Split (1)

train · 253k rows

page_content stringlengths 51 3.15k
Imaginary value Summary Imaginary_value An imaginary number is a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number bi is −b2. For example, 5i is an imaginary number, and its square is −25. By definition, zero is considered to be both real and imaginary.Originally coined in the 17th century by René Descartes as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of Leonhard Euler (in the 18th century) and Augustin-Louis Cauchy and Carl Friedrich Gauss (in the early 19th century). An imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where the real numbers a and b are called, respectively, the real part and the imaginary part of the complex number.
Language construct Summary Language_construct In computer programming, a language construct is a syntactically allowable part of a program that may be formed from one or more lexical tokens in accordance with the rules of the programming language. The term "language construct" is often used as a synonym for control structure. Control flow statements (such as conditionals, foreach loops, while loops, etc) are language constructs, not functions. So while (true) is a language construct, while add(10) is a function call.
Henry's law Effective Henry's law constants Heff Bunsen_solubility_coefficient > Effective Henry's law constants Heff {\displaystyle H_{\rm {s,eff}}={\frac {c_{{\ce {tot}}}}{p\left({\ce {H2CO}}\right)}}={\frac {c\left({\ce {H2CO}}\right)+c\left({\ce {H2C(OH)2}}\right)}{p\left({\ce {H2CO}}\right)}}.} For acids and bases, the effective Henry's law constant is not a useful quantity because it depends on the pH of the solution. In order to obtain a pH-independent constant, the product of the intrinsic Henry's law constant H s cp {\displaystyle H_{\rm {s}}^{{\ce {cp}}}} and the acidity constant K A {\displaystyle K_{{\ce {A}}}} is often used for strong acids like hydrochloric acid (HCl): H ′ = H s cp K A = c ( H + ) c ( Cl − ) p ( HCl ) . {\displaystyle H'=H_{\rm {s}}^{{\ce {cp}}}K_{{\ce {A}}}={\frac {c\left({\ce {H+}}\right)c\left({\ce {Cl^-}}\right)}{p\left({\ce {HCl}}\right)}}.} Although H ′ {\displaystyle H'} is usually also called a Henry's law constant, it is a different quantity and it has different units than H s cp {\displaystyle H_{\rm {s}}^{{\ce {cp}}}} .
Tempering (metallurgy) Normalized steel Tempered_steel > Carbon steel > Normalized steel Tempering provides a way to carefully decrease the hardness of the steel, thereby increasing the toughness to a more desirable point. Cast steel is often normalized rather than annealed, to decrease the amount of distortion that can occur. Tempering can further decrease the hardness, increasing the ductility to a point more like annealed steel.
Force Concept Inventory Summary Force_Concept_Inventory During the collision: the truck exerts a greater amount of force on the car than the car exerts on the truck. the car exerts a greater amount of force on the truck than the truck exerts on the car. neither exerts a force on the other, the car gets smashed simply because it gets in the way of the truck. the truck exerts a force on the car but the car does not exert a force on the truck. the truck exerts the same amount of force on the car as the car exerts on the truck.
Maternal effects High fat diets during gestation correlated with metabolic syndrome Maternal_effect > Maternal diet and environment epigenetically influences susceptibility for adult diseases > High fat diets during gestation correlated with metabolic syndrome Therefore, there was less adiponectin to help cells take up glucose and break down fat, as well as less leptin to cause a feeling of satiety. The decrease in these hormones caused fat mass gain, glucose intolerance, hypertriglyceridemia, abnormal adiponectin and leptin levels, and hypertension throughout the animal's lifetime. However, the effect was abolished after three subsequent generations with normal diets.
Canonical angular momentum Newton's derivation Introduction_to_angular_momentum > History > The Law of Areas > Newton's derivation As a planet orbits the Sun, the line between the Sun and the planet sweeps out equal areas in equal intervals of time. This had been known since Kepler expounded his second law of planetary motion. Newton derived a unique geometric proof, and went on to show that the attractive force of the Sun's gravity was the cause of all of Kepler's laws. During the first interval of time, an object is in motion from point A to point B. Undisturbed, it would continue to point c during the second interval.
Scaling and root planing After scaling Full_mouth_ultrasonic_debridement > Periodontal intervention > After scaling This allows the medication to seep into the tissues and destroy bacteria that may be living within the gingiva, providing even further disinfection and facilitation of healing. Certain site specific antibiotics provide not only this benefit, but also boast an added benefit of reduction in pocket depth. Arestin, a popular site specific brand of the antibiotic minocycline, is claimed to enable regaining of at least 1 mm of gingival reattachment height.
