id int32 0 100k | text stringlengths 20 3.54k | source stringlengths 1 104 | similarity float32 0.8 0.91 |
|---|---|---|---|
5,500 | These results were important to Newton's analysis of planetary motion; they are not immediately obvious, but they can be proven with calculus. (Gauss's law for gravity offers an alternative way to state the theorem.) In addition to gravity, the shell theorem can also be used to describe the electric field generated by ... | Shell theorem | 0.830666 |
5,501 | The extended Euclidean algorithm may be used to compute it. The sedenions are an algebra in which every nonzero element has a multiplicative inverse, but which nonetheless has divisors of zero, that is, nonzero elements x, y such that xy = 0. A square matrix has an inverse if and only if its determinant has an inverse ... | Arithmetic inverse | 0.830663 |
5,502 | Examples such as this demonstrate that preserving a healthy phenotype largely rests on nutritional decision-making skills. The concept that nutrition and diet affect phenotype extends to what the mother eats during pregnancy, which can have drastic effects on the outcome of the phenotype of the child. A recent study by... | Human variability | 0.830663 |
5,503 | Condition 2 is the other De Morgan law. Condition 6 says that the join operation ∨reg on the Boolean algebra Hreg of regular elements of H coincides with the operation ∨ of H. Condition 7 states that every regular element is complemented, i.e., Hreg = Hcomp. | Heyting algebra | 0.830662 |
5,504 | The motivation to invent quantum tic-tac-toe was to explore what it means to be in two places at once. In classical physics, a single object cannot be in two places at once. In quantum physics, however, the mathematics used to describe quantum systems seems to imply that before being subjected to quantum measurement (o... | Quantum tic-tac-toe | 0.830661 |
5,505 | VSim is a cross-platform (Windows, Linux, and macOS) computational framework for multiphysics, including electrodynamics in the presence of metallic and dielectric shapes as well as with or without self-consistent charged particles and fluids. VSim comes with VSimComposer, a full-featured graphical user interface for v... | VSim | 0.830659 |
5,506 | For example, in CIFAR-10, images are only of size 32×32×3 (32 wide, 32 high, 3 color channels), so a single fully connected neuron in the first hidden layer of a regular neural network would have 32*32*3 = 3,072 weights. A 200×200 image, however, would lead to neurons that have 200*200*3 = 120,000 weights. Also, such n... | Convolutional layer | 0.830659 |
5,507 | Poincaré went further; if the area is of the same kind as a disk, as is the case for the cup of coffee, there must necessarily be a fixed point. This fixed point is invariant under all functions which associate to each point of the original surface its position after a short time interval t. If the area is a circular b... | Brouwer fixed-point theorem | 0.830651 |
5,508 | The structure on its sub-object classifier is that of a Heyting algebra. To get a more classical set theory one can look at toposes in which it is moreover a Boolean algebra, or specialising even further, at those with just two truth-values. In that book, the talk is about constructive mathematics; but in fact this can... | History of topos theory | 0.830649 |
5,509 | In general topology and number theory, branches of mathematics, one can define various topologies on the set Z {\displaystyle \mathbb {Z} } of integers or the set Z > 0 {\displaystyle \mathbb {Z} _{>0}} of positive integers by taking as a base a suitable collection of arithmetic progressions, sequences of the form { b ... | Evenly spaced integer topology | 0.830649 |
5,510 | Setting out the principles of power-to-weight ratio in sustaining flight.From the age of ten, Cayley began studying the physics of bird flight and his school notebooks contained sketches in which he was developing his ideas on the theories of flight. It has been claimed that these sketches show that Cayley modeled the ... | Early flying machines | 0.830644 |
5,511 | As the iteration progresses, according to one report, the "attention algorithm ... mimics the way a person might assemble a jigsaw puzzle: first connecting pieces in small clumps—in this case clusters of amino acids—and then searching for ways to join the clumps in a larger whole. "The output of these iterations then i... | AlphaFold 2 | 0.830643 |
5,512 | In metaphysics there are many troubling questions pertaining to parts and wholes. One question addresses constitution and persistence, another asks about composition. | Mereology | 0.83064 |
