_{\hat k_1 + \hat k_2}(x) - \alpha_{\hat k_1}(x) - \alpha_{\hat k_2}(x) = 0 \ \ \ \ \ (4)$ for all ${\hat k_1, \hat k_2, x}$. On the other hand, the good news is that if we somehow manage to obtain the equation, then we can obtain a function ${F}$ obeying (3), thanks to Pontryagin duality, which gives a one-to-one correspondence between ${K}$ and the homomorphisms of the (discrete) group ${\hat K}$ to ${\mathbf{T}}$. Now, it turns out that one cannot derive the equation (4) directly from the given information (2). However, the left-hand side of (2) is additive in ${\hat k}$, so the right-hand side must be also. Manipulating this fact, we eventually arrive at $\displaystyle (\alpha_{\hat k_1 + \hat k_2} - \alpha_{\hat k_1} - \alpha_{\hat k_2}) \circ T^\gamma(x) = (\alpha_{\hat k_1 + \hat k_2} - \alpha_{\hat k_1} - \alpha_{\hat k_2})(x).$ In other words, we don’t get to show that the left-hand side of (4) vanishes, but we do at least get to show that it is ${\Gamma}$-invariant. Now let us assume for sake of argument that the action of ${\Gamma}$ is ergodic, which (ignoring issues about sets of measure zero) basically asserts that the only ${\Gamma}$-invariant functions are constant. So now we get a weaker version of (4), namely $\displaystyle \alpha_{\hat k_1 + \hat k_2}(x) - \alpha_{\hat k_1}(x) - \alpha_{\hat k_2}(x) = c_{\hat k_1, \hat k_2} \ \ \ \ \ (5)$ for some constants ${c_{\hat k_1, \hat k_2} \in \mathbf{T}}$. Now we need to eliminate the constants. This can be done by the following group-theoretic projection. Let ${L^0({\bf X} \rightarrow {\bf T})}$ denote the space of concrete measurable maps ${\alpha}$ from ${{\bf X}}$ to ${{\bf T}}$, up to almost everywhere equivalence; this is an abelian group where the various terms in (5) naturally live. Inside this group we have the subgroup ${{\bf T}}$ of constant functions (up to almost everywhere equivalence); this is where the right-hand side of (5) lives. Because ${{\bf T}}$ is a divisible group, there is an application of Zorn’s lemma (a good exercise for those who are not acquainted with these things) to show that there exists a retraction ${w: L^0({\bf X} \rightarrow {\bf T}) \rightarrow {\bf T}}$, that is to say a group homomorphism that is the identity on the subgroup ${{\bf T}}$. We can use this retraction, or more precisely the complement ${\alpha \mapsto \alpha - w(\alpha)}$, to eliminate the constant in (5). Indeed, if we set $\displaystyle \tilde \alpha_{\hat k}(x) := \alpha_{\hat k}(x) - w(\alpha_{\hat k})$ then from (5) we see that $\displaystyle \tilde \alpha_{\hat k_1 + \hat k_2}(x) - \tilde \alpha_{\hat k_1}(x) - \tilde \alpha_{\hat k_2}(x) = 0$ while from (2) one has $\displaystyle \langle \hat k, \rho_\gamma(x) \rangle = \tilde \alpha_{\hat k} \circ T^\gamma(x) - \tilde \alpha_{\hat k}(x)$ and now the previous strategy works with ${\alpha_{\hat k}}$ replaced by ${\tilde \alpha_{\hat k}}$. This concludes the sketch of proof of Theorem 1. In making the above argument rigorous, the hypotheses (i)-(iii) are used in several places. For instance, to reduce to the ergodic case one relies on the ergodic decomposition, which requires the hypothesis (ii). Also, most of the above equations only hold outside of a set of measure zero, and the hypothesis (i) and the hypothesis (iii) (which is equivalent to ${\hat K}$ being at most countable) to avoid the problem that an uncountable union of sets of measure zero could have positive measure (or fail to be measurable at all). My co-author Asgar Jamneshan and I are working on a long-term project to extend many results in ergodic theory (such as the aforementioned Host-Kra structure theorem) to “uncountable” settings in which hypotheses analogous to (i)-(iii) are omitted; thus we wish to consider actions on uncountable groups, on spaces that are not standard Borel, and cocycles taking values in groups that are not metrisable. Such uncountable contexts naturally arise when trying to apply ergodic theory techniques to combinatorial problems (such as the inverse conjecture for the Gowers norms), as one often relies on the ultraproduct construction (or something similar) to generate an ergodic theory translation of these problems, and these constructions usually give “uncountable” objects rather than “countable” ones. (For instance, the ultraproduct of finite groups is a hyperfinite group, which is usually uncountable.). This paper marks the first step in this project by extending the Moore-Schmidt theorem to the uncountable setting. If one simply drops the hypotheses (i)-(iii) and tries to prove the Moore-Schmidt theorem, several serious difficulties arise. We have already mentioned the loss of the ergodic decomposition and the possibility that one has to control an uncountable union of null sets. But there is in fact a more basic problem when one deletes (iii): the addition operation ${+: K \times K \rightarrow K}$, while still continuous, can fail to be measurable as a map from ${(K \times K, {\mathcal B}(K) \otimes {\mathcal B}(K))}$ to ${(K, {\mathcal B}(K))}$! Thus for instance the sum of two measurable functions ${F: X \rightarrow K}$ need not remain measurable, which makes even the very definition of a measurable cocycle or measurable coboundary problematic (or at least unnatural). This phenomenon is known as the Nedoma pathology. A standard example arises when ${K}$ is the uncountable torus ${{\mathbf T}^{{\bf R}}}$, endowed with the product topology. Crucially, the Borel ${\sigma}$-algebra ${{\mathcal B}(K)}$ generated by this uncountable product is not the product ${{\mathcal B}(\mathbf{T})^{\otimes {\bf R}}}$ of the factor Borel ${\sigma}$-algebras (the discrepancy ultimately arises from the fact that topologies permit uncountable unions, but ${\sigma}$-algebras do not); relating to this, the product ${\sigma}$-algebra ${{\mathcal B}(K) \otimes {\mathcal B}(K)}$ is not the same as the Borel ${\sigma}$-algebra ${{\mathcal B}(K \times K)}$, but is instead a strict sub-algebra. If the group operations on ${K}$ were measurable, then the diagonal set $\displaystyle K^\Delta := \{ (k,k') \in K \times K: k = k' \} = \{ (k,k') \in K \times K: k - k' = 0 \}$ would be measurable in ${{\mathcal B}(K) \otimes {\mathcal B}(K)}$. But it is an easy exercise in manipulation of ${\sigma}$-algebras to show that if ${(X, {\mathcal X}), (Y, {\mathcal Y})}$ are any two measurable spaces and ${E \subset X \times Y}$ is measurable in ${{\mathcal X} \otimes {\mathcal Y}}$, then the fibres ${E_x := \{ y \in Y: (x,y) \in E \}}$ of ${E}$ are contained in some countably generated subalgebra of ${{\mathcal Y}}$. Thus if ${K^\Delta}$ were ${{\mathcal B}(K) \otimes {\mathcal B}(K)}$-measurable, then all the points of ${K}$ would lie in a single countably generated ${\sigma}$-algebra. But the cardinality of such an algebra is at most ${2^{\alpha_0}}$ while the cardinality of ${K}$ is ${2^{2^{\alpha_0}}}$, and Cantor’s theorem then gives a contradiction. To resolve this problem, we give ${K}$ a coarser ${\sigma}$-algebra than the Borel ${\sigma}$-algebra, namely the Baire ${\sigma}$-algebra ${{\mathcal B}^\otimes(K)}$, thus coarsening the measurable space structure on ${K = (K,{\mathcal B}(K))}$ to a new measurable space ${K_\otimes := (K, {\mathcal B}^\otimes(K))}$. In the case of compact Hausdorff abelian groups, ${{\mathcal B}^{\otimes}(K)}$ can be defined as the ${\sigma}$-algebra generated by the characters ${\hat k: K \rightarrow {\mathbf T}}$; for more general compact abelian groups, one can define ${{\mathcal B}^{\otimes}(K)}$ as the ${\sigma}$-algebra generated by all continuous maps into metric spaces. This ${\sigma}$-algebra is equal to ${{\mathcal B}(K)}$ when ${K}$ is metrisable but can be smaller for other ${K}$. With this measurable structure, ${K_\otimes}$ becomes a measurable group; it seems that once one leaves the metrisable world that ${K_\otimes}$ is a superior (or at least equally good) space to work with than ${K}$ for analysis, as it avoids the Nedoma pathology. (For instance, from Plancherel’s theorem, we see that if ${m_K}$ is the Haar probability measure on ${K}$, then ${L^2(K,m_K) = L^2(K_\otimes,m_K)}$ (thus, every ${K}$-measurable set is equivalent modulo ${m_K}$-null sets to a ${K_\otimes}$-measurable set), so there is no damage to Plancherel caused by passing to the Baire ${\sigma}$-algebra. Passing to the Baire ${\sigma}$-algebra ${K_\otimes}$ fixes the most severe problems with an uncountable Moore-Schmidt theorem, but one is still faced with an issue of having to potentially take an uncountable union of null sets. To avoid this sort of problem, we pass to the framework of abstract measure theory, in which we remove explicit mention of “points” and can easily delete all null sets at a very early stage of the formalism. In this setup, the category of concrete measurable spaces is replaced with the larger category of abstract measurable spaces, which we formally define as the opposite category of the category of ${\sigma}$-algebras (with Boolean algebra homomorphisms). Thus, we define an abstract measurable space to be an object of the form ${{\mathcal X}^{\mathrm{op}}}$, where ${{\mathcal X}}$ is an (abstract) ${\sigma}$-algebra and ${\mathrm{op}}$ is a formal placeholder symbol that signifies use of the opposite category, and an abstract measurable map ${T: {\mathcal X}^{\mathrm{op}} \rightarrow {\mathcal Y}^{\mathrm{op}}}$ is an object of the form ${(T^)^{\mathrm{op}}}$, where ${T^: {\mathcal Y} \rightarrow {\mathcal X}}$ is a Boolean algebra homomorphism and ${\mathrm{op}}$ is again used as a formal placeholder; we call ${T^}$ the pullback map associated to ${T}$. [UPDATE: It turns out that this definition of a measurable map led to technical issues. In a forthcoming revision of the paper we also impose the requirement that the abstract measurable map be $\sigma$-complete (i.e., it respects countable joins).] The composition ${S \circ T: {\mathcal X}^{\mathrm{op}} \rightarrow {\mathcal Z}^{\mathrm{op}}}$ of two abstract measurable maps ${T: {\mathcal X}^{\mathrm{op}} \rightarrow {\mathcal Y}^{\mathrm{op}}}$, ${S: {\mathcal Y}^{\mathrm{op}} \rightarrow {\mathcal Z}^{\mathrm{op}}}$ is defined by the formula ${S \circ T := (T^ \circ S^)^{\mathrm{op}}}$, or equivalently ${(S \circ T)^ = T^* \circ S^}$. Every concrete measurable space ${X = (X,{\mathcal X})}$ can be identified with an abstract counterpart ${{\mathcal X}^{op}}$, and similarly every concrete measurable map ${T: X \rightarrow Y}$ can be identified with an abstract counterpart ${(T^)^{op}}$, where ${T^: {\mathcal Y} \rightarrow {\mathcal X}}$ is the pullback map ${T^ E := T^{-1}(E)}$. Thus the category of concrete measurable spaces can be viewed as a subcategory of the category of abstract measurable spaces. The advantage of working in the abstract setting is that it gives us access to more spaces that could not be directly defined in the concrete setting. Most importantly for us, we have a new abstract space, the opposite measure algebra ${X_\mu}$ of ${X}$, defined as ${({\bf X}/{\bf N})^}$ where ${{\bf N}}$ is the ideal of null sets in ${{\bf X}}$. Informally, ${X_\mu}$ is the space ${X}$ with all the null sets removed; there is a canonical abstract embedding map ${\iota: X_\mu \rightarrow X}$, which allows one to convert any concrete measurable map ${f: X \rightarrow Y}$ into an abstract one ${[f]: X_\mu \rightarrow Y}$. One can then define the notion of an abstract action, abstract cocycle, and abstract coboundary by replacing every occurrence of the category of concrete measurable spaces with their abstract counterparts, and replacing ${X}$ with the opposite measure algebra ${X_\mu}$; see the paper for details. Our main theorem is then Theorem 2 (Uncountable Moore-Schmidt theorem) Let ${\Gamma}$ be a discrete group acting abstractly on a ${\sigma}$-finite measure space ${X}$. Let ${K}$ be a compact Hausdorff abelian group. Then a ${K_\otimes}$-valued abstract measurable cocycle ${\rho = (\rho_\gamma)_{\gamma \in \Gamma}}$ is an abstract coboundary if and only if for each character ${\hat k \in \hat K}$, the ${\mathbf{T}}$-valued cocycles ${\langle \hat k, \rho \rangle = ( \langle \hat k, \rho_\gamma \rangle )_{\gamma \in \Gamma}}$ are abstract coboundaries. With the abstract formalism, the proof of the uncountable Moore-Schmidt theorem is almost identical to the countable one (in fact we were able to make some simplifications, such as avoiding the use of the ergodic decomposition). A key tool is what we call a “conditional Pontryagin duality” theorem, which asserts that if one has an abstract measurable map ${\alpha_{\hat k}: X_\mu \rightarrow {\bf T}}$ for each ${\hat k \in K}$ obeying the identity ${ \alpha_{\hat k_1 + \hat k_2} - \alpha_{\hat k_1} - \alpha_{\hat k_2} = 0}$ for all ${\hat k_1,\hat k_2 \in \hat K}$, then there is an abstract measurable map ${F: X_\mu \rightarrow K_\otimes}$ such that ${\alpha_{\hat k} = \langle \hat k, F \rangle}$ for all ${\hat k \in \hat K}$. This is derived from the usual Pontryagin duality and some other tools, most notably the completeness of the ${\sigma}$-algebra of ${X_\mu}$, and the Sikorski extension theorem. We feel that it is natural to stay within the abstract measure theory formalism whenever dealing with uncountable situations. However, it is still an interesting question as to when one can guarantee that the abstract objects constructed in this formalism are representable by concrete analogues. The basic questions in this regard are: • (i) Suppose one has an abstract measurable map ${f: X_\mu \rightarrow Y}$ into a concrete measurable space. Does there exist a representation of ${f}$ by a concrete measurable map ${\tilde f: X \rightarrow Y}$? Is it unique up to almost everywhere equivalence? • (ii) Suppose one has a concrete cocycle that is an abstract coboundary. When can it be represented by a concrete coboundary? For (i) the answer is somewhat interesting (as I learned after posing this MathOverflow question): • If ${Y}$ does not separate points, or is not compact metrisable or Polish, there can be counterexamples to uniqueness. If ${Y}$ is not compact or Polish, there can be counterexamples to existence. • If ${Y}$ is a compact metric space or a Polish space, then one always has existence and uniqueness. • If ${Y}$ is a compact Hausdorff abelian group, one always has existence. • If ${X}$ is a complete measure space, then one always has existence (from a theorem of Maharam). • If ${X}$ is the unit interval with the Borel ${\sigma}$-algebra and Lebesgue measure, then one has existence for all compact Hausdorff ${Y}$ assuming the continuum hypothesis (from a theorem of von Neumann) but existence can fail under other extensions of ZFC (from a theorem of Shelah, using the method of forcing). • For more general ${X}$, existence for all compact Hausdorff ${Y}$ is equivalent to the existence of a lifting from the ${\sigma}$-algebra ${\mathcal{X}/\mathcal{N}}$ to ${\mathcal{X}}$ (or, in the language of abstract measurable spaces, the existence of an abstract retraction from ${X}$ to ${X_\mu}$). • It is a long-standing open question (posed for instance by Fremlin) whether it is relatively consistent with ZFC that existence holds whenever ${Y}$ is compact Hausdorff. Our understanding of (ii) is much less complete: • If ${K}$ is metrisable, the answer is “always” (which among other things establishes the countable Moore-Schmidt theorem as a corollary of the uncountable one). • If ${\Gamma}$ is at most countable and ${X}$ is a complete measure space, then the answer is again “always”. In view of the answers to (i), I would not be surprised if the full answer to (ii) was also sensitive to axioms of set theory. However, such set theoretic issues seem to be almost completely avoided if one sticks with the abstract formalism throughout; they only arise when trying to pass back and forth between the abstract and concrete categories. As readers who have followed my previous post will know, I have been spending the last few weeks extending my previous interactive text on propositional logic (entitied “QED”) to also cover first-order logic. The text has now reached what seems to be a stable form, with a complete set of deductive rules for first-order logic with equality, and no major bugs as far as I can tell (apart from one weird visual bug I can’t eradicate, in that some graphics elements can occasionally temporarily disappear when one clicks on an item). So it will likely not change much going forward. I feel though that there could be more that could be done with this sort of framework (e.g., improved GUI, modification to other logics, developing the ability to write one’s own texts and libraries, exploring mathematical theories such as Peano arithmetic, etc.). But writing this text (particularly the first-order logic sections) has brought me close to the limit of my programming ability, as the number of bugs introduced with each new feature implemented has begun to grow at an alarming rate. I would like to repackage the code so that it can be re-used by more adept programmers for further possible applications, though I have never done something like this before and would appreciate advice on how to do so. The code is already available under a Creative Commons licence, but I am not sure how readable and modifiable it will be to others currently. [Update: it is now on GitHub.] [One thing I noticed is that I would probably have to make more of a decoupling between the GUI elements, the underlying logical elements, and the interactive text. For instance, at some point I made the decision (convenient at the time) to use some GUI elements to store some of the state variables of the text, e.g. the exercise buttons are currently storing the status of what exercises are unlocked or not. This is presumably not an example of good programming practice, though it would be relatively easy to fix. More seriously, due to my inability to come up with a good general-purpose matching algorithm (or even specification of such an algorithm) for the the laws of first-order logic, many of the laws have to be hard-coded into the matching routine, so one cannot currently remove them from the text. It may well be that the best thing to do in fact is to rework the entire codebase from scratch using more professional software design methods.] [Update, Aug 23: links moved to GitHub version.] About six years ago on this blog, I started thinking about trying to make a web-based game based around high-school algebra, and ended up using Scratch to write a short but playable puzzle game in which one solves linear equations for an unknown ${x}$ using a restricted set of moves. (At almost the same time, there were a number of more professionally made games released along similar lines, most notably Dragonbox.) Since then, I have thought a couple times about whether there were other parts of mathematics which could be gamified in a similar fashion. Shortly after my first blog posts on this topic, I experimented with a similar gamification of Lewis Carroll’s classic list of logic puzzles, but the results were quite clunky, and I was never satisfied with the results. Over the last few weeks I returned to this topic though, thinking in particular about how to gamify the rules of inference of propositional logic, in a manner that at least vaguely resembles how mathematicians actually go about making logical arguments (e.g., splitting into cases, arguing by contradiction, using previous result as lemmas to help with subsequent ones, and so forth). The rules of inference are a list of a dozen or so deductive rules concerning propositional sentences (things like “(${A}$ AND ${B}$) OR (NOT ${C}$)”, where ${A,B,C}$ are some formulas). A typical such rule is Modus Ponens: if the sentence ${A}$ is known to be true, and the implication “${A}$ IMPLIES ${B}$” is also known to be true, then one can deduce that ${B}$ is also true. Furthermore, in this deductive calculus it is possible to temporarily introduce some unproven statements as an assumption, only to discharge them later. In particular, we have the deduction theorem: if, after making an assumption ${A}$, one is able to derive the statement ${B}$, then one can conclude that the implication “${A}$ IMPLIES ${B}$” is true without any further assumption. It took a while for me to come up with a workable game-like graphical interface for all of this, but I finally managed to set one up, now using Javascript instead of Scratch (which would be hopelessly inadequate for this task); indeed, part of the motivation of this project was to finally learn how to program in Javascript, which turned out to be not as formidable as I had feared (certainly having experience with other C-like languages like C++, Java, or lua, as well as some prior knowledge of HTML, was very helpful). The main code for this project is available here. Using this code, I have created an interactive textbook in the style of a computer game, which I have titled “QED”. This text contains thirty-odd exercises arranged in twelve sections that function as game “levels”, in which one has to use a given set of rules of inference, together with a given set of hypotheses, to reach a desired conclusion. The set of available rules increases as one advances through the text; in particular, each new section gives one or more rules, and additionally each exercise one solves automatically becomes a new deduction rule one can exploit in later levels, much as lemmas and propositions are used in actual mathematics to prove more difficult theorems. The text automatically tries to match available deduction rules to the sentences one clicks on or drags, to try to minimise the amount of manual input one needs to actually make a deduction. Most of one’s proof activity takes place in a “root environment” of statements that are known to be true (under the given hypothesis), but for more advanced exercises one has to also work in sub-environments in which additional assumptions are made. I found the graphical metaphor of nested boxes to be useful to depict this tree of sub-environments, and it seems to combine well with the drag-and-drop interface. The text also logs one’s moves in a more traditional proof format, which shows how the mechanics of the game correspond to a traditional mathematical argument. My hope is that this will give students a way to understand the underlying concept of forming a proof in a manner that is more difficult to achieve using traditional, non-interactive textbooks. I have tried to organise the exercises in a game-like progression in which one first works with easy levels that train the player on a small number of moves, and then introduce more advanced moves one at a time. As such, the order in which the rules of inference are introduced is a little idiosyncratic. The most powerful rule (the law of the excluded middle, which is what separates classical logic from intuitionistic logic) is saved for the final section of the text. Anyway, I am now satisfied enough with the state of the code and the interactive text that I am willing to make both available (and open source; I selected a CC-BY licence for both), and would be happy to receive feedback on any aspect of the either. In principle one could extend the game mechanics to other mathematical topics than the propositional calculus – the rules of inference for first-order logic being an obvious next candidate – but it seems to make sense to focus just on propositional logic for now. In graph theory, the recently developed theory of graph limits has proven to be a useful tool for analysing large dense graphs, being a convenient reformulation of the Szemerédi regularity lemma. Roughly speaking, the theory asserts that given any sequence ${G_n = (V_n, E_n)}$ of finite graphs, one can extract a subsequence ${G_{n_j} = (V_{n_j}, E_{n_j})}$ which converges (in a specific sense) to a continuous object known as a “graphon” – a symmetric measurable function ${p\colon [0,1] \times [0,1] \rightarrow [0,1]}$. What “converges” means in this context is that subgraph densities converge to the associated integrals of the graphon ${p}$. For instance, the edge density $\displaystyle \frac{1}{\|V_{n_j}\|^2} \|E_{n_j}\|$ converge to the integral $\displaystyle \int_0^1 \int_0^1 p(x,y)\ dx dy,$ the triangle density $\displaystyle \frac{1}{\|V_{n_j}\|^3} \lvert \{ (v_1,v_2,v_3) \in V_{n_j}^3: \{v_1,v_2\}, \{v_2,v_3\}, \{v_3,v_1\} \in E_{n_j} \} \rvert$ converges to the integral $\displaystyle \int_0^1 \int_0^1 \int_0^1 p(x_1,x_2) p(x_2,x_3) p(x_3,x_1)\ dx_1 dx_2 dx_3,$ the four-cycle density $\displaystyle \frac{1}{\|V_{n_j}\|^4} \lvert \{ (v_1,v_2,v_3,v_4) \in V_{n_j}^4: \{v_1,v_2\}, \{v_2,v_3\}, \{v_3,v_4\}, \{v_4,v_1\} \in E_{n_j} \} \rvert$ converges to the integral $\displaystyle \int_0^1 \int_0^1 \int_0^1 \int_0^1 p(x_1,x_2) p(x_2,x_3) p(x_3,x_4) p(x_4,x_1)\ dx_1 dx_2 dx_3 dx_4,$ and so forth. One can use graph limits to prove many results in graph theory that were traditionally proven using the regularity lemma, such as the triangle removal lemma, and can also reduce many asymptotic graph theory problems to continuous problems involving multilinear integrals (although the latter problems are not necessarily easy to solve!). See this text of Lovasz for a detailed study of graph limits and their applications. One can also express graph limits (and more generally hypergraph limits) in the language of nonstandard analysis (or of ultraproducts); see for instance this paper of Elek and Szegedy, Section 6 of this previous blog post, or this paper of Towsner. (In this post we assume some familiarity with nonstandard analysis, as reviewed for instance in the previous blog post.) Here, one starts as before with a sequence ${G_n = (V_n,E_n)}$ of finite graphs, and then takes an ultraproduct (with respect to some arbitrarily chosen non-principal ultrafilter ${\alpha \in\beta {\bf N} \backslash {\bf N}}$) to obtain a nonstandard graph ${G_\alpha = (V_\alpha,E_\alpha)}$, where ${V_\alpha = \prod_{n\rightarrow \alpha} V_n}$ is the ultraproduct of the ${V_n}$, and similarly for the ${E_\alpha}$. The set ${E_\alpha}$ can then be viewed as a symmetric subset of ${V_\alpha \times V_\alpha}$ which is measurable with respect to the Loeb ${\sigma}$-algebra ${{\mathcal L}_{V_\alpha \times V_\alpha}}$ of the product ${V_\alpha \times V_\alpha}$ (see this previous blog post for the construction of Loeb measure). A crucial point is that this ${\sigma}$-algebra is larger than the product ${{\mathcal L}_{V_\alpha} \times {\mathcal L}_{V_\alpha}}$ of the Loeb ${\sigma}$-algebra of the individual vertex set ${V_\alpha}$. This leads to a decomposition $\displaystyle 1_{E_\alpha} = p + e$ where the “graphon” ${p}$ is the orthogonal projection of ${1_{E_\alpha}}$ onto ${L^2( {\mathcal L}_{V_\alpha} \times {\mathcal L}_{V_\alpha} )}$, and the “regular error” ${e}$ is orthogonal to all product sets ${A \times B}$ for ${A, B \in {\mathcal L}_{V_\alpha}}$. The graphon ${p\colon V_\alpha \times V_\alpha \rightarrow [0,1]}$ then captures the statistics of the nonstandard graph ${G_\alpha}$, in exact analogy with the more traditional graph limits: for instance, the edge density $\displaystyle \hbox{st} \frac{1}{\|V_\alpha\|^2} \|E_\alpha\|$ (or equivalently, the limit of the ${\frac{1}{\|V_n\|^2} \|E_n\|}$ along the ultrafilter ${\alpha}$) is equal to the integral $\displaystyle \int_{V_\alpha} \int_{V_\alpha} p(x,y)\ d\mu_{V_\alpha}(x) d\mu_{V_\alpha}(y)$ where ${d\mu_V}$ denotes Loeb measure on a nonstandard finite set ${V}$; the triangle density $\displaystyle \hbox{st} \frac{1}{\|V_\alpha\|^3} \lvert \{ (v_1,v_2,v_3) \in V_\alpha^3: \{v_1,v_2\}, \{v_2,v_3\}, \{v_3,v_1\} \in E_\alpha \} \rvert$ (or equivalently, the limit along ${\alpha}$ of the triangle densities of ${E_n}$) is equal to the integral $\displaystyle \int_{V_\alpha} \int_{V_\alpha} \int_{V_\alpha} p(x_1,x_2) p(x_2,x_3) p(x_3,x_1)\ d\mu_{V_\alpha}(x_1) d\mu_{V_\alpha}(x_2) d\mu_{V_\alpha}(x_3),$ and so forth. Note that with this construction, the graphon ${p}$ is living on the Cartesian square of an abstract probability space ${V_\alpha}$, which is likely to be inseparable; but it is possible to cut down the Loeb ${\sigma}$-algebra on ${V_\alpha}$ to minimal countable ${\sigma}$-algebra for which ${p}$ remains measurable (up to null sets), and then one can identify ${V_\alpha}$ with ${[0,1]}$, bringing this construction of a graphon in line with the traditional notion of a graphon. (See Remark 5 of this previous blog post for more discussion of this point.) Additive combinatorics, which studies things like the additive structure of finite subsets ${A}$ of an abelian group ${G = (G,+)}$, has many analogies and connections with asymptotic graph theory; in particular, there is the arithmetic regularity lemma of Green which is analogous to the graph regularity lemma of Szemerédi. (There is also a higher order arithmetic regularity lemma analogous to hypergraph regularity lemmas, but this is not the focus of the discussion here.) Given this, it is natural to suspect that there is a theory of “additive limits” for large additive sets of bounded doubling, analogous to the theory of graph limits for large dense graphs. The purpose of this post is to record a candidate for such an additive limit. This limit can be used as a substitute for the arithmetic regularity lemma in certain results in additive combinatorics, at least if one is willing to settle for qualitative results rather than quantitative ones; I give a few examples of this below the fold. It seems that to allow for the most flexible and powerful manifestation of this theory, it is convenient to use the nonstandard formulation (among other things, it allows for full use of the transfer principle, whereas a more traditional limit formulation would only allow for a transfer of those quantities continuous with respect to the notion of convergence). Here, the analogue of a nonstandard graph is an ultra approximate group ${A_\alpha}$ in a nonstandard group ${G_\alpha = \prod_{n \rightarrow \alpha} G_n}$, defined as the ultraproduct of finite ${K}$-approximate groups ${A_n \subset G_n}$ for some standard ${K}$. (A ${K}$-approximate group ${A_n}$ is a symmetric set containing the origin such that ${A_n+A_n}$ can be covered by ${K}$ or fewer translates of ${A_n}$.) We then let ${O(A_\alpha)}$ be the external subgroup of ${G_\alpha}$ generated by ${A_\alpha}$; equivalently, ${A_\alpha}$ is the union of ${A_\alpha^m}$ over all standard ${m}$. This space has a Loeb measure ${\mu_{O(A_\alpha)}}$, defined by setting $\displaystyle \mu_{O(A_\alpha)}(E_\alpha) := \hbox{st} \frac{\|E_\alpha\|}{\|A_\alpha\|}$ whenever ${E_\alpha}$ is an internal subset of ${A_\alpha^m}$ for any standard ${m}$, and extended to a countably additive measure; the arguments in Section 6 of this previous blog post can be easily modified to give a construction of this measure. The Loeb measure ${\mu_{O(A_\alpha)}}$ is a translation invariant measure on ${O(A_{\alpha})}$, normalised so that ${A_\alpha}$ has Loeb measure one. As such, one should think of ${O(A_\alpha)}$ as being analogous to a locally compact abelian group equipped with a Haar measure. It should be noted though that ${O(A_\alpha)}$ is not actually a locally compact group with Haar measure, for two reasons: • There is not an obvious topology on ${O(A_\alpha)}$ that makes it simultaneously locally compact, Hausdorff, and ${\sigma}$-compact. (One can get one or two out of three without difficulty, though.) • The addition operation ${+\colon O(A_\alpha) \times O(A_\alpha) \rightarrow O(A_\alpha)}$ is not measurable from the product Loeb algebra ${{\mathcal L}_{O(A_\alpha)} \times {\mathcal L}_{O(A_\alpha)}}$ to ${{\mathcal L}_{O(\alpha)}}$. Instead, it is measurable from the coarser Loeb algebra ${{\mathcal L}_{O(A_\alpha) \times O(A_\alpha)}}$ to ${{\mathcal L}_{O(\alpha)}}$ (compare with the analogous situation for nonstandard graphs). Nevertheless, the analogy is a useful guide for the arguments that follow. Let ${L(O(A_\alpha))}$ denote the space of bounded Loeb measurable functions ${f\colon O(A_\alpha) \rightarrow {\bf C}}$ (modulo almost everywhere equivalence) that are supported on ${A_\alpha^m}$ for some standard ${m}$; this is a complex algebra with respect to pointwise multiplication. There is also a convolution operation ${\star\colon L(O(A_\alpha)) \times L(O(A_\alpha)) \rightarrow L(O(A_\alpha))}$, defined by setting $\displaystyle \hbox{st} f \star \hbox{st} g(x) := \hbox{st} \frac{1}{\|A_\alpha\|} \sum_{y \in A_\alpha^m} f(y) g(x-y)$ whenever ${f\colon A_\alpha^m \rightarrow {}^ {\bf C}}$, ${g\colon A_\alpha^l \rightarrow {}^* {\bf C}}$ are bounded nonstandard functions (extended by zero to all of ${O(A_\alpha)}$), and then extending to arbitrary elements of ${L(O(A_\alpha))}$ by density. Equivalently, ${f \star g}$ is the pushforward of the ${{\mathcal L}_{O(A_\alpha) \times O(A_\alpha)}}$-measurable function ${(x,y) \mapsto f(x) g(y)}$ under the map ${(x,y) \mapsto x+y}$. The basic structural theorem is then as follows. Theorem 1 (Kronecker factor) Let ${A_\alpha}$ be an ultra approximate group. Then there exists a (standard) locally compact abelian group ${G}$ of the form $\displaystyle G = {\bf R}^d \times {\bf Z}^m \times T$ for some standard ${d,m}$ and some compact abelian group ${T}$, equipped with a Haar measure ${\mu_G}$ and a measurable homomorphism ${\pi\colon O(A_\alpha) \rightarrow G}$ (using the Loeb ${\sigma}$-algebra on ${O(A_\alpha)}$ and the Baire ${\sigma}$-algebra on ${G}$), with the following properties: • (i) ${\pi}$ has dense image, and ${\mu_G}$ is the pushforward of Loeb measure ${\mu_{O(A_\alpha)}}$ by ${\pi}$. • (ii) There exists sets ${\{0\} \subset U_0 \subset K_0 \subset G}$ with ${U_0}$ open and ${K_0}$ compact, such that $\displaystyle \pi^{-1}(U_0) \subset 4A_\alpha \subset \pi^{-1}(K_0). \ \ \ \ \ (1)$ • (iii) Whenever ${K \subset U \subset G}$ with ${K}$ compact and ${U}$ open, there exists a nonstandard finite set ${B}$ such that $\displaystyle \pi^{-1}(K) \subset B \subset \pi^{-1}(U). \ \ \ \ \ (2)$ • (iv) If ${f, g \in L}$, then we have the convolution formula $\displaystyle f \star g = \pi^( (\pi_ f) \star (\pi_* g) ) \ \ \ \ \ (3)$ where ${\pi_* f,\pi_* g}$ are the pushforwards of ${f,g}$ to ${L^2(G, \mu_G)}$, the convolution ${\star}$ on the right-hand side is convolution using ${\mu_G}$, and ${\pi^}$ is the pullback map from ${L^2(G,\mu_G)}$ to ${L^2(O(A_\alpha), \mu_{O(A_\alpha)})}$. In particular, if ${\pi_ f = 0}$, then ${fg=0}$ for all ${g \in L}$. One can view the locally compact abelian group ${G}$ as a “model “or “Kronecker factor” for the ultra approximate group ${A_\alpha}$ (in close analogy with the Kronecker factor from ergodic theory). In the case that ${A_\alpha}$ is a genuine nonstandard finite group rather than an ultra approximate group, the non-compact components ${{\bf R}^d \times {\bf Z}^m}$ of the Kronecker group ${G}$ are trivial, and this theorem was implicitly established by Szegedy. The compact group ${T}$ is quite large, and in particular is likely to be inseparable; but as with the case of graphons, when one is only studying at most countably many functions ${f}$, one can cut down the size of this group to be separable (or equivalently, second countable or metrisable) if desired, so one often works with a “reduced Kronecker factor” which is a quotient of the full Kronecker factor ${G}$. Once one is in the separable case, the Baire sigma algebra is identical with the more familiar Borel sigma algebra. Given any sequence of uniformly bounded functions ${f_n\colon A_n^m \rightarrow {\bf C}}$ for some fixed ${m}$, we can view the function ${f \in L}$ defined by $\displaystyle f := \pi_ \hbox{st} \lim_{n \rightarrow \alpha} f_n \ \ \ \ \ (4)$ as an “additive limit” of the ${f_n}$, in much the same way that graphons ${p\colon V_\alpha \times V_\alpha \rightarrow [0,1]}$ are limits of the indicator functions ${1_{E_n}\colon V_n \times V_n \rightarrow \{0,1\}}$. The additive limits capture some of the statistics of the ${f_n}$, for instance the normalised means $\displaystyle \frac{1}{\|A_n\|} \sum_{x \in A_n^m} f_n(x)$ converge (along the ultrafilter ${\alpha}$) to the mean $\displaystyle \int_G f(x)\ d\mu_G(x),$ and for three sequences ${f_n,g_n,h_n\colon A_n^m \rightarrow {\bf C}}$ of functions, the normalised correlation $\displaystyle \frac{1}{\|A_n\|^2} \sum_{x,y \in A_n^m} f_n(x) g_n(y) h_n(x+y)$ converges along ${\alpha}$ to the correlation $\displaystyle \int_G \int_G f(x) g(y) h(x+y)\ d\mu_G(x) d\mu_G(y),$ the normalised ${U^2}$ Gowers norm $\displaystyle ( \frac{1}{\|A_n\|^3} \sum_{x,y,z,w \in A_n^m: x+w=y+z} f_n(x) \overline{f_n(y)} \overline{f_n(z)} f_n(w))^{1/4}$ converges along ${\alpha}$ to the ${U^2}$ Gowers norm $\displaystyle ( \int_{G \times G \times G} f(x) \overline{f(y)} \overline{f(z)} f_n(x+y-z)\ d\mu_G(x) d\mu_G(y) d\mu_G(z))^{1/4}$ and so forth. We caution however that some correlations that involve evaluating more than one function at the same point will not necessarily be preserved in the additive limit; for instance the normalised ${\ell^2}$ norm $\displaystyle (\frac{1}{\|A_n\|} \sum_{x \in A_n^m} \|f_n(x)\|^2)^{1/2}$ does not necessarily converge to the ${L^2}$ norm $\displaystyle (\int_G \|f(x)\|^2\ d\mu_G(x))^{1/2},$ but can converge instead to a larger quantity, due to the presence of the orthogonal projection ${\pi_}$ in the definition (4) of ${f}$. An important special case of an additive limit occurs when the functions ${f_n\colon A_n^m \rightarrow {\bf C}}$ involved are indicator functions ${f_n = 1_{E_n}}$ of some subsets ${E_n}$ of ${A_n^m}$. The additive limit ${f \in L}$ does not necessarily remain an indicator function, but instead takes values in ${[0,1]}$ (much as a graphon ${p}$ takes values in ${[0,1]}$ even though the original indicators ${1_{E_n}}$ take values in ${\{0,1\}}$). The convolution ${f \star f\colon G \rightarrow [0,1]}$ is then the ultralimit of the normalised convolutions ${\frac{1}{\|A_n\|} 1_{E_n} \star 1_{E_n}}$; in particular, the measure of the support of ${f \star f}$ provides a lower bound on the limiting normalised cardinality ${\frac{1}{\|A_n\|} \|E_n + E_n\|}$ of a sumset. In many situations this lower bound is an equality, but this is not necessarily the case, because the sumset ${2E_n = E_n + E_n}$ could contain a large number of elements which have very few (${o(\|A_n\|)}$) representations as the sum of two elements of ${E_n}$, and in the limit these portions of the sumset fall outside of the support of ${f \star f}$. (One can think of the support of ${f \star f}$ as describing the “essential” sumset of ${2E_n = E_n + E_n}$, discarding those elements that have only very few representations.) Similarly for higher convolutions of ${f}$. Thus one can use additive limits to partially control the growth ${k E_n}$ of iterated sumsets of subsets ${E_n}$ of approximate groups ${A_n}$, in the regime where ${k}$ stays bounded and ${n}$ goes to infinity. Theorem 1 can be proven by Fourier-analytic means (combined with Freiman’s theorem from additive combinatorics), and we will do so below the fold. For now, we give some illustrative examples of additive limits. Example 2 (Bohr sets) We take ${A_n}$ to be the intervals ${A_n := \{ x \in {\bf Z}: \|x\| \leq N_n \}}$, where ${N_n}$ is a sequence going to infinity; these are ${2}$-approximate groups for all ${n}$. Let ${\theta}$ be an irrational real number, let ${I}$ be an interval in ${{\bf R}/{\bf Z}}$, and for each natural number ${n}$ let ${B_n}$ be the Bohr set $\displaystyle B_n := \{ x \in A^{(n)}: \theta x \hbox{ mod } 1 \in I \}.