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Vector signal analyzer Operation Vector_signal_analyzer > Operation The vector signal analyzer spectrum analysis process typically has a down-convert & digitizing stage and a DSP & display stage.
Diver navigation Current, wave and surge direction Diving_compass > Techniques > Using natural features > Current, wave and surge direction Current direction can be useful as an orientation cue as long as the direction of the current is known. In rivers it tends to be fairly consistent and reliable, though localised eddies may occur. In the sea it may depend on weather conditions and local topography, as well as the state of the tide.
CG artwork 1960s Triangle_primitives > History > 1960s In 1969, the ACM initiated A Special Interest Group on Graphics (SIGGRAPH) which organizes conferences, graphics standards, and publications within the field of computer graphics. By 1973, the first annual SIGGRAPH conference was held, which has become one of the focuses of the organization. SIGGRAPH has grown in size and importance as the field of computer graphics has expanded over time.
Lie sphere transformation Lie transformations Lie_sphere_transformation > Lie sphere geometry in the plane > Lie transformations This subgroup is isomorphic to the group O(3,1) of Möbius transformations of the sphere. It can also be characterized as the centralizer of the involution ρ, which is itself a Lie transformation. Lie transformations can often be used to simplify a geometrical problem, by transforming circles into lines or points.
Liquid metal embrittlement Mechanisms Liquid_metal_embrittlement > Mechanisms Many theories have been proposed for LME. The major ones are listed below; The dissolution-diffusion model of Robertson and Glickman says that absorption of the liquid metal on the solid metal induces dissolution and inward diffusion. Under stress these processes lead to crack nucleation and propagation. The brittle fracture theory of Stoloff and Johnson, Westwood and Kamdar proposed that the adsorption of the liquid metal atoms at the crack tip weakens inter-atomic bonds and propagates the crack.
Current integrator Mechanical integrators Current_integrator > Mechanical integrators Mechanical integrators were key elements in the mechanical differential analyser, used to solve practical physical problems. Mechanical integration mechanisms were also used in control systems such as regulating flows or temperature in industrial processes. Mechanisms such as the ball-and-disk integrator were used both for computation in differential analysers and as components of instruments such as naval gun directors, flow totalizers and others. A planimeter is a mechanical device used for calculating the definite integral of a curve given in graphical form, or more generally finding the area of a closed curve. An integraph is used to plot the indefinite integral of a function given in graphical form.
Comparison of programming paradigms Allocation of dynamic memory for message and object storage Comparison_of_programming_paradigms > Performance comparison > Pseudocode examples comparing various paradigms > Allocation of dynamic memory for message and object storage Uniquely, the object-oriented paradigm involves dynamic memory allocation from heap storage for both object creation and message passing. A 1994 benchmark - "Memory Allocation Costs in Large C and C++ Programs" conducted by Digital Equipment Corporation on a variety of software, using an instruction-level profiling tool, measured how many instructions were required per dynamic storage allocation. The results showed that the lowest absolute number of instructions executed averaged around 50 but others reached as high as 611. See also "Heap:Pleasures and pains" by Murali R. Krishnan that states "Heap implementations tend to stay general for all platforms, and hence have heavy overhead".
Sedimentary rocks Fossils Sedimentary_Rock > Properties > Fossils The fossil, in the end, consists of a thin layer of pure carbon or its mineralized form, graphite. This form of fossilisation is called carbonisation. It is particularly important for plant fossils. The same process is responsible for the formation of fossil fuels like lignite or coal.
Adenosine Monophosphate Deaminase Deficiency type 1 Mechanism Adenosine_Monophosphate_Deaminase_Deficiency_type_1 > Mechanism This rhabdomyolysis is probably not of exertional, but of hypoglycemic nature, as loaded glycogen-less muscles can rapidly remove glucose from blood, and the normal mechanism of glucose homeostasis lacks the required responsiveness or capacity to prevent hypoglycemia. The broken down myocytes probably do not yield much glucose.
Kinetic Rule Language Summary Kinetic_Rule_Language Kinetic Rule Language (KRL) is a rule-based programming language for creating applications on the Live Web. KRL programs, or rulesets, comprise a number of rules that respond to particular events. KRL has been promoted as language for building personal clouds.KRL is part of an open-source project called KRE, for Kinetic Rules Engine, developed by Kynetx, Inc.
Fall protection Fall prevention Fall_protection > Types of fall protection > Fall prevention Fall guarding is the use of guard rails or other barricades to prevent a person from falling. These barricades are placed near an edge where a fall-hazard can occur, or to surround a weak surface (such as a skylight on a roof) which may break when stepped on. Fall restraint is a class of personal protective equipment to prevent persons who are in a fall hazard area from falling, e.g., fall restraint lanyards.
Tumor suppressor protein p53 Summary P53_protein p53, also known as Tumor protein P53, cellular tumor antigen p53 (UniProt name), or transformation-related protein 53 (TRP53) is a regulatory protein that is often mutated in human cancers. The p53 proteins (originally thought to be, and often spoken of as, a single protein) are crucial in vertebrates, where they prevent cancer formation. As such, p53 has been described as "the guardian of the genome" because of its role in conserving stability by preventing genome mutation. Hence TP53 is classified as a tumor suppressor gene.The TP53 gene is the most frequently mutated gene (>50%) in human cancer, indicating that the TP53 gene plays a crucial role in preventing cancer formation. TP53 gene encodes proteins that bind to DNA and regulate gene expression to prevent mutations of the genome. In addition to the full-length protein, the human TP53 gene encodes at least 15 protein isoforms.
Algebraic signal processing Graph Signal Processing Algebraic_signal_processing > Examples > Graph Signal Processing A weighted graph is an undirected graph G = ( V , E ) {\displaystyle {\mathcal {G}}=({\mathcal {V}},{\mathcal {E}})} with pseudometric on the node set V {\displaystyle {\mathcal {V}}} written a i j {\displaystyle a_{ij}} . A graph signal is simply a real-valued function on the set of nodes of the graph. In graph neural networks, graph signals are sometimes called features. The signal space is the set of all graph signals M = R V {\displaystyle {\mathcal {M}}=\mathbb {R} ^{\mathcal {V}}} where V {\displaystyle {\mathcal {V}}} is a set of n = | V | {\displaystyle n=|{\mathcal {V}}|} nodes in G = ( V , E ) {\displaystyle {\mathcal {G}}=({\mathcal {V}},{\mathcal {E}})} .
Vibrational analysis with scanning probe microscopy AFM-IR setup Vibrational_analysis_with_scanning_probe_microscopy > Theory and instrumentation > NSOM/FTIR, AFM/FTIR and AFM-IR > AFM-IR setup 10 nm diameter and a molecular weight of 400 kDa. InstrumentationIn AFM-IR, an AFM probe is used to measure the absorption response of the sample to infrared radiation. The general approach for AFM/FTIR is shown in Figure 10.