5,513 | The High Elevation Antarctic Terahertz telescope is a far-infrared telescope, established by the University of Arizona and the University of New South Wales located at Ridge A at an altitude of 4,053 metres (13,297 ft), considered the most ideal location for observation in the world. The extraordinary low humidity make... | High Elevation Antarctic Terahertz Telescope | 0.830639 |
5,514 | Unfortunately, this convention clashes badly with the next convention: In algebra, the usual convention is that the language has two constants, 0 and 1, and two binary functions · and +. The function · has the same meaning as ∧, but a+b means a∨b∧¬(a∧b). The reason for this is that the axioms for a Boolean algebra are ... | First-order theories | 0.830639 |
5,515 | In Machine Learning, this theory can be applied in training computer programs. Concept Learning: Inferring a Boolean-valued function from training examples of its input and output. A concept is an idea of something formed by combining all its features or attributes which construct the given concept. Every concept has t... | Concept learning | 0.830638 |
5,516 | Physics is taught from Newtonian mechanics, Fluid Dynamics, Waves, Optics, Electricity, Magnetism, to modern physics, usually ending with STR, Relativistic Dynamics, Quantum Theory, Quantum Mechanics, Molecular Physics, Physical Chemistry, Atomic Physics, Solid State Physics, Quantum Optics, Nuclear Physics, Nuclear En... | Mathematical Grammar School | 0.830637 |
5,517 | "Electrical Engineering. Standards of Measurement page 1024". The Mechanical Engineer's Pocket-book (5th ed.). | Electromagnetic units | 0.830637 |
5,518 | The Wien effect is the experimentally-observed increase in ionic mobility or conductivity of electrolytes at very high gradient of electrical potential. A theoretical explanation has been proposed by Lars Onsager.A related phenomenon is known as the Second Wien Effect or the dissociation field effect, and it involves i... | Wien effect | 0.830636 |
5,519 | Exploring the physics and engineering behind this design, requires looking at basic magnetism. A standard bar magnet has two magnetic poles: north and south. (The north will read positive on a gauss meter and the south will read negative.) Magnetic field are mapped using magnetic flux lines. | Magnetic level gauge | 0.830635 |
5,520 | Classes in botany and evolution that she had taken while pursuing her degree shaped her thinking about the work she was doing in the chemistry laboratory. During her crystallographic studies, Jane Richardson had come to realize that a general classification scheme can be developed from the recurring structural motifs o... | Jane S. Richardson | 0.830634 |
5,521 | Since 1980, western blot has emerged as the most used method in molecular biology for determining the presence and quantity of a certain protein. Over the years, plenty of "advanced" and "optimized" systematical methods have been developed. These developments provide advanced and more sensitive results, with the aid of... | Western blotting | 0.830626 |
5,522 | A special case of the quantum mechanical three-body problem is the hydrogen molecule ion, H+2. Two of the three bodies are nuclei and the third is a fast moving electron. The two nuclei are 1800 times heavier than the electron and thus modeled as fixed centers. It is well known that the Schrödinger wave equation is sep... | Euler's three-body problem | 0.830624 |
5,523 | 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 o... | Charged particle equilibrium | 0.830621 |
5,524 | Equipped with TECAN Evo 200 (robotic platform), HANABHI Harvester PII & PIII (chromosome harvesters), HANABI Spreader, Auto Stainer & Auto Image capture digital microscope, and LIMS. Microbiology Laboratory: Used for the manipulation of pathogenic microorganisms. Equipped with laminar flow hoods, refrigerators, CO2 inc... | Armed Forces Radiobiology Research Institute | 0.830619 |
5,525 | The Mathematics of Games and Gambling is a book on probability theory and its application to games of chance. It was written by Edward Packel, and published in 1981 by the Mathematical Association of America as volume 28 of their New Mathematical Library series, with a second edition in 2006. | The Mathematics of Games and Gambling | 0.830618 |
5,526 | Much of the initial resistance to Joule's work stemmed from its dependence upon extremely precise measurements. He claimed to be able to measure temperatures to within 1⁄200 of a degree Fahrenheit (3 mK). Such precision was certainly uncommon in contemporary experimental physics but his doubters may have neglected his ... | James Prescott Joule | 0.830618 |
5,527 | A lattice is another kind of algebraic structure with two binary operations, ∧ and ∨ . {\displaystyle \,\land {\text{ and }}\lor .} If either of these operations distributes over the other (say ∧ {\displaystyle \,\land \,} distributes over ∨ {\displaystyle \,\lor } ), then the reverse also holds ( ∨ {\displaystyle \,\l... | Antidistributive | 0.830617 |
