id
int32 0
100k
| text
stringlengths 21
3.54k
| source
stringlengths 1
124
| similarity
float32 0.78
0.88
|
|---|---|---|---|
2,000
|
Division algebras, in which multiplicative inverses exist. The finite-dimensional alternative division algebras over the field of real numbers have been classified. They are the real numbers (dimension 1), the complex numbers (dimension 2), the quaternions (dimension 4), and the octonions (dimension 8).
|
Quadratic representation
| 0.836343
|
2,001
|
It is known that most roots of the nth derivatives of J ν ( n ) ( x ) {\displaystyle J_{\nu }^{(n)}(x)} (where n < 18 and J ν ( x ) {\displaystyle J_{\nu }(x)} is the Bessel function of the first kind of order ν {\displaystyle \nu } ) are transcendental. The only exceptions are the numbers ± 3 {\displaystyle \pm {\sqrt {3}}} , which are the algebraic roots of both J 1 ( 3 ) ( x ) {\displaystyle J_{1}^{(3)}(x)} and J 0 ( 4 ) ( x ) {\displaystyle J_{0}^{(4)}(x)} .
|
Square root of 3
| 0.836342
|
2,002
|
Named joint distributions that arise frequently in statistics include the multivariate normal distribution, the multivariate stable distribution, the multinomial distribution, the negative multinomial distribution, the multivariate hypergeometric distribution, and the elliptical distribution.
|
Joint probability
| 0.836325
|
2,003
|
The fundamental prevalence-independent statistics are sensitivity and specificity. Sensitivity or True Positive Rate (TPR), also known as recall, is the proportion of people that tested positive and are positive (True Positive, TP) of all the people that actually are positive (Condition Positive, CP = TP + FN). It can be seen as the probability that the test is positive given that the patient is sick. With higher sensitivity, fewer actual cases of disease go undetected (or, in the case of the factory quality control, fewer faulty products go to the market).
|
Evaluation of binary classifiers
| 0.836278
|
2,004
|
The evaluation of binary classifiers compares two methods of assigning a binary attribute, one of which is usually a standard method and the other is being investigated. There are many metrics that can be used to measure the performance of a classifier or predictor; different fields have different preferences for specific metrics due to different goals. For example, in medicine sensitivity and specificity are often used, while in computer science precision and recall are preferred. An important distinction is between metrics that are independent on the prevalence (how often each category occurs in the population), and metrics that depend on the prevalence – both types are useful, but they have very different properties.
|
Evaluation of binary classifiers
| 0.836278
|
2,005
|
The contingency table and the most common derived ratios are summarized below; see sequel for details. Note that the rows correspond to the condition actually being positive or negative (or classified as such by the gold standard), as indicated by the color-coding, and the associated statistics are prevalence-independent, while the columns correspond to the test being positive or negative, and the associated statistics are prevalence-dependent. There are analogous likelihood ratios for prediction values, but these are less commonly used, and not depicted above.
|
Evaluation of binary classifiers
| 0.836278
|
2,006
|
The basic marginal ratio statistics are obtained by dividing the 2×2=4 values in the table by the marginal totals (either rows or columns), yielding 2 auxiliary 2×2 tables, for a total of 8 ratios. These ratios come in 4 complementary pairs, each pair summing to 1, and so each of these derived 2×2 tables can be summarized as a pair of 2 numbers, together with their complements. Further statistics can be obtained by taking ratios of these ratios, ratios of ratios, or more complicated functions.
|
Evaluation of binary classifiers
| 0.836278
|
2,007
|
Given a data set, a classification (the output of a classifier on that set) gives two numbers: the number of positives and the number of negatives, which add up to the total size of the set. To evaluate a classifier, one compares its output to another reference classification – ideally a perfect classification, but in practice the output of another gold standard test – and cross tabulates the data into a 2×2 contingency table, comparing the two classifications. One then evaluates the classifier relative to the gold standard by computing summary statistics of these 4 numbers. Generally these statistics will be scale invariant (scaling all the numbers by the same factor does not change the output), to make them independent of population size, which is achieved by using ratios of homogeneous functions, most simply homogeneous linear or homogeneous quadratic functions.
|
Evaluation of binary classifiers
| 0.836278
|
2,008
|
An F-score is a combination of the precision and the recall, providing a single score. There is a one-parameter family of statistics, with parameter β, which determines the relative weights of precision and recall. The traditional or balanced F-score (F1 score) is the harmonic mean of precision and recall: F 1 = 2 ⋅ p r e c i s i o n ⋅ r e c a l l p r e c i s i o n + r e c a l l {\displaystyle F_{1}=2\cdot {\frac {\mathrm {precision} \cdot \mathrm {recall} }{\mathrm {precision} +\mathrm {recall} }}} .F-scores do not take the true negative rate into account and, therefore, are more suited to information retrieval and information extraction evaluation where the true negatives are innumerable. Instead, measures such as the phi coefficient, Matthews correlation coefficient, informedness or Cohen's kappa may be preferable to assess the performance of a binary classifier. As a correlation coefficient, the Matthews correlation coefficient is the geometric mean of the regression coefficients of the problem and its dual. The component regression coefficients of the Matthews correlation coefficient are markedness (deltap) and informedness (Youden's J statistic or deltap').
|
Evaluation of binary classifiers
| 0.836278
|
2,009
|
Precision and recall can be interpreted as (estimated) conditional probabilities: Precision is given by P ( C = P | C ^ = P ) {\displaystyle P(C=P|{\hat {C}}=P)} while recall is given by P ( C ^ = P | C = P ) {\displaystyle P({\hat {C}}=P|C=P)} , where C ^ {\displaystyle {\hat {C}}} is the predicted class and C {\displaystyle C} is the actual class. Both quantities are therefore connected by Bayes' theorem.
|
Evaluation of binary classifiers
| 0.836278
|
2,010
|
In radiological physics, charged-particle equilibrium (CPE) occurs when the number of charged particles leaving a volume is equal to the number entering, for each energy and type of particle. When CPE exists in an irradiated medium, the absorbed dose in the volume is equal to the collision kerma. In order for this to occur, energy is needed.
|
Charged particle equilibrium
| 0.836266
|
2,011
|
Translatomics is the study of all open reading frames (ORFs) that are being actively translated in a cell or organism. This collection of ORFs is called the translatome. Characterizing a cell's translatome can give insight into the array of biological pathways that are active in the cell. According to the central dogma of molecular biology, the DNA in a cell is transcribed to produce RNA, which is then translated to produce a protein.
|
Translatomics
| 0.836264
|
2,012
|
Nearing the completion of the Human Genome Project the field of genetics was shifting its focus toward determining the functions of genes. This involved cataloguing other collections of biological materials, like RNA and proteins in cells. These collections of materials were called -omes, evoking the widespread excitement surrounding the sequencing of the human genome.