Tide-predicting machine Principle Tide-predicting_machine > Principle Thomson conceived his aim as to construct a mechanism that would evaluate this trigonometrical sum physically, e.g. as the vertical position of a pen that could then plot a curve on a moving band of paper. There were several mechanisms available to him for converting rotary motion into sinusoidal motion. One of them is shown in the schematic (right). A rotating drive-wheel is fitted with an off-center peg.
Molecular Operating Environment Future Implications Molecular_Operating_Environment > Future Implications Computational/theoretical chemistry and biology methods are continuously pushing the horizon. Recently, DeepMind, which is a company specializing in the development of artificial intelligence (AI), created an AI system named AlphaFold. AlphaFold is the most advanced system to date that can accurately predict a protein's 3D structure from its amino acid sequence. The protein folding problem first began to emerge around the 1960s and ever since, scientists have struggled in determining methods to precisely predict the way a protein will fold solely based on the amino acid sequence.
End group NMR spectroscopy End_group > Analysis of polymers using end groups > NMR spectroscopy The advantage of NMR for end groups is that it allows for not only the identification of the end group units, but also allows for the quantification of the number-average length of the polymer. End-group analysis with NMR requires that the polymer be soluble in organic or aqueous solvents. Additionally, the signal on the end-group must be visible as a distinct spectral frequency, i.e. it must not overlap with other signals.
Non-shivering thermogenesis In avians and eutherians Non-shivering_thermogenesis > Evolutionary history > In avians and eutherians The reason that both avians and eutherians both developed the capacity to perform thermogenesis is a subject of ongoing study by evolutionary biologists, and two competing explanations have been proposed to explain why this character appears in both lineages.One explanation for the convergence is the “aerobic capacity” model. This theory suggests that natural selection favored individuals with higher resting metabolic rates, and that as the metabolic capacity of birds and eutherians increased, they developed the capacity for endothermic thermogenesis. Researchers have linked high levels of oxygen consumption with high resting metabolic rates, suggesting that the two are directly correlated.
Jacob Bernoulli Important works Jacob_Bernoulli > Important works Jacob Bernoulli also discovered a general method to determine evolutes of a curve as the envelope of its circles of curvature. He also investigated caustic curves and in particular he studied these associated curves of the parabola, the logarithmic spiral and epicycloids around 1692. The lemniscate of Bernoulli was first conceived by Jacob Bernoulli in 1694.
Giorgi Japaridze Research Giorgi_Japaridze > Research In "On the system CL12 of computability logic", on the platform of computability logic, Japaridze generalized the traditional concepts of time and space complexities to interactive computations, and introduced a third sort of a complexity measure for such computations, termed "amplitude complexity". Among Japaridze's contributions is the elaboration of a series of systems of (Peano) arithmetic based on computability logic, named "clarithmetics". These include complexity-oriented systems (in the style of bounded arithmetic) for various combinations of time, space and amplitude complexity classes.
Bamberger rearrangement Reaction mechanism Bamberger_rearrangement > Reaction mechanism The mechanism of the Bamberger rearrangement proceeds from the monoprotonation of N-phenylhydroxylamine 1. N-protonation 2 is favored, but unproductive. O-protonation 3 can form the nitrenium ion 4, which can react with nucleophiles (H2O) to form the desired 4-aminophenol 5.
History of speciation Darwin's dilemmas History_of_speciation > Early history > Darwin's dilemmas Chapter 6 of Darwin's book is entitled "Difficulties of the Theory." In discussing these "difficulties" he noted "Firstly, why, if species have descended from other species by insensibly fine gradations, do we not everywhere see innumerable transitional forms? Why is not all nature in confusion instead of the species being, as we see them, well defined?"
Symmetry (geometry) Reflectional symmetry Symmetry_(geometry) > Reflectional symmetry Reflectional symmetry, linear symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection.In one dimension, there is a point of symmetry about which reflection takes place; in two dimensions, there is an axis of symmetry (a.k.a., line of symmetry), and in three dimensions there is a plane of symmetry. An object or figure for which every point has a one-to-one mapping onto another, equidistant from and on opposite sides of a common plane is called mirror symmetric (for more, see mirror image). The axis of symmetry of a two-dimensional figure is a line such that, if a perpendicular is constructed, any two points lying on the perpendicular at equal distances from the axis of symmetry are identical. Another way to think about it is that if the shape were to be folded in half over the axis, the two halves would be identical as mirror images of each other.
