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Sectional chart Summary Sectional_chart In United States aviation, a sectional aeronautical chart, often called a sectional chart or a sectional for short, is a type of aeronautical chart designed for air navigation under visual flight rules (VFR). In Australia, Canada and some other countries, the equivalent charts used for visual flight are called VFR Navigation Charts (VNCs). A sectional chart shows topographical features that are important to aviators, such as terrain elevations, ground features identifiable from altitude (rivers, dams, bridges, buildings, etc.), and ground features useful to pilots (airports, beacons, landmarks, etc.). The chart also shows information on airspace classes, ground-based navigation aids, radio frequencies, longitude and latitude, navigation waypoints, navigation routes.
Pythagorean triangle The Platonic sequence Pythagorean_triple > Special cases and related equations > The Platonic sequence 380 BC): side a: side b = ( a 2 ) 2 − 1: side c = ( a 2 ) 2 + 1 {\displaystyle {\text{side }}a:{\text{side }}b=\left({a \over 2}\right)^{2}-1:{\text{side }}c=\left({a \over 2}\right)^{2}+1} It can be shown that all Pythagorean triples can be obtained, with appropriate rescaling, from the basic Platonic sequence (a, (a2 − 1)/2 and (a2 + 1)/2) by allowing a to take non-integer rational values. If a is replaced with the fraction m/n in the sequence, the result is equal to the 'standard' triple generator (2mn, m2 − n2,m2 + n2) after rescaling. It follows that every triple has a corresponding rational a value which can be used to generate a similar triangle (one with the same three angles and with sides in the same proportions as the original). For example, the Platonic equivalent of (56, 33, 65) is generated by a = m/n = 7/4 as (a, (a2 –1)/2, (a2+1)/2) = (56/32, 33/32, 65/32). The Platonic sequence itself can be derived by following the steps for 'splitting the square' described in Diophantus II.VIII.
Knowledge gap hypothesis Hypothesis operationalization and initial support Knowledge_gap_hypothesis > Hypothesis operationalization and initial support The knowledge gap hypothesis can be operationalized both for cross-sectional and time-series appropriate research. For cross-sectional research, the knowledge gap hypothesis expects that "at any given time, there should be a higher correlation between acquisition of knowledge and education for topics highly publicized in the media than for topics less highly publicized. Tichenor, Donohue, and Olien (1970) tested this hypothesis using an experiment in which participants were asked to read and discuss two news stories of varying publicity.
Impact of the COVID-19 pandemic on people with disabilities Social Impact_of_the_COVID-19_pandemic_on_people_with_disabilities > Impact > Social Children with disabilities are at higher risk of contracting COVID-19 and developing serious complications from the disease. They may not be able to adequately socially distance while interacting with others or may not be able to wear masks due to sensory issues. This may lead to further isolation both for disabled children and their families.The rise of virtual gatherings has allowed some people with disabilities to participate in activities that were previously difficult to attend. For example, individuals with certain physical disabilities do not need to worry about whether a location is wheelchair-accessible when the event is conducted fully online.
Available energy Summary Exergy These benefits include the basis for determining energy quality (or exergy content), enhancing the understanding of fundamental physical phenomena, and improving design, performance evaluation and optimization efforts. In thermodynamics, the exergy of a system is the maximum useful work that can be produced as the system is brought into equilibrium with its environment by an ideal process. The specification of an 'ideal process' allows the determination of 'maximum work' production.
Littoral drift Summary Littoral_drift This process is called "beach drift", but some workers regard it as simply part of "longshore drift" because of the overall movement of sand parallel to the coast. Longshore drift affects numerous sediment sizes as it works in slightly different ways depending on the sediment (e.g. the difference in long-shore drift of sediments from a sandy beach to that of sediments from a shingle beach). Sand is largely affected by the oscillatory force of breaking waves, the motion of sediment due to the impact of breaking waves and bed shear from long-shore current. Because shingle beaches are much steeper than sandy ones, plunging breakers are more likely to form, causing the majority of long shore transport to occur in the swash zone, due to a lack of an extended surf zone.
Forensic epidemiology Hill viewpoints Forensic_epidemiology > Methods and principles > Causal methodology > Hill viewpoints While useful when assessing a previously unexplored association, there is no combination or minimal number of these criteria that must be met in order to conclude that a plausible relationship exists between a known exposure and an observed outcome. In many FE investigations there is no need for a causal plausibility analysis if a general causal relationship is well established. In large part, plausibility of a relationship is entertained once implausibility has been rejected.
3-D rendering Reflection and shading models 3-D_rendering > Reflection and shading models Models of reflection/scattering and shading are used to describe the appearance of a surface. Although these issues may seem like problems all on their own, they are studied almost exclusively within the context of rendering. Modern 3D computer graphics rely heavily on a simplified reflection model called the Phong reflection model (not to be confused with Phong shading). In the refraction of light, an important concept is the refractive index; in most 3D programming implementations, the term for this value is "index of refraction" (usually shortened to IOR). Shading can be broken down into two different techniques, which are often studied independently: Surface shading - how light spreads across a surface (mostly used in scanline rendering for real-time 3D rendering in video games) Reflection/scattering - how light interacts with a surface at a given point (mostly used in ray-traced renders for non-real-time photorealistic and artistic 3D rendering in both CGI still 3D images and CGI non-interactive 3D animations)
Leucine-responsive regulatory protein Summary Leucine-responsive_regulatory_protein Leucine responsive protein, or Lrp, is a global regulator protein, meaning that it regulates the biosynthesis of leucine, as well as the other branched-chain amino acids, valine and isoleucine. In bacteria, it is encoded by the lrp gene. Lrp alternatively activates and represses the expression of acetolactate synthase's (ALS) several isoenzymes. Lrp, in E. coli, along with DAM plays a role in the regulation of the fim operon, a group of genes needed for successful synthesis and trafficking of Type I Pili. These hair like structures are important virulence factors for different pathogenic strains of Bacteria as they can mediate biofilm formation and adhesion to host epithelia. Other examples include Salmonella enterica serovar Typhimurium and Klebsiella pneumoniae.More generally, Lrp facilitates the proliferation and pathogenesis of bacteria in their hosts.
