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Geometric algebra Rotating systems Geometric_algebra > Examples and applications > Rotating systems The mathematical description of rotational forces such as torque and angular momentum often makes use of the cross product of vector calculus in three dimensions with a convention of orientation (handedness). The cross product can be viewed in terms of the exterior product allowing a more natural geometric interpretation of the cross product as a bivector using the dual relationship a × b = − I ( a ∧ b ) . {\displaystyle a\times b=-I(a\wedge b).} For example, torque is generally defined as the magnitude of the perpendicular force component times distance, or work per unit angle.
ShakeAlert Detection methods ShakeAlert > Detection methods The second algorithm was the τ c {\displaystyle \tau _{c}} - P d {\displaystyle P_{d}} OnSite algorithm. By using displacement amplitude P d {\displaystyle P_{d}} and period τ c {\displaystyle \tau _{c}} of the first signs of shaking, the OnSite algorithm more accurately predicted the intensity and size of the earthquake than ElarmS did. The tradeoff of using these algorithms for the earliest detection possible meant having a less reliable approach than regional warning algorithms, however some argued that the added seconds to prepare are more important than reliability.
Language pedagogy Approach, method and technique Language_pedagogy > Approach, method and technique In 1963, the University of Michigan Linguistics Professor Edward Mason Anthony Jr. formulated a framework to describe various language teaching methods, which consisted of three levels: approach, method, and technique. According to Anthony, "The arrangement is hierarchical. The organizational key is that techniques carry out a method which is consistent with an approach."
Integral Molten Salt Reactor Efficiency Integral_Molten_Salt_Reactor > Economics > Efficiency Conventional nuclear reactors, such as pressurized and boiling water reactors, use water as a coolant. Due to water's high vapor pressure at elevated temperatures, they are limited to operating at a relatively low temperature, usually near 300 °C. This limits the thermodynamic efficiency, typically to around 32-34%. In other words, water-cooled power reactors generate 32-34 watts of electricity for every 100 watts of reactor power.
Approximate Bayesian Computation Indispensable quality controls Approximate_Bayesian_Computation > Pitfalls and remedies > Indispensable quality controls Fundamentally novel approaches for model choice that incorporate quality control as an integral step in the process have recently been proposed. ABC allows, by construction, estimation of the discrepancies between the observed data and the model predictions, with respect to a comprehensive set of statistics. These statistics are not necessarily the same as those used in the acceptance criterion.
Nucleosynthesis Empirical evidence Nucleosynthesis > Empirical evidence Theories of nucleosynthesis are tested by calculating isotope abundances and comparing those results with observed abundances. Isotope abundances are typically calculated from the transition rates between isotopes in a network. Often these calculations can be simplified as a few key reactions control the rate of other reactions.
Raw water Reverse osmosis Raw_water > Treatment > Reverse osmosis This efficiency has made reverse osmosis the primary method of water purification, often being used in combination with other methods, as a final treatment. A downside to reverse osmosis is that the removing of most minerals from water can have negative effects on its taste. Minerals are sometimes added to drinking water that was already filtered to improve its taste.
PL/I programming language Programmer issues PL/I_programming_language > Criticisms > Programmer issues Overlay three different types of variable on the same memory location? Anything you say! Write a recursive macro?
Epicentral distance Network measurement method Epicentral_distance > Correlation with epicenter > Network measurement method When the epicentral distance is calculated by at least three seismic stations, the location of the epicenter can be determined by trilateral measurement. This method of measuring epicenters through instruments, commonly known as microscopic epicenters, is called network measurement method. The specific method is done by drawing a circle on the map with the three stations as the center of the circle and the epicentral distance is calculated with the radius according to the corresponding proportion. Then, the intersection of each two circles is connected, and the intersection points of the three strings are the obtained epicenter. Then, the latitude and longitude are calculated (Geographic coordinate system).
Scientific question Summary Scientific_hypothesis A working hypothesis is a provisionally accepted hypothesis proposed for further research in a process beginning with an educated guess or thought.A different meaning of the term hypothesis is used in formal logic, to denote the antecedent of a proposition; thus in the proposition "If P, then Q", P denotes the hypothesis (or antecedent); Q can be called a consequent. P is the assumption in a (possibly counterfactual) What If question. The adjective hypothetical, meaning "having the nature of a hypothesis", or "being assumed to exist as an immediate consequence of a hypothesis", can refer to any of these meanings of the term "hypothesis".
Hydrogen isotope biogeochemistry Intact molecular isotope ratio mass spectrometry Hydrogen_isotope_biogeochemistry > Measurement techniques > Intact molecular isotope ratio mass spectrometry One of the first examples of this type of measurement has been the clumped isotopes of methane. (See section of "natural gas" in Fossil fuels) Another strength of this kind of instruments is the capability of doing site-specific isotopic ratio measurements. This technique is based on measuring D/H ratios of fragments from the ion source (e.g. CH3CH+2 of propane molecule) that samples hydrogen atoms from different parts of the molecule.In summary, direct molecular mass-spectrometry has been commonly used to measure laboratory spiked isotope tracers.
Granular layer (cerebellum) Microanatomy Cerebellar_cortex > Structure > Microanatomy Two types of neuron play dominant roles in the cerebellar circuit: Purkinje cells and granule cells. Three types of axons also play dominant roles: mossy fibers and climbing fibers (which enter the cerebellum from outside), and parallel fibers (which are the axons of granule cells). There are two main pathways through the cerebellar circuit, originating from mossy fibers and climbing fibers, both eventually terminating in the deep cerebellar nuclei.Mossy fibers project directly to the deep nuclei, but also give rise to the following pathway: mossy fibers → granule cells → parallel fibers → Purkinje cells → deep nuclei. Climbing fibers project to Purkinje cells and also send collaterals directly to the deep nuclei.