Control Theory Control specification Control_strategy > Topics in control theory > Control specification These include the rise time (the time needed by the control system to reach the desired value after a perturbation), peak overshoot (the highest value reached by the response before reaching the desired value) and others (settling time, quarter-decay). Frequency domain specifications are usually related to robustness (see after). Modern performance assessments use some variation of integrated tracking error (IAE, ISA, CQI).
Educational research Mixed methods (Pragmatic) Discipline-based_education_research > Methodology > Mixed methods (Pragmatic) There also exists a new school of thought that these derivatives of the scientific method are far too reductionist in nature. Since educational research includes other disciplines such as psychology, sociology, anthropology, science, and philosophy and refers to work done in a wide variety of contexts it is proposed that researchers should use "multiple research approaches and theoretical constructs." This could mean using a combination of qualitative and quantitative methods as well as common methodology from the fields mentioned above. In social research this phenomenon is referred to as triangulation (social science). This idea is well summarized by the work of Barrow in his text An introduction to philosophy of education: Since educational issues are of many different kinds and logical types, it is to be expected that quite different types of research should be brought into play on different occasions. The question therefore is not whether research into teaching should be conducted by means of quantitative measures (on some such grounds as that they are more 'objective') or qualitative measures (on some such grounds as that they are more 'insightful'), but what kind of research can sensibly be utilized to look into this particular aspect of teaching as opposed to that.
Efaproxiral Summary Efaproxiral Efaproxiral (INN) is an analogue of the cholesterol drug bezafibrate developed for the treatment of depression, traumatic brain injury, ischemia, stroke, myocardial infarction, diabetes, hypoxia, sickle cell disease, hypercholesterolemia and as a radio sensitiser.The chemical is a derivative of propanoic acid. One use for efaproxiral is to increase the efficacy of certain chemotherapy drugs which have reduced efficacy against hypoxic tumours, and can thus be made more effective by increased offloading of oxygen into the tumour tissues. No benefit was seen for efaproxiral in phase III clinical trials. The increased oxygenation of tissues could theoretically also produce enhanced exercise capacity in feline, rat and canine models for approximately 100 min.
Size effect on structural strength Type 1: Structures that fail at crack initiation Size_effect > Energetic Size Effect > Type 1: Structures that fail at crack initiation This condition is satisfied by the generalized energetic-statistical size effect law: where r , m {\displaystyle r,m} are empirical constants ( r n d / m < 1 {\displaystyle rn_{d}/m<1} ). The deterministic formula (5) is recovered as the limit case for m → ∞ {\displaystyle m\rightarrow \infty } .
Gene co-expression network Co-expression measure Gene_co-expression_network > Constructing gene co-expression networks > Co-expression measure Moreover, Pearson correlation assumes that the gene expression data follow a normal distribution. Song et al. have suggested biweight midcorrelation (bicor) as a good alternative for Pearson’s correlation. "Bicor is a median based correlation measure, and is more robust than the Pearson correlation but often more powerful than the Spearman's correlation". Furthermore, it has been shown that "most gene pairs satisfy linear or monotonic relationships" which indicates that "mutual information networks can safely be replaced by correlation networks when it comes to measuring co-expression relationships in stationary data".
Ozone Mapping and Profiler Suite Summary Ozone_Mapping_and_Profiler_Suite Ozone Mapping and Profiler Suite (OMPS), is a suite of instruments built by Ball Aerospace that measure the global distribution of ozone and, less frequently, how it is distributed vertically within the stratosphere. The suite flies on the Suomi NPP and NOAA-20 (formerly JPSS-1) satellites along with several other instruments. It had been intended to also fly on the NPOESS, for which the NPP was a preparatory project, but the dissolution of that project was announced in 2010. OMPS launched on October 28, 2011.The three components of the suite are Nadir, which looks straight down, Limb, which looks down at an angle, and the Main Electronics Box (MEB), which controls Nadir, Limb and communication.
Flag and pennant patterns Flag pattern Flag_and_pennant_patterns > Flag pattern The flag pattern is encompassed by two parallel lines. These lines can be either flat or pointed in the opposite direction of the primary market trend. The pole is formed by a line which represents the primary trend in the market. The pattern, which could be bullish or bearish, is seen as the market potentially just taking a "breather" after a big move before continuing its primary trend. The chart below illustrates a bull flag. A bear flag would trend in the opposite direction.
