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Diagram Gallery of diagram types Diagram > Gallery of diagram types There are at least the following types of diagrams: Logical or conceptual diagrams, which take a collection of items and relationships between them, and express them by giving each item a 2D position, while the relationships are expressed as connections between the items or overlaps between the items, for example:Quantitative diagrams, which display a relationship between two variables that take either discrete or a continuous range of values; for example:Schematics and other types of diagrams, for example: Many of these types of diagrams are commonly generated using diagramming software such as Visio and Gliffy. Diagrams may also be classified according to use or purpose, for example, explanatory and/or how to diagrams. Thousands of diagram techniques exist. Some more examples follow:
Shared pair Comparison of VB and MO theories Single_electron_bond > Quantum mechanical description > Comparison of VB and MO theories As molecular orbital theory builds the molecular wavefunction out of delocalized orbitals, it is more suited for the calculation of ionization energies and the understanding of spectral absorption bands.At the qualitative level, both theories contain incorrect predictions. Simple (Heitler–London) valence bond theory correctly predicts the dissociation of homonuclear diatomic molecules into separate atoms, while simple (Hartree–Fock) molecular orbital theory incorrectly predicts dissociation into a mixture of atoms and ions. On the other hand, simple molecular orbital theory correctly predicts Hückel's rule of aromaticity, while simple valence bond theory incorrectly predicts that cyclobutadiene has larger resonance energy than benzene.Although the wavefunctions generated by both theories at the qualitative level do not agree and do not match the stabilization energy by experiment, they can be corrected by configuration interaction.
Glossary of artificial intelligence S Glossary_of_artificial_intelligence > S This can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain platform, hence creating a model of computation. sensor fusion The combining of sensory data or data derived from disparate sources such that the resulting information has less uncertainty than would be possible when these sources were used individually. separation logic An extension of Hoare logic, a way of reasoning about programs.
Multidimensional transform Multidimensional Laplace transform Multidimensional_transform > Multidimensional Laplace transform The multidimensional Laplace transform is useful for the solution of boundary value problems. Boundary value problems in two or more variables characterized by partial differential equations can be solved by a direct use of the Laplace transform. The Laplace transform for an M-dimensional case is defined as F ( s 1 , s 2 , … , s n ) = ∫ 0 ∞ ⋯ ∫ 0 ∞ f ( t 1 , t 2 , … , t n ) e − s n t n − s n − 1 t n − 1 ⋯ ⋯ s 1 t 1 d t 1 ⋯ d t n {\displaystyle F(s_{1},s_{2},\ldots ,s_{n})=\int _{0}^{\infty }\cdots \int _{0}^{\infty }f(t_{1},t_{2},\ldots ,t_{n})e^{-s_{n}t_{n}-s_{n-1}t_{n-1}\cdots \cdots s_{1}t_{1}}\,dt_{1}\cdots \,dt_{n}} where F stands for the s-domain representation of the signal f(t). A special case (along 2 dimensions) of the multi-dimensional Laplace transform of function f(x,y) is defined as F ( s 1 , s 2 ) {\displaystyle F(s_{1},s_{2})} is called the image of f ( x , y ) {\displaystyle f(x,y)} and f ( x , y ) {\displaystyle f(x,y)} is known as the original of F ( s 1 , s 2 ) {\displaystyle F(s_{1},s_{2})} . This special case can be used to solve the Telegrapher's equations.}
Axes of symmetry Symmetric function Reflectional_symmetry > Symmetric function The symmetric function of a two-dimensional figure is a line such that, for each perpendicular constructed, if the perpendicular intersects the figure at a distance 'd' from the axis along the perpendicular, then there exists another intersection of the shape and the perpendicular, at the same distance 'd' from the axis, in the opposite direction along the perpendicular. Another way to think about the symmetric function is that if the shape were to be folded in half over the axis, the two halves would be identical: the two halves are each other's mirror images.Thus a square has four axes of symmetry, because there are four different ways to fold it and have the edges all match. A circle has infinitely many axes of symmetry.
Hash function (cryptography) Cryptographic hash algorithms Cryptographic_hash > Cryptographic hash algorithms There are many cryptographic hash algorithms; this section lists a few algorithms that are referenced relatively often. A more extensive list can be found on the page containing a comparison of cryptographic hash functions.
Rudolphine Tables Previous tables Rudolphine_Tables > Previous tables Star tables had been produced for many centuries and were used to establish the position of the planets relative to the fixed stars (particularly the twelve constellations used in astrology) on a specific date in order to construct horoscopes. Until the end of the 16th century, the most widely used had been the Alphonsine tables, first produced in the 13th century and regularly updated thereafter. These were based on a Ptolemaic, geocentric model of the Solar System. Although the Alphonsine tables were not very accurate, nothing else was available and so they continued to be used.In 1551, following the publication of De revolutionibus orbium coelestium by Nicholas Copernicus, Erasmus Reinhold produced the Prutenic Tables based on a heliocentric model of the Solar System, but these were no more accurate than the earlier tables.
Generative art Questions Generative_art > Theories > Questions What can we learn about art from generative art? For example, can the art world be considered a complex generative system involving many processes outside the direct control of artists, who are agents of production within a stratified global art market? What future developments would force us to rethink our answers?Another question is of postmodernism—are generative art systems the ultimate expression of the postmodern condition, or do they point to a new synthesis based on a complexity-inspired world-view?
Abilene paradox Explanation Abilene_paradox > Explanation The father-in-law then says that he only suggested it because he thought the others might be bored. The group sits back, perplexed that they together decided to take a trip that none of them wanted. They each would have preferred to sit comfortably but did not admit to it when they still had time to enjoy the afternoon. This is in contrast to groupthink, where individuals correctly perceive the preferences of others, are not acting contrary to their conscious wishes in choosing to conform with others, and generally feel good about the resulting group decisions. The Abilene paradox is used to illustrate that groups may have problems in managing not only disagreements, but also agreements.
