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Spectral triple Important concepts Spectral_triple > Important concepts Given a spectral triple (A, H, D), one can apply several important operations to it. The most fundamental one is the polar decomposition D = F\|D\| of D into a self adjoint unitary operator F (the 'phase' of D) and a densely defined positive operator \|D\| (the 'metric' part).
AsO4 Summary AsO4 The arsenate is an ion with the chemical formula AsO3−4. Bonding in arsenate consists of a central arsenic atom, with oxidation state +5, double bonded to one oxygen atom and single bonded to a further three oxygen atoms. The four oxygen atoms orient around the arsenic atom in a tetrahedral geometry. Resonance disperses the ion's −3 charge across all four oxygen atoms.
Root nameservers Root domain Root_DNS_servers > Root domain The DNS is a hierarchical naming system for computers, services, or any resource participating in the Internet. The top of that hierarchy is the root domain. The root domain does not have a formal name and its label in the DNS hierarchy is an empty string. All fully qualified domain names (FQDNs) on the Internet can be regarded as ending with this empty string for the root domain, and therefore ending in a full stop character (the label delimiter), e.g., "www.example.com.".
Plant Physiology Photomorphogenesis Plant_biochemistry > Signals and regulators > Photomorphogenesis While most people know that light is important for photosynthesis in plants, few realize that plant sensitivity to light plays a role in the control of plant structural development (morphogenesis). The use of light to control structural development is called photomorphogenesis, and is dependent upon the presence of specialized photoreceptors, which are chemical pigments capable of absorbing specific wavelengths of light. Plants use four kinds of photoreceptors: phytochrome, cryptochrome, a UV-B photoreceptor, and protochlorophyllide a. The first two of these, phytochrome and cryptochrome, are photoreceptor proteins, complex molecular structures formed by joining a protein with a light-sensitive pigment. Cryptochrome is also known as the UV-A photoreceptor, because it absorbs ultraviolet light in the long wave "A" region.
Small RNA In plants Small_RNA > In plants The first known function in plants was discovered in mutants of Arabidopsis. Specifically with decline in function mutations for RNA-dependent RNA polymerase and DICER-like production. This impairment actually enhanced Arabidopsis resistance against Heterodera schachtii and Meloidogyne javanica.
Bayesian quadrature Advantages and disadvantages Bayesian_quadrature > Bayesian quadrature > Advantages and disadvantages Since Bayesian quadrature is an example of probabilistic numerics, it inherits certain advantages compared with traditional numerical integration methods: It allows uncertainty to be quantified and propagated through all subsequent computations to explicitly model the impact of numerical error. It provides a principled way to incorporate prior knowledge by using a judicious choice of prior distributions for f {\displaystyle f} , which may be more sophisticated compared to the standard Gaussian process just described. It permits more efficient use of information, e.g. jointly inferring multiple related quantities of interest or using active learning to reduce the required number of points.Despite these merits, Bayesian quadrature methods possess the following limitations: Although the Bayesian paradigm allows a principled treatment of the quantification of uncertainty, posterior inference over ν {\displaystyle \nu } is not always tractable, thus requiring a second-level estimation. E.g. for Bayesian quadrature with Gaussian processes, the kernel mean embedding ν {\displaystyle \nu } has no closed-form expression for a general kernel k {\displaystyle k} and measure ν {\displaystyle \nu } .The computational cost of Bayesian quadrature methods based on Gaussian processes is in general O ( n 3 ) {\displaystyle {\mathcal {O}}(n^{3})} due to the cost of inverting n × n {\displaystyle n\times n} matrices, which may defy their applications to large-scale problems.
Interclass correlation Summary Interclass_correlation In statistics, the interclass correlation (or interclass correlation coefficient) is a measure of a relation between two variables of different classes (types), such as the weights of 10-year-old sons and of their 40-year-old fathers. Deviations of a variable are measured from the mean of the data for that class – a son's weight minus the mean of all the sons' weights, or a father's weight minus the mean of all the fathers' weights. The Pearson correlation coefficient is the most commonly used measure of interclass correlation. The interclass correlation contrasts with the intraclass correlation between variables of the same class, such as the weights of women and of their identical twins; here deviations are measured from the mean of all members of the single class, in this example of all women in the set of identical twins. == References ==
Bodybuilding Protein Bodybuilding > Muscle growth > Nutrition > Protein Casein or whey are often used to supplement the diet with additional protein. Whey is the type of protein contained in many popular brands of protein supplements and is preferred by many bodybuilders because of its high biological value (BV) and quick absorption rates. Whey protein also has a bigger effect than casein on insulin levels, triggering about double the amount of insulin release.
Gene Genetic code Expressed_gene > Gene expression > Genetic code The nucleotide sequence of a gene's DNA specifies the amino acid sequence of a protein through the genetic code. Sets of three nucleotides, known as codons, each correspond to a specific amino acid. : 6 The principle that three sequential bases of DNA code for each amino acid was demonstrated in 1961 using frameshift mutations in the rIIB gene of bacteriophage T4 (see Crick, Brenner et al. experiment).
AppleScript Classes (data types) AppleScript > Language essentials > Classes (data types) reference: an object that encapsulates an unevaluated object specifier that may or may not point to a valid object. Can be evaluated on-demand by accessing its contents property.
Glossary of areas of mathematics C Glossary_of_areas_of_mathematics > C Character theory a branch of group theory that studies the characters of group representations or modular representations. Class field theory a branch of algebraic number theory that studies abelian extensions of number fields. Classical differential geometry also known as Euclidean differential geometry.
Rahul Sarpeshkar Research summary Rahul_Sarpeshkar > Research summary For example, the synthesis of biofuels, chemicals, energy, molecular and cellular sensors, network drug design, treatments for cancer, diabetes, auto-immune, infectious, and neural diseases can all impacted be impacted by his fundamental work on analog synthetic and systems biology. Sarpeshkar's work on glucose powered medical implants has been featured in the Economist, WIRED, and Science News and was highlighted by Scientific American among 2012's top scientific breakthroughs . Professor Sarpeshkar's work on a hybrid analog-digital circuit that mimics feedback networks in the brain has appeared on the cover of the journal Nature and has received wide media attention .
