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Bicycle gearing Multi-range gearing Bicycle_gearing > Types of gear change mechanisms > External (derailleur) > Multi-range gearing This style is commonly found on racing bicycles with two chainrings. The relative step on the chainrings (say 35%) is typically around three or four times the relative step on the cogset (say 8% or 10%), e.g. chainrings 39-53 and close-range cogsets 12-13-14-15-16-17-19-21 or 12-13-15-17-19-21-23-25. This arrangement provides much more scope for adjusting the gear ratio to maintain a constant pedalling speed, but any change of chainring must be accompanied by a simultaneous change of 3 or 4 sprockets on the cogset if the goal is to switch to the next higher or lower gear ratio.
Bridge failure Fixed or movable bridges Bridge > Types of bridges > Fixed or movable bridges Most bridges are fixed bridges, meaning they have no moving parts and stay in one place until they fail or are demolished. Temporary bridges, such as Bailey bridges, are designed to be assembled, taken apart, transported to a different site, and re-used. They are important in military engineering and are also used to carry traffic while an old bridge is being rebuilt.
List of limits Limits involving derivatives or infinitesimal changes List_of_limits > Limits for general functions > Limits involving derivatives or infinitesimal changes In these limits, the infinitesimal change h {\displaystyle h} is often denoted Δ x {\displaystyle \Delta x} or δ x {\displaystyle \delta x} . If f ( x ) {\displaystyle f(x)} is differentiable at x {\displaystyle x} , lim h → 0 f ( x + h ) − f ( x ) h = f ′ ( x ) {\displaystyle \lim _{h\to 0}{f(x+h)-f(x) \over h}=f'(x)} . This is the definition of the derivative. All differentiation rules can also be reframed as rules involving limits.
Potassium chlorochromate Reactions Potassium_chlorochromate > Reactions Although air-stable, its aqueous solutions undergo hydrolysis in the presence of strong acids. With concentrated hydrochloric acid, it converts to chromyl chloride, which in turn reacts with water to form chromic acid and additional hydrochloric acid. When treated with 18-crown-6, it forms the lipophilic salt CrO3Cl.Peligot's salt can oxidize benzyl alcohol, a reaction which can be catalyzed by acid. A related salt, pyridinium chlorochromate, is more commonly used for this reaction.
The Variable Flashbacks The_Variable > Plot > Flashbacks Years later, following the crash of Flight 815, Daniel has suffered severe psychological effects from performing experiments on himself; he has lost his mental acuity, and now lives with a caretaker. While watching the news coverage of the discovery of the Flight 815 wreckage in the Sunda Trench, Daniel is visited by Charles, who tells him that he faked the found wreckage and that the real plane actually landed on the island. Charles invites Daniel to go to the island, which Charles claims will cure his psychological problems. Eloise later visits Daniel and further encourages him to go to the island.
Memory and aging Domains of memory spared vs. affected Memory_and_aging > Domains of memory spared vs. affected It has been seen that the more complex a task is, the more difficulty the aging person has with completing this task. Active reorganization and manipulation of information becomes increasingly harder as adults age. When an older individual is completing a task, such as having a conversation or doing work, they are using their working memory to help them complete this task.
Programming games Related areas Programming_game > Related areas Open world games that feature the ability for players to construct environments from an array of building blocks have often been used by more advanced players to construct logic circuits and more advanced programs from the fundamental blocks. Minecraft is one such example, as while the game provides a limited set of blocks that mimic switches and electric circuits, users have been able to create basic functional computers within the virtual world, and at least one modification is aimed to teach children how to program on the virtual computer in a simplistic language.Several sites, such as Codecademy, help to teach real-world programming languages through gamification, where video game principles are used to motivate the user.
Asymmetric federalism Summary Asymmetric_federalism Asymmetric federalism or asymmetrical federalism is found in a federation or other types of union in which different constituent states possess different powers: one or more of the substates has considerably more autonomy than the other substates, although they have the same constitutional status. This is in contrast to symmetric federalism, where no distinction is made between constituent states. As a result, it is frequently proposed as a solution to the dissatisfaction that arises when one or more constituent units feel significantly different needs from the others, as the result of an ethnic, linguistic or cultural difference.
Composite Higgs models Experiments Composite_Higgs_models > Experiments Top partners have also special importance given their role in the naturalness of the theory. After the first run of the LHC direct experimental searches exclude third generation fermionic resonances up to 800 GeV. Bounds on gluon resonances are in the multi-TeV range and somewhat weaker bounds exist for electro-weak resonances.
Goat grazing problem Solution by sector area plus segment area Goat_grazing_problem > Interior grazing problem > Solution by sector area plus segment area Setting the pen's radius to be 1 and trigonometry such as sin ⁡ ( 2 θ ) = 2 sin ⁡ ( θ ) cos ⁡ ( θ ) {\displaystyle \sin(2\theta )=2\sin(\theta )\cos(\theta )} then give θ = arccos ⁡ ( r 2 ) {\displaystyle \theta =\arccos \left({\frac {r}{2}}\right)} . Requiring that half the grazable area be 1/4 of the pen's area gives A s e c t o r + A s e g m e n t = π / 4 {\displaystyle A_{sector}+A_{segment}=\pi /4} . Using the circular sector and circular segment area formulae gives r 2 θ + α − sin ⁡ ( α ) = π 2 {\displaystyle r^{2}\theta +\alpha -\sin(\alpha )={\frac {\pi }{2}}} ,which only assumes 0 < r < 2 {\displaystyle 0
Regenerative variable-frequency drives Speed control Regenerative_variable-frequency_drives > System description and operation > Speed control There are two main ways to control the speed of a VFD; networked or hardwired. Networked involves transmitting the intended speed over a communication protocol such as Modbus, Modbus/TCP, EtherNet/IP, or via a keypad using Display Serial Interface while hardwired involves a pure electrical means of communication. Typical means of hardwired communication are: 4-20mA, 0-10VDC, or using the internal 24VDC power supply with a potentiometer. Speed can also be controlled remotely and locally. Remote control instructs the VFD to ignore speed commands from the keypad while local control instructs the VFD to ignore external control and only abide by the keypad.
PPN formalism Comparisons between theories of gravity Parameterized_post-Newtonian_formalism > Comparisons between theories of gravity A table comparing PPN parameters for 23 theories of gravity can be found in Alternatives to general relativity#Parametric post-Newtonian parameters for a range of theories. Most metric theories of gravity can be lumped into categories. Scalar theories of gravitation include conformally flat theories and stratified theories with time-orthogonal space slices. In conformally flat theories such as Nordström's theory of gravitation the metric is given by g = f η {\displaystyle \mathbf {g} =f{\boldsymbol {\eta }}} and for this metric γ = − 1 {\displaystyle \gamma =-1} , which drastically disagrees with observations.