Protonophore Mechanism of action Protonophore > Mechanism of action The facilitated transport of protons across the biological membrane by anionic protonophore is achieved as follows. The anionic form of the protonophore (P−) is adsorbed onto one side (Positive) of the biological membrane. Protons (H+) from the aqueous solution combine with the anion (P−) to produce the neutral form (PH) PH diffuses across the biological membrane and dissociates into H+ and P− on the other side. This H+ is released from the biological membrane into the other aqueous solution P− returns to the first side of the biological membrane by electrophoresis (its electrostatic attraction to the positive side of the membrane).
Secondary winding Closed-core transformers and parallel power distribution Step-up_transformer > History > Closed-core transformers and parallel power distribution When employed in parallel connected electric distribution systems, closed-core transformers finally made it technically and economically feasible to provide electric power for lighting in homes, businesses and public spaces. Bláthy had suggested the use of closed cores, Zipernowsky had suggested the use of parallel shunt connections, and Déri had performed the experiments; In early 1885, the three engineers also eliminated the problem of eddy current losses with the invention of the lamination of electromagnetic cores.Transformers today are designed on the principles discovered by the three engineers. They also popularized the word 'transformer' to describe a device for altering the EMF of an electric current although the term had already been in use by 1882. In 1886, the ZBD engineers designed, and the Ganz factory supplied electrical equipment for, the world's first power station that used AC generators to power a parallel connected common electrical network, the steam-powered Rome-Cerchi power plant.
Flange focal distance Summary Flange_focal_distance A simple non-optical adapter holds the longer FFD lens the appropriate additional distance away from the sensor or film on the shorter FFD camera. A camera body with a shorter FFD can accept a larger number of lenses (those with a longer FFD) by using a simple adapter. A lens with a longer FFD can be more readily adapted to a larger number of camera bodies (those with a shorter FFD). If the difference is small, other factors such as the sizes and positions of the mounting flanges will influence whether a lens can be adapted without optics.
Nodular fasciitis Pathology Nodular_fasciitis > Pathology The microscopic histopathology of hematoxylin and eosin stained nodular fasciitis tumors consists of spindle-shaped myofibroblastic cells. These cells are in a myxoid or a collagenous (high content of collagen fibers) tissue background. The neoplastic myofibroblasts are arranged in whorls and/or short bundles. These cells may show high rates of replicating as judged by their mitotic index, but these mitoses are normal in appearance.
IBM System/38 Machine Interface IBM_System/38 > Software architecture > Machine Interface They constitute an intermediate compile time step and are translated into the processor's instruction set as the final compilation step. The MI instructions are stored within the final program object, in addition to the executable machine instructions.
Prograde motion Satellite galaxies Prograde_orbit > Galaxies > Satellite galaxies Close-flybys and mergers of galaxies within galaxy clusters can pull material out of galaxies and create small satellite galaxies in either prograde or retrograde orbits around larger galaxies.A galaxy called Complex H, which was orbiting the Milky Way in a retrograde direction relative to the Milky Way's rotation, is colliding with the Milky Way.
Medical Ultrasonography Cardiology (heart) B-scan_ultrasonography > Uses > Cardiology (heart) Echocardiography is an essential tool in cardiology, assisting in evaluation of heart valve function, such as stenosis or insufficiency, strength of cardiac muscle contraction, and hypertrophy or dilatation of the main chambers. (ventricle and atrium)
Variable cost Summary Variable_cost Direct costs are costs that can easily be associated with a particular cost object. However, not all variable costs are direct costs. For example, variable manufacturing overhead costs are variable costs that are indirect costs, not direct costs.
Volumetric titration Acid–base titrations Volumetric_titration > Particular uses > Acid–base titrations For biodiesel fuel: waste vegetable oil (WVO) must be neutralized before a batch may be processed. A portion of WVO is titrated with a base to determine acidity, so the rest of the batch may be neutralized properly. This removes free fatty acids from the WVO that would normally react to make soap instead of biodiesel fuel.
Dynamical pictures Background Dynamical_pictures > Schrödinger picture > Background The differences between the Schrödinger and Heiseinberg pictures of quantum mechanics revolve around how to deal with systems that evolve in time: the time-dependent nature of the system must be carried by some combination of the state vectors and the operators. For example, a quantum harmonic oscillator may be in a state |ψ⟩ for which the expectation value of the momentum, ⟨ ψ | p ^ | ψ ⟩ {\displaystyle \langle \psi |{\hat {p}}|\psi \rangle } , oscillates sinusoidally in time. One can then ask whether this sinusoidal oscillation should be reflected in the state vector |ψ⟩, the momentum operator p ^ {\displaystyle {\hat {p}}} , or both. All three of these choices are valid; the first gives the Schrödinger picture, the second the Heisenberg picture, and the third the interaction picture. The Schrödinger picture is useful when dealing with a time-independent Hamiltonian H, that is, ∂ t H = 0 {\displaystyle \partial _{t}H=0} .
Vasant Honavar Research Vasant_Honavar > Research Honavar has made substantial research contributions in artificial intelligence, machine learning, causal inference, knowledge representation, neural networks, semantic web, big data analytics, and bioinformatics and computational biology. He was a program chair of the Association for the Advancement of Artificial Intelligence(AAAI)'s 36th Conference on Artificial Intelligence. He has published over 300 research articles, including many highly cited ones, as well as several books on these topics. His recent work has focused on federated machine learning algorithms for constructing predictive models from distributed data and linked open data, learning predictive models from high dimensional longitudinal data, estimating causal effects from complex data, reasoning with federated knowledge bases, detecting algorithmic bias, big data analytics, analysis and prediction of protein-protein, protein-RNA, and protein-DNA interfaces and interactions, social network analytics, health informatics, secrecy-preserving query answering, representing and reasoning about preferences, and causal inference and meta analysis.Honavar has been active in fostering national and international scientific collaborations in Artificial Intelligence, Data Sciences, and their applications in addressing national, international, and societal priorities in accelerating science, improving health, transforming agriculture through partnerships that bring together academia, non-profits, and industry. He is also active in making the science policy case for major national research initiatives such as AI for accelerating science and AI for combating the epidemic of diseases of despair.
DEVS Formalism DEVS > Formalism Intuitive ExampleDEVS defines system behavior as well as system structure. System behavior in DEVS formalism is described using input and output events as well as states. For example, for the ping-pong player of Fig. 1, the input event is ?receive, and the output event is !send. Each player, A, B, has its states: Send and Wait.
