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Molecular vibrations Internal coordinates Vibrational_transition > Vibrational coordinates > Internal coordinates The angles do. Rocking is distinguished from wagging by the fact that the atoms in the group stay in the same plane. In ethylene there are 12 internal coordinates: 4 C–H stretching, 1 C–C stretching, 2 H–C–H bending, 2 CH2 rocking, 2 CH2 wagging, 1 twisting.
Reciprocal rule Application to a proof of the quotient rule Reciprocal_rule > Application to a proof of the quotient rule The reciprocal rule is a special case of the quotient rule, which states that if f and g are differentiable at x and g(x) ≠ 0 then The quotient rule can be proved by writing and then first applying the product rule, and then applying the reciprocal rule to the second factor.
Vitamin E Cardiovascular diseases Vitamin_E > Research > Cardiovascular diseases Likewise for subset analysis of natural or synthetic vitamin E, or only above or below 300 IU/day, or whether the enrolled people were healthy or considered to be at higher than normal risk. The authors concluded that there was a lack of clinically important benefit of vitamin E supplementation in the prevention of stroke. One large, multi-year study in which post-menopausal women consumed either placebo or 600 IU of natural-sourced vitamin E on alternate days reported no effect on stroke, but did report a 21% reduction in relative risk of developing a deep vein clot or pulmonary embolism. The beneficial effect was strongest is the subset of women who had a history of a prior thrombotic event or who were genetically coded for clot risk (factor V Leiden or prothrombin mutation).
Murine respirovirus Sendai virus proteolytic processing enzymes are often overexpressed in cancer cells. Murine_respirovirus > As an oncolytic agent > Anticancer mechanism > Direct cancer cells killing. Malignant cells are vulnerable to SeV infection. > Sendai virus proteolytic processing enzymes are often overexpressed in cancer cells. Another F-protein-protease is tryptase beta 2 (TPSB2). This protease (with alias such as tryptase-Clara and mast cell tryptase) is expressed in normal club cells and mast cells, and in some cancers. It's especially high expression is observed in the human mast cell line HMC-1, and in the human erythroleukemia cell line HEL.
Big and Ugly Rendering Project Summary Big_and_Ugly_Rendering_Project Big and Ugly Rendering Project (BURP) is a non-commercial volunteer computing project using the BOINC framework for the rendering of 3D graphics that has been in hibernation as of 2020. The project website currently shows the status as "extended maintenance" until 2027. BURP utilizes the volunteer and grid computing software BOINC, to distribute computing tasks to volunteer computers. BURP is free software distributed under the GNU General Public License V3. Because BURP is used to refer to both the BOINC project and BURP back-end software, some confusion can arise when talking about other services running the BURP software.
Gastrin Function Gastrin > Physiology > Function The presence of gastrin stimulates parietal cells of the stomach to secrete hydrochloric acid (HCl)/gastric acid. This is done both directly on the parietal cell and indirectly via binding onto CCK2/gastrin receptors on ECL cells in the stomach, which then responds by releasing histamine, which in turn acts in a paracrine manner on parietal cells stimulating them to secrete H+ ions. This is the major stimulus for acid secretion by parietal cells.Along with the above-mentioned function, gastrin has been shown to have additional functions as well: Stimulates parietal cell maturation and fundal growth. Causes chief cells to secrete pepsinogen, the zymogen (inactive) form of the digestive enzyme pepsin.
Physics of Failure Summary Physics_of_Failure This approach models the root causes of failure such as fatigue, fracture, wear, and corrosion. An approach to the design and development of reliable product to prevent failure, based on the knowledge of root cause failure mechanisms. The Physics of Failure (PoF) concept is based on the understanding of the relationships between requirements and the physical characteristics of the product and their variation in the manufacturing processes, and the reaction of product elements and materials to loads (stressors) and interaction under loads and their influence on the fitness for use with respect to the use conditions and time.
Random access Summary Random_access In data structures, direct access implies the ability to access any entry in a list in constant time (independent of its position in the list and of the list's size). Very few data structures can make this guarantee other than arrays (and related structures like dynamic arrays). Direct access is required, or at least valuable, in many algorithms such as binary search, integer sorting, or certain versions of sieve of Eratosthenes.Other data structures, such as linked lists, sacrifice direct access to permit efficient inserts, deletes, or re-ordering of data. Self-balancing binary search trees may provide an acceptable compromise, where access time is not equal for all members of a collection, but the maximum time to retrieve a given member grows only logarithmically with its size.
Glossary of string theory H Glossary_of_string_theory > H Hagedorn temperature The temperature above which the partition function diverges due to the exponentially increasing number of string states. h.c. hc Hermitian conjugate HCMS Hadronic center of mass (frame) HDM Higgs doublet model HE Short for heterotic-E28, a heterotic string theory based on the group E28.
Steering law Derivation of the model from Fitts's law Steering_law > Derivation of the model from Fitts's law The total time to navigative through all the goals, and thus through the tunnel, is Note that b is an experimentally fitted constant and let b ~ := b ln ⁡ ( 2 ) {\displaystyle {\tilde {b}}:={\frac {b}{\ln(2)}}} . Therefore, Tstraight tunnel = b ~ ⋅ A W {\displaystyle {\tilde {b}}\cdot {\frac {A}{W}}} . Next, consider a curved tunnel of total length A, parameterized by s varying from 0 to A. Let W(s) be the variable width of the tunnel.
Ramberg–Bäcklund reaction Mechanism Ramberg–Bäcklund_reaction > Mechanism The sulfone group contains an acidic proton in one of the α-positions which is abstracted by a strong base (scheme 1). The negative charge placed on this position (formally a carbanion) is transferred to the halogen residing on the other α-position in a nucleophilic displacement temporarily forming a three-membered cyclic sulfone. This intermediate is unstable and releases sulfur dioxide to form the alkene. Mixtures of cis isomer and trans isomer are usually obtained.The Favorskii rearrangement and the Eschenmoser sulfide contraction are conceptually related reactions.
Classification rule False positives Classification_rule > Confusion Matrix and Classifiers > False positives False positives result when a test falsely (incorrectly) reports a positive result. For example, a medical test for a disease may return a positive result indicating that the patient has the disease even if the patient does not have the disease. False positive is commonly denoted as the top right (Condition negative X test outcome positive) unit in a Confusion matrix.
Molecular models of DNA DNA structure Molecular_models_of_DNA > Fundamental concepts > DNA structure The structure of DNA shows a variety of forms, both double-stranded and single-stranded. The mechanical properties of DNA, which are directly related to its structure, are a significant problem for cells. Every process which binds or reads DNA is able to use or modify the mechanical properties of DNA for purposes of recognition, packaging and modification. The extreme length (a chromosome may contain a 10 cm long DNA strand), relative rigidity and helical structure of DNA has led to the evolution of histones and of enzymes such as topoisomerases and helicases to manage a cell's DNA.
Entropy and life Counteracting the second law tendency Entropy_and_life > Counteracting the second law tendency The robotic machinery requires electrical work input and instructions, but when completed, the manufactured products have less uniformity with their surroundings, or more complexity (higher order) relative to the raw materials they were made from. Thus, system entropy or disorder decreases while the tendency towards uniformity between the system and its environment is counteracted. In this example, the instructions, as well as the source of work may be internal or external to the system, and they may or may not cross the system boundary.