|
Translatomics
| 0.836264
|
2,013
|
Some representations, such as pictures, videos and manipulatives, can motivate because of their richness, possibilities of play, use of technologies, or connections with interesting areas of life. Tasks that involve multiple representations can sustain intrinsic motivation in mathematics, by supporting higher-order thinking and problem solving. Multiple representations may also remove some of the gender biases that exist in math classrooms. For example, explaining probability solely through baseball statistics may potentially alienate students who have no interest in sports. When showing a tie to real-life applications, teachers should choose representations that are varied and of interest to all genders and cultures.
|
Multiple representations (mathematics education)
| 0.836262
|
2,014
|
Several curricula use extensively developed systems of manipulatives and the corresponding representations. For example, Cuisinaire rods, Montessori beads, Algebra Tiles, Base-10 blocks, counters.
|
Multiple representations (mathematics education)
| 0.836262
|
2,015
|
Visual representations, manipulatives, gestures, and to some degree grids, can support qualitative reasoning about mathematics. Instead of only emphasizing computational skills, multiple representations can help students make the conceptual shift to the meaning and use of, and to develop algebraic thinking. By focusing more on the conceptual representations of algebraic problems, students have a better chance of improving their problem solving skills.
|
Multiple representations (mathematics education)
| 0.836262
|
2,016
|
GeoGebra is free software dynamically linking geometric constructions, graphs, formulas, and grids. It can be used in a browser and is light enough for older or low-end computers.Project Interactivate has many activities linking visual, verbal and numeric representations. There are currently 159 different activities available, in many areas of math, including numbers and operations, probability, geometry, algebra, statistics and modeling. Another helpful tool for mathematicians, scientists, engineers is LaTeX. It is a typesetting program that allows one to create tables, figures, graphs etc, and to provide one with a precise visual of the problem being worked on.
|
Multiple representations (mathematics education)
| 0.836262
|
2,017
|
Genoinformatics refers to genome and chromosome dynamics, quantitative biology and modeling, molecular and cellular pathologies. Genome informatics also includes the field of genome design.
|
Genome informatics
| 0.83626
|
2,018
|
Methods of studying a large genomic data include variant-calling, transcriptomic analysis, and variant interpretation. Genome informatics can analyze DNA sequence information and to predict protein sequence and structure. Genome informatics dealing with microbial and metagenomics, sequencing algorithms, variant discovery and genome assembly, evolution, complex traits and phylogenetics, personal and medical genomics, transcriptomics, genome structure and function.
|
Genome informatics
| 0.83626
|
2,019
|
Molecular Biotechnology is a peer-reviewed scientific journal published by Springer Science+Business Media. It publishes original research papers and review articles on the application of molecular biology to biotechnology. It was established in 1994 with John M. Walker as founding editor-in-chief. Prof Aydin Berenjian is the current editor-in-chief of the journal.
|
Molecular Biotechnology
| 0.83622
|
2,020
|
Physics First began as an organized movement among educators around 1990, and has been slowly catching on throughout the United States. The most prominent movement championing Physics First is Leon Lederman's ARISE (American Renaissance in Science Education). Many proponents of Physics First argue that turning this order around lays the foundations for better understanding of chemistry, which in turn will lead to more comprehension of biology.
|
Physics First
| 0.836176
|
2,021
|
Physics First is an educational program in the United States, that teaches a basic physics course in the ninth grade (usually 15-year-olds), rather than the biology course which is more standard in public schools. This course relies on the limited math skills that the students have from pre-algebra and algebra I. With these skills students study a broad subset of the introductory physics canon with an emphasis on topics which can be experienced kinesthetically or without deep mathematical reasoning. Furthermore, teaching physics first is better suited for English Language Learners, who would be overwhelmed by the substantial vocabulary requirements of Biology.
|
Physics First
| 0.836176
|
2,022
|
Others point out that, for example, secondary school students will never study the advanced physics that underlies chemistry in the first place. "nclined planes (frictionless or not) didn't come up in ... high school chemistry class ... and the same can be said for some of the chemistry that really makes sense of biological phenomena." For physics to be relevant to a chemistry course, students have to develop a truly fundamental understanding of the concepts of energy, force, and matter, beyond the context of specific applications like the inclined plane.
|
Physics First
| 0.836175
|
2,023
|
They suggest that instead students first take biology and chemistry which are less mathematics-intensive so that by the time they are in their junior year, students will be advanced enough in mathematics with either an algebra 2 or pre-calculus education to be able to fully grasp the concepts presented in physics. Some argue this even further, saying that at least calculus should be a prerequisite for physics.
|
Physics First
| 0.836175
|
2,024
|
American public schools traditionally teach biology in the first year of high school, chemistry in the second, and physics in the third. The belief is that this order is more accessible, largely because biology can be taught with less mathematics, and will do the most toward providing some scientific literacy for the largest number of students. In addition, many scientists and educators argue that freshmen do not have an adequate background in mathematics to be able to fully comprehend a complete physics curriculum, and that therefore quality of a physics education is lost. While physics requires knowledge of vectors and some basic trigonometry, many students in the Physics First program take the course in conjunction with geometry.
|
Physics First
| 0.836175
|
2,025
|
Due to the tangible nature of most introductory physics experiments, Physics First also lends itself well to an introduction to inquiry-based science education, where students are encouraged to probe the workings of the world in which they live.The majority of high schools which have implemented "physics first" do so by way of offering two separate classes, at two separate levels: simple physics concepts in 9th grade, followed by more advanced physics courses in 11th or 12th grade. In schools with this curriculum, nearly all 9th grade students take a "Physical Science", or "Introduction to Physics Concepts" course. These courses focus on concepts that can be studied with skills from pre-algebra and algebra I. With these ideas in place, students then can be exposed to ideas with more physics related content in chemistry, and other science electives. After this, students are then encouraged to take an 11th or 12th grade course in physics, which does use more advanced math, including vectors, geometry, and more involved algebra. There is a large overlap between the Physics First movement, and the movement towards teaching conceptual physics - teaching physics in a way that emphasizes a strong understanding of physical principles over problem-solving ability.
|
Physics First
| 0.836175
|
2,026
|
On January 19 2021, the College Board discontinued all SAT Subject tests, including the SAT Subject Test in Chemistry. This was effective immediately in the United States, and the tests were to be phased out by the following summer for international students. This was done as a response to changes in college admissions due to the impact of the COVID-19 pandemic on education.
|
SAT Subject Test in Chemistry
| 0.836168
|
2,027
|
The SAT Subject Test in Chemistry was a one-hour multiple choice test given on chemistry by The College Board. A student chose whether to take the test depending upon college entrance requirements for the schools in which the student was planning to apply. Until 1994, the SAT Subject Tests were known as Achievement Tests; until January 2005, they were known as SAT 2s; they are still well known by the latter name.