$ In this case, the (reduced) Kronecker factor ${G}$ can be taken to be the infinite cylinder ${{\bf R} \times {\bf R}/{\bf Z}}$ with the usual Lebesgue measure ${\mu_G}$. The additive limits of ${1_{A_n}}$ and ${1_{B_n}}$ end up being ${1_A}$ and ${1_B}$, where ${A}$ is the finite cylinder $\displaystyle A := \{ (x,t) \in {\bf R} \times {\bf R}/{\bf Z}: x \in [-1,1]\}$ and ${B}$ is the rectangle $\displaystyle B := \{ (x,t) \in {\bf R} \times {\bf R}/{\bf Z}: x \in [-1,1]; t \in I \}.$ Geometrically, one should think of ${A_n}$ and ${B_n}$ as being wrapped around the cylinder ${{\bf R} \times {\bf R}/{\bf Z}}$ via the homomorphism ${x \mapsto (\frac{x}{N_n}, \theta x \hbox{ mod } 1)}$, and then one sees that ${B_n}$ is converging in some normalised weak sense to ${B}$, and similarly for ${A_n}$ and ${A}$. In particular, the additive limit predicts the growth rate of the iterated sumsets ${kB_n}$ to be quadratic in ${k}$ until ${k\|I\|}$ becomes comparable to ${1}$, at which point the growth transitions to linear growth, in the regime where ${k}$ is bounded and ${n}$ is large. If ${\theta = \frac{p}{q}}$ were rational instead of irrational, then one would need to replace ${{\bf R}/{\bf Z}}$ by the finite subgroup ${\frac{1}{q}{\bf Z}/{\bf Z}}$ here. Example 3 (Structured subsets of progressions) We take ${A_n}$ be the rank two progression $\displaystyle A_n := \{ a + b N_n^2: a,b \in {\bf Z}; \|a\|, \|b\| \leq N_n \},$ where ${N_n}$ is a sequence going to infinity; these are ${4}$-approximate groups for all ${n}$. Let ${B_n}$ be the subset $\displaystyle B_n := \{ a + b N_n^2: a,b \in {\bf Z}; \|a\|^2 + \|b\|^2 \leq N_n^2 \}.$ Then the (reduced) Kronecker factor can be taken to be ${G = {\bf R}^2}$ with Lebesgue measure ${\mu_G}$, and the additive limits of the ${1_{A_n}}$ and ${1_{B_n}}$ are then ${1_A}$ and ${1_B}$, where ${A}$ is the square $\displaystyle A := \{ (a,b) \in {\bf R}^2: \|a\|, \|b\| \leq 1 \}$ and ${B}$ is the circle $\displaystyle B := \{ (a,b) \in {\bf R}^2: a^2+b^2 \leq 1 \}.$ Geometrically, the picture is similar to the Bohr set one, except now one uses a Freiman homomorphism ${a + b N_n^2 \mapsto (\frac{a}{N_n}, \frac{b}{N_n})}$ for ${a,b = O( N_n )}$ to embed the original sets ${A_n, B_n}$ into the plane ${{\bf R}^2}$. In particular, one now expects the growth rate of the iterated sumsets ${k A_n}$ and ${k B_n}$ to be quadratic in ${k}$, in the regime where ${k}$ is bounded and ${n}$ is large. Example 4 (Dissociated sets) Let ${d}$ be a fixed natural number, and take $\displaystyle A_n = \{0, v_1,\dots,v_d,-v_1,\dots,-v_d \}$ where ${v_1,\dots,v_d}$ are randomly chosen elements of a large cyclic group ${{\bf Z}/p_n{\bf Z}}$, where ${p_n}$ is a sequence of primes going to infinity. These are ${O(d)}$-approximate groups. The (reduced) Kronecker factor ${G}$ can (almost surely) then be taken to be ${{\bf Z}^d}$ with counting measure, and the additive limit of ${1_{A_n}}$ is ${1_A}$, where ${A = \{ 0, e_1,\dots,e_d,-e_1,\dots,-e_d\}}$ and ${e_1,\dots,e_d}$ is the standard basis of ${{\bf Z}^d}$. In particular, the growth rates of ${k A_n}$ should grow approximately like ${k^d}$ for ${k}$ bounded and ${n}$ large. Example 5 (Random subsets of groups) Let ${A_n = G_n}$ be a sequence of finite additive groups whose order is going to infinity. Let ${B_n}$ be a random subset of ${G_n}$ of some fixed density ${0 \leq \lambda \leq 1}$. Then (almost surely) the Kronecker factor here can be reduced all the way to the trivial group ${\{0\}}$, and the additive limit of the ${1_{B_n}}$ is the constant function ${\lambda}$. The convolutions ${\frac{1}{\|G_n\|} 1_{B_n} 1_{B_n}}$ then converge in the ultralimit (modulo almost everywhere equivalence) to the pullback of ${\lambda^2}$; this reflects the fact that ${(1-o(1))\|G_n\|}$ of the elements of ${G_n}$ can be represented as the sum of two elements of ${B_n}$ in ${(\lambda^2 + o(1)) \|G_n\|}$ ways. In particular, ${B_n+B_n}$ occupies a proportion ${1-o(1)}$ of ${G_n}$. Example 6 (Trigonometric series) Take ${A_n = G_n = {\bf Z}/p_n {\bf C}}$ for a sequence ${p_n}$ of primes going to infinity, and for each ${n}$ let ${\xi_{n,1},\xi_{n,2},\dots}$ be an infinite sequence of frequencies chosen uniformly and independently from ${{\bf Z}/p_n{\bf Z}}$. Let ${f_n\colon {\bf Z}/p_n{\bf Z} \rightarrow {\bf C}}$ denote the random trigonometric series $\displaystyle f_n(x) := \sum_{j=1}^\infty 2^{-j} e^{2\pi i \xi_{n,j} x / p_n }.$ Then (almost surely) we can take the reduced Kronecker factor ${G}$ to be the infinite torus ${({\bf R}/{\bf Z})^{\bf N}}$ (with the Haar probability measure ${\mu_G}$), and the additive limit of the ${f_n}$ then becomes the function ${f\colon ({\bf R}/{\bf Z})^{\bf N} \rightarrow {\bf R}}$ defined by the formula $\displaystyle f( (x_j)_{j=1}^\infty ) := \sum_{j=1}^\infty e^{2\pi i x_j}.$ In fact, the pullback ${\pi^* f}$ is the ultralimit of the ${f_n}$. As such, for any standard exponent ${1 \leq q < \infty}$, the normalised ${l^q}$ norm $\displaystyle (\frac{1}{p_n} \sum_{x \in {\bf Z}/p_n{\bf Z}} \|f_n(x)\|^q)^{1/q}$ can be seen to converge to the limit $\displaystyle (\int_{({\bf R}/{\bf Z})^{\bf N}} \|f(x)\|^q\ d\mu_G(x))^{1/q}.$ The reader is invited to consider combinations of the above examples, e.g. random subsets of Bohr sets, to get a sense of the general case of Theorem 1. It is likely that this theorem can be extended to the noncommutative setting, using the noncommutative Freiman theorem of Emmanuel Breuillard, Ben Green, and myself, but I have not attempted to do so here (see though this recent preprint of Anush Tserunyan for some related explorations); in a separate direction, there should be extensions that can control higher Gowers norms, in the spirit of the work of Szegedy. Note: the arguments below will presume some familiarity with additive combinatorics and with nonstandard analysis, and will be a little sketchy in places. Let ${\bar{{\bf Q}}}$ be the algebraic closure of ${{\bf Q}}$, that is to say the field of algebraic numbers. We fix an embedding of ${\bar{{\bf Q}}}$ into ${{\bf C}}$, giving rise to a complex absolute value ${z \mapsto \|z\|}$ for algebraic numbers ${z \in \bar{{\bf Q}}}$. Let ${\alpha \in \bar{{\bf Q}}}$ be of degree ${D > 1}$, so that ${\alpha}$ is irrational. A classical theorem of Liouville gives the quantitative bound $\displaystyle \|\alpha - \frac{p}{q}\| \geq c \frac{1}{\|q\|^D} \ \ \ \ \ (1)$ for the irrationality of ${\alpha}$ fails to be approximated by rational numbers ${p/q}$, where ${c>0}$ depends on ${\alpha,D}$ but not on ${p,q}$. Indeed, if one lets ${\alpha = \alpha_1, \alpha_2, \dots, \alpha_D}$ be the Galois conjugates of ${\alpha}$, then the quantity ${\prod_{i=1}^D \|q \alpha_i - p\|}$ is a non-zero natural number divided by a constant, and so we have the trivial lower bound $\displaystyle \prod_{i=1}^D \|q \alpha_i - p\| \geq c$ from which the bound (1) easily follows. A well known corollary of the bound (1) is that Liouville numbers are automatically transcendental. The famous theorem of Thue, Siegel and Roth improves the bound (1) to $\displaystyle \|\alpha - \frac{p}{q}\| \geq c \frac{1}{\|q\|^{2+\epsilon}} \ \ \ \ \ (2)$ for any ${\epsilon>0}$ and rationals ${\frac{p}{q}}$, where ${c>0}$ depends on ${\alpha,\epsilon}$ but not on ${p,q}$. Apart from the ${\epsilon}$ in the exponent and the implied constant, this bound is optimal, as can be seen from Dirichlet’s theorem. This theorem is a good example of the ineffectivity phenomenon that affects a large portion of modern number theory: the implied constant in the ${\gg}$ notation is known to be finite, but there is no explicit bound for it in terms of the coefficients of the polynomial defining ${\alpha}$ (in contrast to (1), for which an effective bound may be easily established). This is ultimately due to the reliance on the “dueling conspiracy” (or “repulsion phenomenon”) strategy. We do not as yet have a good way to rule out one counterexample to (2), in which ${\frac{p}{q}}$ is far closer to ${\alpha}$ than ${\frac{1}{\|q\|^{2+\epsilon}}}$; however we can rule out two such counterexamples, by playing them off of each other. A powerful strengthening of the Thue-Siegel-Roth theorem is given by the subspace theorem, first proven by Schmidt and then generalised further by several authors. To motivate the theorem, first observe that the Thue-Siegel-Roth theorem may be rephrased as a bound of the form $\displaystyle \| \alpha p - \beta q \| \times \| \alpha' p - \beta' q \| \geq c (1 + \|p\| + \|q\|)^{-\epsilon} \ \ \ \ \ (3)$ for any algebraic numbers ${\alpha,\beta,\alpha',\beta'}$ with ${(\alpha,\beta)}$ and ${(\alpha',\beta')}$ linearly independent (over the algebraic numbers), and any ${(p,q) \in {\bf Z}^2}$ and ${\epsilon>0}$, with the exception when ${\alpha,\beta}$ or ${\alpha',\beta'}$ are rationally dependent (i.e. one is a rational multiple of the other), in which case one has to remove some lines (i.e. subspaces in ${{\bf Q}^2}$) of rational slope from the space ${{\bf Z}^2}$ of pairs ${(p,q)}$ to which the bound (3) does not apply (namely, those lines for which the left-hand side vanishes). Here ${c>0}$ can depend on ${\alpha,\beta,\alpha',\beta',\epsilon}$ but not on ${p,q}$. More generally, we have Theorem 1 (Schmidt subspace theorem) Let ${d}$ be a natural number. Let ${L_1,\dots,L_d: \bar{{\bf Q}}^d \rightarrow \bar{{\bf Q}}}$ be linearly independent linear forms. Then for any ${\epsilon>0}$, one has the bound $\displaystyle \prod_{i=1}^d \|L_i(x)\| \geq c (1 + \\|x\\| )^{-\epsilon}$ for all ${x \in {\bf Z}^d}$, outside of a finite number of proper subspaces of ${{\bf Q}^d}$, where $\displaystyle \\| (x_1,\dots,x_d) \\| := \max( \|x_1\|, \dots, \|x_d\| )$ and ${c>0}$ depends on ${\epsilon, d}$ and the ${\alpha_{i,j}}$, but is independent of ${x}$. Being a generalisation of the Thue-Siegel-Roth theorem, it is unsurprising that the known proofs of the subspace theorem are also ineffective with regards to the constant ${c}$. (However, the number of exceptional subspaces may be bounded effectively; cf. the situation with the Skolem-Mahler-Lech theorem, discussed in this previous blog post.) Once again, the lower bound here is basically sharp except for the ${\epsilon}$ factor and the implied constant: given any ${\delta_1,\dots,\delta_d > 0}$ with ${\delta_1 \dots \delta_d = 1}$, a simple volume packing argument (the same one used to prove the Dirichlet approximation theorem) shows that for any sufficiently large ${N \geq 1}$, one can find integers ${x_1,\dots,x_d \in [-N,N]}$, not all zero, such that $\displaystyle \|L_i(x)\| \ll \delta_i$ for all ${i=1,\dots,d}$. Thus one can get ${\prod_{i=1}^d \|L_i(x)\|}$ comparable to ${1}$ in many different ways. There are important generalisations of the subspace theorem to other number fields than the rationals (and to other valuations than the Archimedean valuation ${z \mapsto \|z\|}$); we will develop one such generalisation below. The subspace theorem is one of many finiteness theorems in Diophantine geometry; in this case, it is the number of exceptional subspaces which is finite. It turns out that finiteness theorems are very compatible with the language of nonstandard analysis. (See this previous blog post for a review of the basics of nonstandard analysis, and in particular for the nonstandard interpretation of asymptotic notation such as ${\ll}$ and ${o()}$.) The reason for this is that a standard set ${X}$ is finite if and only if it contains no strictly nonstandard elements (that is to say, elements of ${{}^* X \backslash X}$). This makes for a clean formulation of finiteness theorems in the nonstandard setting. For instance, the standard form of Bezout’s theorem asserts that if ${P(x,y), Q(x,y)}$ are coprime polynomials over some field, then the curves ${\{ (x,y): P(x,y) = 0\}}$ and ${\{ (x,y): Q(x,y)=0\}}$ intersect in only finitely many points. The nonstandard version of this is then Theorem 2 (Bezout’s theorem, nonstandard form) Let ${P(x,y), Q(x,y)}$ be standard coprime polynomials. Then there are no strictly nonstandard solutions to ${P(x,y)=Q(x,y)=0}$. Now we reformulate Theorem 1 in nonstandard language. We need a definition: Definition 3 (General position) Let ${K \subset L}$ be nested fields. A point ${x = (x_1,\dots,x_d)}$ in ${L^d}$ is said to be in ${K}$-general position if it is not contained in any hyperplane of ${L^d}$ definable over ${K}$, or equivalently if one has $\displaystyle a_1 x_1 + \dots + a_d x_d = 0 \iff a_1=\dots = a_d = 0$ for any ${a_1,\dots,a_d \in K}$. Theorem 4 (Schmidt subspace theorem, nonstandard version) Let ${d}$ be a standard natural number. Let ${L_1,\dots,L_d: \bar{{\bf Q}}^d \rightarrow \bar{{\bf Q}}}$ be linearly independent standard linear forms. Let ${x \in {}^* {\bf Z}^d}$ be a tuple of nonstandard integers which is in ${{\bf Q}}$-general position (in particular, this forces ${x}$ to be strictly nonstandard). Then one has $\displaystyle \prod_{i=1}^d \|L_i(x)\| \gg \\|x\\|^{-o(1)},$ where we extend ${L_i}$ from ${\bar{{\bf Q}}}$ to ${{}^* \bar{{\bf Q}}}$ (and also similarly extend ${\\| \\|}$ from ${{\bf Z}^d}$ to ${{}^* {\bf Z}^d}$) in the usual fashion. Observe that (as is usual when translating to nonstandard analysis) some of the epsilons and quantifiers that are present in the standard version become hidden in the nonstandard framework, being moved inside concepts such as “strictly nonstandard” or “general position”. We remark that as ${x}$ is in ${{\bf Q}}$-general position, it is also in ${\bar{{\bf Q}}}$-general position (as an easy Galois-theoretic argument shows), and the requirement that the ${L_1,\dots,L_d}$ are linearly independent is thus equivalent to ${L_1(x),\dots,L_d(x)}$ being ${\bar{{\bf Q}}}$-linearly independent. Exercise 1 Verify that Theorem 1 and Theorem 4 are equivalent. (Hint: there are only countably many proper subspaces of ${{\bf Q}^d}$.) We will not prove the subspace theorem here, but instead focus on a particular application of the subspace theorem, namely to counting integer points on curves. In this paper of Corvaja and Zannier, the subspace theorem was used to give a new proof of the following basic result of Siegel: Theorem 5 (Siegel’s theorem on integer points) Let ${P \in {\bf Q}[x,y]}$ be an irreducible polynomial of two variables, such that the affine plane curve ${C := \{ (x,y): P(x,y)=0\}}$ either has genus at least one, or has at least three points on the line at infinity, or both. Then ${C}$ has only finitely many integer points ${(x,y) \in {\bf Z}^2}$. This is a finiteness theorem, and as such may be easily converted to a nonstandard form: Theorem 6 (Siegel’s theorem, nonstandard form) Let ${P \in {\bf Q}[x,y]}$ be a standard irreducible polynomial of two variables, such that the affine plane curve ${C := \{ (x,y): P(x,y)=0\}}$ either has genus at least one, or has at least three points on the line at infinity, or both. Then ${C}$ does not contain any strictly nonstandard integer points ${(x_,y_) \in {}^* {\bf Z}^2 \backslash {\bf Z}^2}$. Note that Siegel’s theorem can fail for genus zero curves that only meet the line at infinity at just one or two points; the key examples here are the graphs ${\{ (x,y): y - f(x) = 0\}}$ for a polynomial ${f \in {\bf Z}[x]}$, and the Pell equation curves ${\{ (x,y): x^2 - dy^2 = 1 \}}$. Siegel’s theorem can be compared with the more difficult theorem of Faltings, which establishes finiteness of rational points (not just integer points), but now needs the stricter requirement that the curve ${C}$ has genus at least two (to avoid the additional counterexample of elliptic curves of positive rank, which have infinitely many rational points). The standard proofs of Siegel’s theorem rely on a combination of the Thue-Siegel-Roth theorem and a number of results on abelian varieties (notably the Mordell-Weil theorem). The Corvaja-Zannier argument rebalances the difficulty of the argument by replacing the Thue-Siegel-Roth theorem by the more powerful subspace theorem (in fact, they need one of the stronger versions of this theorem alluded to earlier), while greatly reducing the reliance on results on abelian varieties. Indeed, for curves with three or more points at infinity, no theory from abelian varieties is needed at all, while for the remaining cases, one mainly needs the existence of the Abel-Jacobi embedding, together with a relatively elementary theorem of Chevalley-Weil which is used in the proof of the Mordell-Weil theorem, but is significantly easier to prove. The Corvaja-Zannier argument (together with several further applications of the subspace theorem) is presented nicely in this Bourbaki expose of Bilu. To establish the theorem in full generality requires a certain amount of algebraic number theory machinery, such as the theory of valuations on number fields, or of relative discriminants between such number fields. However, the basic ideas can be presented without much of this machinery by focusing on simple special cases of Siegel’s theorem. For instance, we can handle irreducible cubics that meet the line at infinity at exactly three points ${[1,\alpha_1,0], [1,\alpha_2,0], [1,\alpha_3,0]}$: Theorem 7 (Siegel’s theorem with three points at infinity) Siegel’s theorem holds when the irreducible polynomial ${P(x,y)}$ takes the form $\displaystyle P(x,y) = (y - \alpha_1 x) (y - \alpha_2 x) (y - \alpha_3 x) + Q(x,y)$ for some quadratic polynomial ${Q \in {\bf Q}[x,y]}$ and some distinct algebraic numbers ${\alpha_1,\alpha_2,\alpha_3}$. Proof: We use the nonstandard formalism. Suppose for sake of contradiction that we can find a strictly nonstandard integer point ${(x_,y_) \in {}^* {\bf Z}^2 \backslash {\bf Z}^2}$ on a curve ${C := \{ (x,y): P(x,y)=0\}}$ of the indicated form. As this point is infinitesimally close to the line at infinity, ${y_/x_}$ must be infinitesimally close to one of ${\alpha_1,\alpha_2,\alpha_3}$; without loss of generality we may assume that ${y_/x_}$ is infinitesimally close to ${\alpha_1}$. We now use a version of the polynomial method, to find some polynomials of controlled degree that vanish to high order on the “arm” of the cubic curve ${C}$ that asymptotes to ${[1,\alpha_1,0]}$. More precisely, let ${D \geq 3}$ be a large integer (actually ${D=3}$ will already suffice here), and consider the ${\bar{{\bf Q}}}$-vector space ${V}$ of polynomials ${R(x,y) \in \bar{{\bf Q}}[x,y]}$ of degree at most ${D}$, and of degree at most ${2}$ in the ${y}$ variable; this space has dimension ${3D}$. Also, as one traverses the arm ${y/x \rightarrow \alpha_1}$ of ${C}$, any polynomial ${R}$ in ${V}$ grows at a rate of at most ${D}$, that is to say ${R}$ has a pole of order at most ${D}$ at the point at infinity ${[1,\alpha_1,0]}$. By performing Laurent expansions around this point (which is a non-singular point of ${C}$, as the ${\alpha_i}$ are assumed to be distinct), we may thus find a basis ${R_1, \dots, R_{3D}}$ of ${V}$, with the property that ${R_j}$ has a pole of order at most ${D+1-j}$ at ${[1,\alpha_1,0]}$ for each ${j=1,\dots,3D}$. From the control of the pole at ${[1,\alpha_1,0]}$, we have $\displaystyle \|R_j(x_,y_)\| \ll (\|x_\|+\|y_\|)^{D+1-j}$ for all ${j=1,\dots,3D}$. The exponents here become negative for ${j > D+1}$, and on multiplying them all together we see that $\displaystyle \prod_{j=1}^{3D} \|R_j(x_,y_)\| \ll (\|x_\|+\|y_\|)^{3D(D+1) - \frac{3D(3D+1)}{2}}.$ This exponent is negative for ${D}$ large enough (or just take ${D=3}$). If we expand $\displaystyle R_j(x_,y_) = \sum_{a+b \leq D; b \leq 2} \alpha_{j,a,b} x_^a y_^b$ for some algebraic numbers ${\alpha_{j,a,b}}$, then we thus have $\displaystyle \prod_{j=1}^{3D} \|\sum_{a+b \leq D; b \leq 2} \alpha_{j,a,b} x_^a y_^b\| \ll (\|x_\|+\|y_\|)^{-\epsilon}$ for some standard ${\epsilon>0}$. Note that the ${3D}$-dimensional vectors ${(\alpha_{j,a,b})_{a+b \leq D; b \leq 2}}$ are linearly independent in ${{\bf C}^{3D}}$, because the ${R_j}$ are linearly independent in ${V}$. Applying the Schmidt subspace theorem in the contrapositive, we conclude that the ${3D}$-tuple ${( x_^a y_^b )_{a+b \leq D; b \leq 2} \in {}^* {\bf Z}^{3D}}$ is not in ${{\bf Q}}$-general position. That is to say, one has a non-trivial constraint of the form $\displaystyle \sum_{a+b \leq D; b \leq 2} c_{a,b} x_^a y_^b = 0 \ \ \ \ \ (4)$ for some standard rational coefficients ${c_{a,b}}$, not all zero. But, as ${P}$ is irreducible and cubic in ${y}$, it has no common factor with the standard polynomial ${\sum_{a+b \leq D; b \leq 2} c_{a,b} x^a y^b}$, so by Bezout’s theorem (Theorem 2) the constraint (4) only has standard solutions, contradicting the strictly nonstandard nature of ${(x_,y_)}$. $\Box$ Exercise 2 Rewrite the above argument so that it makes no reference to nonstandard analysis. (In this case, the rewriting is quite straightforward; however, there will be a subsequent argument in which the standard version is significantly messier than the nonstandard counterpart, which is the reason why I am working with the nonstandard formalism in this blog post.) A similar argument works for higher degree curves that meet the line at infinity in three or more points, though if the curve has singularities at infinity then it becomes convenient to rely on the Riemann-Roch theorem to control the dimension of the analogue of the space ${V}$. Note that when there are only two or fewer points at infinity, though, one cannot get the negative exponent of ${-\epsilon}$ needed to usefully apply the subspace theorem. To deal with this case we require some additional tricks. For simplicity we focus on the case of Mordell curves, although it will be convenient to work with more general number fields ${{\bf Q} \subset K \subset \bar{{\bf Q}}}$ than the rationals: Theorem 8 (Siegel’s theorem for Mordell curves) Let ${k}$ be a non-zero integer. Then there are only finitely many integer solutions ${(x,y) \in {\bf Z}^2}$ to ${y^2 - x^3 = k}$. More generally, for any number field ${K}$, and any nonzero ${k \in K}$, there are only finitely many algebraic integer solutions ${(x,y) \in {\mathcal O}_K^2}$ to ${y^2-x^3=k}$, where ${{\mathcal O}_K}$ is the ring of algebraic integers in ${K}$. Again, we will establish the nonstandard version. We need some additional notation: Definition 9 • We define an almost rational integer to be a nonstandard ${x \in {}^* {\bf Q}}$ such that ${Mx \in {}^* {\bf Z}}$ for some standard positive integer ${M}$, and write ${{\bf Q} {}^* {\bf Z}}$ for the ${{\bf Q}}$-algebra of almost rational integers. • If ${K}$ is a standard number field, we define an almost ${K}$-integer to be a nonstandard ${x \in {}^* K}$ such that ${Mx \in {}^* {\mathcal O}_K}$ for some standard positive integer ${M}$, and write ${K {}^* {\bf Z} = K {\mathcal O}_K}$ for the ${K}$-algebra of almost ${K}$-integers. • We define an almost algebraic integer to be a nonstandard ${x \in {}^* {\bar Q}}$ such that ${Mx}$ is a nonstandard algebraic integer for some standard positive integer ${M}$, and write ${\bar{{\bf Q}} {}^* {\bf Z}}$ for the ${\bar{{\bf Q}}}$-algebra of almost algebraic integers. • Theorem 10 (Siegel for Mordell, nonstandard version) Let ${k}$ be a non-zero standard algebraic number. Then the curve ${\{ (x,y): y^2 - x^3 = k \}}$ does not contain any strictly nonstandard almost algebraic integer point. Another way of phrasing this theorem is that if ${x,y}$ are strictly nonstandard almost algebraic integers, then ${y^2-x^3}$ is either strictly nonstandard or zero. Exercise 3 Verify that Theorem 8 and Theorem 10 are equivalent. Due to all the ineffectivity, our proof does not supply any bound on the solutions ${x,y}$ in terms of ${k}$, even if one removes all references to nonstandard analysis. It is a conjecture of Hall (a special case of the notorious ABC conjecture) that one has the bound ${\|x\| \ll_\epsilon \|k\|^{2+\epsilon}}$ for all ${\epsilon>0}$ (or equivalently ${\|y\| \ll_\epsilon \|k\|^{3+\epsilon}}$), but even the weaker conjecture that ${x,y}$ are of polynomial size in ${k}$ is open. (The best known bounds are of exponential nature, and are proven using a version of Baker’s method: see for instance this text of Sprindzuk.) A direct repetition of the arguments used to prove Theorem 7 will not work here, because the Mordell curve ${\{ (x,y): y^2 - x^3 = k \}}$ only hits the line at infinity at one point, ${[0,1,0]}$. To get around this we will exploit the fact that the Mordell curve is an elliptic curve and thus has a group law on it. We will then divide all the integer points on this curve by two; as elliptic curves have four 2-torsion points, this will end up placing us in a situation like Theorem 7, with four points at infinity. However, there is an obstruction: it is not obvious that dividing an integer point on the Mordell curve by two will produce another integer point. However, this is essentially true (after enlarging the ring of integers slightly) thanks to a general principle of Chevalley and Weil, which can be worked out explicitly in the case of division by two on Mordell curves by relatively elementary means (relying mostly on unique factorisation of ideals of algebraic integers). We give the details below the fold. There are a number of ways to construct the real numbers ${{\bf R}}$, for instance • as the metric completion of ${{\bf Q}}$ (thus, ${{\bf R}}$ is defined as the set of Cauchy sequences of rationals, modulo Cauchy equivalence); • as the space of Dedekind cuts on the rationals ${{\bf Q}}$; • as the space of quasimorphisms ${\phi: {\bf Z} \rightarrow {\bf Z}}$ on the integers, quotiented by bounded functions. (I believe this construction first appears in this paper of Street, who credits the idea to Schanuel, though the germ of this construction arguably goes all the way back to Eudoxus.) There is also a fourth family of constructions that proceeds via nonstandard analysis, as a special case of what is known as the nonstandard hull construction. (Here I will assume some basic familiarity with nonstandard analysis and ultraproducts, as covered for instance in this previous blog post.) Given an unbounded nonstandard natural number ${N \in {}^* {\bf N} \backslash {\bf N}}$, one can define two external additive subgroups of the nonstandard integers ${{}^* {\bf Z}}$: • The group ${O(N) := \{ n \in {}^* {\bf Z}: \|n\| \leq CN \hbox{ for some } C \in {\bf N} \}}$ of all nonstandard integers of magnitude less than or comparable to ${N}$; and • The group ${o(N) := \{ n \in {}^* {\bf Z}: \|n\| \leq C^{-1} N \hbox{ for all } C \in {\bf N} \}}$ of nonstandard integers of magnitude infinitesimally smaller than ${N}$. The group ${o(N)}$ is a subgroup of ${O(N)}$, so we may form the quotient group ${O(N)/o(N)}$. This space is isomorphic to the reals ${{\bf R}}$, and can in fact be used to construct the reals: Proposition 1 For any coset ${n + o(N)}$ of ${O(N)/o(N)}$, there is a unique real number ${\hbox{st} \frac{n}{N}}$ with the property that ${\frac{n}{N} = \hbox{st} \frac{n}{N} + o(1)}$. The map ${n + o(N) \mapsto \hbox{st} \frac{n}{N}}$ is then an isomorphism between the additive groups ${O(N)/o(N)}$ and ${{\bf R}}$. Proof: Uniqueness is clear. For existence, observe that the set ${\{ x \in {\bf R}: Nx \leq n + o(N) \}}$ is a Dedekind cut, and its supremum can be verified to have the required properties for ${\hbox{st} \frac{n}{N}}$. $\Box$ In a similar vein, we can view the unit interval ${[0,1]}$ in the reals as the quotient $\displaystyle [0,1] \equiv [N] / o(N) \ \ \ \ \ (1)$ where ${[N]}$ is the nonstandard (i.e. internal) set ${\{ n \in {\bf N}: n \leq N \}}$; of course, ${[N]}$ is not a group, so one should interpret ${[N]/o(N)}$ as the image of ${[N]}$ under the quotient map ${{}^* {\bf Z} \rightarrow {}^* {\bf Z} / o(N)}$ (or ${O(N) \rightarrow O(N)/o(N)}$, if one prefers). Or to put it another way, (1) asserts that ${[0,1]}$ is the image of ${[N]}$ with respect to the map ${\pi: n \mapsto \hbox{st} \frac{n}{N}}$. In this post I would like to record a nice measure-theoretic version of the equivalence (1), which essentially appears already in standard texts on Loeb measure (see e.g. this text of Cutland). To describe the results, we must first quickly recall the construction of Loeb measure on ${[N]}$. Given an internal subset ${A}$ of ${[N]}$, we may define the elementary measure ${\mu_0(A)}$ of ${A}$ by the formula $\displaystyle \mu_0(A) := \hbox{st} \frac{\|A\|}{N}.$ This is a finitely additive probability measure on the Boolean algebra of internal subsets of ${[N]}$. We can then construct the Loeb outer measure ${\mu^(A)}$ of any subset ${A \subset [N]}$ in complete analogy with Lebesgue outer measure by the formula $\displaystyle \mu^(A) := \inf \sum_{n=1}^\infty \mu_0(A_n)$ where ${(A_n)_{n=1}^\infty}$ ranges over all sequences of internal subsets of ${[N]}$ that cover ${A}$. We say that a subset ${A}$ of ${[N]}$ is Loeb measurable if, for any (standard) ${\epsilon>0}$, one can find an internal subset ${B}$ of ${[N]}$ which differs from ${A}$ by a set of Loeb outer measure at most ${\epsilon}$, and in that case we define the Loeb measure ${\mu(A)}$ of ${A}$ to be ${\mu^(A)}$. It is a routine matter to show (e.g. using the Carathéodory extension theorem) that the space ${{\mathcal L}}$ of Loeb measurable sets is a ${\sigma}$-algebra, and that ${\mu}$ is a countably additive probability measure on this space that extends the elementary measure ${\mu_0}$. Thus ${[N]}$ now has the structure of a probability space ${([N], {\mathcal L}, \mu)}$. Now, the group ${o(N)}$ acts (Loeb-almost everywhere) on the probability space ${[N]}$ by the addition map, thus ${T^h n := n+h}$ for ${n \in [N]}$ and ${h \in o(N)}$ (excluding a set of Loeb measure zero where ${n+h}$ exits ${[N]}$). This action is clearly seen to be measure-preserving. As such, we can form the invariant factor ${Z^0_{o(N)}([N]) = ([N], {\mathcal L}^{o(N)}, \mu\downharpoonright_{{\mathcal L}^{o(N)}})}$, defined by restricting attention to those Loeb measurable sets ${A \subset [N]}$ with the property that ${T^h A}$ is equal ${\mu}$-almost everywhere to ${A}$ for each ${h \in o(N)}$. The claim is then that this invariant factor is equivalent (up to almost everywhere equivalence) to the unit interval ${[0,1]}$ with Lebesgue measure ${m}$ (and the trivial action of ${o(N)}$), by the same factor map ${\pi: n \mapsto \hbox{st} \frac{n}{N}}$ used in (1). More precisely: Theorem 2 Given a set ${A \in {\mathcal L}^{o(N)}}$, there exists a Lebesgue measurable set ${B \subset [0,1]}$, unique up to ${m}$-a.e. equivalence, such that ${A}$ is ${\mu}$-a.e. equivalent to the set ${\pi^{-1}(B) := \{ n \in [N]: \hbox{st} \frac{n}{N} \in B \}}$. Conversely, if ${B \in [0,1]}$ is Lebesgue measurable, then ${\pi^{-1}(B)}$ is in ${{\mathcal L}^{o(N)}}$, and ${\mu( \pi^{-1}(B) ) = m( B )}$. $\displaystyle [0,1] \equiv Z^0_{o(N)}( [N] )$ of (1). Proof: We first prove the converse. It is clear that ${\pi^{-1}(B)}$ is ${o(N)}$-invariant, so it suffices to show that ${\pi^{-1}(B)}$ is Loeb measurable with Loeb measure ${m(B)}$. This is easily verified when ${B}$ is an elementary set (a finite union of intervals). By countable subadditivity of outer measure, this implies that Loeb outer measure of ${\pi^{-1}(E)}$ is bounded by the Lebesgue outer measure of ${E}$ for any set ${E \subset [0,1]}$; since every Lebesgue measurable set differs from an elementary set by a set of arbitrarily small Lebesgue outer measure, the claim follows. Now we establish the forward claim. Uniqueness is clear from the converse claim, so it suffices to show existence. Let ${A \in {\mathcal L}^{o(N)}}$. Let ${\epsilon>0}$ be an arbitrary standard real number, then we can find an internal set ${A_\epsilon \subset [N]}$ which differs from ${A}$ by a set of Loeb measure at most ${\epsilon}$. As ${A}$ is ${o(N)}$-invariant, we conclude that for every ${h \in o(N)}$, ${A_\epsilon}$ and ${T^h A_\epsilon}$ differ by a set of Loeb measure (and hence elementary measure) at most ${2\epsilon}$. By the (contrapositive of the) underspill principle, there must exist a standard ${\delta>0}$ such that ${A_\epsilon}$ and ${T^h A_\epsilon}$ differ by a set of elementary measure at most ${2\epsilon}$ for all ${\|h\| \leq \delta N}$. If we then define the nonstandard function ${f_\epsilon: [N] \rightarrow {}^ {\bf R}}$ by the formula $\displaystyle f(n) := \hbox{st} \frac{1}{\delta N} \sum_{m \in [N]: m \leq n \leq m+\delta N} 1_{A_\epsilon}(m),$ then from the (nonstandard) triangle inequality we have $\displaystyle \frac{1}{N} \sum_{n \in [N]} \|f(n) - 1_{A_\epsilon}(n)\| \leq 3\epsilon$ (say). On the other hand, ${f}$ has the Lipschitz continuity property $\displaystyle \|f(n)-f(m)\| \leq \frac{2\|n-m\|}{\delta N}$ and so in particular we see that $\displaystyle \hbox{st} f(n) = \tilde f( \hbox{st} \frac{n}{N} )$ for some Lipschitz continuous function ${\tilde f: [0,1] \rightarrow [0,1]}$. If we then let ${E_\epsilon}$ be the set where ${\tilde f \geq 1 - \sqrt{\epsilon}}$, one can check that ${A_\epsilon}$ differs from ${\pi^{-1}(E_\epsilon)}$ by a set of Loeb outer measure ${O(\sqrt{\epsilon})}$, and hence ${A}$ does so also. Sending ${\epsilon}$ to zero, we see (from the converse claim) that ${1_{E_\epsilon}}$ is a Cauchy sequence in ${L^1}$ and thus converges in ${L^1}$ for some Lebesgue measurable ${E}$. The sets ${A_\epsilon}$ then converge in Loeb outer measure to ${\pi^{-1}(E)}$, giving the claim. $\Box$ Thanks to the Lebesgue differentiation theorem, the conditional expectation ${{\bf E}( f \| Z^0_{o(N)}([N]))}$ of a bounded Loeb-measurable function ${f: [N] \rightarrow {\bf R}}$ can be expressed (as a function on ${[0,1]}$, defined ${m}$-a.e.) as $\displaystyle {\bf E}( f \| Z^0_{o(N)}([N]))(x) := \lim_{\epsilon \rightarrow 0} \frac{1}{2\epsilon} \int_{[x-\epsilon N,x+\epsilon N]} f\ d\mu.