Franz–Keldysh effect Summary Franz–Keldysh_effect The Airy tails slightly overlap even if the electron and hole are at slightly different potentials (slightly different physical locations along the field). The absorption spectrum now includes a tail at energies below the band gap and some oscillations above it.
Taylor polynomial Third example Maclaurin_series > Calculation of Taylor series > Third example x n . {\displaystyle {\begin{aligned}(1+x)e^{x}&=e^{x}+xe^{x}=\sum _{n=0}^{\infty }{\frac {x^{n}}{n! }}+\sum _{n=0}^{\infty }{\frac {x^{n+1}}{n!
Ductility Ductile–brittle transition temperature Ductility > Ductile–brittle transition temperature The most accurate method of measuring the DBTT of a material is by fracture testing. Typically four-point bend testing at a range of temperatures is performed on pre-cracked bars of polished material. Two fracture tests are typically utilized to determine the DBTT of specific metals: the Charpy V-Notch test and the Izod test.
Skew-symmetric matrix Spectral theory Skew-symmetric_matrix > Properties > Spectral theory Since a matrix is similar to its own transpose, they must have the same eigenvalues. It follows that the eigenvalues of a skew-symmetric matrix always come in pairs ±λ (except in the odd-dimensional case where there is an additional unpaired 0 eigenvalue). From the spectral theorem, for a real skew-symmetric matrix the nonzero eigenvalues are all pure imaginary and thus are of the form λ 1 i , − λ 1 i , λ 2 i , − λ 2 i , … {\displaystyle \lambda _{1}i,-\lambda _{1}i,\lambda _{2}i,-\lambda _{2}i,\ldots } where each of the λ k {\displaystyle \lambda _{k}} are real. Real skew-symmetric matrices are normal matrices (they commute with their adjoints) and are thus subject to the spectral theorem, which states that any real skew-symmetric matrix can be diagonalized by a unitary matrix.
Texas Hold 'Em Starting hands Texas_Hold_'Em > Strategy > Starting hands Because of this equivalence, there are only 169 effectively different hole-card combinations. Thirteen of these are pairs, from deuces (twos) to aces. There are 78 ways to have two cards of different rank (12 possible hands containing one ace, 11 possible hands containing one king but no ace, 10 possible hands containing one queen but no ace or king, etc.).
Convergent prefilter Motivation Limit_point_of_a_filter > Motivation {\displaystyle x_{\bullet }:\mathbb {N} \to X.} Specifically, with the family of sets { x ≥ 1 , x ≥ 2 , … } {\displaystyle \{x_{\geq 1},x_{\geq 2},\ldots \}} in hand, the function x ∙: N → X {\displaystyle x_{\bullet }:\mathbb {N} \to X} is no longer needed to determine convergence of this sequence (no matter what topology is placed on X {\displaystyle X} ). By generalizing this observation, the notion of "convergence" can be extended from sequences/functions to families of sets.
Isothermal Titration Calorimetry Instrumental measurements Isothermal_titration_calorimeter > Instrumental measurements During the experiment, ligand is titrated into the sample cell in precisely known aliquots, causing heat to be either taken up or evolved (depending on the nature of the reaction). Measurements consist of the time-dependent input of power required to maintain equal temperatures between the sample and reference cells.In an exothermic reaction, the temperature in the sample cell increases upon addition of ligand. This causes the feedback power to the sample cell to be decreased (remember: a reference power is applied to the reference cell) in order to maintain an equal temperature between the two cells.
Hopfield neural network General formulation of the modern Hopfield network Hopfield_neural_network > Dense associative memory or modern Hopfield network > General formulation of the modern Hopfield network This network has a global energy function where the first two terms represent the Legendre transform of the Lagrangian function with respect to the neurons' currents x I {\displaystyle x_{I}} . The temporal derivative of this energy function can be computed on the dynamical trajectories leading to (see for details) The last inequality sign holds provided that the matrix M I K {\displaystyle M_{IK}} (or its symmetric part) is positive semi-definite. If, in addition to this, the energy function is bounded from below the non-linear dynamical equations are guaranteed to converge to a fixed point attractor state. The advantage of formulating this network in terms of the Lagrangian functions is that it makes it possible to easily experiment with different choices of the activation functions and different architectural arrangements of neurons. For all those flexible choices the conditions of convergence are determined by the properties of the matrix M I J {\displaystyle M_{IJ}} and the existence of the lower bound on the energy function.
Skin effect Cause Skin_effect > Cause An alternating current may also be induced in a conductor due to an alternating magnetic field according to the law of induction. An electromagnetic wave impinging on a conductor will therefore generally produce such a current; this explains the reflection of electromagnetic waves from metals. Although the term "skin effect" is most often associated with applications involving transmission of electric currents, skin depth also describes the exponential decay of the electric and magnetic fields, as well as the density of induced currents, inside a bulk material when a plane wave impinges on it at normal incidence.
Potts model Partition function and measure Potts_model > Measure-theoretic description > Partition function and measure The corresponding finite-state partition function is given by Z n ( V ) = ∑ s 0 , … , s n ∈ Q exp ⁡ ( − β H n ( C 0 ) ) {\displaystyle Z_{n}(V)=\sum _{s_{0},\ldots ,s_{n}\in Q}\exp(-\beta H_{n}(C_{0}))} with C0 being the cylinder sets defined above. Here, β = 1/kT, where k is Boltzmann's constant, and T is the temperature. It is very common in mathematical treatments to set β = 1, as it is easily regained by rescaling the interaction energy. This partition function is written as a function of the interaction V to emphasize that it is only a function of the interaction, and not of any specific configuration of spins.
Learning theory (education) Using online games for learning Learning_theory_(education) > Multimedia learning > Using online games for learning Many educators and researchers believe that information technology could bring innovation on traditional educational instructions. Teachers and technologists are searching for new and innovative ways to design learner-centered learning environments effectively, trying to engage learners more in the learning process. Claims have been made that online games have the potential to teach, train and educate and they are effective means for learning skills and attitudes that are not so easy to learn by rote memorization. There has been a lot of research done in identifying the learning effectiveness in game based learning.
U4 spliceosomal RNA Biological role U4_spliceosomal_RNA > Biological role The U4 snRNA has been shown to exist in a number of different formats including: bound to proteins as a small nuclear Ribo-Nuclear Protein snRNP, involved with the U6 snRNA in the di-snRNP, as well as involved with both the U6 snRNA and the U5 snRNA in the tri-snRNP. The different formats have been proposed to coincide with different temporal events in the activity of the penta-snRNP, or as intermediates in the step-wise model of spliceosome assembly and activity.The U4 snRNA (and its likely analog snR14 in Yeast) has been shown not to participate directly in the specific catalytic activities of the splicing reaction, and is proposed instead to act as a regulator of the U6 snRNA. The U4 snRNA inhibits spliceosome activity during assembly by complementary base pairing between the U6 snRNA in two highly conserved stem regions.