Timeline of scientific computing 19th century Timeline_of_scientific_computing > Before modern computers > 19th century It is considered the first algorithm ever specifically tailored for implementation on a computer, and thus the first-ever computer programme. The engine was never completed, however, so her code was never tested. Adams-Bashforth method published.
Germline mutation Cancer Germinal_mutation > Clinical implications > Cancer Mutations in tumour suppressor genes or proto-oncogenes can predispose an individual to developing tumours. It is estimated that inherited genetic mutations are involved in 5-10% of cancers. These mutations make a person susceptible to tumour development if the other copy of the oncogene is randomly mutated.
CMOS Sensor Design variants Active-pixel_sensor > Design variants Pixel size can be traded for desirable qualities such as noise reduction or reduced image lag. Noise is a measure of the accuracy with which the incident light can be measured. Lag occurs when traces of a previous frame remain in future frames, i.e. the pixel is not fully reset. The voltage noise variance in a soft-reset (gate-voltage regulated) pixel is V n 2 = k T / 2 C {\displaystyle V_{n}^{2}=kT/2C} , but image lag and fixed pattern noise may be problematic. In rms electrons, the noise is N e = k T C / 2 q {\displaystyle N_{e}={\frac {\sqrt {kTC/2}}{q}}} .
Arcadia (play) Contextual information Arcadia_(play) > Contextual information "Entropy is the measure of the randomness or disorder of a system. The law of increase of entropy states that as a whole, the universe is evolving from order to disorder. This relates to the second law of thermodynamics, which states that heat spontaneously flows in only one direction, from hotter to colder.
Tension-type headache Chronic Tension-type_headache > Treatment > Medications > Chronic Classes of medications involved in treatment of CTTH include tricyclic antidepressants (TCAs), SSRIs, benzodiazepine (Clonazepam in small evening dose), and muscle relaxants. The most commonly utilized TCA is amitriptyline due to the postulated role in decreasing central sensitization and analgesic relief. Another popular TCA used is Doxepine.
Double slit experiment Overview Double-slit_interference > Overview When Thomas Young (1773–1829) first demonstrated this phenomenon, it indicated that light consists of waves, as the distribution of brightness can be explained by the alternately additive and subtractive interference of wavefronts. Young's experiment, performed in the early 1800s, played a crucial role in the understanding of the wave theory of light, vanquishing the corpuscular theory of light proposed by Isaac Newton, which had been the accepted model of light propagation in the 17th and 18th centuries. However, the later discovery of the photoelectric effect demonstrated that under different circumstances, light can behave as if it is composed of discrete particles.
Glossary of genetics (M–Z) T Glossary_of_genetics_(M–Z) > T For example, a DNA-binding protein acts "in trans" if it binds to or interacts with a sequence located on any strand or molecule different from the one on which it is encoded. Contrast cis-acting. trans-splicing transcribed spacer A spacer sequence that is transcribed and thus included in the primary ribosomal RNA transcript (as opposed to a non-transcribed spacer) but subsequently excised and discarded during the maturation of functional RNAs of the ribosome.
T helper cell Hypersensitivity CD4(+)_T_cell > Role in disease > Hypersensitivity Cellular auto-immune disease occurs because the host antigen recognition systems fail, and the immune system believes, by mistake, that a host antigen is foreign. As a result, the CD8+ T cells treat the host cell presenting that antigen as infected, and go on to destroy all host cells (or in the case of transplant rejection, transplant organ) that express that antigen. Some of this section is a simplification.
Perron–Frobenius theorem Lemma Primitive_matrix > Proof methods > Perron root is strictly maximal eigenvalue for positive (and primitive) matrices > Lemma Given a non-negative A, assume there exists m, such that Am is positive, then Am+1, Am+2, Am+3,... are all positive. Am+1 = AAm, so it can have zero element only if some row of A is entirely zero, but in this case the same row of Am will be zero. Applying the same arguments as above for primitive matrices, prove the main claim.
Causa sui Summary Causa_sui Causa sui (pronounced ; transl. cause of itself, self-caused) is a Latin term that denotes something that is generated within itself. Used in relation to the purpose that objects can assign to themselves, the concept was central to the works of Baruch Spinoza, Sigmund Freud, Jean-Paul Sartre, and Ernest Becker.