List of functional programming topics Operational issues List_of_functional_programming_topics > Operational issues Graph reduction Combinator graph reduction Strict programming language Lazy evaluation, eager evaluation Speculative evaluation Side effect Assignment Setq Closure Continuation Continuation passing style Operational semantics State transition system Simulation preorder Bisimulation Monads in functional programming Exception handling Garbage collection
Cell-based therapies for Parkinson's disease Adrenal medulla Cell-based_therapies_for_Parkinson's_disease > List of cell-based sources > Adrenal medulla Following these initial disappointing results however, a trial in Mexico demonstrated significant motor benefits in two patients with Parkinson's disease who had undergone the procedure. This publication incited widespread interest in the field and over the next few years hundreds of patients received adrenal medulla transplants. It was only when a registry was set up to consolidate all the data was it revealed that most patients did not benefit from the procedure to any significant extent. Furthermore, postoperative complications such as psychiatric disturbances were realized. These combined findings eventually led to the abandonment of this transplant procedure, which was largely flawed from the start.
Hydraulic automata Blaise Pascal Hydraulic_automata > History > Modern era (c. 1600–1870) > Blaise Pascal Blaise Pascal (1623–1662) studied fluid hydrodynamics and hydrostatics, centered on the principles of hydraulic fluids. His discovery on the theory behind hydraulics led to his invention of the hydraulic press, which multiplied a smaller force acting on a smaller area into the application of a larger force totaled over a larger area, transmitted through the same pressure (or exact change of pressure) at both locations. Pascal's law or principle states that for an incompressible fluid at rest, the difference in pressure is proportional to the difference in height, and this difference remains the same whether or not the overall pressure of the fluid is changed by applying an external force. This implies that by increasing the pressure at any point in a confined fluid, there is an equal increase at every other end in the container, i.e., any change in pressure applied at any point of the liquid is transmitted undiminished throughout the fluids.
Digital Photography Digitally altered imagery Digital_photographer > Market impact > Social impact > Digitally altered imagery In digital art and media art, digital photos are often edited, manipulated, or combined with other digital images. Scanography is a related process in which digital photos are created using a scanner. New technology in digital cameras and computer editing affects the way photographic images are now perceived. The ability to create and fabricate realistic imagery digitally—as opposed to untouched photos—changes the audience's perception of "truth" in digital photography. Digital manipulation enables pictures to adjust the perception of reality, both past and present, and thereby shape people's identities, beliefs, and opinions.
B programming language Examples B_(programming_language) > Examples The following examples are from the Users' Reference to B by Ken Thompson:
ISO/IEC 80000 International System of Quantities ISO/IEC_80000 > International System of Quantities Part 1 of ISO 80000 introduces the International System of Quantities and describes its relationship with the International System of Units (SI). Specifically, its introduction states "The system of quantities, including the relations among the quantities used as the basis of the units of the SI, is named the International System of Quantities, denoted 'ISQ', in all languages." It further clarifies that "ISQ is simply a convenient notation to assign to the essentially infinite and continually evolving and expanding system of quantities and equations on which all of modern science and technology rests. ISQ is a shorthand notation for the 'system of quantities on which the SI is based'."
Universal computing Smallest machines Universal_Turing_Machine > Smallest machines Marvin Minsky discovered a 7-state 4-symbol universal Turing machine in 1962 using 2-tag systems. Other small universal Turing machines have since been found by Yurii Rogozhin and others by extending this approach of tag system simulation.
Coffee cherry Proteins and amino acids Coffee_beans > Composition > Proteins and amino acids Proteins account for 8% to 12% of dried green coffee beans. A majority of the proteins are of the 11-S storage kind (alpha – component of 32 kDa, beta – component of 22 kDa), most of which are degraded to free amino acids during maturation of green coffee beans. Further, 11-S storage proteins are degraded to their individual amino acids under roasting temperature, thus are an additional source of bitter components due to generation of Maillard reaction products. High temperature and oxygen concentration and low pH degrade 11-S storage proteins of green coffee beans to low-molecular-weight peptides and amino acids.
Context of computational complexity Use in algorithm design Computational_complexity > Use in algorithm design On the other hand, for a list of a million of entries (the phone numbers of a large town, for example), the elementary algorithms that require O ( n 2 ) {\displaystyle O(n^{2})} comparisons would have to do a trillion of comparisons, which would need around three hours at the speed of 10 million of comparisons per second. On the other hand, the quicksort and merge sort require only n log 2 ⁡ n {\displaystyle n\log _{2}n} comparisons (as average-case complexity for the former, as worst-case complexity for the latter). For n = 1,000,000, this gives approximately 30,000,000 comparisons, which would only take 3 seconds at 10 million comparisons per second.
Dimensional models of personality disorders Emerging problems with the categorical model Dimensional_models_of_personality_disorders > History > Emerging problems with the categorical model The dimensional model was developed in response to the limitations of this standard categorical model. The expectations from a Kraepelinian approach were that as systematic research into psychiatric health increased; diagnostic categories would be refined and targeted reliable treatments would be developed. However this reductionist approach to diagnostic categorization has led to disorders with high comorbidity, life course instability, poor treatment effectiveness and poor diagnostic agreement. In addition the findings from psychopathological research have led to an increasing body of evidence suggesting overlaps between normal and maladaptive personality and interrelatedness across disorders. These findings have been further supported by genetic and developmental studies which have constantly pointed towards greater interrelatedness then the diagnostic categories can offer. These consistently disconformity findings, alongside the successful shift to a continuous rather than categorical approach in other areas of research, such as regarding ASD, led to consideration of alternative approaches.
Cycle index Permutation groups and group actions Cycle_index > Permutation groups and group actions The group homomorphism can be thought of as a means for permitting the group G to "act" on the set X (using the permutations associated with the elements of G). Such a group homomorphism is formally called a group action and the image of the homomorphism is a permutation representation of G. A given group can have many different permutation representations, corresponding to different actions.Suppose that group G acts on set X (that is, a group action exists). In combinatorial applications the interest is in the set X; for instance, counting things in X and knowing what structures might be left invariant by G. Little is lost by working with permutation groups in such a setting, so in these applications, when a group is considered, it is a permutation representation of the group which will be worked with, and thus, a group action must be specified. Algebraists, on the other hand, are more interested in the groups themselves and would be more concerned with the kernels of the group actions, which measure how much is lost in passing from the group to its permutation representation.
Deuterium isotope effect Other examples Kinetic_isotope_effect > Case studies > Other examples Another reaction mechanisms that was elucidated using the kinetic isotope effect is the halogenation of toluene: In this particular "intramolecular KIE" study, a benzylic hydrogen undergoes radical substitution by bromine using N-bromosuccinimide as the brominating agent. It was found that PhCH3 brominates 4.86x faster than PhCD3. A large KIE of 5.56 is associated with the reaction of ketones with bromine and sodium hydroxide.