Automated decision Law Automated_decision-making > Applications > Law In legal systems around the world, algorithmic tools such as risk assessment instruments (RAI), are being used to supplement or replace the human judgment of judges, civil servants and police officers in many contexts. In the United States RAI are being used to generate scores to predict the risk of recidivism in pre-trial detention and sentencing decisions, evaluate parole for prisoners and to predict "hot spots" for future crime. These scores may result in automatic effects or may be used to inform decisions made by officials within the justice system. In Canada ADM has been used since 2014 to automate certain activities conducted by immigration officials and to support the evaluation of some immigrant and visitor applications.
Open energy system models OSeMOSYS Open_energy_system_models > Energy system models > OSeMOSYS These resources are not limited to energy commodities and may include, for example, water and land-use. This enables OSeMOSYS to be applied in domains other than energy, such as water systems. Technical constraints, economic restrictions, and/or environmental targets may also be imposed to reflect policy considerations.
Wang and Landau algorithm Wang and Landau molecular dynamics: Statistical Temperature Molecular Dynamics (STMD) Wang_and_Landau_algorithm > Wang and Landau molecular dynamics: Statistical Temperature Molecular Dynamics (STMD) Upon increasing energy bin size, STMC gets the same results over a considerable range, while the performance of WL deteriorates rapidly. STMD can use smaller initial values of f d = f − 1 {\displaystyle f_{d}=f-1} for more rapid convergence. In sum, STMC needs fewer steps to obtain the same quality of results.
Antidementia drug Creutzfeldt–Jakob disease Antidementia_drug > Causes > Creutzfeldt–Jakob disease Creutzfeldt–Jakob disease is a rapidly progressive prion disease that typically causes dementia that worsens over weeks to months. Prions are disease-causing pathogens created from abnormal proteins.
Intestinal gas Odor Rectal_gases > Management > Odor Another study showed that bismuth acted synergistically with various antibiotics to inhibit sulfate-reducing gut bacteria and sulfide production. Some authors proposed a theory that hydrogen sulfide was involved in the development of ulcerative colitis and that bismuth might be helpful in the management of this condition. However, bismuth administration in rats did not prevent them from developing ulcerative colitis despite reduced hydrogen sulfide production.
Cross-training Summary Cross-training Cross-training is athletic training in sports other than the athlete's usual sport. The goal is improving overall performance. It takes advantage of the particular effectiveness of one training method to negate the shortcomings of another.
Three-point locking Summary Three-point_locking This effectively immobilizes the top and bottom of the door, and greatly increases the security of the door-locking compared to a door with only single-point locking.Near the holes in the top and bottom of the door, some restraining device is provided for the rods to pass through, to prevent them from falling away entirely when in the unlocked position, and thus not inserted into the holes in the door. This consists of either a rubber or plastic gasket fitted into the holes in the door and protruding up or down a short distance, or else a small metal plate with a hole in it welded to the inside of the door through which the rod extends in any position.Another three-point locking system is commonly used in lockers. This system uses a "Latch Channel" with 3 vertical slots that attach to 3 hooks on the locker frame. The locker handle is attached directly to the latch channel so that when the channel is lifted, it is released from the hooks and the door is allowed to swing open.
Borel function Properties of measurable functions Measurable_function > Properties of measurable functions The (pointwise) supremum, infimum, limit superior, and limit inferior of a sequence (viz., countably many) of real-valued measurable functions are all measurable as well. The pointwise limit of a sequence of measurable functions f n: X → Y {\displaystyle f_{n}:X\to Y} is measurable, where Y {\displaystyle Y} is a metric space (endowed with the Borel algebra). This is not true in general if Y {\displaystyle Y} is non-metrizable. The corresponding statement for continuous functions requires stronger conditions than pointwise convergence, such as uniform convergence.
Directed differentiation Direct reprogramming Directed_differentiation > Methods > Current methodologies > Direct reprogramming This method, also known as transdifferentiation or direct conversion, consists in overexpressing one or several factors, usually transcription factors, introduced in the cells. The starting material can be either pluripotent stem cells (PSCs), or either differentiated cell type such as fibroblasts. The principle was first demonstrated in 1987 with the myogenic factors MyoD. A drawback of this approach is the introduction of foreign nucleic acid in the cells and the forced expression of transcription factors which effects are not fully understood.
Dexamethasone Pharmacodynamics Dexamethasone > Pharmacology > Pharmacodynamics However, higher doses of dexamethasone override the export capacity of P-glycoprotein and enter the brain to produce central activation of GRs. In conjunction with the suppression of endogenous corticosteroids by dexamethasone, this results in skewed ratios of activation of peripheral versus central GRs as well as skewed ratios of activation of GRs versus MRs when compared to non-synthetic corticosteroids. These differences can have significant clinical relevance.
Natural parametrization Summary Euclidean_geometry_of_curves Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus. Many specific curves have been thoroughly investigated using the synthetic approach. Differential geometry takes another path: curves are represented in a parametrized form, and their geometric properties and various quantities associated with them, such as the curvature and the arc length, are expressed via derivatives and integrals using vector calculus.
Silicon transistor MOSFET (MOS transistor) Silicon_transistor > History > MOSFET (MOS transistor) Atalla and his Korean colleague Dawon Kahng developed the metal–oxide–semiconductor field-effect transistor (MOSFET), or MOS transistor, in 1959, the first transistor that could be miniaturized and mass-produced for a wide range of uses. In a self-aligned CMOS process, a transistor is formed wherever the gate layer (polysilicon or metal) crosses a diffusion layer. : p.1 (see Fig. 1.1) With its high scalability, much lower power consumption, and higher density than bipolar junction transistors, the MOSFET made it possible to build high-density integrated circuits, allowing the integration of more than 10,000 transistors in a single IC.CMOS (complementary MOS) was invented by Chih-Tang Sah and Frank Wanlass at Fairchild Semiconductor in 1963.
Water source heat pump Solar-assisted heat pump Heat_pumps > Types > Solar-assisted heat pump A solar-assisted heat pump either integrates a heat pump and thermal solar panels or photovoltaic solar power in a single system. In the case of thermal solar, typically these two technologies are used separately (or are operated in parallel) to produce hot water. In this system the solar thermal panel is the low-temperature heat source, and the heat produced feeds the heat pump's evaporator. The goal of this system is to get high COP and then produce energy in a more efficient and less expensive way.. In the case of photovoltaic solar heat pumps, or solar air conditioners, electricity to run the heat pump is generated from the sun. Either batteries can be used to store excess solar energy generated to run during cloudy or nighttime periods, or grid power can be used during these periods.
