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Nuclear magnetic resonance spectroscopy of proteins (usually abbreviated protein NMR) is a field of structural biology in which NMR spectroscopy is used to obtain information about the structure and dynamics of proteins, and also nucleic acids, and their complexes. The field was pioneered by Richard R. Ernst and Kurt Wüthrich at the ETH, and by Ad Bax, Marius Clore, Angela Gronenborn at the NIH, and Gerhard Wagner at Harvard University, among others. Structure determination by NMR spectroscopy usually consists of several phases, each using a separate set of highly specialized techniques. The sample is prepared, measurements are made, interpretive approaches are applied, and a structure is calculated and validated.
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Protein nuclear magnetic resonance
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In 1837, Jean-Baptiste Dumas considered the word "chemistry" to refer to the science concerned with the laws and effects of molecular forces. This definition further evolved until, in 1947, it came to mean the science of substances: their structure, their properties, and the reactions that change them into other substances – a characterization accepted by Linus Pauling. More recently, in 1998, Professor Raymond Chang broadened the definition of "chemistry" to mean the study of matter and the changes it undergoes.
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Chemical Science
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The definition of chemistry has changed over time, as new discoveries and theories add to the functionality of the science. The term "chymistry", in the view of noted scientist Robert Boyle in 1661, meant the subject of the material principles of mixed bodies. In 1663, the chemist Christopher Glaser described "chymistry" as a scientific art, by which one learns to dissolve bodies, and draw from them the different substances on their composition, and how to unite them again, and exalt them to a higher perfection.The 1730 definition of the word "chemistry", as used by Georg Ernst Stahl, meant the art of resolving mixed, compound, or aggregate bodies into their principles; and of composing such bodies from those principles.
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Chemical Science
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Scientists engaged in chemical research are known as chemists. Most chemists specialize in one or more sub-disciplines. Several concepts are essential for the study of chemistry; some of them are:
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Chemical Science
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Such behaviors are studied in a chemistry laboratory. The chemistry laboratory stereotypically uses various forms of laboratory glassware. However glassware is not central to chemistry, and a great deal of experimental (as well as applied/industrial) chemistry is done without it.
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Chemical Science
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Despite being unsuccessful in explaining the nature of matter and its transformations, alchemists set the stage for modern chemistry by performing experiments and recording the results. Robert Boyle, although skeptical of elements and convinced of alchemy, played a key part in elevating the "sacred art" as an independent, fundamental and philosophical discipline in his work The Sceptical Chymist (1661).While both alchemy and chemistry are concerned with matter and its transformations, the crucial difference was given by the scientific method that chemists employed in their work. Chemistry, as a body of knowledge distinct from alchemy, became an established science with the work of Antoine Lavoisier, who developed a law of conservation of mass that demanded careful measurement and quantitative observations of chemical phenomena. The history of chemistry afterwards is intertwined with the history of thermodynamics, especially through the work of Willard Gibbs.
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Chemical Science
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The history of chemistry spans a period from very old times to the present. Since several millennia BC, civilizations were using technologies that would eventually form the basis of the various branches of chemistry. Examples include extracting metals from ores, making pottery and glazes, fermenting beer and wine, extracting chemicals from plants for medicine and perfume, rendering fat into soap, making glass, and making alloys like bronze. Chemistry was preceded by its protoscience, alchemy, which operated a non-scientific approach to understanding the constituents of matter and their interactions.
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Chemical Science
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Physical chemistry is a distinct discipline from chemical physics, but again, there is very strong overlap. Theoretical chemistry is the study of chemistry via fundamental theoretical reasoning (usually within mathematics or physics). In particular the application of quantum mechanics to chemistry is called quantum chemistry. Since the end of the Second World War, the development of computers has allowed a systematic development of computational chemistry, which is the art of developing and applying computer programs for solving chemical problems. Theoretical chemistry has large overlap with (theoretical and experimental) condensed matter physics and molecular physics.Others subdivisions include electrochemistry, femtochemistry, flavor chemistry, flow chemistry, immunohistochemistry, hydrogenation chemistry, mathematical chemistry, molecular mechanics, natural product chemistry, organometallic chemistry, petrochemistry, photochemistry, physical organic chemistry, polymer chemistry, radiochemistry, sonochemistry, supramolecular chemistry, synthetic chemistry, and many others.
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Chemical Science
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Physical chemistry is the study of the physical and fundamental basis of chemical systems and processes. In particular, the energetics and dynamics of such systems and processes are of interest to physical chemists. Important areas of study include chemical thermodynamics, chemical kinetics, electrochemistry, statistical mechanics, spectroscopy, and more recently, astrochemistry.
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Chemical Science
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Modern Transmutation is a large component of nuclear chemistry, and the table of nuclides is an important result and tool for this field. Organic chemistry is the study of the structure, properties, composition, mechanisms, and reactions of organic compounds. An organic compound is defined as any compound based on a carbon skeleton.
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Chemical Science
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Primary systems of study include the chemistry of condensed phases (solids, liquids, polymers) and interfaces between different phases. Neurochemistry is the study of neurochemicals; including transmitters, peptides, proteins, lipids, sugars, and nucleic acids; their interactions, and the roles they play in forming, maintaining, and modifying the nervous system. Nuclear chemistry is the study of how subatomic particles come together and make nuclei.
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Chemical Science
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The distinction between organic and inorganic disciplines is not absolute and there is much overlap, most importantly in the sub-discipline of organometallic chemistry. Materials chemistry is the preparation, characterization, and understanding of substances with a useful function. The field is a new breadth of study in graduate programs, and it integrates elements from all classical areas of chemistry with a focus on fundamental issues that are unique to materials.
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Chemical Science
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Biochemistry and organic chemistry are closely related, as in medicinal chemistry or neurochemistry. Biochemistry is also associated with molecular biology and genetics. Inorganic chemistry is the study of the properties and reactions of inorganic compounds.
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Chemical Science
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Analytical chemistry incorporates standardized experimental methods in chemistry. These methods may be used in all subdisciplines of chemistry, excluding purely theoretical chemistry. Biochemistry is the study of the chemicals, chemical reactions and interactions that take place in living organisms.