5,528 | This can help eliminate dependencies and thus enable other optimizations. Certain architectures utilize looping constructs at assembly level that count in a single direction only (e.g., decrement-jump-if-not-zero ). Scheduling – this divides a loop into multiple parts that may be run concurrently on multiple processors... | Loop optimization | 0.830615 |
5,529 | For example, the University of California (UC) system requires three years of "college-preparatory mathematics that include the topics covered in elementary and advanced algebra and two- and three-dimensional geometry" to be admitted. After the California Department of Education adopted the Common Core, the UC system c... | Mathematics education in the United States | 0.830615 |
5,530 | Similarly, MFT can be applied to other types of Hamiltonian as in the following cases: To study the metal–superconductor transition. In this case, the analog of the magnetization is the superconducting gap Δ {\displaystyle \Delta } . The molecular field of a liquid crystal that emerges when the Laplacian of the directo... | Mean-field approximation | 0.830614 |
5,531 | At commercialization, read length had a normal distribution with a mean of about 1100 bases. A new chemistry kit released in early 2012 increased the sequencer's read length; an early customer of the chemistry cited mean read lengths of 2500 to 2900 bases.The XL chemistry kit released in late 2012 increased average rea... | SMRT sequencing | 0.830612 |
5,532 | Elementary algebra builds on and extends arithmetic by introducing letters called variables to represent general (non-specified) numbers. This is useful for several reasons. Variables may represent numbers whose values are not yet known. | Elementary algebra | 0.830609 |
5,533 | This also means that in this situation, there can be more than one Rate-limiting step (biochemistry) in a pathway. Unlike a linear pathway, values for C e 3 J 2 {\displaystyle C_{e_{3}}^{J_{2}}} and C e 1 J 2 {\displaystyle C_{e_{1}}^{J_{2}}} are not bounded between zero and one. Depending on the values of the elastici... | Branched pathways | 0.830607 |
5,534 | Given the binary nature of classification, a natural selection for a loss function (assuming equal cost for false positives and false negatives) would be the 0-1 loss function (0–1 indicator function), which takes the value of 0 if the predicted classification equals that of the true class or a 1 if the predicted class... | Loss functions for classification | 0.8306 |
5,535 | Many historians translate the word to linear algebra today. In this chapter, the process of Gaussian elimination and back-substitution are used to solve systems of equations with many unknowns. Problems were done on a counting board and included the use of negative numbers as well as fractions. The counting board was e... | Chinese mathematics | 0.8306 |
5,536 | The second product is a set of tissue blocks, typically postage stamp-sized portions of tissue sealed in plastic cassettes, which will be processed into slides for microscopic examination. Since only a minority of the tissue from a large specimen can reasonably be subject to microscopic examination, the success of the ... | Gross examination | 0.830598 |
5,537 | Etzioni, Oren (June 15, 2016). "Deep Learning Isn't a Dangerous Magic Genie. It's Just Math". | Oren Etzioni | 0.830598 |
5,538 | Probabilistic methods may be paired with a controlled vocabulary, such as GO; for example, protein-protein interaction (PPI) networks usually place proteins with similar functions close to each other.Machine learning methods are also used to generate functional annotations for novel proteins based on GO terms. Generall... | DNA annotation | 0.830598 |
5,539 | The only two kinds of statements accepted by the Vienna Circle are synthetic statements a posteriori (i.e., scientific statements) and analytic statements a priori (i.e., logical and mathematical statements). However, the persistence of metaphysics is connected not only with logical mistakes but also with "social and e... | Vienna circle | 0.830595 |
5,540 | In general, a larger fraction of molecules in the first state means a higher number of transitions to the second state. This gives a stronger spectral line. However, there are other factors that influence the intensity of a spectral line, such as whether it is caused by an allowed or a forbidden transition. The softmax... | Boltzmann population | 0.830594 |
5,541 | Disc integration, also known in integral calculus as the disc method, is a method for calculating the volume of a solid of revolution of a solid-state material when integrating along an axis "parallel" to the axis of revolution. This method models the resulting three-dimensional shape as a stack of an infinite number o... | Disk integration | 0.830593 |