Gasoline consumption Unit conversions Fuel_mileage > Unit conversions US Gallons1 mpg ≈ 0.425 km/L 235.2/mpg ≈ L/100 km 1 mpg ≈ 1.201 mpg (imp)Imperial gallons1 mpg ≈ 0.354 km/L 282/mpg ≈ L/100 km 1 mpg ≈ 0.833 mpg (US)
Matter wave clock Applications Matter_wave_clock > Matter waves as clocks > Applications In his paper, "Quantum mechanics, matter waves and moving clocks", Müller has suggested that "The description of matter waves as matter-wave clocks ... has recently been applied to tests of general relativity, matter-wave experiments, the foundations of quantum mechanics, quantum space-time decoherence, the matter wave clock/mass standard, and led to a discussion on the role of the proper time in quantum mechanics. It is generally covariant and thus well-suited for use in curved space-time, e.g., gravitational waves."
Architectural element Structural elements Outline_of_architecture > Building construction > Structural elements Doorway – opening in a wall, typically rectangular, providing means of access, usually with a gate or door to provide security and weather protection. Facade – an exterior face of a building, especially the front. Floor – typically a horizontal surface that is walked upon, to support the expected loads of the building.
ER stress Summary ER_stress If these objectives are not achieved within a certain time span or the disruption is prolonged, the UPR aims towards apoptosis. Sustained overactivation of the UPR has been implicated in prion diseases as well as several other neurodegenerative diseases, and inhibiting the UPR could become a treatment for those diseases. Diseases amenable to UPR inhibition include Creutzfeldt–Jakob disease, Alzheimer's disease, Parkinson's disease, and Huntington's disease.
Health risk History Health_risk > History In 1979, when personal desktop computers became readily available, he packaged all 12 assessments together on a floppy disk and marketed it as a comprehensive health risk assessment. It wasn't until 1980, when the Centers for Disease Control and Prevention released a publicly available version, that the HRA became widely used, particularly in workplace settings.Health and Welfare Canada reviewed How to Practice Prospective Medicine and created a mainframe version of the book. The Centers for Disease Control became aware of this product and adapted it to the newly available personal computer.
Paxos (computer science) Production use of Paxos Paxos_(computer_science) > Production use of Paxos Google uses the Paxos algorithm in their Chubby distributed lock service in order to keep replicas consistent in case of failure. Chubby is used by Bigtable which is now in production in Google Analytics and other products. Google Spanner and Megastore use the Paxos algorithm internally. The OpenReplica replication service uses Paxos to maintain replicas for an open access system that enables users to create fault-tolerant objects.
Acute psychotic episode Hallucinations Psychotic_episode > Signs and symptoms > Hallucinations People who experience auditory hallucinations can frequently identify the loudness, location of origin, and may settle on identities for voices. Western cultures are associated with auditory experiences concerning religious content, frequently related to sin. Hallucinations may command a person to do something potentially dangerous when combined with delusions.So-called "minor hallucinations", such as extracampine hallucinations, or false perceptions of people or movement occurring outside of one's visual field, frequently occur in neurocognitive disorders, such as Parkinson's disease.Visual hallucinations occur in roughly a third of people with schizophrenia, although rates as high as 55% are reported.
Sigma Piscium Summary Sigma_Piscium It has an orbital period of 81 days, and the orbit is relatively eccentric, at about 0.9. Both components are B-type main-sequence stars.Sigma Piscium is moving through the Milky Way at a speed of 23.5 km/s relative to the Sun. Its projected galactic orbit carries it between 24,300 and 29,400 light years from the center of the galaxy.Sigma Piscium was a latter designation of 40 Andromedae.
Finite population correction Estimate Standard_error_of_estimation > Standard error of the sample mean > Estimate The standard deviation σ {\displaystyle \sigma } of the population being sampled is seldom known. Therefore, the standard error of the mean is usually estimated by replacing σ {\displaystyle \sigma } with the sample standard deviation σ x {\displaystyle \sigma _{x}} instead: As this is only an estimator for the true "standard error", it is common to see other notations here such as: A common source of confusion occurs when failing to distinguish clearly between: the standard deviation of the population ( σ {\displaystyle \sigma } ), the standard deviation of the sample ( σ x {\displaystyle \sigma _{x}} ), the standard deviation of the mean itself ( σ x ¯ {\displaystyle \sigma _{\bar {x}}} , which is the standard error), and the estimator of the standard deviation of the mean ( σ ^ x ¯ {\displaystyle {\widehat {\sigma }}_{\bar {x}}} , which is the most often calculated quantity, and is also often colloquially called the standard error).
Analog automata Variant definitions of automata Theory_of_automata > Variant definitions of automata Queue memory: An automaton may have memory in the form of a queue. Such a machine is called queue machine and is Turing-complete. Tape memory: The inputs and outputs of automata are often described as input and output tapes.
Diamond buffer High output current derivatives Diamond_buffer > High output current derivatives When the latter switches off, one of the added transistor provides the required base current to the output stage. The idea was used, for example, in the 1987 Burr-Brown OPA633 fast buffer IC.
Complex geometry Idea Complex_geometry > Idea Broadly, complex geometry is concerned with spaces and geometric objects which are modelled, in some sense, on the complex plane. Features of the complex plane and complex analysis of a single variable, such as an intrinsic notion of orientability (that is, being able to consistently rotate 90 degrees counterclockwise at every point in the complex plane), and the rigidity of holomorphic functions (that is, the existence of a single complex derivative implies complex differentiability to all orders) are seen to manifest in all forms of the study of complex geometry. As an example, every complex manifold is canonically orientable, and a form of Liouville's theorem holds on compact complex manifolds or projective complex algebraic varieties. Complex geometry is different in flavour to what might be called real geometry, the study of spaces based around the geometric and analytical properties of the real number line.
Table of elements The order of subshell filling Periodic_Table > Atomic structures of the elements > Electron configurations > The order of subshell filling The sixth row of the table likewise starts with two s-block elements: caesium and barium. After this, the first f-block elements (coloured green below) begin to appear, starting with lanthanum. These are sometimes termed inner transition elements.
Amoebic liver abscess Research Amoebic_liver_abscess > Research Due to the difficulty of exploring host and amebic factors involved in the pathogenesis of amebic liver abscess in humans, most studies have been conducted with animal models (e.g., mice, gerbils, and hamsters). Histopathological findings revealed that the chronic phase of amebic liver abscess in humans corresponds to lytic or liquefactive necrosis, whereas in rodent models there is granulomatous inflammation. However, the use of animal models has provided important information on molecules and mechanisms of the host/parasite interaction in amebic liver abscess.