General anxiety disorder Summary General_anxiety_disorder In general, ICD-10 is more inclusive than DSM-5, so estimates regarding prevalence and lifetime risk tend to be greater using ICD-10. In regard to prevalence, in a given year, about two (2%) percent of adults in the United States and Europe have been suggested to have GAD. However, the risk of developing GAD at any point in life has been estimated at 9.0%. Although it is possible to experience a single episode of GAD during one's life, most people who experience GAD experience it repeatedly over the course of their lives as a chronic or ongoing condition. GAD is diagnosed twice as frequently in women as in men.
Insect central nervous system Brainstem Central_Nervous_System > Structure > Brain > Brainstem It includes nuclei linking distinct parts of the motor system, including the cerebellum, the basal ganglia and both cerebral hemispheres, among others. Additionally, parts of the visual and auditory systems are located in the midbrain, including control of automatic eye movements.The brainstem at large provides entry and exit to the brain for a number of pathways for motor and autonomic control of the face and neck through cranial nerves, Autonomic control of the organs is mediated by the tenth cranial nerve. A large portion of the brainstem is involved in such autonomic control of the body. Such functions may engage the heart, blood vessels, and pupils, among others.The brainstem also holds the reticular formation, a group of nuclei involved in both arousal and alertness.
Unconventional (oil & gas) reservoir Environmental differences Unconventional_gas > Essential differences between conventional and unconventional reservoirs > Environmental differences As with all forms of fossil fuel, there are established issues with greenhouse gas emissions through export (distribution) as well as consumption (combustion), which are identical whether the oil or gas are derived from conventional or unconventional reservoirs. Their carbon footprints, however, are radically different: conventional reservoirs use the natural energy in the environment to flow oil and gas to the surface unaided; unconventional reservoirs require putting energy into the ground for extraction, either as heat (e.g. tar sands and oil shales) or as pressure (e.g. shale gas and CBM). The artificial transfer of heat and pressure require the use of large volumes of fresh water creating supply and disposal issues. The distribution of the resource over large areas creates land use issues, with implications for local communities on infrastructure, freight traffic and local economies. Impact on the environment is an unavoidable consequence of all human activity but the difference between the impact of conventional reservoirs compared with unconventional is significant, measurable and predictable.
Respiratory failure Type 4 Respiratory_insufficiency > Diagnosis > Type 4 Type 4 respiratory failure results from hypoperfusion of respiratory muscles as in patients in shock. Patients in shock often experience respiratory distress due to pulmonary edema (e.g., in cardiogenic shock). Lactic acidosis and anemia can also result in type 4 respiratory failure. However, type 1 and 2 are the most widely accepted.
Determining the number of clusters in a data set Analyzing the kernel matrix Determining_the_number_of_clusters_in_a_data_set > Analyzing the kernel matrix The method proceeds by the eigenvalue decomposition of the kernel matrix. It will then analyze the eigenvalues and eigenvectors to obtain a measure of the compactness of the input distribution.
Endothermic process Distinction between endothermic and endotherm Endothermic_process > Distinction between endothermic and endotherm The terms "endothermic" and "endotherm" are both derived from Greek ἔνδον endon "within" and θέρμη thermē "heat", but depending on context, they can have very different meanings. In physics, thermodynamics applies to processes involving a system and its surroundings, and the term "endothermic" is used to describe a reaction where energy is taken "(with)in" by the system (vs. an "exothermic" reaction, which releases energy "outwards"). In biology, thermoregulation is the ability of an organism to maintain its body temperature, and the term "endotherm" refers to an organism that can do so from "within" by using the heat released by its internal bodily functions (vs. an "ectotherm", which relies on external, environmental heat sources) to maintain an adequate temperature.
Recursion theory The priority method Recursion_theory > Areas of research > The priority method Priority arguments have been employed to solve many problems in computability theory, and have been classified into a hierarchy based on their complexity. Because complex priority arguments can be technical and difficult to follow, it has traditionally been considered desirable to prove results without priority arguments, or to see if results proved with priority arguments can also be proved without them. For example, Kummer published a paper on a proof for the existence of Friedberg numberings without using the priority method.
Experimental Economics Software tools Experimental_Economics > Software tools The setup of an experiment is variable and can be defined in the imperative language z-Tree programming language. This language allows the experimenter to set up a variety of experiments and additional surveys. Alternatively, there is a big number of competing alternative software. Following table presents a growing list of software tools for experimental economics:
Lexell's theorem Opposite arcs of Lexell's circle Lexell's_theorem > Opposite arcs of Lexell's circle The sphere is separated into two hemispheres by the great circle A B , {\displaystyle AB,} and any Lexell circle through A ∗ {\displaystyle A^{}} and B ∗ {\displaystyle B^{}} is separated into two arcs, one in each hemisphere. If the point X {\displaystyle X} is on the opposite arc from C , {\displaystyle C,} then the areas of △ A B C {\displaystyle \triangle ABC} and △ A B X {\displaystyle \triangle ABX} will generally differ. However, if spherical surface area is interpreted to be signed, with sign determined by boundary orientation, then the areas of triangle △ A B C {\displaystyle \triangle ABC} and △ A B X {\displaystyle \triangle ABX} have opposite signs and differ by the area of a hemisphere. Lexell suggested a more general framing.
Digital filters Comparison of analog and digital filters Digital_filters > Comparison of analog and digital filters A digital filter will introduce noise to a signal during analog low pass filtering, analog to digital conversion, digital to analog conversion and may introduce digital noise due to quantization. With analog filters, every component is a source of thermal noise (such as Johnson noise), so as the filter complexity grows, so does the noise. However, digital filters do introduce a higher fundamental latency to the system.
Strained yogurt West Asia and East Mediterranean Strained_yogurt > Geographical variations > West Asia and East Mediterranean It is usually mixed with fresh herbs in a pesto-like purée called delal. Yogurt is a side dish to many Iranian meals. Strained yogurt is used as dips and various appetizers with multitudes of ingredients: cucumbers, onions, shallots, fresh herbs (dill, spearmint, parsley, cilantro), spinach, walnuts, zereshk, garlic, etc. The most popular appetizers are spinach or eggplant borani, ‘'Mâst-o-Khiâr'’ with cucumber, spring onions and herbs, or ‘'Mâst-Musir'’ with wild shallots.
IEEE 1516 Dimensions table High_level_architecture_(simulation) > Object model template (OMT) > Dimensions table The purpose of the dimensions table is to specify the DDM dimensions, used for attributes and interaction classes.