Proton-exchange fuel cells Increasing catalytic activity Proton-exchange_fuel_cells > Science > Catalyst research > Increasing catalytic activity As mentioned above, platinum is by far the most effective element used for PEM fuel cell catalysts, and nearly all current PEM fuel cells use platinum particles on porous carbon supports to catalyze both hydrogen oxidation and oxygen reduction. However, due to their high cost, current Pt/C catalysts are not feasible for commercialization. The U.S. Department of Energy estimates that platinum-based catalysts will need to use roughly four times less platinum than is used in current PEM fuel cell designs in order to represent a realistic alternative to internal combustion engines.
Privacy amplification Summary Privacy_amplification where U is uniform over { 0 , 1 } m {\displaystyle \{0,1\}^{m}} and independent of S. H ∞ ( X ) = − log ⁡ max x Pr {\textstyle H_{\infty }(X)=-\log \max _{x}\Pr} is the min-entropy of X, which measures the amount of randomness X has. The min-entropy is always less than or equal to the Shannon entropy. Note that max x Pr {\textstyle \max _{x}\Pr} is the probability of correctly guessing X.
Homomorphic encryption First-generation FHE Fully_homomorphic_encryption > History > First-generation FHE Finally, he shows that any bootstrappable somewhat homomorphic encryption scheme can be converted into a fully homomorphic encryption through a recursive self-embedding. For Gentry's "noisy" scheme, the bootstrapping procedure effectively "refreshes" the ciphertext by applying to it the decryption procedure homomorphically, thereby obtaining a new ciphertext that encrypts the same value as before but has lower noise. By "refreshing" the ciphertext periodically whenever the noise grows too large, it is possible to compute an arbitrary number of additions and multiplications without increasing the noise too much.
Thromboxane A synthase Mechanism Thromboxane_A_synthase > Mechanism First, there is a fast initial binding to the protein and then a subsequent ligation to the heme iron. In the first step of the mechanism, the heme iron coordinates to the C-9 endoperoxide oxygen. It participates in homolytic cleavage of the O-O bond in the endoperoxide, which represents the rate-limiting step, and undergoes a change in redox state from Fe(III) to Fe(IV).
Field survey Sociology Field_survey > Field research across different disciplines > Sociology Bourdieu's anthropological work was focused on the analysis of the mechanisms of reproduction of social hierarchies. Bourdieu criticized the primacy given to the economic factors, and stressed that the capacity of social actors to actively impose and engage their cultural productions and symbolic systems plays an essential role in the reproduction of social structures of domination. Bourdieu's empirical work played a crucial role in the popularization of correspondence analysis and particularly multiple correspondence analysis.
The Higgs Boson Production Introduction_to_the_Higgs_field > Properties > Production This process is the dominant contribution at the LHC and Tevatron being about ten times more likely than any of the other processes. Higgs Strahlung If an elementary fermion collides with an anti-fermion – e.g., a quark with an anti-quark or an electron with a positron – the two can merge to form a virtual W or Z boson which, if it carries sufficient energy, can then emit a Higgs boson. This process was the dominant production mode at the LEP, where an electron and a positron collided to form a virtual Z boson, and it was the second largest contribution for Higgs production at the Tevatron.
Multidimensional analysis Software Multidimensional_analysis > Software Computer software for MDA include Online analytical processing (OLAP) for data in relational databases, pivot tables for data in spreadsheets, and Array DBMSs for general multi-dimensional data (such as raster data) in science, engineering, and business.
Mental status Summary Mental_status_examination The mental status examination (MSE) is an important part of the clinical assessment process in neurological and psychiatric practice. It is a structured way of observing and describing a patient's psychological functioning at a given point in time, under the domains of appearance, attitude, behavior, mood and affect, speech, thought process, thought content, perception, cognition, insight, and judgment. There are some minor variations in the subdivision of the MSE and the sequence and names of MSE domains. The purpose of the MSE is to obtain a comprehensive cross-sectional description of the patient's mental state, which, when combined with the biographical and historical information of the psychiatric history, allows the clinician to make an accurate diagnosis and formulation, which are required for coherent treatment planning. The data are collected through a combination of direct and indirect means: unstructured observation while obtaining the biographical and social information, focused questions about current symptoms, and formalised psychological tests.The MSE is not to be confused with the mini–mental state examination (MMSE), which is a brief neuropsychological screening test for dementia.
Flight with disabled controls Control techniques Flight_with_disabled_controls > Control techniques A basic means of controlling an aircraft with disabled flight controls is making use of the position of the engines. If the engines are mounted under the centre of gravity, as in underwing passenger jets, then increasing the thrust will raise the nose while decreasing the thrust will lower it. This control method may call for control inputs that go against the pilot's instinct: when the aircraft is in a dive, adding thrust will raise the nose and vice versa. Additionally, asymmetrical thrust has been used for directional control: if the left engine is idled and power is increased on the right side this will result in a yaw to the left, and vice versa.
Function object In PowerShell Function_object > In PowerShell In the Windows PowerShell language, a script block is a collection of statements or expressions that can be used as a single unit. A script block can accept arguments and return values. A script block is an instance of a Microsoft .NET Framework type System.Management.Automation.ScriptBlock.
Continuous (topology) Definition in terms of neighborhoods Continuous_maps > Real functions > Definition > Definition in terms of neighborhoods As neighborhoods are defined in any topological space, this definition of a continuous function applies not only for real functions but also when the domain and the codomain are topological spaces, and is thus the most general definition. It follows that a function is automatically continuous at every isolated point of its domain. As a specific example, every real valued function on the integers is continuous.
Gene cassette Summary Gene_cassette In biology, a gene cassette is a type of mobile genetic element that contains a gene and a recombination site. Each cassette usually contains a single gene and tends to be very small; on the order of 500–1000 base pairs. They may exist incorporated into an integron or freely as circular DNA. Gene cassettes can move around within an organism's genome or be transferred to another organism in the environment via horizontal gene transfer. These cassettes often carry antibiotic resistance genes. An example would be the kanMX cassette which confers kanamycin (an antibiotic) resistance upon bacteria.