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Chemical Science
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Chemistry is typically divided into several major sub-disciplines. There are also several main cross-disciplinary and more specialized fields of chemistry. Analytical chemistry is the analysis of material samples to gain an understanding of their chemical composition and structure.
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Chemical Science
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It is sometimes called the central science because it provides a foundation for understanding both basic and applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the properties of the soil on the moon (cosmochemistry), how medications work (pharmacology), and how to collect DNA evidence at a crime scene (forensics). Chemistry is a study that has existed since ancient times. Over this time frame, it has evolved, and now chemistry encompasses various areas of specialisation, or subdisciplines, that continue to increase in number and interrelate to create further interdisciplinary fields of study. The applications of various fields of chemistry are used frequently for economic purposes in the chemical industry.
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Chemical Science
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Chemistry is the scientific study of the properties and behavior of matter. It is a physical science under natural sciences that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a reaction with other substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology.
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Chemical Science
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The current model of atomic structure is the quantum mechanical model. Traditional chemistry starts with the study of elementary particles, atoms, molecules, substances, metals, crystals and other aggregates of matter. Matter can be studied in solid, liquid, gas and plasma states, in isolation or in combination. The interactions, reactions and transformations that are studied in chemistry are usually the result of interactions between atoms, leading to rearrangements of the chemical bonds which hold atoms together.
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Chemical Science
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A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases (such as solid, liquid or gaseous states) occur and coexist at equilibrium.
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Binary phase diagram
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This particular value of acceleration is typically denoted g {\displaystyle g}: If the body is not released from rest but instead launched upwards and/or horizontally with nonzero velocity, then free fall becomes projectile motion. When air resistance can be neglected, projectiles follow parabola-shaped trajectories, because gravity affects the body's vertical motion and not its horizontal. At the peak of the projectile's trajectory, its vertical velocity is zero, but its acceleration is g {\displaystyle g} downwards, as it is at all times. Setting the wrong vector equal to zero is a common confusion among physics students.
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Newton's Second Law
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For example, a free body diagram of a block sitting upon an inclined plane can illustrate the combination of gravitational force, "normal" force, friction, and string tension.Newton's second law is sometimes presented as a definition of force, i.e., a force is that which exists when an inertial observer sees a body accelerating. In order for this to be more than a tautology — acceleration implies force, force implies acceleration — some other statement about force must also be made. For example, an equation detailing the force might be specified, like Newton's law of universal gravitation. By inserting such an expression for F → {\displaystyle {\vec {F}}} into Newton's second law, an equation with predictive power can be written. Newton's second law has also been regarded as setting out a research program for physics, establishing that important goals of the subject are to identify the forces present in nature and to catalogue the constituents of matter.
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Newton's Second Law
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: 47 In the following centuries, versions of impetus theory were advanced by individuals including Nur ad-Din al-Bitruji, Avicenna, Abu'l-Barakāt al-Baghdādī, John Buridan, and Albert of Saxony. In retrospect, the idea of impetus can be seen as a forerunner of the modern concept of momentum. (The intuition that objects move according to some kind of impetus persists in many students of introductory physics.)
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Newton's Second Law
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Aristotle divided motion into two types: "natural" and "violent". The "natural" motion of terrestrial solid matter was to fall downwards, whereas a "violent" motion could push a body sideways. Moreover, in Aristotelian physics, a "violent" motion requires an immediate cause; separated from the cause of its "violent" motion, a body would revert to its "natural" behavior.
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Newton's Second Law
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The subject of physics is often traced back to Aristotle; however, the history of the concepts involved is obscured by multiple factors. An exact correspondence between Aristotelian and modern concepts is not simple to establish: Aristotle did not clearly distinguish what we would call speed and force, and he used the same term for density and viscosity; he conceived of motion as always through a medium, rather than through space. In addition, some concepts often termed "Aristotelian" might better be attributed to his followers and commentators upon him. These commentators found that Aristotelian physics had difficulty explaining projectile motion.
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Newton's Second Law
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Radiative transfer codes are used in broad range of applications. They are commonly used as forward models for the retrieval of geophysical parameters (such as temperature or humidity). Radiative transfer models are also used to optimize solar photovoltaic systems for renewable energy generation. Another common field of application is in a weather or climate model, where the radiative forcing is calculated for greenhouse gases, aerosols, or clouds.
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Radiative transfer model
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Each of these subarrays is sorted with an in-place sorting algorithm such as insertion sort, to discourage memory swaps, and normal merge sort is then completed in the standard recursive fashion. This algorithm has demonstrated better performance on machines that benefit from cache optimization. (LaMarca & Ladner 1997)
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Tiled merge sort
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On modern computers, locality of reference can be of paramount importance in software optimization, because multilevel memory hierarchies are used. Cache-aware versions of the merge sort algorithm, whose operations have been specifically chosen to minimize the movement of pages in and out of a machine's memory cache, have been proposed. For example, the tiled merge sort algorithm stops partitioning subarrays when subarrays of size S are reached, where S is the number of data items fitting into a CPU's cache.
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Tiled merge sort
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Available MKL libraries include SPG-GMKL: A scalable C++ MKL SVM library that can handle a million kernels. GMKL: Generalized Multiple Kernel Learning code in MATLAB, does ℓ 1 {\displaystyle \ell _{1}} and ℓ 2 {\displaystyle \ell _{2}} regularization for supervised learning. (Another) GMKL: A different MATLAB MKL code that can also perform elastic net regularization SMO-MKL: C++ source code for a Sequential Minimal Optimization MKL algorithm. Does p {\displaystyle p} -n orm regularization.