Pseudoneurotic schizophrenia Signs and symptoms Pseudoneurotic_schizophrenia > Signs and symptoms The diagnosis of pseudoneurotic schizophrenia can be made with clinical observation and by various psychiatrical exams by a mental health professional and by the patient's explanation of his or her experiences. A patient must identify with at least two of these symptoms in order to be distinguished as a pseudoneurotic schizophrenic. The intensity of a symptom may vary with the individual patient's severity of the disorder. The symptoms are organized into disorders of thinking and association, disorders of emotional regulation, disorders of sensorimotor and autonomic functioning, pan-anxiety, pan-neurosis, and pansexuality. The two symptoms can fall under any of these categories.
Convergence in distribution Definition Convergence_in_quadratic_mean > Convergence in probability > Definition A sequence {Xn} of random variables converges in probability towards the random variable X if for all ε > 0 lim n → ∞ P ( \| X n − X \| > ε ) = 0. {\displaystyle \lim _{n\to \infty }\mathbb {P} {\big (}\|X_{n}-X\|>\varepsilon {\big )}=0.} More explicitly, let Pn(ε) be the probability that Xn is outside the ball of radius ε centered at X. Then Xn is said to converge in probability to X if for any ε > 0 and any δ > 0 there exists a number N (which may depend on ε and δ) such that for all n ≥ N, Pn(ε) < δ (the definition of limit). Notice that for the condition to be satisfied, it is not possible that for each n the random variables X and Xn are independent (and thus convergence in probability is a condition on the joint cdf's, as opposed to convergence in distribution, which is a condition on the individual cdf's), unless X is deterministic like for the weak law of large numbers.
Architectural design optimization Model-based optimisation Architectural_design_optimization > Methods of ADO > Model-based optimisation The efficacy of the surrogate model is determined by the accuracy of the mathematical model. For this reason, some of the time-saving features of model-based optimisation could be invalidated by any additional time spent improving the mathematical functions which regulate the surrogate model. Model based optimisation is advantageous as it enables architects to visually articulate design problems and solutions in real time within design interfaces such as Grasshopper, Rhinoceros 3D, Dynamo BIM and GenerativeComponents.
Oral ecology Abiotic Oral_ecology > Oral environment > Abiotic At the microscopic scale, oxygen concentration can dictate where in the mouth aerobic, anaerobic, facultative anaerobic, aerotolerant, or microaerophilic microbes grow or form biofilm. Biofilms themselves can help regulate oxygen exposure and keep anaerobic organisms at the interior, adding to the complexity of the niches within the oral cavity. Another abiotic environmental influence on oral ecology includes the use of drugs, especially antibiotics and orally-administered antibiotics.
Fatigue of welded joints Summary Fatigue_of_welded_joints Under cyclic loading these defects can grow a fatigue crack, causing the assembly to fail even if these cyclic stresses are low and smaller than the base material and weld filler material yield stress. Hence, the fatigue strength of a welded joint does not correlate to the fatigue strength of the base material. Incorporating design considerations in the development phase can reduce failures due to fatigue in welded joints.
Small intestine cancer Summary Small_intestine_cancer (American Cancer Society, 2023) Small intestine cancer can be subdivided into duodenal cancer (the first part of the small intestine) and cancer of the jejunum and ileum (the latter two parts of the small intestine). Duodenal cancer has more in common with stomach cancer, while cancer of the jejunum and ileum have more in common with colorectal cancer. Five-year survival rates are 65%.Experts believe that small intestine cancer develops much like colorectal cancer.
Highway network Model Highway_network > Model The model has two gates in addition to the H(WH, x) gate: the transform gate T(WT, x) and the carry gate C(WC, x). Those two last gates are non-linear transfer functions (by convention Sigmoid function). The H(WH, x) function can be any desired transfer function. The carry gate is defined as C(WC, x) = 1 - T(WT, x). While the transform gate is just a gate with a sigmoid transfer function.
Axiom of limitation of size History Axiom_of_limitation_of_size > History That this condition really gets at the essence of things is seen from the fact that it implies the axiom of choice, which formerly stood quite apart from other existential principles. The inferences, bordering on the paradoxes, which are made possible by this way of looking at things, seem to me, not only very elegant, but also very interesting from the logical point of view. Moreover I believe that only by going farther in this direction, i.e., in the direction opposite to constructivism, will the basic problems of abstract set theory be solved."
Adipogenesis Summary Adipogenesis Adipogenesis is the formation of adipocytes (fat cells) from stem cells. It involves 2 phases, determination, and terminal differentiation. Determination is mesenchymal stem cells committing to the adipocyte precursor cells, also known as preadipocytes which lose the potential to differentiate to other types of cells such as chondrocytes, myocytes, and osteoblasts. Terminal differentiation is that preadipocytes differentiate into mature adipocytes. Adipocytes can arise either from preadipocytes resident in adipose tissue, or from bone-marrow derived progenitor cells that migrate to adipose tissue.
Primordial germ cell Oogenesis Germ_cell > Oogenesis These intensive RNA biosynthese are mirrored in the structure of the chromosomes, which decondense and form lateral loops giving them a lampbrush appearance (see Lampbrush chromosome). Oocyte maturation is the following phase of oocyte development. It occurs at sexual maturity when hormones stimulate the oocyte to complete meiotic division I. The meiotic division I produces 2 cells differing in size: a small polar body and a large secondary oocyte.
Interstellar space travel Time dilation Interstellar_Travel > Proposed methods > Fast, crewed missions > Time dilation Physicists generally believe faster-than-light travel is impossible. Relativistic time dilation allows a traveler to experience time more slowly, the closer their speed is to the speed of light. This apparent slowing becomes noticeable when velocities above 80% of the speed of light are attained. Clocks aboard an interstellar ship would run slower than Earth clocks, so if a ship's engines were capable of continuously generating around 1 g of acceleration (which is comfortable for humans), the ship could reach almost anywhere in the galaxy and return to Earth within 40 years ship-time (see diagram).