Social architecture Summary Social_architecture Social architecture is the conscious design of an environment that encourages a desired range of social behaviors leading towards some goal or set of goals. The environment social architecture influences may be social systems, or digital spaces such as media tools (sometimes synonymous with Web 2.0) and UX strategy. In building design it can refer to the architecture of social spaces such as bars and restaurant.In social systems, "social architects" seek to modify human behaviors (behavior change) through carefully designed programs or workshops that seek to involve the members of a population to improve, for example, the livability and safety or environmental impact of their own communities.
Protein Structure Summary Protein_Structure By physical size, proteins are classified as nanoparticles, between 1–100 nm. Very large protein complexes can be formed from protein subunits. For example, many thousands of actin molecules assemble into a microfilament. A protein usually undergoes reversible structural changes in performing its biological function. The alternative structures of the same protein are referred to as different conformations, and transitions between them are called conformational changes.
DNS management software Background DNS_management_software > Background During the late 1990s, the sheer quantity of DNS data was overwhelming the tools available to manage it. The cost of managing the data instigated the birth of DNS management software. The costs can best be explained by illustration.
NCBI Epigenomics Summary NCBI_Epigenomics The Epigenomics database at the National Center for Biotechnology Information was a database for whole-genome epigenetics data sets. It was retired on 1 June 2016.
DNA oxidation Increased 8-oxo-dG in carcinogenesis and disease DNA_oxidation > Increased 8-oxo-dG in carcinogenesis and disease Deoxycholate increases intracellular production of reactive oxygen resulting in increased oxidative stress, and this may contribute to tumorigenesis and carcinogenesis. Of 22 mice fed the diet supplemented with deoxycholate, 20 (91%) developed colonic tumors after 10 months on the diet, and the tumors in 10 of these mice (45% of mice) included an adenocarcinoma (cancer). Cooke et al. point out that a number of diseases, such as Alzheimer's disease and systemic lupus erythematosus, have elevated 8-oxo-dG but no increased carcinogenesis.
Common Source Data Base Summary Common_Source_Data_Base A Common Source Data Base (CSDB) is to provide the user (mainly technical authors, illustrators and publication managers) with automated processes to handle the complete palette of CSDB objects. Technical documentation is used in many areas of the everyday life. Product liability and many other issues regarding consumer protection have to be covered inside technical documentation. At minimum, a drawing including a few locators has to be provided. Much of this information is in accordance with the international S1000D specification.
Diffusion rate Onsager's equations for multicomponent diffusion and thermodiffusion Diffusion_rate > Basic models of diffusion > Onsager's equations for multicomponent diffusion and thermodiffusion The matrix of the kinetic coefficients L i j {\displaystyle L_{ij}} should be symmetric (Onsager reciprocal relations) and positive definite (for the entropy growth). The transport equations are ∂ n i ∂ t = − div ⁡ J i = − ∑ j ≥ 0 L i j div ⁡ X j = ∑ k ≥ 0 Δ n k . {\displaystyle {\frac {\partial n_{i}}{\partial t}}=-\operatorname {div} \mathbf {J} _{i}=-\sum _{j\geq 0}L_{ij}\operatorname {div} X_{j}=\sum _{k\geq 0}\left\,\Delta n_{k}\ .}
Semi-infinite In ordered structures and Euclidean spaces Semi-infinite > In ordered structures and Euclidean spaces For instance, one might study solutions of the heat equation in an idealised semi-infinite metal bar. A semi-infinite integral is an improper integral over a semi-infinite interval. More generally, objects indexed or parametrised by semi-infinite sets may be described as semi-infinite.Most forms of semi-infiniteness are boundedness properties, not cardinality or measure properties: semi-infinite sets are typically infinite in cardinality and measure.
Quick Sort Optimizations Quick_Sort > Algorithm > Implementation issues > Optimizations Stopping the recursion early leaves the array k-sorted, meaning that each element is at most k positions away from its final sorted position. In this case, insertion sort takes O(kn) time to finish the sort, which is linear if k is a constant. : 117 Compared to the "many small sorts" optimization, this version may execute fewer instructions, but it makes suboptimal use of the cache memories in modern computers.
Lithium naphthalene Redox Lithium_naphthalene > Reactions > Redox With a reduction potential near −2.5 V versus the normal hydrogen electrode, the naphthalene radical anion is a strong reducing agent.