5,542 | Mating conditions are definitions of the relative position of components between each other; for example alignment of axis of two holes or distance of two faces from one another. The final position of all components based on these relationships is calculated using a geometry constraint engine built into the CAD or visu... | Assembly modelling | 0.830592 |
5,543 | In computer science, a search algorithm is an algorithm designed to solve a search problem. Search algorithms work to retrieve information stored within particular data structure, or calculated in the search space of a problem domain, with either discrete or continuous values. Although search engines use search algorit... | Search algorithms | 0.83059 |
5,544 | The GAISE document provides a two-dimensional framework, specifying four components used in statistical problem solving (formulating questions, collecting data, analyzing data, and interpreting results) and three levels of conceptual understanding through which a student should progress (Levels A, B, and C). A direct p... | Guidelines for Assessment and Instruction in Statistics Education | 0.830588 |
5,545 | The philosophy of probability presents problems chiefly in matters of epistemology and the uneasy interface between mathematical concepts and ordinary language as it is used by non-mathematicians. Probability theory is an established field of study in mathematics. It has its origins in correspondence discussing the mat... | Probability interpretations | 0.830588 |
5,546 | Decision trees are a popular method for various machine learning tasks. Tree learning "come closest to meeting the requirements for serving as an off-the-shelf procedure for data mining", say Hastie et al., "because it is invariant under scaling and various other transformations of feature values, is robust to inclusio... | Random multinomial logit | 0.830587 |
5,547 | Frattini's argument shows that a Sylow subgroup of a normal subgroup provides a factorization of a finite group. A slight generalization known as Burnside's fusion theorem states that if G is a finite group with Sylow p-subgroup P and two subsets A and B normalized by P, then A and B are G-conjugate if and only if they... | Sylow group | 0.830584 |
5,548 | In mathematics, a quadratic-linear algebra is an algebra over a field with a presentation such that all relations are sums of monomials of degrees 1 or 2 in the generators. They were introduced by Polishchuk and Positselski (2005, p.101). An example is the universal enveloping algebra of a Lie algebra, with generators ... | Quadratic-linear algebra | 0.830583 |
5,549 | Connectomes of higher organism's brains requires considerable data. For the fruit fly, for example, roughly 10 terabytes of image data are processed, by humans and computers, to generate several gigabyte of connectome data. Easy interaction with this data requires an interactive query interface, where researchers can l... | Neural circuit reconstruction | 0.830582 |
5,550 | This section is based on the paper On the difficulty of training Recurrent Neural Networks by Pascanu, Mikolov, and Bengio. | Vanishing gradient problem | 0.830578 |
5,551 | Space research. Geodesy 53 Physics 531/534 Mechanics 535 Optics 536 Heat. | Universal Decimal Classification | 0.830577 |
5,552 | These were early examples of what would today be called 'precision medicine' programs: using genetics for target discovery and to select trial participants by testing them for disease susceptibility through the same pathway targeted by the drug.In the mid-2000s, deCODE launched a new kind of risk diagnostic focused lar... | DeCODE genetics | 0.830577 |
5,553 | When time-varying magnetic fields are present (which is true whenever there are time-varying electric fields and vice versa), it is not possible to describe the electric field simply in terms of a scalar potential V because the electric field is no longer conservative: ∫ C E ⋅ d ℓ {\displaystyle \textstyle \int _{C}\ma... | Electric scalar potential | 0.830576 |
5,554 | In plane geometry, constructing the diagonal of a square results in a triangle whose three angles are in the ratio 1: 1: 2, adding up to 180° or π radians. Hence, the angles respectively measure 45° (π/4), 45° (π/4), and 90° (π/2). The sides in this triangle are in the ratio 1: 1: √2, which follows immediately from the... | Right isosceles triangle | 0.830574 |
5,555 | Recent studies also involve differentiating between the effect of current on growth direction and the effect of a simple electric field. Studies involving AC and DC fields are also being conducted. This is currently a highly researched topic, in which many neuroscience labs around the world are attempting to be the fir... | Neuronal galvanotropism | 0.83057 |