|
SAT Subject Test in Chemistry
| 0.836168
|
2,028
|
Like most of the SAT Subject Tests, the Chemistry SAT Test was relatively difficult. It tested a very wide breadth of content and expected students to formulate answers in a very short period of time. Many high school students found themselves picking up extra resource material, like prep books and online aids, to help them prepare for the SAT Chemistry test. While the test was challenging, there were distinctions between the SAT Chemistry Test and the AP Chemistry exam, which is a more critical-thinking exam that is used not for college admissions but rather for college placement. Still, an AP course in Chemistry is sufficient preparation for the Chemistry SAT.
|
SAT Subject Test in Chemistry
| 0.836168
|
2,029
|
This test consisted of 85 questions. The first 23 questions numbered 1-23 were 'classification questions'. The next 15 questions, numbered 101-115, were called 'relationship analysis questions'. The SAT Subject Test in Chemistry was currently the only SAT that incorporates the relationship analysis questions.
|
SAT Subject Test in Chemistry
| 0.836168
|
2,030
|
The College Board's recommended preparation was a one-year college preparatory course in chemistry, a one-year course in algebra, and experience in the laboratory. However, some second-year algebra concepts (including logarithms) were tested on this subject test. Given the timed nature of the test, one of the keys of the mathematics that appeared on the SAT II in Chemistry was not the difficulty, but rather the speed at which it had to have been completed. Furthermore, the oft-quoted prerequisite of lab-experience was sometimes unnecessary for the SAT Subject Test in Chemistry due to the nature of the questions concerning experiments; most laboratory concepts could simply be memorized beforehand. Some lab-based questions used diagrams, and thus it was helpful to know what common glassware looks like and how the different pieces are used.
|
SAT Subject Test in Chemistry
| 0.836168
|
2,031
|
Mixed potential theory is a theory used in electrochemistry that relates the potentials and currents from differing constituents into a 'weighted' potential at zero net current. In other words, it is an electrode potential resulting from a simultaneous action of more than a single redox couple, while the net electrode current is zero.
|
Mixed potential theory
| 0.836137
|
2,032
|
The fallacy is the argument that two states or conditions cannot be considered distinct (or do not exist at all) because between them there exists a continuum of states. Strictly, the sorites paradox refers to situations where there are many discrete states (classically between 1 and 1,000,000 grains of sand, hence 1,000,000 possible states), while the continuum fallacy refers to situations where there is (or appears to be) a continuum of states, such as temperature. Whether any continua exist in the physical world is the classic question of atomism, and while both Newtonian physics and quantum physics model the world as continuous, there are some proposals in quantum gravity, such as loop quantum gravity, that suggest that notions of continuous length do not apply at the Planck length, and thus what appear to be continua may simply be as-yet undistinguishable discrete states.
|
Paradox of the heap
| 0.836114
|
2,033
|
The basic experimental procedure of a study on naïve physics involves three steps: prediction of the infant's expectation, violation of that expectation, and measurement of the results. As mentioned above, the physically impossible event holds the infant's attention longer, indicating surprise when expectations are violated.
|
Naïve physics
| 0.836087
|
2,034
|
But research shows that infants, who do not yet have such expansive knowledge of the world, have the same extended reaction to events that appear physically impossible. Such studies hypothesize that all people are born with an innate ability to understand the physical world. Smith and Cassati (1994) have reviewed the early history of naïve physics, and especially the role of the Italian psychologist Paolo Bozzi.
|
Naïve physics
| 0.836087
|
2,035
|
The increasing sophistication of technology makes possible more research on knowledge acquisition. Researchers measure physiological responses such as heart rate and eye movement in order to quantify the reaction to a particular stimulus. Concrete physiological data is helpful when observing infant behavior, because infants cannot use words to explain things (such as their reactions) the way most adults or older children can. Research in naïve physics relies on technology to measure eye gaze and reaction time in particular.
|
Naïve physics
| 0.836087
|
2,036
|
Naïve physics or folk physics is the untrained human perception of basic physical phenomena. In the field of artificial intelligence the study of naïve physics is a part of the effort to formalize the common knowledge of human beings.Many ideas of folk physics are simplifications, misunderstandings, or misperceptions of well-understood phenomena, incapable of giving useful predictions of detailed experiments, or simply are contradicted by more thorough observations. They may sometimes be true, be true in certain limited cases, be true as a good first approximation to a more complex effect, or predict the same effect but misunderstand the underlying mechanism. Naïve physics is characterized by a mostly intuitive understanding humans have about objects in the physical world. Certain notions of the physical world may be innate.
|
Naïve physics
| 0.836087
|
2,037
|
It is underpinned by relevant basic sciences including anatomy and physiology, cell biology, biochemistry, microbiology, genetics and molecular biology, pharmacology, immunology, mathematics and statistics, and bioinformatics. As such the biomedical sciences have a much wider range of academic and research activities and economic significance than that defined by hospital laboratory sciences. Biomedical Sciences are the major focus of bioscience research and funding in the 21st century.
|
Biomedical science
| 0.836077
|
2,038
|
Biomedical sciences are a set of sciences applying portions of natural science or formal science, or both, to develop knowledge, interventions, or technology that are of use in healthcare or public health. Such disciplines as medical microbiology, clinical virology, clinical epidemiology, genetic epidemiology, and biomedical engineering are medical sciences. In explaining physiological mechanisms operating in pathological processes, however, pathophysiology can be regarded as basic science. Biomedical Sciences, as defined by the UK Quality Assurance Agency for Higher Education Benchmark Statement in 2015, includes those science disciplines whose primary focus is the biology of human health and disease and ranges from the generic study of biomedical sciences and human biology to more specialised subject areas such as pharmacology, human physiology and human nutrition.
|
Biomedical science
| 0.836077
|
2,039
|
A sub-set of biomedical sciences is the science of clinical laboratory diagnosis. This is commonly referred to in the UK as 'biomedical science' or 'healthcare science'. There are at least 45 different specialisms within healthcare science, which are traditionally grouped into three main divisions: specialisms involving life sciences specialisms involving physiological science specialisms involving medical physics or bioengineering
|
Biomedical science
| 0.836077
|
2,040
|
Molecular toxicology Molecular pathology Blood transfusion science Cervical cytology Clinical biochemistry Clinical embryology Clinical immunology Clinical pharmacology and therapeutics Electron microscopy External quality assurance Haematology Haemostasis and thrombosis Histocompatibility and immunogenetics Histopathology and cytopathology Molecular genetics and cytogenetics Molecular biology and cell biology Microbiology including mycology Bacteriology Tropical diseases Phlebotomy Tissue banking/transplant Virology
|
Biomedical science
| 0.836077
|
2,041
|
The premier example is photosynthesis, in which most plants use solar energy to convert carbon dioxide and water into glucose, disposing of oxygen as a side-product. Humans rely on photochemistry for the formation of vitamin D, and vision is initiated by a photochemical reaction of rhodopsin. In fireflies, an enzyme in the abdomen catalyzes a reaction that results in bioluminescence. Many significant photochemical reactions, such as ozone formation, occur in the Earth atmosphere and constitute atmospheric chemistry.