Cypher Query Language Graph model Cypher_Query_Language > Graph model Like nodes, relationships can also have properties.Labels can group similar nodes together by assigning zero or more node labels. Labels are kind of like tags and allow you to specify certain types of entities to look for or create. Properties are key-value pairs with a binding of a string key and some value from the Cypher type system. Cypher queries are assembled with patterns of nodes and relationships with any specified filtering on labels and properties to create, read, update, delete data found in the specified pattern.
Intracellular membranes Golgi apparatus Intracellular_membranes > Components of the system > Golgi apparatus In addition to modifying proteins, the Golgi also manufactures macromolecules itself. In plant cells, the Golgi produces pectins and other polysaccharides needed by the plant structure.Once the modification process is completed, the Golgi apparatus sorts the products of its processing and sends them to various parts of the cell. Molecular identification labels or tags are added by the Golgi enzymes to help with this. After everything is organized, the Golgi apparatus sends off its products by budding vesicles from its trans face.
Semiotic elements and classes of signs (Peirce) Classes of signs Semiotic_elements_and_classes_of_signs > Classes of signs Every sign is interpreted either as (rheme) term-like, standing for its object in respect of quality, or as (dicisign) proposition-like, standing for its object in respect of fact, or as (argument) argumentative, standing for its object in respect of habit or law. This is the trichotomy of all signs as building blocks of inference. (Also called sumisigns, dicent signs, and suadisigns, also semes, phemes, and delomes.
Lift (force) Wing tips and spanwise distribution Lift_vector > Three-dimensional flow > Wing tips and spanwise distribution The vertical pressure gradient at the wing tips causes air to flow sideways, out from under the wing then up and back over the upper surface. This reduces the pressure gradient at the wing tip, therefore also reducing lift. The lift tends to decrease in the spanwise direction from root to tip, and the pressure distributions around the airfoil sections change accordingly in the spanwise direction. Pressure distributions in planes perpendicular to the flight direction tend to look like the illustration at right.
Shattered assumptions theory Criticism and related theories Shattered_assumptions_theory > Criticism and related theories Terror management theory states that our self-esteem and worldviews serve as a mechanism to avoid the overwhelming fear and anxiety that we would normally face about death and suffering. We need such mechanisms to perform daily functions, as without them we would be too conscious of our own mortality. Like in the theory of shattered assumptions, the more positively individuals view themselves (through high self-esteem) and the world, the less anxiety they will face about death. == References ==
Leibniz–Newton calculus controversy Invention of differential and integral calculus Newton-Leibniz_calculus_controversy > Background > Invention of differential and integral calculus It is known that a copy of Newton's manuscript had been sent to Ehrenfried Walther von Tschirnhaus in May 1675, a time when he and Leibniz were collaborating; it is not impossible that these extracts were made then. It is also possible that they may have been made in 1676, when Leibniz discussed analysis by infinite series with Collins and Oldenburg. It is probable that they would have then shown him the manuscript of Newton on that subject, a copy of which one or both of them surely possessed.
Methods of neuro-linguistic programming Meta-programs Methods_of_neuro-linguistic_programming > Meta-programs Neuro-linguistic programming (NLP) uses the term 'meta-programs' specifically to indicate general, pervasive and usually habitual patterns used by an individual across a wide range of situations. Examples of NLP meta-programs include the preference for overview or detail, the preference for where to place one's attention during conversation, habitual linguistic patterns and body language, and so on. Related concepts in other disciplines are known as cognitive styles or thinking styles.
Chlorine bleach Whitening Chlorine_bleach > Mechanism of action > Whitening A reducing bleach works by converting double bonds in the chromophore into single bonds. This eliminates the ability of the chromophore to absorb visible light. This is the mechanism of bleaches based on sulfur dioxide.Sunlight acts as a bleach through a process leading to similar results: high energy photons of light, often in the violet or ultraviolet range, can disrupt the bonds in the chromophore, rendering the resulting substance colourless. Extended exposure often leads to massive discolouration usually reducing the colours to a white and typically very faded blue.
Statistical reliability Summary Statistical_reliability If the sequence of estimates can be mathematically shown to converge in probability to the true value θ0, it is called a consistent estimator; otherwise the estimator is said to be inconsistent. Consistency as defined here is sometimes referred to as weak consistency. When we replace convergence in probability with almost sure convergence, then the estimator is said to be strongly consistent. Consistency is related to bias; see bias versus consistency.
Finite volume Summary Finite-volume_method The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative.
Effects of tropical cyclones Heavy rainfall Effects_of_tropical_cyclones > Upon landfall > Heavy rainfall The thunderstorm activity in a tropical cyclone produces intense rainfall, potentially resulting in flooding, mudslides, and landslides. Inland areas are particularly vulnerable to freshwater flooding, due to residents not preparing adequately. Heavy inland rainfall eventually flows into coastal estuaries, damaging marine life in coastal estuaries. The wet environment in the aftermath of a tropical cyclone, combined with the destruction of sanitation facilities and a warm tropical climate, can induce epidemics of disease which claim lives long after the storm passes.
Standard ML Declarative definitions Standard_ML > Language > Declarative definitions The same function can be expressed with clausal function definitions where the if-then-else conditional is replaced with templates of the factorial function evaluated for specific values:
Sodium Fluoride Chemical structure Sodium_Fluoride > Chemical structure Sodium fluoride is an inorganic ionic compound, dissolving in water to give separated Na+ and F− ions. Like sodium chloride, it crystallizes in a cubic motif where both Na+ and F− occupy octahedral coordination sites; its lattice spacing, approximately 462 pm, is smaller than that of sodium chloride (564 pm).
TILLING (molecular biology) Scientific literature TILLING_(molecular_biology) > Scientific literature Methods in Cell Biology. 77: 91–112. doi:10.1016/s0091-679x(04)77005-3.
Wikipedia:Style of policy and guideline pages Include these components Wikipedia:Style_of_policy_and_guideline_pages > Include these components Include the following, in order. Deviation is okay within reason in the interest of clarity and usability. Name. A short, neutral name that clearly communicates the scope of the policy or guideline.