Nahm's equation Summary Nahm_equations In differential geometry and gauge theory, the Nahm equations are a system of ordinary differential equations introduced by Werner Nahm in the context of the Nahm transform – an alternative to Ward's twistor construction of monopoles. The Nahm equations are formally analogous to the algebraic equations in the ADHM construction of instantons, where finite order matrices are replaced by differential operators. Deep study of the Nahm equations was carried out by Nigel Hitchin and Simon Donaldson.
Mathematical optimization Iterative methods Optimization_algorithm > Computational optimization techniques > Iterative methods Conditional gradient method (Frank–Wolfe) for approximate minimization of specially structured problems with linear constraints, especially with traffic networks. For general unconstrained problems, this method reduces to the gradient method, which is regarded as obsolete (for almost all problems).
KMS driver History Graphics_Execution_Manager > History Such code had to be executed using x86 real mode, which prevented it from being invoked by a kernel running in protected mode. The situation changed when Luc Verhaegen and other developers found a way to do the mode-setting natively instead of BIOS-based, showing that it was possible to do it using normal kernel code and laying the groundwork for what would become Kernel Mode Setting. In May 2007 Jesse Barnes (Intel) published the first proposal for a drm-modesetting API and a working native implementation of mode-setting for Intel GPUs within the i915 DRM driver.
Dynamical pictures States Dynamical_pictures > Interaction Picture > Time-evolution equations > States Transforming the Schrödinger equation into the interaction picture gives: i ℏ d d t | ψ I ( t ) ⟩ = H 1 , I ( t ) | ψ I ( t ) ⟩ . {\displaystyle i\hbar {\frac {d}{dt}}|\psi _{I}(t)\rangle =H_{1,I}(t)|\psi _{I}(t)\rangle .} This equation is referred to as the Schwinger–Tomonaga equation.
Peptide vaccine Epitope design Peptide_vaccine > Epitope design Ex. Some IgE-inducing epitopes cause hypersensitivity reactions after vaccination in humans due to the overlap with IgG epitopes in the Na-ASP-2 protein which is an antigen from hookworm. Some short peptide epitopes need elongating to maintain the native conformation. The elongated sequences can include proper secondary structure.
Affine function Augmented matrix Affine_transform > Representation > Augmented matrix The above-mentioned augmented matrix is called an affine transformation matrix. In the general case, when the last row vector is not restricted to be {\displaystyle \left} , the matrix becomes a projective transformation matrix (as it can also be used to perform projective transformations). This representation exhibits the set of all invertible affine transformations as the semidirect product of K n {\displaystyle K^{n}} and GL ⁡ ( n , K ) {\displaystyle \operatorname {GL} (n,K)} .
Quantum laws Overview and fundamental concepts Quantum_mechanical > Overview and fundamental concepts For example, a quantum particle like an electron can be described by a wave function, which associates to each point in space a probability amplitude. Applying the Born rule to these amplitudes gives a probability density function for the position that the electron will be found to have when an experiment is performed to measure it. This is the best the theory can do; it cannot say for certain where the electron will be found.
Pollard's kangaroo algorithm Complexity Pollard's_kangaroo_algorithm > Complexity Pollard gives the time complexity of the algorithm as O ( b − a ) {\displaystyle O({\sqrt {b-a}})} , using a probabilistic argument based on the assumption that f {\displaystyle f} acts pseudorandomly. Since a , b {\displaystyle a,b} can be represented using O ( log ⁡ b ) {\displaystyle O(\log b)} bits, this is exponential in the problem size (though still a significant improvement over the trivial brute-force algorithm that takes time O ( b − a ) {\displaystyle O(b-a)} ). For an example of a subexponential time discrete logarithm algorithm, see the index calculus algorithm.
Biomedical data science Example Biomedical_data_science > Example Some of these algorithms, such as BLAST, are still used in modern bioinformatics. Scientists in the HGP also had to address complexities often associated with biomedical data including noisy data, such as DNA read errors, and privacy rights of the research subjects. The HGP, completed in 2004, has had immense impact both biologically, shedding light on human evolution, and medically, launching the field of bioinformatics and leading to technologies such as genetic screening and gene therapy. == References ==
Bouri Formation Summary Bouri_Formation The Bouri Formation is a sequence of sedimentary deposits that is the source of australopithecine and Homo (that is, hominin) fossils, artifacts, and bones of large mammals with cut marks from butchery with tools by early hominins. It is located in the Middle Awash Valley, in Ethiopia, East Africa, and is a part of the Afar Depression that has provided rich human fossil sites such as Gona and Hadar. The Bouri Formation stretches down much of the length and breadth of the Bouri "peninsula", which projects across the dry bed of the Afar Depression. The Formation is sufficiently eroded to expose three geological members or layers: the Hatayae, the Dakanihylo, and the Herto. Human remains with signs of having been prepared for burial have been found in the Upper Herto layers.
Cell soma Summary Cell_body Although it is often used to refer to neurons, it can also refer to other cell types as well, including astrocytes, oligodendrocytes, and microglia. There are many different specialized types of neurons, and their sizes vary from as small as about 5 micrometres to over 10 millimetres for some of the smallest and largest neurons of invertebrates, respectively. The soma of a neuron (i.e., the main part of the neuron in which the dendrites branch off of) contains many organelles, including granules called Nissl granules, which are composed largely of rough endoplasmic reticulum and free polyribosomes.
Principal Component Analysis Covariance-free computation Characteristic_vector_analysis > Covariance-free computation In practical implementations, especially with high dimensional data (large p), the naive covariance method is rarely used because it is not efficient due to high computational and memory costs of explicitly determining the covariance matrix. The covariance-free approach avoids the np2 operations of explicitly calculating and storing the covariance matrix XTX, instead utilizing one of matrix-free methods, for example, based on the function evaluating the product XT(X r) at the cost of 2np operations.
Umbral calculus The 19th-century umbral calculus Umbral_calculus > The 19th-century umbral calculus The method is a notational procedure used for deriving identities involving indexed sequences of numbers by pretending that the indices are exponents. Construed literally, it is absurd, and yet it is successful: identities derived via the umbral calculus can also be properly derived by more complicated methods that can be taken literally without logical difficulty. An example involves the Bernoulli polynomials. Consider, for example, the ordinary binomial expansion (which contains a binomial coefficient): ( y + x ) n = ∑ k = 0 n ( n k ) y n − k x k {\displaystyle (y+x)^{n}=\sum _{k=0}^{n}{n \choose k}y^{n-k}x^{k}} and the remarkably similar-looking relation on the Bernoulli polynomials: B n ( y + x ) = ∑ k = 0 n ( n k ) B n − k ( y ) x k .
