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Bit vectors Definition Bit_vectors > Definition Whether the least significant bit (of the word) or the most significant bit indicates the smallest-index number is largely irrelevant, but the former tends to be preferred (on little-endian machines). A finite binary relation may be represented by a bit array called a logical matrix. In the calculus of relations, these arrays are composed with matrix multiplication where the arithmetic is Boolean, and such a composition represents composition of relations.
Vacuum energy Origin Vacuum_energy > Origin {\displaystyle {E}={\frac {1}{2}}h\nu .} Summing over all possible oscillators at all points in space gives an infinite quantity.
Higher-order programming Summary Higher-order_programming Higher-order programming is a style of computer programming that uses software components, like functions, modules or objects, as values. It is usually instantiated with, or borrowed from, models of computation such as lambda calculus which make heavy use of higher-order functions. A programming language can be considered higher-order if components, such as procedures or labels, can be used just like data. For example, these elements could be used in the same way as arguments or values.For example, in higher-order programming, one can pass functions as arguments to other functions and functions can be the return value of other functions (such as in macros or for interpreting).
Function prototype Summary Function_prototype In computer programming, a function prototype or function interface is a declaration of a function that specifies the function’s name and type signature (arity, data types of parameters, and return type), but omits the function body. While a function definition specifies how the function does what it does (the "implementation"), a function prototype merely specifies its interface, i.e. what data types go in and come out of it. The term "function prototype" is particularly used in the context of the programming languages C and C++ where placing forward declarations of functions in header files allows for splitting a program into translation units, i.e. into parts that a compiler can separately translate into object files, to be combined by a linker into an executable or a library. The function declaration precedes the function definition, giving details of name, return type, and storage class along with other relevant attributes.Function prototypes can be used when either: Defining an ExternalType Creating an Interface partIn a prototype, parameter names are optional (and in C/C++ have function prototype scope, meaning their scope ends at the end of the prototype), however, the type is necessary along with all modifiers (e.g. if it is a pointer or a reference to const parameter) except const alone. In object-oriented programming, interfaces and abstract methods serve much the same purpose.
Darwin term Spin–orbit coupling Fine_structure > The hydrogen atom > Spin–orbit coupling The two magnetic vectors, B {\displaystyle \mathbf {B} } and μ s {\displaystyle {\boldsymbol {\mu }}_{s}} couple together so that there is a certain energy cost depending on their relative orientation. This gives rise to the energy correction of the form Notice that an important factor of 2 has to be added to the calculation, called the Thomas precession, which comes from the relativistic calculation that changes back to the electron's frame from the nucleus frame. Since by Kramers–Pasternack relations and the expectation value for the Hamiltonian is: Thus the order of magnitude for the spin–orbital coupling is Z 4 n 3 ( j + 1 / 2 ) 10 − 5 eV {\displaystyle {\frac {Z^{4}}{n^{3}(j+1/2)}}10^{-5}{\text{ eV}}} . When weak external magnetic fields are applied, the spin–orbit coupling contributes to the Zeeman effect.
Privacy rights An individual right Privacy_rights > History > An individual right — Alan Westin, Privacy and Freedom, 1968 Under liberal democratic systems, privacy creates a space separate from political life, and allows personal autonomy, while ensuring democratic freedoms of association and expression. Privacy to individuals is the ability to behave, think, speak, and express ideas without the monitoring or surveillance of someone else.
Ionic meter Summary Ionic_meter The ionic (or Ionic) is a four-syllable metrical unit (metron) of light-light-heavy-heavy (u u – –) that occurs in ancient Greek and Latin poetry. According to Hephaestion it was known as the Ionicos because it was used by the Ionians of Asia Minor; and it was also known as the Persicos and was associated with Persian poetry. Like the choriamb, in Greek quantitative verse the ionic never appears in passages meant to be spoken rather than sung. "Ionics" may refer inclusively to poetry composed of the various metrical units of the same total quantitative length (six morae) that may be used in combination with ionics proper: ionics, choriambs, and anaclasis. Equivalent forms exist in English poetry and in classical Persian poetry.
Minkowski space-time Standard basis Minkowski_Space > Mathematical structure > Standard basis The spatial components of a 4-vector v may be identified with a 3-vector v = (v1, v2, v3). In terms of components, the Minkowski inner product between two vectors v and w is given by and Here lowering of an index with the metric was used. There are many possible choices of standard basis obeying the condition η ( e μ , e ν ) = η μ ν .
Periodic table of elements Atomic radius Periodic_table_of_chemical_elements > Periodic trends > Atomic radius These relativistic effects result in heavy elements increasingly having differing properties compared to their lighter homologues in the periodic table. Spin–orbit interaction splits the p-subshell: one p-orbital is relativistically stabilised and shrunken (it fills in thallium and lead), but the other two (filling in bismuth through radon) are relativistically destabilised and expanded.
Sort algorithms Quicksort Sort_algorithms > Popular sorting algorithms > Efficient sorts > Quicksort Finding the median, such as by the median of medians selection algorithm is however an O(n) operation on unsorted lists and therefore exacts significant overhead with sorting. In practice choosing a random pivot almost certainly yields O(n log n) performance.
Maximum absolute deviation Median absolute deviation around a central point Mean_absolute_deviation > Median absolute deviation around a central point While in principle the mean or any other central point could be taken as the central point for the median absolute deviation, most often the median value is taken instead.
Female figure Proportions and dimensions Female_body > Proportions and dimensions The circumferences of bust, waist, and hips (BWH) and the ratios between them are a widespread method of identifying different female body shapes. As noted above, descriptive terms used include "rectangle", "spoon", "inverted triangle", and "hourglass".The waist is typically smaller than the bust and hips, unless there is a high proportion of body fat distributed around it. How much the bust or hips inflect inward, towards the waist, determines a woman's structural shape. The hourglass shape is present in only about 8% of women.A woman's dimensions are often expressed by the circumference around the three inflection points.
Spin (aerodynamic) History Spin_(aerodynamic) > History However, understanding and being able to recover from spins is certainly a skill that a fixed-wing pilot could learn for safety. It is routinely given as part of the training in sailplanes, since gliders often operate slowly enough to be in near-stall conditions while turning. Because of this, in the U.S.