5,556 | According to quantum mechanics, atoms and molecules can only hold certain defined quantities of energy, or exist in specific states. When electromagnetic radiation is absorbed by an atom or molecule, the energy of the radiation changes the state of the atom or molecule from an initial state to a final state. The number... | Absorption bands | 0.830569 |
5,557 | Trajectory optimization is often used to compute trajectories for quadrotor helicopters. These applications typically used highly specialized algorithms. One interesting application shown by the U.Penn GRASP Lab is computing a trajectory that allows a quadrotor to fly through a hoop as it is thrown. Another, this time ... | Trajectory optimization | 0.830566 |
5,558 | Computer Science Department, Cornell University. 93–1380. Stefansson, K. | Set constraint | 0.830557 |
5,559 | 177 (3): 1363–1375. doi:10.1534/genetics.107.075838. | Glutathione transferase | 0.830554 |
5,560 | A 2-year program open to Chemical Engineering technicians with 3–5 years of professional experience. 60 selected topical-courses delivered by the ENSIC Continuing Education Center. | École nationale supérieure des industries chimiques | 0.830552 |
5,561 | Under the same assumption, there are also essentially no other properties that can be used to get polynomial time algorithms. This is formalized as follows: Theorem (Grohe): For a computable class of graphs G {\displaystyle {\mathcal {G}}} , the homomorphism problem for instances ( G , H ) {\displaystyle (G,H)} with G ... | Graph homomorphism | 0.83055 |
5,562 | A Kleinian group Γ is called arithmetic if it is commensurable with the group norm 1 elements of an order of quaternion algebra A ramified at all real places over a number field k with exactly one complex place. Arithmetic Kleinian groups have finite covolume. A Kleinian group Γ is called cocompact if H3/Γ is compact, ... | Kleinian group | 0.830549 |
5,563 | Larger molecules often exist in multiple stable geometries (conformational isomerism) that are close in energy on the potential energy surface. Geometries can also be computed by ab initio quantum chemistry methods to high accuracy. The molecular geometry can be different as a solid, in solution, and as a gas. The posi... | Molecular structure | 0.830548 |
5,564 | Stack search (also known as Stack decoding algorithm) is a search algorithm similar to beam search. It can be used to explore tree-structured search spaces and is often employed in Natural language processing applications, such as parsing of natural languages, or for decoding of error correcting codes where the techniq... | Stack search | 0.830547 |
5,565 | For example, X1X2 does not equal X2X1. More generally, one can construct the free algebra R⟨E⟩ on any set E of generators. Since rings may be regarded as Z-algebras, a free ring on E can be defined as the free algebra Z⟨E⟩. | Noncommutative polynomial ring | 0.830547 |
5,566 | Groups of sectional 2-rank at most 4, classified by the Gorenstein–Harada theorem.The classification of groups of small 2-rank, especially ranks at most 2, makes heavy use of ordinary and modular character theory, which is almost never directly used elsewhere in the classification. All groups not of small 2 rank can be... | Classification of finite simple groups | 0.830546 |
5,567 | Certified Histocompatibility Associate, Certified Histocompatibility Technologist, Certified Histocompatibility Specialist, and Diplomate of the ABHI are titles granted by the American Board of Hisocompatibility and Immunogenetics after meeting education and experience requirements and passing the required examination;... | Medical laboratory scientist | 0.830545 |
5,568 | The Stanford University Department of Electrical Engineering offers Bachelor of Science degrees with a major in electrical engineering, full-time Master of Science degrees, and doctoral of philosophy (EE PhD) degrees.Degree programs offer some flexible options, such as coterminal BS and MS degrees completed in 5 years.... | Stanford University School of Engineering | 0.830544 |
5,569 | 3. Material design: Topology optimization for designing materials with desired mechanical properties. 4. Mechanical component design: Optimization of machine parts for weight reduction, durability, and performance. | Method of moving asymptotes | 0.830543 |
5,570 | A sequence profiling tool in bioinformatics is a type of software that presents information related to a genetic sequence, gene name, or keyword input. Such tools generally take a query such as a DNA, RNA, or protein sequence or ‘keyword’ and search one or more databases for information related to that sequence. Summar... | Sequence profiling tool | 0.830543 |
5,571 | {\displaystyle x|(y\mid (x\mid z))=((z\mid y)\mid y)\mid x.} In 1973, Padmanabhan and Quackenbush demonstrated a method that, in principle, would yield a 1-basis for Boolean algebra. | Minimal axioms for Boolean algebra | 0.830542 |