Centre-of-momentum frame General Center_of_mass_frame > Properties > General The center of momentum frame is defined as the inertial frame in which the sum of the linear momenta of all particles is equal to 0. Let S denote the laboratory reference system and S′ denote the center-of-momentum reference frame. Using a Galilean transformation, the particle velocity in S′ is v ′ = v − V c , {\displaystyle v'=v-V_{c},} where V c = ∑ i m i v i ∑ i m i {\displaystyle V_{c}={\frac {\sum _{i}m_{i}v_{i}}{\sum _{i}m_{i}}}} is the velocity of the mass center.
Magnetic anomaly detection Operation Magnetic_anomaly_detection > Operation MAD devices are usually mounted on aircraft. For example, one study showed that a horizontal detection range of 450–800 m, when aircraft was 200 m above a submarine, decreased to less than 150 m when the aircraft was 400 m above the submarine.If the sea floor has sunken ships, then submarines may operate near them to confuse magnetic anomaly detectors.MAD has certain advantages over other detection methods. It is a passive detection method. Unlike sonar it is not impacted by meteorological conditions; indeed above sea state 5, MAD may be the only reliable method for submarine detection.
Probability space Probability distribution Probability_spaces > Related concepts > Probability distribution Any probability distribution defines a probability measure.
P value Testing the fairness of a coin P_value > Example > Testing the fairness of a coin As the binomial distribution is symmetrical for a fair coin, the two-sided p-value is simply twice the above calculated single-sided p-value: the two-sided p-value is 0.115. In the above example: Null hypothesis (H0): The coin is fair, with Pr(heads) = 0.5 Test statistic: Number of heads Alpha level (designated threshold of significance): 0.05 Observation O: 14 heads out of 20 flips; and Two-tailed p-value of observation O given H0 = 2 × min(Pr(no. of heads ≥ 14 heads), Pr(no. of heads ≤ 14 heads)) = 2 × min(0.058, 0.978) = 2*0.058 = 0.115.The Pr (no. of heads ≤ 14 heads) = 1 - Pr(no. of heads ≥ 14 heads) + Pr (no. of head = 14) = 1 - 0.058 + 0.036 = 0.978; however, the symmetry of this binomial distribution makes it an unnecessary computation to find the smaller of the two probabilities. Here, the calculated p-value exceeds .05, meaning that the data falls within the range of what would happen 95% of the time, if the coin were fair. Hence, the null hypothesis is not rejected at the .05 level. However, had one more head been obtained, the resulting p-value (two-tailed) would have been 0.0414 (4.14%), in which case the null hypothesis would be rejected at the 0.05 level.
Prodiscrete topology C Glossary_of_topology > C Each connected component is closed, and the set of connected components of a space is a partition of that space.Continuous A function from one space to another is continuous if the preimage of every open set is open.Continuum A space is called a continuum if it a compact, connected Hausdorff space.Contractible A space X is contractible if the identity map on X is homotopic to a constant map. Every contractible space is simply connected.Coproduct topology If {Xi} is a collection of spaces and X is the (set-theoretic) disjoint union of {Xi}, then the coproduct topology (or disjoint union topology, topological sum of the Xi) on X is the finest topology for which all the injection maps are continuous.Core-compact spaceCosmic space A continuous image of some separable metric space.Countable chain condition A space X satisfies the countable chain condition if every family of non-empty, pairswise disjoint open sets is countable.Countably compact A space is countably compact if every countable open cover has a finite subcover. Every countably compact space is pseudocompact and weakly countably compact.Countably locally finite A collection of subsets of a space X is countably locally finite (or σ-locally finite) if it is the union of a countable collection of locally finite collections of subsets of X.Cover A collection of subsets of a space is a cover (or covering) of that space if the union of the collection is the whole space.Covering See Cover.Cut point If X is a connected space with more than one point, then a point x of X is a cut point if the subspace X − {x} is disconnected.
General artificial intelligence Potential threat to human existence General_artificial_intelligence > Risks > Potential threat to human existence The thesis that AI poses an existential risk for humans, and that this risk needs much more attention than it currently gets, is controversial but has been endorsed by many public figures including Elon Musk, Bill Gates, and Stephen Hawking. AI researchers like Stuart J. Russell, Roman Yampolskiy, and Alexey Turchin, also support the basic thesis of a potential threat to humanity. Gates states he does not "understand why some people are not concerned", and Hawking criticized widespread indifference in his 2014 editorial: So, facing possible futures of incalculable benefits and risks, the experts are surely doing everything possible to ensure the best outcome, right?
Disruptive selection Overview Magic_trait > Overview Natural selection is known to be one of the most important biological processes behind evolution. There are many variations of traits, and some cause greater or lesser reproductive success of the individual. The effect of selection is to promote certain alleles, traits, and individuals that have a higher chance to survive and reproduce in their specific environment. Since the environment has a carrying capacity, nature acts on this mode of selection on individuals to let only the most fit offspring survive and reproduce to their full potential.
Newton's theorem of revolving orbits Historical context Newton's_theorem_of_revolving_orbits > Historical context According to these laws, planets move on ellipses (not epicycles) about the Sun (not the Earth). Kepler's second and third laws make specific quantitative predictions: planets sweep out equal areas in equal time, and the square of their orbital periods equals a fixed constant times the cube of their semi-major axis. Subsequent observations of the planetary orbits showed that the long axis of the ellipse (the so-called line of apsides) rotates gradually with time; this rotation is known as apsidal precession.
Methods of website linking Directory link Link_popularity > Link types > Acquired link > Directory link Website directories are lists of links to websites which are sorted into categories. Website owners can submit their site to many of these directories. Some directories accept payment for listing in their directory while others are free.
Low Basis Theorem Application Low_Basis_Theorem > Application One application of the low basis theorem is to construct completions of effective theories so that the completions have low Turing degree. For example, the low basis theorem implies the existence of PA degrees strictly below ∅ ′ {\displaystyle \emptyset '} .
Cross training In mixed martial arts Cross_training > In general sports > In mixed martial arts In mixed martial arts and self-defense, cross-training refers to training in multiple martial arts or fighting systems to become proficient in all the phases of unarmed combat. This training is meant to overcome the shortcomings of one style by practicing another style which is strong in the appropriate area. A typical combination involves a striking-based art such as Muay Thai, combined with a grappling-based art such as wrestling and Brazilian Jiu-Jitsu. Many hybrid martial arts can be considered derivatives of such cross-training.Modern mixed martial-arts training generally involves cross-training in the different aspects and ranges of fighting.
COVID-19 pandemic Background COVID-19_pandemic > Epidemiology > Background Controversies about the origins of the virus, including the lab leak theory, heightened geopolitical divisions, notably between the United States and China.The earliest known infected person fell ill on 1 December 2019. That individual did not have a connection with the later wet market cluster. However, an earlier case may have occurred on 17 November. Two-thirds of the initial case cluster were linked with the market. Molecular clock analysis suggests that the index case is likely to have been infected between mid-October and mid-November 2019.