Hash table Collision resolution Hash_table > Collision resolution A search algorithm that uses hashing consists of two parts. The first part is computing a hash function which transforms the search key into an array index. The ideal case is such that no two search keys hashes to the same array index. However, this is not always the case and is impossible to guarantee for unseen given data.
Leonhard Euler Number theory Leonhard_Euler > Contributions to mathematics and physics > Number theory He proved that the sum of the reciprocals of the primes diverges. In doing so, he discovered the connection between the Riemann zeta function and prime numbers; this is known as the Euler product formula for the Riemann zeta function.Euler invented the totient function φ(n), the number of positive integers less than or equal to the integer n that are coprime to n. Using properties of this function, he generalized Fermat's little theorem to what is now known as Euler's theorem. He contributed significantly to the theory of perfect numbers, which had fascinated mathematicians since Euclid.
Skeleton (computer programming) Task-parallel Skeleton_(computer_programming) > Parallel programming > Task-parallel This divides the load for a specific thread, effectively creating a master / slave relationship between the threads. ‘Pipes’ are the more traditional forms of algorithms, where each method or function is run in a sequence.
Azure Cosmos DB Tunable throughput Azure_Cosmos_DB > Tunable throughput Select by 'id' operations consume lower number of RUs compared to Delete, Update, and Insert operations for the same document. Large queries (e.g. aggregations like count) and stored procedure executions can consume hundreds to thousands of RUs depending on the complexity of the operations needed. The minimum billing is per hour.
Strong acid Measures of acid strength Weak_Acid > Measures of acid strength The usual measure of the strength of an acid is its acid dissociation constant ( K a {\displaystyle K_{{\ce {a}}}} ), which can be determined experimentally by titration methods. Stronger acids have a larger K a {\displaystyle K_{{\ce {a}}}} and a smaller logarithmic constant ( p K a = − log ⁡ K a {\displaystyle \mathrm {p} K_{{\ce {a}}}=-\log K_{\text{a}}} ) than weaker acids. The stronger an acid is, the more easily it loses a proton, H + {\displaystyle {\ce {H+}}} .
Hyperfine interaction Magnetic dipole Hyperfine_levels > Theory > Atomic hyperfine structure > Magnetic dipole The magnetic field at the nucleus due to the motion of a single electron, with charge –e at a position r relative to the nucleus, is given by: where −r gives the position of the nucleus relative to the electron. Written in terms of the Bohr magneton, this gives: Recognizing that mev is the electron momentum, p, and that r×p/ħ is the orbital angular momentum in units of ħ, ℓ, we can write: For a many-electron atom this expression is generally written in terms of the total orbital angular momentum, L {\displaystyle \mathbf {L} } , by summing over the electrons and using the projection operator, φ i ℓ {\displaystyle \varphi _{i}^{\ell }} , where ∑ i ℓ i = ∑ i φ i ℓ L {\textstyle \sum _{i}\mathbf {\ell } _{i}=\sum _{i}\varphi _{i}^{\ell }\mathbf {L} } . For states with a well defined projection of the orbital angular momentum, Lz, we can write φ i ℓ = ℓ ^ z i / L z {\displaystyle \varphi _{i}^{\ell }={\hat {\ell }}_{z_{i}}/L_{z}} , giving: The electron spin angular momentum is a fundamentally different property that is intrinsic to the particle and therefore does not depend on the motion of the electron.
Current transformer Construction Current_transformer > Construction Because the gaps in the hinged segment introduce inaccuracy, such devices are not normally used for revenue metering. Current transformers, especially those intended for high voltage substation service, may have multiple taps on their secondary windings, providing several ratios in the same device. This can be done to allow for reduced inventory of spare units, or to allow for load growth in an installation. A high-voltage current transformer may have several secondary windings with the same primary, to allow for separate metering and protection circuits, or for connection to different types of protective devices. For example, one secondary may be used for branch overcurrent protection, while a second winding may be used in a bus differential protective scheme, and a third winding used for power and current measurement.
Social simulation Current research Social_simulation > Current research The models focus on how simple and predictable local interactions generate familiar but highly detailed global patterns, such as emergence of norms and participation of collective action. Michael W. Macy and Robert Willer researched a recent survey of applications and found that there were two main problems with agent-based modeling the self-organization of social structure and the emergence of social order (Macy & Willer 2002). Below is a brief description of each problem Macy and Willer believe there to be; "Emergent structure.
Customer data integration Query processing Data_Integration > Theory > Query processing The theory of query processing in data integration systems is commonly expressed using conjunctive queries and Datalog, a purely declarative logic programming language. One can loosely think of a conjunctive query as a logical function applied to the relations of a database such as " f ( A , B ) {\displaystyle f(A,B)} where A < B {\displaystyle A
Simulacra and Simulation Degrees Simulacra_and_Simulation > Summary > Degrees Simulacra and Simulation identifies three types of simulacra and identifies each with a historical period: First order, associated with the premodern period, where representation is clearly an artificial placemarker for the real item. The uniqueness of objects and situations marks them as irreproducibly real and signification obviously gropes towards this reality. Second order, associated with the modernity of the Industrial Revolution, where distinctions between representation and reality break down due to the proliferation of mass-reproducible copies of items, turning them into commodities.
Maximum sustainable yield MSY model Maximum_sustainable_yield > Modelling MSY > MSY model For low densities (far from carrying capacity), there is little addition (or "recruitment") to the population, simply because there are few organisms to give birth. At high densities, though, there is intense competition for resources, and growth rate is again low because the death rate is high. In between these two extremes, the population growth rate rises to a maximum value ( N M S Y {\displaystyle N_{MSY}} ).
Chemical spills Summary Chemical_accident Chemical accidents are generally understood to be industrial-scale ones, often with important offsite consequences. Unintended exposure to chemicals that occur at smaller work sites, as well as in private premises during everyday activities are usually not referred to as chemical accidents. Process safety is the engineering discipline dealing with chemical accident hazards understanding and management. Process safety's scope extends however to fires and explosions from hazardous materials generally not referred to as 'chemicals', such as refined and unrefined hydrocarbon mixtures.
Table of elements The order of subshell filling Periodic_Table > Atomic structures of the elements > Electron configurations > The order of subshell filling The following elements then proceed to fill the 2p subshell. Boron (1s2 2s2 2p1) puts its new electron in a 2p orbital; carbon (1s2 2s2 2p2) fills a second 2p orbital; and with nitrogen (1s2 2s2 2p3) all three 2p orbitals become singly occupied. This is consistent with Hund's rule, which states that atoms usually prefer to singly occupy each orbital of the same type before filling them with the second electron.