|
Reaction mixture
| 0.836054
|
2,042
|
In photochemical reactions, atoms and molecules absorb energy (photons) of the illumination light and convert it into an excited state. They can then release this energy by breaking chemical bonds, thereby producing radicals. Photochemical reactions include hydrogen–oxygen reactions, radical polymerization, chain reactions and rearrangement reactions.Many important processes involve photochemistry.
|
Reaction mixture
| 0.836054
|
2,043
|
This proved to be false in 1785 by Antoine Lavoisier who found the correct explanation of the combustion as a reaction with oxygen from the air.Joseph Louis Gay-Lussac recognized in 1808 that gases always react in a certain relationship with each other. Based on this idea and the atomic theory of John Dalton, Joseph Proust had developed the law of definite proportions, which later resulted in the concepts of stoichiometry and chemical equations.Regarding the organic chemistry, it was long believed that compounds obtained from living organisms were too complex to be obtained synthetically. According to the concept of vitalism, organic matter was endowed with a "vital force" and distinguished from inorganic materials. This separation was ended however by the synthesis of urea from inorganic precursors by Friedrich Wöhler in 1828. Other chemists who brought major contributions to organic chemistry include Alexander William Williamson with his synthesis of ethers and Christopher Kelk Ingold, who, among many discoveries, established the mechanisms of substitution reactions.
|
Reaction mixture
| 0.836053
|
2,044
|
Further optimization of sulfuric acid technology resulted in the contact process in the 1880s, and the Haber process was developed in 1909–1910 for ammonia synthesis.From the 16th century, researchers including Jan Baptist van Helmont, Robert Boyle, and Isaac Newton tried to establish theories of experimentally observed chemical transformations. The phlogiston theory was proposed in 1667 by Johann Joachim Becher. It postulated the existence of a fire-like element called "phlogiston", which was contained within combustible bodies and released during combustion.
|
Reaction mixture
| 0.836053
|
2,045
|
Uzan, Jean-Philippe (2003-04-07). "The fundamental constants and their variation: observational and theoretical status". Reviews of Modern Physics.
|
Fundamental physical constants
| 0.836028
|
2,046
|
Physics Letters B. 585 (1–2): 29–34. arXiv:astro-ph/0302295.
|
Fundamental physical constants
| 0.836028
|
2,047
|
Physical Review Letters. 90 (15): 150801. arXiv:physics/0212112. Bibcode:2003PhRvL..90o0801M.
|
Fundamental physical constants
| 0.836028
|
2,048
|
Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!
|
Fundamental physical constants
| 0.836028
|
2,049
|
In computing, a memory barrier, also known as a membar, memory fence or fence instruction, is a type of barrier instruction that causes a central processing unit (CPU) or compiler to enforce an ordering constraint on memory operations issued before and after the barrier instruction. This typically means that operations issued prior to the barrier are guaranteed to be performed before operations issued after the barrier. Memory barriers are necessary because most modern CPUs employ performance optimizations that can result in out-of-order execution.
|
Memory barrier
| 0.83602
|
2,050
|
Memory barrier instructions address reordering effects only at the hardware level. Compilers may also reorder instructions as part of the program optimization process. Although the effects on parallel program behavior can be similar in both cases, in general it is necessary to take separate measures to inhibit compiler reordering optimizations for data that may be shared by multiple threads of execution. In C and C++, the volatile keyword was intended to allow C and C++ programs to directly access memory-mapped I/O.
|
Memory barrier
| 0.83602
|
2,051
|
Similarly, if P(A) is not zero, then P ( B ∣ A ) = P ( B ) {\displaystyle P(B\mid A)=P(B)} is also equivalent. Although the derived forms may seem more intuitive, they are not the preferred definition as the conditional probabilities may be undefined, and the preferred definition is symmetrical in A and B. Independence does not refer to a disjoint event.It should also be noted that given the independent event pair and an event C, the pair is defined to be conditionally independent if the product holds true: P ( A B ∣ C ) = P ( A ∣ C ) P ( B ∣ C ) {\displaystyle P(AB\mid C)=P(A\mid C)P(B\mid C)} This theorem could be useful in applications where multiple independent events are being observed. Independent events vs. mutually exclusive events The concepts of mutually independent events and mutually exclusive events are separate and distinct. The following table contrasts results for the two cases (provided that the probability of the conditioning event is not zero). In fact, mutually exclusive events cannot be statistically independent (unless both of them are impossible), since knowing that one occurs gives information about the other (in particular, that the latter will certainly not occur).
|
Conditional probabilities
| 0.835981
|
2,052
|
It should be apparent now that falsely equating the two probabilities can lead to various errors of reasoning, which is commonly seen through base rate fallacies. While conditional probabilities can provide extremely useful information, limited information is often supplied or at hand. Therefore, it can be useful to reverse or convert a conditional probability using Bayes' theorem: P ( A ∣ B ) = P ( B ∣ A ) P ( A ) P ( B ) {\displaystyle P(A\mid B)={{P(B\mid A)P(A)} \over {P(B)}}} . Another option is to display conditional probabilities in a conditional probability table to illuminate the relationship between events.
|
Conditional probabilities
| 0.835981
|
2,053
|
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B) or occasionally PB(A). This can also be understood as the fraction of probability B that intersects with A, or the ratio of the probabilities of both events happening to the "given" one happening (how many times A occurs rather than not assuming B has occurred): P ( A ∣ B ) = P ( A ∩ B ) P ( B ) {\displaystyle P(A\mid B)={\frac {P(A\cap B)}{P(B)}}} .For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing.
|
Conditional probabilities
| 0.835981
|
2,054
|
Without the Good, we would only be able to see with our physical eyes and not the "mind's eye". The sun bequeaths its light so that we may see the world around us. If the source of light did not exist we would be in the dark and incapable of learning and understanding the true realities that surround us.Incidentally, the metaphor of the sun exemplifies a traditional interrelation between metaphysics and epistemology: interpretations of fundamental existence create—and are created by—ways of knowing.
|
Analogy of the sun
| 0.835949
|
2,055
|
: 171 Socrates also makes it clear that the sun cannot be looked at, so it cannot be known from sense perception alone. Even today, we still use all kinds of mathematical models, the physics of electromagnetic measurements, deductions, and logic to further know and understand the real sun as a fascinating being.