Ekman flow Summary Ekman_flow The Ekman layer is the layer in a fluid where there is a force balance between pressure gradient force, Coriolis force and turbulent drag. It was first described by Vagn Walfrid Ekman. Ekman layers occur both in the atmosphere and in the ocean. There are two types of Ekman layers. The first type occurs at the surface of the ocean and is forced by surface winds, which act as a drag on the surface of the ocean. The second type occurs at the bottom of the atmosphere and ocean, where frictional forces are associated with flow over rough surfaces.
Completely randomized design Randomization Completely_randomized_design > Randomization Before each run, one of the slips would be drawn blindly from the box and the level selected would be used for the next run of the experiment. In practice, the randomization is typically performed by a computer program. However, the randomization can also be generated from random number tables or by some physical mechanism (e.g., drawing the slips of paper).
Sequence point C11 and C++11 Sequence_point > Behavior > C11 and C++11 Partially because of the introduction of language support for threads, C11 and C++11 introduced new terminology for evaluation order. An operation may be "sequenced before" another, or the two can be "indeterminately" sequenced (one must complete before the other) or "unsequenced" (the operations in each expression may be interleaved).
Moment magnitude Introduction of an energy-motivated magnitude Mw Moment_magnitude > History > Introduction of an energy-motivated magnitude Mw Most earthquake magnitude scales suffered from the fact that they only provided a comparison of the amplitude of waves produced at a standard distance and frequency band; it was difficult to relate these magnitudes to a physical property of the earthquake. Gutenberg and Richter suggested that radiated energy Es could be estimated as log ⁡ E s ≈ 4.8 + 1.5 M S , {\displaystyle \log E_{s}\approx 4.8+1.5M_{S},} (in Joules). Unfortunately, the duration of many very large earthquakes was longer than 20 seconds, the period of the surface waves used in the measurement of Ms .
Stepped Reckoner Operation Stepped_Reckoner > Operation The first (least significant) digit of the multiplier is set into the multiplier dial as above, and the crank is turned, multiplying the operand by that digit and putting the result in the accumulator. The input section is shifted one digit to the left with the end crank. The next digit of the multiplier is set into the multiplier dial, and the crank is turned again, multiplying the operand by that digit and adding the result to the accumulator.
Named condition Object-oriented programming Named_condition > Features > Identification division > Object-oriented programming Objects are stored as references which may be restricted to a certain type. There are two ways of calling a method: the INVOKE statement, which acts similarly to CALL, or through inline method invocation, which is analogous to using functions.
Theory of computability Name Computability_theory_(computation) > Name The field of mathematical logic dealing with computability and its generalizations has been called "recursion theory" since its early days. Robert I. Soare, a prominent researcher in the field, has proposed that the field should be called "computability theory" instead. He argues that Turing's terminology using the word "computable" is more natural and more widely understood than the terminology using the word "recursive" introduced by Kleene. Many contemporary researchers have begun to use this alternate terminology.
Polynomial eigenvalue problem Special cases Nonlinear_eigenproblem > Special cases {\displaystyle M(\lambda )=A-\lambda B.} The quadratic eigenvalue problem: M ( λ ) = A 0 + λ A 1 + λ 2 A 2 . {\displaystyle M(\lambda )=A_{0}+\lambda A_{1}+\lambda ^{2}A_{2}.}
Meridian arc Quarter meridian Meridian_arc > Quarter meridian {\displaystyle m_{\mathrm {p} }=10\,001\,965.729{\mbox{ m.}}} The polar Earth's circumference is simply four times quarter meridian: C p = 4 m p {\displaystyle C_{p}=4m_{p}} The perimeter of a meridian ellipse can also be rewritten in the form of a rectifying circle perimeter, Cp = 2πMr. Therefore, the rectifying Earth radius is: M r = 0.5 ( a + b ) / c 0 {\displaystyle M_{r}=0.5(a+b)/c_{0}} It can be evaluated as 6367449.146 m.
Parallel all-pairs shortest path algorithm Parallelization for more than |V| processors Parallel_all-pairs_shortest_path_algorithm > Dijkstra algorithm > Parallelization for more than |V| processors Adjust the distance of all neighbors of x {\displaystyle x} in d v {\displaystyle d_{v}} Every processors now knows the global nearest node x {\displaystyle x} and its distance. Based on this information, adjust the neighbors of x {\displaystyle x} in d v {\displaystyle d_{v}} which are managed by the corresponding processor.The total runtime of such an iteration of DijkstraSSSP performed by a partition of size k {\displaystyle k} can be derived based on the performed subtasks: The linear search for x ~ {\displaystyle {\tilde {x}}}: O ( | V | k ) {\displaystyle O({\frac {|V|}{k}})} Broadcast- and Reduce-operations: These can be implemented efficiently for example using binonmialtrees. This yields a communication overhead of O ( log ⁡ k ) {\displaystyle O(\log k)} .For | V | {\displaystyle |V|} -iterations this results in a total runtime of O ( | V | ( | V | k + log ⁡ k ) ) {\displaystyle O(|V|({\frac {|V|}{k}}+\log k))} .
Elliptical distribution Robust statistics: Asymptotics Elliptical_distribution > Applications > Statistics: Generalized multivariate analysis > Robust statistics: Asymptotics Another use of elliptical distributions is in robust statistics, in which researchers examine how statistical procedures perform on the class of elliptical distributions, to gain insight into the procedures' performance on even more general problems, for example by using the limiting theory of statistics ("asymptotics").
Mitochondrial genome The mitochondrial bottleneck Mitochondrial_genes > Mitochondrial inheritance > The mitochondrial bottleneck Entities subject to uniparental inheritance and with little to no recombination may be expected to be subject to Muller's ratchet, the accumulation of deleterious mutations until functionality is lost. Animal populations of mitochondria avoid this through a developmental process known as the mtDNA bottleneck. The bottleneck exploits random processes in the cell to increase the cell-to-cell variability in mutant load as an organism develops: a single egg cell with some proportion of mutant mtDNA thus produces an embryo in which different cells have different mutant loads. Cell-level selection may then act to remove those cells with more mutant mtDNA, leading to a stabilisation or reduction in mutant load between generations. The mechanism underlying the bottleneck is debated, with a recent mathematical and experimental metastudy providing evidence for a combination of the random partitioning of mtDNAs at cell divisions and the random turnover of mtDNA molecules within the cell.
Autophagy Summary Autophagy In macroautophagy (the most thoroughly researched form of autophagy), cytoplasmic components (like mitochondria) are targeted and isolated from the rest of the cell within a double-membrane vesicle known as an autophagosome, which, in time, fuses with an available lysosome, bringing its specialty process of waste management and disposal; and eventually the contents of the vesicle (now called an autolysosome) are degraded and recycled. In crinophagy (the least well-known and researched form of autophagy), unnecessary secretory granules are degraded and recycled.In disease, autophagy has been seen as an adaptive response to stress, promoting survival of the cell; but in other cases, it appears to promote cell death and morbidity. In the extreme case of starvation, the breakdown of cellular components promotes cellular survival by maintaining cellular energy levels.