Udwadia–Kalaba equation Background Udwadia–Kalaba_formulation > Background The Udwadia–Kalaba equation was developed in 1992 and describes the motion of a constrained mechanical system that is subjected to equality constraints.This differs from the Lagrangian formalism, which uses the Lagrange multipliers to describe the motion of constrained mechanical systems, and other similar approaches such as the Gibbs-Appell approach. The physical interpretation of the equation has applications in areas beyond theoretical physics, such as the control of highly nonlinear general dynamical systems.
Cross compiler Early history – 1980s Cross_compile > Microsoft C cross compilers > Early history – 1980s K&R's original needs was not only elegant 2nd level parsed syntax to replace asm 1st level parsed syntax: it was designed so that a minimal amount of asm be written to support each platform (the original design of C was ability to cross compile using C with the least support code per platform, which they needed.). Also yesterdays C directly related to ASM code wherever not platform dependent. Today's C (more-so c++) is no longer C compatible and the asm code underlying can be extremely different than written on a given platform (in Linux: it sometimes replaces and detours library calls with distributor choices). Today's C is a 3rd or 4th level language which is used the old way like a 2nd level language.
Human-agent team Concept Human-agent_team > Concept Software agents that behave as artificial team players satisfy the following general requirements: Observability: agents must make their status, intentions, knowledge observable to others. Predictability: agents must be predictable to others such that others can rely on them when considering their own actions Directability: agents must be capable of directing the behavior of others, as well as be directed by others.To satisfy these OPD requirements, agents exhibit various behaviors such as: Proactively communicating information to other agents to establish shared situation awareness within the team Explaining their decisions and recommendations to other teammates to establish appropriate levels of trust (also known as Explainable artificial intelligence) Receiving instructions at a high level of abstraction. Choosing the right moment of interaction to prevent inconvenient interruptions of other team members. Notifying others when they believe they can no longer contribute their part of the work required to fulfill the team goal.The engineering efforts to develop artificial team members include user interface design, but also the design of specialized social artificial intelligence, that enables agents to reason about whether some piece of information is worthy of sharing.
CAR and CDR Summary CAR_and_CDR In computer programming, CAR (car) and CDR (cdr) ( or ) are primitive operations on cons cells (or "non-atomic S-expressions") introduced in the Lisp programming language. A cons cell is composed of two pointers; the car operation extracts the first pointer, and the cdr operation extracts the second. Thus, the expression (car (cons x y)) evaluates to x, and (cdr (cons x y)) evaluates to y. When cons cells are used to implement singly linked lists (rather than trees and other more complicated structures), the car operation returns the first element of the list, while cdr returns the rest of the list. For this reason, the operations are sometimes given the names first and rest or head and tail.
Software fault tolerance Operating system failure Software_fault_tolerance > Operating system failure Computer applications make a call using the application programming interface (API) to access shared resources, like the keyboard, mouse, screen, disk drive, network, and printer. These can fail in two ways. Blocked Calls Faults
Circuit breakers Standard current ratings Arc_chute > Standard current ratings For low voltage distribution circuit breakers, International Standards, IEC 60898-1 defines the rated current as the maximum current that the breaker is designed to carry continuously. The commonly available preferred values for the rated current are 1 A, 2 A, 4 A, 6 A, 10 A, 13 A, 16 A, 20 A, 25 A, 32 A, 40 A, 50 A, 63 A, 80 A, 100 A, and 125 A. The circuit breaker is labeled with the rated current in amperes prefixed by a letter, which indicates the instantaneous tripping current that causes the circuit breaker to trip without intentional time delay expressed in multiples of the rated current: Circuit breakers are also rated by the maximum fault current that they can interrupt; this allows use of more economical devices on systems unlikely to develop the high short-circuit current found on, for example, a large commercial building distribution system. In the United States, Underwriters Laboratories (UL) certifies equipment ratings, called Series Ratings (or "integrated equipment ratings") for circuit breaker equipment used for buildings.
Bayesian model reduction Theory Bayesian_model_reduction > Theory Consider some model with parameters θ {\displaystyle \theta } and a prior probability density on those parameters p ( θ ) {\displaystyle p(\theta )} . The posterior belief about θ {\displaystyle \theta } after seeing the data p ( θ ∣ y ) {\displaystyle p(\theta \mid y)} is given by Bayes rule: The second line of Equation 1 is the model evidence, which is the probability of observing the data given the model. In practice, the posterior cannot usually be computed analytically due to the difficulty in computing the integral over the parameters. Therefore, the posteriors are estimated using approaches such as MCMC sampling or variational Bayes. A reduced model can then be defined with an alternative set of priors p ~ ( θ ) {\displaystyle {\tilde {p}}(\theta )}: The objective of Bayesian model reduction is to compute the posterior p ~ ( θ ∣ y ) {\displaystyle {\tilde {p}}(\theta \mid y)} and evidence p ~ ( y ) {\displaystyle {\tilde {p}}(y)} of the reduced model from the posterior p ( θ ∣ y ) {\displaystyle p(\theta \mid y)} and evidence p ( y ) {\displaystyle p(y)} of the full model. Combining Equation 1 and Equation 2 and re-arranging, the reduced posterior p ~ ( θ ∣ y ) {\displaystyle {\tilde {p}}(\theta \mid y)} can be expressed as the product of the full posterior, the ratio of priors and the ratio of evidences: The evidence for the reduced model is obtained by integrating over the parameters of each side of the equation: And by re-arrangement:
Higher order coherence Definition Higher_order_coherence > Definition The electric field E ( r , t ) {\displaystyle E(\mathbf {r} ,t)} can be separated into its positive and negative frequency components E ( r , t ) = E + ( r , t ) + E − ( r , t ) {\displaystyle E(\mathbf {r} ,t)=E^{+}(\mathbf {r} ,t)+E^{-}(\mathbf {r} ,t)} . Either of the two frequency components, contains all the physical information about the wave. The classical first-order, second order and nth order correlation function are defined as follows G c ( 1 ) ( x 1 , x 2 ) = ⟨ E − ( x 1 ) E + ( x 2 ) ⟩ {\displaystyle G_{c}^{(1)}(x_{1},x_{2})=\langle E^{-}(x_{1})E^{+}(x_{2})\rangle } , G c ( 2 ) ( x 1 , x 2 , x 3 , x 4 ) = ⟨ E − ( x 1 ) E − ( x 2 ) E + ( x 3 ) E + ( x 4 ) ⟩ {\displaystyle G_{c}^{(2)}(x_{1},x_{2},x_{3},x_{4})=\langle E^{-}(x_{1})E^{-}(x_{2})E^{+}(x_{3})E^{+}(x_{4})\rangle } , G c ( n ) ( x 1 , x 2 , . .