Combined central and peripheral demyelination Treatment Chronic_inflammatory_demyelinating_polyneuropathy > Treatment (In MS, the ASTIMS RCT provides evidence for superior effect of HSCT to the then-best practice for treatment of aggressive MS. The more recent MIST RCT confirmed its superiority in MS.) Physical therapy and occupational therapy may improve muscle strength, activities of daily living, mobility, and minimize the shrinkage of muscles and tendons and distortions of the joints.
Cauchy interlacing theorem Compact operators Variational_theorem > Compact operators Let A be a compact, Hermitian operator on a Hilbert space H. Recall that the spectrum of such an operator (the set of eigenvalues) is a set of real numbers whose only possible cluster point is zero. It is thus convenient to list the positive eigenvalues of A as ⋯ ≤ λ k ≤ ⋯ ≤ λ 1 , {\displaystyle \cdots \leq \lambda _{k}\leq \cdots \leq \lambda _{1},} where entries are repeated with multiplicity, as in the matrix case. (To emphasize that the sequence is decreasing, we may write λ k = λ k ↓ {\displaystyle \lambda _{k}=\lambda _{k}^{\downarrow }} .) When H is infinite-dimensional, the above sequence of eigenvalues is necessarily infinite.
Neurogenomics Personalized neurobiology Neurogenomics > Neuropharmacology > Personalized neurobiology Firstly, the causative network biology of several spectrum disorders with neurogenomic underpinnings is not fully understood yet, in spite of extensive studies conducted with disorders like Autism Spectrum and schizophrenia. Thus, the analytical validity of standing hypotheses concerning the etiology of neurogenomic disorders has still not been fully established and is subject to debate and controversy. The clinical validity of genetic variants that have shown to be highly correlated with specific neurogenomic disorders is often a major cause of concern.
Fourier transformations Square-integrable functions, one-dimensional Fourier_transforms > Tables of important Fourier transforms > Square-integrable functions, one-dimensional The Fourier transforms in this table may be found in Campbell & Foster (1948), Erdélyi (1954), or Kammler (2000, appendix).
Abstract computer Imperative languages Abstract_computer > Programming language implementation > Imperative languages In the late 1950s, the Association for Computing Machinery (ACM) and other allied organisations developed many proposals for Universal Computer Oriented Language (UNCOL), such as Conway's machine. The UNCOL concept is good, but it has not been widely used due to the poor performance of the generated code. In many areas of computing, its performance will continue to be an issue despite the development of the Java Virtual Machine in the late 1990s. Algol Object Code (1964), P4-machine (1976), UCSD P-machine (1977), and Forth (1970) are some successful abstract machines of this kind.
Kinetic theory of gases Assumptions Kinetic_Molecular_Theory > Assumptions All these collisions are perfectly elastic, which means the molecules are perfect hard spheres. Except during collisions, the interactions among molecules are negligible. They exert no other forces on one another.Thus, the dynamics of particle motion can be treated classically, and the equations of motion are time-reversible.
Gadget (machine instruction sequence) Background Gadget_(machine_instruction_sequence) > Background Return-oriented programming is an advanced version of a stack smashing attack. Generally, these types of attacks arise when an adversary manipulates the call stack by taking advantage of a bug in the program, often a buffer overrun. In a buffer overrun, a function that does not perform proper bounds checking before storing user-provided data into memory will accept more input data than it can store properly. If the data is being written onto the stack, the excess data may overflow the space allocated to the function's variables (e.g., "locals" in the stack diagram to the right) and overwrite the return address.
Chi-square distribution Introduction Chisquare_distribution > Definitions > Introduction The subscript 1 indicates that this particular chi-squared distribution is constructed from only 1 standard normal distribution. A chi-squared distribution constructed by squaring a single standard normal distribution is said to have 1 degree of freedom. Thus, as the sample size for a hypothesis test increases, the distribution of the test statistic approaches a normal distribution.
Object diagram Overview Object_diagram > Overview In the Unified Modeling Language (UML), an object diagram focuses on some particular set of objects and attributes, and the links between these instances. A correlated set of object diagrams provides insight into how an arbitrary view of a system is expected to evolve over time. Early UML specifications described object diagrams as such: "An object diagram is a graph of instances, including objects and data values. A static object diagram is an instance of a class diagram; it shows a snapshot of the detailed state of a system at a point in time.
DNS name Transport protocols Domain_name_services > Transport protocols When the length of the answer exceeds 512 bytes and both client and server support Extension Mechanisms for DNS (EDNS), larger UDP packets may be used. Use of DNS over UDP is limited by, among other things, its lack of transport-layer encryption, authentication, reliable delivery, and message length.DNS over TCP/53 (Do53/TCP) In 1989, RFC 1123 specified optional Transmission Control Protocol (TCP) transport for DNS queries, replies and, particularly, zone transfers. Via fragmentation of long replies, TCP allows longer responses, reliable delivery, and re-use of long-lived connections between clients and servers.DNS over TLS (DoT) DNS over TLS emerged as an IETF standard for encrypted DNS in 2016, utilizing Transport Layer Security (TLS) to protect the entire connection, rather than just the DNS payload.
Bayesian interpretation of kernel regularization A Bayesian perspective Bayesian_interpretation_of_kernel_regularization > A Bayesian perspective The notion of a kernel plays a crucial role in Bayesian probability as the covariance function of a stochastic process called the Gaussian process.
Li-Fraumeni syndrome Pathology Li-Fraumeni_syndrome > Pathology If these DNA mutations are left unchecked, some cells can divide uncontrollably, forming tumors (cancers). Further mutations in the DNA could lead to malignant cells that can travel to, and develop cancer in, different areas of the body. Many individuals with Li–Fraumeni syndrome have been shown to be heterozygous for a TP53 mutation.
Exponential response formula Comparison with method of undetermined coefficients Exponential_response_formula > Comparison with method of undetermined coefficients On the other hand, the exponential response formula method requires characteristic polynomial P ( s ) = s 2 + 1 {\displaystyle P(s)=s^{2}+1} to be found, after which the non-homogeneous terms f ( t ) = B e γ t , B = 1 , γ = 1 {\displaystyle f(t)=Be^{\gamma t},B=1,\gamma =1} is complex replaced. The particular solution is then found using formula y p ( t ) = e λ t P ( λ ) = e λ t λ 2 + 1 . {\displaystyle y_{p}(t)={\frac {e^{\lambda t}}{P(\lambda )}}={\frac {e^{\lambda t}}{\lambda ^{2}+1}}.}
Environmental governance Ozone layer Environmental_governance > Environmental governance issues > Ozone layer On 16 September 1987 the United Nations General Assembly signed the Montreal Protocol to address the declining ozone layer. Since that time, the use of chlorofluorocarbons (industrial refrigerants and aerosols) and farming fungicides such as methyl bromide has mostly been eliminated, although other damaging gases are still in use.