Energy of activation Temperature dependence and the relation to the Arrhenius equation Activation_enthalpy > Temperature dependence and the relation to the Arrhenius equation There are two objections to associating this activation energy with the threshold barrier for an elementary reaction. First, it is often unclear as to whether or not reaction does proceed in one step; threshold barriers that are averaged out over all elementary steps have little theoretical value. Second, even if the reaction being studied is elementary, a spectrum of individual collisions contributes to rate constants obtained from bulk ('bulb') experiments involving billions of molecules, with many different reactant collision geometries and angles, different translational and (possibly) vibrational energies—all of which may lead to different microscopic reaction rates.
Public-key infrastructure Capabilities Public-key_infrastructure > Capabilities Integrity: Assurance that if an entity changed (tampered) with transmitted data in the slightest way, it would be obvious it happened as its integrity would have been compromised. Often it is not of utmost importance to prevent the integrity being compromised (tamper proof), however, it is of utmost importance that if integrity is compromised there is clear evidence of it having done so (tamper evident). Authenticity: Assurance that every entity has certainty of what it is connecting to, or can evidence its legitimacy when connecting to a protected service. The former is termed server-side authentication - typically used when authenticating to a web server using a password. The latter is termed client-side authentication - sometimes used when authenticating using a smart card (hosting a digital certificate and private key).
Peetre theorem Proof Peetre_theorem > The original Peetre theorem > Proof Rescale s by a factor of 2C/g. Then if g is non-zero, by the linearity of D, \|Ds(y)\|=2C>C, which is impossible by Lemma 1. This proves the theorem in the punctured neighborhood V\{x}.Now, we must continue the differential operator to the central point x in the punctured neighborhood.
Psychoneuroimmunology Connections between glucocorticoids and immune system Psychoneuroimmunology > Psychoneuroimmunological effects > Connections between glucocorticoids and immune system Anti-inflammatory hormones that enhance the organism's response to a stressor. Prevent the overreaction of the body's own defense system. Overactivation of glucocorticoid receptors can lead to health risks. Regulators of the immune system.
Implosion-type nuclear weapon Summary Fusion_weapon The first stage is normally a boosted fission weapon as above (except for the earliest thermonuclear weapons, which used a pure fission weapon instead). Its detonation causes it to shine intensely with x-radiation, which illuminates and implodes the second stage filled with a large quantity of fusion fuel. This sets in motion a sequence of events which results in a thermonuclear, or fusion, burn.
Respiratory distress Differential diagnosis Breathing_difficulties > Differential diagnosis On a pathophysiological basis the causes can be divided into: (1) an increased awareness of normal breathing such as during an anxiety attack, (2) an increase in the work of breathing and (3) an abnormality in the ventilatory or respiratory system.The tempo of onset and the duration of dyspnea are useful in knowing the etiology of dyspnea. Acute shortness of breath is usually connected with sudden physiological changes, such as laryngeal edema, bronchospasm, myocardial infarction, pulmonary embolism, or pneumothorax. Patients with COPD and idiopathic pulmonary fibrosis (IPF) have a mild onset and gradual progression of dyspnea on exertion, punctuated by acute exacerbations of shortness of breath. In contrast, most asthmatics do not have daily symptoms, but have intermittent episodes of dyspnea, cough, and chest tightness that are usually associated with specific triggers, such as an upper respiratory tract infection or exposure to allergens.
Principles of Optics Original editions Principles_of_Optics > Publication history > Original editions Principles of optics; electromagnetic theory of propagation, interference and diffraction of light (3rd rev. ed.). Oxford; London; Edinburgh: Pergamon Press.
Open Data-Link Interface Summary Open_Data-Link_Interface The Open Data-Link Interface (ODI), developed by Apple and Novell, serves the same function as Microsoft and 3COM's Network Driver Interface Specification (NDIS). Originally, ODI was written for NetWare and Macintosh environments. Like NDIS, ODI provides rules that establish a vendor-neutral interface between the protocol stack and the adapter driver. It resides in Layer 2, the Data Link layer, of the OSI model. This interface also enables one or more network drivers to support one or more protocol stacks.
Inverse filtering Continuous-time frequency analysis Minimum_phase > Frequency analysis > Continuous-time frequency analysis Analysis for the continuous-time case proceeds in a similar manner except that we use the Laplace transform for frequency analysis. The time-domain equation is the following. where δ ( t ) {\displaystyle \delta (t)} is the Dirac delta function. The Dirac delta function is the identity operator in the continuous-time case because of the sifting property with any signal x(t).
Reprogramming Summary Reprogramming After the blastocyst is formed, methylation can begin, and with formation of the epiblast a wave of methylation then takes place until the implantation stage of the embryo. Another period of rapid and almost complete demethylation occurs during gametogenesis within the primordial germ cells (PGCs). Other than the PGCs, in the post-implantation stage, methylation patterns in somatic cells are stage- and tissue-specific with changes that presumably define each individual cell type and last stably over a long time.
Filter bag Unit collectors Dust_collector > Electrostatic precipitators (ESP) > Unit collectors Unlike central collectors, unit collectors control contamination at its source. They are small and self-contained, consisting of a fan and some form of dust collector. They are suitable for isolated, portable, or frequently moved dust-producing operations, such as bins and silos or remote belt-conveyor transfer points. Advantages of unit collectors include small space requirements, the return of collected dust to main material flow, and low initial cost.
Game mechanic Game mechanics vs. gameplay Game_mechanics > Game mechanics vs. gameplay In a graphic adventure game, the basic gameplay is usually to solve puzzles related to the context. The basic gameplay of poker is to produce certain numerical or categorical combinations. Golf's basic gameplay is to hit a ball and reach a designated spot.
Abjadi order Uses of the Abjad system Abjadi_order > Uses of the Abjad system ", and "C." (or, rarer, Roman numerals: I, II, III, IV), in Arabic, thus "أ", then "ب", then "ج", not the first three letters of the modern hijāʼī order. The abjad numbers are also used to assign numerical values to Arabic words for purposes of numerology. The common Islamic phrase بسم الله الرحمن الرحيم bismillāh al-Raḥmān al-Raḥīm ('In the name of Allah, the most merciful, the most compassionate' – see Basmala) has a numeric value of 786 (from a letter-by-letter cumulative value of 2+60+40+1+30+30+5+1+30+200+8+40+50+1+30+200+8+10+40). The name Allāh الله by itself has the value 66 (1+30+30+5).