Glossary of field theory Basic definitions Field_homomorphism > Basic definitions The degree is called the imperfect degree of F. The field F is perfect if and only if its imperfect degree is 1. For example, if F is a function field of n variables over a finite field of characteristic p>0, then its imperfect degree is pn. Algebraically closed field A field F is algebraically closed if every polynomial in F has a root in F; equivalently: every polynomial in F is a product of linear factors.
Abortive initiation Function DNA_scrunching > Function There are no widely accepted functions for the resulting truncated RNA transcripts. However, a study in 1981 found evidence that there was a relationship between the amount of abortive transcripts produced and the time until long RNA strands are successfully produced. When RNA polymerase undergoes abortive transcription in the presence of ATP, UTP, and GTP, a complex is formed that has a much lower capacity for abortive recycling and a much higher rate of synthesis of the full-length RNA transcript. A study in 2010 did find evidence supporting that these truncated transcripts inhibit termination of RNA synthesis by a RNA hairpin-dependent intrinsic terminator.
Energy harvesting devices Motivation Power_stealing > Motivation Energy harvesting devices can utilize renewable and clean sources of energy that are abundant and ubiquitous in the environment, such as solar, thermal, wind, and kinetic energy. Energy harvesting devices can also reduce the need for power transmission and distribution systems that cause energy losses and environmental impacts. Energy harvesting devices can therefore contribute to the development of a more sustainable and resilient energy system.
Data-driven programming Applications Data-driven_programming > Applications An extreme example of the latter is pcap, which only consists of filtering, with the only action being “capture”. Less extremely, sieve has filters and actions, but in the base standard has no variables or loops, only allowing stateless filtering statements: each input element is processed independently. Variables allow state, which allow operations that depend on more than one input element, such as aggregation (summing inputs) or throttling (allow at most 5 mails per hour from each sender, or limiting repeated log messages).
ECgene Summary ECgene ECgene in computational biology is a database of genomic annotations taking alternative splicing events into consideration.
Diode-transistor logic Speed improvement Diode-transistor_logic > Speed improvement In his patent the Schottky diode prevented the transistor from saturating by minimizing the forward bias on the collector–base transistor junction, thus reducing the minority carrier injection to a negligible amount. The diode could also be integrated on the same die, had a compact layout, no minority-carrier charge storage, and was faster than a conventional junction diode. His patent also showed how the Schottky transistor could be used in DTL circuits and improve the switching speed of other saturated logic designs, such as Schottky-TTL, at a low cost.
Claasen's law Summary Claasen's_law Claasen's logarithmic law of usefulness is named after technologist Theo A. C. M. Claasen, who introduced the idea in 1999 when he was CTO of Philips Semiconductors: Usefulness = log(Technology)The law can also be expressed as: Technology = exp(Usefulness)
Aesthetic criticism Theoretical criticism Aesthetic_criticism > Theoretical criticism In other words, at issue is the relationship between many linked ideas. What effect does the adoption of one idea have for a lot of related ideas, and how does a theory relate to all the evidence it can be called upon to explain. A theory can consist of one major hypothesis, but usually a theory consists of a series of linked hypotheses.
Mersenne number About Mersenne primes Mersenne_primes > About Mersenne primes The current lack of any simple test to determine whether a given Mersenne number is prime makes the search for Mersenne primes a difficult task, since Mersenne numbers grow very rapidly. The Lucas–Lehmer primality test (LLT) is an efficient primality test that greatly aids this task, making it much easier to test the primality of Mersenne numbers than that of most other numbers of the same size. The search for the largest known prime has somewhat of a cult following.
AeroLift CycloCrane Design and development AeroLift_CycloCrane > Design and development As soon as the stalk begins to point forward the thrust generated by that engine starts the airship center body into rotation. After a revolution or two the other engine (or engines) are started. When the rate of rotation (in the two ton slingload Cyclocrane) reaches thirteen revolutions per minute the relative wind over the wings, is sixty-miles-per-hour.
Plasma osmolality Osmolality versus osmolarity Plasma_osmolality > Osmolality versus osmolarity However, at low concentrations (below about 500 mM), the mass of the solute is negligible compared to the mass of the solvent, and osmolarity and osmolality are very similar.Technically, the terms can be compared as follows: Therefore, bedside calculations are actually in units of osmolarity, whereas laboratory measurements will provide readings in units of osmolality. In practice, there is almost negligible difference between the absolute values of the different measurements. For this reason, both terms are often used interchangeably, even though they refer to different units of measurement.
Large scale Manufacturers G_scale > Manufacturers American Model Builders: 1:24 Aristo-Craft (REA), which closed in 2013, made two scales: 1:29 and the "Classic" series (generally 1:24 but some models were closer to 1:32 scale). Aster (C&S Mogul): 1:32, 1:30 for Japanese prototypes and 1:22.5 for European and Japanese narrow gauge. Bachmann's "Big Haulers" series: 1:22.5, while their "Spectrum" series is to 1:20.3 scale and their train streetcars: 1:29 Buddy "L" (Keystone) (modern): 1:22.5 scale (almost identical to Bachmann, except cab is taller), older (legacy) equipment runs on rails spaced 3-1/4 inches from the pre WWII era.
Adversarial machine learning HopSkipJump Attack General_adversarial_network > Specific attack types > Adversarial examples > Black box attacks > HopSkipJump Attack This black box attack was also proposed as a query efficient attack, but one that relies solely on access to any input's predicted output class. In other words, the HopSkipJump attack does not require the ability to calculate gradients or access to score values like the Square Attack, and will require just the model's class prediction output (for any given input). The proposed attack is split into two different settings, targeted and untargeted, but both are built from the general idea of adding minimal perturbations that leads to a different model output. In the targeted setting, the goal is to cause the model to misclassify the perturbed image to a specific target label (that is not the original label).
Hypothalamic–pituitary–adrenal axis Stress and disease Hypothalamic–pituitary–adrenal_axis > Stress > Stress and disease Stressors can be of many different types—in experimental studies in rats, a distinction is often made between "social stress" and "physical stress", but both types activate the HPA axis, though via different pathways. Several monoamine neurotransmitters are important in regulating the HPA axis, especially dopamine, serotonin and norepinephrine (noradrenaline). There is evidence that an increase in oxytocin, resulting for instance from positive social interactions, acts to suppress the HPA axis and thereby counteracts stress, promoting positive health effects such as wound healing.The HPA axis is a feature of mammals and other vertebrates.