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Multiple kernel learning
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These approaches solve an optimization problem to determine parameters for the kernel combination function. This has been done with similarity measures and structural risk minimization approaches. For similarity measures such as the one defined above, the problem can be formulated as follows: max β , tr ( K t r a ′ ) = 1 , K ′ ≥ 0 A ( K t r a ′ , Y Y T ) . {\displaystyle \max _{\beta ,\operatorname {tr} (K'_{tra})=1,K'\geq 0}A(K'_{tra},YY^{T}).}
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Multiple kernel learning
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Multiple kernel learning refers to a set of machine learning methods that use a predefined set of kernels and learn an optimal linear or non-linear combination of kernels as part of the algorithm. Reasons to use multiple kernel learning include a) the ability to select for an optimal kernel and parameters from a larger set of kernels, reducing bias due to kernel selection while allowing for more automated machine learning methods, and b) combining data from different sources (e.g. sound and images from a video) that have different notions of similarity and thus require different kernels. Instead of creating a new kernel, multiple kernel algorithms can be used to combine kernels already established for each individual data source. Multiple kernel learning approaches have been used in many applications, such as event recognition in video, object recognition in images, and biomedical data fusion.
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Multiple kernel learning
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E {\displaystyle \mathrm {E} } is typically the square loss function (Tikhonov regularization) or the hinge loss function (for SVM algorithms), and R {\displaystyle R} is usually an ℓ n {\displaystyle \ell _{n}} norm or some combination of the norms (i.e. elastic net regularization). This optimization problem can then be solved by standard optimization methods. Adaptations of existing techniques such as the Sequential Minimal Optimization have also been developed for multiple kernel SVM-based methods.
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Multiple kernel learning
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In physics and electrical engineering, a conductor is an object or type of material that allows the flow of charge (electric current) in one or more directions. Materials made of metal are common electrical conductors. The flow of negatively charged electrons generates electric current, positively charged holes, and positive or negative ions in some cases.
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Electrical Conductor
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In probability theory and information theory, the variation of information or shared information distance is a measure of the distance between two clusterings (partitions of elements). It is closely related to mutual information; indeed, it is a simple linear expression involving the mutual information. Unlike the mutual information, however, the variation of information is a true metric, in that it obeys the triangle inequality.
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Variation of information
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The first edition of Core-Plus Mathematics was designed to meet the curriculum, teaching, and assessment standards from the National Council of Teachers of Mathematics and the broad goals outlined in the National Research Council report, Everybody Counts: A Report to the Nation on the Future of Mathematics Education. Later editions were designed to also meet the American Statistical Association Guidelines for Assessment and Instruction in Statistics Education (GAISE) and most recently the standards for mathematical content and practice in the Common Core State Standards for Mathematics (CCSSM).The program puts an emphasis on teaching and learning mathematics through mathematical modeling and mathematical inquiry. Each year, students learn mathematics in four interconnected strands: algebra and functions, geometry and trigonometry, statistics and probability, and discrete mathematical modeling.
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Core-Plus Mathematics Project
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Important theorems in geometry are not justified. Moreover, with the way the material is sequenced, some of these theorems cannot be justified".According to Prof. Harel, the Core-Plus program "excels in providing ample experience in solving application problems and in ensuring that students understand the meanings of the different parts of the modeling functions. The program also excels in its mission to contextualize the mathematics taught". However, it fails "to convey critical mathematical concepts and ideas that should and can be within reach for high school students".
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Core-Plus Mathematics Project
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Like in the algebra texts, the geometry text does not lead to a clear logical structure of the material taught. Because theoretical material is concealed within the text of the problems, "a teacher must identify all the critical problems and know in advance the intended structure to establish the essential mathematical progression. This task is further complicated by the fact that many critical problems appear in the homework sections.
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Core-Plus Mathematics Project
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In the algebra section, fundamental theorems on linear functions and quadratic functions were found not justified, except for the quadratic formula. Theorems are often presented without proof.
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Core-Plus Mathematics Project
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In 2009 professor of mathematics at the University of California in San Diego, Guershon Harel reviewed four high-school mathematics programs. The examined programs included Core-Plus Courses 1, 2, and 3. The examination focused on two topics in algebra and one topic in geometry, deemed by Prof. Harel central to the high school curriculum. The examination was intended "to ensure these topics are coherently developed, completely covered, mathematically correct, and provide students a solid foundation for further study in mathematics".From the outset, Prof. Harel noted that the content presentation in Core-Plus program is unusual in that its instructional units, from the start to the end, are made of word problems involving "real-life" situations.
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Core-Plus Mathematics Project
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The percentages of students who eventually passed a technical calculus course showed a statistically significant decline averaging 27 percent a year; this trend was accompanied by an obvious and statistically significant increase in percentages of students who placed into low-level and remedial algebra courses. Except for some top students, graduates of Core-Plus mathematics were struggling in college mathematics, earning below average grades. They were less well prepared than either graduates in the Control group (who came from a broad mix of curricula) or graduates of their own high schools before the implementation of Core-Plus mathematics.
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Core-Plus Mathematics Project
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Wilson says that the Core-Plus program "has a multitude of good problems, but never develops the core of the mathematics of linear functions. The problems are set in contexts and mathematics itself is rarely considered as a legitimate enterprise to investigate". The program lacks attention to algebraic manipulation" to the point that "symbolic algebra is minimized".In regards to geometry portion, Prof. Wilson concludes that the program fails to build geometry up from foundations in a mathematically sound and coherent way". He stresses out that "one significant goal of a geometry course is to teach logic, and this program fails on that account".Overall, the "unacceptable nature of geometry" and the fashion in which the program downplays "algebraic structure and skills" make the Core-Plus program unacceptable.
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Core-Plus Mathematics Project
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Likewise, there is never an attempt to show that a line graph comes from the usual form of a linear equation". Prof. Wilson considered this approach to be "a significant flaw in the mathematical foundation".Quoting the textbook, "Linear functions relating two variables x and y can be represented using tables, graphs, symbolic rules, or verbal descriptions", Prof. Wilson laments that although this statement is true, "the essence of algebra involves abstraction using symbols".Prof.
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Core-Plus Mathematics Project
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Professor W. Stephen Wilson from Johns Hopkins University evaluated the mathematical development and coherence of the Core-Plus program in 2009. In particular, he examined "the algebraic concepts and skills associated with linear functions because they are a critical foundation for the further study of algebra", and evaluated how the program presents the theorem that the sum of the angles of a triangle is 180 degrees, "which is a fundamental theorem of Euclidean geometry and it connects many of the basics in geometry to each other".Prof. Wilson noted that the major theme of the algebra portion of the program seems to involve creating a table from data, graphing the points from the table; given the table students are asked to find a corresponding function. In case of linear function, "at no point is there an attempt to show that the equation's graph really is a line.