Black Hole Entropy and thermodynamics Black_Holes > Open questions > Entropy and thermodynamics This allows the formulation of the first law of black hole mechanics as an analogue of the first law of thermodynamics, with the mass acting as energy, the surface gravity as temperature and the area as entropy.One puzzling feature is that the entropy of a black hole scales with its area rather than with its volume, since entropy is normally an extensive quantity that scales linearly with the volume of the system. This odd property led Gerard 't Hooft and Leonard Susskind to propose the holographic principle, which suggests that anything that happens in a volume of spacetime can be described by data on the boundary of that volume.Although general relativity can be used to perform a semi-classical calculation of black hole entropy, this situation is theoretically unsatisfying.
Contour map Graphical design Isarithmic_map > Graphical design Line type refers to whether the basic contour line is solid, dashed, dotted or broken in some other pattern to create the desired effect. Dotted or dashed lines are often used when the underlying base map conveys very important (or difficult to read) information. Broken line types are used when the location of the contour line is inferred.
Statistical hypothesis test The testing process Statistical_hypothesis_testing > The testing process The latter process relied on extensive tables or on computational support not always available. The explicit calculation of a probability is useful for reporting.
Matrix (printing) Description Matrix_(printing) > Description In a low-pressure hand mould matrices are long-lasting and so could be used many times. In the hot metal typesetting systems of the later years of metal type printing, from the late nineteenth century onwards, new type is cast for each job under the control of a keyboard. The matrix or mats for a complete font are loaded into a matrix-case and inserted into a casting machine, which casts the required sorts (or, in a Linotype machine, a solid block for each line) for a page composition automatically, often from a paper reel.
Microscopic scale Geology Microscopic_scale > Microscopic scale in the laboratory > Geology Branches of geology involve the study of the Earth's structure at a microscopic level. Physical characteristics of rocks are recorded, and in petrography there is a specific focus on the examination of microscopic details of rocks. Similar to scanning electron microscopes, electron microprobes can be used in petrology to observe the condition that allows rocks to form, which can inform the origin of these samples. In structural geology, petrographic microscopes allow the study of rock microstructures, to determine how geologic features such as tectonic plates affect the likelihood of earthquakes and groundwater movement.
Stock market prediction Machine learning Stock_market_prediction > Prediction methods > Machine learning With the advent of the digital computer, stock market prediction has since moved into the technological realm. The most prominent technique involves the use of artificial neural networks (ANNs) and genetic algorithms (GA). Scholars found bacterial chemotaxis optimization method may perform better than GA.
Molecular models of DNA History Molecular_models_of_DNA > History Although such initial studies of DNA structures with the help of molecular models were essentially static, their consequences for explaining the in vivo functions of DNA were significant in the areas of protein biosynthesis and the quasi-universality of the genetic code. Epigenetic transformation studies of DNA in vivo were however much slower to develop despite their importance for embryology, morphogenesis and cancer research. Such chemical dynamics and biochemical reactions of DNA are much more complex than the molecular dynamics of DNA physical interactions with water, ions and proteins/enzymes in living cells.
Jorge Pullin Quantum mechanics Jorge_Pullin > Quantum mechanics Pullin, along with R. Gambini, has proposed a new interpretation of quantum mechanics, called the `Montevideo interpretation'. This name was chosen for its similarity with the more orthodox `Copenhagen interpretation' and a reference to the city of origin. The Montevideo interpretation is an alternative to the Copenhagen interpretation, both seeking to understand the deepest meaning of quantum mechanics. The need for an interpretation is because the extremely-well-verified equations of quantum mechanics leaves unaddressed various issue concerning the nature of reality, the ultimate accuracy of measurement, hidden variables, and the idea of multiple universes.
Fair computational tree logic Summary Fair_computational_tree_logic Fair computational tree logic is conventional computational tree logic studied with explicit fairness constraints.
Minimax path problem All pairs Minimax_path_problem > Directed graphs > All pairs The all-pairs widest path problem has applications in the Schulze method for choosing a winner in multiway elections in which voters rank the candidates in preference order. The Schulze method constructs a complete directed graph in which the vertices represent the candidates and every two vertices are connected by an edge. Each edge is directed from the winner to the loser of a pairwise contest between the two candidates it connects, and is labeled with the margin of victory of that contest. Then the method computes widest paths between all pairs of vertices, and the winner is the candidate whose vertex has wider paths to each opponent than vice versa.
Immune function Humoral immune response Immune_function > Adaptive immune system > Humoral immune response Several layers of passive protection are provided by the mother. During pregnancy, a particular type of antibody, called IgG, is transported from mother to baby directly through the placenta, so human babies have high levels of antibodies even at birth, with the same range of antigen specificities as their mother. Breast milk or colostrum also contains antibodies that are transferred to the gut of the infant and protect against bacterial infections until the newborn can synthesize its own antibodies.
Opinion poll Margin of error due to sampling Opinion_poll > Potential for inaccuracy > Margin of error due to sampling For example, if you assume that the breakdown of the US population by party identification has not changed since the previous presidential election, you may underestimate a victory or a defeat of a particular party candidate that saw a surge or decline in its party registration relative to the previous presidential election cycle. A caution is that an estimate of a trend is subject to a larger error than an estimate of a level. This is because if one estimates the change, the difference between two numbers X and Y, then one has to contend with errors in both X and Y. A rough guide is that if the change in measurement falls outside the margin of error it is worth attention.