Jig borer History Jig_borer > History The jig borer was a logical extension of manual machine tool technology that began to incorporate some then-novel concepts that would become routine with NC and CNC control, such as: coordinate dimensioning (dimensioning of all locations on the part from a single reference point); working routinely in "tenths" (ten-thousandths of an inch, 0.0001 inch) as a fast, everyday machine capability (whereas it had been the exclusive domain of special, time-consuming, craftsman-dependent manual skills); and circumventing jigs altogether.Franklin D. Jones, in his textbook Machine Shop Training Course (5th ed), noted: "In many cases, a jig borer is a 'jig eliminator.' In other words, such a machine may be used instead of a jig either when the quantity of work is not large enough to warrant making a jig or when there is insufficient time for jig making.
Ring of symmetric functions Generating functions Ring_of_symmetric_functions > Properties of the ring of symmetric functions > Generating functions The first definition of ΛR as a subring of R ] {\displaystyle R]} allows the generating functions of several sequences of symmetric functions to be elegantly expressed. Contrary to the relations mentioned earlier, which are internal to ΛR, these expressions involve operations taking place in R] but outside its subring ΛR], so they are meaningful only if symmetric functions are viewed as formal power series in indeterminates Xi. We shall write "(X)" after the symmetric functions to stress this interpretation.
Views of Lyndon LaRouche and the LaRouche movement Ozone hole Views_of_Lyndon_LaRouche_and_the_LaRouche_movement > Environment and energy > Ozone hole It has been called "probably the best known and most widely quoted text aimed at debunking the concept of ozone depletion". Its assertions were repeated by Dixy Lee Ray in her 1993 book Environmental Overkill, by Rush Limbaugh, and by Ronald Bailey. Some atmospheric scientists have said that it is based on poor research.At a 1994 shareholder's meeting, Smith called on Dupont to continue producing CFCs, saying there was no evidence of their harmfulness and that "This is nothing less than genocide". By 1995 LaRouche was noted as calling the ozone hole a "myth". Maduro's writings were the basis for the Arizona legislature's passage of a 1995 bill to allow the production of CFCs in the state despite federal and international prohibitions.
Clinical medicine Basic sciences Human_medicine > Branches > Basic sciences Epidemiology is the study of the demographics of disease processes, and includes, but is not limited to, the study of epidemics. Genetics is the study of genes, and their role in biological inheritance. Gynecology is the study of female reproductive system.
Conservation of Angular Momentum General considerations Introduction_to_angular_momentum > Conservation of angular momentum > General considerations A rotational analog of Newton's third law of motion might be written, "In a closed system, no torque can be exerted on any matter without the exertion on some other matter of an equal and opposite torque about the same axis." Hence, angular momentum can be exchanged between objects in a closed system, but total angular momentum before and after an exchange remains constant (is conserved).Seen another way, a rotational analogue of Newton's first law of motion might be written, "A rigid body continues in a state of uniform rotation unless acted by an external influence." Thus with no external influence to act upon it, the original angular momentum of the system remains constant.The conservation of angular momentum is used in analyzing central force motion. If the net force on some body is directed always toward some point, the center, then there is no torque on the body with respect to the center, as all of the force is directed along the radius vector, and none is perpendicular to the radius.
Glossary of module theory Summary Glossary_of_module_theory Module theory is the branch of mathematics in which modules are studied. This is a glossary of some terms of the subject. See also: Glossary of linear algebra, Glossary of ring theory, Glossary of representation theory.
Cell physiology Endocytosis in animal cells Cell_physiology > Physiological processes > Endocytosis in animal cells Endocytosis is a form of active transport where a cell takes in molecules, using the plasma membrane, and packages them into vesicles. : 139–140
Jesús Mosterín Philosophy of biology Jesús_Mosterín > Philosophy of science > Philosophy of biology It is true that all organisms on Earth share many characteristics, from the encoding of genetic information in DNA to the storage of energy in ATP, but these common features merely reflect the inheritance from a common ancestor that possibly acquired them in a random way. From that point of view, our biology is the parochial science of life on Earth, rather than a universal science of life in general. Such a general biology seems impossible, as long as we do not detect and come to know other forms of life in the galaxy (if they exist).
Seven-dimensional space Summary Seventh_dimension In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space. When n = 7, the set of all such locations is called 7-dimensional space. Often such a space is studied as a vector space, without any notion of distance. Seven-dimensional Euclidean space is seven-dimensional space equipped with a Euclidean metric, which is defined by the dot product.More generally, the term may refer to a seven-dimensional vector space over any field, such as a seven-dimensional complex vector space, which has 14 real dimensions.
Dichromatic symmetry Summary Dichromatic_symmetry Dichromatic symmetry, also referred to as antisymmetry, black-and-white symmetry, magnetic symmetry, counterchange symmetry or dichroic symmetry, is a symmetry operation which reverses an object to its opposite. A more precise definition is "operations of antisymmetry transform objects possessing two possible values of a given property from one value to the other." Dichromatic symmetry refers specifically to two-coloured symmetry; this can be extended to three or more colours in which case it is termed polychromatic symmetry. A general term for dichromatic and polychromatic symmetry is simply colour symmetry. Dichromatic symmetry is used to describe magnetic crystals and in other areas of physics, such as time reversal, which require two-valued symmetry operations.
Local search algorithm Description Local_search_algorithm > Description The same problem may have multiple distinct neighborhoods defined on it; local optimization with neighborhoods that involve changing up to k components of the solution is often referred to as k-opt. Typically, every candidate solution has more than one neighbor solution; the choice of which one to select is taken using only information about the solutions in the neighborhood of the current assignment, hence the name local search. When the choice of the neighbor solution is done by taking the one locally maximizing the criterion, i.e.: a greedy search, the metaheuristic takes the name hill climbing.
Homology theory Surfaces Homology_theories > Background > Surfaces Cutting a manifold along a cycle homologous to zero separates the manifold into two or more components. For example, cutting the sphere along a produces two hemispheres. This is not generally true of cycles on other surfaces.