Diffraction topography Literature Diffraction_topography > Literature Journal of Applied Physics. AIP Publishing. 29 (3): 597–598.
National Ambient Air Quality Objectives Summary National_Ambient_Air_Quality_Objectives In 1992, a review of the NAAQOs suggested that many air pollutants had no effect thresholds (e.g. tropospheric ozone or very low effect thresholds). As such, scientifically defensible effect levels could not be identified. In 2000, the revised NAAQOs framework specifies a Reference Level, above which there are demonstrated effects on human health and/or the environment, and an Air Quality Objective (AQO), which is meant to be protective for the general public and environment and which also considers aspects of technical feasibility.
Euclid's postulates 18th century Planar_geometry > Later history > 18th century For example, the problem of trisecting an angle with a compass and straightedge is one that naturally occurs within the theory, since the axioms refer to constructive operations that can be carried out with those tools. However, centuries of efforts failed to find a solution to this problem, until Pierre Wantzel published a proof in 1837 that such a construction was impossible. Other constructions that were proved impossible include doubling the cube and squaring the circle. In the case of doubling the cube, the impossibility of the construction originates from the fact that the compass and straightedge method involve equations whose order is an integral power of two, while doubling a cube requires the solution of a third-order equation. Euler discussed a generalization of Euclidean geometry called affine geometry, which retains the fifth postulate unmodified while weakening postulates three and four in a way that eliminates the notions of angle (whence right triangles become meaningless) and of equality of length of line segments in general (whence circles become meaningless) while retaining the notions of parallelism as an equivalence relation between lines, and equality of length of parallel line segments (so line segments continue to have a midpoint).
Use of force Use of force continuum Use_of_force > Use of force continuum The use of force may be standardized by a Use of Force Continuum, which presents guidelines as to the degree of force appropriate in a given situation. One source identifies five very generalized steps, increasing from least use of force to greatest. This kind of continuum generally has many levels, and officers are instructed to respond with a level of force appropriate to the situation at hand, acknowledging that the officer may move from one part of the continuum to another in a matter of seconds.
Glossary of artificial intelligence M Glossary_of_artificial_intelligence > M A general field of study of algorithms and systems for audio understanding by machine. machine perception The capability of a computer system to interpret data in a manner that is similar to the way humans use their senses to relate to the world around them. mechanism design A field in economics and game theory that takes an engineering approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally.
War of the currents Summary War_of_the_currents Brown also claimed that alternating current was more dangerous than direct current and tried to prove this by publicly killing animals with both currents, with technical assistance from Edison Electric. The Edison company and Brown colluded further in their parallel goals to limit the use of AC with attempts to push through legislation to severely limit AC installations and voltages. Both also colluded with Westinghouse's chief AC rival, the Thomson-Houston Electric Company, to make sure the first electric chair was powered by a Westinghouse AC generator.
Cognitive dissonance COVID-19 Cognitive_dissonance > Applications > COVID-19 The COVID-19 pandemic, an extreme public health crisis, cases rose to the hundred million and deaths at nearly four million worldwide. Reputable health organizations such as Lyu and Wehby studied the effects of wearing a face mask on the spread of COVID-19. They found evidence that suggests that COVID patients were reduced by 2%, averting nearly 200,000 cases by the end of the following month. Despite this fact having been proven and encouraged by major health organizations, there was still a resistance to wearing the mask and keeping a safe distance away from others.
Approximate Bayesian Computation Choice and sufficiency of summary statistics Approximate_Bayesian_Computation > Pitfalls and remedies > Choice and sufficiency of summary statistics Instead, the partial least squares regression approach uses information from all the candidate statistics, each being weighted appropriately. Recently, a method for constructing summaries in a semi-automatic manner has attained a considerable interest. This method is based on the observation that the optimal choice of summary statistics, when minimizing the quadratic loss of the parameter point estimates, can be obtained through the posterior mean of the parameters, which is approximated by performing a linear regression based on the simulated data.
Strain crystallization Effects of strain crystallization Strain_crystallization > Effects of strain crystallization The mechanical properties of materials are greatly affected by the orientation of the crystals in their micro-structure. The process of strain crystallization directly affects the micro-structure of the material by adding crystalline structures. Strain crystallization's effect on the micro-structure greatly increases the strength of the polymer or elastomer it is induced in. This effect of strain crystallization can be viewed in vulcanized natural rubber, a material that is known for its toughness and tensile stress.
Kepler-4 Nomenclature and history Kepler-4 > Nomenclature and history Kepler-4 is named for the Kepler spacecraft, a NASA telescope tasked with finding Earth-like planets that transit their stars as seen from Earth. As the previous three planets that Kepler confirmed had already been confirmed by others, Kepler-4 and its planet were the first to be discovered by the Kepler team. The star and its system were announced in Washington, D.C. at the 215th meeting of the American Astronomical Society on January 4, 2010, along with Kepler-5, Kepler-6, Kepler-7, and Kepler-8.
PKCS 7 Summary PKCS_7 In cryptography, "PKCS #7: Cryptographic Message Syntax" (a.k.a. "CMS") is a standard syntax for storing signed and/or encrypted data. PKCS #7 is one of the family of standards called Public-Key Cryptography Standards (PKCS) created by RSA Laboratories.
Linear partial differential equation Linear equations of second order Analytical_solutions_of_partial_differential_equations > Classification > Linear equations of second order Elliptic: the eigenvalues are all positive or all negative. Parabolic: the eigenvalues are all positive or all negative, except one that is zero. Hyperbolic: there is only one negative eigenvalue and all the rest are positive, or there is only one positive eigenvalue and all the rest are negative. Ultrahyperbolic: there is more than one positive eigenvalue and more than one negative eigenvalue, and there are no zero eigenvalues.The theory of elliptic, parabolic, and hyperbolic equations have been studied for centuries, largely centered around or based upon the standard examples of the Laplace equation, the heat equation, and the wave equation.