Convergence proof techniques Convergent subsequences Convergence_proof_techniques > Convergence in Rn > Convergent subsequences Every bounded sequence in R n {\displaystyle \mathbb {R} ^{n}} has a convergent subsequence, by the Bolzano–Weierstrass theorem. If these all have the same limit, then the original sequence converges to that limit. If it can be shown that all of the subsequences of f {\displaystyle f} have the same limit, such as by showing that there is a unique fixed point of the transformation T {\displaystyle T} , then the initial sequence must also converge to that limit.
Common integrals in quantum field theory Integrals with a complex argument of the exponent Common_integrals_in_quantum_field_theory > Variations on a simple Gaussian integral > Integrals with a complex argument of the exponent The integral of interest is (for an example of an application see Relation between Schrödinger's equation and the path integral formulation of quantum mechanics) We now assume that a and J may be complex. Completing the square By analogy with the previous integrals This result is valid as an integration in the complex plane as long as a is non-zero and has a semi-positive imaginary part. See Fresnel integral.
UxuA RNA motif Summary UxuA_RNA_motif However, since the RNAs are found in relatively closely related organisms, it is possible that the apparent gene association arose by chance. Therefore, uxuA RNAs might also function in trans as small RNAs. == References ==
Muon Muon decay Muon_decay > Muon decay Muons are unstable elementary particles and are heavier than electrons and neutrinos but lighter than all other matter particles. They decay via the weak interaction. Because leptonic family numbers are conserved in the absence of an extremely unlikely immediate neutrino oscillation, one of the product neutrinos of muon decay must be a muon-type neutrino and the other an electron-type antineutrino (antimuon decay produces the corresponding antiparticles, as detailed below). Because charge must be conserved, one of the products of muon decay is always an electron of the same charge as the muon (a positron if it is a positive muon).
Particle damping Introduction Particle_damping > Introduction Impact damping refers to only a single (somewhat larger) auxiliary mass in a cavity, whereas particle damping is used to imply multiple auxiliary masses of small size in a cavity. The principle behind particle damping is the removal of vibratory energy through losses that occur during impact of granular particles which move freely within the boundaries of a cavity attached to a primary system. In practice, particle dampers are highly nonlinear dampers whose energy dissipation, or damping, is derived from a combination of loss mechanisms, including friction and momentum exchange. Because of the ability of particle dampers to perform through a wide range of temperatures and frequencies and survive for a longer life, they have been used in applications such as the weightless environments of outer space, in aircraft structures, to attenuate vibrations of civil structures, and even in tennis rackets.
Walrasian equilibrium Indivisible items Walrasian_equilibrium > Examples > Indivisible items . , n {\displaystyle i=1,...,n} . There is a single type of good.
Linked lists Random-access lists Linked_list > Internal and external storage > Random-access lists A random-access list is a list with support for fast random access to read or modify any element in the list. One possible implementation is a skew binary random-access list using the skew binary number system, which involves a list of trees with special properties; this allows worst-case constant time head/cons operations, and worst-case logarithmic time random access to an element by index. Random-access lists can be implemented as persistent data structures.Random-access lists can be viewed as immutable linked lists in that they likewise support the same O(1) head and tail operations.A simple extension to random-access lists is the min-list, which provides an additional operation that yields the minimum element in the entire list in constant time (without mutation complexities).
Planarian Nervous system Planarian > Anatomy and physiology > Nervous system There are two auricles (earlike projections) at the base of the head, which are sensitive to touch and the presence of certain chemicals. The mouth is located in the middle of the underside of the body, which is covered with hairlike projections (cilia). There are no circulatory or respiratory systems; oxygen enters and carbon dioxide leaves the planarian's body by diffusing through the body wall.
Metallic crystal Alloys Metallic_crystal > Alloys Copper alloys have been known since prehistory—bronze gave the Bronze Age its name—and have many applications today, most importantly in electrical wiring. The alloys of the other three metals have been developed relatively recently; due to their chemical reactivity they need electrolytic extraction processes. The alloys of aluminum, titanium, and magnesium are valued for their high strength-to-weight ratios; magnesium can also provide electromagnetic shielding. These materials are ideal for situations where high strength-to-weight ratio is more important than material cost, such as in aerospace and some automotive applications. Alloys specially designed for highly demanding applications, such as jet engines, may contain more than ten elements.
G-force Acceleration and forces G-force > Acceleration and forces Therefore, if an automobile is capable of braking at 1 g and is traveling at 35 kilometres per hour (22 mph), it can brake to a standstill in one second and the driver will experience a deceleration of 1 g. The automobile traveling at three times this speed, 105 km/h (65 mph), can brake to a standstill in three seconds. In the case of an increase in speed from 0 to v with constant acceleration within a distance of s this acceleration is v2/(2s). Preparing an object for g-tolerance (not getting damaged when subjected to a high g-force) is called g-hardening. This may apply to, e.g., instruments in a projectile shot by a gun.
HLA type In infectious diseases Human_lymphocyte_antigen > Functions > In infectious diseases Once a T-cell recognizes a peptide within an MHC class II molecule, it can stimulate B-cells that also recognize the same molecule in their B-cell receptors. Thus, T-cells help B-cells make antibodies to the same foreign antigens. Each HLA can bind many peptides, and each person has 3 HLA types and can have 4 isoforms of DP, 4 isoforms of DQ and 4 Isoforms of DR (2 of DRB1, and 2 of DRB3, DRB4, or DRB5) for a total of 12 isoforms. In such heterozygotes, it is difficult for disease-related proteins to escape detection.
Chronic obstructive pulmonary disorder Pathophysiology Chronic_obstructive_pulmonary_disease > Pathophysiology General muscle wasting that often occurs in COPD may be partly due to inflammatory mediators released by the lungs into the blood. Narrowing of the airways occurs due to inflammation and subsequent scarring within them. This contributes to the inability to breathe out fully.
Introduction to evolution Coevolution Introduction_to_evolution > Coevolution Rather, across a population small genetic changes in both ant and tree benefited each. The benefit gave a slightly higher chance of the characteristic being passed on to the next generation. Over time, successive mutations created the relationship we observe today.
PlayStation Move Motion controller PlayStation_Move > Hardware > Motion controller On the tail end of the controller is the wrist strap, USB port, and extension port.The motion controller features vibration-based haptic technology. In addition to providing a tracking reference, the controller's orb light can be used to provide visual feedback, simulating aesthetic effects such as the muzzle flash of a gun or the paint on a brush.Using different orb colors for each controller, up to four motion controllers can be tracked at once on the PlayStation 3. Demonstrations for the controller have featured activities using a single motion controller, as well as those in which the user wields two motion controllers, with one in each hand.