Inverse polymerase chain reaction Summary Inverse_PCR Inverse polymerase chain reaction (Inverse PCR) is a variant of the polymerase chain reaction that is used to amplify DNA with only one known sequence. One limitation of conventional PCR is that it requires primers complementary to both termini of the target DNA, but this method allows PCR to be carried out even if only one sequence is available from which primers may be designed. Inverse PCR is especially useful for the determination of insert locations. For example, various retroviruses and transposons randomly integrate into genomic DNA.
Chemotherapeutic agents Limitations Cytostatic_antineoplastic_agent > Limitations Chemotherapy does not always work, and even when it is useful, it may not completely destroy the cancer. People frequently fail to understand its limitations. In one study of people who had been newly diagnosed with incurable, stage 4 cancer, more than two-thirds of people with lung cancer and more than four-fifths of people with colorectal cancer still believed that chemotherapy was likely to cure their cancer.The blood–brain barrier poses an obstacle to delivery of chemotherapy to the brain. This is because the brain has an extensive system in place to protect it from harmful chemicals.
Funarg problem Summary Funarg_problem In computer science, the funarg problem (function argument problem) refers to the difficulty in implementing first-class functions (functions as first-class objects) in programming language implementations so as to use stack-based memory allocation of the functions. The difficulty only arises if the body of a nested function refers directly (i.e., not by argument passing) to identifiers defined in the environment in which the function is defined, but not in the environment of the function call. A standard resolution is either to forbid such references or to create closures.There are two subtly different versions of the funarg problem. The upwards funarg problem arises from returning (or otherwise transmitting "upwards") a function from a function call. The downwards funarg problem arises from passing a function as a parameter to another function call.
Hypovolemic shock Blood loss Hypovolemic_shock > Pathophysiology > Blood loss The simultaneous loss of coagulation factors via hemorrhage, hemodilution with resuscitation fluids, and coagulation cascade dysfunction secondary to acidosis and hypothermia have been traditionally thought to be the cause of coagulopathy in trauma. However, this traditional model of trauma-induced coagulopathy may be too limited. Further studies have shown that a degree of coagulopathy begins in 25% to 56% of patients before initiation of the resuscitation.
Epigenetic regulation Definitions Epigenetic_landscape > Definitions The term epigenesis has a generic meaning of "extra growth" that has been used in English since the 17th century. In scientific publications, the term epigenetics started to appear in the 1930s (see Fig. on the right). However, its contemporary meaning emerged only in the 1990s. A definition of the concept of epigenetic trait as a "stably heritable phenotype resulting from changes in a chromosome without alterations in the DNA sequence" was formulated at a Cold Spring Harbor meeting in 2008, although alternate definitions that include non-heritable traits are still being used widely.
Area integral Change of variables Double_integral > Methods of integration > Change of variables The function is f(x, y) = (x − 1)2 + √y; if one adopts the substitution u = x − 1, v = y therefore x = u + 1, y = v one obtains the new function f2(u, v) = (u)2 + √v. Similarly for the domain because it is delimited by the original variables that were transformed before (x and y in example). the differentials dx and dy transform via the absolute value of the determinant of the Jacobian matrix containing the partial derivatives of the transformations regarding the new variable (consider, as an example, the differential transformation in polar coordinates).There exist three main "kinds" of changes of variable (one in R2, two in R3); however, more general substitutions can be made using the same principle.
Gramian matrix Gram determinant Gramian_matrix > Gram determinant The Gram determinant or Gramian is the determinant of the Gram matrix: If v 1 , … , v n {\displaystyle v_{1},\dots ,v_{n}} are vectors in R m {\displaystyle \mathbb {R} ^{m}} then it is the square of the n-dimensional volume of the parallelotope formed by the vectors. In particular, the vectors are linearly independent if and only if the parallelotope has nonzero n-dimensional volume, if and only if Gram determinant is nonzero, if and only if the Gram matrix is nonsingular. When m < n the determinant and volume are zero. When m = n, this reduces to the standard theorem that the absolute value of the determinant of n n-dimensional vectors is the n-dimensional volume.
Advanced Query Syntax Summary Windows_Live_Search_Center Windows Search (also known as Instant Search) is a content index desktop search platform by Microsoft introduced in Windows Vista as a replacement for both the previous Indexing Service of Windows 2000 and the optional MSN Desktop Search for Windows XP and Windows Server 2003, designed to facilitate local and remote queries for files and non-file items in compatible applications including Windows Explorer. It was developed after the postponement of WinFS and introduced to Windows constituents originally touted as benefits of that platform. Windows Search creates a locally managed Index of files — documents, emails, folders, programs, photos, tracks, and videos — and file contents, as well as of non-file items including those of Microsoft Outlook for which users can perform incremental searches based on details such as authors, contents, dates, file names, file types, people, and sizes; the Index stores actual prose from inside documents and metadata properties from other content.
Oxygen 3 Ozone as a greenhouse gas Ozone_generator > Ozone in Earth's atmosphere > Ozone as a greenhouse gas Although ozone was present at ground level before the Industrial Revolution, peak concentrations are now far higher than the pre-industrial levels, and even background concentrations well away from sources of pollution are substantially higher. Ozone acts as a greenhouse gas, absorbing some of the infrared energy emitted by the earth. Quantifying the greenhouse gas potency of ozone is difficult because it is not present in uniform concentrations across the globe. However, the most widely accepted scientific assessments relating to climate change (e.g. the Intergovernmental Panel on Climate Change Third Assessment Report) suggest that the radiative forcing of tropospheric ozone is about 25% that of carbon dioxide.
Trustworthy AI Summary Trustworthy_AI Trustworthy AI is a programme of work of the ITU (United Nations Specialized Agency for ICT) under its AI for Good programme. The programme advances the standardization of a number of Privacy-enhancing technologies (PETs), including homomorphic encryption, federated learning, secure multi-party computation, differential privacy, zero-knowledge proof.Privacy-Enhancing Technologies apply complex and sometimes counterintuitive operations to process signals and information while safeguarding privacy. For instance, homomorphic encryption allows for computing on encrypted data, where the outcomes or result is still encrypted and unknown to those performing the computation, but decryptable by the original encryptor.
COVID-19 drug repurposing research Vitamin D COVID-19_drug_repurposing_research > Vitamins > Vitamin D During the COVID-19 pandemic, there has been interest in vitamin D status and supplements, given the significant overlap in the risk factors for severe COVID-19 and vitamin D deficiency. These include obesity, older age, and Black or Asian ethnic origin, and it is notable that vitamin D deficiency is particularly common within these groups.The National Institutes of Health (NIH) COVID-19 Treatment Guidelines states "there is insufficient evidence to recommend either for or against the use of vitamin D for the prevention or treatment of COVID-19. "The general recommendation to consider taking vitamin D supplements, particularly given the levels of vitamin D deficiency in Western populations, has been repeated. As of February 2021, the English National Institute for Health and Care Excellence (NICE) continued to recommend small doses of supplementary vitamin D for people with little exposure to sunshine, but recommended that practitioners should not offer a vitamin D supplement solely to prevent or treat COVID-19, except as part of a clinical trial.Multiple studies have reported links between pre-existing vitamin D deficiency and the severity of the disease.