DE-9 connector Description, nomenclature, and variants DE-9_connector > Description, nomenclature, and variants A D-sub contains two or more parallel rows of pins or sockets usually surrounded by a D-shaped metal shield that provides mechanical support, ensures correct orientation, and may screen against electromagnetic interference. D-sub connectors have gender: parts with pin contacts are called male connectors or plugs, while those with socket contacts are called female connectors or sockets. The socket's shield fits tightly inside the plug's shield. Panel-mounted connectors usually have #4-40 UNC (as designated with the Unified Thread Standard) jackscrews that accept screws on the cable end connector cover that are used for locking the connectors together and offering mechanical strain relief, and can be tightened with a 3/16" (or 5mm) hex socket.
Lichen sclerosus Main treatment Lichen_sclerosus > Treatment > Main treatment In a prospective longitudinal cohort study of 507 women throughout 6 years, cancer occurred for 4.7% of patients who were only "partially compliant" with corticosteroid treatment, while it occurred in 0% of cases where they were "fully compliant". In a second study, of 129 patients, cancer occurred in 11% of patients, none of which were fully compliant with corticosteroid treatment. Both these studies however also said that a corticosteroid as powerful as clobetasol is not necessary in most cases.
Chow–Liu tree Variations on Chow–Liu trees Chow–Liu_tree > Variations on Chow–Liu trees The obvious problem which occurs when the actual distribution is not in fact a second-order dependency tree can still in some cases be addressed by fusing or aggregating together densely connected subsets of variables to obtain a "large-node" Chow–Liu tree (Huang, King & Lyu 2002), or by extending the idea of greedy maximum branch weight selection to non-tree (multiple parent) structures (Williamson 2000). (Similar techniques of variable substitution and construction are common in the Bayes network literature, e.g., for dealing with loops. See Pearl (1988).) Generalizations of the Chow–Liu tree are the so-called t-cherry junction trees.
Schrödinger representation Historical overview Weyl_calculus > Historical overview The mathematical formulation of quantum mechanics by Werner Heisenberg and Erwin Schrödinger was originally in terms of unbounded self-adjoint operators on a Hilbert space. The fundamental operators corresponding to position and momentum satisfy the Heisenberg commutation relations. Quadratic polynomials in these operators, which include the harmonic oscillator, are also closed under taking commutators.
Bayesian vector autoregression Summary Bayesian_vector_autoregression In statistics and econometrics, Bayesian vector autoregression (BVAR) uses Bayesian methods to estimate a vector autoregression (VAR) model. BVAR differs with standard VAR models in that the model parameters are treated as random variables, with prior probabilities, rather than fixed values. Vector autoregressions are flexible statistical models that typically include many free parameters. Given the limited length of standard macroeconomic datasets relative to the vast number of parameters available, Bayesian methods have become an increasingly popular way of dealing with the problem of over-parameterization.
Thunderclap headache Summary Thunderclap_headache A thunderclap headache is a headache that is severe and has a sudden onset. It is defined as a severe headache that takes seconds to minutes to reach maximum intensity. Although approximately 75% are attributed to "primary" headaches—headache disorder, non-specific headache, idiopathic thunderclap headache, or uncertain headache disorder—the remainder are secondary to other causes, which can include some extremely dangerous acute conditions, as well as infections and other conditions. Usually, further investigations are performed to identify the underlying cause.
Hybrid algorithm Examples Hybrid_algorithm > Examples Another example of hybrid algorithms for performance reasons are introsort and introselect, which combine one algorithm for fast average performance, falling back on another algorithm to ensure (asymptotically) optimal worst-case performance. Introsort begins with a quicksort, but switches to a heap sort if quicksort is not progressing well; analogously introselect begins with quickselect, but switches to median of medians if quickselect is not progressing well. Centralized distributed algorithms can often be considered as hybrid algorithms, consisting of an individual algorithm (run on each distributed processor), and a combining algorithm (run on a centralized distributor) – these correspond respectively to running the entire algorithm on one processor, or running the entire computation on the distributor, combining trivial results (a one-element data set from each processor).
Cognitive model Associative memory Cognitive_model > Dynamical systems > Early dynamical systems > Associative memory By letting the network learn on its own, structure and computational properties naturally arise. Unlike previous models, “memories” can be formed and recalled by inputting a small portion of the entire memory. Time ordering of memories can also be encoded. The behavior of the system is modeled with vectors which can change values, representing different states of the system. This early model was a major step toward a dynamical systems view of human cognition, though many details had yet to be added and more phenomena accounted for.
DeepDream Process DeepDream > Process As internal variations are modified in deep neural networks the output image reflect these changes. This specific manipulation demonstrates how inner brain mechanisms are analogous to internal layers of neural networks. Internal noise level modifications represent how hallucinogens omit external sensory information leading internal preconceived conceptions to strongly influence visual perception.
Recursive data type Example Recursive_data_type > Example An example is the list type, in Haskell: This indicates that a list of a's is either an empty list or a cons cell containing an 'a' (the "head" of the list) and another list (the "tail"). Another example is a similar singly linked type in Java: This indicates that non-empty list of type E contains a data member of type E, and a reference to another List object for the rest of the list (or a null reference to indicate that this is the end of the list).
Watching-eye effect Summary Watching-eye_effect The watching-eye effect says that people behave more altruistically and exhibit less antisocial behavior in the presence of images that depict eyes, because these images insinuate that they are being watched. Eyes are strong signals of perception for humans. They signify that our actions are being seen and paid attention to even through mere depictions of eyes.It has been demonstrated that these effects are so pronounced that even depictions of eyes are enough to trigger them.
Small nucleolar RNA Z248 Summary Small_nucleolar_RNA_Z248 In molecular biology, Z248 is a member of the C/D class of snoRNA which contain the C (UGAUGA) and D (CUGA) box motifs. Most of the members of the box C/D family function in directing site-specific 2'-O-methylation of substrate RNAs.
Outline of category theory Summary Outline_of_category_theory The following outline is provided as an overview of and guide to category theory, the area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows (also called morphisms, although this term also has a specific, non category-theoretical sense), where these collections satisfy certain basic conditions. Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories.