5,572 | However, in isotropic rules, the positions of neighbour cells relative to each other may be taken into account in determining a cell's future state—not just the total number of those neighbours. Some variations on the Game of Life modify the geometry of the universe as well as the rule. The above variations can be thou... | Conway game | 0.83054 |
5,573 | Many mathematical suites are computer algebra systems that use symbolic mathematics. They are designed to solve classical algebra equations and problems in human readable notation. | Mathematical software | 0.830538 |
5,574 | This concept can be extended to other algebraic structures than Z ; {\displaystyle \mathbb {Z} ;} for example, polynomials whose greatest common divisor is 1 are called coprime polynomials. | Pairwise relatively prime | 0.830537 |
5,575 | 15). Rooted trees, often with an additional structure such as an ordering of the neighbors at each vertex, are a key data structure in computer science; see tree data structure. In a context where trees typically have a root, a tree without any designated root is called a free tree. | Rooted tree | 0.830531 |
5,576 | Despite its simplicity, Dulong–Petit law offers fairly good prediction for the heat capacity of many elementary solids with relatively simple crystal structure at high temperatures. This agreement is because in the classical statistical theory of Ludwig Boltzmann, the heat capacity of solids approaches a maximum of 3R ... | Dulong–Petit law | 0.830529 |
5,577 | The study of electromagnetism in higher education, as a fundamental part of both physics and engineering, is typically accompanied by textbooks devoted to the subject. The American Physical Society and the American Association of Physics Teachers recommend a full year of graduate study in electromagnetism for all physi... | List of textbooks in electromagnetism | 0.830529 |
5,578 | Some classical construction problems of geometry — namely trisecting an arbitrary angle or doubling the cube — are proven to be unsolvable using compass and straightedge, but can be solved using only a few paper folds. Paper fold strips can be constructed to solve equations up to degree 4. The Huzita–Justin axioms or H... | Mathematical origami | 0.830529 |
5,579 | With an established target exposure for optimized treatment effectiveness with minimized toxicities, dosing can be personalized to achieve target exposure and optimal results for each person. Such an algorithm was used in the clinical trials cited above and resulted in significantly improved treatment outcomes.Oncologi... | Chemotherapeutic agents | 0.830528 |
5,580 | The converse of the theorem is also true: Given a triangle with sides of length a, b, and c, if a2 + b2 = c2, then the angle between sides a and b is a right angle. For any three positive real numbers a, b, and c such that a2 + b2 = c2, there exists a triangle with sides a, b and c as a consequence of the converse of t... | Pythagorean equation | 0.830525 |
5,581 | Thermosphaera are found mainly in sulfuric pools, where they thrive on the extreme temperatures. In terms of research and economic significance, learning more about these organisms and their properties may help advancements in biotechnology. | Thermosphaera | 0.830525 |
5,582 | It takes as input a set of declarations in a frame language about a domain such as medical research or molecular biology. For example, the names of classes, sub-classes, properties, and restrictions on allowable values. Deep Blue was a chess-playing computer developed by IBM. | Glossary of artificial intelligence | 0.830518 |
5,583 | According to classical mechanics, a diatomic molecule like nitrogen should have more degrees of internal freedom, corresponding to vibration of the two atoms that stretch and compress the bond between them. For thermodynamic purposes, each direction in which an atom can independently vibrate relative to the rest of the... | Molar heat capacity | 0.830517 |
5,584 | The simplest are rules that always reduce the size of the expression, like E − E → 0 or sin(0) → 0. They are systematically applied in computer algebra systems. A difficulty occurs with associative operations like addition and multiplication. | Computational algebra | 0.830515 |
5,585 | The geometry, on the other hand, would seem quite different. Supposing the inhabitants were to view rods believed to be rigid, or measure distance with light rays. They would find that a geodesic is not a straight line, and that the ratio of a circle’s circumference to its radius is greater than 2 π {\displaystyle 2\pi... | Sphere-world | 0.830513 |