Thermal fluctuation Summary Thermal_fluctuations Thermal fluctuations are a source of noise in many systems. The random forces that give rise to thermal fluctuations are a source of both diffusion and dissipation (including damping and viscosity). The competing effects of random drift and resistance to drift are related by the fluctuation-dissipation theorem. Thermal fluctuations play a major role in phase transitions and chemical kinetics.
MO diagram Dihelium and diberyllium MO_diagram > Diatomic MO diagrams > Dihelium and diberyllium Another molecule that is precluded based on this principle is diberyllium. Beryllium has an electron configuration 1s22s2, so there are again two electrons in the valence level. However, the 2s can mix with the 2p orbitals in diberyllium, whereas there are no p orbitals in the valence level of hydrogen or helium.
Scientific theory Essential criteria Scientific_theories > Characteristics > Essential criteria For any theory to be accepted within most academia there is usually one simple criterion. The essential criterion is that the theory must be observable and repeatable. The aforementioned criterion is essential to prevent fraud and perpetuate science itself. The defining characteristic of all scientific knowledge, including theories, is the ability to make falsifiable or testable predictions.
Eye piece Field of view Ocular_lens > Properties > Field of view The field of view, often abbreviated FOV, describes the area of a target (measured as an angle from the location of viewing) that can be seen when looking through an eyepiece. The field of view seen through an eyepiece varies, depending on the magnification achieved when connected to a particular telescope or microscope, and also on properties of the eyepiece itself. Eyepieces are differentiated by their field stop, which is the narrowest aperture that light entering the eyepiece must pass through to reach the field lens of the eyepiece. Due to the effects of these variables, the term "field of view" nearly always refers to one of two meanings: Actual field of view The angular size of the amount of sky that can be seen through an eyepiece when used with a particular telescope, producing a specific magnification.
Glossary of calculus H Glossary_of_calculus > H A first order differential equation is said to be homogeneous if it may be written f ( x , y ) d y = g ( x , y ) d x , {\displaystyle f(x,y)dy=g(x,y)dx,} where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form d x x = h ( u ) d u , {\displaystyle {\frac {dx}{x}}=h(u)du,} which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives. In the case of linear differential equations, this means that there are no constant terms. The solutions of any linear ordinary differential equation of any order may be deduced by integration from the solution of the homogeneous equation obtained by removing the constant term. hyperbolic function Hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
Scoring rule Summary Proper_score_function On the other side, a scoring function provides a summary measure for the evaluation of point predictions, i.e. one predicts a property or functional T ( F ) {\displaystyle T(F)} , like the expectation or the median. Scoring rules and scoring functions can be thought of as "cost function" or "loss function". They are evaluated as empirical mean of a given sample, simply called score.
Einstein synchronisation Literature Einstein_protocol > Literature Darrigol, Olivier (2005), "The Genesis of the theory of relativity" (PDF), Séminaire Poincaré, 1: 1–22, Bibcode:2006eins.book....1D, doi:10.1007/3-7643-7436-5_1, ISBN 978-3-7643-7435-8 D. Dieks, Becoming, relativity and locality, in The Ontology of Spacetime, online D. Dieks (ed. ), The Ontology of Spacetime, Elsevier 2006, ISBN 0-444-52768-0 D. Malament, 1977. "Causal Theories of Time and the Conventionality of Simultaniety," Noûs 11, 293–300.
Approximate Bayesian Computation General risks in statistical inference exacerbated in ABC Approximate_Bayesian_Computation > Pitfalls and remedies > General risks in statistical inference exacerbated in ABC This section reviews risks that are strictly speaking not specific to ABC, but also relevant for other statistical methods as well. However, the flexibility offered by ABC to analyze very complex models makes them highly relevant to discuss here.
Hypothyroidism Signs and symptoms Hypothyroidism > Signs and symptoms People with hypothyroidism often have no or only mild symptoms. Numerous symptoms and signs are associated with hypothyroidism and can be related to the underlying cause, or a direct effect of having not enough thyroid hormones. Hashimoto's thyroiditis may present with the mass effect of a goitre (enlarged thyroid gland). In middle-aged women, the symptoms may be mistaken for those of menopause. Delayed relaxation after testing the ankle jerk reflex is a characteristic sign of hypothyroidism and is associated with the severity of the hormone deficit.
English determiners Summary English_determiners The determinative function is typically obligatory in a singular, countable, common noun phrase (compare I have a new cat to I have new cat). Semantically, determiners are usually definite or indefinite (e.g., the cat versus a cat), and they often agree with the number of the head noun (e.g., a new cat but not many new cat). Morphologically, they are usually simple and do not inflect.
Opposite vector Representations Antiparallel_vector > Representations As an example in two dimensions (see figure), the vector from the origin O = (0, 0) to the point A = (2, 3) is simply written as The notion that the tail of the vector coincides with the origin is implicit and easily understood. Thus, the more explicit notation O A → {\displaystyle {\overrightarrow {OA}}} is usually deemed not necessary (and is indeed rarely used). In three dimensional Euclidean space (or R3), vectors are identified with triples of scalar components: also written, This can be generalised to n-dimensional Euclidean space (or Rn).
Hierarchical Temporal Memory The validity of the CLAs Hierarchical_Temporal_Memory > As an evolving model > Second generation: cortical learning algorithms > The validity of the CLAs The following question was posed to Jeff Hawkins in September 2011 with regard to cortical learning algorithms: "How do you know if the changes you are making to the model are good or not?" To which Jeff's response was "There are two categories for the answer: one is to look at neuroscience, and the other is methods for machine intelligence. In the neuroscience realm, there are many predictions that we can make, and those can be tested. If our theories explain a vast array of neuroscience observations then it tells us that we’re on the right track.
Voltage converter AC and DC Voltage_converter > AC and DC AC voltage conversion uses a transformer. Conversion from one DC voltage to another requires electronic circuitry (electromechanical equipment was required before the development of semiconductor electronics), like a DC-DC converter. Mains power (called household current in the US) is universally AC.