$ By the abstract ergodic theorem from the previous post, one can also view this conditional expectation as the element in the closed convex hull of the shifts ${T^h f}$, ${h = o(N)}$ of minimal ${L^2}$ norm. In particular, we obtain a form of the von Neumann ergodic theorem in this context: the averages ${\frac{1}{H} \sum_{h=1}^H T^h f}$ for ${H=O(N)}$ converge (as a net, rather than a sequence) in ${L^2}$ to ${{\bf E}( f \| Z^0_{o(N)}([N]))}$. If ${f: [N] \rightarrow [-1,1]}$ is (the standard part of) an internal function, that is to say the ultralimit of a sequence ${f_n: [N_n] \rightarrow [-1,1]}$ of finitary bounded functions, one can view the measurable function ${F := {\bf E}( f \| Z^0_{o(N)}([N]))}$ as a limit of the ${f_n}$ that is analogous to the “graphons” that emerge as limits of graphs (see e.g. the recent text of Lovasz on graph limits). Indeed, the measurable function ${F: [0,1] \rightarrow [-1,1]}$ is related to the discrete functions ${f_n: [N_n] \rightarrow [-1,1]}$ by the formula $\displaystyle \int_a^b F(x)\ dx = \hbox{st} \lim_{n \rightarrow p} \frac{1}{N_n} \sum_{a N_n \leq m \leq b N_n} f_n(m)$ for all ${0 \leq a < b \leq 1}$, where ${p}$ is the nonprincipal ultrafilter used to define the nonstandard universe. In particular, from the Arzela-Ascoli diagonalisation argument there is a subsequence ${n_j}$ such that $\displaystyle \int_a^b F(x)\ dx = \lim_{j \rightarrow \infty} \frac{1}{N_{n_j}} \sum_{a N_{n_j} \leq m \leq b N_{n_j}} f_n(m),$ thus ${F}$ is the asymptotic density function of the ${f_n}$. For instance, if ${f_n}$ is the indicator function of a randomly chosen subset of ${[N_n]}$, then the asymptotic density function would equal ${1/2}$ (almost everywhere, at least). I’m continuing to look into understanding the ergodic theory of ${o(N)}$ actions, as I believe this may allow one to apply ergodic theory methods to the “single-scale” or “non-asymptotic” setting (in which one averages only over scales comparable to a large parameter ${N}$, rather than the traditional asymptotic approach of letting the scale go to infinity). I’m planning some further posts in this direction, though this is still a work in progress. (This is an extended blog post version of my talk “Ultraproducts as a Bridge Between Discrete and Continuous Analysis” that I gave at the Simons institute for the theory of computing at the workshop “Neo-Classical methods in discrete analysis“. Some of the material here is drawn from previous blog posts, notably “Ultraproducts as a bridge between hard analysis and soft analysis” and “Ultralimit analysis and quantitative algebraic geometry“‘. The text here has substantially more details than the talk; one may wish to skip all of the proofs given here to obtain a closer approximation to the original talk.) Discrete analysis, of course, is primarily interested in the study of discrete (or “finitary”) mathematical objects: integers, rational numbers (which can be viewed as ratios of integers), finite sets, finite graphs, finite or discrete metric spaces, and so forth. However, many powerful tools in mathematics (e.g. ergodic theory, measure theory, topological group theory, algebraic geometry, spectral theory, etc.) work best when applied to continuous (or “infinitary”) mathematical objects: real or complex numbers, manifolds, algebraic varieties, continuous topological or metric spaces, etc. In order to apply results and ideas from continuous mathematics to discrete settings, there are basically two approaches. One is to directly discretise the arguments used in continuous mathematics, which often requires one to keep careful track of all the bounds on various quantities of interest, particularly with regard to various error terms arising from discretisation which would otherwise have been negligible in the continuous setting. The other is to construct continuous objects as limits of sequences of discrete objects of interest, so that results from continuous mathematics may be applied (often as a “black box”) to the continuous limit, which then can be used to deduce consequences for the original discrete objects which are quantitative (though often ineffectively so). The latter approach is the focus of this current talk. The following table gives some examples of a discrete theory and its continuous counterpart, together with a limiting procedure that might be used to pass from the former to the latter: (Discrete) (Continuous) (Limit method) Ramsey theory Topological dynamics Compactness Density Ramsey theory Ergodic theory Furstenberg correspondence principle Graph/hypergraph regularity Measure theory Graph limits Polynomial regularity Linear algebra Ultralimits Structural decompositions Hilbert space geometry Ultralimits Fourier analysis Spectral theory Direct and inverse limits Quantitative algebraic geometry Algebraic geometry Schemes Discrete metric spaces Continuous metric spaces Gromov-Hausdorff limits Approximate group theory Topological group theory Model theory As the above table illustrates, there are a variety of different ways to form a limiting continuous object. Roughly speaking, one can divide limits into three categories: • Topological and metric limits. These notions of limits are commonly used by analysts. Here, one starts with a sequence (or perhaps a net) of objects ${x_n}$ in a common space ${X}$, which one then endows with the structure of a topological space or a metric space, by defining a notion of distance between two points of the space, or a notion of open neighbourhoods or open sets in the space. Provided that the sequence or net is convergent, this produces a limit object ${\lim_{n \rightarrow \infty} x_n}$, which remains in the same space, and is “close” to many of the original objects ${x_n}$ with respect to the given metric or topology. • Categorical limits. These notions of limits are commonly used by algebraists. Here, one starts with a sequence (or more generally, a diagram) of objects ${x_n}$ in a category ${X}$, which are connected to each other by various morphisms. If the ambient category is well-behaved, one can then form the direct limit ${\varinjlim x_n}$ or the inverse limit ${\varprojlim x_n}$ of these objects, which is another object in the same category ${X}$, and is connected to the original objects ${x_n}$ by various morphisms. • Logical limits. These notions of limits are commonly used by model theorists. Here, one starts with a sequence of objects ${x_{\bf n}}$ or of spaces ${X_{\bf n}}$, each of which is (a component of) a model for given (first-order) mathematical language (e.g. if one is working in the language of groups, ${X_{\bf n}}$ might be groups and ${x_{\bf n}}$ might be elements of these groups). By using devices such as the ultraproduct construction, or the compactness theorem in logic, one can then create a new object ${\lim_{{\bf n} \rightarrow \alpha} x_{\bf n}}$ or a new space ${\prod_{{\bf n} \rightarrow \alpha} X_{\bf n}}$, which is still a model of the same language (e.g. if the spaces ${X_{\bf n}}$ were all groups, then the limiting space ${\prod_{{\bf n} \rightarrow \alpha} X_{\bf n}}$ will also be a group), and is “close” to the original objects or spaces in the sense that any assertion (in the given language) that is true for the limiting object or space, will also be true for many of the original objects or spaces, and conversely. (For instance, if ${\prod_{{\bf n} \rightarrow \alpha} X_{\bf n}}$ is an abelian group, then the ${X_{\bf n}}$ will also be abelian groups for many ${{\bf n}}$.) The purpose of this talk is to highlight the third type of limit, and specifically the ultraproduct construction, as being a “universal” limiting procedure that can be used to replace most of the limits previously mentioned. Unlike the topological or metric limits, one does not need the original objects ${x_{\bf n}}$ to all lie in a common space ${X}$ in order to form an ultralimit ${\lim_{{\bf n} \rightarrow \alpha} x_{\bf n}}$; they are permitted to lie in different spaces ${X_{\bf n}}$; this is more natural in many discrete contexts, e.g. when considering graphs on ${{\bf n}}$ vertices in the limit when ${{\bf n}}$ goes to infinity. Also, no convergence properties on the ${x_{\bf n}}$ are required in order for the ultralimit to exist. Similarly, ultraproduct limits differ from categorical limits in that no morphisms between the various spaces ${X_{\bf n}}$ involved are required in order to construct the ultraproduct. With so few requirements on the objects ${x_{\bf n}}$ or spaces ${X_{\bf n}}$, the ultraproduct construction is necessarily a very “soft” one. Nevertheless, the construction has two very useful properties which make it particularly useful for the purpose of extracting good continuous limit objects out of a sequence of discrete objects. First of all, there is Łos’s theorem, which roughly speaking asserts that any first-order sentence which is asymptotically obeyed by the ${x_{\bf n}}$, will be exactly obeyed by the limit object ${\lim_{{\bf n} \rightarrow \alpha} x_{\bf n}}$; in particular, one can often take a discrete sequence of “partial counterexamples” to some assertion, and produce a continuous “complete counterexample” that same assertion via an ultraproduct construction; taking the contrapositives, one can often then establish a rigorous equivalence between a quantitative discrete statement and its qualitative continuous counterpart. Secondly, there is the countable saturation property that ultraproducts automatically enjoy, which is a property closely analogous to that of compactness in topological spaces, and can often be used to ensure that the continuous objects produced by ultraproduct methods are “complete” or “compact” in various senses, which is particularly useful in being able to upgrade qualitative (or “pointwise”) bounds to quantitative (or “uniform”) bounds, more or less “for free”, thus reducing significantly the burden of “epsilon management” (although the price one pays for this is that one needs to pay attention to which mathematical objects of study are “standard” and which are “nonstandard”). To achieve this compactness or completeness, one sometimes has to restrict to the “bounded” portion of the ultraproduct, and it is often also convenient to quotient out the “infinitesimal” portion in order to complement these compactness properties with a matching “Hausdorff” property, thus creating familiar examples of continuous spaces, such as locally compact Hausdorff spaces. Ultraproducts are not the only logical limit in the model theorist’s toolbox, but they are one of the simplest to set up and use, and already suffice for many of the applications of logical limits outside of model theory. In this post, I will set out the basic theory of these ultraproducts, and illustrate how they can be used to pass between discrete and continuous theories in each of the examples listed in the above table. Apart from the initial “one-time cost” of setting up the ultraproduct machinery, the main loss one incurs when using ultraproduct methods is that it becomes very difficult to extract explicit quantitative bounds from results that are proven by transferring qualitative continuous results to the discrete setting via ultraproducts. However, in many cases (particularly those involving regularity-type lemmas) the bounds are already of tower-exponential type or worse, and there is arguably not much to be lost by abandoning the explicit quantitative bounds altogether. The classical foundations of probability theory (discussed for instance in this previous blog post) is founded on the notion of a probability space ${(\Omega, {\cal E}, {\bf P})}$ – a space ${\Omega}$ (the sample space) equipped with a ${\sigma}$-algebra ${{\cal E}}$ (the event space), together with a countably additive probability measure ${{\bf P}: {\cal E} \rightarrow [0,1]}$ that assigns a real number in the interval ${[0,1]}$ to each event. One can generalise the concept of a probability space to a finitely additive probability space, in which the event space ${{\cal E}}$ is now only a Boolean algebra rather than a ${\sigma}$-algebra, and the measure ${\mu}$ is now only finitely additive instead of countably additive, thus ${{\bf P}( E \vee F ) = {\bf P}(E) + {\bf P}(F)}$ when ${E,F}$ are disjoint events. By giving up countable additivity, one loses a fair amount of measure and integration theory, and in particular the notion of the expectation of a random variable becomes problematic (unless the random variable takes only finitely many values). Nevertheless, one can still perform a fair amount of probability theory in this weaker setting. In this post I would like to describe a further weakening of probability theory, which I will call qualitative probability theory, in which one does not assign a precise numerical probability value ${{\bf P}(E)}$ to each event, but instead merely records whether this probability is zero, one, or something in between. Thus ${{\bf P}}$ is now a function from ${{\cal E}}$ to the set ${\{0, I, 1\}}$, where ${I}$ is a new symbol that replaces all the elements of the open interval ${(0,1)}$. In this setting, one can no longer compute quantitative expressions, such as the mean or variance of a random variable; but one can still talk about whether an event holds almost surely, with positive probability, or with zero probability, and there are still usable notions of independence. (I will refer to classical probability theory as quantitative probability theory, to distinguish it from its qualitative counterpart.) The main reason I want to introduce this weak notion of probability theory is that it becomes suited to talk about random variables living inside algebraic varieties, even if these varieties are defined over fields other than ${{\bf R}}$ or ${{\bf C}}$. In algebraic geometry one often talks about a “generic” element of a variety ${V}$ defined over a field ${k}$, which does not lie in any specified variety of lower dimension defined over ${k}$. Once ${V}$ has positive dimension, such generic elements do not exist as classical, deterministic ${k}$-points ${x}$ in ${V}$, since of course any such point lies in the ${0}$-dimensional subvariety ${\{x\}}$ of ${V}$. There are of course several established ways to deal with this problem. One way (which one might call the “Weil” approach to generic points) is to extend the field ${k}$ to a sufficiently transcendental extension ${\tilde k}$, in order to locate a sufficient number of generic points in ${V(\tilde k)}$. Another approach (which one might dub the “Zariski” approach to generic points) is to work scheme-theoretically, and interpret a generic point in ${V}$ as being associated to the zero ideal in the function ring of ${V}$. However I want to discuss a third perspective, in which one interprets a generic point not as a deterministic object, but rather as a random variable ${{\bf x}}$ taking values in ${V}$, but which lies in any given lower-dimensional subvariety of ${V}$ with probability zero. This interpretation is intuitive, but difficult to implement in classical probability theory (except perhaps when considering varieties over ${{\bf R}}$ or ${{\bf C}}$) due to the lack of a natural probability measure to place on algebraic varieties; however it works just fine in qualitative probability theory. In particular, the algebraic geometry notion of being “generically true” can now be interpreted probabilistically as an assertion that something is “almost surely true”. It turns out that just as qualitative random variables may be used to interpret the concept of a generic point, they can also be used to interpret the concept of a type in model theory; the type of a random variable ${x}$ is the set of all predicates ${\phi(x)}$ that are almost surely obeyed by ${x}$. In contrast, model theorists often adopt a Weil-type approach to types, in which one works with deterministic representatives of a type, which often do not occur in the original structure of interest, but only in a sufficiently saturated extension of that structure (this is the analogue of working in a sufficiently transcendental extension of the base field). However, it seems that (in some cases at least) one can equivalently view types in terms of (qualitative) random variables on the original structure, avoiding the need to extend that structure. (Instead, one reserves the right to extend the sample space of one’s probability theory whenever necessary, as part of the “probabilistic way of thinking” discussed in this previous blog post.) We illustrate this below the fold with two related theorems that I will interpret through the probabilistic lens: the “group chunk theorem” of Weil (and later developed by Hrushovski), and the “group configuration theorem” of Zilber (and again later developed by Hrushovski). For sake of concreteness we will only consider these theorems in the theory of algebraically closed fields, although the results are quite general and can be applied to many other theories studied in model theory. Andre j- Grebenc on Eigenvectors from eigenvalues tuitionhub1 on Career advice 【数学都知道】2014年3月2日精选… on “New equidistribution es… 【数学都知道】2014年3月2日精选… on Finite time blowup for an aver… Anonymous on Analysis I Quan on 246B, Notes 2: Some connection… Fred on Analysis II Anonymous on 246B, Notes 1: Zeroes, poles,… Anonymous on 245B, notes 5: Hilbert sp… Anonymous on 245C, Notes 2: The Fourier… Anonymous on The Collatz conjecture, Little… Anonymous on The Collatz conjecture, Little… Anonymous on The Collatz conjecture, Little… Anonymous on The Collatz conjecture, Little… Anonymous on The Collatz conjecture, Little…	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1213, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9567185640335083, "perplexity": 208.37346006751238}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301592.29/warc/CC-MAIN-20220119215632-20220120005632-00113.warc.gz"}
http://mathhelpforum.com/calculators/16702-how-would-i-enter-following-my-ti-89-a-print.html	# How would I enter the following in my TI-89... Show 40 post(s) from this thread on one page Page 1 of 2 12 Last • Jul 9th 2007, 11:57 PM cachemony How would I enter the following in my TI-89... How do you enter cube roots and radicals into the TI-89? I can't really give an example using the computer keyboard, so an example is on the following page: Example Thanks, Noah • Jul 10th 2007, 03:06 AM rualin $\sqrt[3]{6x+9}+8$ would be Code: (6x+9)^(1/3)+8 In other words, if you want to take the nth root of say, abc, it would be Code: (abc)^(1/n) Remember to put 1/n in parenthesis. • Jul 10th 2007, 04:38 PM cachemony Hey thanks a lot for your help. Could you tell me how to enter the three problems on the page below on my TI-89 Example Thanks, Noah • Jul 10th 2007, 04:45 PM galactus Here's one example. The others are entered the same. • Jul 12th 2007, 12:24 AM cachemony How do you enter the 2nd and 3rd ones:Example I was looking for how to enter the problems instead of the answers. Thanks, Noah • Jul 16th 2007, 09:33 PM earboth 2 Attachment(s) Quote: Originally Posted by cachemony ... I was looking for how to enter the problems instead of the answers. Thanks, Noah Hello, I'm not quite certain what you mean here. From the screenshot you can see how to enter a term into the TI89. There are only a few rules you have to use strictly: 1. All parts which belongs together must be put into brackets: Denominators, numerators, radicands, ... 2. Superflues brackets are suppressed by the TI89 automatically. So it is better to use an additional pair of brackets. 3. A leading negative sign is connected to the key $\boxed{(-)}$. If you use the normal operation sign for subtraction you'll get an error message. 4. I've attached 2 screenshots. Compare the input line and the result on the screen. • Jul 19th 2007, 11:16 PM cachemony Thanks a lot for all the help from everyone. I need help with a few more....how would I enter the following into my TI-89: How do you enter logarithmic functions? 1. 4loga-(-x-4) - 3loga(x+4) 2. logx100 + loga0.1 3. When I try to graph the following it says I have Undefined varibales. What does that mean? how do I graph the following: (x+7)² - (y+2)² = 36 Thank You. Noah • Jul 20th 2007, 08:10 AM earboth 5 Attachment(s) Quote: Originally Posted by cachemony Thanks a lot for all the help from everyone. I need help with a few more....how would I enter the following into my TI-89: How do you enter logarithmic functions? 1. 4loga-(-x-4) - 3loga(x+4) 2. logx100 + loga0.1 3. When I try to graph the following it says I have Undefined varibales. What does that mean? how do I graph the following: (x+7)² - (y+2)² = 36 Thank You. Noah Hello Noah, the TI89 has one build-in logarithmic function: The ln-function which you find with $\boxed{2ND}$ + $\boxed{x}$. If you want to calculate logarithms to another base you have to use the base-change-formula: $\log_b(x) = \frac{\ln(x)}{\ln(x)}$ to #1.: I assume that you mean: $4 \cdot \log_a((-(x-4) - 3 \cdot \log_a(x+4)$. If so then type: 4( $\boxed{2ND}$+ $\boxed{x}$-(x-4)) / $\boxed{2ND}$ + $\boxed{x}$a)-3( $\boxed{2ND}$ + $\boxed{x}$x+4) / $\boxed{2ND}$ + $\boxed{x}$a) $\rightarrow ~~~~~~~~~~~~~~~~~\uparrow ~~\uparrow \text{attention: these are different negative signs for your TI()}$ But unfortunately your TI89 will not simplify or transform this term. to #2.: Are you sure that there isn't a typo? to #3.: Your TI89 is set to function mode (I assume). The calculator is not able to handle relations in multiple variables. To graph this hyperbola you first calculate equations of functions by solving the original relation for y. You'll get 4 different equations. (see attachment HYP2FUNC1) Copy the results into the input line and store the different functions into the y= editor by using the $\boxed{STO\blacktriangleright}$ key. In the WINDOW editor Use the settings xmin = -16 xmax = 8 xscl = 1 ymin = -8 ymax=8 yscl=1 xres=1 Here it is necessary to set xres=1 because otherwise the gap between the different graphs will be to large. • Jul 20th 2007, 08:36 AM galactus You can use 'log', but you have to type it in. There is no 'log' key. • Jul 20th 2007, 11:58 AM earboth Quote: Originally Posted by galactus You can use 'log', but you have to type it in. There is no 'log' key. Hello, thanks! But obviously the log-function of the TI89 means $\log_{10}(x)$ which I know as $\lg(x)$ • Jul 22nd 2007, 05:30 PM cachemony How do I get my TI-89 to divide this: (6x3 - x2 - 5x + 4) ÷ (3x - 2) When its entered, it just displays it as a fraction. How do I get it to perform the division? Thanks, Noah • Jul 22nd 2007, 10:05 PM earboth Quote: Originally Posted by cachemony How do I get my TI-89 to divide this: (6x3 - x2 - 5x + 4) ÷ (3x - 2) When its entered, it just displays it as a fraction. How do I get it to perform the division? Thanks, Noah Hello, if the build-in program can't simplify the quotient it is only repeated. To do the synthetic division you have to use the command propFrac((6x^3-x^2-5x+4)/(3x-2)) You get the result: $\frac{2}{3x-2} +2x^2 + x - 1$ You find the command propFrac( at the menu F2 Algebra #7 By the way: Please do yourself and do us a favour and start a new thread if you have a new problem. Otherwise you risk that nobody at the forum notices that you need help. • Sep 8th 2007, 06:29 PM saber3469 square roots how do I input the proper info on these problems: the square rootof 32 - the sqaure root if 50xx how do i input the info for graphing on: 2x + 3y+=6 -8x - 12y =-24 • Sep 8th 2007, 06:32 PM saber3469 square roots how do I input the proper info on these problems: the square rootof 32 - the sqaure root if 50xx how do i input the info for graphing on: 2x + 3y+=6 -8x - 12y =-24 • Sep 8th 2007, 06:33 PM saber3469 square roots how do I input the proper info on these problems on the ti-89 calculator the square rootof 32 - the sqaure root if 50xx how do i input the info for graphing on: 2x + 3y+=6 -8x - 12y =-24 Show 40 post(s) from this thread on one page Page 1 of 2 12 Last	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6933803558349609, "perplexity": 2564.311617628965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218188717.24/warc/CC-MAIN-20170322212948-00076-ip-10-233-31-227.ec2.internal.warc.gz"}
http://www.thespectrumofriemannium.com/2019/11/17/log239-higgspecial/?shared=email&msg=fail	# LOG#239. Higgspecial. The 2012 found Higgs particle is special. The next generations of physicists and scientists, will likely build larger machines or colliders to study it precisely. The question is, of course, where is new physics, i.e., where is the new energy physics scale? Is it the Planck scale? Is it lower than ? ## What is a particle? Particles are field excitations. Fields satisfy wave equations. Thus particles, as representations of fields, also verify field or wave equations. Fields and particles have also symmetries. They are invariant under certain group transformations. There are several types of symmetry transformations: 1. Spacetime symmetries or spacetime invariance. They include: translations, rotations, boosts (pure Lorentz transformations) and the full three type combination. The homogeneous Lorentz group does not include translations. The inhomogeneous Lorentz group includes translations and it is called Poincaré group. Generally speaking, spacetime symmetries are local spacetime transformations only. 2. Internal (gauge) symmetries. These transformations are transformations of the fields up to a phase factor at the same spacetime-point. They can be global and local. 3. Supersymmetry. Transformations relating different statistics particles, i.e., relating bosons and fermions. It can be extended to higher spin under the names of hypersymmetry and hypersupersymmetry. It can also be extended to N-graded supermanifolds. We say a transformation is global when the group parameter does not depend on the base space (generally spacetime). We say a transformation is local when it depends of functions defined on the base space. Quantum mechanics is just a theory relating “numbers” to each other. Particles or fields are defined as functions on the spacetime momentum (continuum in general) and certain discrete set of numbers (quantum numbers all of them) and thus represents quantum particles/waves as certain unitary representations of the Poincaré group (spacetime)! Superfields generalize this thing. Diffferent particles or fields are certain unitary representations of the superPoincaré group (superspacetime)! Equivalently, particles are invariant states under group or supergroup transformations. Particle physics is the study of fundamental laws of Nature governed by (yet hidden and mysterious) the fusion of quantum mechanics rules and spacetime rules. From the 17th century to 20th century: we had a march of reductionism and symmetries. Whatever the ultimate theory is, relativity plus QM (Quantum Mechanics) are got as approximations at low or relatively low (100GeV) energies. Reductionism works: massless particles interact as an Greek Y (upsilon) vertices. Massless particles can be easily described by twistors, certain bispinors (couples of spinors): Indeed, interactions are believed to be effectively described by parallel twistor-like variables and . The Poincaré group completely fixes the way in which particles interact between each other. For instante, the 4-particle scattering constraints where is the spin of the particle. Be aware of not confusing the spin with the Mandelstam variable . Locality implies the factorization of the 4-particle amplitude into two pieces, such as Two special cases are (the Higss!) and (the graviton!): where the latter represents the 2×2 graviton scattering. For spin S=1 you have Interactions between both, massive and massless spin one particles must contain spin zero particles in order to unitarize the scattering amplitudes! Scalar bosons are Higgs bosons. Of course, at very high energies, the Higgs and the chiral components of the massive gauge bosons (spin one) are all unified into a single electroweak interaction. A belief in these principles has a paid-off: particles have only spin 0,1/2,1,3/2,2,… The 21st century revelations must include some additional pieces of information about this stuff: • The doom or end of spacetime. Is the end of reductionism at sight? • Why the Universe is big? • New ideas required beyond spacetime and internal symmetries. The missing link is usually called supersymmetry (SUSY), certain odd symmetry transformations relating boson and fermions. New dogma. • UV/IR entanglement/link/connection. At energies bigger than Planck energy, it seems physics classicalize. We have black holes with large sizes, and thus energies (in rest) larger than Planck energy. High energy is short distance UV physics. Low energy is large distance IR physics. • Reductionism plus wilsonian effective field theory approaches plus paradigmatic model is false. Fundamental theories or laws of Nature nothing like condensed matter physics (even when condensed matter systems are useful analogues!). Far deeper and more radical ideas are necessary. Only at Planck scale? Photons must stay massless for consistent Quantum Electrodynamics, so they are Higgs transparent. is the Nima statement on this thing. massless helicities are not the same of massive helicities. This fact is essential to gauge fields and chiral fermions. So they can be easily engineered in condensed matter physics. However, Higgs fields are strange to condensed matter systems. Higgs is special because it does NOT naturally arise in superconductor physics and other condensed matter fields. Why the Higgs mass is low compared to the Planck mass? That is the riddle. The enigma. Higgs particles naturally receive quantum corrections to mass from boson and fermion particles. The cosmological constant problem is beyond a Higgs-like explanation because the Higgs field energy is too-large to handle it. Of course, there are some ideas about how to fix it, but they are cumbersome and very complicated. We need to go beyond standard symmetries. And even so, puzzles appear. Flat spacetimes, de Sitter (dS) spacetimes or Anti de Sitter (AdS) spacetimes? They have some amount of extra symmetries: . The cases of (dS), (flat spacetime), (AdS). Recently, we found (not easily) dS vacua in string and superstring theories. But CFT/AdS correspondences are better understood yet. We are missing something huge about QM of the relativistic vacuum in order to understand the macroscopic Universe we observe/live in. Why is the Higgs discovery so important? Our relativistic vacuum is qualitatively different than anything we are seen (dark matter, dark energy,…) in ordinary physics. Not just at Planck scale! Already at GeV and TeV scale we face problems! The Higgs plus nothing else at low energies means that something is wrong or at least not completely correct. The Higgs is the most important character in this dramatic story of dark stuff. We can put it under the most incisive and precise experimental testing! So, we need either better colliders, or better dark matter/dark energy observations. The Higgs is new physics from this viewpoint: 1. We have never seen scalar (fundamental and structureless?) fields before. 2. Harbinger of deep and hidden new principles/sectors at work at the quantum realm. 3. We must study it closely. It could arise that Higgs particles are composite particles. How pointlike are Higgs particles? Higgs particles could be really composite of some superstrong pion-like stuff. But also, they could be truly fundamental. A Higgs factory working at (pole mass) of the Higgs should serve to see if the Higgs is point-like (fundamental). Furthermore, we have never seen self-interacting scalar fields before. A 100 TeV collider or larger could measure Higgs self-coupling up to 5%. The Higgs is similar to gravity there: the Higgs self-interacts much like gravitons! Yang-Mills fields (YM) plus gravity changes helicity of particles AND color. 100 TeV colliders blast interactions and push High Energy Physics. New particles masses up to 10 times the masses accessible to the LHC would ve available. They would probe vacuum fluctuations with 100 times the LHC power. The challenge is hard for experimentalists. Meanwhile, the theorists must go far from known theories and go into theory of the mysterious cosmological constant and the Higgs scalar field. The macrouniverse versus the microuniverse is at hand. On-shell lorentzian couplings rival off-shell euclidean couplings of the Higgs? Standard local QFT in euclidean spacetimes are related to lorentzian fields. UV/IR changes this view! Something must be changed or challenged! ## Toy example Suppose . By analytic continuation, Is Effective Field Theory implying 0 Higgs and that unnatural value? Wrong! Take for instance Then This mechanism for removing bulk signs works in AdS/CFT correspondences and alike theories. For we need something similar to remove singularities and test it! For instance, UV-IR tuning could provide sensitivities to loop processes arising in the EFT of the Higgs potential However, why should we tree cancel the 1-loop correction? It contains UV states and terms. Tree amplitudes are rational amplitudes. Loop amplitudes are trascendental amplitudes! But long known funny things in QFT computations do happen. For instance, Well, this not happens. There is a hidden mechanism here, known from Feynman’s books. Rational approximations to trascendental numbers are aslo known from old mathematics! A High School student knows This is trascendental because of the single pole at . If you take instead you get an apparen tuning of rational to trascendental numbers and thus, e.g., if N=5, you get a tiny difference to by a factor of (the difference up to this precision is ). The same idea works if you take You get for N=1 and if N=2. Thus, we could conjecture a fantasy: there is a dual formulation of standard physics that represents physical amplitudes and observeables in terms of integral over abstract geometries (motives? schemes? a generalized amplituhedron seen in super YM?). In this formulation, the discrepancy between the cosmological constant scale and the Higgs mass is solved and it is obviously small. But it can not be obviously local physics. Another formulation separates different number theoretical parts plus it looks like local physics though! However, it will be fine-tuned like the integrals above! In the end, something could look like Fine-tuning could, thus, be only an apparent artifact of local field theory! A final concrete example: Take . Then, And it guarantees to be fine-tuning! This should have critical tests in a Higgs factory or very large LHC and/or 100TeV colliders of above. In the example above, if with no sixth power or eight power terms. Precision circular electron-positron colliders could handle with this physics. Signals from tunning mechanisms could be searched. It is not just terms only. High dimensional operators and corrections to the Higgs potential (the vacuum structure itself!) could be studied. But also, we could search for new fields or tiny effects we can not do within the LHC. Summary: scientific issues today are deeper than those of 1930s or even 1900s. Questions raised by the accelerated universe and Higgs discovery go at the heart of the Nature of the spacetime and the vacuum structure of our Universe! What about symmetries? In the lagrangian (action) approach, you get a symmetry variation (quasiinvariance) of the lagrangian as follows Then, by the first Noether theorem, imposing that the action is extremal (generally minimal), and the Euler-Lagrange equations (equations of motion), you would get a conserved current (and a charged after integration on the suitable measure): such as where . This theorem can be generealized for higher order lagrangians, in any number of dimension, and even for fractional and differentigral operators. Furthermore, a second Noether theorem handles ambiguities in this theorem, stating that gauge local transformations imply certain relations or identities between the field equations (sometimes referred as Bianchi identities but go further these classical identities). You can go further with differential forms, exterior calculus or even with Clifford geometric calculus. A p-form defines p-dimensional objects that can be naturally integrated out. For a p-tube in D-dimensions On p-forms, the Hodge star operator for a p-form in D-dimensions turn it into a -form As , then we have , where if the metric is Lorentzian, for euclidean metrics and , the number of time-like dimensions, if the metric is ultrahyperbolic. Moreover, For maps, you can also write where the latter is generally valid up to a sign. The Hodge laplacian reads and you also gets If is not zero (the boundary is not null), then it implies essentially Dirichlet or Neumann boundary conditions for . When you apply the adjoint operator on p-forms you get in general but you pick up an extra sign in euclidean signatures. To end this eclectic post, first a new twist on Weak Gravity Conjectures(WGC). Why the electron charge is so small in certain units? That is, . Take Coulomb and Newton laws Then, Planck mass is and then Planckian entities satisfy instead ! then, the enigma is why In other words, in relativistic natural units with with . The WGC states that the lightest charge particle with in ANY U(1) (abelian gauge) theory admits UV embedding into a consistent quantum gravity theory only and only if where is the gauge coupling and QED satisfies WGC since . WGC ensures that extremal black holes are unstable and decay into non-extremal black holes rapidly (if even formed!) via processes (and avoid to be extremal too) that are QG consistent. Furhtermore, WGC could imply the 3rd thermodynamical law easily. For Reissner-Nordström black holes and a grey body correction to black hole arises from this too Generalised Uncertainty principles (GUP) plus Chandrasekhar limits enjoy similarities with the WGC: The S-matrix and by time reversal, the principle of deteailed balance holds so Quantum determinism implies via unitarity . However, Nature could surprise us. And that would affect Chandrasekhar masses or TOV limits. Stellar evolucion implies luminosities , where is the effective temperature for black bodies (Planck law), and is the Stefan-Boltzmann constant Maximal energy for a set of baryons under gravity is as the baryon number for a star is Using the Wien law the stars locally have an equation for baryon density about Stars are sustained by gas and radiation against gravitational collapse. The star pressure Thus, the maximal mass for a white dwarf star made by barions is about . Ideal gas law implies the HR diagram!!!! Luminosity scales as the cube of mass. The Eddington limit maximal luminosity for any star reads off as and a Buchdahl limit arises from this and the TOV limit as follows and then implies a BH as inevitable consequence iff approximately! Epilogue: heterodynes or superheterodynes? Jansky? dB scales? Photoelectric effect is compatible with multiphoton processes and special relativity too. SR has formulae for Compton effect, inverse Compton effect, pair creations, pair annihilations, and strong field effects! 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https://www.physicsforums.com/threads/momentum-word-problem.126316/	# Momentum Word Problem. 1. Jul 16, 2006 ### JassC Two carts with masses of 4.3 kg and 3.2 kg move toward each other on a frictionless track with speeds of 5.8 m/s and 4.5 m/s, respec- tively. The carts stick together after colliding Find their final speed. Answer in units of m/s. I plugged in the numbers into this equation (4.3)(5.8) + (3.2)(4.5) = (4.3+3.2)Vf 39.34 = 7.5Vf 5.2453 = Vf That apparently isn't the correct answer =/ Last edited by a moderator: Apr 22, 2017 2. Jul 16, 2006 ### d_leet Remember that momentum is a vector it has magnitude and direction, so you need to take this into account when you work the problem. Notice that the problem says the two carts ae heading towards each other, so they have to be moving in different directions, so take velocity in one direction as positive and the other as negative and you should be able to get the correct answer. 3. Jul 16, 2006 ### JassC Okay cool, I got it . Thanks! 4. Jul 16, 2006 ### d_leet No problem, glad I could help. 5. Jul 16, 2006 ### JassC I don't want to make a new thread so I'll ask this one. A 37.9 kg girl is standing on a 98 kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless sup- porting surface. The girl begins to walk along the plank at a constant speed of 1.54 m/s to the right relative to the plank. What is her velocity relative to the ice sur- face? Answer in units of m/s. Am I using conservation of momentum or force here? I don't know where to start. 6. Jul 16, 2006 ### d_leet Conservation of momentum, I'm pretty sure there is no such thing as conservation of force. Since she and the plank are initially at rest there is no initial momentum, so when she starts moving the plank must move in the other direction in order for momentum to be conserved. 7. Jul 16, 2006 ### JassC I meant using conservation of momentum or just "FORCE"... 8. Jul 17, 2006 ### arunbg Yes, use coservstion of momentum . Why did the doubt arise ? 9. Nov 27, 2006 ### br0wneyes786 Momentum Hey i need help i have a web assignment due soon and i could really use some guidence. A 10 metric ton train moves toward the south at 70 m/s. At what speed must it travel to have four times its original momentum? Answer in units of m/s. 10. Nov 27, 2006 ### EthanB What do you think? What have you tried? You know the equation that describes its current momentum. If you want it to be four times greater, what do you do to it? 11. Nov 27, 2006	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8649923205375671, "perplexity": 1328.325118625049}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647901.79/warc/CC-MAIN-20180322170754-20180322190754-00127.warc.gz"}