5,586 | Organizing a Global Coordinate System from Local Information on an Amorphous Computer, 1999 Nagpal. Techniques for creating coordinate systems by gradient formation and analyzes precision limits. Amorphous Computing: examples, mathematics and theory, 2013 W Richard Stark. This paper presents nearly 20 examples varying ... | Amorphous computing | 0.830512 |
5,587 | Amongst groups that are not Lie groups, and so do not carry the structure of a manifold, examples are the additive group Zp of p-adic integers, and constructions from it. In fact any profinite group is a compact group. This means that Galois groups are compact groups, a basic fact for the theory of algebraic extensions... | Compact group | 0.830505 |
5,588 | Consider a situation where a small ball is being tossed up in the air and then we measure its heights of ascent hi at various moments in time ti. Physics tells us that, ignoring the drag, the relationship can be modeled as h i = β 1 t i + β 2 t i 2 + ε i , {\displaystyle h_{i}=\beta _{1}t_{i}+\beta _{2}t_{i}^{2}+\varep... | Regression coefficient | 0.830504 |
5,589 | The identity keeping the object fixed is always a symmetry of an object. Existence of inverses is guaranteed by undoing the symmetry and the associativity comes from the fact that symmetries are functions on a space, and composition of functions is associative. Frucht's theorem says that every group is the symmetry gro... | Infinite group theory | 0.830502 |
5,590 | The following groups do not appear in the conclusion of Fisher's theorem as they are solvable (with order a power of 2 times a power of 3). S 1 = S U 1 ( 2 ) = P S U 1 ( 2 ) = O 1 ± , ± ( 3 ) = P O 1 ± , ± ( 3 ) = P O 1 ± , ∓ ( 3 ) {\displaystyle S_{1}=SU_{1}(2)=PSU_{1}(2)=O_{1}^{\pm ,\pm }(3)=PO_{1}^{\pm ,\pm }(3)=PO_... | 3-transposition group | 0.830501 |
5,591 | Naval Academy) employs spherical trigonometry to solve an oblique spherical triangle based on sextant measurements of the 'altitude' of two heavenly bodies. This problem can also be addressed using vector analysis. Historically, graphical techniques – e.g., the intercept method – were employed. | True-range multilateration | 0.8305 |
5,592 | In electrical engineering, electric machine is a general term for machines using electromagnetic forces, such as electric motors, electric generators, and others. They are electromechanical energy converters: an electric motor converts electricity to mechanical power while an electric generator converts mechanical powe... | Electrical machines | 0.830493 |
5,593 | Elasticity – In physics, 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 forces are applied to them. If the material is elastic, the object will return to its initial shape ... | Glossary of mechanical engineering | 0.830492 |
5,594 | In abstract algebra, an additive monoid ( M , 0 , + ) {\displaystyle (M,0,+)} is said to be zerosumfree, conical, centerless or positive if nonzero elements do not sum to zero. Formally: ( ∀ a , b ∈ M ) a + b = 0 ⟹ a = b = 0 {\displaystyle (\forall a,b\in M)\ a+b=0\implies a=b=0\!} This means that the only way zero can... | Zerosumfree monoid | 0.830492 |
5,595 | This suggests that clinical trial data could provide a practical source for machine learning-based tools for precision medicine. Precision medicine may be susceptible to subtle forms of algorithmic bias. For example, the presence of multiple entry fields with values entered by multiple observers can create distortions ... | Precision Medicine | 0.830492 |
5,596 | Analogous to the tensor formulation, two objects, one for the electromagnetic field and one for the current density, are introduced. In geometric algebra (GA) these are multivectors. | Mathematical descriptions of the electromagnetic field | 0.830492 |
5,597 | Simple computational techniques can provide descriptive data such as word frequencies and document lengths. Machine learning classifiers can greatly increase the number of texts that can be labeled, but the scientific utility of doing so is a matter of debate. Further, numerous computer-aided text analysis (CATA) compu... | Text analysis | 0.830491 |
5,598 | The linear region of the HIV ribosomal frameshift signal contains a highly conserved UUU UUU A slippery sequence; many of the other predicted structures contain candidates for slippery sequences as well. The mRNA sequences in the images can be read according to a set of guidelines. While A, T, C, and G represent a part... | Ribosomal frameshifting | 0.83049 |
5,599 | Mannosyl groups may be transferred to tryptophan to generate C-mannosyl tryptophan, which is relatively abundant in eukaryotes. Transferases may also use lipids as an acceptor, forming glycolipids, and even use lipid-linked sugar phosphate donors, such as dolichol phosphates in eukaryotic organism, or undecaprenyl phos... | Glycosyl transferase | 0.830488 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.