|
Analogy of the sun
| 0.835949
|
2,056
|
Labeling studies establish the following regiochemistry: RCDO + CH2=CHR' → RC(O)CH2CHDR'In terms of the reaction mechanism, hydroacylation begins with oxidative addition of the aldehydic carbon-hydrogen bond. The resulting acyl hydride complex next binds the alkene. The sequence of oxidative addition and alkene coordination is often unclear. Via migratory insertion, the alkene inserts into either the metal-acyl or the metal-hydride bonds.
|
Hydroacylation
| 0.835936
|
2,057
|
Humans have known about stress inside materials since ancient times. Until the 17th century, this understanding was largely intuitive and empirical, though this did not prevent the development of relatively advanced technologies like the composite bow and glass blowing.Over several millennia, architects and builders in particular, learned how to put together carefully shaped wood beams and stone blocks to withstand, transmit, and distribute stress in the most effective manner, with ingenious devices such as the capitals, arches, cupolas, trusses and the flying buttresses of Gothic cathedrals. Ancient and medieval architects did develop some geometrical methods and simple formulas to compute the proper sizes of pillars and beams, but the scientific understanding of stress became possible only after the necessary tools were invented in the 17th and 18th centuries: Galileo Galilei's rigorous experimental method, René Descartes's coordinates and analytic geometry, and Newton's laws of motion and equilibrium and calculus of infinitesimals. With those tools, Augustin-Louis Cauchy was able to give the first rigorous and general mathematical model of a deformed elastic body by introducing the notions of stress and strain. Cauchy observed that the force across an imaginary surface was a linear function of its normal vector; and, moreover, that it must be a symmetric function (with zero total momentum). The understanding of stress in liquids started with Newton, who provided a differential formula for friction forces (shear stress) in parallel laminar flow.
|
Stress (mechanics)
| 0.835889
|
2,058
|
Stress analysis is a branch of applied physics that covers the determination of the internal distribution of internal forces in solid objects. It is an essential tool in engineering for the study and design of structures such as tunnels, dams, mechanical parts, and structural frames, under prescribed or expected loads. It is also important in many other disciplines; for example, in geology, to study phenomena like plate tectonics, vulcanism and avalanches; and in biology, to understand the anatomy of living beings.
|
Stress (mechanics)
| 0.835889
|
2,059
|
In three dimensions, angular displacement is an entity with a direction and a magnitude. The direction specifies the axis of rotation, which always exists by virtue of the Euler's rotation theorem; the magnitude specifies the rotation in radians about that axis (using the right-hand rule to determine direction). This entity is called an axis-angle. Despite having direction and magnitude, angular displacement is not a vector because it does not obey the commutative law for addition. Nevertheless, when dealing with infinitesimal rotations, second order infinitesimals can be discarded and in this case commutativity appears.
|
Angles of rotation
| 0.835828
|
2,060
|
The following are a few known oracle complexity results (up to numerical constants), for obtaining optimization error ϵ {\displaystyle \epsilon } for some small enough ϵ {\displaystyle \epsilon } , and over the domain R d {\displaystyle \mathbb {R} ^{d}} where d {\displaystyle d} is not fixed and can be arbitrarily large (unless stated otherwise). We also assume that the initialization point x 1 {\displaystyle \mathbf {x} _{1}} satisfies ‖ x 1 − x ∗ ‖ ≤ B {\displaystyle \|\mathbf {x} _{1}-\mathbf {x} ^{*}\|\leq B} for some parameter B {\displaystyle B} , where x ∗ {\displaystyle \mathbf {x} ^{*}} is some global minimizer of the objective function.
|
Oracle complexity (optimization)
| 0.835816
|
2,061
|
This is known as the oracle complexity of this class of optimization problems: Namely, the number of iterations such that on one hand, there is an algorithm that provably requires only this many iterations to succeed (for any function in F {\displaystyle {\mathcal {F}}} ), and on the other hand, there is a proof that no algorithm can succeed with fewer iterations uniformly for all functions in F {\displaystyle {\mathcal {F}}} . The oracle complexity approach is inherently different from computational complexity theory, which relies on the Turing machine to model algorithms, and requires the algorithm's input (in this case, the function f {\displaystyle f} ) to be represented as a bit of strings in memory. Instead, the algorithm is not computationally constrained, but its access to the function f {\displaystyle f} is assumed to be constrained. This means that on the one hand, oracle complexity results only apply to specific families of algorithms which access the function in a certain manner, and not any algorithm as in computational complexity theory. On the other hand, the results apply to most if not all iterative algorithms used in practice, do not rely on any unproven assumptions, and lead to a nuanced understanding of how the function's geometry and type of information used by the algorithm affects practical performance.
|
Oracle complexity (optimization)
| 0.835816
|
2,062
|
This algorithm can be modeled in the framework above, where given any x t {\displaystyle \mathbf {x_{t}} } , the oracle returns the gradient ∇ f ( x t ) {\displaystyle \nabla f(\mathbf {x_{t}} )} , which is then used to choose the next point x t + 1 {\displaystyle \mathbf {x_{t+1}} } . In this framework, for each choice of function family F {\displaystyle {\mathcal {F}}} and oracle O {\displaystyle {\mathcal {O}}} , one can study how many oracle calls/iterations are required, to guarantee some optimization criterion (for example, ensuring that the algorithm produces a point x T {\displaystyle \mathbf {x} _{T}} such that f ( x T ) − inf x ∈ X f ( x ) ≤ ϵ {\displaystyle f(\mathbf {x} _{T})-\inf _{\mathbf {x} \in {\mathcal {X}}}f(\mathbf {x} )\leq \epsilon } for some ϵ > 0 {\displaystyle \epsilon >0} ).
|
Oracle complexity (optimization)
| 0.835816
|
2,063
|
Some common choices include convex vs. strongly-convex vs. non-convex functions, smooth vs. non-smooth functions (say, in terms of Lipschitz properties of the gradients or higher-order derivatives), domains with bounded dimension d {\displaystyle d} , vs. domains with unbounded dimension, and sums of two or more functions with different properties. In terms of the oracle O {\displaystyle {\mathcal {O}}} , it is common to assume that given a point x {\displaystyle \mathbf {x} } , it returns the value of the function at x {\displaystyle \mathbf {x} } , as well as derivatives up to some order (say, value only, value and gradient, value and gradient and Hessian, etc.). Sometimes, one studies more complicated oracles. For example, a stochastic oracle returns the values and derivatives corrupted by some random noise, and is useful for studying stochastic optimization methods. Another example is a proximal oracle, which given a point x {\displaystyle \mathbf {x} } and a parameter γ {\displaystyle \gamma } , returns the point y {\displaystyle \mathbf {y} } minimizing f ( y ) + γ ‖ y − x ‖ 2 {\displaystyle f(\mathbf {y} )+\gamma \|\mathbf {y} -\mathbf {x} \|^{2}} .