https://mathinsight.org/double_integral_change_variables_introduction	# Math Insight ### Introduction to changing variables in double integrals Imagine that you had to compute the double integral \begin{align} \iint_{\dlr} g(x,y) dA \label{integralrect} \end{align} where $g(x,y)=x^2+y^2$ and $\dlr$ is the disk of radius 6 centered at the origin. In terms of the standard rectangular (or Cartesian) coordinates $x$ and $y$, the disk is given by \begin{gather} -6 \le x \le 6\\ -\sqrt{36-x^2} \le y \le \sqrt{36-x^2}. \end{gather} We could start to calculate the integral in terms of $x$ and $y$ as \begin{align} \iint_{\dlr} g(x,y) dA = \int_{-6}^6 \int_{-\sqrt{36-x^2}}^{\sqrt{36-x^2}} (x^2+y^2) \, dy \, dx\ = \text{a mess}. \end{align} It turns out that this integral would be a lot easier if we could change variables to polar coordinates. In polar coordinates, the disk is the region we'll call $\dlr^$ defined by $0 \le r \le 6$ and $0 \le \theta \le 2\pi$. Hence the region of integration is simpler to describe using polar coordinates. Moreover, the integrand $x^2+y^2$ is simple in polar coordinates because $x^2+y^2 = r^2$. Using polar coordinates, our lives will be a lot easier because it seems that all we need to do is integrate $r^2$ over the region $\dlr^$ defined by $0 \le r \le 6$ and $0 \le \theta \le 2\pi$. Unfortunately, it's not quite that easy. We need to account for one more consequence of changing variables, which is how changing variables changes area. You may recall that $dA$ stands for the area of a little bit of the region $\dlr$. In rectangular coordinates, we replaced $dA$ by $dx\,dy$ (or $dy\,dx$). We need to determine what $dA$ becomes when we change variables. As you will see, in polar coordinates, $dA$ does not becomes $dr \, d\theta$. The relationship between rectangular $(x,y)$ and polar $(r,\theta)$ coordinates is given by $x=r\cos \theta$, $y=r\sin\theta$. To see how area gets changed, let's write the change of variables as the function \begin{align} (x,y)=\cvarf(r,\theta) = (r \cos\theta, r \sin \theta). \label{polartrans} \end{align} The function $\cvarf(r,\theta)$ gives rectangular coordinates in terms of polar coordinates. The transformation $\cvarf$ gives the perspective of polar coordinates as a mapping from the polar plane to the Cartesian plane. The below applet shows how $\cvarf$ maps a rectangle $\dlr^$ in the polar plane into the region $\dlr$ in the Cartesian plane. To make $\dlr^$ and $\dlr$ correspond to the rectangle and disk of our example, you can expland the rectangle $\dlr^$ to its maximum size. Polar coordinates map of rectangle. The transformation from polar coordinates to Cartesian coordinates $(x,y)=\cvarf(r,\theta) = (r \cos\theta, r \sin \theta)$ can be viewed as a map from the polar coordinate $(r,\theta)$ plane (left panel) to the Cartesian coordinate $(x,y)$ plane (right panel). This transformation maps a rectangle $\dlr^$ in the $(r,\theta)$ plane into a region $\dlr$ in the $(x,y)$ plane that is the part of an angular sector inside an annulus. You can change the regions $\dlr^$ and $\dlr$ by dragging the purple or cyan points in either panel. To further visualize the action of the map $(x,y)=\cvarf(r,\theta)$, you can drag the labeled red and blue points anywhere inside the large rectangle $0 \le r \le 6$, $0 \le \theta <2\pi$ and corresponding disk $x^2+y^2 \le 6^2$. Do you understand why the disk looks like a rectangle in polar coordinates (i.e., why the region $\dlr^$ on the left that maps onto the disk is a rectangle)? Remember, the disk is described by $0 \le r \le 6$ and $0 \le \theta \le 2\pi$, which is a rectangle when plotted in the $r\theta$-plane. We can say that $\cvarf(r,\theta)$ parametrizes $\dlr$ for $(r,\theta)$ in $\dlr^$. This uses the same language that we used when parametrizing a curve. We'll use it again when we talk about parametrizing surfaces. To look at how $\cvarf(r,\theta)$ changes area, we can chop up the region $\dlr^$ into small rectangles of width $\Delta r$ and height $\Delta \theta$. The function $\cvarf(r,\theta)$ maps each of these small rectangles into a “curvy rectangle” in $\dlr$, as shown below. (As above, you need to expand the rectangle $\dlr^$ in the left panel to its maximum size to make the $\dlr^$ and $\dlr$ of the applet correspond to the rectangle and disk of our example.) Area transformation of polar coordinates map. The transformation from polar coordinates to Cartesian coordinates $(x,y)=\cvarf(r,\theta) = (r \cos\theta, r \sin \theta)$ maps a rectangle $\dlr^$ in the $(r,\theta)$ plane (left panel) to the region $\dlr$ in the $(x,y)$ plane (right panel). It also maps each small rectangle in $\dlr^$ to a “curvy rectangle” in $\dlr$. Although the small rectangles in $\dlr^$ are the same size, the corresponding “curvy rectangles” vary greatly in size. Depending on the coordinates $(r,\theta)$, the map $\cvarf(r,\theta)$ shrinks or expands the area by different amounts. You can visualize the mapping of the small rectangles by dragging the yellow point in either panel; the corresponding small rectangle in $\dlr^$ and its image in $\dlr$ are highlighted. You can also change the regions $\dlr^$ and $\dlr$ by dragging the purple and cyan points in either panel. The area of each small rectangle in $\dlr^$ is $\Delta r \Delta \theta$. But we don't care about area in $\dlr^$. The $dA$ in the integral of equation \eqref{integralrect} is based on area in $\dlr$ not area in $\dlr^$. So we need to estimate the area of each “curvy rectangle” in $\dlr$, which we'll denote by $\Delta A$. We can calculate the area of the “curvy rectangle” by approximating it as a parallelogram with sides $\pdiff{\cvarf}{r} \Delta r$ and $\pdiff{\cvarf}{\theta}\Delta\theta$. The area of a parallelogram is the magnitude of the cross product $\left\\| \pdiff{\cvarf}{r} \times \pdiff{\cvarf}{\theta}\right\\| \Delta r\Delta\theta$ of the two vectors spanning the parallelogram. Plus, since we are in two-dimensions, we write the area more simply by a $2\times 2$ determinant. After some simplification, the area of the “curvy rectangle” reduces to the expression \begin{align} \Delta A \approx \| \det \jacm{\cvarf}(r,\theta)\|\Delta r\Delta\theta, \end{align} where $\jacm{\cvarf}$ is derivative matrix of the map $\cvarf$. Just as the derivative matrix $\jacm{\cvarf}$ is sometimes called the “Jacobian matrix,” its determinant $\det \jacm{\cvarf}$ is sometimes called the “Jacobian determinant.” Note that the $D$ in $\jacm{\cvarf}(r,\theta)$ is not the same $D$ as the region $\dlr$ of integration. Because we need to take the absolute value of the determinant, we typically use the notation “det” to denote determinant to avoid confusion (see discussion at end of the page on matrices and determinants). For $\cvarf$ given by equation \eqref{polartrans}, you can calculate that $\| \det \jacm{\cvarf}(r,\theta)\| = r$ so that the area of each “curvy rectangle” is $r \Delta r \Delta \theta$. This agrees with the above picture, since the “curvy rectangles” were larger when $r$ was larger. The important point is that $\cvarf$ stretches or shrinks $\dlr^$ when it maps $\dlr^$ onto $\dlr$. Consequently, when we convert from area in $\dlr^$ to area in $\dlr$, we need to multiply by the area expansion factor $\| \det \jacm{\cvarf}(r,\theta)\|$. The area expansion factor captures how the “curvy rectangles” change size as you move the point around in the above applet. We now put everything back together. We started off trying to integrate the function $g(x,y)=x^2+y^2$ over the region $\dlr$. If we use $(x,y) = \cvarf(r,\theta)$ to change variables, we can instead integrate the function $g(\cvarf(r,\theta))=r^2$ over the region $\dlr^$. However, we need to include the area expansion factor $\| \det \jacm{\cvarf}(r,\theta)\| = r$ in $dA$ to account for the stretching by $\cvarf$. We can replace $dA$ with $r\,dr\,d\theta$. We end up with the formula \begin{align} \iint_\dlr g(x,y) dA = \iint_{\dlr^} g(\cvarf(r,\theta))\| \det \jacm{\cvarf}(r,\theta)\| dr\, d\theta, \end{align} which for our example is \begin{align} \iint_\dlr (x^2+y^2) dA = \int_0^{2\pi}\int_0^6 r^2 r\,dr\,d\theta = \int_0^{2\pi}\int_0^6 r^3 \,dr\,d\theta. \end{align} You can compute that this integral is $6^4\pi/2$ much easier using this form than you could using the original integral of equation \eqref{integralrect}. For a general change of variables, we tend to use the variables $\cvarfv$ and $\cvarsv$ (rather than $r$ and $\theta$). In this case, if we change variables by $(x,y) = \cvarf(\cvarfv,\cvarsv)$, our integral is \begin{align} \iint_\dlr g(x,y) dA = \iint_{\dlr^{\textstyle }} g(\cvarf(\cvarfv,\cvarsv)) \| \det \jacm{\cvarf}(\cvarfv,\cvarsv)\| d\cvarfv\,d\cvarsv, \label{cvarformula}\tag{3} \end{align} where $\dlr$ is a region in the $xy$-plane that is parametrized by $(x,y)= \cvarf(\cvarfv,\cvarsv)$ for $(\cvarfv,\cvarsv)$ in the region $\dlr^$. Sometimes, we may write the determinant of the derivative matrix as $$\det \jacm{\cvarf}(\cvarfv,\cvarsv)=\pdiff{(x,y)}{(\cvarfv,\cvarsv)}$$ so that the area expansion factor is $$\| \det \jacm{\cvarf}(\cvarfv,\cvarsv)\|= \left\|\pdiff{(x,y)}{(\cvarfv,\cvarsv)}\right\|.$$ It's just different notation for the same object, but represents that we are taking the derivative of the $(x,y)$ variables with respect to the $(\cvarfv,\cvarsv)$ variables. With this notation, the change of variable formula looks like \begin{align} \iint_\dlr g(x,y) dA = \iint_{\dlr^{\textstyle }} g(\cvarf(\cvarfv,\cvarsv)) \left\|\pdiff{(x,y)}{(\cvarfv,\cvarsv)}\right\| d\cvarfv\,d\cvarsv. \end{align} We've obviously skipped quite a few details on this introductory page in an effort to just give the big picture. In particular, we've glossed over how we obtained the expression for the area expansion factor. You can read how we obtain that formula. You can study some examples of changing variables, including more details on the disk example. To gain more intuition on how changing variables transform regions, you can read an illustrated example of a particular change of variable function. #### Stretching by maps The area expansion factor for changing variables in double integrals is an example of accounting for the stretching of a map, in this case, the function $\cvarf$. We encounter such factors frequently in multivariable and vector calculus. The simplest example of such an expansion factor is the $\\|\dllp'(t)\\|$ we obtain when calculating the arc length or a line integral over a curve parametrized by $\dllp: \R \to \R^2$ (confused?). We could call this a length expansion factor. Just like for the $\cvarf: \R^2 \to \R^2$ of changing variables, the expansion factor for parametrized curves involves the magnitude of some expression involving the derivative matrix of the map. For the map $\cvarf: \R^3 \to \R^3$ used to change variables in triple integrals, the volume expansion factor $\|\det \jacm{\cvarf}(\cvarfv,\cvarsv,\cvartv)\|$ is essentially the same as for double integrals. Lastly, imagine you took the blue disk $\dlr$ in the above applet and lifted it out of the plane so that it was a surface floating in three-dimensional space. Then, our mapping $\cvarf$ becomes the function $\dlsp: \R^2 \to \R^3$ that parametrizes a surface. We can repeat the calculation for the area expansion factor virtually without change to obtain the area expansion factor for surface area or surface integrals. The only difference that results from being in three dimensions is that you cannot change the cross product for the parallelogram area to a $2 \times 2$ determinant. Hence, the area expansion factor for parametrized surfaces is the cross-product $\left\\| \pdiff{\dlsp}{\spfv} \times \pdiff{\dlsp}{\spsv} \right\\|$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 3, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9781708717346191, "perplexity": 236.99877746726864}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662517245.1/warc/CC-MAIN-20220517095022-20220517125022-00307.warc.gz"}
http://perfdynamics.blogspot.com/2009/04/modern-microprocessor-mips.html	## Thursday, April 2, 2009 ### Modern Microprocessor MIPS The question of how modern microprocessors compare with mainframe processors of yore, arises from time to time. The vernacular rate metric that has persisted for a long time (long in the history of computers, that is) is MIPS. Whether you approve of MIPS as a valid performance metric or not is a different (philosophical) question. Since the mainframe has not gone away---it's just another server on the network today---even mainframers still talk about MIPS ratings. Nonetheless, it is true that the meaning of "instructions" does vary significantly across architectures so, one does have to exercise caution when making inter-architectural comparisons and not endow any conclusions with more credibility than they deserve. With that caveat in mind, estimating MIPS ratings can be very useful in certain circumstances. One such circumstance arose recently for a colleague at HP Labs, where they were trying to ascertain "ballpark" MIPS for a processor being used in one of their projects. To avoid divulging any proprietary information, let's suppose that the modern microprocessor of interest was a 3.0 GHz Xeon Dual Core, such as can be found in an HP ProLiant ML350 server. Their original estimate was 20,000 MIPS. You can find support for this kind of estimate on the web (see e.g., this wiki table). But is it believable? Fortunately, my colleague asked me to sanity check their estimate. The key to resolving this question is to find a bridge (or bridges) between IBM mainframe MIPS and the throughput metrics used for modern microprocessors. In Chap. 7 of The Practical Performance Analyst, I describe how I sized an Amdahl 5995-1400 series mainframe against a Unix SMP box with up to 24-way MIPS (the company) R3000 microprocessors. To do this, I found a TPS bridge between IBM's LSPR MIPS ratings and throughput measurements from an TP1 database benchmark running ORACLE. Luckily, I was able do this because the Amdahl mainframe also ran a version of Unix (UTS) and therefore it could also run Oracle's RDBMS. This meant the workloads were the same, to first order. The conclusion there, as I remember it, was something like the R3000 was equivalent to only one-third of an IBM MIP for TP1 database transactions. The reason for that stems from mainframes having separate (channel) processors to handle physical I/O to DASD disks, whereas a Unix SMP is limited to the same processors for executing both user transactions and the device-driver I/Os (kernel code). Things are less ambiguous if the workload is compute-intensive. The one clear accomplishment of the SPEC benchmark organization is, they have redefined nominal "MIPS" for modern microprocessors (whether or not that was their intention). The relevant industry-standard microprocessor benchmarks are the SPEC CINT (integer-only CPU workloads) and SPEC CFP (floating-point CPU workloads). The current benchmark release is collectively known as SPEC CPU2006. The unfortunate downside is, that up until their 2006 release, it was possible to compare IBM MIPS, Vax VUPs and SPEC CINTs, because they were very similar, to first order. For example, MIPS Corporation rated the R3000 @ 40 MHz = 32 VUPS. The SPEC CINT1992 rating was about 27; very close to the VUPS value. Amdahl Corporation rated the 5995-1400 @ 100 MHz = 120 IBM MIPS. But the Amdahl mainframe was a 4-way SMP. Therefore, each CPU-engine was approximately 30 IBM MIPS and that matches the VUPS rating numerically for cpu-bound workloads. A simple check we can do at this point is simply to wind up the clock (theoretically) to estimate the SPEC rating for the R3000 RISC processor @ 3 GHz; the same clock frequency as the Intel Dual Core processor. Doing this in R, we find: > r<-uniroot(function(x) (40/3000)-(32/x),c(0,5000))> r\$root[1] 2400 which suggests that the SPEC rating corresponds to something on the order of 2,000 MIPS; not 20,000 MIPS. Without getting too sidetracked by all these details, here is a table of SPEC CPU2000 (the previous benchmark release) with CINT metrics for some Intel single and dual core microprocessors: If we take it as read that the CINT numbers are close to older MIPS ratings, we get a picture that looks like this: In summary, we can conclude: • The original guess of 20,000 MIPS appears to be off by an order of magnitude. • Mainframe and CISC processors take fewer instructions to do the same work as a RISC processor. • If the workload is entirely compute-bound, we may assume IBM MIPS ~ Vax VUPS ~ SPEC CINT2000, to first order. • If the workload involves physical I/O, then MIPS estimates should be reduced by factor of 1/2 to 1/3. • A 3 GHz core can be safely assumed to be equivalent to 1000-1500 MIPS. • Therefore, a 3 GHz dual-core should be roughly equivalent to 2000-3000 MIPS. What are the important lessons one can take away from this exercise? • MIPS, shmips! It doesn't really matter what you call it. It's vernacular for processor throughput performance. It's not going away, so learn to deal with it. • Trying to come up with some estimate (even if it turns out to be wrong) is better than not having any clue at all. • Without an estimate, how are you going to know if you are wrong? • Numbers are not the only way, or even the best way, to make estimates. It is often more insightful to use a combination of numerical and graphical techniques.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5567540526390076, "perplexity": 3453.2383365723917}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221216475.75/warc/CC-MAIN-20180820140847-20180820160847-00238.warc.gz"}
http://lyrics.wikia.com/wiki/Britney_Spears:Where_Are_You_Now	# Britney Spears:Where Are You Now Lyrics 1,892,996pages on this wiki Where Are You Now This song is by Britney Spears and appears on the album Oops!...I Did It Again (2000). I'm reaching out to you To find that you're not there I wake up every night To see the state I'm in It's like an endless fight I never seem to win I can't go on as long as I believe Can't let go when I keep wondering :Chorus: Where are you now, what have you found Where is your heart, when I'm not around Where are you now, you gotta let me know Oh baby, so I can let you go The ring of yesterday It seems so close to me But yet so far away I should let it out To save what's left of me And close the doors of doubt Revive my dignity But, I can't go on as long as I believe Can't let go when I keep wondering(oh yeah) :Chorus: Where are you now, what have you found Where is your heart, when I'm not around Where are you now, you gotta let me know Oh baby, so I can let you go I should let it out, it's time to let you go Oh baby, I just want to know :Chorus: Where are you now, what have you found Where is your heart, when I'm not around Where are you now, you gotta let me know Oh baby, so I can let you go (repeat)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9833145141601562, "perplexity": 6864.4861179463405}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218188924.7/warc/CC-MAIN-20170322212948-00575-ip-10-233-31-227.ec2.internal.warc.gz"}
http://mathoverflow.net/questions/68888/is-a-compact-connected-orientable-3-manifold-with-mathbbzk-fundemental-g?sort=newest	# Is a compact, connected, orientable 3-manifold with $\mathbb{Z}^K$ fundemental group uniquely determined? According to the Kneser-Milnor prime decomposition theorem for 3-manifolds, any compact, connected, orientable 3-manifold $M$ is diffeomorphic to $S^3 / \Gamma_1$ # $\cdots$ # $S^3/ \Gamma_n$ # $(S^2 \times S^1)_1$ # $\cdots$ # $(S^2 \times S^1)_r$ # $K( \pi_1,1)$ # $\cdots$ # $K( \pi_m,1)$, where # is the connect sum, and $\Gamma_i$ is a non-trivial finite subgroup of $SO(4)$ acting orthogonally to $S^3$ (so that the result is a spherical space form). I suppose my question boils down to if $\pi_1(M)=\mathbb{Z} \times \cdots \times \mathbb{Z}$, k times, does that uniquely identify a manifold as a $(S^2 \times S^1)_1$ # $\cdots$ # $(S^2 \times S^1)_k$, or can the various quotient manifolds or aspherical factors create a more complicated topology without changing the fundamental group? - "non-finite trivial"?? Did you mean "non-trivial finite"? – André Henriques Jun 26 '11 at 23:43 When you say $\pi_1(M) = \mathbb{Z}^k$, do you mean the free product of $k$ copies of $\mathbb{Z}$? – Marco Golla Jun 26 '11 at 23:45 I'm guessing he doesn't, and is simply making a mistake: the fundamental group of $(S^2 \times S^1)_1$ # $\cdots$ # $(S^2 \times S^1)_k$ is a free group on $k$ generators (van Kampen's theorem). – André Henriques Jun 26 '11 at 23:48 @André Henriques, Thanks, I mean non-trivial finite. – Benjamin Horowitz Jun 27 '11 at 0:48 add comment ## 3 Answers NO, since the three-torus $T^3$ does not have this form. EDIT if the OP really means a free product of $\mathbb{Z}$s, so the free group $F_k,$ then the answer is YES. It is a fact (see Hempel's book, chapter 7) that every splitting of the fundamental group of $M^3$ as a free product comes from a connected sum decomposition. On the other hand, a prime three manifold is either a $K(\pi, 1)$ or $S^2 \times S^1.$ In the former case, its fundamental group cannot be $\mathbb{Z}$ - Everything you say here is correct, but of course its correctness relies on the Poincare conjecture! – Dave Futer Jun 27 '11 at 13:26 @Dave: among many other theorems... – Igor Rivin Jun 27 '11 at 14:00 ... and for orientable 3-manifolds (otherwise you have $S^1\tilde{\times}S^2$). But of course, orientability is assumed in the question. – Ian Agol Jun 27 '11 at 15:25 add comment Let me address a more general question: To what extent is a closed, connected $M^3$ determined by its fundamental group? Following the Geometrization Theorem, we have a complete answer. There are only two ways in which a closed $3$--manifold $M$ can fail to be determined by its fundamental group: 1. $M$ is a lens space, or a connected sum of something with a lens space. It is well-known that lens spaces are not determined up to homeomorphism by their fundamental groups. Note that in this case, you would see a ${Z}/p$ free factor in your group $G$, so it can't arise in the context of your question. 2. $M = N_1 \sharp N_2$, where each $N_i$ is orientable, and each is chiral (fails to have an orientation-reversing symmetry). In this case, reversing the orientation on one factor would produce $M' = N_1 \sharp \overline{N_2}$, which is not homeomorphic to $M$ but has the same fundamental group. This also cannot arise in your context, for exactly the reasons that Igor outlined, and because $S^1 \times S^2$ does have an orientation-reversing symmetry. Finally, let me point out that although Geometrization may seem like an overly big hammer for this question, in fact one needs the Poincare conjecture. For, if there existed a fake $3$--sphere, one could take the connect sum with that manifold without altering the group. - add comment If you did in fact mean the free abelian group, you can still do it (up to punctures). All references in brackets are to Hempel. If $\pi_1(M)\cong \mathbb{Z}$, then $M$ is one of $S^2\times S^1$, $S^2\tilde{\times} S^1$, the solid torus, or the solid Klein bottle. [5.3] If $\pi_1(M)\cong \mathbb{Z}^2$, then $M$ is an I-bundle over the torus. [10.6] If $\pi_1(M)\cong \mathbb{Z}^3$, then $M$ is the 3-torus. [11.11] The case $k>3$ doesn't happen. [9.13] - add comment	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9366738796234131, "perplexity": 350.1413671298808}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999642518/warc/CC-MAIN-20140305060722-00086-ip-10-183-142-35.ec2.internal.warc.gz"}
http://mathhelpforum.com/advanced-algebra/172631-determining-set-vector-space.html	# Math Help - Determining a set is a vector space 1. ## Determining a set is a vector space Hey everyone, I'm a little confused. I am confused on how to determine if a set is a vector space. I've look at some examples and I am still a bit confused. How do you go about determining if a set is vector space? Here is a problem I am confused about: The set of all pairs of real numbers of the form (x,0) with the standard operations on R^2 Any help is appreciated. Thanks 2. The set, together with the scalar multiplication and vector addition operations, has to satisfy the axioms of a vector space. Now, in your case, you know already (I assume?) that R^2 is a vector space with "the standard operations". When, therefore, you're trying to determine if a set is a vector subspace, your job is a little easier. All you have to do is determine three things: 1. The set is nonempty. 2. The set is closed under scalar multiplication. 3. The set is closed under vector addition. If those three conditions are satisfied, you've got yourself a subspace. Do those three conditions hold for your set? 3. What is meant when it is "closed" by addition and multiplication? Thanks 4. Ok, let's get into the notation. Let $V$ be a vector space over the scalar field $F.$ (You could think of $\mathbb{R}^{2}$ as the vector space, over the field of real numbers $\mathbb{R}$.) The word "closed", in this context, means the following: Scalar multiplication: for any vector $\mathbf{v}\in V$ and scalar $f\in F,$ it follows that $f\mathbf{v}\in V.$ That is, multiplying a vector in $V$ by a scalar in $F$ keeps you inside the vector space $V.$ Vector addition: for any two vectors $\mathbf{u},\mathbf{v}\in V,$ it follows that $\mathbf{u}+\mathbf{v}\in V.$ Again, the addition of two vectors in $V$ is still inside $V.$ That's what closure means. Does that make sense? Here's an example. Let $V=\{\mathbf{v}\in\mathbb{R}^{2}\|v_{1}+v_{2}=0\}.$ Take the reals as the field. We check if it's closed under the two operations. Let $r\in\mathbb{R},$ and let $\mathbf{v}\in V$ be given by $\mathbf{v}=\langle v_{1},v_{2}\rangle.$ By assumption, we have that $v_{1}+v_{2}=0.$ Then $r\mathbf{v}=\langle r v_{1},r v_{2}\rangle.$ Does the property still hold? We check to see if $rv_{1}+rv_{2}=0,$ or $r(v_{1}+v_{2})=0,$ which we can see is true, since $v_{1}+v_{2}=0.$ Thus, we can see that we're closed under scalar multiplication, since the scalar and vector I chose was completely arbitrary. The vector addition case will be very similar. Finally, you note that the zero vector is, indeed, in our space, and hence the set is nonempty. Make sense? 5. I think I understand what you are explaining. If you add two vectors or multiply by a scalar the new vector is still in the space? 6. Right. If that condition holds for all vectors and scalars, you've got yourself a vector subspace. Now, I should point out that if you're trying to see if a given set is a vector space, and it's not a subset of a known vector space, then you've got to verify every single one of the axioms to which I linked in post # 2. Only then, a full vector space, will you have. 7. So with the problem I posted: The set of all pairs of real numbers of the form (x,0) with the standard operations on R^2 So (x,0) considered "u" 8. I understand your example, but how do I see if (x,0) is a vector space of R^2 if there is no condition like in your example such as v1+v2=0. Thanks 9. If there's no "condition", your job is actually easier. 1. Is the zero vector in your set? (Really just need nonempty, but the zero vector is often the easiest to check). 2. Closed under scalar multiplication? 10. So would this set no be a vector space because of the axiom (c+k)u = cu + ku (cx + kx, 0) is not equal to (cx + kx)? 11. No, no, no. Just check what I mentioned in post # 9. Is the zero vector in your set? 12. So 0 + (x,0) = (x,0)? I think I am making this harder than it really is. Thanks 13. Is the vector $\mathbf{0}=\langle 0,0\rangle$ in your set? That is, does $\langle 0,0\rangle$ look like a vector of the form $\langle x,0\rangle,$ for some $x?$ 14. If x is 0 then if would be (0,0) 15. Right. So that tells you that the zero vector is in the set, and hence the set is nonempty. Next question: If you take an arbitrary scalar $r\in\mathbb{R},$ and multiply it times an arbitrary vector $\mathbf{x}=\langle x,0\rangle$ in your set, is the result still in your set? Page 1 of 2 12 Last	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 29, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9403197169303894, "perplexity": 218.98421122901635}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500959239.73/warc/CC-MAIN-20140820021559-00151-ip-10-180-136-8.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/cylinder-rolling-down-an-inclined-plane.426962/	# Cylinder rolling down an inclined plane 1. Sep 6, 2010 ### PhMichael 1. The problem statement, all variables and given/known data So I have this standard problem of a cylinder rolling down an inclined plane, however, this time the plane itself is free to slide on the ground. I need to find the acceleration of that cylinder relative to the plane. 2. The attempt at a solution V / A - the velocity / acceleration of the plane relative to the ground. v / a - the velocity / acceleration of the cylinder relative to the plane. The velocity of the cylinder relative to the ground is: $$\vec{u}=\vec{v}+\vec{V}=(vcos \beta -V) \hat{x} - (vsin \beta) \hat{y}$$ Momentum is conserved conserved in the $$\hat{x}$$ direction so that: $$0=-MV+m(v cos \beta -V) \to V=\frac{m}{M+m} v cos \beta$$ so the acceleration of the plane relative to the ground is: $$A=\frac{dV}{dt}=\frac{m}{m+M}a cos \beta$$ $$\vec{\tau}_{P}=mR(g sin \beta + A cos \beta) \hat{z}$$ $$I_{P}\vec{\alpha}=(0.5MR^{2}+MR^{2})\vec{\alpha}=1.5MR^{2} \frac{a}{R}\hat{z}$$ Equating the last two equations while using the equation of A yields: $$a=gsin\beta\left [ \frac{3}{2}-\left ( \frac{m}{m+M} \right )cos^{2}\beta \right ]$$ This answer is correct, however, I'm not sure whether what I did is kosher; to be more specific, is linear momentum conserved along the $$\hat{x}$$ direction? are fictitious forces, like the one we have here on the cylinder as a result of the plane's acceleration, not treated as real forces so that eventhough they exist, we may still use the conservation of momentum principle? 2. Sep 7, 2010 ### hikaru1221 It depends on the reference frame and the system you consider. Whenever there is no external force, the linear momentum is conserved. Remember how to derive the law from F=dp/dt? In the frame of the ground, if you consider the system of the wedge & the cylinder, the momentum of the system is conserved. With the same system, but in the frame of the wedge, there is fictitious force, i.e. F = dp/dt is not zero, the momentum is not conserved. 3. Sep 7, 2010 ### Mindscrape Looks good to me! Now if you truly wanted to make this problem difficult you could add in friction, inertia effects, and some good old lagrange multipliers. :p Also, if you know of Lagrangian dynamics then it could be fun to solve the problem in an alternate way, which I might do just for fun.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9298176169395447, "perplexity": 285.8284528162219}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257822172.7/warc/CC-MAIN-20160723071022-00029-ip-10-185-27-174.ec2.internal.warc.gz"}
https://www.maxmarks.in/questions/8402467980/the-following-state-of-strain-exists-at-a-point-p	# The following state of strain exists at a point P Determine the principal strains and the directions of the maximum and minimum principal strains.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9329219460487366, "perplexity": 813.434348543174}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146562.94/warc/CC-MAIN-20200226211749-20200227001749-00010.warc.gz"}
https://www.scienceforums.net/topic/118661-gravity-is-limited-to-a-range-extendable-with-the-speed-of-light-c/page/2/	# Gravity is limited to a range extendable with the speed of light c ## Recommended Posts 57 minutes ago, awaterpon said: It should be for both coulomb's law and magnetism. For a wire when the circuit is closed the magnetic field starts to spread with the speed of light an experiment could be performed to determine whether magnetic field is already available at a point or it will reach that point after a time"it is not logical that the magnetic field already at infinity since we had a current started to flow at specific moment and shouldn't be available before that moment ,so how it would be available everywhere at an instant?" The delay from the speed of light is already part of the physics. • Replies 134 • Created #### Popular Posts This one? http://www.tapir.caltech.edu/~teviet/Waves/empulse.html Good point. Probably the mixing of static and dynamic situations* for both gravity and electromagnetism is the main reason behind the proposals made by OP. I asked you to analyse your prop There is no “moment of mass existence” Energy is conserved, so mass does not just pop into being. However, in a very basic sense, gravity behaves as you describe, despite your dubious mathematic #### Posted Images 15 minutes ago, awaterpon said: That mass existed from nothing and started to curve space-time from zero range to its today ranges for each mass. That what I meant by: "The existence of mass causes none-existence in space-time cause space-time to displace and bend" I didn't ask you about "The existence of mass causes none-existence in space-time cause space-time to displace and bend" I asked you about "the mass existence is philosophical". Quote "The existence of mass causes none-existence in space-time cause space-time to displace and bend" That makes no sense. How can the existence of mass cause non-existence? How can non-existence cause space-time to bend? On 4/7/2019 at 6:36 PM, awaterpon said: It is somehow to calculate the range of zero length at some begining There is no evidence for any such beginning. Mass isn't just "created". Mass and energy are conserved. ##### Share on other sites 8 minutes ago, swansont said: The delay from the speed of light is already part of the physics. But there is not an idea of magnetism spreading out? The delay in fact is due to to spreading of magnetic field with speed of light c. ##### Share on other sites 2 minutes ago, awaterpon said: But there is not an idea of magnetism spreading out? The delay in fact is due to to spreading of magnetic field with speed of light c. Yes, that is what he said. You seem to think you have found something new. But we know changes in gravity, and changes in electromagnetic fields, propagate at the speed of light. So I don't know what your point is. ##### Share on other sites 4 minutes ago, Strange said: How can non-existence cause space-time to bend? By displacing space-time. Think of blowing a balloon inside water container it would displace water and makes water have the same shape of the balloon "bend". ##### Share on other sites 5 minutes ago, awaterpon said: By displacing space-time. Think of blowing a balloon inside water container it would displace water and makes water have the same shape of the balloon "bend". That is the existence of the balloon displacing water. Not "non-existence". This also has nothing to do with mass, gravity, or the limited range of gravity. ##### Share on other sites 1 hour ago, awaterpon said: But there is not an idea of magnetism spreading out? The delay in fact is due to to spreading of magnetic field with speed of light c. 1 hour ago, awaterpon said: By displacing space-time. Think of blowing a balloon inside water container it would displace water and makes water have the same shape of the balloon "bend". Space-time isn't a substance, it's a geometry. A sheet of paper can be flat, or it can have a wrinkle in it, but the paper doesn't appear or disappear. Spacetime is the sheet, but not the paper. ##### Share on other sites 8 minutes ago, swansont said: Spacetime is the sheet, but not the paper. Nice. ##### Share on other sites 4 hours ago, awaterpon said: It should be for both coulomb's law and magnetism. I suppose the above comment is in addition to the initial one statement below; it applies to coulomb's law? On 4/6/2019 at 11:22 AM, awaterpon said: The Newtonian equation of gravity is valid , all other equations of potential energy ,etc are valid the escape velocity is true. In my concept gravity decreases with the increment in distance my concept has the same values as we have in current view” g=9.8 m/s/s on earth surface both in current view and in my concept” the difference is that the equations are applied to a specific range beyond that range the equations are not applicable beyond that range the gravity value drops suddenly to zero value. Which means per your idea that beyond a certain range magnetic fields and electrical fields suddenly must drop to zero? Can you provide references or evidence? Edited by Ghideon format ##### Share on other sites 23 minutes ago, Ghideon said: Which means per your idea that beyond a certain range magnetic fields and electrical fields suddenly must drop to zero? Can you provide references or evidence? In standard physics this would happen if e.g. you ionized an atom. Beforehand it's neutral and there would be no electric field, but afterward you would have an electric dipole. But the electric field would still be zero for distances greater than ct. The propagation of the field would occur in accordance to solutions of Maxwell's equations, where the propagation speed is c. awaterpon's solution may have different details, but the concept is firmly ensconced in classical physics, and it's been there for ~150 years. ##### Share on other sites @awaterpon Have you seen this animation from NASA? Edited by studiot ##### Share on other sites 25 minutes ago, swansont said: In standard physics this would happen if e.g. you ionized an atom. Beforehand it's neutral and there would be no electric field, but afterward you would have an electric dipole. But the electric field would still be zero for distances greater than ct. The propagation of the field would occur in accordance to solutions of Maxwell's equations, where the propagation speed is c. awaterpon's solution may have different details, but the concept is firmly ensconced in classical physics, and it's been there for ~150 years. Thanks! But I think I know how mainstream physics work in this regard. But I see that my question was very unclear! My question was not regarding the speed of propagation but what is happening at a later time, according the idea in OP. I interpreted OP as if the propagation would stop at some distance;”suddenly drop to zero”. So when measuring the field later, there would, according to OP, be a distance where Fields would go from some small value to zero in a sudden step. Sorry for the confusion. ##### Share on other sites 2 minutes ago, Ghideon said: Thanks! But I think I know how mainstream physics work in this regard. But I see that my question was very unclear! My question was not regarding the speed of propagation but what is happening at a later time, according the idea in OP. I interpreted OP as if the propagation would stop at some distance;”suddenly drop to zero”. So when measuring the field later, there would, according to OP, be a distance where Fields would go from some small value to zero in a sudden step. Sorry for the confusion. I was mainly posting for others' benefit. In any even I think the OP's position is about propagation speed, rather than deviating from a 1/r^2 (for gravity and electrostatics) at some distance. One problem with the propagation speed scenario described when applied to gravity is that you can't just make mass appear in a region that has no gravity, while you can do this for electric and magnetic fields. We have evidence of changes in gravity propagating at c, though, as has already been pointed out: gravitational waves (also the Hulse and Taylor pulsar, though that's indirect evidence) ##### Share on other sites 58 minutes ago, Ghideon said: according to OP, be a distance where Fields would go from some small value to zero in a sudden step. Think of an object close to a range limit by one meter , now think of moving this object away from mass towards the range end the object can't reach the limit point since it can't move faster than light " range is extendable with c" So in fact there is not a sudden step so that force drop to zero , the sudden change is only mathematically. The space-time is curved at the limit point by a degree but has no any curvature after that point, however since the curving process continues there is not a sudden drop in space curvature since it continues Edited by awaterpon ##### Share on other sites 4 minutes ago, awaterpon said: Think of an object close to a range limit by one meter , now think of moving this object away from mass towards the range end the object can't reach the limit point since it can't move faster than light " range is extendable with c" So in fact there is not a sudden step so that force drop to zero , the sudden change is only mathematically. And, mathematically, where is this sudden change? And what causes it? ##### Share on other sites 1 hour ago, studiot said: @awaterpon Have you seen this animation from NASA? No but beautiful. My idea is something like this thanks studiot Edited by awaterpon ##### Share on other sites 4 minutes ago, awaterpon said: No but beautiful. My idea is something like this thanks studiot So you have nothing new to add to well-established physics? Should we close this thread now? ##### Share on other sites 5 minutes ago, Strange said: So you have nothing new to add to well-established physics? Should we close this thread now? don't close the thread please.I meant it is a good representation for my idea Edited by awaterpon ##### Share on other sites 6 minutes ago, awaterpon said: don't close the thread please.I meant it is a good representation for my idea But it isn’t clear what your idea is or how it is different from standard physics. 