Ravi Gomatam Education Ravi_Gomatam > Education B.E. 1972 Electrical and Electronics Engineering, Annamalai University, India M.E. 1974 Electronics Engineering, Birla Institute of Technology & Science, Pilani, India Ph. D. 1998 Foundations of Quantum Mechanics, Mumbai University, India. Dissertation Title: Toward a realist interpretation of quantum theory – Integrating Bohr and Einstein.
Haber's rule Summary Haber's_rule In toxicology, Haber's rule or Haber's law is a mathematical statement of the relationship between the concentration of a poisonous gas and how long the gas must be breathed to produce death, or other toxic effect. The rule was formulated by German chemist Fritz Haber in the early 1900s.
Generalized variance Summary Generalized_variance The generalized variance is a scalar value which generalizes variance for multivariate random variables. It was introduced by Samuel S. Wilks. The generalized variance is defined as the determinant of the covariance matrix, det ( Σ ) {\displaystyle \det(\Sigma )} . It can be shown to be related to the multidimensional scatter of points around their mean. == References ==
Taylor diagram Taylor diagram variants Taylor_diagram > Taylor diagram variants Among the several minor variations on the diagram that have been suggested are (see, Taylor, 2001): extension to a second "quadrant" (to the left of the quadrant shown in Figure 1) to accommodate negative correlations; normalization of dimensional quantities (dividing both the RMS difference and the standard deviation of the "test" field by the standard deviation of the observations) so that the "observed" point is plotted at unit distance from the origin along the x-axis, and statistics for different fields (with different units) can be shown in a single plot; omission of the isolines on the diagram to make it easier to see the plotted points; use of an arrow to connect two related points on the diagram. For example, an arrow can be drawn from the point representing an older version of a model to a newer version, which makes it easier to indicate more clearly whether or not the model is moving toward "truth," as defined by observations.One of the main limitation of the Taylor diagram is the absence of explicit information about the prediction bias. A variant of the Taylor diagram that accounts for the prediction bias is provided by the solar diagram (see, Wadoux et al., 2022).
HMG-CoA reductase inhibitor Drug interactions HMG-CoA_reductase_inhibitor > Adverse effects > Drug interactions Combining any statin with a fibrate or niacin (other categories of lipid-lowering drugs) increases the risks for rhabdomyolysis to almost 6.0 per 10,000 person-years. Monitoring liver enzymes and creatine kinase is especially prudent in those on high-dose statins or in those on statin/fibrate combinations, and mandatory in the case of muscle cramps or of deterioration in kidney function.Consumption of grapefruit or grapefruit juice inhibits the metabolism of certain statins, and bitter oranges may have a similar effect. Furanocoumarins in grapefruit juice (i.e. bergamottin and dihydroxybergamottin) inhibit the cytochrome P450 enzyme CYP3A4, which is involved in the metabolism of most statins (however, it is a major inhibitor of only lovastatin, simvastatin, and to a lesser degree, atorvastatin) and some other medications (flavonoids (i.e. naringin) were thought to be responsible). This increases the levels of the statin, increasing the risk of dose-related adverse effects (including myopathy/rhabdomyolysis).
Vaccine Production Delivery_system > Production Although this is a conceptually simple part of the vaccine manufacture process, it is often a bottleneck in the process of distributing and administering vaccines.Vaccine production techniques are evolving. Cultured mammalian cells are expected to become increasingly important, compared to conventional options such as chicken eggs, due to greater productivity and low incidence of problems with contamination. Recombination technology that produces genetically detoxified vaccines is expected to grow in popularity for the production of bacterial vaccines that use toxoids. Combination vaccines are expected to reduce the quantities of antigens they contain, and thereby decrease undesirable interactions, by using pathogen-associated molecular patterns.
Virtual memory Address space swapping Virtual_address_translation > Address space swapping Some operating systems provide for swapping entire address spaces, in addition to whatever facilities they have for paging and segmentation. When this occurs, the OS writes those pages and segments currently in real memory to swap files. In a swap-in, the OS reads back the data from the swap files but does not automatically read back pages that had been paged out at the time of the swap out operation. IBM's MVS, from OS/VS2 Release 2 through z/OS, provides for marking an address space as unswappable; doing so does not pin any pages in the address space. This can be done for the duration of a job by entering the name of an eligible main program in the Program Properties Table with an unswappable flag. In addition, privileged code can temporarily make an address space unswappable using a SYSEVENT Supervisor Call instruction (SVC); certain changes in the address space properties require that the OS swap it out and then swap it back in, using SYSEVENT TRANSWAP.Swapping does not necessarily require memory management hardware, if, for example, multiple jobs are swapped in and out of the same area of storage.
Fuel efficient Energy content of fuel Gas_mileage > Energy content of fuel (This is given by the change in Gibbs free energy, and is around 45.7 MJ/kg for gasoline.) The actual amount of mechanical work obtained from fuel (the inverse of the specific fuel consumption) depends on the engine. A figure of 17.6 MJ/kg is possible with a gasoline engine, and 19.1 MJ/kg for a diesel engine. See Brake specific fuel consumption for more information.
Perceptual control theory Selected bibliography Perceptual_control_theory > Selected bibliography Gravel Switch, KY: Control Systems Group. Robertson, R. J., Goldstein, D.M., Mermel, M., & Musgrave, M. (1999).
Interval FEM Interval solution versus probabilistic solution Interval_finite_element > Interval solution versus probabilistic solution Imprecise probability is understood in a very wide sense. It is used as a generic term to cover all mathematical models which measure chance or uncertainty without sharp numerical probabilities. It includes both qualitative (comparative probability, partial preference orderings, ...) and quantitative modes (interval probabilities, belief functions, upper and lower previsions, ...). Imprecise probability models are needed in inference problems where the relevant information is scarce, vague or conflicting, and in decision problems where preferences may also be incomplete .
DO-178C Processes and documents DO-178C > Processes and documents Processes are intended to support the objectives, according to the software level (A through D—Level E was outside the purview of DO-178C). Processes are described as abstract areas of work in DO-178C, and it is up to the planners of a real project to define and document the specifics of how a process will be carried out. On a real project, the actual activities that will be done in the context of a process must be shown to support the objectives. These activities are defined by the project planners as part of the Planning process.