Vaccine overload Effectiveness Vaccine_hesitancy > Effectiveness Studies have been done that compare vaccinated to unvaccinated people, but the studies are typically not randomized. Moreover, literature already exists that demonstrates the safety of vaccines using other experimental methods.Other critics argue that the immunity granted by vaccines is only temporary and requires boosters, whereas those who survive the disease become permanently immune. As discussed below, the philosophies of some alternative medicine practitioners are incompatible with the idea that vaccines are effective.
LIRS caching algorithm Quantifying the locality LIRS_caching_algorithm > Summary > Quantifying the locality . . . . ^----Reuse Distance---^--Recency--^ T1 T2 T3
Energy Storage Aluminum Gravitational_potential_energy_storage > Methods > Chemical > Biofuels > Aluminum Aluminum has been proposed as an energy store by a number of researchers. Its electrochemical equivalent (8.04 Ah/cm3) is nearly four times greater than that of lithium (2.06 Ah/cm3). Energy can be extracted from aluminum by reacting it with water to generate hydrogen. However, it must first be stripped of its natural oxide layer, a process which requires pulverization, chemical reactions with caustic substances, or alloys. The byproduct of the reaction to create hydrogen is aluminum oxide, which can be recycled into aluminum with the Hall–Héroult process, making the reaction theoretically renewable. If the Hall-Heroult Process is run using solar or wind power, aluminum could be used to store the energy produced at higher efficiency than direct solar electrolysis.
Rocket body Energy efficiency Rocket_launch > Physics > Energy > Energy efficiency Since the energy ultimately comes from fuel, these considerations mean that rockets are mainly useful when a very high speed is required, such as ICBMs or orbital launch. For example, NASA's Space Shuttle fired its engines for around 8.5 minutes, consuming 1,000 tonnes of solid propellant (containing 16% aluminium) and an additional 2,000,000 litres of liquid propellant (106,261 kg of liquid hydrogen fuel) to lift the 100,000 kg vehicle (including the 25,000 kg payload) to an altitude of 111 km and an orbital velocity of 30,000 km/h. At this altitude and velocity, the vehicle had a kinetic energy of about 3 TJ and a potential energy of roughly 200 GJ.
Zero is even Students' knowledge Evenness_of_zero > Education > Students' knowledge The chart on the right depicts children's beliefs about the parity of zero, as they progress from Year 1 to Year 6 of the English education system. The data is from Len Frobisher, who conducted a pair of surveys of English schoolchildren. Frobisher was interested in how knowledge of single-digit parity translates to knowledge of multiple-digit parity, and zero figures prominently in the results.In a preliminary survey of nearly 400 seven-year-olds, 45% chose even over odd when asked the parity of zero. A follow-up investigation offered more choices: neither, both, and don't know.
Jeyes Fluid Composition Jeyes_Fluid > Composition It has a pH between 8.0 and 10.0 (moderately alkaline).
Influential observations Outliers, leverage and influence Influential_observation > Outliers, leverage and influence An outlier may be defined as a data point that differs significantly from other observations. A high-leverage point are observations made at extreme values of independent variables. Both types of atypical observations will force the regression line to be close to the point. In Anscombe's quartet, the bottom right image has a point with high leverage and the bottom left image has an outlying point.
Gas gangrene Pathophysiology Gas_gangrene > Pathophysiology If the necrotic damage is allowed to continue throughout an affected limb, then often that entire limb is lost permanently.It is often difficult to identify the extent of muscle damage, as C. perfringens may be at work in deeper fascial layers below the skin. Unlike other anaerobic infections, discharge in these infections is often not purulent (filled with pus). Instead, the discharge is often described as "sweetly putrid" or "dishwater pus" because it is much thinner than normal pus.
Hydrational fluid Reduced-osmolarity Oral_rehydration_therapy > Preparation > Reduced-osmolarity In 2003, WHO and UNICEF recommended that the osmolarity of oral rehydration solution be reduced from 311 to 245 mOsm/L. These guidelines were also updated in 2006. This recommendation was based on multiple clinical trials showing that the reduced osmolarity solution reduces stool volume in children with diarrhea by about twenty-five percent and the need for IV therapy by about thirty percent when compared to standard oral rehydration solution.
Virtual computer History Virtual_Machine > History Both system virtual machines and process virtual machines date to the 1960s and remain areas of active development. System virtual machines grew out of time-sharing, as notably implemented in the Compatible Time-Sharing System (CTSS). Time-sharing allowed multiple users to use a computer concurrently: each program appeared to have full access to the machine, but only one program was executed at the time, with the system switching between programs in time slices, saving and restoring state each time. This evolved into virtual machines, notably via IBM's research systems: the M44/44X, which used partial virtualization, and the CP-40 and SIMMON, which used full virtualization, and were early examples of hypervisors.
Micro-g environment Weightlessness in Newtonian mechanics Micro-g_environment > Weightlessness in Newtonian mechanics Speed, not position or lack of gravity, keeps satellites in orbit around the Earth. From the perspective of an observer not moving with the object (i.e. in an inertial reference frame) the force of gravity on an object in free fall is exactly the same as usual. A classic example is an elevator car where the cable has been cut and it plummets toward Earth, accelerating at a rate equal to the 9.81 meters per second per second.
Graph algorithm Routing for graphs List_of_algorithms > Combinatorial algorithms > Graph algorithms > Routing for graphs Edmonds' algorithm (also known as Chu–Liu/Edmonds' algorithm): find maximum or minimum branchings Euclidean minimum spanning tree: algorithms for computing the minimum spanning tree of a set of points in the plane Longest path problem: find a simple path of maximum length in a given graph Minimum spanning tree Borůvka's algorithm Kruskal's algorithm Prim's algorithm Reverse-delete algorithm Nonblocking minimal spanning switch say, for a telephone exchange Shortest path problem Bellman–Ford algorithm: computes shortest paths in a weighted graph (where some of the edge weights may be negative) Dijkstra's algorithm: computes shortest paths in a graph with non-negative edge weights Floyd–Warshall algorithm: solves the all pairs shortest path problem in a weighted, directed graph Johnson's algorithm: all pairs shortest path algorithm in sparse weighted directed graph Transitive closure problem: find the transitive closure of a given binary relation Traveling salesman problem Christofides algorithm Nearest neighbour algorithm Warnsdorff's rule: a heuristic method for solving the Knight's tour problem
Photo-active material Photoluminescence properties of direct-gap semiconductors Photoluminescence > Photoluminescence properties of direct-gap semiconductors In a typical PL experiment, a semiconductor is excited with a light-source that provides photons with an energy larger than the bandgap energy. The incoming light excites a polarization that can be described with the semiconductor Bloch equations. Once the photons are absorbed, electrons and holes are formed with finite momenta k {\displaystyle \mathbf {k} } in the conduction and valence bands, respectively. The excitations then undergo energy and momentum relaxation towards the band-gap minimum.