Feed forward (control) Gene regulation and feed-forward Feed-forward_control > Applications > Gene regulation and feed-forward In this system the concentration of active Far1 depends on the time integral of a function of the external mating pheromone concentration. This dependence on past levels of mating pheromone is a form of cellular memory. This system simultaneously allows for the stability and reversibility.
Ductility Ductile–brittle transition temperature Ductility > Ductile–brittle transition temperature The plastic deformation of ductile metals is important as it can be a sign of the potential failure of the metal. Yet, the point at which the material exhibits a ductile behavior versus a brittle behavior is not only dependent on the material itself but also on the temperature at which the stress is being applied to the material. The temperature where the material changes from brittle to ductile or vice versa is crucial for the design of load-bearing metallic products.
Addition polymer History Addition_polymer > History They left the reaction vessel overnight, and the next morning they found a small amount of a white waxy solid. It was shown later that this solid was polyethylene. The term "addition polymerization" is deprecated by IUPAC (International Union of Pure and Applied Chemistry) which recommends the alternative term chain polymerization.
Classical theories of gravitation Summary Classical_theories_of_gravitation Alternatives to general relativity are physical theories that attempt to describe the phenomenon of gravitation in competition with Einstein's theory of general relativity. There have been many different attempts at constructing an ideal theory of gravity.These attempts can be split into four broad categories based on their scope. In this article, straightforward alternatives to general relativity are discussed, which do not involve quantum mechanics or force unification. Other theories which do attempt to construct a theory using the principles of quantum mechanics are known as theories of quantized gravity.
Lighthouse paradox Summary Lighthouse_paradox The lighthouse paradox is a thought experiment in which the speed of light is apparently exceeded. The rotating beam of light from a lighthouse is imagined to be swept from one object to shine on a second object. The farther the two objects are away from the lighthouse, the farther the distance between them crossed by the light beam. If the objects are sufficiently far away from the lighthouse, the places where the beam hits object 2 will traverse the object with an apparent speed faster than light, possibly communicating a signal on object 2 with superluminal velocity, which violates Albert Einstein's theory of special relativity.
Perlite Aquatic filtration Perlite > Uses > Aquatic filtration Perlite is currently used in commercial pool filtration technology, as a replacement to diatomaceous earth filters. Perlite is an excellent filtration aid and is used extensively as an alternative to diatomaceous earth. The popularity of perlite usage as a filter medium is growing considerably worldwide.
Blue Gene Design Blue_Gene > Blue Gene/Q > Design The L2 cache is multi-versioned, supporting transactional memory and speculative execution, and has hardware support for atomic operations. L2 cache misses are handled by two built-in DDR3 memory controllers running at 1.33 GHz. The chip also integrates logic for chip-to-chip communications in a 5D torus configuration, with 2GB/s chip-to-chip links.
Driveway alarm Sensors Driveway_alarm > Sensors Will only alarm when a vehicle moves by and are generally more costly than the passive infrared units. Rubber hose When pressure is applied on top of the hose air is pushed up the hose triggering an alarm. Common in commercial applications.
Minimum Sudoku problem Summary Minimum_Sudoku_problem Experimental mathematics is an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns. It has been defined as "that branch of mathematics that concerns itself ultimately with the codification and transmission of insights within the mathematical community through the use of experimental (in either the Galilean, Baconian, Aristotelian or Kantian sense) exploration of conjectures and more informal beliefs and a careful analysis of the data acquired in this pursuit. "As expressed by Paul Halmos: "Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork. You want to find out what the facts are, and what you do is in that respect similar to what a laboratory technician does."
Kinetic kill vehicle Summary Kinetic_energy_weapon Typical kinetic energy weapons are blunt projectiles such as rocks and round shots, pointed ones such as arrows, and somewhat pointed ones such as bullets. Among projectiles that do not contain explosives are those launched from railguns, coilguns, and mass drivers, as well as kinetic energy penetrators.
Skin oiliness Epidermis Skin_aging > Structure > Epidermis The epidermis can be further subdivided into the following strata (beginning with the outermost layer): corneum, lucidum (only in palms of hands and bottoms of feet), granulosum, spinosum, and basale. Cells are formed through mitosis at the basale layer. The daughter cells (see cell division) move up the strata changing shape and composition as they die due to isolation from their blood source.
Redox (operating system) History Redox_(operating_system) > History Redox was created by Jeremy Soller and was first published on 20 April 2015 on GitHub. As of July 2021, the Redox repository had a total of 79 contributors.
Angular wavevector Summary Propagation_vector A closely related vector is the angular wave vector (or angular wavevector), with a typical unit being radian per metre. The wave vector and angular wave vector are related by a fixed constant of proportionality, 2π radians per cycle.It is common in several fields of physics to refer to the angular wave vector simply as the wave vector, in contrast to, for example, crystallography. It is also common to use the symbol k for whichever is in use. In the context of special relativity, wave vector can refer to a four-vector, in which the (angular) wave vector and (angular) frequency are combined.
Reaction formation Theory Reaction_formation > Theory In addition, "igh ideals of virtue and goodness may be reaction formations against primitive object cathexes rather than realistic values that are capable of being lived up to. Romantic notions of chastity and purity may mask crude sexual desires, altruism may hide selfishness, and piety may conceal sinfulness." Even more counter-intuitively, according to this model " phobia is an example of a reaction formation.
P53 DNA damage and repair P53_protein > Function > DNA damage and repair In this cell type, p53 activates numerous microRNAs (like miR-302a, miR-302b, miR-302c, and miR-302d) that directly inhibit the p21 expression in hESCs. The p21 protein binds directly to cyclin-CDK complexes that drive forward the cell cycle and inhibits their kinase activity, thereby causing cell cycle arrest to allow repair to take place. p21 can also mediate growth arrest associated with differentiation and a more permanent growth arrest associated with cellular senescence.
Umkehr effect Summary Umkehr_effect The Umkehr is the time variation of the ratio of the scattered intensity at two different wavelengths. The word means 'reversal' in German. The Umkehr effect is observed when measurements are made with ultraviolet spectrophotometer of the ratio of the zenith sky light intensities of two wavelengths in the solar ultraviolet when the sun is near the horizon. The shorter of two wavelengths (intensity I) is strongly absorbed and the other (intensity I' ) is weakly absorbed.