Cache stampede Probabilistic early expiration Cache_stampede > Cache stampede mitigation > Probabilistic early expiration function x-fetch(key, ttl, beta=1) { value, delta, expiry ← cache_read(key) if (!value \|\| (time() - delta * beta * log(rand(0,1))) ≥ expiry) { start ← time() value ← recompute_value() delta ← time() – start cache_write(key, (value, delta), ttl) } return value } The parameter beta can be set to a value greater than 1 to favor earlier recomputations and further reduce stampedes but the authors show that setting beta=1 works well in practice. The variable delta represents the time to recompute the value and is used to scale the probability distribution appropriately. This approach is simple to implement and effectively reduces cache stampedes by automatically favoring early recomputations when the traffic rate increases. One drawback is that it takes more memory in cache as we need to bundle the value delta with the cache item - when the caching system does not support retrieval of the key expiration time, we also need to store the expiry (that is, time() + ttl) in the bundle.
Prokaryotic cells Reproduction Prokaryotic_cell > Reproduction Bacteria and archaea reproduce through asexual reproduction, usually by binary fission. Genetic exchange and recombination still occur, but this is a form of horizontal gene transfer and is not a replicative process, simply involving the transference of DNA between two cells, as in bacterial conjugation.
Congruence modulo m Applications Modular_math > Applications In pure mathematics, modular arithmetic is one of the foundations of number theory, touching on almost every aspect of its study, and it is also used extensively in group theory, ring theory, knot theory, and abstract algebra. In applied mathematics, it is used in computer algebra, cryptography, computer science, chemistry and the visual and musical arts. A very practical application is to calculate checksums within serial number identifiers.
BQP Sum of Histories BQP > Relationship to other complexity classes > BQP and PSPACE > Sum of Histories Source:Sum of histories is a technique introduced by physicist Richard Feynman for path integral formulation. We apply this technique to quantum computing to solve APPROX-QCIRCUIT-PROB. Consider a quantum circuit C, which consists of t gates, g 1 , g 2 , ⋯ , g m {\displaystyle g_{1},g_{2},\cdots ,g_{m}} , where each g j {\displaystyle g_{j}} comes from a universal gate set and acts on at most two qubits. To understand what the sum of histories is, we visualize the evolution of a quantum state given a quantum circuit as a tree.
Symmetric distribution Summary Symmetric_distribution In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged when its probability density function (for continuous probability distribution) or probability mass function (for discrete random variables) is reflected around a vertical line at some value of the random variable represented by the distribution. This vertical line is the line of symmetry of the distribution. Thus the probability of being any given distance on one side of the value about which symmetry occurs is the same as the probability of being the same distance on the other side of that value.
Predictive Analysis Time series models Predictive_Analytics > Analytical techniques > Time series models Time series models are a subset of machine learning that utilize time series in order to understand and forecast data using past values. A time series is the sequence of a variable's value over equally spaced periods, such as years or quarters in business applications. To accomplish this, the data must be smoothed, or the random variance of the data must be removed in order to reveal trends in the data. There are multiple ways to accomplish this.
Complex Lie group Summary Complex_Lie_group In geometry, a complex Lie group is a Lie group over the complex numbers; i.e., it is a complex-analytic manifold that is also a group in such a way G × G → G , ( x , y ) ↦ x y − 1 {\displaystyle G\times G\to G,(x,y)\mapsto xy^{-1}} is holomorphic. Basic examples are GL n ⁡ ( C ) {\displaystyle \operatorname {GL} _{n}(\mathbb {C} )} , the general linear groups over the complex numbers. A connected compact complex Lie group is precisely a complex torus (not to be confused with the complex Lie group C ∗ {\displaystyle \mathbb {C} ^{*}} ). Any finite group may be given the structure of a complex Lie group. A complex semisimple Lie group is a linear algebraic group. The Lie algebra of a complex Lie group is a complex Lie algebra.
Chiller How absorption technology works Chiller > How absorption technology works The solution surrounds a bundle of tubes which carries either steam or hot water. The steam or hot water transfers heat into the pool of dilute lithium bromide solution. The solution boils, sending refrigerant vapor upward into the condenser and leaving behind concentrated lithium bromide.
Bibliometrics From altmetrics to open metrics Bibliometrics > Bibliometrics and open science > From altmetrics to open metrics "The concept of alt-metrics was introduced in 2009 by Cameron Neylon and Shirly Wu as article-level metrics. In contrast with the focus of leading metrics on journals (impact factor) or, more recently, on individual researchers (h-index), the article-level metrics makes it possible to track the circulation of individual publications: "(an) article that used to live on a shelf now lives in Mendeley, CiteULike, or Zotero – where we can see and count it" As such they are more compatible with the diversity of publication strategies that has characterized open science: preprints, reports or even non-textual outputs like dataset or software may also have associated metrics. In their original research proposition, Neylon and Wu favored the use of data from reference management software like Zotero or Mendeley.
Chronic lymphangitis Summary Chronic_lymphangitis Lymphangitis is an inflammation or an infection of the lymphatic channels that occurs as a result of infection at a site distal to the channel. The most common cause of lymphangitis in humans is Streptococcus pyogenes (Group A strep), hemolytic streptococci, and in some cases, mononucleosis, cytomegalovirus, tuberculosis, syphilis, and the fungus Sporothrix schenckii. Lymphangitis is sometimes mistakenly called "blood poisoning". In reality, "blood poisoning" is synonymous with sepsis.
Kansa method History and recent developments Kansa_method > History and recent developments The BEM is an alternative method in some engineering problems, such as inverse, unbounded domain, and thin-walled structure problems. However, its applications are largely limited by the availability of the fundamental solution of the governing equation. In the recent several decades, “meshless” or “element-free” methods attract great attention.
Double hashing Analysis Double_hashing > Analysis Bradford and Katehakis showed the expected number of probes for an unsuccessful search in T {\displaystyle T} , still using these initially chosen hash functions, is 1 1 − α {\displaystyle {\tfrac {1}{1-\alpha }}} regardless of the distribution of the inputs. Pair-wise independence of the hash functions suffices.
Ferranti Orion Magnetic amplifiers Ferranti_Orion > History > Magnetic amplifiers One such system was the magnetic amplifier. Similar to magnetic core memory, or "cores", magnetic amplifiers used small toroids of ferrite as a switching element. When current passed through the core, a magnetic field would be induced that would reach a maximum value based on the saturation point of the material being used.