Log driving History Log_driving > History When the first sawmills were established, they were usually small water-powered facilities located near the source of timber, which might be converted to grist mills after farming became established when the forests had been cleared. Later, bigger circular sawmills were developed in the lower reaches of a river, with the logs floated down to them by log drivers. In the broader, slower stretches of a river, the logs might be bound together into timber rafts. In the smaller, wilder stretches of a river where rafts couldn't get through, masses of individual logs were driven down the river like huge herds of cattle.
Einstein–Cartan theory Overview Einstein–Cartan_theory > Overview The chief difference between a Riemann–Cartan geometry and Riemannian geometry is that in the former, the affine connection is independent of the metric, while in the latter it is derived from the metric as the Levi-Civita connection, the difference between the two being referred to as the contorsion. In particular, the antisymmetric part of the connection (referred to as the torsion) is zero for Levi-Civita connections, as one of the defining conditions for such connections. Because the contorsion can be expressed linearly in terms of the torsion, then is also possible to directly translate the Einstein–Hilbert action into a Riemann–Cartan geometry, the result being the Palatini action (see also Palatini variation).
Screw threads Summary Screw_thread In most applications, the lead of a screw thread is chosen so that friction is sufficient to prevent linear motion being converted to rotary, that is so the screw does not slip even when linear force is applied, as long as no external rotational force is present. This characteristic is essential to the vast majority of its uses. The tightening of a fastener's screw thread is comparable to driving a wedge into a gap until it sticks fast through friction and slight elastic deformation.
Periodic table of topological invariants Classification of invariants Periodic_table_of_topological_invariants > Classification of invariants The strong topological invariants of a many-band system in d {\displaystyle d} dimensions can be labeled by the elements of the d {\displaystyle d} -th homotopy group of the symmetric space. These groups are displayed in this table, called the periodic table of topological insulators: There may also exist weak topological invariants (associated to the fact that the suspension of the Brillouin zone is in fact equivalent to a d + 1 {\displaystyle d+1} sphere wedged with lower-dimensional spheres), which are not included in this table. Furthermore, the table assumes the limit of an infinite number of bands, i.e. involves N × N {\displaystyle N\times N} Hamiltonians for N → ∞ {\displaystyle N\to \infty } .
Dedekind-Peano axioms Set-theoretic models Overspill_(arithmetic) > Historical second-order formulation > Models > Set-theoretic models The Peano axioms can be derived from set theoretic constructions of the natural numbers and axioms of set theory such as ZF. The standard construction of the naturals, due to John von Neumann, starts from a definition of 0 as the empty set, ∅, and an operator s on sets defined as: s ( a ) = a ∪ { a } {\displaystyle s(a)=a\cup \{a\}} The set of natural numbers N is defined as the intersection of all sets closed under s that contain the empty set. Each natural number is equal (as a set) to the set of natural numbers less than it: 0 = ∅ 1 = s ( 0 ) = s ( ∅ ) = ∅ ∪ { ∅ } = { ∅ } = { 0 } 2 = s ( 1 ) = s ( { 0 } ) = { 0 } ∪ { { 0 } } = { 0 , { 0 } } = { 0 , 1 } 3 = s ( 2 ) = s ( { 0 , 1 } ) = { 0 , 1 } ∪ { { 0 , 1 } } = { 0 , 1 , { 0 , 1 } } = { 0 , 1 , 2 } {\displaystyle {\begin{aligned}0&=\emptyset \\1&=s(0)=s(\emptyset )=\emptyset \cup \{\emptyset \}=\{\emptyset \}=\{0\}\\2&=s(1)=s(\{0\})=\{0\}\cup \{\{0\}\}=\{0,\{0\}\}=\{0,1\}\\3&=s(2)=s(\{0,1\})=\{0,1\}\cup \{\{0,1\}\}=\{0,1,\{0,1\}\}=\{0,1,2\}\end{aligned}}} and so on. The set N together with 0 and the successor function s: N → N satisfies the Peano axioms.
Chemoreceptor Physiology Chemoreceptor > Physiology Carotid bodies and aortic bodies detect changes primarily in pCO2 and H+ ion concentration. They also sense decrease in partial pressure of O2, but to a lesser degree than for pCO2 and H+ ion concentration. The chemoreceptor trigger zone is an area of the medulla in the brain that receives inputs from blood-borne drugs or hormones, and communicates with the vomiting center (area postrema) to induce vomiting. Primary cilia play important roles in chemosensation. In adult tissues, these cilia regulate cell proliferation in response to external stimuli, such as tissue damage. In humans, improper functioning of primary cilia is associated with important diseases known as ciliopathies.
Self-confrontation method Valuation theory Self-confrontation_method > Theories > Valuation theory He believes that story or narrative is a method for organizing one's plot and action. In addition, he explains that narratives organize people's silent stories, fantasies and daydreams, plans, memories, and even love and hates. The central factors of the narrative are real or fictional events that can only be understood in the context of time and space.
Protein aggregates Aggregate localization Protein_aggregates > Aggregate localization Several studies have shown that cellular responses to protein aggregation are well-regulated and organized. Protein aggregates localize to specific areas in the cell, and research has been done on these localizations in prokaryotes (E.coli) and eukaryotes (yeast, mammalian cells).