Pulmonary function tests Diffusing capacity Pulmonary_function_testing > Tests > Diffusing capacity Measurement of the single-breath diffusing capacity for carbon monoxide (DLCO) is a fast and safe tool in the evaluation of both restrictive and obstructive lung disease.
Shinumo Quartzite Sedimentary structures Shinumo_Quartzite > Sedimentary structures The Shinumo Quartzite exhibits a variety of sedimentary structures. The sandstones of the lower and lower-middle members exhibit centimeter- to meter-scale planar tabular cross-stratification and trough cross-beds. These cross beds record north-directed paleocurrents along with subordinate bidirectional paleocurrents. The upper-middle member exhibits abundant cross beds, clay galls, and mudcracks.
James (Mac) Hyman Summary James_(Mac)_Hyman James Macklin "Mac" Hyman (born 1950) is an applied mathematician formerly at Los Alamos National Laboratory and currently at Tulane University in the United States. He received his undergraduate degree from Tulane University and his PhD in 1976 from NYU's Courant Institute of Mathematical Sciences under Peter Lax with thesis The method of lines solution of partial differential equations.Hyman served as president of the Society for Industrial and Applied Mathematics (SIAM) in 2003–2005. He was named a fellow of the Society for Industrial and Applied Mathematics in 2009.
Photosensitizer Parameters Photosensitizer > Theory > Parameters For a molecule to be considered a photosensitizer: The photosensitizer must impart a physicochemical change upon a substrate after absorbing incident light. Upon imparting a chemical change, the photosensitizer returns to its original chemical form.It is important to differentiate photosensitizers from other photochemical interactions including, but not limited to, photoinitiators, photocatalysts, photoacids and photopolymerization. Photosensitizers utilize light to enact a chemical change in a substrate; after the chemical change, the photosensitizer returns to its initial state, remaining chemically unchanged from the process. Photoinitiators absorb light to become a reactive species, commonly a radical or an ion, where it then reacts with another chemical species.
Triple-alpha process Triple-alpha process in stars Helium_fusion > Triple-alpha process in stars The net energy release of the process is 7.275 MeV. As a side effect of the process, some carbon nuclei fuse with additional helium to produce a stable isotope of oxygen and energy: 126C + 42He → 168O + γ (+7.162 MeV)Nuclear fusion reactions of helium with hydrogen produces lithium-5, which also is highly unstable, and decays back into smaller nuclei with a half-life of 3.7×10−22 s. Fusing with additional helium nuclei can create heavier elements in a chain of stellar nucleosynthesis known as the alpha process, but these reactions are only significant at higher temperatures and pressures than in cores undergoing the triple-alpha process. This creates a situation in which stellar nucleosynthesis produces large amounts of carbon and oxygen, but only a small fraction of those elements are converted into neon and heavier elements. Oxygen and carbon are the main "ash" of helium-4 burning.
Continuous spectrum (functional analysis) Classification of points in the spectrum Continuous_spectrum_(functional_analysis) > Classification of points in the spectrum The set of approximate eigenvalues (which includes the point spectrum) is called the approximate point spectrum of T, denoted by σap(T). λ ∈ σ ( T ) {\displaystyle \lambda \in \sigma (T)} if T − λ I {\displaystyle T-\lambda I} does not have dense range. The set of such λ is called the compression spectrum of T, denoted by σ c p ( T ) {\displaystyle \sigma _{\mathrm {cp} }(T)} . If T − λ I {\displaystyle T-\lambda I} does not have dense range but is injective, λ is said to be in the residual spectrum of T, denoted by σ r e s ( T ) {\displaystyle \sigma _{\mathrm {res} }(T)} .Note that the approximate point spectrum and residual spectrum are not necessarily disjoint (however, the point spectrum and the residual spectrum are). The following subsections provide more details on the three parts of σ(T) sketched above.
Parkinson's disease Prognosis Parkinson's_disease > Prognosis Age is an appropriate predictor of disease progression. The rate of motor decline is greater in those with less impairment at the time of diagnosis, while cognitive impairment is more frequent in those who are over 70 years of age at symptom onset.Disability is mainly related to nonmotor symptoms of the disease and therapies exist to improve these. Nevertheless, the relationship between disease progression and disability is independent of each other.
Plant invasion Species-based mechanisms Invasive_plant > Causes > Species-based mechanisms This explains how many introduced species are able to establish and become invasive in new environments. In addition, the rate at which an invasive species can spread can be difficult to ascertain by biologists since population growth occurs geometrically, rather than linearly. When bottlenecks and founder effects cause a great decrease in the population size and may constrict genetic variation, the individuals begin to show additive variance as opposed to epistatic variance.
Data plot Overview Data_plot > Overview There are also many statistical tools generally referred to as graphical techniques. These include: scatter plots spectrum plots histograms probability plots residual plots box plots, and block plotsGraphical procedures such as plots are a short path to gaining insight into a data set in terms of testing assumptions, model selection, model validation, estimator selection, relationship identification, factor effect determination, outlier detection. Statistical graphics give insight into aspects of the underlying structure of the data.Graphs can also be used to solve some mathematical equations, typically by finding where two plots intersect.
4-Hydroxyphenylpyruvate dioxygenase Function Α-ketoisocaproate_dioxygenase > Function In nearly all aerobic beings, 4-hydroxyphenylpyruvate dioxygenase is responsible for converting 4-hydroxyphenylpyruvate into homogentisate. This conversion is one of many steps in breaking L-tyrosine into acetoacetate and fumarate. While the overall products of this cycle are used to create energy, plants and higher order eukaryotes utilize HPPD for a much more important reason. In eukaryotes, HPPD is used to regulate blood tyrosine levels, and plants utilize this enzyme to help produce the cofactors plastoquinone and tocopherol which are essential for the plant to survive.