Object-based attention Distractors Object-based_attention > Nature and effects of object-based attention > Distractors The third theory contends that there is greater interference of object-based attention when any flanking distractors (e.g., visual scene crowding or noise) are present. Particularly, if these distractors belong to the same object or object-group as that being attended (noise similar), as opposed to coming from different objects (noise dissimilar)—irrespective of the distinguishing characteristics of the objects themselves (e.g., colour, motion direction, shape, orientation). An influencing element is that an object-like representation can engage attention even when it is not the intended target of a visual search. Therefore, an important consideration is that the perceptual resemblance between distractors and a target object influences the efficiency of visual search; increases in similarity among the distractors, increases search efficiency. Similarly, visual search efficiency increases the less similar the target is to the distractors.
Law of effect Influence Law_of_effect > Influence The law of work for psychologist B. F. Skinner almost half a century later on the principles of operant conditioning, "a learning process by which the effect, or consequence, of a response influences the future rate of production of that response." Skinner would later use an updated version of Thorndike's puzzle box, called the operant chamber, or Skinner box, which has contributed immensely to our perception and understanding of the law of effect in modern society and how it relates to operant conditioning. It has allowed a researcher to study the behavior of small organisms in a controlled environment.
Mathematical formulation of the Standard Model Electroweak sector Mathematical_formulation_of_the_Standard_Model > Lagrangian formalism > Coupling terms > Electroweak sector The electroweak sector interacts with the symmetry group U(1) × SU(2)L, where the subscript L indicates coupling only to left-handed fermions. Where Bμ is the U(1) gauge field; YW is the weak hypercharge (the generator of the U(1) group); Wμ is the three-component SU(2) gauge field; and the components of τ are the Pauli matrices (infinitesimal generators of the SU(2) group) whose eigenvalues give the weak isospin. Note that we have to redefine a new U(1) symmetry of weak hypercharge, different from QED, in order to achieve the unification with the weak force. The electric charge Q, third component of weak isospin T3 (also called Tz, I3 or Iz) and weak hypercharge YW are related by (or by the alternative convention Q = T3 + YW).
Statistical learning theory Regularization Statistical_learning_theory > Regularization In machine learning problems, a major problem that arises is that of overfitting. Because learning is a prediction problem, the goal is not to find a function that most closely fits the (previously observed) data, but to find one that will most accurately predict output from future input. Empirical risk minimization runs this risk of overfitting: finding a function that matches the data exactly but does not predict future output well. Overfitting is symptomatic of unstable solutions; a small perturbation in the training set data would cause a large variation in the learned function.
Moment of mass Galilean frame transforms Moment_of_mass > Galilean frame transforms For classical (Galileo-Newtonian) mechanics, the transformation law from one inertial or accelerating (including rotation) frame (reference frame traveling at constant velocity - including zero) to another is the Galilean transform. Unprimed quantities refer to position, velocity and acceleration in one frame F; primed quantities refer to position, velocity and acceleration in another frame F' moving at translational velocity V or angular velocity Ω relative to F. Conversely F moves at velocity (—V or —Ω) relative to F'. The situation is similar for relative accelerations.
Graham's Law Examples Graham's_Law > Examples First Example: Let gas 1 be H2 and gas 2 be O2. (This example is solving for the ratio between the rates of the two gases) Rate H 2 Rate O 2 = M ( O 2 ) M ( H 2 ) = 32 2 = 16 = 4 {\displaystyle {{\mbox{Rate H}}_{2} \over {\mbox{Rate O}}_{2}}={\sqrt {M(O_{2}) \over M(H_{2})}}={{\sqrt {32}} \over {\sqrt {2}}}={\sqrt {16}}=4} Therefore, hydrogen molecules effuse four times faster than those of oxygen. Graham's Law can also be used to find the approximate molecular weight of a gas if one gas is a known species, and if there is a specific ratio between the rates of two gases (such as in the previous example). The equation can be solved for the unknown molecular weight.
Asch conformity experiments Method Asch_conformity_experiments > Initial conformity experiment > Method Groups of eight male college students participated in a simple "perceptual" task. In reality, all but one of the participants were actors, and the true focus of the study was about how the remaining participant would react to the actors' behavior. The actors knew the true aim of the experiment, but were introduced to the subject as other participants. Each student viewed a card with a line on it, followed by another with three lines labeled A, B, and C (see accompanying figure).
Power band Applications Power_band > Applications A mechanical transmission with a selection of different gear ratios is designed to make satisfactory power available over the full range of vehicle speeds. The goal of the selection of gear ratios is to keep the engine operating in its power band. The narrower the band, the more gears are needed, closer together in ratio. By careful gear selection, an engine can be operated in its power band, throughout all vehicle speeds.
Flight test Analysis and reporting Flight_test > Flight test processes > Analysis and reporting Because of the vast amount of information that can be extracted from this type of chart, it is important to be very accurate in reading the chart. A small error in the beginning can lead to a large error at the end. The remainder of this section covers performance information for aircraft in general and discusses what information the charts contain and how to extract information from the charts by direct reading and interpolation methods.
The Pythagorean theorem Arbitrary triangle Pythagorean_equation > Generalizations > Arbitrary triangle (The two triangles share the angle at vertex A, both contain the angle θ, and so also have the same third angle by the triangle postulate.) Consequently, ABC is similar to the reflection of CAD, the triangle DAC in the lower panel. Taking the ratio of sides opposite and adjacent to θ, c b = b r .
Cross-linked enzyme aggregate Summary Cross-linked_enzyme_aggregate In biochemistry, a cross-linked enzyme aggregate is an immobilized enzyme prepared via cross-linking of the physical enzyme aggregates with a difunctional cross-linker. They can be used as stereoselective industrial biocatalysts.