Work-energy theorem Derivation for a particle moving along a straight line Work_(physics) > Work–energy principle > Derivation for a particle moving along a straight line In the case the resultant force F is constant in both magnitude and direction, and parallel to the velocity of the particle, the particle is moving with constant acceleration a along a straight line. The relation between the net force and the acceleration is given by the equation F = ma (Newton's second law), and the particle displacement s can be expressed by the equation which follows from v 2 2 = v 1 2 + 2 a s {\displaystyle v_{2}^{2}=v_{1}^{2}+2as} (see Equations of motion). The work of the net force is calculated as the product of its magnitude and the particle displacement. Substituting the above equations, one obtains: Other derivation: In the general case of rectilinear motion, when the net force F is not constant in magnitude, but is constant in direction, and parallel to the velocity of the particle, the work must be integrated along the path of the particle:
Plasticity index Liquid limit Liquid_limit > Laboratory tests > Liquid limit The liquid limit (LL) is conceptually defined as the water content at which the behavior of a clayey soil changes from the plastic state to the liquid state. However, the transition from plastic to liquid behavior is gradual over a range of water contents, and the shear strength of the soil is not actually zero at the liquid limit. The precise definition of the liquid limit is based on standard test procedures described below.
Baker's map Summary Baker's_map In dynamical systems theory, the baker's map is a chaotic map from the unit square into itself. It is named after a kneading operation that bakers apply to dough: the dough is cut in half, and the two halves are stacked on one another, and compressed. The baker's map can be understood as the bilateral shift operator of a bi-infinite two-state lattice model. The baker's map is topologically conjugate to the horseshoe map.
Cumulative effects (environment) Energy production and consumption Cumulative_effects_(environment) > Factors contributing to cumulative effects > Energy production and consumption Additionally, the inundation of surrounding ecosystems by water results in a loss in terrestrial habitat and wildlife in the area. The energy production sector can result in many negative impacts on the environment, such as air pollution, acid rain, deforestation, emission of radioactive substances, and ozone depletion, all of which contribute to climate change. Energy production is associated with large amounts of infrastructure, such as power plants, pipelines, wind and solar farms, and dams, which contribute to the environmental effects of land use change.
Filter bag Wet scrubbers Filter_bag > Wet scrubbers The "cleaned" gases are normally passed through a mist eliminator (demister pads) to remove water droplets from the gas stream. The dirty water from the scrubber system is either cleaned and discharged or recycled to the scrubber. Dust is removed from the scrubber in a clarification unit or a drag chain tank. In both systems solid material settles on the bottom of the tank. A drag chain conveyor system removes the sludge and deposits in into a dumpster or stockpile.
Linnett Double-Quartet Theory Basic principles Linnett_Double-Quartet_Theory > Formulation of Linnett double-quartet theory > Basic principles A key trait of LDQ theory that is shared with Lewis theory is the importance of using formal charges to determine the most important electronic structure. LDQ theory produces the spatial distributions of the electrons by considering the two fundamental physical properties of said electrons: The mutual repulsion of electrons with like spins, in accordance with the Pauli exclusion principle. Hence, electrons with like (parallel) spins tend to keep as far away from each other as possible by refusing to occupy the same spatial region, while electrons with unlike (antiparallel) spins can occupy the same spatial region. This effect is known as ‘spin correlation’.
Pill testing Analysis technologies Pill_testing > Analysis technologies A range of analysis techniques are in use by drug checking services. The most common are reagent testing, fourier transform infrared spectroscopy, ultraviolet-visible spectroscopy, raman spectroscopy, and gas chromatography mass spectrometry. Reagent testing uses chemical indicators that show a colour change in the presence of particular drugs. These tests are widely available and affordable.
Molecular circuit Theoretical basis Molecular_circuit > Theoretical basis In inelastic tunneling, an elegant formalism based on the non-equilibrium Green's functions of Leo Kadanoff and Gordon Baym, and independently by Leonid Keldysh was advanced by Ned Wingreen and Yigal Meir. This Meir-Wingreen formulation has been used to great success in the molecular electronics community to examine the more difficult and interesting cases where the transient electron exchanges energy with the molecular system (for example through electron-phonon coupling or electronic excitations). Further, connecting single molecules reliably to a larger scale circuit has proven a great challenge, and constitutes a significant hindrance to commercialization.
Trace metal stable isotope biogeochemistry Chemistry Trace_metal_stable_isotope_biogeochemistry > Iron > Chemistry One of the most prevalent features of iron chemistry is its redox chemistry. Iron has three oxidation states: metallic iron (Fe0), ferrous iron (Fe2+), and ferric iron (Fe3+). Ferrous iron is the reduced form of iron, and ferric iron is the oxidized form of iron. In the presence of oxygen, ferrous iron is oxidized to ferric iron, thus ferric iron is the dominant redox state of iron at Earth's surface conditions.
Complex societies Summary Complex_societies A complex society is a concept that is shared by a range of disciplines including anthropology, archaeology, history and sociology to describe a stage of social formation. The concept was formulated by scholars attempting to understand how modern states emerged, specifically the transition from small kin-based societies to large hierarchically structured societies.A complex society is characterized by features such as: State with a large population wherein its economy is structured according to specialization and a division of labor. These economic features spawn a bureaucratic class and institutionalize inequality.
Depth-first search Properties Depth-first_search > Properties In the artificial intelligence mode of analysis, with a branching factor greater than one, iterative deepening increases the running time by only a constant factor over the case in which the correct depth limit is known due to the geometric growth of the number of nodes per level. DFS may also be used to collect a sample of graph nodes. However, incomplete DFS, similarly to incomplete BFS, is biased towards nodes of high degree.
Ada (programming language) History Ada_programming_language > History HOLWG crafted the Steelman language requirements, a series of documents stating the requirements they felt a programming language should satisfy. Many existing languages were formally reviewed, but the team concluded in 1977 that no existing language met the specifications. Requests for proposals for a new programming language were issued and four contractors were hired to develop their proposals under the names of Red (Intermetrics led by Benjamin Brosgol), Green (Honeywell, led by Jean Ichbiah), Blue (SofTech, led by John Goodenough) and Yellow (SRI International, led by Jay Spitzen).