Log likelihood Discrete probability distribution Log_likelihood > Definition > Discrete probability distribution Let X {\displaystyle X} be a discrete random variable with probability mass function p {\displaystyle p} depending on a parameter θ {\displaystyle \theta } . Then the function considered as a function of θ {\displaystyle \theta } , is the likelihood function, given the outcome x {\displaystyle x} of the random variable X {\displaystyle X} . Sometimes the probability of "the value x {\displaystyle x} of X {\displaystyle X} for the parameter value θ {\displaystyle \theta } " is written as P(X = x \| θ) or P(X = x; θ).
Point-set topology Summary General_topology In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. The fundamental concepts in point-set topology are continuity, compactness, and connectedness: Continuous functions, intuitively, take nearby points to nearby points. Compact sets are those that can be covered by finitely many sets of arbitrarily small size.
Biofluid dynamics Basic Principles of Fluid Dynamics Biofluid_dynamics > Basic Principles of Fluid Dynamics Example - Cream – the longer it is whipped, the thicker it gets. Shear Thinning Fluid: Its viscosity decreases with increased stress. Example – Blood, Tomato sauce.
Polymerase (DNA directed), alpha 1 Summary Polymerase_(DNA_directed),_alpha_1 DNA polymerase alpha also known as Pol α is an enzyme complex found in eukaryotes that is involved in initiation of DNA replication. The DNA polymerase alpha complex consists of 4 subunits: POLA1, POLA2, PRIM1, and PRIM2.Pol α has limited processivity and lacks 3′ exonuclease activity for proofreading errors. Thus it is not well suited to efficiently and accurately copy long templates (unlike Pol Delta and Epsilon). Instead it plays a more limited role in replication.
Grid storage Thermal Grid_energy_storage > Forms > Thermal This thermal storage can provide load-shifting or even more complex ancillary services by increasing power consumption (charging the storage) during off-peak times and lowering power consumption (discharging the storage) during higher-priced peak times. For example, off-peak electricity can be used to make ice from water, and the ice can be stored. The stored ice can be used to cool the air in a large building which would have normally used electric AC, thereby shifting the electric load to off-peak hours.
Quantum decoherence Mechanisms Quantum_decoherence > Mechanisms To examine how decoherence operates, an "intuitive" model is presented below. The model requires some familiarity with quantum theory basics. Analogies are made between visualizable classical phase spaces and Hilbert spaces. A more rigorous derivation in Dirac notation shows how decoherence destroys interference effects and the "quantum nature" of systems. Next, the density matrix approach is presented for perspective.
Choreographic programming Languages Choreographic_programming > Languages A core theoretical model for choreographic programming. A mechanised implementation is available in Coq.
Exponential algorithm Constant time Subquadratic_time > Constant time Despite the name "constant time", the running time does not have to be independent of the problem size, but an upper bound for the running time has to be independent of the problem size. For example, the task "exchange the values of a and b if necessary so that a ≤ b {\textstyle a\leq b} " is called constant time even though the time may depend on whether or not it is already true that a ≤ b {\textstyle a\leq b} . However, there is some constant t such that the time required is always at most t.
Filler (materials) Fatigue resistance Filler_(materials) > Mechanical properties > Fatigue resistance Filler can have a negative or positive effect on fatigue resistance depending on the filler type and shape. In general fillers create small discontinuities in the matrix. This can contribute to crack initiation point. If the filler is brittle fatigue resistance will be low, whereas if the filler is very ductile the composite will be fatigue resistant.
Salivary gland dysfunction Infective Salivary_gland_dysfunction > Acquired > Infective Infections involving the salivary glands can be viral or bacterial (or rarely fungal). Mumps is the most common viral sialadenitis. It usually occurs in children and involves pain in front of the ear, swelling of the parotid, fever, chills, and headaches.
Tuberous Sclerosis Complex Diagnosis Tuberous_Sclerosis_Complex > Diagnosis However, some mutations are less clear in their effect, and so not sufficient alone for diagnosis. Between 1 in 10 and 1 in 4 of individuals with TSC have no mutation that can be identified. Once a particular mutation is identified in someone with TSC, this mutation can be used to make confident diagnoses in other family members.For clinical diagnosis, there isn't one sign that is unique (pathognomonic) to TSC, nor are all signs seen in all individuals.
Allergic to penicillin Penicillin units Penicillin > Nomenclature > Penicillin units The "unit" of penicillin has had three previous definitions, and each definition was chosen as being roughly equivalent to the previous one. Oxford or Florey unit (1941). This was originally defined as the minimum amount of penicillin dissolved in 50 ml of meat extract that would inhibit the growth of a standard strain of Staphylococcus aureus (the Oxford Staphylococcus).
Molecular orbitals Linear combinations of atomic orbitals (LCAO) Molecular_Orbital > Qualitative discussion > Linear combinations of atomic orbitals (LCAO) Linear combinations of atomic orbitals (LCAO) can be used to estimate the molecular orbitals that are formed upon bonding between the molecule's constituent atoms. Similar to an atomic orbital, a Schrödinger equation, which describes the behavior of an electron, can be constructed for a molecular orbital as well. Linear combinations of atomic orbitals, or the sums and differences of the atomic wavefunctions, provide approximate solutions to the Hartree–Fock equations which correspond to the independent-particle approximation of the molecular Schrödinger equation.
Group 5 element Oxyanions Group_V_elements > Chemical properties > Compounds > Oxyanions Vanadic acid, H3VO4 exists only at very low concentrations because protonation of the tetrahedral species − results in the preferential formation of the octahedral + species. In strongly acidic solutions, pH < 2, + is the predominant species, while the oxide V2O5 precipitates from solution at high concentrations. The oxide is formally the acid anhydride of vanadic acid.
Percent point function Strictly monotonic distribution function Quantile_function > Definition > Strictly monotonic distribution function With reference to a continuous and strictly monotonic cumulative distribution function F X: R → {\displaystyle F_{X}\colon \mathbb {R} \to } of a random variable X, the quantile function Q: → R {\displaystyle Q\colon \to \mathbb {R} } maps its input p to a threshold value x so that the probability of X being less or equal than x is p. In terms of the distribution function F, the quantile function Q returns the value x such that F X ( x ) := Pr ( X ≤ x ) = p , {\displaystyle F_{X}(x):=\Pr(X\leq x)=p\,,} which can be written as inverse of the c.d.f. Q ( p ) = F X − 1 ( p ) . {\displaystyle Q(p)=F_{X}^{-1}(p)\,.}
Complexity Applications Complexity > Applications These problems are called intractable. There is another form of complexity called hierarchical complexity. It is orthogonal to the forms of complexity discussed so far, which are called horizontal complexity.