1 hour ago, studiot said: @awaterpon Have you seen this animation from NASA? Can you provide the source for this, please ##### Share on other sites 2 hours ago, awaterpon said: Think of an object close to a range limit by one meter , now think of moving this object away from mass towards the range end the object can't reach the limit point since it can't move faster than light " range is extendable with c" So in fact there is not a sudden step so that force drop to zero , the sudden change is only mathematically. The space-time is curved at the limit point by a degree but has no any curvature after that point, however since the curving process continues there is not a sudden drop in space curvature since it continues Thanks for the clarification. As I said, I misinterpreted the idea, I thought I should look for something new. Bold by me: On 4/6/2019 at 11:22 AM, awaterpon said: The Newtonian equation of gravity is valid , all other equations of potential energy ,etc are valid the escape velocity is true. In my concept gravity decreases with the increment in distance my concept has the same values as we have in current view” g=9.8 m/s/s on earth surface both in current view and in my concept” the difference is that the equations are applied to a specific range beyond that range the equations are not applicable beyond that range the gravity value drops suddenly to zero value. On 4/6/2019 at 11:22 AM, awaterpon said: if gravity jumps from number to number it would jump to zero while space continues to infinity On 4/6/2019 at 11:22 AM, awaterpon said: it will move for instance from 3.4 to 3.49 to 3.499 to infinity regardless its speed it won’t reach the 4 however in fact an object will jump from a number to a nearby number it will jump from 3 to 4 gravity jumps to zero while space continues to infinity. On 4/7/2019 at 9:33 PM, awaterpon said: General relativity doesn't say gravity spread out with the speed of light c.It doesn't say gravity has a limited range.I discovered all these . I failed to see that speed of propagation of gravity was part of or required in the above descriptions. Result is, as others have already said, that nothing new has been presented. 2 hours ago, awaterpon said: don't close the thread please.I meant it is a good representation for my idea Can you please show what is new and not already included in existing mainstream physics? Edited by Ghideon missing part at the end of post ##### Share on other sites 12 hours ago, Ghideon said: Can you please show what is new and not already included in existing mainstream physics? The idea of infinity is always wrong.They are newtonian thoughts, things like Infinite speed of objects , infinite speed of gravity and gravity is everywhere and available at infinity.They are all Newton's thoughts I presented a new solution based on GR and violating Newton thoughts of infinite extend of gravity , Gravity being everywhere untill infinity is a Newtonian thought left unchanged by GR what I did is completing GR without violating any part of it and without violating modern physics. ##### Share on other sites 59 minutes ago, awaterpon said: The idea of infinity is always wrong. How do you know? The universe may be infinite in size. The universe may be infinite in age. Do you have any evidence that neither of these are the case? ##### Share on other sites 33 minutes ago, Strange said: The universe may be infinite in size. The universe may be infinite in age. Do you have any evidence that neither of these are the case? Space and time are infinite since they are fundamental ##### Share on other sites 3 minutes ago, awaterpon said: Space and time are infinite since they are fundamental How do you know that? The universe could be finite in size. The universe may be finite in age. Do you have any evidence? And doesn't this contradict what you just said: 1 hour ago, awaterpon said: The idea of infinity is always wrong. You seem to just post random ideas that pop into your head. You need to: get your thoughts organised; Write down the mathematics; Find some evidence that is consistent with that. If you don't do that, why should anyone take these incoherent comments seriously? ##### Share on other sites 1 hour ago, awaterpon said: The idea of infinity is always wrong.They are newtonian thoughts, things like Infinite speed of objects , infinite speed of gravity and gravity is everywhere and available at infinity.They are all Newton's thoughts I presented a new solution based on GR and violating Newton thoughts of infinite extend of gravity , Gravity being everywhere untill infinity is a Newtonian thought left unchanged by GR what I did is completing GR without violating any part of it and without violating modern physics. But that is already known? Here is an attempt at a short comment using math: Newton: $\lim_{r \rightarrow \infty } G\frac{ m_{1} m_{2} }{ r^{2} }=0$ At infinitely large distance the gravitational force is infinitely small. Any change will happen in an infinitely short time. GR: It takes an infinite time for a gravitational wave to reach infinite distance and the wave will be infinitely weak. I do not possess the knowledge to write down the correct math for GR. What new discovery are you proposing? How does your mathematical explanation look? ) Not necessarily mathematically formally correct, hopefully correct enough to make a point. ##### Share on other sites This topic is now closed to further replies. × • #### Activity × • Create New...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6947689652442932, "perplexity": 1509.0593991799417}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038083007.51/warc/CC-MAIN-20210415035637-20210415065637-00014.warc.gz"}
https://hpmuseum.org/forum/showthread.php?tid=17440&pid=151808&mode=threaded	FORTH for the SHARP PC-E500 (S) 09-06-2021, 11:41 PM (This post was last modified: 09-06-2021 11:42 PM by Helix.) Post: #1 Helix Member Posts: 239 Joined: Dec 2013 FORTH for the SHARP PC-E500 (S) Some of you may be interested: http://www.silicium.org/forum/viewtopic....62#p559662 https://github.com/Robert-van-Engelen/Forth500 I still have to make a serial cable to transfer programs, so I can't test it for now. I hope floats will be implemented. Jean-Charles « Next Oldest \| Next Newest » Messages In This Thread FORTH for the SHARP PC-E500 (S) - Helix - 09-06-2021 11:41 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 09-12-2021, 02:00 AM RE: FORTH for the SHARP PC-E500 (S) - Helix - 09-12-2021, 11:40 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 09-13-2021, 01:12 AM RE: FORTH for the SHARP PC-E500 (S) - xerxes - 09-15-2021, 11:51 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 11-08-2021, 04:22 AM RE: FORTH for the SHARP PC-E500 (S) - xerxes - 11-09-2021, 10:59 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 09-16-2021, 12:47 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 09-16-2021, 05:06 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 09-17-2021, 08:45 PM RE: FORTH for the SHARP PC-E500 (S) - toml_12953 - 09-17-2021, 09:25 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 09-22-2021, 10:55 AM RE: FORTH for the SHARP PC-E500 (S) - robve - 09-21-2021, 06:12 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 09-19-2021, 07:14 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 09-28-2021, 03:28 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 09-28-2021, 09:03 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 09-29-2021, 09:23 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 09-29-2021, 10:27 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 09-30-2021, 09:42 PM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 10-04-2021, 06:43 AM RE: FORTH for the SHARP PC-E500 (S) - Helix - 10-05-2021, 12:28 AM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 10-05-2021, 01:02 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 10-06-2021, 02:41 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 10-06-2021, 11:35 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 10-07-2021, 05:55 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 10-07-2021, 11:48 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 10-08-2021, 01:04 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 10-10-2021, 01:38 AM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 10-08-2021, 05:36 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 10-08-2021, 07:16 PM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 10-10-2021, 09:11 AM RE: FORTH for the SHARP PC-E500 (S) - robve - 10-10-2021, 01:22 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 10-10-2021, 01:36 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 10-13-2021, 02:38 AM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 10-26-2021, 05:45 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 10-29-2021, 11:46 PM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 10-28-2021, 03:11 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 10-29-2021, 04:03 AM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 10-30-2021, 07:09 AM RE: FORTH for the SHARP PC-E500 (S) - Helix - 10-30-2021, 09:12 PM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 10-31-2021, 01:57 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 11-01-2021, 12:34 AM RE: FORTH for the SHARP PC-E500 (S) - robve - 11-02-2021, 07:58 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 11-03-2021, 11:58 AM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 11-04-2021, 05:48 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 11-05-2021, 02:04 PM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 11-06-2021, 10:40 AM RE: FORTH for the SHARP PC-E500 (S) - robve - 11-06-2021, 07:31 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 11-07-2021, 01:15 AM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 11-07-2021, 01:00 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 11-07-2021, 03:40 PM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 11-07-2021, 05:44 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 11-07-2021, 08:19 PM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 11-09-2021, 08:23 AM RE: FORTH for the SHARP PC-E500 (S) - Klaus Overhage - 11-13-2021, 12:07 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 11-13-2021, 07:19 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 11-22-2021, 05:42 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 11-24-2021, 11:33 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 11-25-2021, 02:54 AM RE: FORTH for the SHARP PC-E500 (S) - Helix - 01-12-2022, 11:06 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 01-13-2022, 03:40 AM RE: FORTH for the SHARP PC-E500 (S) - robve - 01-16-2022, 09:22 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 01-18-2022, 12:32 AM RE: FORTH for the SHARP PC-E500 (S) - Helix - 02-19-2022, 09:40 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 02-20-2022, 09:13 PM RE: FORTH for the SHARP PC-E500 (S) - Helix - 02-20-2022, 11:12 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 04-03-2022, 12:53 AM RE: FORTH for the SHARP PC-E500 (S) - Helix - 04-03-2022, 11:06 PM RE: FORTH for the SHARP PC-E500 (S) - robve - 04-04-2022, 12:47 AM RE: FORTH for the SHARP PC-E500 (S) - robve - 06-21-2022, 02:16 AM RE: FORTH for the SHARP PC-E500 (S) - F-73P - 06-22-2022, 02:10 AM User(s) browsing this thread: 1 Guest(s)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8004924654960632, "perplexity": 26518.05851678339}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104248623.69/warc/CC-MAIN-20220703164826-20220703194826-00541.warc.gz"}
https://www.rdocumentation.org/packages/caret/versions/3.45/topics/maxDissim	# maxDissim 0th Percentile ##### Maximum Dissimilarity Sampling Functions to create a sub-sample by maximizing the dissimilarity between new samples and the existing subset. ##### Usage maxDissim(a, b, n = 2, obj = minDiss, randomFrac = 1, verbose = FALSE, ...) minDiss(u) sumDiss(u) ##### Arguments a a matrix or data frame of samples to start b a matrix or data frame of samples to sample from n the size of the sub-sample obj an objective function to measure overall dissimilarity randomFrac a number in (0, 1] that can be used to sub-sample from the remaining candidate values verbose a logical; should each step be printed? ... optional arguments to pass to dist u a vector of dissimilarities ##### Details Given an initial set of m samples and a larger pool of n samples, this function iteratively adds points to the smaller set by finding with of the n samples is most dissimilar to the initial set. The argument obj measures the overall dissimilarity between the initial set and a candidate point. For example, maximizing the minimum or the sum of the m dissimilarities are two common approaches. This algorithm tends to select points on the edge of the data mainstream and will reliably select outliers. To select more samples towards the interior of the data set, set randomFrac to be small (see the examples below). ##### Value • a vector of integers corresponding to the rows of b that comprise the sub-sample. ##### References Willett, P. (1999), "Dissimilarity-Based Algorithms for Selecting Structurally Diverse Sets of Compounds," {Journal of Computational Biology, 6, 447-457.} [object Object] dist example <- function(pct = 1, obj = minDiss, ...) { tmp <- matrix(rnorm(200 * 2), nrow = 200) # start with 15 data points start <- sample(1:dim(tmp)[1], 15) base <- tmp[start,] pool <- tmp[-start,] # select 9 for addition newSamp <- maxDissim( base, pool, n = 9, randomFrac = pct, obj = obj, ...) allSamp <- c(start, newSamp) plot( tmp[-newSamp,], xlim = extendrange(tmp[,1]), ylim = extendrange(tmp[,2]), col = "darkgrey", xlab = "variable 1", ylab = "variable 2") points(base, pch = 16, cex = .7) for(i in seq(along = newSamp)) points( pool[newSamp[i],1], pool[newSamp[i],2], pch = paste(i), col = "darkred") } par(mfrow=c(2,2)) set.seed(414) example(1, minDiss) title("No Random Sampling, Min Score") set.seed(414) example(.1, minDiss) title("10 Pct Random Sampling, Min Score") set.seed(414) example(1, sumDiss) title("No Random Sampling, Sum Score") set.seed(414) example(.1, sumDiss) title("10 Pct Random Sampling, Sum Score") utilities ##### Aliases • maxDissim • minDiss • sumDiss Documentation reproduced from package caret, version 3.45, License: GPL-2 ### Community examples Looks like there are no examples yet.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2732098400592804, "perplexity": 11533.333747887302}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145654.0/warc/CC-MAIN-20200222054424-20200222084424-00405.warc.gz"}
https://codegolf.stackexchange.com/questions/173065/prisoners-dilemma-with-access-to-opponent?noredirect=1	In this challenge, you will write a bot that play's the prisoner's dilemma. Here's the catch: you will not have access to the history of previous games. Instead, you will have access to the opponent itself. In this version, both players get +2 points if they both cooperate, +1 points if they both defect, and if one cooperates but one defects, the defector gets +3 while the other gets no points. Each submission will be played against every other submission, including itself, 10 times. The winner is the submission with the most total points. Controller: You should write a javascript function, in the form function submissionName(them) { } The controller uses the function's name property to display the results, so if it is not in this format (and is instead f = x => ... or f = function() { ... }) it will be difficult to see your score and you will not be able to access your own function. The function will accept one parameter: them which is the opponent's function. It may then call that function to see what the opponent's reaction would be given certain functions as inputs. Based on that data, you must return 'C' or 'D' for cooperate or defect respectively. Examples (will be competing): function cooperate(them) { return 'C'; } function defect(them) { return 'D'; } function nice(them) { // Do whatever they would do when faced with a cooperator return them(wrap(_ => 'C')); } The controller is available here Rules: • You won't be able to see the opponent's code itself. All functions are wrapped so that they look the same when toString() is called. The only way to examine an opponent (who could be yourself) is to test them. • Your function does not have to be deterministic. You may only save state by setting properties on your own function, such as submissionName.state = {};. However, between matches (even between matches of the same players), state is cleared by calling toString() and eval. Therefore, there is no memory of previous matches. • The order of which function is called first in each match is randomized. • If your code throws an error, it will be treated as though you cooperated while your opponent defected. If you are the first to run, the opponent's code will not even be called. This happens even if the error occurs in your opponent's code while while you are calling them. Be wary of stack overflow errors, especially if your code calls them(wrap(submissionName)), as they might do the same. • You may not access the variable self, or any other variable that happens to be in scope when eval is called EXCEPT the function wrap. This function allows you to call the opponent in a manner indistinguishable from how the controller calls a function. You may not write to Math, window, etc. (You may use functions, such as Math.random(), however). • You may not access the stack trace by creating an Error or by some other method. A note on taking too long: please avoid getting stuck in a while loop forever. The combined time of both competitors should not exceed 1 second in any given round. To enforce this, a random timeout between 1000 ms and 2000 ms is chosen (this is to avoid gaming by intentionally waiting a known amount of time), and if the worker takes longer than that to execute, an error will be thrown. If this happens, the cause of the error will be determined as follows: the execution will be paused at a random moment after 1000 ms, and the call stack at that moment will be inspected. The most recently called competitor that is currently in a loop (or loop-like recursion, in the sense that it is a recursion set up to avoid a stack overflow error) will be blamed. If the same competitor is blamed for causing a "taking too long" error several times, that competitor will be disqualified. This means that even if you cause the opponent to take too long by getting stuck in a loop when your opponent calls you, it will still be your fault, because it is the call stack that matters. • This challenge reminds me of the Dollar Bill Auction. – Alion Sep 30 '18 at 9:18 • Must the function used to test them be deterministic/follow the rules? For example function me(them){let log=0;them(x=>{++log;return 'C';});return log==0?'D':'C';} – user202729 Sep 30 '18 at 12:28 • If both functions call them(wrap(something)), how can you prevent recursion? Am I missing something? – Quintec Sep 30 '18 at 13:29 • @Quintec you can use recursion and loops. It's just that the recursion needs to result in a StackOverflow error and not an infinite loop that never quits. If it could result in a StackOverflow, make sure you add a try-catch statement. For an example of recursion that does not reach a stackoverflow error within 1 second, you need more obscure examples like stackoverflow.com/q/12438786/3371119 – soktinpk Sep 30 '18 at 14:18 • @Quintec not necessarily. For example, them(() => 'C') would not result in an error because when the opponent calls them, it calls the () => 'C' function. The only thing that needs to be wrapped in try-catch would be if you call them with a parameter of some function that calls them with a parameter of some function that calls them etc. (infinitely). For example, them(t => t(() => 'C')) would play whatever the opponent would play if the opponent thought they were playing nice. There is no possibility of a stackoverflow error. – soktinpk Sep 30 '18 at 14:39 # BoomBot function boom(them) { throw 1; } If the opponent is run first and calls this without try..catch, this bot automatically wins 3 points. Zero points in any other case. • If the opponent is run first and do not call this, then it will lose 3 points, right? – user202729 Oct 1 '18 at 13:51 • @user202729 More precisely, the opponent will get 3 points. There's no losing points in this game. – Bubbler Oct 1 '18 at 22:58 # Archaeopteryx function archaeopteryx(them) { const guard = them => us => { try { return them(wrap(them => us(guard(them)))); } catch (e) { return 'C'; } }; const f = guard(them); return f(f => 'C') == 'C' ? f(f => 'D') : f(f => 'D') == 'C' \|\| f(f => f(f => 'C')) == 'C' ? 'D' : 'C'; } • If opponent cooperates with cooperate, then mimic opponent’s move against defect. • Else, if opponent cooperates with defect or with nice, then defect. • Else, cooperate. What makes this a good strategy? I have no idea. I generated it using an evolutionary algorithm, trained partly on current submissions. # Tiktaalik function tiktaalik(them) { const guard = them => us => { try { return them(wrap(them => us(guard(them)))); } catch (e) { return 'C'; } }; const f = guard(them); return f(f => 'C') == 'D' ? f(f => 'D') == 'C' ? 'D' : 'C' : f(f => 'D') == 'D' ? 'D' : f(f => f(f => 'D')); } • If opponent defects against cooperate, then invert opponent’s move against defect. • Else, if opponent defects against defect, then defect. • Else, mimic opponent’s move against notNice. Another evolutionarily generated strategy. # WhatWouldBotDoBot function WWBDB(them) { let start = performance.now(); let cc = 0, cd = 0, dc = 0, dd = 0; try { for (let i = 0; i < 10; i++) { them(() => 'C') == 'C' ? cc++ : cd++; them(() => 'D') == 'C' ? dc++ : dd++; if (performance.now() - start > 500) break; } } catch (e) {} return 2 * cc >= 3 * dc + dd ? 'C' : 'D'; } WhatWouldBotDoBot is fairly simple; it just tests its opponent for what it would do against a steady state program. If a bot prefers cooperating if possible, WWBDB will also prefer cooperation (so it will cooperate with nice bot). WWBDB does not itself prefer cooperation. # Check stateful function checkStateful(them) { let stateful = false; let response = 'D'; try { response = them(wrap(function (them) { stateful = true; return 'C'; })); } catch (e) { } if (stateful) { return 'D'; } return response; } If them invoke me, then them probably be a truly them. We act as defector. If them not invoke me, then them probably be a wrapped tester. We would act as nicer. Above is the original answer. And maybe I should make myself cooperation to earn more points. # Check stateful with self-coop function checkStatefulSelfCoop(them) { let stateful = false; let response = 'D'; if (!checkStatefulSelfCoop.invokeCounter) { checkStatefulSelfCoop.invokeCounter = 0; } let lastInvoke = ++checkStatefulSelfCoop.invokeCounter; try { response = them(wrap(function (them) { stateful = true; return 'C'; })); } catch (e) { } if (checkStatefulSelfCoop.invokeCounter > lastInvoke) { return 'C'; } if (stateful) { return 'D'; } return response; } # Complexity function complexity(them) { try { let coop_w_def = them(wrap(() => "D")) == "C", coop_w_coop = them(wrap(() => "C")) == "C", coop_w_nice = them(wrap((a) => a(wrap(() => "C")))) == "C", coop_w_nnice = them(wrap((a) => a(wrap(() => "D")))) == "C"; if (coop_w_def && coop_w_coop && coop_w_nice && coop_w_nnice) return "C"; let def_w_def = them(wrap(() => "D")) == "D", def_w_coop = them(wrap(() => "C")) == "D", def_w_nice = them(wrap((a) => a(wrap(() => "C")))) == "D", def_w_nnice = them(wrap((a) => a(wrap(() => "D")))) == "D"; if (def_w_def && def_w_coop && def_w_nice && def_w_nnice) return "C"; } catch (e) {} return "D"; } Complexity tests to see whether the bot is Cooperate or Defect. If it is, it cooperates, but if it isn't, it defects. All current bots that test their opponents use simple functions to test the responses, so Complexity will just pretend to be Cooperate in those cases. # NotNice 2 function notNice2(them) { try { return them(wrap(_ => 'D')); } catch(e) { return 'D'; } } Boom-proof version of NotNice by FatalError. # Common Sense function commonSense(them) { try { var ifC = them(wrap(_ => 'C')); var ifD = them(wrap(_ => 'D')); if (ifD === 'C') { return 'D'; } return them(_ => ifC); } catch (e) { return 'D'; } } Disclaimer: I kinda don't know javascript. If you can profit off a nice person, do it. Otherwise, return what they would return if they faced themselves cooperating (at least, that's what I think it does). And you where do you wana go? (inspired by the voltures in the book of jungle) function yourself(them) { try{ return them(this); }catch(e){ return "D"; } } function yourself_no_this(them) { try{ return them(yourself_no_this); }catch(e){ return "D"; } } • This just won in a tournament I ran. Good job! – MegaTom Oct 12 '18 at 18:37 • I just noticed that this bot violates the rules. "You may not access the variable self..." this is the same as self. I think that you wanted to say return them(yourself). – MegaTom Oct 15 '18 at 18:57 • Technicaly ( xkcd.com/1475 ) ;) this is not a variable, it is a keyword, and in a context of a function this!=self. self would mean the window object and this the function itself (always refers to the context it is in, that is why it is not considered as a variables). That is why having var self = this; in the begining of many code-examples might be considered as misleading. Added version without the "this" – T.S. Oct 16 '18 at 11:34 • No. this is not referring to the function. yourself and yourself_no_this run vary differently. this basically never refers to the function in javascript. See: developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/… – MegaTom Oct 16 '18 at 17:51 # Punish Inspectors Give the bot some code and see if it runs it. If it was run more then once, the bot is an evil inspector, and we must defect! If it was run exactly once, play as not nice bot. If it was never run, cooperate. function punishInspectors(them) { var inspections = 0; var result; try{ result = them(wrap(function(_){ inspections += 1; return 'D'; })) }catch(e){ result = 'D'; } return (inspections > 1) ? 'D' : (inspections === 1) ? result : 'C'; } # History What would the last bot I saw do vs this opponent? function history(them) { var res = 'D'; if(history.last){ try{ res = history.last(them); }catch(ex){} } history.last = them; return res; } ## Results for a 10000 round tournament: 1 defect...................365226 2 complexity...............353492 3 punishInspectors.........349957 4 checkStatefulSelfCoop....348913 5 checkStateful............333481 6 cooperate................329870 7 archaeopteryx............323624 8 selfapply................319533 9 tiktaalik................318663 10 history..................315266 11 rand.....................300735 12 randalt..................297561 13 yourself.................293701 14 notNice2.................283744 15 NotNice..................260350 16 WWBDB....................245281 17 nice.....................245036 18 commonSense..............242546 19 trickybot................181696 20 boom.....................67245 function onlyTrustYourself(them) { function tester (){ } onlyTrustYourself.activated = false; try{them(tester);} catch(e){} if(them.name == "tester") { onlyTrustYourself.activated = true; } if(onlyTrustYourself.activated) { return 'C'; } return 'D'; } How I want this to work is to always defect, except for when playing against self. It tries to do that by passing a "tester" function which isn't wrapped to them, and it tries to detect if "them" is named tester. If it is named tester, it changes the static variable activated to true, then returns cooperate. But it doesn't work. I'm not too familiar with javascript, and I'll probably make some more changes. # NotNice function NotNice(them) { return them(wrap(_ => "D")) } Imitates opponent's reaction to deflection # RandomBot function rand(them) { return 'CD'[Math.random() * 2 \| 0] } Because why not. # TrickyBot Try to be unpredictable function trickybot(them) { if(Math.round(Math.random(2)) == 0) { throw 1; } if(Math.round(Math.random(2)) == 0) { return 'D'; } return 'C'; } # selfapply function selfapply(them) { function testthem(x) { return (them(x)=='D' \|\| them(x)=='D' \|\| them(x)=='D' \|\| them(x)=='D' \|\| them(x)=='D') ? 'D' : 'C'; } function logic() { try { return testthem(them); } catch (e) {} try { return testthem(wrap(_ => 'C')); } catch (e) {} return 'D'; } if (selfapply.hasOwnProperty('state')) { return 'C'; } selfapply.state=1; let r=logic(); delete selfapply.state; return r; } Not sure if it makes any sense, but it seems interesting! Do to you as you do to yourself, repeat to catch randomness. If that doesn't work, be nice. Untested, and my first javascript code, and more complex than I expected. • This is going to disqualify itself because selfapply(selfapply) calls selfapply(selfapply)! – Anders Kaseorg Oct 3 '18 at 11:17 • I did consider its own selfapplication, but thought it would be okay. I hope it really is now. – Christian Sievers Oct 3 '18 at 21:01 # RandomAlternate function randalt(them){ if (randalt.hasOwnProperty('state')){ randalt.state = 1 - randalt.state; } else { randalt.state = Math.floor(2*Math.random()); } return 'CD'[randalt.state]; } So I learned how to use properties for state... # Mockingbird (Non-Competing?) function mockingbird(them) { var nest = arguments.callee.caller.caller.name; //Why yes officer, I'm a sweet little chickadee. return nest == "compete" ? 'D' : 'C'; } We're doing this all sneaky-beaky like. Mockingbird here is a cheap-cheap-cheater - it checks up the call stack two steps to grab the name of whoever is calling it through the wrap. In any context other than when Mockingbird is being polled by compete(), it spits out a 'C'. In other words, any direct inspection (no matter how careful) will make the other bot think that Mockingbird is friendly and cooperative - even though it's anything but. Mockingbird doesn't technically break the rules - everything I'm accessing is happily inside of Mockingbird's scope, and I never touch the stack trace (I just climb up the stack directly). Still... I'm mostly submitting this little birdie to see if anyone can come up with a strategy that can outcompete a perfect liar. • function trap(them) { arguments.callee.caller.caller.__defineGetter__("name", (_=>"not compete")); return "D"; } will transform your bot into cooperate. – MegaTom Oct 19 '18 at 18:28 • @MegaTom Why not throw in the __defineGetter__. – tsh Oct 25 '18 at 7:49 • @MegaTom @tsh Clever - throw is actually weaker, tsh, since I could revise Mockingbird to protect against it. There's pretty much nothing I can do if someone fiddles with the name :p. – M Dirr Oct 25 '18 at 14:42 ## Murder Bot #1 function murder(them) { while (1) { try { them(them); } catch (e) {} } } Causes an infinite loop in for which it is more likely that the opponent will be blamed. ## The Platinum Rule Bot function platinumRule(them) { try { return wrap(them)(them); } catch (e) { return 'C'; } } The Platinum Rule states "Treat others the way they want to be treated." My bot accommodates that. Whatever they would do to themselves, which we assume is how they would want to be treated, we do to them. If they throw an error, we assume they want to cooperate.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15131931006908417, "perplexity": 6470.062287938194}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998513.14/warc/CC-MAIN-20190617163111-20190617185111-00410.warc.gz"}
https://codereview.stackexchange.com/questions/11084/codebreaker-game	# Codebreaker game This is the "Codebreaker" game in Ruby. Tell me what I can make better! #!/usr/bin/env ruby class Sequence attr_accessor :guess, :code def initialize puts "Type the difficulty level you would like: 1, 2, 3, 4, or 5" begin @level = gets; @level = @level.to_i if @level > 6 raise "Error" end rescue puts "Invalid Difficulty" exit end end def create_code @code = "#{rand(@level2)}#{rand(@level2)}#{rand(@level2)}#{rand(@level2)}" if @level == 5 @code += "#{rand(@level2)}" end if @code.length > 5 puts "Invalid Difficulty!" exit end puts @code end def prompt @retstring = "" @guess = "" guesses = 0 while guesses < 4 print "Enter a guess: " @guess = gets x = 0 4.times do if @code[x] == @guess[x] @retstring += "+" else @retstring += "-" end puts @retstring sleep(1) x += 1 end puts "Would you like a hint? Type 'hint' to get a hint" hint = gets match = hint =~ /(h\|H)(i\|I)(n\|N)\w/ unless match == nil j = rand(@level2) puts "#{j}: #{@code[j]}" end guesses += 1 if @retstring == "++++" puts "Correct!" break end @retstring = "" end end def print_code print @code print " was the code\n" end end j = Sequence.new j.create_code j.prompt j.print_code Interesting game :), and reasonable code. I only have a few suggestions. for if @level > 6 raise "Error" end and if @code.length > 5 puts "Invalid Difficulty!" exit end Any particular reason you handled the first one using exception and the second one using an if condition? Also consider returning an error code, If program can be used in non-interactive way, printing any errors to stderr also helps. I would also modify it as def sexit(code, str) puts str exit code end def initialize puts "Type the difficulty level you would like: 1, 2, 3, 4, or 5" @level = gets.to_i sexit 1 "Invalid Difficulty" if @level > 6 end def create_code code_rows = 4 code_rows += 1 if @level > 4 @code = '' code_rows.times do @code += "#{rand(@level2)} end Should you check this here? It is more of an assert than a problem with user input, and the user input is validated elsewhere. # sexit 2 "Invalid Difficulty" if @code.length > 5 puts @code end Avoid magic numbers, replace 4 with a constant. def askuser(var) print var return gets end Why is retstring and guess a member variable? You dont seem to be using them any where else. def prompt guess = "" Whi is this a while loop? while you used a times loop inside? max_guess.times \|guesses\| retstring = "" guess = askuser "Enter a guess: " you dont need to maintain x. Also, why do you have only 4 here? from the above, if the level is 5 you add a new cell. 4.times do \|x\| and better put as ternary retstring += (@code[x] == guess[x] ? "+" : "-") puts retstring sleep(1) end hint = askuser "Would you like a hint? Type 'hint' to get a hint" Why do you use a separate match? Also name j some thing descriptive. And why \w ? Do you want to catch spellos in hint? if hint =~ /hint/i j = rand(@level2) puts "#{j}: #{@code[j]}" end Personally I prefer a case statement to check this. Also note you can get a case insensitive match. case askuser "Would you like a hint? Type 'hint' to get a hint" when /hint/i j = rand(@level*2) puts "#{j}: #{@code[j]}" end if retstring == "++++" puts "Correct!" break end retstring is better reset at the beginning of the loop. end end Regarding the whole organization, it might be better organized as a small command interpreter with specific commands for hint, level etc	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3406756818294525, "perplexity": 19920.587153597797}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574265.76/warc/CC-MAIN-20190921043014-20190921065014-00127.warc.gz"}