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Core-Plus Mathematics Project
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Mathematics programs initially developed in the 1990s that were based on the NCTM's Curriculum and Evaluation Standards for School Mathematics, like Core-Plus Mathematics, have been the subject of controversy due to their differences from more conventional mathematics programs. In the case of Core-Plus Mathematics, there has been debate about (a) the international-like integrated nature of the curriculum, whereby each year students learn algebra, geometry, statistics, probability, and discrete mathematical modeling, as opposed to conventional U.S. curricula in which just a single subject is studied each year, (b) a concern that students may not adequately develop conventional algebraic skills, (c) a concern that students may not be adequately prepared for college, and (d) a mode of instruction that relies less on teacher lecture and demonstration and more on inquiry, problem solving in contextualized settings, and collaborative work by students.
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Core-Plus Mathematics Project
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The programs were obsessed with electronic calculators, and basic skills were disparaged.Specifically, Core-Plus Mathematics was criticized for exhibiting "too shallow a coverage of traditional algebra, and a focus on highly contextualized work". R. James Milgram, Professor of Mathematics at Stanford University, analyzed the program's effect on students in a top-performing high school. According to Milgram, "...there was no measure represented in the survey, such as ACT scores, SAT Math scores, grades in college math courses, level of college math courses attempted, where the students even met, let alone surpassed the comparison group ."
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Core-Plus Mathematics Project
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The letter was co-signed by more than 200 American scientists and mathematicians.Prof. Klein asserts that the mathematics programs criticized by the open letter had common features: they overemphasized data analysis and statistics, while de-emphasizing far more important areas of arithmetic and algebra. Many of the "higher-order thinking projects" turned out to be just aimless activities.
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Core-Plus Mathematics Project
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A study conducted by Schoen and Hirsch, two authors of Core-Plus Mathematics, reported that students using early versions of Core-Plus Mathematics did as well as or better than those in traditional single-subject curricula on all measures except paper-and-pencil algebra skills.A study on field-test versions of Core-Plus Mathematics, supported by a grant from the National Science Foundation (Award MDR 9255257) and published in 2000 in the Journal for Research in Mathematics Education, reported that students using the first field-test versions of Core-Plus Mathematics scored significantly better on tests of conceptual understanding and problem solving, while Algebra II students in conventional programs scored significantly better on a test of paper-and-pencil procedures.Other studies reported that Core-Plus Mathematics students displayed qualities such as engagement, eagerness, communication, flexibility, and curiosity to a much higher degree than did students who studied from more conventional programs. A review of research in 2008 concluded that there were modest effects for Core-Plus Mathematics on mostly standardized tests of mathematics.With regard to achievement of students in minority groups, an early peer-reviewed paper documenting the performance of students from under-represented groups using Core-Plus Mathematics reported that at the end of each of Course 1, Course 2, and Course 3, the posttest means on standardized mathematics achievement tests of Core-Plus Mathematics students in all minority groups (African Americans, Asian Americans, Hispanics, and Native/Alaskan Americans) were greater than those of the national norm group at the same pretest levels. Hispanics made the greatest pretest to posttest gains at the end of each course.
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Core-Plus Mathematics Project
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The course was re-organized around interwoven strands of algebra and functions, geometry and trigonometry, statistics and probability, and discrete mathematics. Lesson structure was updated, and technology tools, including CPMP-Tools software was introduced.
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Core-Plus Mathematics Project
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The course was aligned with the Common Core State Standards (CCSS) mathematical practices and content expectations. Expanded and enhanced Teacher's Guides include a CCSS pathway and a CPMP pathway through each unit. Course 4 was split into two versions: one called Preparation for Calculus, for STEM-oriented students, and an alternative course, Transition to College Mathematics and Statistics (TCMS), for college-bound students whose intended program of study does not require calculus.
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Core-Plus Mathematics Project
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The algorithm was developed by Google for use in machine translation.Similar earlier work includes Tomáš Mikolov's 2012 PhD thesis.In 2019, Facebook announced its use in symbolic integration and resolution of differential equations. The company claimed that it could solve complex equations more rapidly and with greater accuracy than commercial solutions such as Mathematica, MATLAB and Maple. First, the equation is parsed into a tree structure to avoid notational idiosyncrasies. An LSTM neural network then applies its standard pattern recognition facilities to process the tree.In 2020, Google released Meena, a 2.6 billion parameter seq2seq-based chatbot trained on a 341 GB data set.
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Seq2seq
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Seq2seq is a family of machine learning approaches used for natural language processing. Applications include language translation, image captioning, conversational models, and text summarization.
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Seq2seq
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There are various proofs of this theorem, by either analytic methods such as Liouville's theorem, or topological ones such as the winding number, or a proof combining Galois theory and the fact that any real polynomial of odd degree has at least one real root. Because of this fact, theorems that hold for any algebraically closed field apply to C . {\displaystyle \mathbb {C} .} For example, any non-empty complex square matrix has at least one (complex) eigenvalue.
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Complex value
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Given any complex numbers (called coefficients) a0, ..., an, the equation has at least one complex solution z, provided that at least one of the higher coefficients a1, ..., an is nonzero. This is the statement of the fundamental theorem of algebra, of Carl Friedrich Gauss and Jean le Rond d'Alembert. Because of this fact, C {\displaystyle \mathbb {C} } is called an algebraically closed field. This property does not hold for the field of rational numbers Q {\displaystyle \mathbb {Q} } (the polynomial x2 − 2 does not have a rational root, since √2 is not a rational number) nor the real numbers R {\displaystyle \mathbb {R} } (the polynomial x2 + a does not have a real root for a > 0, since the square of x is positive for any real number x).
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Complex value
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The complex number field is intrinsic to the mathematical formulations of quantum mechanics, where complex Hilbert spaces provide the context for one such formulation that is convenient and perhaps most standard. The original foundation formulas of quantum mechanics – the Schrödinger equation and Heisenberg's matrix mechanics – make use of complex numbers.