Loop modeling Summary Loop_modeling More constrained versions of loop modeling are also used in the data fitting stages of solving a protein structure by X-ray crystallography, because loops can correspond to regions of low electron density and are therefore difficult to resolve. Regions of a structural model that are predicted by non-template-based loop modeling tend to be much less accurate than regions that are predicted using template-based techniques. The extent of the inaccuracy increases with the number of amino acids in the loop.
Feature learning Local linear embedding Feature_learning > Unsupervised > Local linear embedding Local linear embedding (LLE) is a nonlinear learning approach for generating low-dimensional neighbor-preserving representations from (unlabeled) high-dimension input. The approach was proposed by Roweis and Saul (2000). The general idea of LLE is to reconstruct the original high-dimensional data using lower-dimensional points while maintaining some geometric properties of the neighborhoods in the original data set. LLE consists of two major steps.
Hunting oscillation Mathematical analysis Hunting_oscillation > Railway wheelsets > Kinematic analysis > Mathematical analysis If the motion is substantially parallel with the rails, the angular displacement of the wheel set ( θ ) {\displaystyle \left(\theta \right)} is given by: Hence: The angular deflection also follows a simple harmonic motion, which lags behind the side to side motion by a quarter of a cycle. In many systems which are characterised by harmonic motion involving two different states (in this case the axle yaw deflection and the lateral displacement), the quarter cycle lag between the two motions endows the system with the ability to extract energy from the forward motion. This effect is observed in "flutter" of aircraft wings and "shimmy" of road vehicles, as well as hunting of railway vehicles.
Latent tuberculosis Latent disease Latent_tuberculosis > Transmission > Latent disease "It usually takes prolonged exposure to someone with active TB disease for someone to become infected. After exposure, it usually takes 8 to 10 weeks before the TB test would show if someone had become infected. "Depending on ventilation and other factors, these tiny droplets can remain suspended in the air for several hours.
Glossary of cell biology A Glossary_of_cell_biology > A acetyl-CoA A molecule that participates in many biochemical reactions in protein, carbohydrate, and lipid metabolism, notably the citric acid cycle. action potential The local change in voltage that occurs when the membrane potential of a specific location along the membrane of a cell rapidly depolarizes, such as when a nerve impulse is transmitted between neurons. active transport Transport of a substance (such as a protein or drug) across a cell membrane against a concentration gradient. Unlike passive transport, active transport requires an expenditure of energy.
Electron tunneling Faster than light Tunneling_Effect > Faster than light In particular, the group velocity of a wave packet does not measure its speed, but is related to the amount of time the wave packet is stored in the barrier. But the problem remains that the wave function still rises inside the barrier at all points at the same time. In other words, in any region that is inaccessible to measurement, non-local propagation is still mathematically certain. A 2020 experiment, overseen by Aephraim M. Steinberg, showed that particles should be able to tunnel at apparent speeds faster than light.
Carbonyl complex History Metal_carbonyl_complex > History In these reactions, for example, nickel tetracarbonyl or cobalt carbonyls act as catalysts. Reppe also discovered the cyclotrimerization and tetramerization of acetylene and its derivatives to benzene and benzene derivatives with metal carbonyls as catalysts.
T helper cell Hypersensitivity CD4(+)_T_cell > Role in disease > Hypersensitivity Antibodies do not play a direct role in this allergy type. T cells play an important role in this hypersensitivity, as they activate against the stimulus itself and promote the activation of other cells; particularly macrophages via Th1 cytokines.Other cellular hypersensitivities include cytotoxic T cell mediated auto-immune disease, and a similar phenomenon; transplant rejection. Helper T cells are required to fuel the development of these diseases.
Logarithmic algorithm Log tables Generic_logarithm > Logarithm tables, slide rules, and historical applications > Log tables These tables listed the values of log10 x for any number x in a certain range, at a certain precision. Base-10 logarithms were universally used for computation, hence the name common logarithm, since numbers that differ by factors of 10 have logarithms that differ by integers. The common logarithm of x can be separated into an integer part and a fractional part, known as the characteristic and mantissa.
Multidimensional discrete convolution Problem statement and basics Multidimensional_discrete_convolution > Definition > Problem statement and basics . . , k M ) x ( n 1 − k 1 , n 2 − k 2 , .
Empirical limits in science Summary Empirical_analysis However, empiricists may argue that traditions (or customs) arise due to relations of previous sensory experiences.Historically, empiricism was associated with the "blank slate" concept (tabula rasa), according to which the human mind is "blank" at birth and develops its thoughts only through later experience.Empiricism in the philosophy of science emphasizes evidence, especially as discovered in experiments. It is a fundamental part of the scientific method that all hypotheses and theories must be tested against observations of the natural world rather than resting solely on a priori reasoning, intuition, or revelation. Empiricism, often used by natural scientists, says that "knowledge is based on experience" and that "knowledge is tentative and probabilistic, subject to continued revision and falsification". Empirical research, including experiments and validated measurement tools, guides the scientific method.
Velocity vector Polar coordinates Velocity > Polar coordinates The expression m r 2 {\displaystyle mr^{2}} is known as moment of inertia. If forces are in the radial direction only with an inverse square dependence, as in the case of a gravitational orbit, angular momentum is constant, and transverse speed is inversely proportional to the distance, angular speed is inversely proportional to the distance squared, and the rate at which area is swept out is constant. These relations are known as Kepler's laws of planetary motion.
Salience (language) Communication studies Salience_(language) > Communication studies Another key aspect of whether a particular memory or knowledge will be activated is whether it is applicable to the situation. If it is not applicable, it will not be salient and is unlikely to be activated for that situation. "According to the synapse model…, the process begins with the stimulus, which increases the excitation level of stored knowledge as a function of the features of the match between the attended features of the stimulus and the features of the stored knowledge."