Benzilic acid rearrangement Reaction mechanism Benzilic_acid_rearrangement > Reaction mechanism This sequence resembles a nucleophilic acyl substitution. Calculations show that when R is methyl the charge build-up on this group in the transition state can be as high as 0.22 and that the methyl group is positioned between the central carbon carbon bond! The carboxylic acid in intermediate 4 is less basic than the alkoxide and therefore reversible proton transfer takes place favoring intermediate 5 which is protonated on acidic workup to the final α-hydroxy–carboxylic acid 6.
Magnetic torquer Summary Magnetic_torquers A magnetorquer or magnetic torquer (also known as a torque rod) is a satellite system for attitude control, detumbling, and stabilization built from electromagnetic coils. The magnetorquer creates a magnetic dipole that interfaces with an ambient magnetic field, usually Earth's, so that the counter-forces produced provide useful torque.
Paxos algorithm Optimisations Paxos_algorithm > Optimisations "Acceptors do not care what value is chosen. They simply respond to Prepare and Accept! messages to ensure that, despite failures, only a single value can be chosen.
Bond Order Bond order in molecular orbital theory Bond_Order > Bond order in molecular orbital theory In molecular orbital theory, bond order is defined as half the difference between the number of bonding electrons and the number of antibonding electrons as per the equation below. This often but not always yields similar results for bonds near their equilibrium lengths, but it does not work for stretched bonds. Bond order is also an index of bond strength and is also used extensively in valence bond theory.
Tipping point (physics) Cell biology and genetics Hysteresis > In biology > Cell biology and genetics In neural tissue, this hysteresis is regulated by a homeodomain (HD) feedback circuit that amplifies Shh signaling. In this circuit, expression of Gli transcription factors, the executors of the Shh pathway, is suppressed. Glis are processed to repressor forms (GliR) in the absence of Shh, but in the presence of Shh, a proportion of Glis are maintained as full-length proteins allowed to translocate to the nucleus, where they act as activators (GliA) of transcription. By reducing Gli expression then, the HD transcription factors reduce the total amount of Gli (GliT), so a higher proportion of GliT can be stabilized as GliA for the same concentration of Shh.
Bayesian operational modal analysis Connection with maximum likelihood method Bayesian_operational_modal_analysis > Connection with maximum likelihood method Bayesian method and maximum likelihood method (non-Bayesian) are based on different philosophical perspectives but they are mathematically connected; see, e.g., and Section 9.6 of. For example, Assuming a uniform prior, the most probable value (MPV) of parameters in a Bayesian method is equal to the location where the likelihood function is maximized, which is the estimate in Maximum Likelihood Method Under a Gaussian approximation of the posterior distribution of parameters, their covariance matrix is equal to the inverse of Hessian of the negative log of likelihood function at the MPV. Generally, this covariance depends on data. However, if one assumes (hypothetically; non-Bayesian) that the data is indeed distributed as the likelihood function, then for large data size it can be shown that the covariance matrix is asymptotically equal to the inverse of the Fisher information matrix (FIM) of parameters (which has a non-Bayesian origin).
Classic RISC pipeline Instruction fetch Classic_RISC_pipeline > The classic five stage RISC pipeline > Instruction fetch Then during the cycle, the instruction is read out of instruction memory, and at the same time, a calculation is done to determine the next PC. The next PC is calculated by incrementing the PC by 4, and by choosing whether to take that as the next PC or to take the result of a branch/jump calculation as the next PC. Note that in classic RISC, all instructions have the same length.
Autogenous vaccines In humans Autogenous_vaccines > Applications > In humans The application process usually involves a gradual increase in doses and intervals. Another administration method is by oral therapy, especially in bronchial asthma. In light of possible adverse effects, the patient should be observed for an hour after the administration.
List of named differential equations Orbital mechanics List_of_named_differential_equations > Engineering > Orbital mechanics Clohessy–Wiltshire equations
Reversible queueing system History Queueing_theory > History In 1953, David George Kendall solved the GI/M/k queue and introduced the modern notation for queues, now known as Kendall's notation. In 1957, Pollaczek studied the GI/G/1 using an integral equation. John Kingman gave a formula for the mean waiting time in a G/G/1 queue, now known as Kingman's formula.Leonard Kleinrock worked on the application of queueing theory to message switching in the early 1960s and packet switching in the early 1970s.
Variable (mathematics) Specific kinds of variables Mathematical_variable > Specific kinds of variables This is typically the case in sentences like "function of a real variable", "x is the variable of the function f: x ↦ f(x)", "f is a function of the variable x" (meaning that the argument of the function is referred to by the variable x). In the same context, variables that are independent of x define constant functions and are therefore called constant. For example, a constant of integration is an arbitrary constant function that is added to a particular antiderivative to obtain the other antiderivatives.
Diesel Particulate Filter Regeneration Diesel_particulate_filtration > Regeneration The family of Mg doped catalysts, named Grindstaff catalysts after the chemist who started the work, has been the subject of much investigation across industry and academia with the tightening of emissions regulations on particulate matter world wide.In some cases, in the absence of a fuel-borne catalyst, the combustion of the particulate matter can raise temperatures so high, that they are above the structural integrity threshold of the filter material, which can cause catastrophic failure of the substrate. Various strategies have been developed to limit this possibility. Note that unlike a spark-ignited engine, which typically has less than 0.5% oxygen in the exhaust gas stream before the emission control device(s), diesel engines have a very high ratio of oxygen available.
Computer Go Minimax tree search Computer_Go > System design > Minimax tree search However, both of these options introduce a significant risk of not considering a vital move which would have changed the course of the game. Results of computer competitions show that pattern matching techniques for choosing a handful of appropriate moves combined with fast localized tactical searches (explained above) were once sufficient to produce a competitive program. For example, GNU Go was competitive until 2008.
Pythagorean equation Proofs by dissection and rearrangement The_Pythagorean_theorem > Other proofs of the theorem > Proofs by dissection and rearrangement Another by rearrangement is given by the middle animation. A large square is formed with area c2, from four identical right triangles with sides a, b and c, fitted around a small central square. Then two rectangles are formed with sides a and b by moving the triangles.
Splay trees Implementation and variants Dynamic_Optimality_Conjecture > Implementation and variants The first two contain all items of original tree known to be less than or greater than current item respectively. The middle tree consists of the sub-tree rooted at the current node.
NK cells Activating receptors NK_Cell > NK cell receptors > Activating receptors They recognize PAMPs (pathogen-associated molecular patterns) and DAMPs (damage-associated molecular patterns) as their ligands. These receptors are crucial for the induction of the immune respose. TLR induction amplyfies the immune response by promoting the production of inflammatory cytokines and chemokines and ultimately leads to the activation of NK cell effector functions.