Bending Moment Computing the bending moment Bending_Moment > Computing the bending moment However, physical interpretations of bending moments in beams and plates have a straightforward interpretation as the stress resultants in a cross-section of the structural element. For example, in a beam in the figure, the bending moment vector due to stresses in the cross-section A perpendicular to the x-axis is given by M x = ∫ A r × ( σ x x e x + σ x y e y + σ x z e z ) d A where r = y e y + z e z . {\displaystyle \mathbf {M} _{x}=\int _{A}\mathbf {r} \times (\sigma _{xx}\mathbf {e} _{x}+\sigma _{xy}\mathbf {e} _{y}+\sigma _{xz}\mathbf {e} _{z})\,dA\quad {\text{where}}\quad \mathbf {r} =y\,\mathbf {e} _{y}+z\,\mathbf {e} _{z}\,.}
171 (number) In mathematics 171_(number) > In mathematics 171 is a triangular number and a Jacobsthal number.There are 171 transitive relations on three labeled elements, and 171 combinatorially distinct ways of subdividing a cuboid by flat cuts into a mesh of tetrahedra, without adding extra vertices.The diagonals of a regular decagon meet at 171 points, including both crossings and the vertices of the decagon.There are 171 faces and edges in the 57-cell, an abstract 4-polytope with hemi-dodecahedral cells that is its own dual polytope.Within moonshine theory of sporadic groups, the friendly giant M {\displaystyle \mathbb {M} } is defined as having cyclic groups ⟨ m {\displaystyle m} ⟩ that are linked with the function, f m ( τ ) = q − 1 + a 1 q + a 2 q 2 + . . . , a k {\displaystyle f_{m}(\tau )=q^{-1}+a_{1}q+a_{2}q^{2}+...,{\text{ }}a_{k}} ∈ Z , q = e 2 π i τ , τ > 0 ; {\displaystyle \mathbb {Z} ,{\text{ }}q=e^{2\pi i\tau },{\text{ }}\tau >0;} where q {\displaystyle q} is the character of M {\displaystyle \mathbb {M} } at m {\displaystyle m} .This generates 171 moonshine groups within M {\displaystyle \mathbb {M} } associated with f m {\displaystyle f_{m}} that are principal moduli for different genus zero congruence groups commensurable with the projective linear group P S L 2 ⁡ ( Z ) {\displaystyle \operatorname {PSL_{2}} (\mathbb {Z} )} .It is the number of 3-digit Duck Numbers, i.e., Numbers with at least one digit zero, in Decimal Base.
Prime divisor Open questions Prime_number > Elementary properties > Open questions + n {\displaystyle n!+2,n!+3,\dots ,n!+n} consists of n − 1 {\displaystyle n-1} composite numbers, for any natural number n . {\displaystyle n.} However, large prime gaps occur much earlier than this argument shows.
Cytoskeletal protein Yeast cytoskeleton Cytoskeletal_protein > Eukaryotic cytoskeleton > Yeast cytoskeleton In budding yeast (an important model organism), actin forms cortical patches, actin cables, and a cytokinetic ring and the cap. Cortical patches are discrete actin bodies on the membrane and are vital for endocytosis, especially the recycling of glucan synthase which is important for cell wall synthesis. Actin cables are bundles of actin filaments and are involved in the transport of vesicles towards the cap (which contains a number of different proteins to polarize cell growth) and in the positioning of mitochondria. The cytokinetic ring forms and constricts around the site of cell division.
Schwarzschild's equation for radiative transfer Relationship to Planck's and Beer's laws Schwarzschild's_equation_for_radiative_transfer > Relationship to Planck's and Beer's laws Both Beer's Law and Planck's Law can be derived from Schwarzschild's equation. In a sense, they are corollaries of Schwarzschild's equation. When the spectral intensity of radiation is not changing as it passes through a medium, dIλ = 0.
Generative Adversarial Network Summary Generative_Adversarial_Network A generative adversarial network (GAN) is a class of machine learning framework and a prominent framework for approaching generative AI. The concept was initially developed by Ian Goodfellow and his colleagues in June 2014. In a GAN, two neural networks contest with each other in the form of a zero-sum game, where one agent's gain is another agent's loss. Given a training set, this technique learns to generate new data with the same statistics as the training set.
Birthday attack Mathematics Birthday_attack > Mathematics However, determining the balance of a hash function will typically require all possible inputs to be calculated and thus is infeasible for popular hash functions such as the MD and SHA families. The subexpression ln ⁡ 1 1 − p {\displaystyle \ln {\frac {1}{1-p}}} in the equation for n ( p ; H ) {\displaystyle n(p;H)} is not computed accurately for small p {\displaystyle p} when directly translated into common programming languages as log(1/(1-p)) due to loss of significance. When log1p is available (as it is in C99) for example, the equivalent expression -log1p(-p) should be used instead. If this is not done, the first column of the above table is computed as zero, and several items in the second column do not have even one correct significant digit.
Bi-infinite sequence Definition Finite_sequence > Formal definition and basic properties > Definition {\displaystyle (a_{n}).} Here A is the domain, or index set, of the sequence.
Fundamental theorem of Galois theory Summary Fundamental_theorem_of_Galois_theory In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions in relation to groups. It was proved by Évariste Galois in his development of Galois theory. In its most basic form, the theorem asserts that given a field extension E/F that is finite and Galois, there is a one-to-one correspondence between its intermediate fields and subgroups of its Galois group. (Intermediate fields are fields K satisfying F ⊆ K ⊆ E; they are also called subextensions of E/F.)
Tiffeneau–Demjanov rearrangement Early development of mechanism Tiffeneau–Demjanov_rearrangement > Early development of mechanism Alkyl substitutions as opposed to aryl substitutions result in diminished TDRs. Smith and Baer assert that these observations support their mechanism. Since substitution stabilizes the carbonium ion after damnification, the resulting carbonium ion is more likely to react with a nucleophile present (water in this case) and not undergo rearrangement. Five member rings rearrange due to the ring strain encouraging the maneuver. This strain makes the carbocation unstable enough to cause a carbon to shift.