Ampere-Maxwell equation Extending the original law: the Ampère–Maxwell equation Ampère's_Law > Extending the original law: the Ampère–Maxwell equation On the other hand, treating all charges on the same footing (disregarding whether they are bound or free charges), the generalized Ampère's equation, also called the Maxwell–Ampère equation, is in integral form (see the "proof" section below): In differential form, In both forms J includes magnetization current density as well as conduction and polarization current densities. That is, the current density on the right side of the Ampère–Maxwell equation is: J f + J D + J M = J f + J P + J M + ε 0 ∂ E ∂ t = J + ε 0 ∂ E ∂ t , {\displaystyle \mathbf {J} _{\mathrm {f} }+\mathbf {J} _{\mathrm {D} }+\mathbf {J} _{\mathrm {M} }=\mathbf {J} _{\mathrm {f} }+\mathbf {J} _{\mathrm {P} }+\mathbf {J} _{\mathrm {M} }+\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}=\mathbf {J} +\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\,,} where current density JD is the displacement current, and J is the current density contribution actually due to movement of charges, both free and bound. Because ∇ ⋅ D = ρ, the charge continuity issue with Ampère's original formulation is no longer a problem.
DriveNets Technologies DriveNets > Technologies DriveNets markets a scalable network operating system (NOS) based on a cloud. The network cloud architecture creates a software routing framework that can grow linearly to a large scale from a centralized cloud. The company leverages Telco-hierarchy cloud design principles such as containerized microservices, shared facilities, and inexpensive white boxes. Another product that the company sells is a network operating system that relies on Ethernet to connect AI-optimized systems in a distributed cluster. The approach applies the Open Compute Project Distributed Disaggregated Chassis architecture, which enables AI clusters to scale at an adequate performance while keeping JCT low.
Immunotherapy of cancer Summary Cell_transfer_therapy Cancer immunotherapy (sometimes called immuno-oncology) is the stimulation of the immune system to treat cancer, improving on the immune system's natural ability to fight the disease. It is an application of the fundamental research of cancer immunology and a growing subspecialty of oncology. Cancer immunotherapy exploits the fact that cancer cells often have tumor antigens, molecules on their surface that can be detected by the antibody proteins of the immune system, binding to them.
Ethical AI Biases in AI systems AI_ethics > Ethical challenges > Biases in AI systems Friedman and Nissenbaum identify three categories of bias in computer systems: existing bias, technical bias, and emergent bias. In natural language processing, problems can arise from the text corpus — the source material the algorithm uses to learn about the relationships between different words.Large companies such as IBM, Google, etc. have made efforts to research and address these biases. One solution for addressing bias is to create documentation for the data used to train AI systems.
Jakob Nielsen (usability consultant) Articles Jakob_Nielsen_(usability_consultant) > Bibliography > Articles 413–414. doi:10.1145/259963.260531. ISBN 0897916514.
Inverse iteration Implementation options Inverse_power_iteration > Implementation options The method is defined by the formula: There are, however, multiple options for its implementation.
Matrix polar decomposition Alternative planar decompositions Matrix_polar_decomposition > Alternative planar decompositions In the Cartesian plane, alternative planar ring decompositions arise as follows:
Cardiovascular medicine The heart Cardiovascular_medicine > The heart The system that carries this potential is called the electrical conduction system. Dysfunction of the electrical system manifests in many ways and may include Wolff–Parkinson–White syndrome, ventricular fibrillation, and heart block.The mechanical system of the heart is centered on the fluidic movement of blood and the functionality of the heart as a pump. The mechanical part is ultimately the purpose of the heart and many of the disorders of the heart disrupt the ability to move blood. Heart failure is one condition in which the mechanical properties of the heart have failed or are failing, which means insufficient blood is being circulated. Failure to move a sufficient amount of blood through the body can cause damage or failure of other organs and may result in death if severe.
A-star algorithm Implementation details A-star_algorithm > Description > Implementation details If it does, then the priority and parent pointers are changed to correspond to the lower-cost path. A standard binary heap based priority queue does not directly support the operation of searching for one of its elements, but it can be augmented with a hash table that maps elements to their position in the heap, allowing this decrease-priority operation to be performed in logarithmic time. Alternatively, a Fibonacci heap can perform the same decrease-priority operations in constant amortized time.
Earth's circumference determination Posidonius Earth's_circumference_determination > History > Posidonius Posidonius calculated the Earth's circumference by reference to the position of the star Canopus. As explained by Cleomedes, Posidonius observed Canopus on but never above the horizon at Rhodes, while at Alexandria he saw it ascend as far as 7+1⁄2 degrees above the horizon (the meridian arc between the latitude of the two locales is actually 5 degrees 14 minutes). Since he thought Rhodes was 5,000 stadia due north of Alexandria, and the difference in the star's elevation indicated the distance between the two locales was 1/48 of the circle, he multiplied 5,000 by 48 to arrive at a figure of 240,000 stadia for the circumference of the earth. It is generally thought that the stadion used by Posidonius was almost exactly 1/10 of a modern statute mile.
Centrifugal clutch Operation Centrifugal_clutch > Operation As the load increases, the speed drops, disengaging the clutch, letting the speed rise again, and reengaging the clutch. If tuned properly, the clutch will tend to keep the speed at or near the torque peak of the engine. This results in a fair bit of waste heat, but over a broad range of speeds, it is much more useful than a direct drive in many applications.
Anion exchange membrane electrolysis Anode reaction Anion_exchange_membrane_electrolysis > Science > Reactions > Anode reaction Where the * indicate species adsorbed to the surface of the catalyst.
Theoretical framework Formality Theoretical_framework > Formality Theories are analytical tools for understanding, explaining, and making predictions about a given subject matter. There are theories in many and varied fields of study, including the arts and sciences. A formal theory is syntactic in nature and is only meaningful when given a semantic component by applying it to some content (e.g., facts and relationships of the actual historical world as it is unfolding). Theories in various fields of study are expressed in natural language, but are always constructed in such a way that their general form is identical to a theory as it is expressed in the formal language of mathematical logic.