|
Oracle complexity (optimization)
| 0.835816
|
2,064
|
Oracle complexity has been applied to quite a few different settings, depending on the optimization criterion, function class F {\displaystyle {\mathcal {F}}} , and type of oracle O {\displaystyle {\mathcal {O}}} . In terms of optimization criterion, by far the most common one is finding a near-optimal point, namely making f ( x T ) − inf x ∈ X f ( x ) ≤ ϵ {\displaystyle f(\mathbf {x} _{T})-\inf _{\mathbf {x} \in {\mathcal {X}}}f(\mathbf {x} )\leq \epsilon } for some small ϵ > 0 {\displaystyle \epsilon >0} . Some other criteria include finding an approximately-stationary point ( ‖ ∇ f ( x T ) ‖ ≤ ϵ {\displaystyle \|\nabla f(\mathbf {x} _{T})\|\leq \epsilon } ), or finding an approximate local minima. There are many function classes F {\displaystyle {\mathcal {F}}} that have been studied.
|
Oracle complexity (optimization)
| 0.835816
|
2,065
|
In mathematical optimization, oracle complexity is a standard theoretical framework to study the computational requirements for solving classes of optimization problems. It is suitable for analyzing iterative algorithms which proceed by computing local information about the objective function at various points (such as the function's value, gradient, Hessian etc.). The framework has been used to provide tight worst-case guarantees on the number of required iterations, for several important classes of optimization problems.
|
Oracle complexity (optimization)
| 0.835816
|
2,066
|
Medical algorithms are part of a broader field which is usually fit under the aims of medical informatics and medical decision-making. Medical decisions occur in several areas of medical activity including medical test selection, diagnosis, therapy and prognosis, and automatic control of medical equipment. In relation to logic-based and artificial neural network-based clinical decision support systems, which are also computer applications used in the medical decision-making field, algorithms are less complex in architecture, data structure and user interface. Medical algorithms are not necessarily implemented using digital computers. In fact, many of them can be represented on paper, in the form of diagrams, nomographs, etc.
|
Medical algorithms
| 0.835807
|
2,067
|
The second phase of the $170 million Human Microbiome Project was focused on integrating patient data to different omic datasets, considering host genetics, clinical information and microbiome composition. The phase one focused on characterization of communities in different body sites. Phase 2 focused in the integration of multiomic data from host & microbiome to human diseases. Specifically, the project used multiomics to improve the understanding of the interplay of gut and nasal microbiomes with type 2 diabetes, gut microbiomes and inflammatory bowel disease and vaginal microbiomes and pre-term birth.
|
Multiomics
| 0.835784
|
2,068
|
A major limitation of classical omic studies is the isolation of only one level of biological complexity. For example, transcriptomic studies may provide information at the transcript level, but many different entities contribute to the biological state of the sample (genomic variants, post-translational modifications, metabolic products, interacting organisms, among others). With the advent of high-throughput biology, it is becoming increasingly affordable to make multiple measurements, allowing transdomain (e.g. RNA and protein levels) correlations and inferences.
|
Multiomics
| 0.835784
|
2,069
|
In parallel to the advances in highthroughput biology, machine learning applications to biomedical data analysis are flourishing. The integration of multi-omics data analysis and machine learning has led to the discovery of new biomarkers. For example, one of the methods of the mixOmics project implements a method based on sparse Partial Least Squares regression for selection of features (putative biomarkers). A unified and flexible statistical framewok for heterogeneous data integration called "Regularized Generalized Canonical Correlation Analysis" (RGCCA ) enables identifying such putative biomarkers. This framework is implemented and made freely avalaible within the RGCCA R package .
|
Multiomics
| 0.835784
|
2,070
|
The OmicTools service lists more than 99 softwares related to multiomic data analysis, as well as more than 99 databases on the topic. Systems biology approaches are often based upon the use of panomic analysis data. The American Society of Clinical Oncology (ASCO) defines panomics as referring to "the interaction of all biological functions within a cell and with other body functions, combining data collected by targeted tests ... and global assays (such as genome sequencing) with other patient-specific information."
|
Multiomics
| 0.835784
|
2,071
|
The wave function can also be written in the complex exponential (polar) form: where R, S are real functions of r and t. Written this way, the probability density is and the probability current is: The exponentials and R∇R terms cancel: Finally, combining and cancelling the constants, and replacing R2 with ρ, If we take the familiar formula for the mass flux in hydrodynamics: where ρ {\displaystyle \rho } is the mass density of the fluid and v is its velocity (also the group velocity of the wave). In the classical limit, we can associate the velocity with ∇ S m , {\displaystyle {\tfrac {\nabla S}{m}},} which is the same as equating ∇S with the classical momentum p = mv. This interpretation fits with Hamilton–Jacobi theory, in which in Cartesian coordinates is given by ∇S, where S is Hamilton's principal function. The de Broglie-Bohm theory equates the velocity with ∇ S m {\displaystyle {\tfrac {\nabla S}{m}}} in general (not only in the classical limit) so it is always well defined. It is an interpretation of quantum mechanics.
|
Probability current
| 0.835734
|
2,072
|
If the particle has spin, it has a corresponding magnetic moment, so an extra term needs to be added incorporating the spin interaction with the electromagnetic field. According to Landau-Lifschitz's Course of Theoretical Physics the electric current density is in Gaussian units: And in SI units: Hence the probability current (density) is in SI units: where S is the spin vector of the particle with corresponding spin magnetic moment μS and spin quantum number s. It is doubtful if this formula is vaild for particles with an interior structure. The neutron has zero charge but non-zero magnetic moment, so μ S q s ℏ {\displaystyle {\frac {\mu _{S}}{qs\hbar }}} would be impossible (except ∇ × ( Ψ ∗ S Ψ ) {\displaystyle \nabla \times (\Psi ^{*}\mathbf {S} \Psi )} would also be zero in this case). For composite particles with a non-zero charge – like the proton which has spin quantum number s=1/2 and µS= 2.7927·µN or the deuteron (H-2 nucleus) which has s=1 and µS=0.8574·µN – it is mathematically possible but doubtful.
|
Probability current
| 0.835734
|
2,073
|
The definition of probability current and Schrödinger's equation can be used to derive the continuity equation, which has exactly the same forms as those for hydrodynamics and electromagnetism: where the probability density ρ {\displaystyle \rho \,} is defined as If one were to integrate both sides of the continuity equation with respect to volume, so that then the divergence theorem implies the continuity equation is equivalent to the integral equation ∂ ∂ t ∫ V | Ψ | 2 d V + {\displaystyle {\frac {\partial }{\partial t}}\int _{V}|\Psi |^{2}\mathrm {d} V+} S {\displaystyle \scriptstyle S} j ⋅ d S = 0 {\displaystyle \mathbf {j} \cdot \mathrm {d} \mathbf {S} =0} where V is any volume and S is the boundary of V. This is the conservation law for probability in quantum mechanics. In particular, if Ψ is a wavefunction describing a single particle, the integral in the first term of the preceding equation, sans time derivative, is the probability of obtaining a value within V when the position of the particle is measured. The second term is then the rate at which probability is flowing out of the volume V. Altogether the equation states that the time derivative of the probability of the particle being measured in V is equal to the rate at which probability flows into V.