Fast INfrared Exoplanet Spectroscopy Survey Explorer Principle Fast_INfrared_Exoplanet_Spectroscopy_Survey_Explorer > Principle FINESSE would have measured the atmospheric light spectra of exoplanets transiting or eclipsing their parent star. The proposed spectrometer functions in the infrared (0.5-5.0 μm). It would have used a 75 cm diameter primary mirror.
Electrolytic capacitors Ripple current Electrolytic_capacitor > Electrical characteristics > Ripple current Non-sinusoidal ripple currents have to be analyzed and separated into their single sinusoidal frequencies by means of Fourier analysis and summarized by squared addition the single currents. I R = i 1 2 + i 2 2 + i 3 2 + i n 2 {\displaystyle I_{R}={\sqrt {{i_{1}}^{2}+{i_{2}}^{2}+{i_{3}}^{2}+{i_{n}}^{2}}}} In non-solid electrolytic capacitors the heat generated by the ripple current causes the evaporation of electrolytes, shortening the lifetime of the capacitors. Exceeding the limit tends to result in explosive failure.
Finite-difference frequency-domain Comparison with FDTD and FEM Finite-difference_frequency-domain > Comparison with FDTD and FEM The FDFD method is very similar to the finite element method (FEM), though there are some major differences. Unlike the FDTD method, there are no time steps that must be computed sequentially, thus making FDFD easier to implement. This might also lead one to imagine that FDFD is less computationally expensive; however, this is not necessarily the case. The FDFD method requires solving a sparse linear system, which even for simple problems can be 20,000 by 20,000 elements or larger, with over a million unknowns.
Hermitian matrix Main diagonal values are real Hermitian_matrix > Properties > Main diagonal values are real The entries on the main diagonal (top left to bottom right) of any Hermitian matrix are real. Only the main diagonal entries are necessarily real; Hermitian matrices can have arbitrary complex-valued entries in their off-diagonal elements, as long as diagonally-opposite entries are complex conjugates.
Shear wall Modeling techniques Shear_wall > Modeling techniques Modeling techniques have been progressively updated during the last two decades, moving from linear static to nonlinear dynamic, enabling more realistic representation of global behavior, and different failure modes. Different modeling techniques shear walls span from macro models such as modified beam-column elements, to micro models such as 3D finite element models. An appropriate modeling technique should: Be capable of predicting the inelastic response Incorporating important materials characteristics Simulate behavioural feature: Lap splice and Bar Slip Represent the migration of the neutral axis Tension stiffening Interaction of flexure and shear actionsDifferent models have been developed over time, including macro-models, vertical line element models, finite-element models, and multi-layer models. More recently, fiber-section beam-columns elements have become popular, as they can model most of the global response and failure modes properly, while avoiding sophistications associated with finite element models.
Prion protein Neurons and synapses Prion_protein > Function > Nervous system > Neurons and synapses PrP is present in both the pre- and post-synaptic compartments, with the greatest concentration in the pre-synaptic portion. Considering this and PrP's suite of behavioral influences, the neural cell functions and interactions are of particular interest. Based on the copper ligand, one proposed function casts PrP as a copper buffer for the synaptic cleft. In this role, the protein could serve as either a copper homeostasis mechanism, a calcium modulator, or a sensor for copper or oxidative stress.
Department of Genetics, University of Cambridge Summary Department_of_Genetics,_University_of_Cambridge The Department of Genetics is a department of the University of Cambridge that conducts research and teaching in genetics.
Size of groups, organizations, and communities Characteristics of larger groups Size_of_groups,_organizations,_and_communities > Characteristics of larger groups Certain things have to be done for a group to form and continue: people have to be motivated to come together and cooperate; goals must be set; tasks assigned, scheduled, and carried out; problems solved. A few people who trust each other and share an important purpose can sometimes do all of that in a spontaneous and equalitarian way. Large groups almost always depend on recognized leaders to manage operations. Diversity increases, providing more resources for problem solving but impeding communication and cooperation and making consensus more difficult to reach. Bureaucratic procedures tend to develop, such as assigning different tasks to different subgroups and adopting standard procedures.
OBject EXchange Comparison to HTTP OBject_EXchange > Comparison to HTTP Other such "bindings" of OBEX are possible, such as over USB. HTTP uses human-readable text, but OBEX uses binary-formatted type–length–value triplets named "Headers" to exchange information about a request or an object. These are much easier to parse by resource-limited devices.
Evaluation methods Standards Evaluation_methods > Standards They provide guidelines about basing value judgments on systematic inquiry, evaluator competence and integrity, respect for people, and regard for the general and public welfare.The American Evaluation Association has created a set of Guiding Principles for evaluators. The order of these principles does not imply priority among them; priority will vary by situation and evaluator role.
Nephrotic syndrome Diagnosis Nephrotic_syndrome > Diagnosis Electrolytes and urea levels may also be analysed at the same time as creatinine (EUC test) in order to evaluate kidney function. A lipid profile will also be carried out as high levels of cholesterol (hypercholesterolemia), specifically elevated LDL, usually with concomitantly elevated VLDL, is indicative of nephrotic syndrome.A kidney biopsy may also be used as a more specific and invasive test method. A study of a sample's anatomical pathology may then allow the identification of the type of glomerulonephritis involved. However, this procedure is usually reserved for adults as the majority of children experience minimal change disease that has a remission rate of 95% with corticosteroids. A biopsy is usually only indicated for children that are corticosteroid resistant as the majority have focal and segmental glomeruloesclerosis.Further investigations are indicated if the cause is not clear including analysis of auto-immune markers (ANA, ASOT, C3, cryoglobulins, serum electrophoresis), or ultrasound of the whole abdomen.
Gravity model Summary Gravity_model Gravity models are used in various social sciences to predict and describe certain behaviors that mimic gravitational interaction as described in Isaac Newton's laws of gravity. Generally, the social science models contain some elements of mass and distance, which lends them to the metaphor of physical gravity. A gravity model provides an estimate of the volume of flows of, for example, goods, services, or people between two or more locations. This could be the movement of people between cities or the volume of trade between countries. A gravity model cannot accurately predict flows, but is instead a measure against which actual observed values can be compared, highlighting where those flows are unexpectedly high or low. Social science gravity models: Gravity model of trade Trip distribution Gravity model of migration Two-step floating catchment area (2SFCA) method Reilly's law of retail gravitation == References ==
Periodic table group Summary Group_(periodic_table) Similar variation on the inner transition metals continues to exist in textbooks, although the correct positioning has been known since 1948 and was twice endorsed by IUPAC in 1988 (together with the 1–18 numbering) and 2021. Groups may also be identified using their topmost element, or have a specific name. For example, group 16 is also described as the "oxygen group" and as the "chalcogens". An exception is the "iron group", which usually refers to "group 8", but in chemistry may also mean iron, cobalt, and nickel, or some other set of elements with similar chemical properties. In astrophysics and nuclear physics, it usually refers to iron, cobalt, nickel, chromium, and manganese.