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Complex value
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The definition of the complex numbers involving two arbitrary real values immediately suggests the use of Cartesian coordinates in the complex plane. The horizontal (real) axis is generally used to display the real part, with increasing values to the right, and the imaginary part marks the vertical (imaginary) axis, with increasing values upwards. A charted number may be viewed either as the coordinatized point or as a position vector from the origin to this point. The coordinate values of a complex number z can hence be expressed in its Cartesian, rectangular, or algebraic form. Notably, the operations of addition and multiplication take on a very natural geometric character, when complex numbers are viewed as position vectors: addition corresponds to vector addition, while multiplication (see below) corresponds to multiplying their magnitudes and adding the angles they make with the real axis. Viewed in this way, the multiplication of a complex number by i corresponds to rotating the position vector counterclockwise by a quarter turn (90°) about the origin—a fact which can be expressed algebraically as
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Complex value
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These puzzles are based on algebra with binary variables taking a pair of values, for example, (no, yes), (false, true), (not exists, exists), (0, 1). It invites the player quickly establish some equations, and inequalities for the solution. The partitioning can be used to reduce the complexity of the problem. Moreover, if the puzzle is prepared in a way that there exists a unique solution only, this fact can be used to eliminate some variables without calculation. The problem can be modeled as binary integer linear programming which is a special case of integer linear programming.
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Board puzzles with algebra of binary variables
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In algebraic form we have two equations: a + b + c + d = 1a + b + c + d + e + f + g = 1Here a, b, c, and d correspond to the top four grayed cells in Figure 6. The cell with Δ is represented by the variable f, and the other two grayed cells are marked as e and g. If we set f = 1, then a = 0, b = 0, c = 0, d = 0, e = 0, g = 0. The first equation above will have the left hand side equal to 0 while the right hand side has 1.
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Board puzzles with algebra of binary variables
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Board puzzles with algebra of binary variables ask players to locate the hidden objects based on a set of clue cells and their neighbors marked as variables (unknowns). A variable with value of 1 corresponds to a cell with an object. Contrary, a variable with value of 0 corresponds to an empty cell—no hidden object.
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Board puzzles with algebra of binary variables
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This leads to the fact that c must be 1. The modification of a large equation into smaller form is not difficult. However, an equation set with binary variables cannot be always solved by applying linear algebra.
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Board puzzles with algebra of binary variables
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A game based on the algebra with binary variables can be visualized in many different ways. One generic way is to represent the right side of an equation as a clue in a cell (clue cell), and the neighbors of a clue cell as variables. A simple case is shown in Figure 1. The neighbors can be assumed to be the up/down, left/right, and corner cells that are sharing an edge or a corner.
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Board puzzles with algebra of binary variables
| 0.839276
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1,459
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Lodovico Ferrari is attributed with the discovery of the solution to the quartic in 1540, but since this solution, like all algebraic solutions of the quartic, requires the solution of a cubic to be found, it could not be published immediately. The solution of the quartic was published together with that of the cubic by Ferrari's mentor Gerolamo Cardano in the book Ars Magna (1545). The proof that this was the highest order general polynomial for which such solutions could be found was first given in the Abel–Ruffini theorem in 1824, proving that all attempts at solving the higher order polynomials would be futile. The notes left by Évariste Galois before his death in a duel in 1832 later led to an elegant complete theory of the roots of polynomials, of which this theorem was one result.
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Quartic equation
| 0.839272
|
1,460
|
The unifying characteristic is that there was some definition based on some standard. Eventually cubits and strides gave way to "customary units" to meet the needs of merchants and scientists. In the metric system and other recent systems, underlying relationships between quantities, as expressed by formulae of physics such as Newton's laws of motion, is used to select a small number of base quantities for which a unit is defined for each, from which all other units may be derived. Secondary units (multiples and submultiples) are derived from these base and derived units by multiplying by powers of ten, so for example where the unit of length is the metre; a distance of 1 m is 1,000 millimetres, or 0.001 kilometres.
|
Measurement system
| 0.83927
|
1,461
|
Preface Advertisement Chapter 1: Vector Analysis Chapter 2: Electrostatics Chapter 3: Potentials Chapter 4: Electric Fields in Matter Chapter 5: Magnetostatics Chapter 6: Magnetic Fields in Matter Chapter 7: Electrodynamics Chapter 8: Conservation Laws Chapter 9: Electromagnetic Waves Chapter 10: Potentials and Fields Chapter 11: Radiation Chapter 12: Electrodynamics and Relativity Appendix A: Vector Calculus in Curvilinear Coordinates Appendix B: The Helmholtz Theorem Appendix C: Units Index
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Introduction to Electrodynamics
| 0.839254
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1,462
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It contains no computer exercises. Nevertheless, it is perfectly adequate for undergraduate instruction in physics. As of June 2005, Inglefield has taught three semesters using this book.Physicists Yoni Kahn of Princeton University and Adam Anderson of the Fermi National Accelerator Laboratory indicated that Griffiths' Electrodynamics offers a dependable treatment of all materials in the electromagnetism section of the Physics Graduate Record Examinations (Physics GRE) except circuit analysis.
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Introduction to Electrodynamics
| 0.839254
|
1,463
|
The first chapter offers a valuable review of vector calculus, which is essential for understanding this subject. While most other authors, including those aimed at a more advanced audience, denote the distance from the source point to the field point by | x − x ′ | {\displaystyle |\mathbf {x} -\mathbf {x} '|} , Griffiths uses a script r {\displaystyle r} (see figure). Unlike some comparable books, the level of mathematical sophistication is not particularly high.
|
Introduction to Electrodynamics
| 0.839254
|
1,464
|
Moreover, the tone is clear and entertaining. Using this book "rejuvenated" his enthusiasm for teaching the subject.Colin Inglefield, an associate professor of physics at Weber State University (Utah), commented that the third edition is notable for its informal and conversational style that may appeal to a large class of students. The ordering of its chapters and its contents are fairly standard and are similar to texts at the same level.
|
Introduction to Electrodynamics
| 0.839254
|
1,465
|
According to Robert W. Scharstein from the Department of Electrical Engineering at the University of Alabama, the mathematics used in the third edition is just enough to convey the subject and the problems are valuable teaching tools that do not involve the "plug and chug disease." Although students of electrical engineering are not expected to encounter complicated boundary-value problems in their career, this book is useful to them as well, because of its emphasis on conceptual rather than mathematical issues. He argued that with this book, it is possible to skip the more mathematically involved sections to the more conceptually interesting topics, such as antennas.
|
Introduction to Electrodynamics
| 0.839254
|
1,466
|
The author sometimes referred to the reader directly. Physics received the primary focus. Equations are derived and explained, and common misconceptions are addressed.