|
Probability current
| 0.835734
|
2,074
|
Probability currents are analogous to mass currents in hydrodynamics and electric currents in electromagnetism. As in those fields, the probability current (i.e. the probability current density) is related to the probability density function via a continuity equation. The probability current is invariant under gauge transformation. The concept of probability current is also used outside of quantum mechanics, when dealing with probability density functions that change over time, for instance in Brownian motion and the Fokker–Planck equation.
|
Probability current
| 0.835734
|
2,075
|
In quantum mechanics, the probability current (sometimes called probability flux) is a mathematical quantity describing the flow of probability. Specifically, if one thinks of probability as a heterogeneous fluid, then the probability current is the rate of flow of this fluid. It is a real vector that changes with space and time.
|
Probability current
| 0.835734
|
2,076
|
Since the 1980s, artificial neural networks have been applied to the prediction of protein structures. The evolutionary conservation of secondary structures can be exploited by simultaneously assessing many homologous sequences in a multiple sequence alignment, by calculating the net secondary structure propensity of an aligned column of amino acids. In concert with larger databases of known protein structures and modern machine learning methods such as neural nets and support vector machines, these methods can achieve up to 80% overall accuracy in globular proteins.
|
Protein structure prediction
| 0.835717
|
2,077
|
AlphaFold2, was introduced in CASP14, and is capable of predicting protein structures to near experimental accuracy. AlphaFold was swiftly followed by RosettaTTAFold and later by OmegaFold and the ESM Metagenomic Atlas. In a recent study, Sommer et al. 2022 demonstrated the application of protein structure prediction in genome annotation, specifically in identifying functional protein isoforms using computationally predicted structures, available at https://www.isoform.io. This study highlights the promise of protein structure prediction as a genome annotation tool and presents a practical, structure-guided approach that can be used to enhance the annotation of any genome. The European Bioinformatics Institute together with DeepMind have constructed the AlphaFold - EBI database for predicted protein structures.
|
Protein structure prediction
| 0.835717
|
2,078
|
AlphaFold was one of the first AIs to predict protein structures. It was introduced by Google's DeepMind in the 13th CASP competition, which was held in 2018. AlphaFold relies on a neural network approach, which directly predicts the 3D coordinates of all non-hydrogen atoms for a given protein using the amino acid sequence and aligned homologous sequences. The AlphaFold network consists of a trunk which processes the inputs through repeated layers, and a structure module which introduces an explicit 3D structure. Earlier neural networks for protein structure prediction used LSTM. Since AlphaFold outputs protein coordinates directly, AlphaFold produces predictions in graphic processing unit (GPU) minutes to GPU hours, depending on the length of protein sequence.
|
Protein structure prediction
| 0.835717
|
2,079
|
A great number of software tools for protein structure prediction exist. Approaches include homology modeling, protein threading, ab initio methods, secondary structure prediction, and transmembrane helix and signal peptide prediction. In particular, deep learning based on long short-term memory has been used for this purpose since 2007, when it was successfully applied to protein homology detection and to predict subcellular localization of proteins.
|
Protein structure prediction
| 0.835717
|
2,080
|
Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its secondary and tertiary structure from primary structure. Structure prediction is different from the inverse problem of protein design. Protein structure prediction is one of the most important goals pursued by computational biology; and it is important in medicine (for example, in drug design) and biotechnology (for example, in the design of novel enzymes). Starting in 1994, the performance of current methods is assessed biannually in the CASP experiment (Critical Assessment of Techniques for Protein Structure Prediction). A continuous evaluation of protein structure prediction web servers is performed by the community project CAMEO3D.
|
Protein structure prediction
| 0.835717
|
2,081
|
PSIPRED and JPRED are some of the most known programs based on neural networks for protein secondary structure prediction. Next, support vector machines have proven particularly useful for predicting the locations of turns, which are difficult to identify with statistical methods.Extensions of machine learning techniques attempt to predict more fine-grained local properties of proteins, such as backbone dihedral angles in unassigned regions. Both SVMs and neural networks have been applied to this problem. More recently, real-value torsion angles can be accurately predicted by SPINE-X and successfully employed for ab initio structure prediction.
|
Protein structure prediction
| 0.835717
|
2,082
|
First artificial neural networks methods were used. As a training sets they use solved structures to identify common sequence motifs associated with particular arrangements of secondary structures. These methods are over 70% accurate in their predictions, although beta strands are still often underpredicted due to the lack of three-dimensional structural information that would allow assessment of hydrogen bonding patterns that can promote formation of the extended conformation required for the presence of a complete beta sheet.
|
Protein structure prediction
| 0.835717
|
2,083
|
Weak contributions from each of many neighbors can add up to strong effects overall. The original GOR method was roughly 65% accurate and is dramatically more successful in predicting alpha helices than beta sheets, which it frequently mispredicted as loops or disorganized regions.Another big step forward, was using machine learning methods.
|
Protein structure prediction
| 0.835717
|
2,084
|
Proteins of very different amino acid sequences may fold into a structure that produces the same active site. Architecture is the relative orientations of secondary structures in a three-dimensional structure without regard to whether or not they share a similar loop structure. Fold (topology) a type of architecture that also has a conserved loop structure.
|
Protein structure prediction
| 0.835717
|
2,085
|
The more commonly used terms for evolutionary and structural relationships among proteins are listed below. Many additional terms are used for various kinds of structural features found in proteins. Descriptions of such terms may be found at the CATH Web site, the Structural Classification of Proteins (SCOP) Web site, and a Glaxo Wellcome tutorial on the Swiss bioinformatics Expasy Web site. Active site a localized combination of amino acid side groups within the tertiary (three-dimensional) or quaternary (protein subunit) structure that can interact with a chemically specific substrate and that provides the protein with biological activity.
|
Protein structure prediction
| 0.835717
|
2,086
|
Most tertiary structure modelling methods, such as Rosetta, are optimized for modelling the tertiary structure of single protein domains. A step called domain parsing, or domain boundary prediction, is usually done first to split a protein into potential structural domains. As with the rest of tertiary structure prediction, this can be done comparatively from known structures or ab initio with the sequence only (usually by machine learning, assisted by covariation). The structures for individual domains are docked together in a process called domain assembly to form the final tertiary structure.