Reproducing kernel particle method History Reproducing_kernel_particle_method > History One of the earliest meshfree methods is smoothed particle hydrodynamics, presented in 1977. Libersky et al. were the first to apply SPH in solid mechanics. The main drawbacks of SPH are inaccurate results near boundaries and tension instability that was first investigated by Swegle.In the 1990s a new class of meshfree methods emerged based on the Galerkin method. This first method called the diffuse element method (DEM), pioneered by Nayroles et al., utilized the MLS approximation in the Galerkin solution of partial differential equations, with approximate derivatives of the MLS function.
Re-entry vehicle Actively cooled Ballistic_reentry > Thermal protection systems > Actively cooled Advantages included the possibility of more all-metal designs which would be cheaper to develop, be more rugged, and eliminate the need for classified and unknown technology. The disadvantages are increased weight and complexity, and lower reliability. The concept has never been flown, but a similar technology (the plug nozzle) did undergo extensive ground testing.
Bayes' Rule Drug testing Bayes_rule > Examples > Drug testing Suppose, a particular test for whether someone has been using cannabis is 90% sensitive, meaning the true positive rate (TPR) = 0.90. Therefore, it leads to 90% true positive results (correct identification of drug use) for cannabis users. The test is also 80% specific, meaning true negative rate (TNR) = 0.80.
Absorbance Logarithmic vs. directly proportional measurements Absorbance > Measurements > Logarithmic vs. directly proportional measurements The amount of light transmitted through a material diminishes exponentially as it travels through the material, according to the Beer–Lambert law (A=(ε)(l)). Since the absorbance of a sample is measured as a logarithm, it is directly proportional to the thickness of the sample and to the concentration of the absorbing material in the sample. Some other measures related to absorption, such as transmittance, are measured as a simple ratio so they vary exponentially with the thickness and concentration of the material.
Programming language research Timeline Programming_language_theory > History > Timeline A team of scientists at Xerox PARC led by Alan Kay develop Smalltalk, an object-oriented language widely known for its innovative development environment. In 1974, John C. Reynolds discovers System F. It had already been discovered in 1971 by the mathematical logician Jean-Yves Girard. From 1975, Gerald Jay Sussman and Guy Steele develop the Scheme programming language, a Lisp dialect incorporating lexical scoping, a unified namespace, and elements from the actor model including first-class continuations.
Summary statistics Summary Summary_statistic In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in a measure of location, or central tendency, such as the arithmetic mean a measure of statistical dispersion like the standard mean absolute deviation a measure of the shape of the distribution like skewness or kurtosis if more than one variable is measured, a measure of statistical dependence such as a correlation coefficientA common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot. Entries in an analysis of variance table can also be regarded as summary statistics. : 378
Unnormalized sinc function Series expansion Unnormalized_sinc_function > Series expansion The Taylor series of the unnormalized sinc function can be obtained from that of the sine (which also yields its value of 1 at x = 0): The series converges for all x. The normalized version follows easily: Euler famously compared this series to the expansion of the infinite product form to solve the Basel problem.
Deoxyribonuclease I Summary DNase_I However, since actin-bound DNase I is enzymatically inactive, the DNase-actin complex might be a storage form of DNase I that prevents damage of the genetic information. This protein is stored in the zymogen granules of the nuclear envelope and functions by cleaving DNA in an endonucleolytic manner. At least six autosomal codominant alleles of the gene DNASE 1 have been characterized, DNASE11 through DNASE16, and the sequence of DNASE1*2 represented in this record.
Autoimmmune response Pathogenesis of autoimmunity Epitope_spreading > Pathogenesis of autoimmunity However, there is nothing as far as we know that requires this. All that is required is that a B cell recognising antigen X endocytoses and processes a protein Y (normally =X) and presents it to a T cell. Roosnek and Lanzavecchia showed that B cells recognising IgGFc could get help from any T cell responding to an antigen co-endocytosed with IgG by the B cell as part of an immune complex.
Chronic hepatitis B Cirrhosis Hepatitis_B > Prognosis > Cirrhosis A number of different tests are available to determine the degree of cirrhosis present. Transient elastography (FibroScan) is the test of choice, but it is expensive. Aspartate aminotransferase to platelet ratio index may be used when cost is an issue.
Stephen Childress Published books Stephen_Childress > Published books 2012: Natural Locomotion in Fluids and on Surfaces Swimming, Flying, and Sliding. Edited with Anette Hosoi, William W. Schultz, Jane Wang. Hardcover ISBN 978-1-4614-3996-7, Softcover ISBN 978-1-4899-9916-0, eBook ISBN 978-1-4614-3997-4 2018: Construction of Steady-state Hydrodynamic Dynamos. I. Spatially Periodic Fields, ISBN 978-1378904725
The Limits to Growth Method The_Limits_to_Growth > Method The World3 model is based on five variables: "population, food production, industrialization, pollution, and consumption of nonrenewable natural resources". : 25 At the time of the study, all these variables were increasing and were assumed to continue to grow exponentially, while the ability of technology to increase resources grew only linearly. The authors intended to explore the possibility of a sustainable feedback pattern that would be achieved by altering growth trends among the five variables under three scenarios.
Consumer behaviour Evaluation of alternatives Consumer_behaviour > The purchase decision and its context > Evaluation of alternatives Consumer evaluation can be viewed as a distinct stage. Alternatively, evaluation may occur continuously throughout the entire decision process. Consumers evaluate alternatives in terms of the functional (also called utilitarian) and psycho-social (also called the value-expressive or the symbolic) benefits offered. Functional benefits are the tangible outcomes that can be experienced by the consumer such as taste or physical appearance.

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