Streamgraph Summary Streamgraph A streamgraph, or stream graph, is a type of stacked area graph which is displaced around a central axis, resulting in a flowing, organic shape. Unlike a traditional stacked area graph in which the layers are stacked on top of an axis, in a streamgraph the layers are positioned to minimize their "wiggle". More formally, the layers are displaced to minimize the sum of the squared slopes of each layer, weighted by the area of the layer. Streamgraphs display data with only positive values, and are not able to represent both negative and positive values.Streamgraphs and their use were popularized by Amanda Cox in a February 2008 New York Times article on movie box office revenues. Cox got the idea from then-undergraduate Lee Byron, who had used a similar method for visualizing his music listening history.A related graph, sometimes conflated with streamgraphs, is the ThemeRiver, in which the "silhouette" of the graph is symmetrically arranged around the central axis.Streamgraphs were found to be more readable than basic stacked area graphs or ThemeRivers for value comparison tasks.Streamgraphs are officially supported by Matplotlib and D3.js.Marco Di Bartolomeo and Yifan Hu (2016) propose several improvements to streamgraphs, such as using 1-norm minimization instead of 2-norm minimization.
Great power Power dimensions Great_power > Characteristics > Power dimensions 3. High technology and education. 4.
Double-layer capacitor Types Supercapacitor > Types Electrical energy is stored in supercapacitors via two storage principles, static double-layer capacitance and electrochemical pseudocapacitance; and the distribution of the two types of capacitance depends on the material and structure of the electrodes. There are three types of supercapacitors based on storage principle: Double-layer capacitors (EDLCs) — with activated carbon electrodes or derivatives with much higher electrostatic double-layer capacitance than electrochemical pseudocapacitance Pseudocapacitors — with transition metal oxide or conducting polymer electrodes with a high electrochemical pseudocapacitance Hybrid capacitors — with asymmetric electrodes, one of which exhibits mostly electrostatic and the other mostly electrochemical capacitance, such as lithium-ion capacitorsBecause double-layer capacitance and pseudocapacitance both contribute inseparably to the total capacitance value of an electrochemical capacitor, a correct description of these capacitors only can be given under the generic term. The concepts of supercapattery and supercabattery have been recently proposed to better represent those hybrid devices that behave more like the supercapacitor and the rechargeable battery, respectively.The capacitance value of a supercapacitor is determined by two storage principles: Double-layer capacitance – electrostatic storage of the electrical energy achieved by separation of charge in a Helmholtz double layer at the interface between the surface of a conductor electrode and an electrolytic solution electrolyte. The separation of charge distance in a double-layer is on the order of a few ångströms (0.3–0.8 nm) and is static in origin.
Amino acid metabolism Protein folding Amino_acid_metabolism > Protein synthesis > Polypeptide synthesis > Protein folding Once a polypeptide chain is fully folded, it is called a protein. Often many subunits will combine to make a fully functional protein although physiological proteins do exist that contain only one polypeptide chain. Proteins may also incorporate other molecules such as the heme group in hemoglobin, a protein responsible for carrying oxygen in the blood.
Beneficial mutation Overview Beneficial_mutation > Overview Another effect of these mobile DNA sequences is that when they move within a genome, they can mutate or delete existing genes and thereby produce genetic diversity.Nonlethal mutations accumulate within the gene pool and increase the amount of genetic variation. The abundance of some genetic changes within the gene pool can be reduced by natural selection, while other "more favorable" mutations may accumulate and result in adaptive changes. For example, a butterfly may produce offspring with new mutations.
Turing Tumble Summary Turing_Tumble Turing Tumble is a game and demonstration of logic gates via mechanical computing.
Force Equilibrium Attractive_(force) > Combining forces > Equilibrium A body is in static equilibrium with respect to a frame of reference if it at rest and not accelerating, whereas a body in dynamic equilibrium is moving at a constant speed in a straight line, i.e., moving but not accelerating. What one observer sees as static equilibrium, another can see as dynamic equilibrium and vice versa. : 566
Ternary search tree Hash maps Ternary_search_tree > Comparison to other data structures > Hash maps Hashtables can also be used in place of ternary search trees for mapping strings to values. However, hash maps also frequently use more memory than ternary search trees (but not as much as tries). Additionally, hash maps are typically slower at reporting a string that is not in the same data structure, because it must compare the entire string rather than just the first few characters. There is some evidence that shows ternary search trees running faster than hash maps. Additionally, hash maps do not allow for many of the uses of ternary search trees, such as near-neighbor lookups.
Finite volume General conservation law Finite_volume > General conservation law The actual numerical scheme will depend upon problem geometry and mesh construction. MUSCL reconstruction is often used in high resolution schemes where shocks or discontinuities are present in the solution. Finite volume schemes are conservative as cell averages change through the edge fluxes. In other words, one cell's loss is always another cell's gain!
Human sweat Mechanism Human_sweat > Mechanism Sweating allows the body to regulate its temperature. Sweating is controlled from a center in the preoptic and anterior regions of the brain's hypothalamus, where thermosensitive neurons are located. The heat-regulatory function of the hypothalamus is also affected by inputs from temperature receptors in the skin. High skin temperature reduces the hypothalamic set point for sweating and increases the gain of the hypothalamic feedback system in response to variations in core temperature.
Thermel Practical concerns Thermocouple > Practical concerns Thermocouples ideally should be very simple measurement devices, with each type being characterized by a precise E ( T ) {\displaystyle \scriptstyle E(T)} curve, independent of any other details. In reality, thermocouples are affected by issues such as alloy manufacturing uncertainties, aging effects, and circuit design mistakes/misunderstandings.
Selfish gene theory The gene as the unit of selection Gene-centered_view_of_evolution > Overview > The gene as the unit of selection Williams argued that "he natural selection of phenotypes cannot in itself produce cumulative change, because phenotypes are extremely temporary manifestations." Each phenotype is the unique product of the interaction between genome and environment. It does not matter how fit and fertile a phenotype is, it will eventually be destroyed and will never be duplicated.

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