Astronomical refraction Astronomical refraction Astronomical_refraction > Astronomical refraction The altitude of a celestial body is normally given for the center of the body's disc. In the case of the Moon, additional corrections are needed for the Moon's horizontal parallax and its apparent semi-diameter; both vary with the Earth–Moon distance. Refraction near the horizon is highly variable, principally because of the variability of the temperature gradient near the Earth's surface and the geometric sensitivity of the nearly horizontal rays to this variability.
Index of object-oriented programming articles P Index_of_object-oriented_programming_articles > P Package Parametric overloading Parameterized classes Parnas's principles Partial class Patterns Policy-based design Polymorphic Primitive data type private, a way of encapsulation in object-oriented programming Programming paradigm protected, a way of encapsulation in object-oriented programming Protocol Prototype pattern Prototype-based programming public, a way of encapsulation in object-oriented programming Pure polymorphism Pure virtual function (also called pure virtual method)
Multiple factor analysis Summary Multiple_factor_analysis Multiple factor analysis (MFA) is a factorial method devoted to the study of tables in which a group of individuals is described by a set of variables (quantitative and / or qualitative) structured in groups. It is a multivariate method from the field of ordination used to simplify multidimensional data structures. MFA treats all involved tables in the same way (symmetrical analysis). It may be seen as an extension of: Principal component analysis (PCA) when variables are quantitative, Multiple correspondence analysis (MCA) when variables are qualitative, Factor analysis of mixed data (FAMD) when the active variables belong to the two types.
Imperial and US customary measurement systems Units in use Imperial_and_US_customary_measurement_systems > Units in use The tables below catalogue the imperial units of measure that were permitted for use in trade in the United Kingdom on the eve of metrication (1976) and the customary "units of measurement that have traditionally been used in the United States". In addition, named units of measure that are used in the engineering industry are also catalogued. Prior to metrication, the units of measure used in Ireland were the same as those used in the United Kingdom while those used in the British Commonwealth and in South Africa were in most cases a subset of those used in the United Kingdom with, in certain cases, local differences. Unless otherwise specified, the units of measure quoted below were used in both the United States, the United Kingdom. The SI equivalents are quoted to four significant figures.
Weak heap Description Weak_heap > Description A weak heap is most easily understood as a heap-ordered multi-way tree stored as a binary tree using the "right-child left-sibling" convention. (This is equivalent to, but reversed from, the usual left-child right-sibling binary tree.) In the multi-way tree, and assuming a max-heap, each parent's key is greater than or equal to (≥) all the child keys (and thus, by induction, all members of the subtree). Expressed as a binary tree, this translates to the following invariants: The root node has no left child For every node, the value associated with that node is greater than or equal to the values associated with all nodes in its right subtree.
Starting capacitor Summary Motor_capacitor A motor capacitor is an electrical capacitor that alters the current to one or more windings of a single-phase alternating-current induction motor to create a rotating magnetic field. There are two common types of motor capacitors, start capacitor and run capacitor (including a dual run capacitor).Motor capacitors are used with single-phase electric motors: 11 that are in turn used to drive air conditioners, hot tub/jacuzzi spa pumps, powered gates, large fans or forced-air heat furnaces for example. A "dual run capacitor" is used in some air conditioner compressor units, to boost both the fan and compressor motors.
Indeterminism Quantum mechanics Indeterminism > Science > Quantum mechanics Non-deterministic behavior in wave function collapse is not only a feature of the Copenhagen interpretation, with its observer-dependence, but also of objective collapse and other theories. Opponents of quantum indeterminism suggested that determinism could be restored by formulating a new theory in which additional information, so-called hidden variables, would allow definite outcomes to be determined. For instance, in 1935, Einstein, Podolsky and Rosen wrote a paper titled "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"
Selection sort Variants Selection_sort > Variants Heapsort greatly improves the basic algorithm by using an implicit heap data structure to speed up finding and removing the lowest datum. If implemented correctly, the heap will allow finding the next lowest element in Θ ( log ⁡ n ) {\displaystyle \Theta (\log n)} time instead of Θ ( n ) {\displaystyle \Theta (n)} for the inner loop in normal selection sort, reducing the total running time to Θ ( n log ⁡ n ) {\displaystyle \Theta (n\log n)} . A bidirectional variant of selection sort (called double selection sort or sometimes cocktail sort due to its similarity to cocktail shaker sort) finds both the minimum and maximum values in the list in every pass. This requires three comparisons per two items (a pair of elements is compared, then the greater is compared to the maximum and the lesser is compared to the minimum) rather than regular selection sort's one comparison per item, but requires only half as many passes, a net 25% savings.
Jefimenko's equations Heaviside–Feynman formula Jefimenko's_equations > Heaviside–Feynman formula The last term, proportional to the second derivative of the unit direction vector e r ′ {\displaystyle e_{r'}} , is sensitive to charge motion perpendicular to the line of sight. It can be shown that the electric field generated by this term is proportional to a t / r ′ {\displaystyle a_{t}/r'} , where a t {\displaystyle a_{t}} is the transverse acceleration in the retarded time. As it decreases only as 1 / r ′ {\displaystyle 1/r'} with distance compared to the standard 1 / r ′ 2 {\displaystyle 1/r'^{2}} Coulombic behavior, this term is responsible for the long-range electromagnetic radiation caused by the accelerating charge. The Heaviside–Feynman formula can be derived from Maxwell's equations using the technique of the retarded potential. It allows, for example, the derivation of the Larmor formula for overall radiation power of the accelerating charge.
Darboux integral A Darboux-integrable function Darboux_integral > Examples > A Darboux-integrable function Suppose we want to show that the function f ( x ) = x {\displaystyle f(x)=x} is Darboux-integrable on the interval {\displaystyle } and determine its value. To do this we partition {\displaystyle } into n {\displaystyle n} equally sized subintervals each of length 1 / n {\displaystyle 1/n} . We denote a partition of n {\displaystyle n} equally sized subintervals as P n {\displaystyle P_{n}} . Now since f ( x ) = x {\displaystyle f(x)=x} is strictly increasing on {\displaystyle } , the infimum on any particular subinterval is given by its starting point.