|
Protein structure prediction
| 0.835717
|
2,087
|
This topic emphasises systematic development of formulas for calculating expected values associated with the geometric objects derived from random points, and can in part be viewed as a sophisticated branch of multivariate calculus. Stochastic geometry emphasises the random geometrical objects themselves. For instance: different models for random lines or for random tessellations of the plane; random sets formed by making points of a spatial Poisson process be (say) centers of discs.
|
Geometric probability
| 0.835708
|
2,088
|
What is the chance that three random points in the plane form an acute (rather than obtuse) triangle? What is the mean area of the polygonal regions formed when randomly oriented lines are spread over the plane?For mathematical development see the concise monograph by Solomon.Since the late 20th century, the topic has split into two topics with different emphases. Integral geometry sprang from the principle that the mathematically natural probability models are those that are invariant under certain transformation groups.
|
Geometric probability
| 0.835708
|
2,089
|
A cDNA library represents a sample of the mRNA purified from a particular source (either a collection of cells, a particular tissue, or an entire organism), which has been converted back to a DNA template by the use of the enzyme reverse transcriptase. It thus represents the genes that were being actively transcribed in that particular source under the physiological, developmental, or environmental conditions that existed when the mRNA was purified. cDNA libraries can be generated using techniques that promote "full-length" clones or under conditions that generate shorter fragments used for the identification of "expressed sequence tags". cDNA libraries are useful in reverse genetics, but they only represent a very small (less than 1%) portion of the overall genome in a given organism. Applications of cDNA libraries include: Discovery of novel genes Cloning of full-length cDNA molecules for in vitro study of gene function Study of the repertoire of mRNAs expressed in different cells or tissues Study of alternative splicing in different cells or tissues
|
DNA library
| 0.835704
|
2,090
|
Typical examples of building block collections for medicinal chemistry are libraries of fluorine-containing building blocks. Introduction of the fluorine into a molecule has been shown to be beneficial for its pharmacokinetic and pharmacodynamic properties, therefore, the fluorine-substituted building blocks in drug design increase the probability of finding drug leads. Other examples include natural and unnatural amino acid libraries, collections of conformationally constrained bifunctionalized compounds and diversity-oriented building block collections. == References ==
|
Molecular building blocks
| 0.835694
|
2,091
|
Building block is a term in chemistry which is used to describe a virtual molecular fragment or a real chemical compound the molecules of which possess reactive functional groups. Building blocks are used for bottom-up modular assembly of molecular architectures: nano-particles, metal-organic frameworks, organic molecular constructs, supra-molecular complexes. Using building blocks ensures strict control of what a final compound or a (supra)molecular construct will be.
|
Molecular building blocks
| 0.835694
|
2,092
|
The building block approach to drug discovery changed the landscape of chemical industry which supports medicinal chemistry. Major chemical suppliers for medicinal chemistry like Maybridge, Chembridge, Enamine adjusted their business correspondingly. By the end of the 1990th the use of building block collections prepared for fast and reliable construction of small-molecule sets of compounds (libraries) for biological screening became one of the major strategies for pharmaceutical industry involved in drug discovery; modular, usually one-step synthesis of compounds for biological screening from building blocks turned out to be in most cases faster and more reliable than multistep, even convergent syntheses of target compounds.There are online web-resources.
|
Molecular building blocks
| 0.835694
|
2,093
|
Organic functionalized molecules (reagents), carefully selected for the use in modular synthesis of novel drug candidates, in particular, by combinatorial chemistry, or in order to realize the ideas of virtual screening and drug design are also called building blocks. To be practically useful for the modular drug or drug candidate assembly, the building blocks should be either mono-functionalised or possessing selectively chemically addressable functional groups, for example, orthogonally protected. Selection criteria applied to organic functionalized molecules to be included in the building block collections for medicinal chemistry are usually based on empirical rules aimed at drug-like properties of the final drug candidates. Bioisosteric replacements of the molecular fragments in drug candidates could be made using analogous building blocks.
|
Molecular building blocks
| 0.835694
|
2,094
|
In medicinal chemistry, the term defines either imaginable, virtual molecular fragments or chemical reagents from which drugs or drug candidates might be constructed or synthetically prepared.
|
Molecular building blocks
| 0.835694
|
2,095
|
Every probability measure is a continuous submeasure, so as the corresponding Boolean algebra of measurable sets modulo measure zero sets is complete, it is a Maharam algebra. Michel Talagrand (2008) solved a long-standing problem by constructing a Maharam algebra that is not a measure algebra, i.e., that does not admit any countably additive strictly positive finite measure.
|
Maharam algebra
| 0.83569
|
2,096
|
A continuous submeasure or Maharam submeasure on a Boolean algebra is a real-valued function m such that m ( 0 ) = 0 , m ( 1 ) = 1 , {\displaystyle m(0)=0,m(1)=1,} and m ( x ) > 0 {\displaystyle m(x)>0} if x ≠ 0 {\displaystyle x\neq 0} . If x ≤ y {\displaystyle x\leq y} , then m ( x ) ≤ m ( y ) {\displaystyle m(x)\leq m(y)} . m ( x ∨ y ) ≤ m ( x ) + m ( y ) − m ( x ∧ y ) {\displaystyle m(x\vee y)\leq m(x)+m(y)-m(x\wedge y)} . If x n {\displaystyle x_{n}} is a decreasing sequence with greatest lower bound 0, then the sequence m ( x n ) {\displaystyle m(x_{n})} has limit 0.A Maharam algebra is a complete Boolean algebra with a continuous submeasure.
|
Maharam algebra
| 0.83569
|
2,097
|
In mathematics, a Maharam algebra is a complete Boolean algebra with a continuous submeasure (defined below). They were introduced by Dorothy Maharam (1947).
|
Maharam algebra
| 0.83569
|
2,098
|
In statistics, the conditional probability table (CPT) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities of a single variable with respect to the others (i.e., the probability of each possible value of one variable if we know the values taken on by the other variables). For example, assume there are three random variables x 1 , x 2 , x 3 {\displaystyle x_{1},x_{2},x_{3}} where each has K {\displaystyle K} states. Then, the conditional probability table of x 1 {\displaystyle x_{1}} provides the conditional probability values P ( x 1 = a k ∣ x 2 , x 3 ) {\displaystyle P(x_{1}=a_{k}\mid x_{2},x_{3})} – where the vertical bar | {\displaystyle |} means “given the values of” – for each of the K possible values a k {\displaystyle a_{k}} of the variable x 1 {\displaystyle x_{1}} and for each possible combination of values of x 2 , x 3 . {\displaystyle x_{2},\,x_{3}.}
|
Conditional probability table
| 0.835687
|
2,099
|
Molecular modeling and design. It can solve distance geometry problems. SNLSDPclique. MATLAB code for locating sensors in a sensor network based on the distances between the sensors.
|
Distance geometry problem
| 0.835686
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.