Ford–Fulkerson algorithm Complexity Ford–Fulkerson_algorithm > Complexity However, this situation only occurs with irrational flow values. When the capacities are integers, the runtime of Ford–Fulkerson is bounded by O ( E f ) {\displaystyle O(Ef)} (see big O notation), where E {\displaystyle E} is the number of edges in the graph and f {\displaystyle f} is the maximum flow in the graph. This is because each augmenting path can be found in O ( E ) {\displaystyle O(E)} time and increases the flow by an integer amount of at least 1 {\displaystyle 1} , with the upper bound f {\displaystyle f} . A variation of the Ford–Fulkerson algorithm with guaranteed termination and a runtime independent of the maximum flow value is the Edmonds–Karp algorithm, which runs in O ( V E 2 ) {\displaystyle O(VE^{2})} time.
Dental sealant Background Dental_sealants > Background These molar teeth are considered the most susceptible teeth to dental caries due to the anatomy of the chewing surfaces of these teeth, which inhibits protection from saliva and fluoride and instead favours plaque accumulation. This approach facilitates prevention and early intervention, in order to prevent or stop the dental caries process before it reaches the ends stage of the disease, which is also known as the "hole" or cavitation of a tooth. Once the tooth is cavitated, it requires a dental restoration in order to repair the damage, which emphasizes the importance of prevention in preserving teeth for a lifetime of chewing.
Radical cyclisation Typical conditions Radical_cyclisation > Experimental conditions and procedure > Typical conditions Radical reactions must be carried out under inert atmosphere as dioxygen is a triplet radical which will intercept radical intermediates. Because the relative rates of a number of processes are important to the reaction, concentrations must be carefully adjusted to optimize reaction conditions. Reactions are generally carried out in solvents whose bonds have high bond dissociation energies (BDEs), including benzene, methanol or benzotrifluoride. Even aqueous conditions are tolerated, since water has a strong O-H bond with a BDE of 494 kJ/mol. This is in contrast to many polar processes, where hydroxylic solvents (or polar X-H bonds in the substrate itself) may not be tolerated due to the nucleophilicity or acidity of the functional group.
Web developer Summary Web_developer A web developer is a programmer who develops World Wide Web applications using a client–server model. The applications typically use HTML, CSS, and JavaScript in the client, and any general-purpose programming language in the server. HTTP is used for communications between client and server. A web developer may specialize in client-side applications (Front-end web development), server-side applications (back-end development), or both (full-stack development).
Consensus forecast Background Consensus_forecast > Background Another argument in favour of this method is that individual forecasts may be subject to numerous behavioural biases, but these can be minimised by combining independent forecasts together. Hence, combining is seen as helping to improve forecast accuracy by reducing the forecast errors of individual forecasts. Furthermore, averaging forecasts is likely to be more useful when the data and the forecasting techniques that the component forecasts are drawn from differ substantially.
Beneficial mutation By effect on function Reversion_(genetics) > Classification of types > By effect on function In humans, dominant negative mutations have been implicated in cancer (e.g., mutations in genes p53, ATM, CEBPA, and PPARgamma). Marfan syndrome is caused by mutations in the FBN1 gene, located on chromosome 15, which encodes fibrillin-1, a glycoprotein component of the extracellular matrix. Marfan syndrome is also an example of dominant negative mutation and haploinsufficiency.
Einstein's thought experiments Magnet and conductor Einstein's_thought_experiments > Special relativity > Magnet and conductor In the very first paragraph of Einstein's seminal 1905 work introducing special relativity, he writes: It is well known that Maxwell's electrodynamics—as usually understood at present—when applied to moving bodies, leads to asymmetries that do not seem to attach to the phenomena. Let us recall, for example, the electrodynamic interaction between a magnet and a conductor. The observable phenomenon depends here only on the relative motion of conductor and magnet, while according to the customary conception the two cases, in which, respectively, either the one or the other of the two bodies is the one in motion, are to be strictly differentiated from each other. For if the magnet is in motion and the conductor is at rest, there arises in the surroundings of the magnet an electric field endowed with a certain energy value that produces a current in the places where parts of the conductor are located.
Quantum memory Summary Quantum_memory In quantum computing, quantum memory is the quantum-mechanical version of ordinary computer memory. Whereas ordinary memory stores information as binary states (represented by "1"s and "0"s), quantum memory stores a quantum state for later retrieval. These states hold useful computational information known as qubits. Unlike the classical memory of everyday computers, the states stored in quantum memory can be in a quantum superposition, giving much more practical flexibility in quantum algorithms than classical information storage.
Uniform absolute convergence Generalizations Uniform_absolute_convergence > Generalizations If a series of functions is uniformly absolutely-convergent on some neighborhood of each point of a topological space, it is locally uniformly absolutely-convergent. If a series is uniformly absolutely-convergent on all compact subsets of a topological space, it is compactly (uniformly) absolutely-convergent. If the topological space is locally compact, these notions are equivalent.
Reproductive biology Oogenesis Reproductive_biology > Gametogenesis > Oogenesis Human females are born with all the primary oocytes they will ever have. Starting at puberty the process of meiosis can complete resulting in the secondary oocyte and the first polar body. The secondary oocyte can later be fertilized with the male sperm.
Essential discontinuity Discontinuities of derivatives Removable_discontinuity > Discontinuities of derivatives In fact, if x 0 ∈ I {\displaystyle x_{0}\in I} is a point of discontinuity of f {\displaystyle f} , then necessarily x 0 {\displaystyle x_{0}} is an essential discontinuity of f {\displaystyle f} .This means in particular that the following two situations cannot occur: Furtherly, two other situations have to be excluded (see John Klippert): Observe that whenever one of the conditions (i), (ii), (iii), or (iv) is fulfilled for some x 0 ∈ I {\displaystyle x_{0}\in I} one can conclude that f {\displaystyle f} fails to possess an antiderivative, F {\displaystyle F} , on the interval I {\displaystyle I} . On the other hand, a new type of discontinuity with respect to any function f: I → R {\displaystyle f:I\to \mathbb {R} } can be introduced: an essential discontinuity, x 0 ∈ I {\displaystyle x_{0}\in I} , of the function f {\displaystyle f} , is said to be a fundamental essential discontinuity of f {\displaystyle f} if and Therefore if x 0 ∈ I {\displaystyle x_{0}\in I} is a discontinuity of a derivative function f: I → R {\displaystyle f:I\to \mathbb {R} } , then necessarily x 0 {\displaystyle x_{0}} is a fundamental essential discontinuity of f {\displaystyle f} . Notice also that when I = {\displaystyle I=} and f: I → R {\displaystyle f:I\to \mathbb {R} } is a bounded function, as in the assumptions of Lebesgue's Theorem, we have for all x 0 ∈ ( a , b ) {\displaystyle x_{0}\in (a,b)}: and Therefore any essential discontinuity of f {\displaystyle f} is a fundamental one.