Augmented sphenocorona Cartesian coordinates Augmented_sphenocorona > Cartesian coordinates To calculate Cartesian coordinates for the augmented sphenocorona, one may start by calculating the coordinates of the sphenocorona. Let k ≈ 0.85273 be the smallest positive root of the quartic polynomial 60 x 4 − 48 x 3 − 100 x 2 + 56 x + 23. {\displaystyle 60x^{4}-48x^{3}-100x^{2}+56x+23.}
MALT lymphoma Treatment Mucosa-associated_lymphoid_tissue_lymphoma > Treatment Owing to the causal relationship between H. pylori infection and MALT lymphoma, identification of the infection is imperative. Histological examination of GI biopsies yields a sensitivity of 95% with five biopsies, but these should be from sites uninvolved by lymphoma and the identification of the organism may be compromised by areas of extensive intestinal metaplasia. As proton-pump inhibition can suppress infection, any treatment with this class of drug should be ceased 2 weeks prior to biopsy retrieval.
Loop (CTA) Operations Loop_(CTA) > Operations Its trains run in both directions along the Lake and Wabash sides from Tower 18 to Tower 12, connecting the Lake Street branch and the South Side Elevated.In the CTA system, the entire loop taken as a whole is considered the termination point of a line, just like a single station or stop is considered the termination point when outside the downtown loop. Both of the 'L' lines with 24 hour service, the Blue Line and the Red Line, run in subways through the center of the Loop, and have both in-system and out-of-system transfers to Loop stations. The Yellow Line is the only 'L' line that does not run on or connect to the Loop.
Fetal warfarin syndrome Summary Fetal_warfarin_syndrome Warfarin is a teratogen which can cross from the mother to the developing fetus. The inhibition of clotting factors can lead to internal bleeding of the fetus while the inhibition of osteocalcin causes lower bone growth. As well as birth defects, warfarin can induce spontaneous abortion or stillbirth. Because of this, warfarin is contraindicated during pregnancy.
Eshelby's inclusion Summary Eshelby's_inclusion In that situation, the inclusion and the surrounding material remains in a stressed state. Also the strain states in the body and the inclusion are potentially inhomogeneous and complicated. Eshelby found that the resulting elastic field can be found using a "sequence of imaginary cutting, straining and welding operations." Eshelby's finding that the strain and stress field inside the ellipsoidal inclusion is uniform and has a closed-form solution, regardless of the material properties and initial transformation strain (also called the eigenstrain), has spawned a large amount of work in the mechanics of composites. The results find their applications in the effective medium theory for heterogeneous elastic materials.
Discrete component Classification Discrete_device > Classification Active components include amplifying components such as transistors, triode vacuum tubes (valves), and tunnel diodes. Passive components cannot introduce net energy into the circuit. They also cannot rely on a source of power, except for what is available from the (AC) circuit they are connected to.
Rational Choice Theory Overview Rational_Choice_Theory > Overview Contemporary theory bases rational choice on a set of choice axioms that need to be satisfied, and typically does not specify where the goal (preferences, desires) comes from. It mandates just a consistent ranking of the alternatives. : 501 Individuals choose the best action according to their personal preferences and the constraints facing them. E.g., there is nothing irrational in preferring fish to meat the first time, but there is something irrational in preferring fish to meat in one instant and preferring meat to fish in another, without anything else having changed.
Velocity addition Historical Velocity_addition_formula > References > Historical 57: 385–404. Fizeau, H. (1860).
Acetylene hydratase Summary Acetylene_hydratase This enzyme relies on tungsten as the metal center and is the heaviest metal that plays a prominent part in the nitrogen, sulfur and carbon metabolic processes. The cubane keeps the W in the reduced W(IV) state, the most stable reduced oxidation state, while W(VI) is the other stable oxidation state (2nd and 3rd row transition metals are usually most stable in their highest oxidation state). Mo and W enzymes ubiquitously involve W(IV)/W(VI) in the catalysis, however AH is very unique since the tungstoenzyme stays as W(IV) in the catalysis.
Taylor polynomial Summary Taylor_series In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century.
Concepts, Techniques, and Models of Computer Programming Summary Concepts,_Techniques,_and_Models_of_Computer_Programming Concepts, Techniques, and Models of Computer Programming is a textbook published in 2004 about general computer programming concepts from MIT Press written by Université catholique de Louvain professor Peter Van Roy and Royal Institute of Technology, Sweden professor Seif Haridi. Using a carefully selected progression of subsets of the Oz programming language, the book explains the most important programming concepts, techniques, and models (paradigms). Translations of this book have been published in French (by Dunod Éditeur, 2007), Japanese (by Shoeisha, 2007) and Polish (by Helion, 2005).
Friction extrusion Typical microstructure resulting from friction extrusion Friction_extrusion > Typical microstructure resulting from friction extrusion Figure 6 shows the cross section and microstructure of a titanium wire produced by friction extrusion of Ti-6-4 powder. Notably, the cross section is fully consolidated and the transformed b microstructure indicates that extrusion likely occurred near 1000 °C (above the beta transus for the alloy). Figure 7 shows grain size and crystallographic orientation typical of thin walled tubing extruded from AZ91 melt spun flake.
Polyphosphoric acid Phosphoric acid Phosphoric_acids > Acids > Phosphoric acid The simplest and most commonly encountered of the phosphoric acids is orthophosphoric acid, H3PO4. Indeed, the term phosphoric acid often means this compound specifically (and this is also the current IUPAC nomenclature).
Carbocation Structure and properties Carbocation > Structure and properties Carbonium ions can be thought of as protonated alkanes. Although alkanes are usually considered inert, under superacid conditions (e.g., HF/SbF5), the C-H sigma bond can act as a donor to H+. This results in a species that contains a 3c-2e bond between a carbon and two hydrogen atoms, a type of bonding common in boron chemistry, though relatively uncommon for carbon. As an alternative view point, the 3c-2e bond of carbonium ions could be considered as a molecule of H2 coordinated to a carbenium ion (see below).
McRae Formation Description McRae_Formation > Description The formation consists of a basal conglomerate interbedded with shale and siltstone and a sequence of alternating sandstone and shale. The lower conglomerates contain volcanic debris, while the upper beds contain sparse nonvolcanic rock fragments. The shales are reddish brown to purplish while the sandstones are light gray. The sandstones are medium bedded to massive and sometimes form hogbacks.

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