Ruhpolding Formation Summary Ruhpolding_Formation The Ruhpolding Formation is a sedimentary formation of the Northern Calcareous Alps deposited during the Upper Jurassic. The open marine radiolarite is very rich in silica.
Thermonuclear energy Mechanism Nuclear_fusion_power > Background > Mechanism Since hydrogen has a single proton in its nucleus, it requires the least effort to attain fusion, and yields the most net energy output. Also since it has one electron, hydrogen is the easiest fuel to fully ionize. The repulsive electrostatic interaction between nuclei operates across larger distances than the strong force, which has a range of roughly one femtometer—the diameter of a proton or neutron.
Retraction (category theory) Terminology Split_epimorphism > Terminology The concept of a retraction in category theory comes from the essentially similar notion of a retraction in topology: f: X → Y {\displaystyle f:X\to Y} where Y {\displaystyle Y} is a subspace of X {\displaystyle X} is a retraction in the topological sense, if it's a retraction of the inclusion map i: Y ↪ X {\displaystyle i:Y\hookrightarrow X} in the category theory sense. The concept in topology was defined by Karol Borsuk in 1931.Borsuk's student, Samuel Eilenberg, was with Saunders Mac Lane the founder of category theory, and (as the earliest publications on category theory concerned various topological spaces) one might have expected this term to have initially be used. In fact, their earlier publications, up to, e.g., Mac Lane (1963)'s Homology, used the term right inverse. It was not until 1965 when Eilenberg and John Coleman Moore coined the dual term 'coretraction' that Borsuk's term was lifted to category theory in general. The term coretraction gave way to the term section by the end of the 1960s. Both use of left/right inverse and section/retraction are commonly seen in the literature: the former use has the advantage that it is familiar from the theory of semigroups and monoids; the latter is considered less confusing by some because one does not have to think about 'which way around' composition goes, an issue that has become greater with the increasing popularity of the synonym f;g for g∘f.
Companion matrix Cyclic shift matrix Companion_matrix > Cyclic shift matrix In the case of p ( x ) = x n − 1 {\displaystyle p(x)=x^{n}-1} , when the eigenvalues are the complex roots of unity, the companion matrix and its transpose both reduce to Sylvester's cyclic shift matrix, a circulant matrix.
CH3CH(OH)COOH Summary CH3CH(OH)COOH This higher acidity is the consequence of the intramolecular hydrogen bonding between the α-hydroxyl and the carboxylate group. Lactic acid is chiral, consisting of two enantiomers. One is known as L-lactic acid, (S)-lactic acid, or (+)-lactic acid, and the other, its mirror image, is D-lactic acid, (R)-lactic acid, or (−)-lactic acid.
Dot Com Summary Dot_Com The domain com is a top-level domain (TLD) in the Domain Name System (DNS) of the Internet. Created in the first group of Internet domains at the beginning of 1985, its name is derived from the word commercial, indicating its original intended purpose for subdomains registered by commercial organizations. Later, the domain opened for general purposes. The domain was originally administered by the United States Department of Defense, but is today operated by Verisign, and remains under ultimate jurisdiction of U.S.
Educational programming language University Educational_programming_language > University It is built on a semantic framework based in category theory, with a syntax similar to that of Pascal or Modula-2. It is designed for education only, so efficiency and ease of implementation are far less vital in its development than generality and range of application. It was created to play a strong role in forming a formal algorithmic foundation for first-year college math students.
Polyatomic ion Summary Polyatomic_ions Often, a polyatomic ion can be considered as the conjugate acid or base of a neutral molecule. For example, the conjugate base of sulfuric acid (H2SO4) is the polyatomic hydrogen sulfate anion (HSO−4). The removal of another hydrogen ion produces the sulfate anion (SO2−4).
Principal axis (mechanics) Scalar moment of inertia in a plane Figure_axis > Motion in space of a rigid body, and the inertia matrix > Scalar moment of inertia in a plane To relate this scalar moment of inertia to the inertia matrix of the body, introduce the skew-symmetric matrix {\displaystyle \left} such that y = k ^ × y {\displaystyle \left\mathbf {y} =\mathbf {\hat {k}} \times \mathbf {y} } , then we have the identity noting that k ^ {\displaystyle \mathbf {\hat {k}} } is a unit vector. The magnitude squared of the perpendicular vector is The simplification of this equation uses the triple scalar product identity where the dot and the cross products have been interchanged. Exchanging products, and simplifying by noting that Δ r i {\displaystyle \Delta \mathbf {r} _{i}} and k ^ {\displaystyle \mathbf {\hat {k}} } are orthogonal: Thus, the moment of inertia around the line L {\displaystyle L} through R {\displaystyle \mathbf {R} } in the direction k ^ {\displaystyle \mathbf {\hat {k}} } is obtained from the calculation where I R {\displaystyle \mathbf {I_{R}} } is the moment of inertia matrix of the system relative to the reference point R {\displaystyle \mathbf {R} } . This shows that the inertia matrix can be used to calculate the moment of inertia of a body around any specified rotation axis in the body.
Mobile secure gateway Summary Mobile_secure_gateway The client is a library that is linked with the mobile application. It establishes secure connectivity to Gateway using cryptographic protocol typically SSL/TLS. This represents a secured channel used for communication between the mobile application and hosts. Gateway separates internal IT infrastructure from the Internet, allowing only an authorized client requests to reach a specific set of hosts inside restricted network.
VITESS Working principle VITESS > Working principle VITESS simulations are carried out by means of a Monte Carlo ray-tracing method. Neutron trajectories are created in a source module or loaded from a file created in a previous simulation. Each neutron is assigned a count rate which is modified on each interaction with the instrument, like the reflection at or transmission through a (super)mirror plate. The trajectory is discarded if the neutron does not hit the subsequent component or gets absorbed.
Principal parts Summary Principal_parts In language learning, the principal parts of a verb are those forms that a student must memorize in order to be able to conjugate the verb through all its forms. The concept originates in the humanist Latin schools, where students learned verbs by chanting them in the four key forms from which all other forms can be deduced, for example: ferō - ferre - tulī - lātum ('to carry')Not all languages have to be taught in this way. In French, for example, regular verbs can be deduced from a single form, the infinitive, and irregular verbs are too random to be systematized under fixed parts. But the concept can be carried over to many languages in which the verbs have some kind of "regular irregularity", i.e. irregularity always occurs at the same place in an otherwise regular system.