History of randomness 17th–19th centuries History_of_randomness > 17th–19th centuries Clausius was the first to state "entropy always increases".From the time of Newton until about 1890, it was generally believed that if one knows the initial state of a system with great accuracy, and if all the forces acting on the system can be formulated with equal accuracy, it would be possible, in principle, to make predictions of the state of the universe for an infinitely long time. The limits to such predictions in physical systems became clear as early as 1893 when Henri Poincaré showed that in the three-body problem in astronomy, small changes to the initial state could result in large changes in trajectories during the numerical integration of the equations.During the 19th century, as probability theory was formalized and better understood, the attitude towards "randomness as nuisance" began to be questioned. Goethe wrote: The tissue of the world is built from necessities and randomness; the intellect of men places itself between both and can control them; it considers the necessity and the reason of its existence; it knows how randomness can be managed, controlled, and used.
Classical scaling dimension Free field theories Anomalous_scaling_dimension > Scale-invariant quantum field theory > Free field theories Free theories are the simplest scale-invariant quantum field theories. In free theories, one makes a distinction between the elementary operators, which are the fields appearing in the Lagrangian, and the composite operators which are products of the elementary ones. The scaling dimension of an elementary operator O is determined by dimensional analysis from the Lagrangian (in four spacetime dimensions, it is 1 for elementary bosonic fields including the vector potentials, 3/2 for elementary fermionic fields etc.). This scaling dimension is called the classical dimension (the terms canonical dimension and engineering dimension are also used). A composite operator obtained by taking a product of two operators of dimensions Δ 1 {\displaystyle \Delta _{1}} and Δ 2 {\displaystyle \Delta _{2}} is a new operator whose dimension is the sum Δ 1 + Δ 2 {\displaystyle \Delta _{1}+\Delta _{2}} . When interactions are turned on, the scaling dimension receives a correction called the anomalous dimension (see below).
Renewable energy policy Renewable energy targets Renewable-energy_economy > Public policy landscape > Renewable energy targets Developing countries with renewable energy targets include China, India, Indonesia, Malaysia, the Philippines, Thailand, Brazil, Egypt, Mali, and South Africa. The targets set by many developing countries are quite modest when compared with those in some industrialized countries.Renewable energy targets in most countries are indicative and nonbinding but they have assisted government actions and regulatory frameworks. The United Nations Environment Program has suggested that making renewable energy targets legally binding could be an important policy tool to achieve higher renewable energy market penetration.
Parallel processing (psychology) Activation rule Parallel_processing_(psychology) > Aspects of a parallel distributed processing model > Activation rule A new state of activation is produced for every unit by joining the net inputs of impinging units combined and the current state of activation for that unit.
Pumping lemma for regular languages General version of pumping lemma for regular languages Pumping_lemma_for_regular_languages > General version of pumping lemma for regular languages If a language L {\displaystyle L} is regular, then there exists a number p ≥ 1 {\displaystyle p\geq 1} (the pumping length) such that every string u w v {\displaystyle uwv} in L {\displaystyle L} with \| w \| ≥ p {\displaystyle \|w\|\geq p} can be written in the form u w v = u x y z v {\displaystyle uwv=uxyzv} with strings x {\displaystyle x} , y {\displaystyle y} and z {\displaystyle z} such that \| x y \| ≤ p {\displaystyle \|xy\|\leq p} , \| y \| ≥ 1 {\displaystyle \|y\|\geq 1} and u x y i z v {\displaystyle uxy^{i}zv} is in L {\displaystyle L} for every integer i ≥ 0 {\displaystyle i\geq 0} .From this, the above standard version follows a special case, with both u {\displaystyle u} and v {\displaystyle v} being the empty string. Since the general version imposes stricter requirements on the language, it can be used to prove the non-regularity of many more languages.
False Discovery Rate Literature False_Discovery_Rate > History > Literature Soric used the expected number of false discoveries divided by the number of discoveries ( E / R ) {\displaystyle \left(E/R\right)} as a warning that "a large part of statistical discoveries may be wrong". This led Benjamini and Hochberg to the idea that a similar error rate, rather than being merely a warning, can serve as a worthy goal to control.The BH procedure was proven to control the FDR for independent tests in 1995 by Benjamini and Hochberg. In 1986, R. J. Simes offered the same procedure as the "Simes procedure", in order to control the FWER in the weak sense (under the intersection null hypothesis) when the statistics are independent.
Index of energy articles E Index_of_energy_articles > E - Ecological energetics - Electric Bond and Share Company - Electric potential energy - Electrochemical energy conversion - Embodied energy - Encircled energy - Energy - Energy accidents - Energy accounting - Energy amplifier - Energy applications of nanotechnology - Energy balance (biology) - Energy bar - Energy barrier - Energy being - Energy carrier - Energy Catalyzer - Energy cell - Energy charge - Energy conservation - Energy conversion efficiency - Energy crop - Energy current - Energy density - Energy-depth relationship in a rectangular channel - Energy development - Energy-dispersive X-ray spectroscopy - Energy distance - Energy drift - Energy drink - Energy efficiency gap - Energy-Efficient Ethernet - Energy-efficient landscaping - Energy elasticity - Energy engineering - Energy (esotericism) - Energy expenditure - Energy factor - Energy field disturbance - Energy filtered transmission electron microscopy - Energy transfer - Energy flow (ecology) - Energy flux - Energy forestry - Energy functional - Energy gel - Energy harvesting - Energy independence - Energy input labeling - Energy landscape - Energy level - Energy level splitting - Energy management software - Energy management system - Energy–maneuverability theory - Energy Manufacturing Co. Inc - Energy medicine - Energy–momentum relation - Energy monitoring and targeting - Energy Probe - Energy profile (chemistry) - Energy quality - Energy recovery ventilation - Energy security - Energy (signal processing) - Energy Slave - Energy Star - Energy statistics - Energy Storage Challenge - Energy storage - Energy system - Energy technology - Energy tower (downdraft) - Energy transfer - Energy transfer upconversion - Energy transformation - Energy value of coal - Energy vortex (stargate) - Enthalpy - Entropy - Equipartition theorem - E-statistic - Exertion
Model-based testing Model checking Model-based_testing > Deriving tests algorithmically > Model checking Model checkers can also be used for test case generation. Originally model checking was developed as a technique to check if a property of a specification is valid in a model. When used for testing, a model of the system under test, and a property to test is provided to the model checker.
Multiple sclerosis signs and symptoms Tremor and ataxia Multiple_sclerosis_signs_and_symptoms > Tremor and ataxia Tremor is an unintentional, somewhat rhythmic, muscle movement involving to-and-fro movements (oscillations) of one or more parts of the body. It is the most common of all involuntary movements and can affect the hands, arms, head, face, vocal cords, trunk, and legs. Ataxia is an unsteady and clumsy motion of the limbs or torso due to a failure of the gross coordination of muscle movements. People with ataxia experience a failure of muscle control in their arms and legs, resulting in a lack of balance and coordination or a disturbance of gait.