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Introduction to Electrodynamics
| 0.839254
|
1,467
|
Paul D. Scholten, a professor at Miami University (Ohio), opined that the first edition of this book offers a streamlined, though not always in-depth, coverage of the fundamental physics of electrodynamics. Special topics such as superconductivity or plasma physics are not mentioned. Breaking with tradition, Griffiths did not give solutions to all the odd-numbered questions in the book. Another unique feature of the first edition is the informal, even emotional, tone.
|
Introduction to Electrodynamics
| 0.839254
|
1,468
|
The front cover has a picture of the handwritten Poisson's equations for electricity and magnetism on a chalkboard. The first inner cover contains vector identities, vector derivatives in Cartesian, spherical, and cylindrical coordinates, and the fundamental theorems of vector calculus. The second inner cover contains the basic equations of electrodynamics, the accepted values of some fundamental constants, and the transformation equations for spherical and cylindrical coordinates.
|
Introduction to Electrodynamics
| 0.839254
|
1,469
|
This book uses SI units (the mks convention) exclusively. A table for converting between SI and Gaussian units is given in Appendix C.Griffiths said he was able to reduce the price of his textbook on quantum mechanics simply by changing the publisher, from Pearson to Cambridge University Press. He has done the same with this one. (See the ISBN in the box to the right.)
|
Introduction to Electrodynamics
| 0.839254
|
1,470
|
As noted above, for small deformations, most elastic materials such as springs exhibit linear elasticity and can be described by a linear relation between the stress and strain. This relationship is known as Hooke's law. A geometry-dependent version of the idea was first formulated by Robert Hooke in 1675 as a Latin anagram, "ceiiinosssttuv". He published the answer in 1678: "Ut tensio, sic vis" meaning "As the extension, so the force", a linear relationship commonly referred to as Hooke's law. This law can be stated as a relationship between tensile force F and corresponding extension displacement x {\displaystyle x} , F = k x , {\displaystyle F=kx,} where k is a constant known as the rate or spring constant. It can also be stated as a relationship between stress σ {\displaystyle \sigma } and strain ε {\displaystyle \varepsilon }: σ = E ε , {\displaystyle \sigma =E\varepsilon ,} where E is known as the Young's modulus.Although the general proportionality constant between stress and strain in three dimensions is a 4th-order tensor called stiffness, systems that exhibit symmetry, such as a one-dimensional rod, can often be reduced to applications of Hooke's law.
|
Elasticity (solid mechanics)
| 0.839249
|
1,471
|
In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to plasticity, in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials.
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Elasticity (solid mechanics)
| 0.839249
|
1,472
|
In molecular biology, protein fold classes are broad categories of protein tertiary structure topology. They describe groups of proteins that share similar amino acid and secondary structure proportions. Each class contains multiple, independent protein superfamilies (i.e. are not necessarily evolutionarily related to one another).
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Protein fold class
| 0.839248
|
1,473
|
In mass spectrometry of peptides and proteins, knowledge of the masses of the residues is useful. The mass of the peptide or protein is the sum of the residue masses plus the mass of water (Monoisotopic mass = 18.01056 Da; average mass = 18.0153 Da). The residue masses are calculated from the tabulated chemical formulas and atomic weights. In mass spectrometry, ions may also include one or more protons (Monoisotopic mass = 1.00728 Da; average mass* = 1.0074 Da). *Protons cannot have an average mass, this confusingly infers to Deuterons as a valid isotope, but they should be a different species (see Hydron (chemistry)) § Monoisotopic mass
|
Proteinogenic amino acids
| 0.839244
|
1,474
|
Modern x86 processors are heavily optimized with techniques such as instruction pipelines, out-of-order execution, memory prefetching, memory dependence prediction, and branch prediction to preemptively load memory from RAM (and other caches) to speed up execution even further. With this amount of complexity from performance optimization, it is difficult to state with certainty the effects memory timings may have on performance. Different workloads have different memory access patterns and are affected differently in performance by these memory timings.
|
Memory timing
| 0.839215
|
1,475
|
Modern pharmacology is interdisciplinary and involves biophysical and computational sciences, and analytical chemistry. A pharmacist needs to be well-equipped with knowledge on pharmacology for application in pharmaceutical research or pharmacy practice in hospitals or commercial organisations selling to customers. Pharmacologists, however, usually work in a laboratory undertaking research or development of new products. Pharmacological research is important in academic research (medical and non-medical), private industrial positions, science writing, scientific patents and law, consultation, biotech and pharmaceutical employment, the alcohol industry, food industry, forensics/law enforcement, public health, and environmental/ecological sciences. Pharmacology is often taught to pharmacy and medicine students as part of a Medical School curriculum.
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Therapeutic drugs
| 0.839182
|
1,476
|
The study of chemicals requires intimate knowledge of the biological system affected. With the knowledge of cell biology and biochemistry increasing, the field of pharmacology has also changed substantially. It has become possible, through molecular analysis of receptors, to design chemicals that act on specific cellular signaling or metabolic pathways by affecting sites directly on cell-surface receptors (which modulate and mediate cellular signaling pathways controlling cellular function). Chemicals can have pharmacologically relevant properties and effects. Pharmacokinetics describes the effect of the body on the chemical (e.g. half-life and volume of distribution), and pharmacodynamics describes the chemical's effect on the body (desired or toxic).