Discrete sine transform Informal overview Discrete_sine_transform > Informal overview Like any Fourier-related transform, discrete sine transforms (DSTs) express a function or a signal in terms of a sum of sinusoids with different frequencies and amplitudes. Like the discrete Fourier transform (DFT), a DST operates on a function at a finite number of discrete data points. The obvious distinction between a DST and a DFT is that the former uses only sine functions, while the latter uses both cosines and sines (in the form of complex exponentials).
Chemotherapeutic drugs Treatment strategies Cytotoxic_drug > Treatment strategies Maintenance chemotherapy is a repeated low-dose treatment to prolong remission. : 55–59 Salvage chemotherapy or palliative chemotherapy is given without curative intent, but simply to decrease tumor load and increase life expectancy. For these regimens, in general, a better toxicity profile is expected.
Chest radiograph Limitations Chest_X-ray > Limitations While chest radiographs are a relatively cheap and safe method of investigating diseases of the chest, there are a number of serious chest conditions that may be associated with a normal chest radiograph and other means of assessment may be necessary to make the diagnosis. For example, a patient with an acute myocardial infarction may have a completely normal chest radiograph.
Depletion force The Asakura–Oosawa model Depletion_force > The Asakura–Oosawa model Asakura and Oosawa described four cases in which depletion forces would occur. They first described the most general case as two solid plates in a solution of macromolecules. The principles for the first case were then extended to three additional cases.
Spindle checkpoint Checkpoint deactivation Spindle_assembly_checkpoint > Spindle assembly checkpoint overview > Checkpoint deactivation When this happens the enzyme complex polyubiquitinates the anaphase inhibitor securin. The ubiquitination and destruction of securin at the end of metaphase releases the active protease called separase. Separase cleaves the cohesion molecules that hold the sister chromatids together to activate anaphase.
Low-carbon energy Definitions Green_power > Definitions and background > Definitions Historically, the concept of sustainable energy development has focused on emissions and on energy security. Since the early 1990s, the concept has broadened to encompass wider social and economic issues.The environmental dimension of sustainability includes greenhouse gas emissions, impacts on biodiversity and ecosystems, hazardous waste and toxic emissions, water consumption, and depletion of non-renewable resources.
Data architecture Elements of data architecture Data_architecture > Elements of data architecture It is also important to design interfaces to the data by other systems, as well as a design for the infrastructure that is to support common data operations (i.e. emergency procedures, data imports, data backups, external transfers of data). Without the guidance of a properly implemented data architecture design, common data operations might be implemented in different ways, rendering it difficult to understand and control the flow of data within such systems. This sort of fragmentation is undesirable due to the potential increased cost and the data disconnects involved.
Multisystem inflammatory syndrome in children Characteristics Paediatric_multisystem_inflammatory_syndrome > Characteristics MIS-C / PIMS-TS is a systemic disorder involving persistent fever, extreme inflammation (hyperinflammation), and organ dysfunction, which is temporally associated with exposure to COVID-19. Onset may be delayed or contemporary with ongoing SARS-CoV-2 infection, which may pass without symptoms. The time the syndrome takes to appear following the initial viral infection is debated, though it may develop between the first and second week. Epidemiological data suggest that recognition of the disease may typically be delayed by 2–6 weeks, and usually by 3–4 weeks.
Neural modeling fields Concept models and similarity measures Neural_modeling_fields > Concept models and similarity measures Coefficients r(m), called priors in probability theory, contain preliminary biases or expectations, expected objects m have relatively high r(m) values; their true values are usually unknown and should be learned, like other parameters Sm. Note that in probability theory, a product of probabilities usually assumes that evidence is independent. Expression for L contains a product over n, but it does not assume independence among various signals X(n).
Glossary of engineering: A–L E Glossary_of_engineering:_A–L > E In the International System of Units (SI), it is expressed in units of coulomb per meter squared (C⋅m−2). Electric generatorIn electricity generation, a generator,also called electric generator, electrical generator, and electromagnetic generator.
Laplace domain History Laplace_transforms > History He used an integral of the form akin to a Mellin transform, to transform the whole of a difference equation, in order to look for solutions of the transformed equation. He then went on to apply the Laplace transform in the same way and started to derive some of its properties, beginning to appreciate its potential power.Laplace also recognised that Joseph Fourier's method of Fourier series for solving the diffusion equation could only apply to a limited region of space, because those solutions were periodic. In 1809, Laplace applied his transform to find solutions that diffused indefinitely in space.
Telomere-binding protein TERF1 Telomere-binding_protein > Function > TERF1 TERF1 binds near the N-terminus on a highly conserved domain to form a homodimer interaction. Since TERF1 bends the telomeric site, it may be a critical step in properly functioning telomeres to maintain its length. TERF1 also serves to prevent problematic secondary structures from hindering progression by interacting with helicase for unobstructed unwinding.
Hash table Open addressing Hash_tables > Collision resolution > Open addressing : 272 Double hashing, in which the interval between probes is computed by a secondary hash function. : 272–273 The performance of open addressing may be slower compared to separate chaining since the probe sequence increases when the load factor α {\displaystyle \alpha } approaches 1.: 93 The probing results in an infinite loop if the load factor reaches 1, in the case of a completely filled table. : 471 The average cost of linear probing depends on the hash function's ability to distribute the elements uniformly throughout the table to avoid clustering, since formation of clusters would result in increased search time. : 472
Philosophy of physics Newtonian physics Philosophy_of_physics > History > Newtonian physics The implicit axioms of Aristotelian physics with respect to movement of matter in space were superseded in Newtonian physics by Newton's First Law of Motion.Every body perseveres in its state either of rest or of uniform motion in a straight line, except insofar as it is compelled to change its state by impressed forces. "Every body" includes the Moon, and an apple; and includes all types of matter, air as well as water, stones, or even a flame. Nothing has a natural or inherent motion. Absolute space being three-dimensional Euclidean space, infinite and without a center. Being "at rest" means being at the same place in absolute space over time. The topology and affine structure of space must permit movement in a straight line at a uniform velocity; thus both space and time must have definite, stable dimensions.