Volume element Volume element of a linear subspace Differential_volume_element > Volume element of a linear subspace Consider the linear subspace of the n-dimensional Euclidean space Rn that is spanned by a collection of linearly independent vectors X 1 , … , X k . {\displaystyle X_{1},\dots ,X_{k}.} To find the volume element of the subspace, it is useful to know the fact from linear algebra that the volume of the parallelepiped spanned by the X i {\displaystyle X_{i}} is the square root of the determinant of the Gramian matrix of the X i {\displaystyle X_{i}}: det ( X i ⋅ X j ) i , j = 1 … k . {\displaystyle {\sqrt {\det(X_{i}\cdot X_{j})_{i,j=1\dots k}}}.}
Model maker Summary Model_maker Most milling and other machining methods are subtractive, progressively using smaller and finer tools to remove material from the rough shape to get to the level of detail needed in the final model.Model makers may use a combination of these methods and technologies to create the model in the most expeditious manner. The parts are usually test fitted, then sanded and painted to represent the intended finish or look. Model makers are required to recreate many faux finishes like brick, stone, grass, molded plastic textures, glass, skin and even water.
Born–von Karman boundary condition Summary Born–von_Karman_boundary_condition Note, however, the Born–von Karman boundary conditions are useful when Ni are large (infinite). The Born–von Karman boundary condition is important in solid state physics for analyzing many features of crystals, such as diffraction and the band gap. Modeling the potential of a crystal as a periodic function with the Born–von Karman boundary condition and plugging in Schrödinger's equation results in a proof of Bloch's theorem, which is particularly important in understanding the band structure of crystals. However, since any real crystal always has a finite size, the electronic states in the crystal do not satisfy the Born–von Karman boundary condition. Consequently, the conventional theory of electronic states in crystals based on the Bloch's theorem has some fundamental difficulties.
History of the International System of Units The improvisation of units History_of_the_International_System_of_Units > History > The improvisation of units Napoleon ridiculed it, and in 1812, introduced a replacement system, the mesures usuelles or "customary measures" which restored many of the old units, but redefined in terms of the metric system. During the first half of the 19th century there was little consistency in the choice of preferred multiples of the base units: typically the myriametre (10000 metres) was in widespread use in both France and parts of Germany, while the kilogram (1000 grams) rather than the myriagram was used for mass.In 1832, the German mathematician Carl Friedrich Gauss, assisted by Wilhelm Weber, implicitly defined the second as a base unit when he quoted the Earth's magnetic field in terms of millimetres, grams, and seconds. Prior to this, the strength of the Earth's magnetic field had only been described in relative terms.
Social judgment theory Simulations Social_judgment_theory > Simulations Attitudes were ranked on three scales: risk, benefit, and process. The data was fed into an agent-based social simulation. In each time-period, two random agents were selected to interact.
Behavior trees (artificial intelligence, robotics and control) Key concepts Behavior_tree_(artificial_intelligence,_robotics_and_control) > Key concepts A behavior tree is graphically represented as a directed tree in which the nodes are classified as root, control flow nodes, or execution nodes (tasks). For each pair of connected nodes the outgoing node is called parent and the incoming node is called child. The root has no parents and exactly one child, the control flow nodes have one parent and at least one child, and the execution nodes have one parent and no children. Graphically, the children of a control flow node are placed below it, ordered from left to right.The execution of a behavior tree starts from the root which sends ticks with a certain frequency to its child. A tick is an enabling signal that allows the execution of a child. When the execution of a node in the behavior tree is allowed, it returns to the parent a status running if its execution has not finished yet, success if it has achieved its goal, or failure otherwise.
Traumatic memories Consolidation Traumatic_memories > Effects > Consolidation Stimulation of beta-adrenergic receptors during arousal and stress strengthens memory consolidation. Increased release of Norepinephrine inhibits the prefrontal cortex, which plays a role in emotion control as well as extinction or suppression of memory. Additionally, the release also serves to stimulate the amygdala which plays a key role in generating fear behaviors.
L'Hôpital's rule General form Bernoulli's_rule > General form The general form of L'Hôpital's rule covers many cases. Let c and L be extended real numbers (i.e., real numbers, positive infinity, or negative infinity). Let I be an open interval containing c (for a two-sided limit) or an open interval with endpoint c (for a one-sided limit, or a limit at infinity if c is infinite). The real valued functions f and g are assumed to be differentiable on I except possibly at c, and additionally g ′ ( x ) ≠ 0 {\displaystyle g'(x)\neq 0} on I except possibly at c. It is also assumed that lim x → c f ′ ( x ) g ′ ( x ) = L .
Surface ocean wave Summary Ocean_surface_wave Swell consists of wind-generated waves that are not significantly affected by the local wind at that time. They have been generated elsewhere and sometimes previously.
Spiral of Theodorus Construction Spiral_of_Theodorus > Construction The spiral is started with an isosceles right triangle, with each leg having unit length. Another right triangle is formed, an automedian right triangle with one leg being the hypotenuse of the prior triangle (with length the square root of 2) and the other leg having length of 1; the length of the hypotenuse of this second triangle is the square root of 3. The process then repeats; the n {\displaystyle n} th triangle in the sequence is a right triangle with the side lengths n {\displaystyle {\sqrt {n}}} and 1, and with hypotenuse n + 1 {\displaystyle {\sqrt {n+1}}} . For example, the 16th triangle has sides measuring 4 = 16 {\displaystyle 4={\sqrt {16}}} , 1 and hypotenuse of 17 {\displaystyle {\sqrt {17}}} .
Hepatic steatosis Epidemiology Fatty_liver > Epidemiology The scans also found that 2.4% had a degree of liver fibrosis, which can lead to cirrhosis.After the lockdown of the COVID-19 pandemic, a study demonstrated that 48% of patients with liver steatosis gained weight, while 16% had a worsened steatosis grade. Weight gain was associated with poor adherence to the suggested diet, reduced levels of physical activity, and increased prevalence of homozygosity for the PNPLA3 rs738409 single nucleotide polymorphism. PNPLA3 rs738409 is already a known risk factor for NAFLD.
Proof verification Summary Proof_verification In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics.