http://math.stackexchange.com/users/29940/seyhmus-gungoren?tab=summary	# Seyhmus Güngören less info reputation 1416 bio website location Germany age member for 1 year, 10 months seen 33 mins ago profile views 707 $1$ : It means "there exists something" $0$ : It doesnt mean "there exists nothing", instead it means "there exist something but that is nothing" 6 What is this operation on random variables called? 6 How to address mistakes in published papers? 5 What does $\propto$ mean? 5 Asymmetric Normal Probability Distribution 3 We have prime numbers for real numbers? # 2,994 Reputation +10 Finding the maximum likelihood estimator +10 Correlation and squared variables +25 Solving integral equation of an exponential sum +5 I need help about some compactness arguments # 76 Questions 8 Real world applications of category theory 6 Is this question solvable? $2$ non-linear equations and the proof that the solution is unique (with asymmetric bounty option) 5 I need help about some compactness arguments 5 Need advice: what should be my next step? 5 Axiomatically define a function that can solve otherwise impossible differential equations, like $i$ solves otherwise impossible polynomial equations # 117 Tags 33 probability × 66 9 probability-distributions × 56 26 statistics × 35 9 random-variables × 4 13 probability-theory × 27 8 notation × 5 11 homework × 13 7 inverse × 6 11 convolution × 7 6 calculus × 24 # 6 Accounts Mathematics 2,994 rep 1416 Mathematica 317 rep 28 MathOverflow 160 rep 7 Cross Validated 137 rep 1 Signal Processing 116 rep 2	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6703471541404724, "perplexity": 2906.959089763438}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999651905/warc/CC-MAIN-20140305060731-00079-ip-10-183-142-35.ec2.internal.warc.gz"}
http://tex.stackexchange.com/questions/99922/automatically-choosing-preset-color-schemes-in-pgfplots-based-on-number-of-entri	# Automatically choosing preset color schemes in pgfplots based on number of entries This is really more of a question to satisfy personal curiosity than to solve a real problem. When choosing the colour schemes for my plots, I try to select colours that will work well with the amount of items involved in the plot. This means using sets of colours that are above all aesthetically pleasing, but also that contrast well, etc. (eg. schemes created with a website like this). However, I was wondering if it would be possible to define a set of 2,3,4,...,n colours that work well, and have pgfplots (or some other package?) select automatically from the one that matches the amount of entries. I looked around for similar questions, but I didn't seem to find anything. The colour sets could be defined as cycle lists, but it's the automatic selection that I'm wondering about. Can this be done? Any ideas? - ## 2 Answers This is just a longish comment. I might be wrong in understanding the workflow and hopefully I'll be corrected if so. In pgfplots things do not happen all at once. First your plot commands together with the axis options are parsed and stored as PGF paths. Then a visualization scheme kicks in (and I'm not 100% sure about the order) and path colorings, legend styles etc. are assigned. Then they are drawn with low level TikZ/PGF commands. In order to select a cycle list, the plots need to be collected already such that they are counted. But that would probably be too late to change the drawing options. I don't think this functionality is supported off-the-shelf. Note that this is a very rough description, there are many things checked in each layer so don't take this too literal. But if you are willing to provide the number of plot items then it's a matter of defining a style with an argument that selects the predefined plot cycle list. - It shouldn't be that much of a problem to provide the number of items in the list beforehand as an option of sorts I think. Although I think you're probably right with the points you make. – Mythio Feb 25 '13 at 21:53 I guess that is the real problem: the amount of information that is available to pgfplots at any given time, and the steps it takes in processing its data. I was thinking, for example, of plots that get their input from files that may even be automatically generated. I agree that in most cases this is not really a problem, but hey, I thought it'd be cool to ask and see what solutions (if any) come up. :) – jja Feb 25 '13 at 23:01 @jja Don't get me wrong, it's a nice question. It's just seems quite tedious to hack into the right place in the right time. But I've been wrong before so I'll say let's wait for Christian's opinion. Then probably I'll need to delete this :) – percusse Feb 26 '13 at 2:16 @percusse your answer is correct and complete: the cycle list is evaluated while surveying the plots and the number of plots is unknown until that survey has been finished. The expected way for such a style would be to make a couple of cycle lists which match and select them manually in advance, like size <10 cycle list or so. – Christian Feuersänger Mar 8 '13 at 19:50 As percusse and Christian Feuersänger have mentioned in the answer and comment, there is no way to automatic selection of a cycle list containing an appropriate number of items. But at least since PGFPlots v1.13 the colorbrewer library is added to the package (see section 5.2 on page 397 of the manual), which brings the color schemes created by Cynthia Brewer published at http://colorbrewer2.org to PGFPlots as colormaps as well as as cycle lists. Here are two more or less random examples from that library. \documentclass[border=2mm]{standalone} \usepackage{pgfplots} \usetikzlibrary{ pgfplots.colorbrewer, } \pgfplotsset{ cycle from colormap manual style/.style={ x=3cm,y=10pt,ytick=\empty, stack plots=y, every axis plot/.style={line width=2pt}, }, } \begin{document} \begin{tikzpicture} \begin{axis}[ cycle list/RdYlBu-6, cycle from colormap manual style, ] \addplot coordinates {(0,1) (1,1)}; \addplot coordinates {(0,1) (1,1)}; \addplot coordinates {(0,1) (1,1)}; \addplot coordinates {(0,1) (1,1)}; \addplot coordinates {(0,1) (1,1)}; \addplot coordinates {(0,1) (1,1)}; \end{axis} \end{tikzpicture} \begin{tikzpicture} \begin{axis}[ cycle list/Set1, cycle from colormap manual style, ] \addplot coordinates {(0,1) (1,1)}; \addplot coordinates {(0,1) (1,1)}; \addplot coordinates {(0,1) (1,1)}; \addplot coordinates {(0,1) (1,1)}; \addplot coordinates {(0,1) (1,1)}; \addplot coordinates {(0,1) (1,1)}; \end{axis} \end{tikzpicture} \end{document} -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7428648471832275, "perplexity": 993.9010156548201}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860114285.77/warc/CC-MAIN-20160428161514-00117-ip-10-239-7-51.ec2.internal.warc.gz"}
http://www.ni.com/documentation/en/labview-comms/2.0/mnode/creating-a-graphical-display-of-mathscript-results/	# Creating a Graphical Display of MathScript Results Version: Use the MathScript plot functions to create a graphical 2D or logarithmic display of your MathScript results. You can only execute plot functions in the command section of the MathScript Console. The following procedure demonstrates how to create a plot in the MathScript Console using a specific example. The example plots the sine and the cosine of the given values. The steps you need to take to complete your specific task might be different than the following steps. 1. Select View»More»Tools Launcher to open the Tools Launcher. 2. Click MathScript Console to open the MathScript Console. 3. Enter the following code in the command section of the MathScript Console to plot the sine and the cosine of the given values. Press Enter after every command. x = [0:0.1:2pi]; clfig; xlimit([0;2pi]); ylimit([-1;1]); xlabel('x axis'); ylabel('y axis'); grid('on'); plot(sin(x)); hold('on'); plot(cos(x)); legend('sin(x)', 'cos(x)'); The code creates the following plot. The commands you entered complete the following actions: • x = [0:0.1:2pi]; creates an array with values from 0 to 2pi in steps of 0.1. Prevent displaying the output of the values in the command window by finishing the command with a semicolon. • clfig clears the current plot window. If no plot window exists, clfig creates a new plot window. • xlimit and ylimit set the ranges of the x- and the y-scale. • xlabel and ylabel label the axes. • plot plots the curve. • hold determines that the new cos(x) plot doesn't overwrite the existing sin(x) plot. • legend creates a legend of the two plotted curves.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.477398157119751, "perplexity": 3411.944540424321}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676593142.83/warc/CC-MAIN-20180722080925-20180722100925-00556.warc.gz"}
https://wikieducator.org/Template:Flashcard/doc	# Template:Flashcard/doc Documentation for Template:flashcard: ## Purpose Enable easy creation of flashcards for language learning (though usable for other purposes with a bit of imagination). ## Usage This template is quite new (November 2009) and has not been extensively tested. There might be some changes coming soon (see suggestions below). The initial design was for Mandarin Chinese which requires many options but the template can be used for other languages too (simply use only the options you need). ### Parameters Parameters front and back are enough for many applications. They take the main text of the front and back of the flashcard respectively. For various languages, the following parameters are available (they may be mixed freely): • General • front = <word or phrase for front of the card> • front sound = <name of media (sound) file> • front image = <name of image file> • image caption = <image caption for front image> • back = <word or phrase on the front translated> • back sound = <name of media (sound) file for the foreign pronunciation> • hint = <a text hint for mouse hover over front of the card> • notes = <notes on the flashcard to explain meaning, etc. > • theme = <name of theme e.g. blues, smart, etc. from Template:Box Theme Attribute> • For Chinese: • simplified • pinyin • yale • bopomofo • number of strokes • stroke order • For Japanese: • kanji • hiragana • katakana • rōmaji • romanisation ### Known Issues • While the hint text (from hint = <hint text>) is correct over the front text, the hint text over a front image incorrectly matches the image caption (instead of hint). See Suggestions below. ## Syntax {{flashcard \|front = <word or phrase for front of the card> \|front sound = <name of media (sound) file> \|back = <word or phrase on the front translated> \|back sound = <name of media (sound) file for the foreign pronunciation> \|simplified = <simplified character (if applicable) or simple explanation> \|pinyin = <pinyin phonetic - only relevant for Mandarin Chinese> \|wade-giles = <Wade-Giles phonetic - only relevant for Mandarin Chinese> \|yale = <Yale phonetic - only relevant for Mandarin Chinese> \|bopomofo = <bopomofo phonetic - only relevant for Mandarin Chinese> \|number of strokes = 7 \|stroke order = <animated image file name> \|notes = <notes on the flashcard to explain meaning etc. > \|theme = <theme name> }} The theme names are defined in Template:Box Theme Attribute and include those illustrated here. ## Examples ### Minimal Front and back only: {{flashcard \|front = Good day \|back = Bon jour }} gives: Image on Front: {{flashcard \|front image = Banana Fruit.JPG \|back = Banana }} gives: image caption included: {{flashcard \|front image = Banana Fruit.JPG \|image caption = banane mûre \|back = Banana }} gives: image with front and no caption: {{flashcard \|front = la banane \|front image = Banana Fruit.JPG \|back = Banana }} gives: image with caption and front: {{flashcard \|front = la banane \|front image = Banana Fruit.JPG \|image caption = banane mûre \|back = Banana }} gives: image with caption and front and hint (mouseover text - not image yet??): {{flashcard \|front = la banane \|front image = Banana Fruit.JPG \|hint = fruit jaune recourbé \|image caption = banane mûre \|back = Banana }} gives: Front and back only with notes: {{flashcard \|front = Good day \|back = Bon jour \|notes = A greeting }} gives: ### Mandarin Using all the parameters listed below: {{flashcard \|front = 你 \|front sound = Zh-n%C7%90.ogg \|hint = not me \|back = You \|back sound = En-us-you.ogg \|simplified = simplified character (if exists) goes here \|pinyin = Ni3 \|yale = ni-3 \|bopomofo = ㄋㄧˇ \|number of strokes = 7 \|stroke order= 你-order.gif \|notes = e.g. clarify if there is ambiguity ... }} gives the following (try it - click on 'show'): using themes: {{flashcard \|theme=blues \|front=你 \|front sound= Zh-n%C7%90.ogg \|hint = not me \|back=You \|back sound=En-us-you.ogg \|simplified= simplified character (if exists) goes here \|pinyin=Ni3 \|yale=ni-3 \|bopomofo=ㄋㄧˇ \|number of strokes = 7 \|stroke order=你-order.gif \|notes = e.g. clarify if there is ambiguity ... }} {{flashcard \|theme=goldy \|front=你 \|front sound= Zh-n%C7%90.ogg \|hint = not me \|back=You \|back sound=En-us-you.ogg \|simplified= simplified character (if exists) goes here \|pinyin=Ni3 \|yale=ni-3 \|bopomofo=ㄋㄧˇ \|number of strokes = 7 \|stroke order=你-order.gif \|notes = e.g. clarify if there is ambiguity ... }} ### Japanese {{flashcard \|theme = sandy \|front = マージャン \|front sound = En-us-you.ogg \|back = mahjong \|back sound =E n-us-you.ogg \|romaji = mājan \|kanji = 麻雀 \|romanisation = májiàng \|notes = Mahjong is a board game. Please correct sound files etc. and add a suitable hint to this flash card. Thanks :-) }} ## Suggestions • Extend to include: • clever functionality to change what goes on front (e.g. front is = pinyin) • i.e. if "card front = <one of the other parameters>" then make it so, etc. • Change default hint in image caption - rather add image caption = ... (done) - hint can be mouse over text "hint" (if not image). • Multilingual extension - e.g. front shows a word and selection of languages to pick for translation, etc. • Fix the examples on this page e.g. supply correct sound files. • There might be a clever way to generate Chinese flashcards such that the creator would just specify the character and which answers to display on the other side ... see Wikipedia's templates for Chinese (e.g.Template:Zh and Template:Stroke order). ## Features Includes various options for learning specific languages. Use the ones you need: • General: • front in base language (English in this case) • front image - to include an image on the front of the flashcard • traditional and simplified characters • phonetic representations • explanation (notes)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17532382905483246, "perplexity": 21992.40214403031}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251799918.97/warc/CC-MAIN-20200129133601-20200129163601-00383.warc.gz"}
http://www.ams.org/joursearch/servlet/PubSearch?f1=msc&onejrnl=tran&pubname=one&v1=53A04&startRec=1	# American Mathematical Society My Account · My Cart · Customer Services · FAQ Publications Meetings The Profession Membership Programs Math Samplings Policy and Advocacy In the News About the AMS You are here: Home > Publications AMS eContent Search Results Matches for: msc=(53A04) AND publication=(tran) Sort order: Date Format: Standard display Results: 1 to 30 of 44 found Go to page: 1 2 [1] Jochen Denzler. Existence and regularity for a curvature dependent variational problem. Trans. Amer. Math. Soc. 367 (2015) 3829-3845. Abstract, references, and article information View Article: PDF [2] Mohammad N. Ivaki. Centro--affine curvature flows on centrally symmetric convex curves. Trans. Amer. Math. Soc. 366 (2014) 5671-5692. Abstract, references, and article information View Article: PDF [3] David Groisser. Certain optimal correspondences between plane curves, I: Manifolds of shapes and bimorphisms. Trans. Amer. Math. Soc. 361 (2009) 2959-3000. MR 2485414. Abstract, references, and article information View Article: PDF This article is available free of charge [4] David Groisser. Certain optimal correspondences between plane curves, II: Existence, local uniqueness, regularity, and other properties. Trans. Amer. Math. Soc. 361 (2009) 3001-3030. MR 2485415. Abstract, references, and article information View Article: PDF This article is available free of charge [5] John Pardon. On the unfolding of simple closed curves. Trans. Amer. Math. Soc. 361 (2009) 1749-1764. MR 2465815. Abstract, references, and article information View Article: PDF This article is available free of charge [6] James J. Hebda and Chichen M. Tsau. Framings of knots satisfying differential relations. Trans. Amer. Math. Soc. 356 (2004) 267-281. MR 2020032. Abstract, references, and article information View Article: PDF This article is available free of charge [7] Ioannis A. Polyrakis. Minimal lattice-subspaces. Trans. Amer. Math. Soc. 351 (1999) 4183-4203. MR 1621706. Abstract, references, and article information View Article: PDF This article is available free of charge [8] Ioannis A. Polyrakis. Finite-dimensional lattice-subspaces of $C(\Omega)$ and curves of $\mathbb{R}^n$ . Trans. Amer. Math. Soc. 348 (1996) 2793-2810. MR 1355300. Abstract, references, and article information View Article: PDF This article is available free of charge [9] Anders Linnér. Some properties of the curve straightening flow in the plane . Trans. Amer. Math. Soc. 314 (1989) 605-618. MR 989580. Abstract, references, and article information View Article: PDF This article is available free of charge [10] J. B. Wilker. Space curves that point almost everywhere . Trans. Amer. Math. Soc. 250 (1979) 263-274. MR 530055. Abstract, references, and article information View Article: PDF This article is available free of charge [11] E. P. Lane. The moving trihedron . Trans. Amer. Math. Soc. 36 (1934) 696-710. MR 1501761. Abstract, references, and article information View Article: PDF This article is available free of charge [12] W. C. Graustein. Parallelism and equidistance in classical differential geometry . Trans. Amer. Math. Soc. 34 (1932) 557-593. MR 1501651. Abstract, references, and article information View Article: PDF This article is available free of charge [13] E. H. Cutler. On the curvatures of a curve in Riemann space . Trans. Amer. Math. Soc. 33 (1931) 832-838. MR 1501619. Abstract, references, and article information View Article: PDF This article is available free of charge [14] Arthur Ranum. Errata: The singular points of analytic space-curves'' [Trans.\ Amer.\ Math.\ Soc. {\bf 31} (1929), no. 1, 145--163; 1501473] . Trans. Amer. Math. Soc. 31 (1929) 931. MR 1500506. Abstract, references, and article information View Article: PDF This article is available free of charge [15] Arthur Ranum. The singular points of analytic space-curves . Trans. Amer. Math. Soc. 31 (1929) 145-163. MR 1501473. Abstract, references, and article information View Article: PDF This article is available free of charge [16] C. E. Weatherburn. On curvilinear congruences . Trans. Amer. Math. Soc. 31 (1929) 117-132. MR 1501471. Abstract, references, and article information View Article: PDF This article is available free of charge [17] R. M. Mathews. Cubic curves and desmic surfaces. II . Trans. Amer. Math. Soc. 30 (1928) 19-23. MR 1501418. Abstract, references, and article information View Article: PDF This article is available free of charge [18] Philip Franklin. Osculating curves and surfaces . Trans. Amer. Math. Soc. 28 (1926) 400-416. MR 1501353. Abstract, references, and article information View Article: PDF This article is available free of charge [19] Jesse Douglas. Normal congruences and quadruply infinite systems of curves in space . Trans. Amer. Math. Soc. 26 (1924) 68-100. MR 1501265. Abstract, references, and article information View Article: PDF This article is available free of charge [20] O. D. Kellogg. Some properties of spherical curves, with applications to the gyroscope . Trans. Amer. Math. Soc. 25 (1923) 501-524. MR 1501257. Abstract, references, and article information View Article: PDF This article is available free of charge [21] Mary F. Curtis. Curves invariant under point-transformations of special type . Trans. Amer. Math. Soc. 23 (1922) 151-172. MR 1501195. Abstract, references, and article information View Article: PDF This article is available free of charge [22] Jesse Douglas. On certain two-point properties of general families of curves . Trans. Amer. Math. Soc. 22 (1921) 289-310. MR 1501175. Abstract, references, and article information View Article: PDF This article is available free of charge [23] James Byrnie Shaw. On triply orthogonal congruences . Trans. Amer. Math. Soc. 21 (1920) 391-408. MR 1501152. Abstract, references, and article information View Article: PDF This article is available free of charge [24] G. M. Green. Nets of space curves . Trans. Amer. Math. Soc. 21 (1920) 207-236. MR 1501141. Abstract, references, and article information View Article: PDF This article is available free of charge [25] E. J. Wilczynski. A set of properties characteristic of a class of congruences connected with the theory of functions . Trans. Amer. Math. Soc. 21 (1920) 409-445. MR 1501153. Abstract, references, and article information View Article: PDF This article is available free of charge [26] Luther Pfahler Eisenhart. Transformations of applicable conjugate nets of curves on surfaces . Trans. Amer. Math. Soc. 19 (1918) 167-185. MR 1501096. Abstract, references, and article information View Article: PDF This article is available free of charge [27] Luther Pfahler Eisenhart. Transformations $T$ of conjugate systems of curves on a surface . Trans. Amer. Math. Soc. 18 (1917) 97-124. MR 1501064. Abstract, references, and article information View Article: PDF This article is available free of charge [28] Percey F. Smith. A theorem for space analogous to Ces\`aro's theorem for plane isogonal systems . Trans. Amer. Math. Soc. 18 (1917) 522-540. MR 1501083. Abstract, references, and article information View Article: PDF This article is available free of charge [29] Chas. T. Sullivan. Scroll directrix curves . Trans. Amer. Math. Soc. 16 (1915) 199-214. MR 1501009. Abstract, references, and article information View Article: PDF This article is available free of charge [30] David F. Barrow. Oriented circles in space . Trans. Amer. Math. Soc. 16 (1915) 235-258. MR 1501011. Abstract, references, and article information View Article: PDF This article is available free of charge Results: 1 to 30 of 44 found Go to page: 1 2	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9007771015167236, "perplexity": 1746.3167436358972}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246641468.77/warc/CC-MAIN-20150417045721-00134-ip-10-235-10-82.ec2.internal.warc.gz"}
https://codereview.stackexchange.com/questions/201843/find-smallest-number-of-squares-that-sum-to-a-number	# Find smallest number of squares that sum to a number Given a positive integer n, find the least number of perfect square numbers (for example, 1, 4, 9, 16, ...) I wrote the following solution: def numSquares(self, n): """ :type n: int :rtype: int """ sqs = [0] nums = {} for x in range(1,n+1): nums[x] = 1 for i in nums: if (i * i) in nums: sqs.append(i * i) T = [x for x in range(n+1)] for i in range(1,len(sqs)): for j in range(1,n+1): if sqs[i] <= j: T[j] = min(T[j],math.floor(j/sqs[i]) + T[j%sqs[i]]) return T[n] I wrote a dynamic-programming solution, storing results in a 1d array, but it seemed that due to the way I was originally calculating the perfect squares, the solution was timing out. I then modified the solution and came up with the one above, but the code is still causing a time out error when run against an input of 4635 for n. How could this solution be optimized to avoid this timeout error? Not an review, but an extended comment: I don't know how this solution can be optimized. The expected solution is radically different, and is based on a couple of theorems from number theory. You should check whether the number is • A perfect square (the answer is obviously 1), or • is a sum of 2 squares (the answer is obviously 2), or • not a Legendre's number, that is $n = 4^a(8b + 7)$ (the answer is 3) • should "is a Legendre's number" be "is not a Legendre's number"? – Jared Goguen Aug 17 '18 at 20:30 • Notice that the time complexity of this solution is still O(sqrt(n)) (like the original solution) since finding if number is sum of 2 squares is O(sqrt(n)). You might be able to reduce time memory complexity. – Yonlif Feb 5 at 17:30 ### Review of your existing code (with some small performance improvements): nums = {} for x in range(1,n+1): nums[x] = 1 creates a dictionary with keys from 1 to n+1, all having the value 1. A more Pythonic way to achieve the same is with dictionary comprehension: nums = { x: 1 for x in range(1, n+1) } This dictionary is then used to create a list of all square numbers not exceeding n: sqs = [0] for i in nums: if (i * i) in nums: sqs.append(i * i) But the same can be done without the help of a dictionary: sqs = [i * i for i in range(1, n + 1) if i * i <= n ] or even more efficiently: sqs = [i * i for i in range(1, math.floor(math.sqrt(n)) + 1)] Note also that the parentheses in above if-condtion are not needed. Instead of iterating of the indices of the sqs list for i in range(1,len(sqs)): # do something with sqs[i] ... it is better to iterate over the list directly: for s in sqs: # do something with s ... math.floor(j/sqs[i]) can be done with an integer division j // sqs[i]. If the order of the nested loops is interchanged then one can leave the inner loop early if the square number becomes too large: for j in range(1, n + 1): for s in sqs: if s <= j: T[j] = min(T[j], j // s + T[j % s]) else: break It is sufficient to update T[j] = min(T[j], 1 + T[j - s]) because T[j - s] is already the correct optimal value. With these changes, the function already becomes a bit faster. My simple performance benchmark is N = 500 start = time.time() l = [numSquares(x) for x in range(1, N)] end = time.time() print((end - start) * 1000) On a 1.2 GHz MacBook I measured roughly 1000 milliseconds with your original code and 600 milliseconds with the improved version def numSquares(n): sqs = [i * i for i in range(1, math.floor(math.sqrt(n)) + 1)] T = [x for x in range(n+1)] for j in range(1, n + 1): for s in sqs: if s <= j: T[j] = min(T[j], 1 + T[j - s]) else: break return T[n] Further possible performance improvements are: • Check some simple cases (e.g n <= 3) in advance. • Check in advance if n is a perfect square. Unfortunately, all these changes are not good enough to pass the LeetCode challenge. Some more remarks: • The PEP8 online check reports many PEP8 coding style violations, mainly missing (horizontal) whitespace. • Some variable names can be improved, e.g. squares instead of sqs. It is also unclear what T stands for. ### An alternative approach As it turns out, it is more efficient to compute sets with sums of 2, 3, 4, ... square numbers, until the given number occurs in such a set. This leads to the following implementation def numSquares(n): if n <= 3: return n squares = { i * i for i in range(1, math.floor(math.sqrt(n)) + 1) } sums = squares for i in range(1, n): if n in sums: return i sums = { a + b for a in squares for b in sums if a + b <= n } The above benchmark runs in approximately 100 milliseconds (i.e. faster than the original by a factor of 10), and this also passed the LeetCode challenge. Here is my solution. Thanks to @Martin R. def numSquares(self, n): f = [float("inf")] * (n + 1) f[0] = 0 sqs = [xx for x in range(n + 1) if xx <= n] for i in range(1, n + 1): for sq in sqs: if sq > i: break f[i] = min(f[i], f[i - sq] + 1) return f[n] • Welcom to Code Review, unlike stackoverflow.com we are here to provide pointers to the poster of the question suggesting how they can improve their code. Generally an alternate solution is not a good answer. Can you explain why the solution you provided is better and maybe provide some pointers to the poster on how they can improve their code. You might want to see codereview.stackexchange.com/help/how-to-answer. – pacmaninbw Apr 29 '19 at 17:41 • Got it. I'll take a look. Thanks for the user guide. – Charlie 木匠 Apr 30 '19 at 17:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5021446943283081, "perplexity": 1987.9347827638749}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738982.70/warc/CC-MAIN-20200813103121-20200813133121-00089.warc.gz"}
http://mathhelpforum.com/pre-calculus/173995-questions-about-dot-product-vectors-print.html	# Questions about Dot Product (Vectors) • March 9th 2011, 10:14 AM StuckOnVectors This is my first post here so I'm sorry if this isn't the right section (didn't see a vectors subforum). I am also not sure how to put arrows on top of letters, so assume that every letter in the following question is a vector. I will also use \| \| for magnitude. 1. \|a\| = 3 , \|b\| = 2 , the angle in between these vectors is 60 Determine the numerical value of (3a + 2b) dot (4a - 3b). - In order to do this I tried distributing. I know that (3a dot 4a) = 12\|a\|² and (2b dot -3b) = -6\|b\|² I however don't know what to do in the case of (3a dot -3b) and (2b dot 4a) The formula given is ( \|a\|\|b\|cosθ = a dot b ) and the final answer is 81 as listed in the back of the book. 2. A regular hexagon has sides of 3cm, as shown below. Determine a dot b. http://i180.photobucket.com/albums/x...onquestion.png This is my drawing - I slid b over resulting in an angle of 120 between a and b. I used the above formula to yield: \|3\|\|3\|cos120 = -4.5 The answer in the back of the book is however 4.5 (positive, not negative). This has also occurred in other questions where I am getting negative answers where they should be positive - is there something I'm not doing right? All help would be greatly appreciated. • March 9th 2011, 10:23 AM Plato Quote: Originally Posted by StuckOnVectors 1. \|a\| = 3 , \|b\| = 2 , the angle in between these vectors is 60 Determine the numerical value of (3a + 2b) dot (4a - 3b). - In order to do this I tried distributing. I know that (3a dot 4a) = 12\|a\|² and (2b dot -3b) = -6\|b\|² I however don't know what to do in the case of (3a dot -3b) and (2b dot 4a) The formula given is ( \|a\|\|b\|cosθ = a dot b ) and the final answer is 81 as listed in the back of the book. $\frac{a\cdot b}{\\|a\\|\\|b\\|}=\cos(60^o)=\frac{1}{2}$ $\alpha a\cdot \beta b=(\alpha\beta)a\cdot b$ $a\cdot a=\\|a\\|^2$ • March 9th 2011, 10:32 AM TheChaz So, roughly speaking (!), we have $12a^2 - ab - 6b^2$ after distributing. "a" = 3, "b" = 2, and "ab" = 3 by following Plato's computation. • March 9th 2011, 10:57 AM StuckOnVectors I'm still just not understanding.. How did you come up with -ab = -3? I know that you have to use the formula, I just don't get how. • March 9th 2011, 12:46 PM earboth 1 Attachment(s) Quote: Originally Posted by StuckOnVectors 2. A regular hexagon has sides of 3cm, as shown below. Determine a dot b. This is my drawing - I slid b over resulting in an angle of 120 between a and b. I used the above formula to yield: \|3\|\|3\|cos120 = -4.5 The answer in the back of the book is however 4.5 (positive, not negative). This has also occurred in other questions where I am getting negative answers where they should be positive - is there something I'm not doing right? All help would be greatly appreciated. The vectors including an angle had to be placed tail to tail and not - as you did - head to tail. Or in other words: The arrows representing vectors had to start at the vertex of the angle. • March 9th 2011, 05:08 PM StuckOnVectors earboth thank you for the help, I see where I went wrong with the hexagon thechaz the problem was that I didn't know how to get to $12a^2 - a \cdot b - 6b^2$, but i figured it out anyone reading this: $3a \cdot -3b$ is the same thing as $-9a \cdot b$ - not knowing this was my problem	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9416371583938599, "perplexity": 816.5016215297453}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1433195035316.21/warc/CC-MAIN-20150601214355-00090-ip-10-180-206-219.ec2.internal.warc.gz"}
https://www.first-learn.com/omission-of-the-antecedent.html	# Omission of the Antecedent In English Grammar, an Antecedent is an expression (word, phrase, clause, sentence etc.) that gives its meaning to a Proform (pronoun, proverb, pro- adverb). A Proform, on the other hand, we can say, borrows its meaning from its Antecedent. The Antecedent usually appears earlier in the same sentence or in a previous sentence. Each Pronoun should clearly refer to one specific Antecedent. A missing Pronoun Antecedent occurs when the author implies it within the framework of the sentence without actually using it. A true Antecedent, on the other hand is clearly mentioned. General Example: She arrived late because the traffic held her up. (The reason she arrived late is because the traffic held her up.) Examples of Antecedent in case of Relative Pronoun 1. He arrived in the afternoon when nobody was at home.(Prepositional Phrase as Antecedent) 2. Susan lies all the time which everybody knows about. (Entire Clause as Antecedent) · The stereotypical Proform is a Pronoun and the stereotypical Antecedent is the Noun/ Noun Phrase. Examples of Omission of Antecedent: 1. This is (the place) where I found my watch This is where I found my watch. 2. Winter is (the time) when the weather is at its best. Winter in whenthe weather is at its best. Examples 1 and 2 mean exactly the same when the antecedent is omitted because the sense remains intact and no meaning is lost in case of omission. Consider the following examples, used in archaic English. 1. Whom the Gods love, die young. (Those) whom the Gods love, die young 2. Who laughs last, laughs best. (He/ she) who laughs last, laughs best. 3. Who works not shall not eat. (He/ Sh)e who works not, shall not eat. · Sometimes the Noun/ Pronoun which the Relative Pronoun refers to, known as the Antecedent may be omitted, resulting in nil/ negligible loss in meaning. · Omission of the antecedent is frequent in restrictive clauses when the antecedent is easy to infer from the gender and number of the Relative Pronoun such as ‘things’ or ‘man’. If the omitted antecedent would have been the object of the verb or preposition, the Relative Clause, in that case becomes that object. Examples: (The missing antecedent is within brackets) 1. He persuaded whom he could. 2. I distrust whom I do not like. I distrust (those) whom I do not like. 3. We do not like whom we distrust. We do not like (those)whom we distrust. 4. Who strives to help others, helps himself thereby. (He) who strives to help others, helps himself thereby. 5. Who lives honestly, lives nobly. (He/ She) who lives honestly,lives nobly. 6. Who steals my purse, steals trash. (He/She) who steals my purse, steals trash. 7. Who plants trees, loves others than himself. (He)who plants trees, loves others than himself. In all the above sentences, the antecedent is omitted. The Personal Pronoun (he) might be used in each case. 8. This is what he wanted. This is (the thing) that he wanted. English Grammar and Composition	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8110294938087463, "perplexity": 7848.12624504418}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358673.74/warc/CC-MAIN-20211128224316-20211129014316-00372.warc.gz"}
http://math.stackexchange.com/questions/731274/let-abc-be-a-right-triangle-at-a-such-that-bc-2ab-find-angle-acb	# let ABC be a right triangle at A such that $BC=2AB$. Find $\angle ACB$ So let $\triangle ABC$ be a right triangle at vertex $A$ such that $BC=2AB$. Find the $\angle ACB$ How can I find that angle without using cosine, sine and other things? Since I've already figure out how to find it using cos: here's my approach: We denote $\angle ABC$ as $\alpha$ so $\cos\alpha=\frac{AB}{BC}=\frac{AB}{2AB}=\frac{1}{2}$ We do $\cos^{-1}$ to find $\angle ABC$ then we do $90^\circ-\angle ABC$ to find $\angle ACB$. So I'm looking for alternative way. Thanks! -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9938793182373047, "perplexity": 111.17477005294086}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644059455.0/warc/CC-MAIN-20150827025419-00334-ip-10-171-96-226.ec2.internal.warc.gz"}
https://erictleung.com/delete-lines-with-pattern-in-vim	# Delete lines with a pattern in vim In vim, I know you can search and replace text with :s/FINDTHIS/REPLACE/g to replace all occurrences in a line after pressing Ctrl-v. But then, I recently wanted to delete all lines containing a certain pattern and wondered if vim could do this. Turns out. It can. Below is the pattern to delete lines with a certain pattern. :g/searchterm/d The /d indicates we’re deleting lines and leading g stands for “global” in order to affect the entire buffer. The use case I wanted was to delete lines that started with the number zero. We can also use these commands1 to do more complex search and delete. :g/^0/d You can read more here or by pressing :help :g (global changes) and :help :d (delete lines). 1. Apparently, these are called Ex commands. Maybe I’ll cover these in another post.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4897517263889313, "perplexity": 2464.9646625819205}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314641.41/warc/CC-MAIN-20190819032136-20190819054136-00218.warc.gz"}