Information gain in decision trees Formal definition Information_gain_in_decision_trees > Formal definition In this case, the relative entropies subtracted from the total entropy are 0. In particular, the values v ∈ v a l s ( a ) {\displaystyle v\in vals(a)} defines a partition of the training set data T into mutually exclusive and all-inclusive subsets, inducing a categorical probability distribution P a ( v ) {\textstyle P_{a}{(v)}} on the values v ∈ v a l s ( a ) {\textstyle v\in vals(a)} of attribute a. The distribution is given P a ( v ) := \| S a ( v ) \| \| T \| {\textstyle P_{a}{(v)}:={\frac {\|S_{a}{(v)}\|}{\|T\|}}} . In this representation, the information gain of T given a can be defined as the difference between the unconditional Shannon entropy of T and the expected entropy of T conditioned on a, where the expectation value is taken with respect to the induced distribution on the values of a.
UPnP AV media server NAT traversal UPnP_AV_media_server > NAT traversal For consumer routers, only AVM and the open source router software projects OpenWrt, OPNsense, and pfSense are currently known to support PCP as an alternative to UPnP. AVM's UPnP IGDv2 and PCP implementation has been very buggy since its introduction. In many cases it does not work. The open source router software projects use the MiniUPnPd server, which supports all three protocols.
TPEN Toxicity TPEN > Toxicity Additionally, the same study found that TPEN increased the expression of pro-apoptotic genes and led to the activation of caspase-11, a mammalian protease. These results suggest that the p53 tumor suppressor protein may play a role in regulating TPEN-induced neuronal apoptosis. Although these studies found that TPEN induces apoptosis, another study found that TPEN inhibits sodium dithionite and glucose deprivation (SDGD)-Induced neuronal death by modulating apoptosis.
Koszul cohomology Summary Koszul_cohomology In mathematics, the Koszul cohomology groups K p , q ( X , L ) {\displaystyle K_{p,q}(X,L)} are groups associated to a projective variety X with a line bundle L. They were introduced by Mark Green (1984, 1984b), and named after Jean-Louis Koszul as they are closely related to the Koszul complex. Green (1989) surveys early work on Koszul cohomology, Eisenbud (2005) gives an introduction to Koszul cohomology, and Aprodu & Nagel (2010) gives a more advanced survey.
Koopmans' theorem For electron affinities Koopmans'_theorem > Generalizations > For electron affinities It is sometimes claimed that Koopmans' theorem also allows the calculation of electron affinities as the energy of the lowest unoccupied molecular orbitals (LUMO) of the respective systems. However, Koopmans' original paper makes no claim with regard to the significance of eigenvalues of the Fock operator other than that corresponding to the HOMO. Nevertheless, it is straightforward to generalize the original statement of Koopmans' to calculate the electron affinity in this sense.
Glossary of areas of mathematics L Glossary_of_areas_of_mathematics > L Extensions of the methods used belong to multilinear algebra. Linear functional analysis Linear programming a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. List of graphical methods Included are diagram techniques, chart techniques, plot techniques, and other forms of visualization.
Online relationship Effects on face-to-face interactions Online_relationship > Effects on face-to-face interactions In the past, postal services made communication possible without the necessity of physical presence, and the invention of the telephone allowed synchronous communication between people across long distances. The internet combined the advantages of both mail and telephone, unifying the speed of the telephone with the written character of the mail service. The evolution of communication within the Internet has arguably changed the nature of individuals' relationships with one another.Some see a major negative impact resulting in an increased use of internet communication is of its diversion of true community because online interaction via computers is often regarded as a more impersonal communication medium than face-to-face communication.
Certifying algorithm Examples Certifying_algorithm > Examples Many examples of problems with checkable algorithms come from graph theory. For instance, a classical algorithm for testing whether a graph is bipartite would simply output a Boolean value: true if the graph is bipartite, false otherwise. In contrast, a certifying algorithm might output a 2-coloring of the graph in the case that it is bipartite, or a cycle of odd length if it is not. Any graph is bipartite if and only if it can be 2-colored, and non-bipartite if and only if it contains an odd cycle.
Derivatives pricing Basics Embedded_derivative > Basics The market risk inherent in the underlying asset is attached to the financial derivative through contractual agreements and hence can be traded separately. The underlying asset does not have to be acquired. Derivatives therefore allow the breakup of ownership and participation in the market value of an asset.
Glossary of computer science S Glossary_of_computer_science > 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. sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order does matter. Like a set, it contains members (also called elements, or terms).
Human reproductive system Production of gametes Human_genitals > Reproduction > Production of gametes Since the scrotum, where the testes is present, is situated outside the body cavity, it provides a temperature about 3 °C below normal body temperature. In females, gametogenesis is known as oogenesis; this occurs in the ovarian follicles of the ovaries. This process does not produce mature ovum until puberty.
Forest dieback Climate change Forest_dieback > Consequences of forest dieback > Climate change Changes in mean annual temperature and drought are major contributing factors to forest dieback. As more carbon is released from dead trees, especially in the Amazon and Boreal forests, more greenhouse gases are released into the atmosphere. Increased levels of greenhouse gases increase the temperature of the atmosphere. Projections for dieback vary, but the threat of global climate change only stands to increase the rate of dieback.
RNA virus Replication RNA_virus > Replication Animal RNA viruses are classified by the ICTV. There are three distinct groups of RNA viruses depending on their genome and mode of replication: Double-stranded RNA viruses (Group III) contain from one to a dozen different RNA molecules, each coding for one or more viral proteins. Positive-sense ssRNA viruses (Group IV) have their genome directly utilized as mRNA, with host ribosomes translating it into a single protein that is modified by host and viral proteins to form the various proteins needed for replication. One of these includes RNA-dependent RNA polymerase (RNA replicase), which copies the viral RNA to form a double-stranded replicative form.
Fibonacci Numbers Combinatorial proofs Fibonacci_series > Combinatorial identities > Combinatorial proofs . , 1 } } {\displaystyle \{\{1,1,...,1,2\}\},\{\{1,1,...,1\}\}} each with cardinality 1. Following the same logic as before, by summing the cardinality of each set we see that F n + 2 = F n + F n − 1 + .
Thermodynamic arrow Cosmology Entropy_as_an_arrow_of_time > Current research > Cosmology Some processes that involve high energy particles and are governed by the weak force (such as K-meson decay) defy the symmetry between time directions. However, all known physical processes do preserve a more complicated symmetry (CPT symmetry), and are therefore unrelated to the second law of thermodynamics, or to the day-to-day experience of the arrow of time. A notable exception is the wave function collapse in quantum mechanics, an irreversible process which is considered either real (by the Copenhagen interpretation) or apparent only (by the Many-worlds interpretation of quantum mechanics). In either case, the wave function collapse always follows quantum decoherence, a process which is understood to be a result of the Second Law of Thermodynamics.
Plasma osmolality Osmolar gap (OG) Plasma_osmolality > Osmolar gap (OG) The osmolar gap is the difference between the measured osmolality and the calculated osmolarity. The difference in units is attributed to the difference in the way that blood solutes are measured in the laboratory versus the way they are calculated. The laboratory value measures the freezing point depression, properly called osmolality while the calculated value is given in units of osmolarity. Even though these values are presented in different units, when there is a small amount of solute compared to total volume of solution, the absolute values of osmolality vs. osmolarity are very close.