Class (complexity theory) Important complexity classes Complexity_class > Other models of computation > Boolean circuits > Important complexity classes These classes are defined not only in terms of their circuit size but also in terms of their depth. The depth of a circuit is the length of the longest directed path from an input node to the output node. The class NC is the set of languages that can be solved by circuit families that are restricted not only to having polynomial-size but also to having polylogarithmic depth. The class AC is defined similarly to NC, however gates are allowed to have unbounded fan-in (that is, the AND and OR gates can be applied to more than two bits). NC is a notable class because it can be equivalently defined as the class of languages that have efficient parallel algorithms.
Advertising Classification Commercial_message > Classification The purpose of an ad may be to raise awareness (brand advertising), or to elicit an immediate sale (direct response advertising). The term above the line (ATL) is used for advertising involving mass media; more targeted forms of advertising and promotion are referred to as below the line (BTL). The two terms date back to 1954 when Procter & Gamble began paying their advertising agencies differently from other promotional agencies. In the 2010s, as advertising technology developed, a new term, through the line (TTL) began to come into use, referring to integrated advertising campaigns.
Unital associative algebra Constructions Linear_associative_algebra > Constructions Tensor products The tensor product of two R-algebras is also an R-algebra in a natural way. See tensor product of algebras for more details. Given a commutative ring R and any ring A the tensor product R ⊗Z A can be given the structure of an R-algebra by defining r · (s ⊗ a) = (rs ⊗ a).
Autoinducer Mechanism Autoinducer > Mechanism In the most simplified quorum sensing systems, bacteria only need two components to make use of autoinducers. They need a way to produce a signal and a way to respond to that signal. These cellular processes are often tightly coordinated and involve changes in gene expression. The production of autoinducers generally increases as bacterial cell densities increase.
Bonding in solids Network covalent solids Bonding_in_solids > Basic classes of solids > Network covalent solids A network covalent solid consists of atoms held together by a network of covalent bonds (pairs of electrons shared between atoms of similar electronegativity), and hence can be regarded as a single, large molecule. The classic example is diamond; other examples include silicon, quartz and graphite.
Speed ratio Wide-ratio vs. close-ratio transmission Gear_ratio > Automotive applications > Wide-ratio vs. close-ratio transmission A close-ratio transmission is a transmission in which there is a relatively little difference between the gear ratios of the gears. For example, a transmission with an engine shaft to drive shaft ratio of 4:1 in first gear and 2:1 in second gear would be considered wide-ratio when compared to another transmission with a ratio of 4:1 in first and 3:1 in second. This is because the close-ratio transmission has less of a progression between gears. For the wide-ratio transmission, the first gear ratio is 4:1 or 4, and in second gear it is 2:1 or 2, so the progression is equal to 4/2 = 2 (or 200%).
Hydrogen isotope biogeochemistry Lakes and rivers Hydrogen_isotope_biogeochemistry > Observed variations in isotope abundance > Hydrosphere > Lakes and rivers The δD values vs. VSMOW of lakes in different regions are shown on the map. The general pattern observed indicates that the δD values of the surface waters including lakes and rivers are similar to that of local precipitation.
Balancing domain decomposition method Summary Balancing_domain_decomposition In numerical analysis, the balancing domain decomposition method (BDD) is an iterative method to find the solution of a symmetric positive definite system of linear algebraic equations arising from the finite element method. In each iteration, it combines the solution of local problems on non-overlapping subdomains with a coarse problem created from the subdomain nullspaces. BDD requires only solution of subdomain problems rather than access to the matrices of those problems, so it is applicable to situations where only the solution operators are available, such as in oil reservoir simulation by mixed finite elements.
Viscous forces Summary Dynamic_Viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area.
Visual spatial attention Splitting spatial attention Visual_spatial_attention > Splitting spatial attention These findings have proposed that attention cannot be split across two non-contiguous regions. However, other studies have demonstrated that spatial attention can be split across two locations. For example, observers were able to attend simultaneously to two different targets located in opposite hemifields.
Chemical reaction kinetics Surface area of solid state Chemical_reaction_kinetics > Factors affecting reaction rate > Surface area of solid state In a solid, only those particles that are at the surface can be involved in a reaction. Crushing a solid into smaller parts means that more particles are present at the surface, and the frequency of collisions between these and reactant particles increases, and so reaction occurs more rapidly. For example, Sherbet (powder) is a mixture of very fine powder of malic acid (a weak organic acid) and sodium hydrogen carbonate. On contact with the saliva in the mouth, these chemicals quickly dissolve and react, releasing carbon dioxide and providing for the fizzy sensation.
Behavioral activation Methods Behavioral_activation > Methods A depression loop is when a temporary coping method reduces the overall depression, such as the temporary relief provided by alcohol or other drugs, escape or avoidance or rumination. : 37 When patterns of dysfunctional responding, or loops, are identified alternative coping responses are attempted to break the loop. : 39 This method is described with the acronym "TRAP" (Trigger, Response, Avoidance Pattern) which is to be replaced with a "TRAC" (Trigger, Response, Alternate Coping response).
Lenslet Summary Lenslet Lenslets have many uses. One of the key applications for lenslets is in integral imaging and light field displays. Lenslets are commonly found in Shack–Hartmann wavefront sensors and beam homogenization optics for projection systems. == References ==
Drug facilitated sexual assault Summary Drug_facilitated_sexual_assault Drug-facilitated sexual assault (DFSA) is a sexual assault (rape or otherwise) carried out on a person after the person has become intoxicated due to being under the influence of any mind-altering substances, such as having consumed alcohol or been intentionally administered another date rape drug. The rape form of DFSA is also known as predator rape. 75% of all acquaintance rapes involve alcohol and/or drugs.
Rate of natural increase Uses Rate_of_natural_increase > Uses Looking at this difference across regions reveals those that are changing mainly due to births exceeding deaths and those changing mainly due to migration. The map shows just such an analysis for the US. The trend of RNI over time can indicate what stage of the Demographic Transition Model (DTM) a region or country is in.
Twelvefold way Surjective functions from N to X Twelvefold_way > Formulas > Details of the different cases > Surjective functions from N to X For each surjective function f: N → X, its orbit under permutations of X has x! elements, since composition (on the left) with two distinct permutations of X never gives the same function on N (the permutations must differ at some element of X, which can always be written as f(i) for some i ∈ N, and the compositions will then differ at i). It follows that the number for this case is x! times the number for the previous case, that is x !