Linearized polynomial Summary Linearised_polynomial In mathematics, a linearised polynomial (or q-polynomial) is a polynomial for which the exponents of all the constituent monomials are powers of q and the coefficients come from some extension field of the finite field of order q. We write a typical example as where each a i {\displaystyle a_{i}} is in F q m ( = GF ⁡ ( q m ) ) {\displaystyle F_{q^{m}}(=\operatorname {GF} (q^{m}))} for some fixed positive integer m {\displaystyle m} . This special class of polynomials is important from both a theoretical and an applications viewpoint. The highly structured nature of their roots makes these roots easy to determine.
Anelasticity Static response functions Anelasticity > Static response functions The initial value of J ( t ) {\displaystyle J(t)} is called the unrelaxed compliance, the equilibrium value is called relaxed compliance J R {\displaystyle J_{R}} and their difference δ J {\displaystyle \delta J} is called the relaxation of the compliance. After a creep experiment has been run for a while, when stress is released the elastic spring-back is in general followed by a time dependent decay of the strain. This effect is called the elastic aftereffect or “creep recovery”.
Neuron Membrane Neuron > Anatomy and histology > Membrane Like all animal cells, the cell body of every neuron is enclosed by a plasma membrane, a bilayer of lipid molecules with many types of protein structures embedded in it. A lipid bilayer is a powerful electrical insulator, but in neurons, many of the protein structures embedded in the membrane are electrically active. These include ion channels that permit electrically charged ions to flow across the membrane and ion pumps that chemically transport ions from one side of the membrane to the other. Most ion channels are permeable only to specific types of ions.
Spin glasses Non-ergodic behavior and applications Spin_glasses > Non-ergodic behavior and applications The participation ratio counts the number of states that are accessible from a given instance, that is, the number of states that participate in the ground state. The ergodic aspect of spin glass was instrumental in the awarding of half the 2021 Nobel Prize in Physics to Giorgio Parisi.For physical systems, such as dilute manganese in copper, the freezing temperature is typically as low as 30 kelvins (−240 °C), and so the spin-glass magnetism appears to be practically without applications in daily life. The non-ergodic states and rugged energy landscapes are, however, quite useful in understanding the behavior of certain neural networks, including Hopfield networks, as well as many problems in computer science optimization and genetics.
Neurological examination Summary Neurological_exam If a problem is found either in an investigative or screening process, then further tests can be carried out to focus on a particular aspect of the nervous system (such as lumbar punctures and blood tests). In general, a neurological examination is focused on finding out whether there are lesions in the central and peripheral nervous systems or there is another diffuse process that is troubling the patient. Once the patient has been thoroughly tested, it is then the role of the physician to determine whether these findings combine to form a recognizable medical syndrome or neurological disorder such as Parkinson's disease or motor neurone disease. Finally, it is the role of the physician to find the cause for why such a problem has occurred, for example finding whether the problem is due to inflammation or is congenital.
Outline of probability Time series Outline_of_probability > Stochastic processes > Time series Moving-average and autoregressive processes Correlation function and autocorrelation
Cross ratio Differential-geometric point of view Projective_invariant > Differential-geometric point of view The theory takes on a differential calculus aspect as the four points are brought into proximity. This leads to the theory of the Schwarzian derivative, and more generally of projective connections.
Electronic Hamiltonian Harmonic nuclear motion Hamiltonian Electronic_molecular_Hamiltonian > Harmonic nuclear motion Hamiltonian In order to simplify the expression for the kinetic energy we introduce mass-weighted displacement coordinates . Since the kinetic energy operator becomes, If we make a Taylor expansion of V around the equilibrium geometry, and truncate after three terms (the so-called harmonic approximation), we can describe V with only the third term. The term V0 can be absorbed in the energy (gives a new zero of energy).
Condenser coil Flow arrangement Heating_coil > Flow arrangement For efficiency, heat exchangers are designed to maximize the surface area of the wall between the two fluids, while minimizing resistance to fluid flow through the exchanger. The exchanger's performance can also be affected by the addition of fins or corrugations in one or both directions, which increase surface area and may channel fluid flow or induce turbulence. The driving temperature across the heat transfer surface varies with position, but an appropriate mean temperature can be defined. In most simple systems this is the "log mean temperature difference" (LMTD). Sometimes direct knowledge of the LMTD is not available and the NTU method is used.
Skyrmion Summary Skyrmion It has since found application in solid-state physics, as well as having ties to certain areas of string theory. Skyrmions as topological objects are important in solid-state physics, especially in the emerging technology of spintronics. A two-dimensional magnetic skyrmion, as a topological object, is formed, e.g., from a 3D effective-spin "hedgehog" (in the field of micromagnetics: out of a so-called "Bloch point" singularity of homotopy degree +1) by a stereographic projection, whereby the positive north-pole spin is mapped onto a far-off edge circle of a 2D-disk, while the negative south-pole spin is mapped onto the center of the disk.
Loop route Summary Loop_route In road transportation in the United States, a special route is a road in a numbered highway system that diverts a specific segment of related traffic away from another road. They are featured in many highway systems; most are found in the Interstate Highway System, U.S. highway system, and several state highway systems. Each type of special route possesses generally defined characteristics and has a defined relationship with its parent route.
Infrared Radiation Art conservation and analysis Thermal_infrared_radiation > Applications > Art conservation and analysis Infrared reflectography can be applied to paintings to reveal underlying layers in a non-destructive manner, in particular the artist's underdrawing or outline drawn as a guide. Art conservators use the technique to examine how the visible layers of paint differ from the underdrawing or layers in between (such alterations are called pentimenti when made by the original artist). This is very useful information in deciding whether a painting is the prime version by the original artist or a copy, and whether it has been altered by over-enthusiastic restoration work. In general, the more pentimenti, the more likely a painting is to be the prime version.
Scientific paradigm Scientific paradigm Scientific_paradigm > Scientific paradigm The Oxford English Dictionary defines a paradigm as "a pattern or model, an exemplar; a typical instance of something, an example". The historian of science Thomas Kuhn gave the word its contemporary meaning when he adopted the word to refer to the set of concepts and practices that define a scientific discipline at any particular period of time. In his book, The Structure of Scientific Revolutions (first published in 1962), Kuhn defines a scientific paradigm as: "universally recognized scientific achievements that, for a time, provide model problems and solutions to a community of practitioners, i.e., what is to be observed and scrutinized the kind of questions that are supposed to be asked and probed for answers in relation to this subject how these questions are to be structured what predictions made by the primary theory within the discipline how the results of scientific investigations should be interpreted how an experiment is to be conducted, and what equipment is available to conduct the experiment.In The Structure of Scientific Revolutions, Kuhn saw the sciences as going through alternating periods of normal science, when an existing model of reality dominates a protracted period of puzzle-solving, and revolution, when the model of reality itself undergoes sudden drastic change. Paradigms have two aspects.