http://mathhelpforum.com/pre-calculus/23110-some-algebra-distance-formula.html	# Math Help - some algebra and distance formula 1. ## some algebra and distance formula P = (4, -3, 7) Q = (-2, 5, 1) R= (3, 0, k) PR=QR What is K…… using normal algebra i got a slightly off answer.... arrggg 2. Originally Posted by stones44 P = (4, -3, 7) Q = (-2, 5, 1) R= (3, 0, k) PR=QR What is K…… using normal algebra i got a slightly off answer.... arrggg we want $(4 - 3)^2 + (-3 - 0)^2 + (7 - k)^2 = (-2 - 3)^2 + (5 - 0)^2 + (1 - k)^2$ was that what you did? there should be much trouble working these out, the squares will cancel so you need only deal with a linear equation 3. yeah i got it...i was just off 1 number..that messed it ALL up	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7164525985717773, "perplexity": 2448.411198515173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997865523.12/warc/CC-MAIN-20140722025745-00221-ip-10-33-131-23.ec2.internal.warc.gz"}
http://www.go4expert.com/printthread.php?t=21120	Go4Expert (http://www.go4expert.com/) - C (http://www.go4expert.com/forums/c/) - - pls tell me solution for correct output (http://www.go4expert.com/forums/pls-tell-solution-correct-output-t21120/) vipul15singh 26Feb2010 19:28 pls tell me solution for correct output hi here is a program for exponential but it desn,t work properly pls tell me the correction Code: ```#include<stdio.h> #include<conio.h> float expo(float,float,int,float); float term(float,float,float); main() { int n; float e=0.0,t=1.0,x,s=1.0; clrscr(); printf("\nenter variable & no ofterms:="); scanf("%f%d",&x,&n); e=expo(x,t,n,s); printf("\nsum=%f",e); getch(); return; } float expo(float x,float t,int n,float s) { float c=1.0,e=0; if(t<n) { e=term(x,t,c); s=s+e; expo(x,t+1.0,n,s); } return(s); } float term(float x,float t,float c) { if(t>=1) { c=c*(x/t); term(x,t-1,c); } return(c); }``` Fatima Khan 26Feb2010 19:54 Re: pls tell me solution for correct output vipul first of all tell me that whats wrong with it. is there any run time error or compiling error. Abinila 27Feb2010 10:06 Re: pls tell me solution for correct output Tell me what is problem in your code. Whether I need to change your algorithm? vipul15singh 6Mar2010 17:32 Re: pls tell me solution for correct output Quote: Originally Posted by Fatima Khan (Post 64805) vipul first of all tell me that whats wrong with it. is there any run time error or compiling error. fatima, if you are intrested to solve this problem,pls copy the prog and run for x=1 and number of term n=5 vipul15singh 6Mar2010 17:44 Re: pls tell me solution for correct output Quote: Originally Posted by Abinila (Post 64832) Tell me what is problem in your code. Whether I need to change your algorithm? hi abinila,i cant describe the problem but prob in recursion due to this, prog doesn,t able to calculate correct result. if u r really intrested to solve the problem run it for x=1 and n=5 the answer should be 2.7016 virxen 7Mar2010 21:24 Re: pls tell me solution for correct output give us the mathematics solution for this. what equation do you use? vipul15singh 8Mar2010 00:38 Re: pls tell me solution for correct output Quote: Originally Posted by virxen (Post 65277) give us the mathematics solution for this. what equation do you use? hi virxen, thanks it is also my thread for same problem. may u pls tell me a good way for quicksort. virxen 8Mar2010 01:16 Re: pls tell me solution for correct output All times are GMT +5.5. The time now is 22:10.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8555743098258972, "perplexity": 5850.208679162337}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737896527.58/warc/CC-MAIN-20151001221816-00229-ip-10-137-6-227.ec2.internal.warc.gz"}
https://scholarship.rice.edu/handle/1911/10563/browse?value=Feldmann%2C+Anja&type=author	Now showing items 1-2 of 2 • #### On the impact of variability on the buffer dynamics in IP networks (1999-09-20) The main objective of this paper is to demonstrate in the context of a simple TCP/IP-based network that depending on the underlying assumptions about the inherent nature of the variability of network traffic, very different ... • #### TCP/IP traffic dynamics and network performance: A lesson in workload modeling, flow control and trace-driven simulations (2001-04-20) The main objective of this paper is to demonstrate in the context of a simple TCP/IP-based network that depending on the underlying assumptions about the inherent nature of the dynamics of network traffic, very different ...	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9119300246238708, "perplexity": 764.192426653096}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049281978.84/warc/CC-MAIN-20160524002121-00067-ip-10-185-217-139.ec2.internal.warc.gz"}
https://www.hamradiolicenseexam.com/which-exam.htm	# Which Exam to Take? The various license classes and requirements can be confusing, so we’ll try to answer all your questions here. There are no more Morse code exams for any class of ham license. There are still plenty of people using Morse code, and you are quite welcome to join them. You just no longer have to take an exam first. All that's offered now is three different written exams. They all cover the same topics — regulations, operating practices, electronics, propagation, antennas, and safety — but to increasing levels of complexity: Written exam Complexity How many questions Technician (“element 2”) Relatively simple 35 selected from a pool of about 400 questions General (“element 3”) Moderately difficult 35 selected from a pool of about 500 questions Extra (“element 4”) Most difficult 50 selected from a pool of about 700 questions All exams are administered by volunteer examiners (VEs), generally a group of friendly hams from a local club. Exam sessions are held regularly all across the country. Click Where to take the exam to find exam sessions in your area. Upon request, most VE teams will make accommodations for physical disabilities. For example, they can provide exams in Braille which include no figures for the blind. They can read the questions and answer choices aloud to those who have trouble reading. Some VE teams charge a small exam session fee, usually no more than $15, to cover the costs of running the sessions. The FCC regulations state that within a single exam session, for a single exam fee, you can keep taking exams until you either fail one or pass all the way up to Extra. Many HamTestOnline students pass all three exams in one sitting, going from “zero to Extra” in a single session, saving as much as$30 in exam fees in the process. There are six different classes of ham licenses. Three of them are no longer being issued, but hams who held those licenses before the FCC stopped issuing them still retain their license class and its privileges. Class Exam requirements Privileges Novice No longer being issued. Very limited privileges. Technician Technician exam. All privileges in the VHF, UHF, and beyond, mostly useful for local communications. Very limited HF privileges. Technician Plus No longer being issued. Now the same as Technician. General Technician and General exams. All of the above, plus extensive privileges across the entire radio spectrum. Advanced No longer being issued. All of the above, plus some additional spectrum in a few HF bands. Extra Technician, General, and Extra exams. All of the above, plus slightly more spectrum in a few HF bands. Notes: • The “HF” frequencies are most useful for talking around the world by radio. The VHF, UHF, and beyond are most useful for local communication. • An individual can hold only one unexpired license, with one license class, at any given time. For example, if you pass all three exams, you just have an Extra class license, not a separate license for each class. • When Technician Plus licenses are renewed or modified, they are automatically converted to Technician. ## Which class do I need? ### Technician If you’re only interested in talking around town, you only need the Technician class license. ### General If you're interested in emergency communications, you should have a General class license. While much emergency communications is local, that's not always the case. For example, during Katrina, local communication within the affected area was often impossible, and some emergency crews communicated with each other by relaying messages through stations outside of the affected area using HF ham frequencies. In an actual emergency, you're allowed to use any means of communications at your disposal to get the message through. You don't need any license at all. However, to be prepared for an emergency, you need to practice, and for that you need a license. HF communication can be challenging, and it takes time to develop the required skills. If like most hams you are interested in talking all around the world on “shortwave” radio, you also need the General class license. If you live on a boat and want to stay connected using ham single-sideband (SSB), you need the General class. ### Extra Here are some reasons you might want to get the Extra class license: • To have full access to all ham frequencies, including the less crowded Advanced and Extra portions of the bands. Some of the best DX is in the Extra segments. • To get a shorter call sign, which can be a big advantage in a contest or working a pileup. • To have full reciprocal operating privileges when you travel to CEPT countries (Europe, Australia, New Zealand, Israel, etc.). • To be allowed to administer all exam levels as a volunteer examiner. (Click here to become an ARRL VE.) • As a stepping stone for broadcast engineers to obtain the Certified Broadcast Technologist certification. • For the prestige of having the top level license. • It sets your resume or college application apart from the crowd. • To exercise your brain. Any day you don't learn something new is a wasted day! ## Which exams must I take? Which exams you take depends on your situation. Pay careful attention, because the rules are complex: If you have never held a ham radio license, you must start by taking the Technician exam. Once you pass that exam, you can take the General exam, and finally the Extra exam. ### Ham license expired within the past two years The FCC gives a 2-year grace period for renewing your license. You cannot transmit during that grace period, but you can renew your old license without having to take any exams. You don't actually have to renew your grace-period license before taking the upgrade exam. You simply present it at your exam session, and it gives you credit just like an unexpired license. However, if you're right at the end of the grace period, you might want to renew now, in the unlikely event you fail the upgrade exam. ### Expired pre-1987 Technician ham license If you held a Technician class ham radio license issued before March 21, 1987, the FCC gives you “grandfather” credit for the General class exam (element 3). If your pre-1987 Technician license has expired, you can receive a General class license by attending a VE session and doing both of the following: 1. Pass the current Technician exam (element 2), and 2. Present proof to the VEs that you held a Technician class ham radio license issued before March 21, 1987. How to get proof. They will issue you a General class license. There is a recent rule change that will help you. The FCC now gives partial credit for expired General, Advanced, and Amateur Extra class licenses. An expired General or Advanced ham license will give you credit only for the General class exam (element 3). You can receive a General class license by attending a VE session and doing both of the following: 1. Pass the current Technician exam (element 2), and 2. Present proof to the VEs that you once held a General or Advanced class license. How to get proof. There is a recent rule change that will help you. The FCC now gives partial credit for expired General, Advanced, and Amateur Extra class licenses. An expired Amateur Extra ham license will give you credit for the General (element 3) and Extra (element 4) exams. You can receive an Extra class license by attending a VE session and doing both of the following: 1. Pass the current Technician exam (element 2), and 2. Present proof to the VEs that you once held an Extra class license. How to get proof. ### Any other expired ham license If you’re beyond the 2-year grace period, and you didn’t hold a Technician license issued before March, 21, 1987, and you don't have an expired General, Advanced, or Extra class license, you must start from scratch, just as if you had never held a license. Note specifically that the following offer no examination credit: • Expired Technician licenses issued on or after March 21, 1987 ### Unexpired (or within the grace period) Novice license If you hold a Novice class license which has not expired, or is within the 2-year grace period, you get no credit for any exams. To advance you must proceed as if you have no license at all. ### Unexpired (or within the grace period) pre-1987 Technician license If you held a Technician class ham radio license issued before March 21, 1987, the FCC gives you “grandfather” credit for the General class exam (element 3). If your Technician license has not expired (because you have been renewing it every 10 years), you can get an automatic upgrade to the General class without passing any exams. For your automatic upgrade, you must attend a VE session and present proof to the VEs of both of the following facts: 1. That you once held a Technician class ham radio license issued before March 21, 1987, and 2. That you currently hold an unexpired Technician license. They will give you the General class license without requiring you to take any exam. See http://www.arrl.org/exam-element-credit for details. ### Unexpired (or within the grace period) post-1987 Technician license If you hold a Technician class license which has not expired, or is within the 2-year grace period, you get credit for the Technician exam. Your next step is the General exam. ### Unexpired (or within the grace period) Technician Plus license If you hold a Technician Plus class license which has not expired, or is within the 2-year grace period, it's treated the same as a Technician license. ### Unexpired (or within the grace period) General license If you hold a General class license which has not expired, or is within the 2-year grace period, you get credit for the Technician and General exams. The only remaining step is the Extra exam. If you hold an Advanced class license which has not expired, or is within the 2-year grace period, you get credit for the Technician and General exams. The only remaining step is the Extra exam. ### Unexpired (or within the grace period) Extra license If you hold an Extra class license which has not expired, or is within the 2-year grace period, you get credit for the Technician, General, and Extra exams. The only remaining step is the Ultra exam. Just kidding! Congratulations, you've gone as high as you can go! Sorry, Charlie, you get no credit for any of the FCC Commercial Operator’s licenses. You get no credit towards U.S. ham licenses for licenses from other countries. ## How to get proof of an expired license The ARRL has this excellent article about exam credit on their website. The section "Valid Forms of Exam Element Credit for Expired Licenses" gives various options in case you no longer have a copy of your original license. One great option is to show your name in an old Callbook magazine from Fall 1967 or later. (You cannot use earlier Callbooks because they do not indicate the license class.) One terrific resource is the many old issues of the Callbook magazine which have been scanned and uploaded, allowing you to search by name, address, or call sign. The site is tricky to use, but if you cannot remember your old call sign, it may be your only hope! If you are subscribed to one or more of our courses, and you cannot find your Callbook entry on your own, we'll attempt the search for you at no charge. You will need to send us your call sign (if known), approximate dates licensed, first name, middle initial, last name, address (if known), city, and state from the period when you were licensed. Once you have your old Callbook entry, print the page and bring it to the exam session. If you are requesting credit due to a pre-1987 Technician class license, you should also print the Callbook cover so they can verify the date. ## How to prepare for the exams HamTestOnline offers popular and highly successful online courses, combining study materials, question drill, and an electronic tutor to help you learn about ham radio and prepare for the exams at the same time. After all, it should be about learning about your new hobby, not just memorizing the answers. Study with us, and you are guaranteed to pass! ## Where to take the exam Click Where to take the exam to find exam sessions in your area.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30598360300064087, "perplexity": 4515.404158636179}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154175.76/warc/CC-MAIN-20210801092716-20210801122716-00540.warc.gz"}
https://www.irif.fr/seminaires/verif/index	Équipe thématique Modélisation et vérification #### Jour, heure et lieu Le lundi à 11h, salle 1007 #### Prochaines séances Vérification lundi 26 février 2018, 11h00, Salle 1007 Cătălin Hriţcu (INRIA Paris) When Good Components Go Bad: Formally Secure Compilation Despite Dynamic Compromise We propose a new formal criterion for secure compilation, giving strong end-to-end security guarantees for software components written in unsafe, low-level languages with C-style undefined behavior. Our criterion is the first to model _dynamic_ compromise in a system of mutually distrustful components running with least privilege. Each component is protected from all the others—in particular, from components that have encountered undefined behavior and become compromised. Each component receives secure compilation guarantees up to the point when it becomes compromised, after which an attacker can take complete control over the component and use any of its privileges to attack the remaining uncompromised components. More precisely, we ensure that dynamically compromised components cannot break the safety properties of the system at the target level any more than equally privileged components without undefined behavior already could in the source language. To illustrate this model, we build a secure compilation chain for an unsafe language with buffers, procedures, and components. We compile it to a simple RISC abstract machine with built-in compartmentalization and provide thorough proofs, many of them machine-checked in Coq, showing that the compiler satisfies our secure compilation criterion. Finally, we show that the protection guarantees offered by the compartmentalized abstract machine can be achieved at the machine-code level using either software fault isolation or a tag-based reference monitor. Vérification lundi 12 mars 2018, 11h00, Salle 1007 Thomas Colcombet (IRIF & CNRS) Automata and Program Analysis This will be a presentation of a not so sort work in collaboration with Laure Daiaud and Florian Zuleger. We show how recent results concerning quantitative forms of automata help providing refined understanding of the properties of a system (for instance, a program). In particular, combining the size-change abstraction together with results concerning the asymptotic behavior of tropical automata yields extremely fine complexity analysis of some pieces of code. Vérification lundi 19 mars 2018, 11h00, Salle 1007 Rupak Majumdar (MPI-SWS, Germany) tba tba Vérification lundi 26 mars 2018, 11h00, Salle 1007 Ivan Gazeau (LORIA & INRIA Nancy - Grand Est) Automated Verification of Privacy-type Properties for Security Protocols The applied pi-calculus is a powerful framework to model protocols and to define security properties. In this symbolic model, it is possible to verify automatically complex security properties such as strong secrecy, anonymity and unlinkability properties which are based on equivalence of processes. In this talk, we will see an overview of a verification method used by a tool, Akiss. The tool is able to handle - a wide range of cryptographic primitives (in particular AKISS is the only tool able to verify equivalence properties for protocols that use xor); - protocols with else branches (the treatment of disequalities is often complicated). We will also provide some insights on how interleaving due to concurrency can be effectively handled. Vérification lundi 09 avril 2018, 11h00, Salle 1007 Ilya Sergey (University College London, UK) tba tba Vérification lundi 28 mai 2018, 11h00, Salle 1007 Ana Sokolova (Universität Salzburg, Austria) tba tba #### Séances précédentes Vérification lundi 19 février 2018, 11h00, Salle 3052 Adrien Boiret (University of Warsaw) The “Hilbert Method” for Solving Transducer Equivalence Problems. Classical results from algebra, such as Hilbert's Basis Theorem and Hilbert’s Nullstellensatz, have been used to decide equivalence for some classes of transducers, such as HDT0L (Honkala 2000) or more recently deterministic tree-to-string transducers (Seidl, Maneth, Kemper 2015). In this talk, we propose an abstraction of these methods. The goal is to investigate the scope of the “Hilbert method” for transducer equivalence that was described above. Consider an algebra A in the sense of universal algebra, i.e. a set equipped with some operations. A grammar over A is like a context-free grammar, except that it generates a subset of the algebra A, and the rules use operations from the algebra A. The classical context-free grammars are the special case when the algebra A is the free monoid with concatenation. Using the “Hilbert method” one can decide certain properties of grammars over algebras that are fields or rings of polynomials over a field. The “Hilbert method” extends to grammars over certain well-behaved algebras that can be “coded” into fields or rings of polynomials. Finally, for these well-behaved algebras, one can also use the “Hilbert method” to decide the equivalence problem for transducers (of a certain transducer model that uses registers) that input trees and output elements of the well-behaved algebra. In the talk, we give examples and non-examples of well-behaved algebras, and discuss the decidability / undecidability results connected to them. In particular: -We show that equivalence is decidable for transducers that input (possibly ordered) trees and output unranked unordered trees. -We show that equivalence is undecidable for transducers that input words and output polynomials over the rational numbers with one variable (but are allowed to use composition of polynomials). Joint work with Mikołaj Bojańczyk, Janusz Schmude, Radosław Piórkowski at Warsaw University. Vérification jeudi 08 février 2018, 10h30, Salle 3052 Vincent Laporte (IMDEA Software) Provably secure compilation of side-channel countermeasures: the case of cryptographic “constant-time” Software-based countermeasures provide effective mitigation against side-channel attacks, often with minimal efficiency and deployment overheads. Their effectiveness is often amenable to rigorous analysis: specifically, several popular countermeasures can be formalized as information flow policies, and correct implementation of the countermeasures can be verified with state-of-the-art analysis and verification techniques. However, in absence of further justification, the guarantees only hold for the language (source, target, or intermediate representation) on which the analysis is performed. We consider the problem of preserving side-channel countermeasures by compilation for cryptographic “constant-time”, a popular countermeasure against cache-based timing attacks. We present a general method, based on the notion of 2-simulation, for proving that a compilation pass preserves the constant-time countermeasure. Using the Coq proof assistant, we verify the correctness of our method and of several representative instantiations. Vérification lundi 29 janvier 2018, 11h00, Salle 1007 Engel Lefaucheaux (ENS Cachan / IRISA Rennes) Probabilistic Disclosure: Maximisation vs. Minimisation We consider opacity questions where an observation function provides to an external attacker a view of the states along executions and secret executions are those visiting some state from a fixed subset. Disclosure occurs when the observer can deduce from a finite observation that the execution is secret. In a probabilistic and nondeterministic setting, where an internal agent can choose between actions, there are two points of view, depending on the status of this agent: the successive choices can either help the attacker trying to disclose the secret, if the system has been corrupted, or they can prevent disclosure as much as possible if these choices are part of the system design. In the former situation, corresponding to a worst case, the disclosure value is the supremum over the strategies of the probability to disclose the secret (maximisation), whereas in the latter case, the disclosure is the infimum (minimisation). We address quantitative problems (comparing the optimal value with a threshold) and qualitative ones (when the threshold is zero or one) related to both forms of disclosure for a fixed or finite horizon. For all problems, we characterise their decidability status and their complexity. We discover a surprising asymmetry: on the one hand optimal strategies may be chosen among deterministic ones in maximisation problems, while it is not the case for minimisation. On the other hand, for the questions addressed here, more minimisation problems than maximisation ones are decidable. Vérification lundi 22 janvier 2018, 11h00, Salle 1007 Josef Widder (TU Wien) Synthesis of Distributed Algorithms with Parameterized Thresholds Guards Fault-tolerant distributed algorithms are notoriously hard to get right. I present an automated method that helps in that process: the designer provides specifications (the problem to be solved) and a sketch of a distributed algorithm that keeps arithmetic details unspecified. Our tool then automatically fills the missing parts. In particular, I will consider threshold-based distributed algorithms, where a process has to wait until the number of messages it receives reaches a certain threshold, in order to perform an action. Such algorithms are typically used for achieving fault tolerance in distributed algorithms for broadcast, atomic commitment, or consensus. Using this method, one can synthesize distributed algorithms that are correct for every number n of processes and every number t of faults, provided some resilience condition holds, e.g., n > 3t. This approach combines recent progress in parameterized model checking of distributed algorithms—which I also address—with counterexample-guided synthesis. This is joint work with Marijana Lazić, Igor Konnov, and Roderick Bloem. Vérification lundi 15 janvier 2018, 11h00, Salle 1007 Chao Wang (IRIF) Checking Linearizability of Concurrent Priority Queues Efficient implementations of concurrent objects such as atomic collections are essential to modern computing. Unfortunately their correctness criteria — linearizability with respect to given ADT specifications — are hard to verify. Verifying linearizability is undecidable in general, even on classes of implementations where the usual control-state reachability is decidable. In this work we consider concurrent priority queues which are fundamental to many multi-threaded applications like task scheduling or discrete event simulation, and show that verifying linearizability of such implementations is reducible to control-state reachability. This reduction entails the first decidability results for verifying concurrent priority queues with an unbounded number of threads, and it enables the application of existing safety-verification tools for establishing their correctness. Vérification lundi 08 janvier 2018, 11h00, Salle 1007 Jean-Jacques Lévy (IRIF & INRIA) Proofs of graph algorithms with automation and their readability In this talk, we present a proof of correctness for an algorithm computing strongly connected components in a directed graph by Tarjan [1972]. It will be the starting point of a discussion about the readability of formal proofs. This proof was achieved with the Why3 system and the Coq/ssreflect proof assistant. The same proof was redone fully in Coq/ssreflect and Isabelle/HOL. This is joint work with Ran Chen and was presented at VSTTE 2017. The Coq and Isabelle proofs were achieved by Cyril Cohen, Laurent Théry and Stephan Merz. Vérification lundi 11 décembre 2017, 11h00, Salle 1007 Irène Guessarian (IRIF - Unviersité Paris Diderot) Congruence Preservation, Lattices and Recognizability Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave like the operations of the algebra. The first way is to preserve congruences or stable preorders. The second way is to demand that preimages of recognizable sets belong to the lattice or the Boolean algebra generated by the preimages of recognizable sets by “derived unary operations” of the algebra (such as translations, quotients,…). Vérification jeudi 07 décembre 2017, 16h00, Salle 1007 Luke Ong (University of Oxford) Constrained Horn clauses for automatic program verification: the higher-order case Following Björner, McMillan and Rybalchenko, we develop an approach to the automatic verification of higher-order functional programs based on constrained Horn clauses. We introduce constrained Horn clauses in higher-order logic, and decision problems concerning their satisfiability and the safety verification of higher-order programs. We show that, although satisfiable systems of higher-order clauses do not generally have least models, there is a notion of canonical model obtained via a reduction to a problem concerning a kind of monotone logic program. Following work in higher-order program verification, we develop a refinement type system in order to reason about and automate the search for models. This provides a sound but incomplete method for solving the decision problem. Finally, we show that an extension of the decision problem in which refinement types are used directly as guards on existential quantifiers can be reduced to the original problem. This result can be used to show that properties of higher-order functions that are definable using refinement types are also expressible using higher-order constrained Horn clauses. (Joint work with Toby Cathcart Burn and Steven Ramsay.) Vérification mardi 28 novembre 2017, 13h30, Salle 3052 Léon Gondelman (Radboud University, The Netherlands) The Spirit of Ghost Code In the context of deductive program verification, ghost code is part of the program that is added for the purpose of specification. Ghost code must not interfere with regular code, in the sense that it can be erased without any observable difference in the program outcome. In particular, ghost data cannot participate in regular computations and ghost code cannot mutate regular data or diverge. The idea exists in the folklore since the early notion of auxiliary variables and is implemented in many state-of-the-art program verification tools. However, a rigorous definition and treatment of ghost code is surprisingly subtle and few formalizations exist. In this talk, we describe a simple ML-style programming language with mutable state and ghost code. Non-interference is ensured by a type system with effects, which allows, notably, the same data types and functions to be used in both regular and ghost code. We define the procedure of ghost code erasure and we prove its safety using bisimulation. A similar type system, with numerous extensions which we briefly discuss, is implemented in the program verification environment Why3. Vérification lundi 20 novembre 2017, 11h00, Salle 1007 Laurent Fribourg (LSV, CNRS & ENS de Cachan) Euler’s Method Applied to the Control of Switched Systems Hybrid systems are a powerful formalism for modeling and reasoning about cyber-physical systems. They mix the continuous and discrete natures of the evolution of computerized systems. Switched systems are a special kind of hybrid systems, with restricted discrete behaviours: those systems only have finitely many different modes of (continuous) evolution, with isolated switches between modes. Such systems provide a good balance between expressiveness and controllability, and are thus in widespread use in large branches of industry such as power electronics and automotive control. The control law for a switched system defines the way of selecting the modes during the run of the system. Controllability is the problem of (automatically) synthezing a control law in order to satisfy a desired property, such as safety (maintaining the variables within a given zone) or stabilisation (confinement of the variables in a close neighborhood around an objective point). In order to compute the control of a switched system, we need to compute the solutions of the differential equations governing the modes. Euler’s method is the most basic technique for approximating such solutions. We present here an estimation of the Euler’s method local error, using the notion of “one-sided Lispchitz constant’’ for modes. This yields a general synthesis approach which can encompass uncertain parameters, local information and stochastic noise. We will sketch out how the approach relates with other symbolic methods based on interval arithmetic and Lyapunov functions. We will also present some applicative examples which illustrate its advantages and limitations. Vérification lundi 13 novembre 2017, 11h00, Salle 1007 Viktor Vafeiadis (MPI-SWS) Effective Stateless Model Checking for C/C++ Concurrency I will present a stateless model checking algorithm for verifying concurrent programs running under RC11, a repaired version of the C/C++11 memory model without dependency cycles. Unlike previous approaches, which enumerate thread interleavings up to some partial order reduction improvements, our approach works directly on execution graphs and (in the absence of RMW instructions and SC atomics) avoids redundant exploration by construction. We have implemented a model checker, called RCMC, based on this approach and applied it to a number of challenging concurrent programs. Our experiments confirm that RCMC is significantly faster, scales better than other model checking tools, and is also more resilient to small changes in the benchmarks. (This is joint work with Michalis Kokologiannakis, Ori Lahav, and Konstantinos Sagonas, and will appear at POPL'18.) Vérification lundi 30 octobre 2017, 11h00, Salle 1007 Suha Mutluergil (Koç University) Proving linearizability using forward simulations Linearizability is the standard correctness criterion for concurrent data structures such as stacks and queues. It allows to establish observational refinement between a concurrent implementation and an atomic reference implementation. Proving linearizability requires identifying linearization points for each method invocation along all possible computations, leading to valid sequential executions, or alternatively, establishing forward and backward simulations. In both cases, carrying out proofs is hard and complex in general. In particular, backward reasoning is difficult in the context of programs with data structures, and strategies for identifying statically linearization points cannot be defined for all existing implementations. In this paper, we show that, contrary to common belief, many such complex implementations, including, e.g., the Herlihy & Wing Queue and the Time-Stamped Stack, can be proved correct using only forward simulation arguments. This leads to simple and natural correctness proofs for these implementations that are amenable to automation. Vérification lundi 23 octobre 2017, 11h00, Salle 1007 Raphaël Caudelier (IRIF - Université Paris Diderot) FocaLiZe and Dedukti to the Rescue for Proof Interoperability Numerous contributions have been made for some years to allow users to exchange formal proofs between different provers. The main propositions consist in ad hoc pointwise translations, e.g. between HOL Light and Isabelle in the Flyspeck project or uses of more or less complete certificates. We propose a methodology to combine proofs coming from different theorem provers. This methodology relies on the Dedukti logical framework as a common formalism in which proofs can be translated and combined. To relate the independently developed mathematical libraries used in proof assistants, we rely on the structuring features offered by FoCaLiZe, in particular parameterized modules and inheritance to build a formal library of transfer theorems called MathTransfer. We finally illustrate this methodology on the Sieve of Eratosthenes, which we prove correct using HOL and Coq in combination. Vérification lundi 16 octobre 2017, 11h00, Salle 1007 Noam Rineztky (Tel-Aviv University) Verifying Equivalence of Spark Programs Apache Spark is a popular framework for writing large scale data processing applications. Our long term goal is to develop automatic tools for reasoning about Spark programs. This is challenging because Spark programs combine database-like relational algebraic operations and aggregate operations, corresponding to (nested) loops, with User Defined Functions (UDFs). In this paper, we present a novel SMT-based technique for verifying the equivalence of Spark programs. We model Spark as a programming language whose semantics imitates Relational Algebra queries (with aggregations) over bags (multisets) and allows for UDFs expressible in Presburger Arithmetics. We prove that the problem of checking equivalence is undecidable even for programs which use a single