Learning health systems Ethical considerations Learning_health_systems > Ethical considerations Bioethics scholars including Faden, Asch, Finkelstein, Morain, and Platt have averred that in a learning health system, consideration should be given to both clinical ethics and research ethics. Faden, Kass and colleagues have put forth an ethics framework for the learning health system that is anchored on seven essential obligations: (1) respecting dignity and rights of all patients; (2) respecting clinical judgment; (3) providing optimal care to every patient; (4) avoiding the introduction of non-clinical burdens and risks; (5) reducing health inequities; (6) ensuring responsible activities are conducted in a way that fosters learning; and (7) contributing to the overall aim of improving quality and value in health care. This framework and several companion articles were published as a special report from the Hastings Center. Subsequent articles by Finkelstein et al, as well as Asch and colleagues seek to use examples of learning activities as a means to describe different approaches to research oversight and compliance. Rigorous deliberations about the approach to informed consent are also germane to the ethics of learning activities in the healthcare context.
Turbine Engine Theory of operation Combustion_turbine > Theory of operation In an ideal gas turbine, gases undergo four thermodynamic processes: an isentropic compression, an isobaric (constant pressure) combustion, an isentropic expansion and heat rejection. Together, these make up the Brayton cycle, also known as the "constant pressure cycle". It is distinguished from the Otto cycle, in that all the processes (compression, ignition combustion, exhaust), occur at the same time, continuously.In a real gas turbine, mechanical energy is changed irreversibly (due to internal friction and turbulence) into pressure and thermal energy when the gas is compressed (in either a centrifugal or axial compressor). Heat is added in the combustion chamber and the specific volume of the gas increases, accompanied by a slight loss in pressure.
Write buffer Summary Write_buffer Some software disciplines, like C11's data-race-freedom, are sufficient to regain a sequentially consistent view of memory. A variation of write-through caching is called buffered write-through.Use of a write buffer in this manner frees the cache to service read requests while the write is taking place. It is especially useful for very slow main memory in that subsequent reads are able to proceed without waiting for long main memory latency.
Representational systems (NLP) Sensory predicates and eye accessing cues Representational_systems_(NLP) > Representational systems within NLP > Sensory predicates and eye accessing cues Grinder and Bandler believed they identified pattern of relationship between the sensory-based language people use in general conversation, and for example, their eye movement (known as eye accessing cues).A common (but not universal) style of processing in the West is shown in the attached chart, where eye flickers in specific directions often seem to tie into specific kinds of internal (mental) processing. NLP also suggests that sometimes (again not universally) such processing is associated with sensory word use; for example, a person asked what they liked about the beach, may flick their eyes briefly in some characteristic direction (visual memory access, often upwards) and then also use words that describe it in a visual sense ("The sea looked lovely", and so on). Likewise asked about a problem, someone may look in a different direction for a while (kinesthetic access, typically downwards) and then look puzzled and say "I just can't seem to get a grip on things". Taken together, NLP suggests such eye accessing cues (1) are idiosyncratic and habitual for each person, and (2) may form significant clues as to how a person is processing or representing a problem to themselves unconsciously.
Diabetes Signs and symptoms Diabetes_mellitus > Signs and symptoms The classic symptoms of untreated diabetes are polyuria, thirst, and weight loss. Several other non-specific signs and symptoms may also occur, including fatigue, blurred vision, and genital itchiness due to Candida infection. About half of affected individuals may also be asymptomatic. Type 1 presents abruptly following a pre-clinical phase, while type 2 has a more insidious onset; patients may remain asymptomatic for many years.Diabetic ketoacidosis is an medical emergency that occurs most commonly in type 1, but may also occur in type 2 if it has been longstanding or if the individual has significant β-cell dysfunction.
Object-Oriented Turing Open implementations Object-Oriented_Turing > Open implementations Currently, there are two open source alternative implementations of Turing: Open Turing, an open source version of the original interpreter, and TPlus, a native compiler for the concurrent systems programming language variant Turing Plus. OpenT, a project to develop a compiler for Turing, is no longer in development.
Atrial natriuretic factor receptor Mechanism Atrial_natriuretic_peptide_receptor > Mechanism This is why nitroglycerine is given to a person having a heart attack. The nitroglycerine will be metabolized to nitric oxide, which will stimulate soluble guanylyl cyclase. This will result in a decrease in total peripheral resistance and a decrease in preload on the heart. As a result, work done by the heart will decrease and will allow the heart to contract less strongly. Weaker contractions will lead to more blood flow in the coronary arteries, which will help the ischemic cardiac myocytes.
No-SCAR genome editing Plasmids No-SCAR_genome_editing > Methodology > Plasmids More specifically, the cell lethality is a consequence of Cas9 cleaving the E. coli DNA that matches the sgRNA. In order to circumvent this issue, multiple plasmids are used in order to maintain expressional control of both cas9 and sgRNA. The PTET promoter plays an integral role in the expression of both plasmids.
Smart power United States Smart_power > History > United States For Nossel, "Smart power means knowing that the United States' own hand is not always its best tool: U.S. interests are furthered by enlisting others on behalf of U.S. goals.
RNA Interference MicroRNA RNA_Interference > Cellular mechanism > MicroRNA This complex consists of an RNase III enzyme called Drosha and a dsRNA-binding protein DGCR8. The dsRNA portion of this pre-miRNA is bound and cleaved by Dicer to produce the mature miRNA molecule that can be integrated into the RISC complex; thus, miRNA and siRNA share the same downstream cellular machinery.
Intermembrane space of mitochondria Origin and evolution Mitochondrial_intermembrane_space > Origin and evolution There are two hypotheses about the origin of mitochondria: endosymbiotic and autogenous. The endosymbiotic hypothesis suggests that mitochondria were originally prokaryotic cells, capable of implementing oxidative mechanisms that were not possible for eukaryotic cells; they became endosymbionts living inside the eukaryote. In the autogenous hypothesis, mitochondria were born by splitting off a portion of DNA from the nucleus of the eukaryotic cell at the time of divergence with the prokaryotes; this DNA portion would have been enclosed by membranes, which could not be crossed by proteins. Since mitochondria have many features in common with bacteria, the endosymbiotic hypothesis is the more widely accepted of the two accounts.A mitochondrion contains DNA, which is organized as several copies of a single, usually circular chromosome.
Separate continuity Summary Separate_continuity In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments. Matrix multiplication is an example.

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