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Therapeutic drugs
| 0.839182
|
1,477
|
Receptors are typically categorised based on structure and function. Major receptor types studied in pharmacology include G protein coupled receptors, ligand gated ion channels and receptor tyrosine kinases. Network pharmacology is a subfield of pharmacology that combines principles from pharmacology, systems biology, and network analysis to study the complex interactions between drugs and targets (e.g., receptors or enzymes etc) in biological systems. The topology of a biochemical reaction network determines the shape of drug dose-response curve as well as the type of drug-drug interactions, thus can help designing efficient and safe therapeutic strategies. The topology Network pharmacology utilizes computational tools and network analysis algorithms to identify drug targets, predict drug-drug interactions, elucidate signaling pathways, and explore the polypharmacology of drugs.
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Therapeutic drugs
| 0.839182
|
1,478
|
The field encompasses drug composition and properties, functions, sources, synthesis and drug design, molecular and cellular mechanisms, organ/systems mechanisms, signal transduction/cellular communication, molecular diagnostics, interactions, chemical biology, therapy, and medical applications and antipathogenic capabilities. The two main areas of pharmacology are pharmacodynamics and pharmacokinetics. Pharmacodynamics studies the effects of a drug on biological systems, and pharmacokinetics studies the effects of biological systems on a drug.
|
Therapeutic drugs
| 0.839182
|
1,479
|
The study of pharmacology overlaps with biomedical sciences and is the study of the effects of drugs on living organisms. Pharmacological research can lead to new drug discoveries, and promote a better understanding of human physiology. Students of pharmacology must have a detailed working knowledge of aspects in physiology, pathology, and chemistry. They may also require knowledge of plants as sources of pharmacologically-active compounds.
|
Therapeutic drugs
| 0.839182
|
1,480
|
Pharmacology is a branch of medicine, biology, and pharmaceutical sciences concerned with drug or medication action, where a drug may be defined as any artificial, natural, or endogenous (from within the body) molecule which exerts a biochemical or physiological effect on the cell, tissue, organ, or organism (sometimes the word pharmacon is used as a term to encompass these endogenous and exogenous bioactive species). It is the science of drugs including their origin, composition, pharmacokinetics, therapeutic use, and toxicology. More specifically, it is the study of the interactions that occur between a living organism and chemicals that affect normal or abnormal biochemical function. If substances have medicinal properties, they are considered pharmaceuticals.
|
Therapeutic drugs
| 0.839182
|
1,481
|
A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an object is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical proofs. Typically, a mathematical object can be a value that can be assigned to a variable, and therefore can be involved in formulas. Commonly encountered mathematical objects include numbers, sets, functions, expressions, geometric objects, transformations of other mathematical objects, and spaces. Mathematical objects can be very complex; for example, theorems, proofs, and even theories are considered as mathematical objects in proof theory. The ontological status of mathematical objects has been the subject of much investigation and debate by philosophers of mathematics.
|
Mathematical objects
| 0.839165
|
1,482
|
The benefit of the through and across analogy is that when the through Hamiltonian variable is chosen to be a conserved quantity, Kirchhoff's node rule can be used, and the model will have the same topology as the real system. Thus, in the electrical domain the across variable is voltage and the through variable is current. In the mechanical domain the analogous variables are velocity and force, as in the mobility analogy.
|
Mechanical–electrical analogies
| 0.839141
|
1,483
|
Mobility analogies, also called the Firestone analogy, are the electrical duals of impedance analogies. That is, the effort variable in the mechanical domain is analogous to current (the flow variable) in the electrical domain, and the flow variable in the mechanical domain is analogous to voltage (the effort variable) in the electrical domain. The electrical network representing the mechanical system is the dual network of that in the impedance analogy.The mobility analogy is characterised by admittance in the same way that the impedance analogy is characterised by impedance. Admittance is the algebraic inverse of impedance. In the mechanical domain, mechanical admittance is more usually called mobility.
|
Mechanical–electrical analogies
| 0.839141
|
1,484
|
In the impedance analogy, the ratio of the power conjugate variables is always a quantity analogous to electrical impedance. For instance force/velocity is mechanical impedance. The mobility analogy does not preserve this analogy between impedances across domains, but it does have another advantage over the impedance analogy. In the mobility analogy the topology of networks is preserved, a mechanical network diagram has the same topology as its analogous electrical network diagram.
|
Mechanical–electrical analogies
| 0.839141
|
1,485
|
The usual choice for a translational mechanical system is force (F) and velocity (u) but it is not the only choice. A different pair may be more appropriate for a system with a different geometry, such as a rotational system.Even after the mechanical fundamental variables have been chosen, there is still not a unique set of analogs. There are two ways that the two pairs of power conjugate variables can be associated with each other in the analogy.
|
Mechanical–electrical analogies
| 0.839141
|
1,486
|
The closest pair of points problem or closest pair problem is a problem of computational geometry: given n {\displaystyle n} points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane was among the first geometric problems that were treated at the origins of the systematic study of the computational complexity of geometric algorithms.
|
Closest pair problem
| 0.839133
|
1,487
|
Parallel coordinates were often said to be invented by Philbert Maurice d'Ocagne in 1885, but even though the words "Coordonnées parallèles" appear in the book title this work has nothing to do with the visualization techniques of the same name; the book only describes a method of coordinate transformation. But even before 1885, parallel coordinates were used, for example in Henry Gannetts "General Summary, Showing the Rank of States, by Ratios, 1880", or afterwards in Henry Gannetts "Rank of States and Territories in Population at Each Census, 1790-1890" in 1898. They were popularised again 87 years later by Alfred Inselberg in 1985 and systematically developed as a coordinate system starting from 1977. Some important applications are in collision avoidance algorithms for air traffic control (1987—3 USA patents), data mining (USA patent), computer vision (USA patent), Optimization, process control, more recently in intrusion detection and elsewhere.
|
Parallel coordinates
| 0.839058
|
1,488
|
A pair of lines intersects at a unique point which has two coordinates and, therefore, can correspond to a unique line which is also specified by two parameters (or two points). By contrast, more than two points are required to specify a curve and also a pair of curves may not have a unique intersection. Hence by using curves in parallel coordinates instead of lines, the point line duality is lost together with all the other properties of projective geometry, and the known nice higher-dimensional patterns corresponding to (hyper)planes, curves, several smooth (hyper)surfaces, proximities, convexity and recently non-orientability.