Gauge covariant derivative Overview Gauge_covariant_derivative > Overview Note that Lie groups do not come equipped with a metric. A yet more complicated, yet more accurate and geometrically enlightening, approach is to understand that the gauge covariant derivative is (exactly) the same thing as the exterior covariant derivative on a section of an associated bundle for the principal fiber bundle of the gauge theory; and, for the case of spinors, the associated bundle would be a spin bundle of the spin structure. Although conceptually the same, this approach uses a very different set of notation, and requires a far more advanced background in multiple areas of differential geometry.
Database query language Examples Information_retrieval_query_language > Examples Used in the Poliqarp search engine; PQL is a special-purpose programming language for managing process models based on information about scenarios that these models describe; PRQL PRQL (Pipelined Relational Query Language) is a modern language for transforming data. Consists of a curated set of orthogonal transformations, which are combined together to form a pipeline.
Boundary layer separation Summary Boundary_layer_separation Separation occurs in flow that is slowing down, with pressure increasing, after passing the thickest part of a streamline body or passing through a widening passage, for example. Flowing against an increasing pressure is known as flowing in an adverse pressure gradient. The boundary layer separates when it has travelled far enough in an adverse pressure gradient that the speed of the boundary layer relative to the surface has stopped and reversed direction.
Reaction rates Formal definition Rate_of_reactions > Formal definition For an open system, the full mass balance must be taken into account: where FA0 is the inflow rate of A in molecules per second; FA the outflow; v is the instantaneous reaction rate of A (in number concentration rather than molar) in a given differential volume, integrated over the entire system volume V at a given moment.When applied to the closed system at constant volume considered previously, this equation reduces to: , where the concentration is related to the number of molecules NA by = N A N 0 V . {\displaystyle ={\tfrac {N_{\rm {A}}}{N_{0}V}}.} Here N0 is the Avogadro constant.
Neurological deficit History Neurological_deficit > History Eliot Slater, after studying the condition in the 1950s, was outspoken against the condition, as there has never been any evidence to prove that it exists. He stated that "The diagnosis of 'hysteria' is a disguise for ignorance and a fertile source of clinical error. It is, in fact, not only a delusion but also a snare".In 1980, the DSM III added 'conversion disorder' to its list of conditions.
Architectural metals Aluminium Architectural_metals > Metal types > Aluminium Much like copper, Aluminium is highly resistant to corrosion. It also has the added benefit of being a third lighter than steel with comparable strength. Aluminium can also be easily and repeatedly recycled. It has been estimated that of the estimated 900 million tonnes of aluminium produced since 1880, three quarters is still in productive use, 35% of which is in building construction.Aluminium was unavailable at reasonable cost or in sufficient quantities for general architectural use until after the beginning of the 20th century.
Bachman diagram Bachman diagram Bachman_diagram > Bachman diagram A Bachman diagram is a certain type of data structure diagram, and is used to design the data with a network or relational "logical" model, separating the data model from the way the data is stored in the system. The model is named after database pioneer Charles Bachman, and mostly used in computer software design. In a relational model, a relation is the cohesion of attributes that are fully and not transitive functional dependent of every key in that relation.
Reasoning under uncertainty Summary Automated_reasoning_system In information technology a reasoning system is a software system that generates conclusions from available knowledge using logical techniques such as deduction and induction. Reasoning systems play an important role in the implementation of artificial intelligence and knowledge-based systems. By the everyday usage definition of the phrase, all computer systems are reasoning systems in that they all automate some type of logic or decision. In typical use in the Information Technology field however, the phrase is usually reserved for systems that perform more complex kinds of reasoning.
Matrix eigenvalue problem Eigenvectors of normal 3×3 matrices Eigenvalue_algorithm > Direct calculation > 3×3 matrices > Eigenvectors of normal 3×3 matrices In this case λ {\displaystyle \lambda } is an eigenvalue of multiplicity 2, so any vector perpendicular to the column space will be an eigenvector. Suppose v {\displaystyle \mathbf {v} } is a non-zero column of A − λ I {\displaystyle A-\lambda I} . Choose an arbitrary vector u {\displaystyle \mathbf {u} } not parallel to v {\displaystyle \mathbf {v} } . Then v × u {\displaystyle \mathbf {v} \times \mathbf {u} } and ( v × u ) × v {\displaystyle (\mathbf {v} \times \mathbf {u} )\times \mathbf {v} } will be perpendicular to v {\displaystyle \mathbf {v} } and thus will be eigenvectors of λ {\displaystyle \lambda } . This does not work when A {\displaystyle A} is not normal, as the null space and column space do not need to be perpendicular for such matrices.
Open building Open building terminology Open_building > Open building terminology Fit-out (tenant work): the physical products and spaces controlled by the individual inhabitant or occupant used to make habitable space in a base building. Fit-out can change without forcing the base building to change. Capacity: the measurable quality of a base building to accommodate a range of variations in floor plan and use within the constraints of a given base building. More generally, capacity concerns the degree of Open Building freedom offered by a higher level to a lower level.
Cross-validation (statistics) k-fold cross-validation with validation and test set Out_of_sample_testing > Nested cross-validation > k-fold cross-validation with validation and test set Then, one by one, one of the remaining sets is used as a validation set and the other k - 2 sets are used as training sets until all possible combinations have been evaluated. Similar to the k*l-fold cross validation, the training set is used for model fitting and the validation set is used for model evaluation for each of the hyperparameter sets. Finally, for the selected parameter set, the test set is used to evaluate the model with the best parameter set. Here, two variants are possible: either evaluating the model that was trained on the training set or evaluating a new model that was fit on the combination of the training and the validation set.
Concurrent hash table Locking Concurrent_hash_table > Contention handling > Locking With the help of locks, operations trying to concurrently access the table or values within it can be handled in a way that ensures correct behavior. This can however lead to negative performance impacts, in particular when the locks used are too restrictive, thus blocking accesses that would otherwise not contend and could execute without causing any problems. Further considerations have to be made to avoid even more critical problems that threaten correctness, as with livelocks, deadlocks or starvation.
Architecture domain Overview Architectural_domain > Overview Since Stephen Spewak's book called enterprise architecture planning (EAP) in 1993, and perhaps before then, it has been normal to recognise four types of architecture domain. The British Computer Society's "Reference Model for Enterprise and Solution Architecture" also follows this subdivision but additionally mentions the (single) application architecture level just below the applications architecture as well as the domains of information architecture, information systems architecture, or security architecture (a cross-cutting concern): Business architecture: The structure and behaviour of a business system (not necessarily related to computers). Covers business goals, business functions or capabilities, business processes and roles etc. Business functions and business processes are often mapped to the applications and data they need. Data architecture: The data structures used by a business and/or its applications.