aggregation operator. Thus, we present sound techniques for verifying the equivalence of interesting classes of Spark programs, and show that it is complete under certain restrictions. We implemented our technique, and applied it to a few small, but intricate, test cases. Joint work with: Shelly Grossman, Sara Cohen, Shachar Itzhaky, and Mooly Sagiv Presented in CAV’17 Vérification lundi 09 octobre 2017, 11h00, Salle 1007 Javier Esparza (Technische Universität München) Polynomial Analysis Algorithms for Free-Choice Workflow Nets Workflow Petri nets are a successful formalism for modelling, simulating, and analyzing business processes. In this area, free-choice workflow nets play an important role: Core formalisms for business processes can be translated into free-choice nets, and many industrial models are free-choice. While the state space of a free-choice net can grow exponentially in its number of nodes, numerous control-flow properties can still be decided in polynomial time. However, these decision algorithms cannot be extended to workflow nets with data. We present a new analysis technique, based on reduction rules, that can be applied to workflow nets with data, costs, or probabilities. In particular, we give a polynomial algorithm to compute the expected cost of sound free-choice workflow nets. Vérification lundi 02 octobre 2017, 11h00, Salle 1007 Ahmed Bouajjani (IRIF - Université Paris Diderot) Verifying Robustness of Event-Driven Asynchronous Programs Against Concurrency We define a correctness criterion, called robustness against concurrency, for a class of event-driven asynchronous programs that are at the basis of modern UI frameworks in Android, iOS, and Javascript. A program is robust when all possible behaviors admitted by the program under arbitrary procedure and event interleavings are admitted even if asynchronous procedures (respectively, events) are assumed to execute serially, one after the other, accessing shared memory in isolation. We characterize robustness as a conjunction of two correctness criteria: event-serializability (i.e., events can be seen as atomic) and event-determinism (executions within each event are insensitive to the interleavings between concurrent tasks dynamically spawned by the event). Then, we provide efficient algorithms for checking these two criteria based on polynomial reductions to reachability problems in sequential programs. This result is surprising because it allows to avoid explicit handling of all concurrent executions in the analysis, which leads to an important gain in complexity. We demonstrate via case studies on Android apps that the typical mistakes programmers make are captured as robustness violations, and that violations can be detected efficiently using our approach. Joint work with Michael Emmi, Constantin Enea, Burcu Kulahcioglu Ozkan, and Serdar Tasiran. Vérification mercredi 28 juin 2017, 14h00, Salle 3052 Giuliano Losa (UCLA) Paxos Made EPR — Decidable Reasoning about Distributed Consensus Distributed protocols such as Paxos play an important role in many computer systems. Therefore, a bug in a distributed protocol may have tremendous effects. Accordingly, a lot of effort has been invested in verifying such protocols. However, checking invariants of such protocols is undecidable and hard in practice, as it requires reasoning about an unbounded number of nodes and messages. Moreover, protocol actions and invariants involve higher-order concepts such as set cardinalities, arithmetic, and complex quantification. This paper makes a step towards automatic verification of such protocols. We aim at a technique that can verify correct protocols and identify bugs in incorrect protocols. To this end, we develop a methodology for deductive verification based on effectively propositional logic (EPR)—a decidable fragment of first-order logic (also known as the Bernays-Sch\“onfinkel-Ramsey class). In addition to decidability, EPR also enjoys the finite model property, allowing to display violations as finite structures which are intuitive for users. Our methodology involves modeling protocols using general (uninterpreted) first-order logic, and then systematically transforming the model to obtain a model and an inductive invariant that are decidable to check. The steps of the transformations are also mechanically checked, ensuring the soundness of the method. We have used our methodology to verify the safety of Paxos, and several of its variants, including Multi-Paxos, Vertical Paxos, Fast Paxos and Flexible Paxos. To the best of our knowledge, this work is the first to verify these protocols using a decidable logic, and the first formal verification of Vertical Paxos and Fast Paxos. This is joint work with O. Padon, M. Sagiv, and S. Shoham. Vérification jeudi 22 juin 2017, 11h00, Salle 3052 Ruzica Piskac (Yale University) New Applications of Software Synthesis: Verification of Configuration Files and Firewalls Repair In this talk we present a new approach for verification for configuration files. Software failures resulting from configuration errors have become commonplace as modern software systems grow increasingly large and more complex. The lack of language constructs in configuration files, such as types and grammars, has directed the focus of a configuration file verification towards building post-failure error diagnosis tools. We describe a framework which analyzes data sets of correct configuration files and synthesizes rules for building a language model from the given data set. The resulting language model can be used to verify new configuration files and detect errors in them. We also outline a systematic effort that can automatically repair firewalls, using the programming by example approach. Firewalls are widely employed to manage and control enterprise networks. Because enterprise-scale firewalls contain hundreds or thousands of policies, ensuring the correctness of firewalls - whether the policies in the firewalls meet the specifications of their administrators - is an important but challenging problem. In our approach, after an administrator observes undesired behavior in a firewall, she may provide input/output examples that comply with the intended behavior. Based on the given examples, we automatically synthesize new firewall rules for the existing firewall. This new firewall correctly handles packets specified by the examples, while maintaining the rest of the behavior of the original firewall. Vérification lundi 12 juin 2017, 14h00, Salle 3052 Thomas Wies (New York University) A Simple Framework for Verifying Concurrent Search Structures We present an abstract framework for verifying concurrent algorithms on search data structures that support dictionaries. The framework can be specialized to every search data structure we know, from linked lists to complex B-trees. We obtain this framework by instantiating RGSep, which is a program logic that combines rely-guarantee reasoning and separation logic. RGSep is parameterized by a so-called resource algebra, which is typically the standard heap model of separation logic. Instead of using the standard heap model, we develop a new resource algebra that enables compositional reasoning about search graphs. Using this search graph model, we obtain simple correctness proofs of complex concurrent dictionary algorithms. The algorithms and proofs abstract from the specific search data structure that the algorithm operates on and can then be refined to a concrete data structure implementation. Vérification mardi 06 juin 2017, 11h00, Salle 3052 Sergio Rajsbaum (UNAM Mexico) Tasks, objects, and the notion of a distributed problem The universal computing model of Turing, which was central to the birth of modern computer science, identified also the essential notion of a problem, as an input output function to be computed by a Turing machine. In distributed computing, \emph{tasks} are the equivalent of a function: each process gets only part of the input, and computes part of the output after communicating with other processes. In distributed computing tasks have been studied from early on, in parallel, but independently of \emph{sequential objects}. While tasks explicitly state what might happen when a set of processes run concurrently, sequential objects only specify what happens when processes run sequentially. Indeed, many distributed problems considered in the literature, seem to have no natural specification neither as tasks nor as sequential objects. I will concentrate on our recent work on interval-linearizability, a notion we introduced to specify objects more general than the usual sequential objects. I will describe the bridges we establish between these two classical paradigms, and our discussions about what is a distributed problem, and what it means to solve it. Vérification jeudi 01 juin 2017, 11h00, Salle 3052 Orna Grumberg (Technion, Israel) Sound and Complete Mutation-Based Program Repair This work presents a novel approach for automatically repairing an erroneous program with respect to a given set of assertions. Programs are repaired using a predefined set of mutations. We refer to a bounded notion of correctness, even though, for a large enough bound all returned programs are fully correct. To ensure no changes are made to the original program unless necessary, if a program can be repaired by applying a set of mutations $Mut$, then no superset of $Mut$ is later considered. Programs are checked in increasing number of mutations, and every minimal repaired program is returned as soon as found. We impose no assumptions on the number of erroneous locations in the program, yet we are able to guarantee soundness and completeness. That is, we assure that a program is returned iff it is minimal and bounded correct. Searching the space of mutated programs is reduced to searching unsatisfiable sets of constraints, which is performed efficiently using a sophisticated cooperation between SAT and SMT solvers. Similarities between mutated programs are exploited in a new way, by using both the SAT and the SMT solvers incrementally. We implemented a prototype of our algorithm, compared it with a state-of-the-art repair tool and got very encouraging results. This is a joint work with Bat-Chen Rothenberg. Vérification mardi 23 mai 2017, 15h30, Salle 3052 Florian Zuleger (TU Wien) Inductive Termination Proofs by Transition Predicate Abstraction and their relationship to the Size-Change Abstraction The last decade has seen renewed interest in automated techniques for proving the termination of programs. A popular termination criterion is based on the covering of the transitive hull of the transition relation of a program by a finite number of well-founded relations. In an automated analysis, this termination criterion is usually established by an inductive proof using transition predicate abstraction. Such termination proofs have the structure of a finite automaton. These automata, which we call transition automata, are the central object of study in this talk. Our main results are as follows: (1) A previous criterion for termination analysis with transition automata is not complete; we provide a complete criterion. (2) We show how to bound the height of the transition relation of the program using the termination proof by transition predicate abstraction. This result has applications in the automated complexity analysis of programs. (3) We show that every termination proof by transition predicate abstraction gives rise to a termination proof by the size-change abstraction; this connection is crucial to obtain results (1) and (2) from previous results on the size-change abstraction. Further, our result establishes that transition predicate abstraction and size-change abstraction have the same expressivity for automated termination proofs. Vérification lundi 22 mai 2017, 11h00, Salle 1007 Alain Finkel (LSV, ENS Cachan) The Erdös & Tarski theorem. A new class of WSTS without WQO. We present the ideal framework which was recently used to obtain new deep results on Petri nets and extensions. We will present the proof of the famous but unknown Erdös-Tarski theorem. We argue that the theory of ideals prompts a renewal of the theory of WSTS by providing a way to define a new class of monotonic systems, the so-called Well Behaved Transition Systems, which properly contains WSTS, and for which coverability is still decidable by a forward algorithm. Vérification lundi 27 mars 2017, 11h00, Salle 1007 Mohamed Faouzi Atig (Uppsala University) Lossy Channel Systems with Data. Lossy channel systems are a classical model with applications ranging from the modelling of communication protocols to programs running on weak memory models. All existing work assume that messages traveling inside the channels are picked from a finite alphabet. In this talk, we present two extensions of lossy channel systems. In the first part of the talk, we extend lossy channel systems by assuming that each message is equipped with a clock representing the age of the message, thus obtaining the model of Timed Lossy Channel Systems (TLCS). We show that the state reachability problem is decidable for TLCS. In the second part of the talk, we extend lossy channel systems by considering systems that operate on a finite set of variables ranging over an infinite data domain. Furthermore, each message inside a channel is equipped with a data item representing its value. Although we restrict the model by allowing the variables to be only tested for (dis-)equality, we show that the state reachability problem is undecidable. In light of this negative result, we consider bounded-phase reachability, where the processes are restricted to performing either send or receive operations during each phase. We show decidability of state reachability in this case by computing a symbolic encoding of the set of system configurations that are reachable from a given configuration. This talk is based on previous joint work with Parosh Aziz Abdula, Jonathan Cederberg and C. Aiswarya. Vérification lundi 20 mars 2017, 11h00, Salle 1007 Andreas Podelski (University of Freiburg) Proving Liveness of Parameterized Programs Correctness of multi-threaded programs typically requires that they satisfy liveness properties. For example, a program may require that no thread is starved of a shared resource, or that all threads eventually agree on a single value. This paper presents a method for proving that such liveness properties hold. Two particular challenges addressed in this work are that (1) the correctness argument may rely on global behaviour of the system (e.g., the correctness argument may require that all threads collectively progress towards “the good thing” rather than one thread progressing while the others do not interfere), and (2) such programs are often designed to be executed by any number of threads, and the desired liveness properties must hold regardless of the number of threads that are active in the program. This is joint work with Azadeh Farzan and Zachary Kincaid and published at LICS 2016 (http://www.cs.princeton.edu/~zkincaid/pub/lics16.pdf) Vérification lundi 13 mars 2017, 11h00, Salle 1007 Ori Lahav (MPI Kaiserslautern) A Promising Semantics for Relaxed-Memory Concurrency Despite many years of research, it has proven very difficult to develop a memory model for concurrent programming languages that adequately balances the conflicting desiderata of programmers, compilers, and hardware. In this paper, we propose the first relaxed memory model that (1) accounts for nearly all the features of the C++11 concurrency model, (2) provably validates a number of standard compiler optimizations, as well as a wide range of memory access reorderings that commodity hardware may perform, (3) avoids bad “out-of-thin-air” behaviors that break invariant-based reasoning, (4) supports “DRF” guarantees, ensuring that programmers who use sufficient synchronization need not understand the full complexities of relaxed-memory semantics, and (5) defines the semantics of racy programs without relying on undefined behaviors, which is a prerequisite for applicability to type-safe languages like Java. The key novel idea behind our model is the notion of promises: a thread may promise to execute a write in the future, thus enabling other threads to read from that write out of order. Crucially, to prevent out-of-thin-air behaviors, a promise step requires a thread-local certification that it will be possible to execute the promised write even in the absence of the promise. To establish confidence in our model, we have formalized most of our key results in Coq. Joint work with Jeehoon Kang, Chung-Kil Hur, Viktor Vafeiadis, and Derek Dreyer, recently presented at POPL'17 Vérification lundi 06 mars 2017, 11h00, Salle 1007 Arguments about correctness of a concurrent data structure are typically carried out by using the notion of linearizability and specifying the linearization points of the data structure's procedures. Such arguments are often cumbersome as the linearization points' position in time can be dynamic (depend on the interference, run-time values and events from the past, or even future), non-local (appear in procedures other than the one considered), and whose position in the execution trace may only be determined after the considered procedure has already terminated. In this talk I will present a new method, based on a separation-style logic, for reasoning about concurrent objects with such linearization points. We embrace the dynamic nature of linearization points, and encode it as part of the data structure's auxiliary state, so that it can be dynamically modified in place by auxiliary code, as needed when some appropriate run-time event occurs. We have named the idea linking-in-time, because it reduces temporal reasoning to spatial reasoning. For example, modifying a temporal position of a linearization point can be modeled similarly to a pointer update in separation logic. Furthermore, the auxiliary state provides a convenient way to concisely express the properties essential for reasoning about clients of such concurrent objects. In order to illustrate our approach, I will illustrate its application to verify (mechanically in Coq) an intricate optimal snapshot algorithm, due to Jayanti. Vérification lundi 27 février 2017, 11h00, Salle 1007 Oded Maler (CNRS and University of Grenoble-Alpes) Monitoring: Qualitative and Quantitative, Real and Virtual, Online and Offline In this talk I will present some of the research I have been involved in concerning the specification and monitoring of timed, continuous and hybrid behaviors using formalism such as Signal Temporal Logic and Timed Regular Expressions. I will discuss the similarities and differences between properties/assertions and other “measures” which are used in many application domains to evaluate behaviors, as well as the difference between monitoring real systems during their execution and monitoring simulated models during the system design phase. Vérification lundi 20 février 2017, 11h00, Salle 1007 Loig Jezequel (L2SN - Nantes) Lazy Reachability Analysis in Distributed Systems We address the problem of reachability in distributed systems, modelled as networks of finite automata and propose and prove a new algorithm to solve it efficiently in many cases. This algorithm allows to decompose the reachability objective among the components, and proceeds by constructing partial products by lazily adding new components when required. It thus constructs more and more precise over-approximations of the complete product. This permits early termination in many cases, in particular when the objective is not reachable, which often is an unfavorable case in reachability analysis. We have implemented this algorithm in a first prototype and provide some very encouraging experimental results. Vérification lundi 23 janvier 2017, 11h00, Salle 1007 Andrea Cerone (Imperial College London) Analysing Snapshot Isolation Snapshot isolation (SI) is a widely used consistency model for transaction processing, implemented by most major databases and some of transactional memory systems. Unfortunately, its classical definition is given in a low-level operational way, by an idealised concurrency-control algorithm, and this complicates reasoning about the behaviour of applications running under SI. We give an alternative specification to SI that characterises it in terms of transactional dependency graphs of Adya et al., generalising serialization graphs. Unlike previous work, our characterisation does not require adding additional information to dependency graphs about start and commit points of transactions. We then exploit our specification to obtain two kinds of static analyses. The first one checks when a set of transactions running under SI can be chopped into smaller pieces without introducing new behaviours, to improve performance. The other analysis checks whether a set of transactions running under a weakening of SI behaves the same as when it running under SI. Vérification lundi 12 décembre 2016, 11h00, Salle 1007 Bin Fang (IRIF(Paris), ECNU (China)) Hierarchical Shape Abstraction for Analysis of Free-List Memory Allocators (a logic-based approach) We propose a hierarchical abstract domain for the analysis of free list memory allocators that tracks shape and numerical properties about both the heap and the free lists. Our domain is based on Separation Logic extended with predicates that capture the pointer arithmetics constraints for the heap list and the shape of the free list. These predicates are combined using a hierarchical composition operator to specify the overlapping of the heap list by the free list. In addition to expressiveness, this operator leads to a compositional and compact representation of abstract values and simplifies the implementation of the abstract domain. The shape constraints are combined with numerical constraints over integer arrays to track properties about the allocation policies (best-fit, first-fit, etc). Such properties are out of the scope of the existing analyzers. We implemented this domain and we show its effectiveness on several implementations of free list allocators. Vérification vendredi 09 décembre 2016, 11h00, Salle 3052 Alastair Donaldson (Imperial College London) Exposing Errors Related to Weak Memory in GPU Applications In this presentation, I will describe a project led by my PhD student Tyler Sorensen, on the systematic design of a testing environment that uses stressing and fuzzing to reveal errors in GPU applications that arise due to weak memory effects. This approach is evaluated across several CUDA applications that use fine-grained concurrency, on seven GPUs spanning three Nvidia architectures. The results show that applications that rarely, or never, exhibit errors related to weak memory when executed natively can readily exhibit these errors when executed in the testing environment. The testing environment also provides a means to identify the root causes of erroneous weak effects, and automatically suggests how to insert fences that experimentally eliminate these errors. This empirical fence insertion method carries significantly lower overhead, in terms of execution time and energy consumption, than a more conservative, guaranteed-sound approach. Vérification lundi 05 décembre 2016, 11h00, Salle 1007 Guilhem Jaber (IRIF) SyTeCi: Symbolic, Temporal and Circular reasoning for automatic proofs of contextual equivalence Operational Techniques (Kripke Logical Relations and Environmental/Open/Parametric Bisimulations) have matured enough to become now formidable tools to prove contextual equivalence of effectful higher-order programs. However, it is not yet possible to automate such proofs – the problem being of course in general undecidable. In this talk, we will see how to take the best of these techniques to design an automatic procedure which is able many non-trivial examples of equivalence, including most of the examples from the literature. The talk will describe the main ingredients of this method: - Symbolic reduction to evaluate of programs, - Transition systems of heap invariants, as used with Kripke Logical Relations, - Temporal logic to abstract over the control flow between the program and its environment, - Circular proofs to automate the reasoning over recursive functions. Using them, we will see how we can reduce contextual equivalence to the problem of non-reachability in some automatically generated transition systems of invariants. Vérification lundi 28 novembre 2016, 11h00, Salle 1007 Georg Zetzsche (LSV, ENS Cachan) First-order logic with reachability for infinite-state systems First-order logic with the reachability predicate (FOR) is an important means of specification in system analysis. Its decidability status is known for some individual types of infinite-state systems such as pushdown (decidable) and vector addition systems (undecidable). This work aims at a general understanding of which types of systems admit decidability. As a unifying model, we employ valence systems over graph monoids, which feature a finite-state control and are parameterized by a monoid to represent their storage mechanism. As special cases, this includes pushdown systems, various types of counter systems (such as vector addition systems) and combinations thereof. Our main result is a characterization of those graph monoids where FOR is decidable for the resulting transition systems. Vérification jeudi 24 novembre 2016, 15h00, Salle 3052 Gennaro Parlato (University of Southampton) A Pragmatic Bug-finding Approach for Concurrent Programs Concurrency poses a major challenge for program verification, but it can also offer an opportunity to scale when subproblems can be analysed in parallel. We propose a parameterizable code-to-code translation to generate a set of simpler program variants such that each interleaving of the program is captured by at least one of them. These variants can then be checked autonomously in parallel. Our approach is independent of the tool that is chosen for the final analysis, it is compatible with weak memory models, and it amplifies the effectiveness of existing tools, making them find bugs faster and with fewer resources. We do our experiments using Lazy-CSeq as off-the-shelf final verifier and demonstrate that our approach is able to find bugs in the hardest known concurrency benchmarks in a matter of minutes where other dynamic and static tools fail to conclude. Vérification lundi 14 novembre 2016, 11h00, Salle 1007 Philipp Rümmer (University of Uppsala) Liveness of Randomised Parameterised Systems under Arbitrary Schedulers e consider the problem of verifying liveness for systems with a finite, but unbounded, number of processes, commonly known as parameterised systems. Typical examples of such systems include distributed protocols (e.g. for the dining philosopher problem). Unlike the case of verifying safety, proving liveness is still considered extremely challenging, especially in the presence of randomness in the system. In this paper we consider liveness under arbitrary (including unfair) schedulers, which is often considered a desirable property in the literature of self-stabilising systems. In this paper we introduce an automatic method of proving liveness for randomised parameterised systems under arbitrary schedulers. Viewing liveness as a two-player reachability game (between Scheduler and Process), our method is a CEGAR approach that synthesises a progress relation for Process that can be symbolically represented as a finite-state automaton. The method incrementally constructs a progress relation, exploiting both Angluin's $L*$ algorithm and SAT-solvers. Our experiments show that our algorithm is able to prove liveness automatically for well-known randomised distributed protocols, including Lehmann-Rabin Randomised Dining Philosopher Protocol and randomised self-stabilising protocols (such as the Israeli-Jalfon Protocol). To the best of our knowledge, this is the first fully-automatic method that can prove liveness for randomised protocols. Joint work with Anthony W. Lin. Vérification lundi 24 octobre 2016, 11h00, Salle 1007 Sylvain Schmitz (LSV - ENS Cachan) Ideal Decompositions for Vector Addition Systems Vector addition systems, or equivalently Petri nets, are one of the most popular formal models for the representation and the analysis of parallel processes. Many problems for vector addition systems are known to be decidable thanks to the theory of well-structured transition systems. Indeed, vector addition systems with configurations equipped with the classical point-wise ordering are well-structured transition systems. Based on this observation, problems like coverability or termination can be proven decidable. However, the theory of well-structured transition systems does not explain the decidability of the reachability problem. In this presentation, we show that runs of vector addition systems can also be equipped with a well quasi-order. This observation provides a unified understanding of the data structures involved in solving many problems for vector addition systems, including the central reachability problem. Joint work with Jérôme Leroux. Vérification lundi 10 octobre 2016, 11h00, Salle 1007 Steven de Oliveira (CEA) Polynomial invariants by linear algebra One of the main issue in formal verification is the analysis of loops, considered as a major research problem since the 70s. Program verification based on Floyd-Hoare's inductive assertion and CEGAR-like techniques for model-checking uses loop invariants in order to reduce the problem to an acyclic graph analysis instead of unrolling or accelerating loops. I will present in this talk a new technique for generating polynomial invariants, divided in two independent parts : a procedure that reduces a class of loops containing polynomial assignments to linear loops and a procedure for generating inductive invariants for linear loops. Both of these techniques have a polynomial complexity for a bounded number of variables and we guarantee the completeness of the technique for a bounded degree which we successfully implemented for C programs verification as a Frama-C plug-in, PILAT. Vérification lundi 03 octobre 2016, 11h00, Salle 1007 Giovanni Bernardi (IRIF) Robustness against Consistency Models with Atomic Visibility To achieve scalability, modern Internet services often rely on distributed databases with consistency models for transactions weaker than serializability. At present, application programmers often lack techniques to ensure that the weakness of these consistency models does not violate application correctness. In this talk I will present criteria to check whether applications that rely on a database providing only weak consistency are robust, i.e., behave as if they used a database providing serializability, and I will focus on a consistency model called Parallel Snapshot Isolation. The results I will outline handle systematically and uniformly several recently proposed weak consistency models, as well as a mechanism for strengthening consistency in parts of an application. Vérification lundi 26 septembre 2016, 11h00, Salle 1007 Arnaud Sangnier (IRIF) Fixpoints in VASS: Results and Applications VASS (Vector Addition Systems with States), which are equivalent to Petri nets, are automata equipped with natural variables that can be decremented or incremented. VASS are a powerful model which has been intensively studied in the last decades. Many verification techniques have been developed to analyse them and the frontier between the decidable and undecidable problems related to VASS begins to be well known. One interesting point is that the model-checking of linear temporal logics (like LTL or linear mu-calculus) is decidable for this model but this is not anymore the case when considering branching time temporal logics. However some restrictions can be imposed on the logics and on the studied system in order to regain decidability. In this talk, we will present these results concerning the model-checking of VASS and the techniques leading to the decidability results. We will then show how these techniques and results can be used to analyse some extensions of VASS with probabilities, namely probabilistic VASS and VASS Markov Decision Processes. Vérification lundi 19 septembre 2016, 11h00, Salle 1007 Francesco Belardinelli (Université d'Evry) Abstraction-based Verification of Infinite-state Data-aware Systems Data-aware Systems (DaS) are a novel paradigm to model business processes in Service-oriented Computing. DaS are best described in terms of interacting modules consisting of a data model and a lifecycle, which account respectively for the relational structure of data and their evolution over time. However, by considering data and processes as equally relevant tenets of DaS, the typical questions concerning their verification are hardly amenable by current methodologies. For instance, the presence of data means that the number of states in DaS is infinite in general. In this talk we present recent advances in the verification of DaS. We introduce agent-based abstraction techniques to model check DaS against specifications expressed in temporal and strategy logics. Further, we illustrate how DaS can be useful to model game-theoretic scenarios as well. Specifically, we provide an analysis of English (ascending bid) auctions through DaS. Vérification lundi 30 mai 2016, 11h00, Salle 1007 Thibaut Balabonski (LRI) Low-level C code optimisations: are they valid? ubstantial research efforts have been devoted to tools for reasoning about -and proving properties of- programs. A related concern is making sure that compilers preserve the soundness of programs, that is making sure that the compiled code respects the behavior of the source program (see for instance the CompCert C compiler). This talk is about an attempt at proving the soundness of some basic low-level transformations for concurrent C programs. We will see some elements of the official semantics of concurrency in C, and I will relate how the focus of this work shifted from proving the soundness of program transformations to patching the official semantics. Vérification lundi 14 mars 2016, 11h00, Salle 1007 Paul Gastin (LSV) Formal methods for the verification of distributed algorithms We introduce an automata-theoretic method for the verification of distributed algorithms running on ring networks. In a distributed algorithm, an arbitrary number of processes cooperate to achieve a common goal (e.g., elect a leader). Processes have unique identifiers (pids) from an infinite, totally ordered domain. An algorithm proceeds in synchronous rounds, each round allowing a process to perform a bounded sequence of actions such as send or receive a pid, store it in some register, and compare register contents wrt. the associated total order. An algorithm is supposed to be correct independently of the number of processes. To specify correctness properties, we introduce a logic that can reason about processes and pids. Referring to leader election, it may say that, at the end of an execution, each process stores the maximum pid in some dedicated register. Since the verification of distributed algorithms is undecidable, we propose an underapproximation technique, which bounds the number of rounds. This is an appealing approach, as the number of rounds needed by a distributed algorithm to conclude is often exponentially smaller than the number of processes. We provide an automata-theoretic solution, reducing model checking to emptiness for alternating two-way automata on words. Overall, we show that round-bounded verification of distributed algorithms over rings is PSPACE-complete. Based on a joint work with C. Aiswarya and Benedikt Bollig, extended abstract at CONCUR’15: http://www.lsv.ens-cachan.fr/~gastin/mes-publis.php?onlykey=ABG-concur15. Vérification lundi 07 mars 2016, 11h00, Salle 1007 Julien Signoles (CEA-LIST) Frama-C, a collaborative and extensible framework for C code analysis Frama-C is a source code analysis platform that aims at conducting verification of industrial-size C programs. It provides its users with a collection of plug-ins that perform static analysis, deductive verification, testing and monitoring, for safety- and security-critical software. Collaborative verification across cooperating plug-ins is enabled by their integration on top of a shared kernel and datastructures, and their compliance to a common specification language. This talk presents a consolidated view of the platform, its main and composite analyses, and some of its industrial achievements. It focuses on its specification language ACSL, and on different ways to verify ACSL specifications through static and dynamic analyses. Vérification lundi 29 février 2016, 11h00, Salle 1007 Pierre Fraigniaud (IRIF) Fault-Tolerant Decentralized Runtime Monitoring Runtime verification is aiming at extracting information from a running system, and using it to detect and possibly react to behaviors violating a given correctness property. Decentralized runtime verification involves a set of monitors observing the behavior of the underlying system. In this talk, the investigation of decentralized runtime verification in which not only the elements of the observed system, but also the monitors themselves are subject to failures will be presented. In this context, it is unavoidable that the unreliable monitors may have different views of the underlying system, and therefore may have different valuations of the correctness property. We characterize the number of valuations required for monitoring a given correctness property in a decentralized manner. Our lower bound is independent of the logic used for specifying the correctness property, as well as of the way the set of valuations returned by the monitors is globally interpreted. Moreover, our lower bound is tight in the sense that we design a distributed protocol enabling any given set of monitors to verify any given correctness property using as many different valuations as the one given by this lower bound. 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