Psychomotor speed Reaction time as a function of individual differences Mental_chronometry > Reaction time as a function of individual differences Differential psychologists frequently investigate the causes and consequences of information processing modeled by chronometric studies from experimental psychology. While traditional experimental studies of RT are conducted within-subjects with RT as a dependent measure affected by experimental manipulations, a differential psychologist studying RT will typically hold conditions constant to ascertain between-subjects variability in RT and its relationships with other psychological variables.
IBM Watson Health Intel IBM_Watson_Health > Industry considerations and challenges > Intel Large technology companies such as IBM and Google, and startups such as Welltok and Ayasdi, have also developed AI algorithms for healthcare. Additionally, hospitals are looking to AI solutions to support operational initiatives that increase cost saving, improve patient satisfaction, and satisfy their staffing and workforce needs. Companies are developing predictive analytics solutions that help healthcare managers improve business operations through increasing utilization, decreasing patient boarding, reducing length of stay and optimizing staffing levels.The following medical fields are of interest in artificial intelligence research:
Variational perturbation theory Summary Variational_perturbation_theory The convergence is exponentially fast.After its success in quantum mechanics, VPT has been developed further to become an important mathematical tool in quantum field theory with its anomalous dimensions. Applications focus on the theory of critical phenomena. It has led to the most accurate predictions of critical exponents. More details can be read here.
Strain theory (sociology) Sources and further reading Strain_theory_(sociology) > Sources and further reading American Sociological Review. 24 (2): 147–163. doi:10.2307/2089426.
Doppler Limit Atomic structure Doppler_cooling > Limits > Atomic structure Only certain atoms and ions have optical transitions amenable to laser cooling, since it is extremely difficult to generate the amounts of laser power needed at wavelengths much shorter than 300 nm. Furthermore, the more hyperfine structure an atom has, the more ways there are for it to emit a photon from the upper state and not return to its original state, putting it in a dark state and removing it from the cooling process. It is possible to use other lasers to optically pump those atoms back into the excited state and try again, but the more complex the hyperfine structure is, the more (narrow-band, frequency locked) lasers are required.
Addition to pi ligands Effects of types of ligands on regiochemistry of attack Addition_to_pi_ligands > Effects of types of ligands on regiochemistry of attack Nucleophilic attack at terminal position of allyl ligands when π accepting ligand is present. If sigma donating ligands are present they pump electrons into the ligand and attack occurs at the internal position.
Data brokers Privacy issues and regulation Information_broker > Privacy issues and regulation Information privacy laws are not as strict in the United States as in the European Union, where data brokers work hard to get around the General Data Protection Regulation (GDPR) regulations, brought into operation in 2018. Under GDPR, data can only be collected for re-use on one of six legal bases. The rather vague term "legitimate interest" is often abused or misinterpreted. Explicit consent from users is required for information storage.
Principles of Electronics Summary Principles_of_Electronics Principles of Electronics is a 2002 book by Colin Simpson designed to accompany the Electronics Technician distance education program and contains a concise and practical overview of the basic principles, including theorems, circuit behavior and problem-solving procedures of Electronic circuits and devices. The textbook reinforces concepts with practical "real-world" applications as well as the mathematical solution, allowing readers to more easily relate the academic to the actual. Principles of Electronics presents a broad spectrum of topics, such as atomic structure, Kirchhoff's laws, energy, power, introductory circuit analysis techniques, Thevenin's theorem, the maximum power transfer theorem, electric circuit analysis, magnetism, resonance, control relays, relay logic, semiconductor diodes, electron current flow, and much more. Smoothly integrates the flow of material in a nonmathematical format without sacrificing depth of coverage or accuracy to help readers grasp more complex concepts and gain a more thorough understanding of the principles of electronics.
Proof of knowledge Summary Proof_of_knowledge As the program of the prover does not necessarily spit out the knowledge itself (as is the case for zero-knowledge proofs) a machine with a different program, called the knowledge extractor is introduced to capture this idea. We are mostly interested in what can be proven by polynomial time bounded machines. In this case the set of knowledge elements is limited to a set of witnesses of some language in NP.
Magnetic helicity Topological interpretation Magnetic_helicity > Topological interpretation Thus, the presence of magnetic helicity can be interpreted as helical magnetic field lines, interlinked magnetic structures, but also magnetic field lines turning around each other. Magnetic field lines turning around each other can take several shapes. Let's consider for example a set of turning magnetic field lines in a close neighborhood, which forms a so-called "magnetic flux tube" (see figure for an illustration).
Computability Formal models of computation Computability > Formal models of computation Register machine A theoretical idealization of a computer. There are several variants. In most of them, each register can hold a natural number (of unlimited size), and the instructions are simple (and few in number), e.g. only decrementation (combined with conditional jump) and incrementation exist (and halting).
Quinaldine red Uses Quinaldine_red > Uses Another variation to detecting the QR probes is by measuring the fluorescence via a spectrofluorometer. This allows the concentration of the QR-substance (could be a protein or nucleic acids) to be measured. This also indirectly allows the binding ability of QR to the substance to be measured.
Seiberg–Witten gauge theory Seiberg–Witten curves Seiberg–Witten_theory > Seiberg–Witten curves In general, effective Lagrangians of supersymmetric gauge theories are largely determined by their holomorphic (really, meromorphic) properties and their behavior near the singularities. In gauge theory with N = 2 {\displaystyle {\mathcal {N}}=2} extended supersymmetry, the moduli space of vacua is a special Kähler manifold and its Kähler potential is constrained by above conditions. In the original approach, by Seiberg and Witten, holomorphy and electric-magnetic duality constraints are strong enough to almost uniquely constrain the prepotential F {\displaystyle {\mathcal {F}}} (a holomorphic function which defines the theory), and therefore the metric of the moduli space of vacua, for theories with SU(2) gauge group. More generally, consider the example with gauge group SU(n).

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