Linear-quadratic-Gaussian control Continuous time Linear-quadratic-Gaussian_control > Mathematical description of the problem and solution > Continuous time Consider the continuous-time linear dynamic system x ˙ ( t ) = A ( t ) x ( t ) + B ( t ) u ( t ) + v ( t ) , {\displaystyle {\dot {\mathbf {x} }}(t)=A(t)\mathbf {x} (t)+B(t)\mathbf {u} (t)+\mathbf {v} (t),} y ( t ) = C ( t ) x ( t ) + w ( t ) , {\displaystyle \mathbf {y} (t)=C(t)\mathbf {x} (t)+\mathbf {w} (t),} where x {\displaystyle {\mathbf {x} }} represents the vector of state variables of the system, u {\displaystyle {\mathbf {u} }} the vector of control inputs and y {\displaystyle {\mathbf {y} }} the vector of measured outputs available for feedback. Both additive white Gaussian system noise v ( t ) {\displaystyle \mathbf {v} (t)} and additive white Gaussian measurement noise w ( t ) {\displaystyle \mathbf {w} (t)} affect the system. Given this system the objective is to find the control input history u ( t ) {\displaystyle {\mathbf {u} }(t)} which at every time t {\displaystyle {\mathbf {} }t} may depend linearly only on the past measurements y ( t ′ ) , 0 ≤ t ′ < t {\displaystyle {\mathbf {y} }(t'),0\leq t' 0 , {\displaystyle F\geq 0,\quad Q(t)\geq 0,\quad R(t)>0,} where E {\displaystyle \mathbb {E} } denotes the expected value. The final time (horizon) T {\displaystyle {\mathbf {} }T} may be either finite or infinite.
Kepler-11e Summary Kepler-11e Its low density can probably be attributed to a large hydrogen and helium atmosphere. Kepler-11e has a mass eight times of Earth's mass and a radius 4.5 times that of Earth. The planet orbits its star every 31 days in an ellipse that would fit within the orbit of Mercury. Kepler-11e was announced on February 2, 2011 with its five sister planets after it was confirmed by several observatories.
Study of animal locomotion Neuromechanical models Study_of_animal_locomotion > Modeling animal locomotion > Neuromechanical models An environment that incorporates physics is essential in simulating realistic movement of neuromechanical models because they will abide by the laws of physics. Environments used for physics simulation include, Opensim, PyBullet, and MuJoCo. == References ==
Invention of radio Wireless communication theories and methods previous to radio Invention_of_radio > Wireless communication theories and methods previous to radio In the United States, Thomas Edison, in the mid-1880s, patented an electromagnetic induction system he called "grasshopper telegraphy", which allowed telegraphic signals to jump the short distance between a running train and telegraph wires running parallel to the tracks. In the United Kingdom, William Preece was able to develop an electromagnetic induction telegraph system that, with antenna wires many kilometers long, could transmit across gaps of about 5 kilometres (3.1 miles). Inventor Nathan Stubblefield, between 1885 and 1892, also worked on an induction transmission system.
Takotsubo syndrome Pathophysiology Takotsubo_cardiomyopathy > Pathophysiology Further bolstering this idea is the concentration of these kinds of receptors in the heart. Higher concentrations of the receptor effected to produce cardiac stunning are found closer to the apex of the ventricle. This is what creates the classic ballooning effect of the ventricle.It is likely that there are multiple factors at play that could include some amount of vasospasm and failure of the microvasculature.
Pole mass Propagator pole Pole_mass > Propagator pole A loop in a Feynman diagram requires an integral over a continuum of possible energies and momenta. In general, the integrals of products of Feynman propagators diverge at propagator poles, and the divergences must be removed by renormalization. The process of renormalization might be thought of as a theory of cancellations of virtual particle paths, thus revealing the "bare" or renormalized physics, such as the pole mass.
Quadratic formula By Lagrange resolvents Quadratic_formula > Derivations of the formula > By Lagrange resolvents The resolvents can be recognized as r1/2 = −p/2 = −b/2a being the vertex, and r22 = p2 − 4q is the discriminant (of a monic polynomial). A similar but more complicated method works for cubic equations, where one has three resolvents and a quadratic equation (the "resolving polynomial") relating r2 and r3, which one can solve by the quadratic equation, and similarly for a quartic equation (degree 4), whose resolving polynomial is a cubic, which can in turn be solved. The same method for a quintic equation yields a polynomial of degree 24, which does not simplify the problem, and, in fact, solutions to quintic equations in general cannot be expressed using only roots.
Thomas Bayes Bayesianism Thomas_Bayes > Bayesianism As Stigler points out, this is a subjective definition, and does not require repeated events; however, it does require that the event in question be observable, for otherwise it could never be said to have "happened". Stigler argues that Bayes intended his results in a more limited way than modern Bayesians.
Climate change feedback Lapse rate Climate_change_feedback > Mechanisms with positive or negative feedback > Lapse rate The lapse rate is the rate at which an atmospheric variable, normally temperature in Earth's atmosphere, falls with altitude. It is therefore a quantification of temperature, related to radiation, as a function of altitude, and is not a separate phenomenon in this context. The lapse rate feedback is generally a negative feedback.
Cylindrical slide rule Logarithms and exponentials Slide_rules > Operation > Other operations > Logarithms and exponentials Base-10 logarithms and exponentials are found using the L scale, which is linear. Some slide rules have a Ln scale, which is for base e. Logarithms to any other base can be calculated by reversing the procedure for calculating powers of a number. For example, log2 values can be determined by lining up either leftmost or rightmost 1 on the C scale with 2 on the LL2 scale, finding the number whose logarithm is to be calculated on the corresponding LL scale, and reading the log2 value on the C scale.
Cultural-historical activity theory (CHAT) Leontiev and social development Cultural-historical_activity_theory_(CHAT) > Informing research and practice > Leontiev and social development From the 1960s onwards, starting in the global South, and independently from the mainstream European developmental line, Leontiev's core Objective Activity concept has been used in a Social Development context. In the Organization Workshop's Large Group Capacitation-method, objective/ized activity acts as the core causal principle which postulates that, in order to change the mind-set of (large groups of) individuals, we need to start with changes to their activity – and/or to the object that "suggests" their activity. In Leontievian vein, the Organization Workshop is all about semiotically mediated activities through which (large groups of) participants learn how to manage themselves and the organizations they create to perform tasks that require a complex division of labor.
Bipolar transistors Early manufacturing techniques Bipolar_transistors > History > Early manufacturing techniques Epitaxial transistor – a bipolar junction transistor made using vapor-phase deposition. See Epitaxy. Allows very precise control of doping levels and gradients.
Variational Monte Carlo Wave-function optimization in VMC Variational_Monte_Carlo > Further reading > Wave-function optimization in VMC 100 (10): 7416–7420. Bibcode:1994JChPh.100.7416T. doi:10.1063/1.466885.