Glossary of electrical and electronics engineering H Glossary_of_electrical_and_electronics_engineering > H H infinity An optimization strategy for certain classes of control problems. Hall effect sensor A device that detects and measures magnetic field by the Hall effect voltage induced in a current-carrying semiconductor. harmonic distortion An effect of a non-linear signal path that introduces frequencies that are integer multiples of an input frequency. harmonic oscillator An oscillator which produces sinusoidal output, such as a simple RLC oscillator.
Dihydrogen cation Born-Oppenheimer approximation Hydrogen_molecule-ion > Quantum mechanical analysis > Born-Oppenheimer approximation Once the energy function Etot(R) has been obtained, one can compute the quantum states of rotational and vibrational motion of the nuclei, and thus of the molecule as a whole. The corresponding ``nuclear´´ Schrödinger equation is a one-dimensional ordinary differential equation, where the nucleus-nucleus distance R is the independent coordinate. The equation describes the motion of a fictitious particle of mass equal to the reduced mass of the two nuclei, in the potential Etot(R)+VL(R), where the second term is the centrifugal potential due to rotation with angular momentum described by the quantum number L. The eigenenergies of this Schrödinger equation are the total energies of the whole molecule, electronic plus nuclear.
PCI Compliance Compliance versus validation of compliance PCI_DSS > Compliance versus validation of compliance Although the PCI DSS must be implemented by all entities which process, store or transmit cardholder data, formal validation of PCI DSS compliance is not mandatory for all entities. Visa and Mastercard require merchants and service providers to be validated according to the PCI DSS; Visa also offers a Technology Innovation Program (TIP), an alternative program which allows qualified merchants to discontinue the annual PCI DSS validation assessment. Merchants are eligible if they take alternative precautions against fraud, such as the use of EMV or point-to-point encryption.Issuing banks are not required to undergo PCI DSS validation, although they must secure sensitive data in a PCI DSS-compliant manner. Acquiring banks must comply with PCI DSS and have their compliance validated with an audit. In a security breach, any compromised entity which was not PCI DSS-compliant at the time of the breach may be subject to additional penalties (such as fines) from card brands or acquiring banks.
Masdar City The Catalyst Masdar_City > Commercial tenants and population > The Catalyst Masdar City partnered with oil giant BP to created The Catalyst, an investor that supports clean-tech start-ups. As of May 2023, The Catalyst supports eight start-ups. It aims to attract companies focusing on green technology, and they accept applications from local and international businesses and entrepreneurs.
Deep Learning History Deep_neural_network > History The principle of elevating "raw" features over hand-crafted optimization was first explored successfully in the architecture of deep autoencoder on the "raw" spectrogram or linear filter-bank features in the late 1990s, showing its superiority over the Mel-Cepstral features that contain stages of fixed transformation from spectrograms. The raw features of speech, waveforms, later produced excellent larger-scale results.Speech recognition was taken over by LSTM. In 2003, LSTM started to become competitive with traditional speech recognizers on certain tasks.
OMG IDL Benefits CORBA_IDL > Benefits CORBA's benefits include language- and OS-independence, freedom from technology-linked implementations, strong data-typing, high level of tunability, and freedom from the details of distributed data transfers. Language independence CORBA was designed to free engineers from limitations of coupling their designs to a particular software language. Currently there are many languages supported by various CORBA providers, the most popular being Java and C++. There are also C++11, C-only, Smalltalk, Perl, Ada, Ruby, and Python implementations, just to mention a few.OS-independence CORBA's design is meant to be OS-independent.
Inflammatory disorders Vasodilation and increased permeability Inflammatory_reaction > Vascular component > Vasodilation and increased permeability As defined, acute inflammation is an immunovascular response to inflammatory stimuli, which can include infection or trauma. This means acute inflammation can be broadly divided into a vascular phase that occurs first, followed by a cellular phase involving immune cells (more specifically myeloid granulocytes in the acute setting). The vascular component of acute inflammation involves the movement of plasma fluid, containing important proteins such as fibrin and immunoglobulins (antibodies), into inflamed tissue.
Chemistry of wetland dredging Redox reactions Chemistry_of_wetland_dredging > Wetland dredging chemistry > Redox reactions Common wetland redox reactions include: 2NO3− +10e− +12H+ → N2 +6H2O SO4 +8e− +9H+ → HS− +4H2O CO2 +8e− +8H+ → CH4 + 2H2O MnO2 +2e− +4H+ → Mn2+ + 2H2O Fe(OH)3 +e− +3H+ → Fe3+ + 3H2ODredging allows for an increased flow of water through wetlands, causing anaerobic soil conditions. This change in wetland type results in a change in redox state for each reaction undergone and thus changes the plant species available to grow in those areas. The redox potential (Eh) can help to show the relationship of the redox reactions through the Nernst equation: Eh=E0-(RT/nF)ln(a/bb) This equation allows for the calculation of the extent of reaction between two redox systems and can be used, for example, to decide whether a particular reaction will go to completion or not. An example of a change in these circumstances affecting the wetland system is in the transformation of pyrite (FeS2) through the reduction of SO42− (found in seawater). Fe(OH)3 + e− + H+ → Fe(OH)2 + H2O SO42− + 6e− + 8H+ → S + 4H2O S + 2e− + 2H+ → H2S Fe(OH)2 + H2S → FeS + 2H2O FeS + S → FeS2 (pyrite)The drainage of the resulted pyrite then results in oxidation to ferric hydroxide and sulfuric acid, causing extreme acidity (pH < 2).
Drowning Oxygen deprivation Drowning > Pathophysiology > Oxygen deprivation There can be central nervous system damage, cardiac arrhythmia, pulmonary injury, reperfusion injury, and multiple-organ secondary injury with prolonged tissue hypoxia.A lack of oxygen or chemical changes in the lungs may cause the heart to stop beating. This cardiac arrest stops the flow of blood and thus stops the transport of oxygen to the brain. Cardiac arrest used to be the traditional point of death, but at this point, there is still a chance of recovery.
Measurement (journal) Summary Measurement_(journal) Measurement is a peer-reviewed scientific journal covering all aspects of metrology. It was established in 1983 and is published 18 times per year. It is published by Elsevier on behalf of the International Measurement Confederation and the editor-in-chief is Paolo Carbone (University of Perugia). According to the Journal Citation Reports, the journal has a 2021 impact factor of 5.131.
Combinatorial biology Summary Combinatorial_biology In biotechnology, combinatorial biology is the creation of a large number of compounds (usually proteins or peptides) through technologies such as phage display. Similar to combinatorial chemistry, compounds are produced by biosynthesis rather than organic chemistry. This process was developed independently by Richard A. Houghten and H. Mario Geysen in the 1980s.
Theory of errors Inverse tangent function Theory_of_errors > Example calculations > Inverse tangent function We can calculate the uncertainty propagation for the inverse tangent function as an example of using partial derivatives to propagate error. Define where Δ x {\displaystyle \Delta _{x}} is the absolute uncertainty on our measurement of x. The derivative of f(x) with respect to x is Therefore, our propagated uncertainty is where Δ f {\displaystyle \Delta _{f}} is the absolute propagated uncertainty.