|
Parallel coordinates
| 0.839058
|
1,489
|
Part B of the book discusses the potential-based method by which the Erdős–Selfridge theorem was proven, and extends it to additional examples, including some in which the maker wins. Part C covers more advanced techniques of determining the outcome of a positional game, and introduces more complex games of this type, including picker-chooser games in which one player picks two unchosen elements and the other player chooses which one to give to each player. Part D includes the decomposition of games and the use of techniques from Ramsey theory to prove theorems about games. A collection of open problems in this area is provided at the end of the book.
|
Combinatorial Games: Tic-Tac-Toe Theory
| 0.83903
|
1,490
|
Part A looks at the distinction between weak wins (the player can force the existence of a winning configuration) and strong wins (the winning configuration can be forced to exist before the other player gets a win). It shows that, for maker-breaker games over the points on the plane in which the players attempt to create a congruent copy of some finite point set, the maker always has a weak win, but to do so must sometimes allow the breaker to form a winning configuration earlier. It also includes an extensive analysis of tic-tac-toe-like symmetric line-forming games, and discusses the Erdős–Selfridge theorem according to which sparse-enough sets of winning configurations lead to drawn maker-breaker games.
|
Combinatorial Games: Tic-Tac-Toe Theory
| 0.83903
|
1,491
|
A positional game is a game in which players alternate in taking possession of a given set of elements, with the goal of forming a winning configuration of elements; for instance, in tic-tac-toe and gomoku, the elements are the squares of a grid, and the winning configurations are lines of squares. These examples are symmetric: both players have the same winning configurations. However, positional games also include other possibilities such as the maker-breaker games in which one player (the "maker") tries to form a winning configuration and the other (the "breaker") tries to put off that outcome indefinitely or until the end of the game. In symmetric positional games one can use a strategy-stealing argument to prove that the first player has an advantage, but realizing this advantage by a constructive strategy can be very difficult.According to the Hales–Jewett theorem, in tic-tac-toe-like games involving forming lines on a grid or higher-dimensional lattice, grids that are small relative to their dimension cannot lead to a drawn game: once the whole grid is partitioned between the two players, one of them will necessarily have a line.
|
Combinatorial Games: Tic-Tac-Toe Theory
| 0.83903
|
1,492
|
In 2019, Haojia et al compared both scRNA-seq and snRNA-seq in a genomic study around the kidney. They found snRNA-seq accomplishes an equivalent gene detection rate to that of scRNA-seq in adult kidney with several significant advantages (including compatibility with frozen samples, reduced dissociation bias and so on ). In 2019, Joshi et al used snRNA-seq in a human lung biology study in which they found snRNA-seq allowed unbiased identification of cell types from frozen healthy and fibrotic lung tissues. Adult mammalian heart tissue can be extremely hard to dissociate without damaging cells, which does not allow for easy sequencing of the tissue. However, in 2020, German scientists presented the first report of sequencing an adult mammalian heart by using snRNA-seq and were able to provide practical cell‐type distributions within the heart
|
SnRNA-seq
| 0.83901
|
1,493
|
In neuroscience, neurons have an interconnected nature which makes it extremely hard to isolate intact single neurons. As snRNA-seq has emerged as an alternative method of assessing a cell's transcriptome through the isolation of single nuclei, it has been possible to conduct single-neuron studies from postmortem human brain tissue. snRNA-seq has also enabled the first single neuron analysis of immediate early gene expression (IEGs) associated with memory formation in the mouse hippocampus. In 2019, Dmitry et al used the method on cortical tissue from ASD patients to identify ASD-associated transcriptomic changes in specific cell types, which is the first cell-type-specific transcriptome assessment in brains affected by ASD.Outside of neuroscience, snRNA-seq has also been used in other research areas.
|
SnRNA-seq
| 0.83901
|
1,494
|
In geometry, line coordinates are used to specify the position of a line just as point coordinates (or simply coordinates) are used to specify the position of a point.
|
Line coordinates
| 0.838934
|
1,495
|
z = ( tanh d 2 ) ( sinh s + j cosh s ) {\displaystyle z=\left(\tanh {\frac {d}{2}}\right)(\sinh s+j\cosh s)} denotes the ultraparallel line. : 118 The motions of the line geometry are described with linear fractional transformations on the appropriate complex planes. : 87, 123
|
Line coordinates
| 0.838934
|
1,496
|
The angular momentum problem is a problem in astrophysics identified by Leon Mestel in 1965.It was found that the angular momentum of a protoplanetary disk is misappropriated when compared to models during stellar birth. The Sun and other stars are predicted by models to be rotating considerably faster than they actually are. The Sun, for example, only accounts for about 0.3 percent of the total angular momentum of the Solar System while about 60% is attributed to Jupiter.
|
Angular momentum problem
| 0.838918
|
1,497
|
Testing is trying something to find out about it ("To put to the proof; to prove the truth, genuineness, or quality of by experiment" according to the Collaborative International Dictionary of English) and to validate is to prove that something is valid ("To confirm; to render valid" Collaborative International Dictionary of English). With this perspective, the most common use of the terms test set and validation set is the one here described. However, in both industry and academia, they are sometimes used interchanged, by considering that the internal process is testing different models to improve (test set as a development set) and the final model is the one that needs to be validated before real use with an unseen data (validation set). "The literature on machine learning often reverses the meaning of 'validation' and 'test' sets. This is the most blatant example of the terminological confusion that pervades artificial intelligence research." Nevertheless, the important concept that must be kept is that the final set, whether called test or validation, should only be used in the final experiment.
|
Training data
| 0.838889
|
1,498
|
In 1968 these journals were merged to form part of the Journal of Physics series of journals, A to E, the fifth journal in the series being Journal of Physics E: Scientific Instruments. In 1990 the journal was renamed as Measurement Science and Technology to reflect the shift away from many scientists making their own instruments. Since 2003 the journal archive containing all articles published since 1874 are available online.
|
Measurement Science and Technology
| 0.838884
|
1,499
|
The Institute of Physics merged with the Physical Society of London in 1960. By this time the Proceedings of the Physical Society had grown in size and the quality of the applied journals, British Journal of Applied Physics and Journal of Scientific Instruments, had been improved.
|
Measurement Science and Technology
| 0.838884
|
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