Interleukin 1 family IL-1 in disease and its clinical significance Interleukin_1 > IL-1 in disease and its clinical significance It has also been prescribed to patients with indolent or smoldering myeloma with a high risk of progression to multiple myeloma. In combination with other medication, IL-1Ra provides a significant increase in the number of years of progression-free disease in its recipients. The benefits of this treatment are the natural structure and no toxicity or gastrointestinal disturbances. == References ==
Point groups Four dimensions Rosette_groups > List of point groups > Four dimensions The four-dimensional point groups (chiral as well as achiral) are listed in Conway and Smith, Section 4, Tables 4.1-4.3. The following list gives the four-dimensional reflection groups (excluding those that leave a subspace fixed and that are therefore lower-dimensional reflection groups). Each group is specified as a Coxeter group, and like the polyhedral groups of 3D, it can be named by its related convex regular 4-polytope. Related pure rotational groups exist for each with half the order, and can be represented by the bracket Coxeter notation with a '+' exponent, for example + has three 3-fold gyration points and symmetry order 60. Front-back symmetric groups like and can be doubled, shown as double brackets in Coxeter's notation, for example ] with its order doubled to 240.
First mover advantage Endogeneity and exogeneity of first-mover opportunities Free-rider_effect > General conceptual issues > Endogeneity and exogeneity of first-mover opportunities An example of technical proficiency aiding first-mover advantage is Procter and Gamble's first disposable baby diaper. The ability to get ahead of the market through technical breakthroughs, the use of materials that were low in cost, as well as their general manufacturing proficiency and distribution channels, allowed P&G to dominate the disposable diaper industry. Luck can also have a large effect on profits in first-mover-advantage situations, specifically in terms of timing and creativity.
Gauge covariant derivative Overview Gauge_covariant_derivative > Overview This is because the fibers of the frame bundle must necessarily, by definition, connect the tangent and cotangent spaces of space-time. In contrast, the gauge groups employed in particle physics could in principle be any Lie group at all, although in practice the Standard Model only uses U(1), SU(2) and SU(3).
NOD mice Identifying IDDM susceptibility loci NOD_mice > Identifying IDDM susceptibility loci Genetic Loci associated with susceptibility to IDDM have been identified in the NOD mouse strain through the development of congenic mouse strains, which have identified several insulin dependent diabetes (Idd) loci. The most important is idd1 which is the major histocompatibility complex class II loci I-Ag7.NOD mice have polymorphisms in the Idd3 locus which are linked to IL-2 production. IL-2 promotes either immunity or tolerance in a concentration dependent fashion by acting on T helper cells, CTL and NK cells. Low amounts of IL-2 may be needed to promote survival of Treg in mice.
H-theorem Loschmidt's paradox H-theorem > Criticism and exceptions > Loschmidt's paradox Soon after Boltzmann published his H theorem, Johann Josef Loschmidt objected that it should not be possible to deduce an irreversible process from time-symmetric dynamics and a time-symmetric formalism. If the H decreases over time in one state, then there must be a matching reversed state where H increases over time (Loschmidt's paradox). The explanation is that Boltzmann's equation is based on the assumption of "molecular chaos", i.e., that it follows from, or at least is consistent with, the underlying kinetic model that the particles be considered independent and uncorrelated. It turns out that this assumption breaks time reversal symmetry in a subtle sense, and therefore begs the question.
Jet Engine Energy efficiency relating to aircraft jet engines Jet_Engine > General physical principles > Energy efficiency relating to aircraft jet engines This has improved constantly over time as new materials have been introduced to allow higher maximum cycle temperatures. For example, composite materials, combining metals with ceramics, have been developed for HP turbine blades, which run at the maximum cycle temperature. The efficiency is also limited by the overall pressure ratio that can be achieved.
Inverse filter In speech science Inverse_filter > In speech science If the input is from a microphone, and not a CV mask or its equivalent, the inverse filter also must have a pole at zero frequency (an integration operation) to account for the radiation characteristic that connects volume velocity with acoustic pressure. Inverse filtering the output of a CV mask retains the level of zero flow, while inverse filtering a microphone signal does not. Inverse filtering depends on the source-filter model and a vocal tract filter that is linear system, however, the source and filter need not be independent. == References ==
B-star search algorithm Extension to two-player games B* > Details > Extension to two-player games The B* algorithm applies to two-player deterministic zero-sum games. In fact, the only change is to interpret "best" with respect to the side moving in that node. So you would take the maximum if your side is moving, and the minimum if the opponent is moving. Equivalently, you can represent all intervals from the perspective of the side to move, and then negate the values during the back-up operation.
Agent-based social simulation Summary Agent-based_social_simulation Agent-based social simulation (or ABSS) consists of social simulations that are based on agent-based modeling, and implemented using artificial agent technologies. Agent-based social simulation is a scientific discipline concerned with simulation of social phenomena, using computer-based multiagent models. In these simulations, persons or group of persons are represented by agents. MABSS is a combination of social science, multiagent simulation and computer simulation.
Integral basis Group rings Free_abelian_group > Applications > Group rings The integral group ring Z {\displaystyle \mathbb {Z} } , for any group G {\displaystyle G} , is a ring whose additive group is the free abelian group over G {\displaystyle G} . When G {\displaystyle G} is finite and abelian, the multiplicative group of units in Z {\displaystyle \mathbb {Z} } has the structure of a direct product of a finite group and a finitely generated free abelian group. == References ==
Coumarin Toxicity Coumarin > Toxicity In Europe, popular examples of such beverages are Maiwein, white wine with woodruff, and Żubrówka, vodka flavoured with bison grass. Coumarin is subject to restrictions on its use in perfumery, as some people may become sensitized to it, however the evidence that coumarin can cause an allergic reaction in humans is disputed.Minor neurological dysfunction was found in children exposed to the anticoagulants acenocoumarol or phenprocoumon during pregnancy. A group of 306 children were tested at ages 7–15 years to determine subtle neurological effects from anticoagulant exposure.
Ouvrage Boussois Summary Ouvrage_Boussois Ouvrage Boussois is a petit ouvrage of the Maginot Line, built as part of the "New Fronts" program to address shortcomings in the Line's coverage of the border with Belgium. Like the other three ouvrages near Maubeuge, it is built on an old Séré de Rivières fortification, near the town of Boussois. The fortification surrendered to the Germans twice, in the First World War on 6 September 1914, and in the Second World War on 22 May 1940. The site is now abandoned.
Deuterium isotope effect Other examples Kinetic_isotope_effect > Case studies > Other examples For this reaction, isotopic substitution happens to produce an inverse kinetic isotope effect, and the authors report a kinetic isotope effect as low as 1.74 x 10−4, which is the smallest kinetic isotope effect ever reported.The kinetic isotope effect leads to a specific distribution of deuterium isotopes in natural products, depending on the route they were synthesized in nature. By NMR spectroscopy, it is therefore easy to detect whether the alcohol in wine was fermented from glucose, or from illicitly added saccharose.

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