G2-M DNA damage checkpoint Pathway response to DNA damage G2/M_checkpoint > Pathway response to DNA damage These pathways also stimulate the tumor suppressor p53. p53 regulates the function of the Cdk2 inhibitor p21 and the 14-3-3 proteins that phosphorylate (and thereby inactivate) and sequester Cdc25 in the cytoplasm, respectively. Recent studies have also suggested that Cdk1 and 14-3-3 positively regulate Wee1 in a similar manner.
Quantum Bayesianism Other uses of Bayesian probability in quantum physics Quantum_Bayesian > Relation to other interpretations > Other uses of Bayesian probability in quantum physics QBism should be distinguished from other applications of Bayesian inference in quantum physics, and from quantum analogues of Bayesian inference. For example, some in the field of computer science have introduced a kind of quantum Bayesian network, which they argue could have applications in "medical diagnosis, monitoring of processes, and genetics". Bayesian inference has also been applied in quantum theory for updating probability densities over quantum states, and MaxEnt methods have been used in similar ways. Bayesian methods for quantum state and process tomography are an active area of research.
Feature space vector Summary Features_(pattern_recognition) In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a phenomenon. Choosing informative, discriminating and independent features is a crucial element of effective algorithms in pattern recognition, classification and regression. Features are usually numeric, but structural features such as strings and graphs are used in syntactic pattern recognition. The concept of "feature" is related to that of explanatory variable used in statistical techniques such as linear regression.
Bitmap Index Summary Bitmap_Index A bitmap index is a special kind of database index that uses bitmaps. Bitmap indexes have traditionally been considered to work well for low-cardinality columns, which have a modest number of distinct values, either absolutely, or relative to the number of records that contain the data. The extreme case of low cardinality is Boolean data (e.g., does a resident in a city have internet access? ), which has two values, True and False.
Particle physics and representation theory Approximate symmetries Particle_physics_and_representation_theory > Approximate symmetries Although the above symmetries are believed to be exact, other symmetries are only approximate.
Introduction to Automata Theory, Languages, and Computation Edition history and reception Introduction_to_Automata_Theory,_Languages,_and_Computation > Edition history and reception Introduction to Automata Theory, Languages, and Computation (3rd ed.). Addison-Wesley. ISBN 0-321-45536-3.
Learning Operant conditioning Learning > Types > Associative learning > Operant conditioning Operant conditioning is a way in which behavior can be shaped or modified according to the desires of the trainer or head individual. Operant conditioning uses the thought that living things seek pleasure and avoid pain, and that an animal or human can learn through receiving either reward or punishment at a specific time called trace conditioning. Trace conditioning is the small and ideal period of time between the subject performing the desired behavior, and receiving the positive reinforcement as a result of their performance. The reward needs to be given immediately after the completion of the wanted behavior.Operant conditioning is different from classical conditioning in that it shapes behavior not solely on bodily reflexes that occur naturally to a specific stimulus, but rather focuses on the shaping of wanted behavior that requires conscious thought, and ultimately requires learning.Punishment and reinforcement are the two principal ways in which operant conditioning occurs.
Integration by reduction formulae How to compute the integral Integration_by_reduction_formulae > How to compute the integral To compute the integral, we set n to its value and use the reduction formula to express it in terms of the (n – 1) or (n – 2) integral. The lower index integral can be used to calculate the higher index ones; the process is continued repeatedly until we reach a point where the function to be integrated can be computed, usually when its index is 0 or 1. Then we back-substitute the previous results until we have computed In.
Infinite scroll Implementation Scrolling > Computing > Implementation Scrolling is often carried out on a computer by the CPU (software scrolling) or by a graphics processor. Some systems feature hardware scrolling, where an image may be offset as it is displayed, without any frame buffer manipulation (see also hardware windowing). This was especially common in 8 and 16bit video game consoles.
Transition metal isocyanide complexes Scope of isocyanide ligands Transition_metal_isocyanide_complexes > Scope of isocyanide ligands Several thousand isocyanides are known, but the coordination chemistry is dominated by a few ligands. Common isonitrile ligands are methyl isocyanide, tert-butyl isocyanide, phenyl isocyanide, and cyclohexylisocyanide. Isocyanides are electronically similar to CO, but for most R groups, isocyanides are superior Lewis bases and weaker pi-acceptors. Trifluoromethylisocyanide is the exception, its coordination properties are very similarly to those of CO.
Periodic boundary conditions Summary Periodic_boundary_condition . , x n ) , {\displaystyle {\frac {\partial ^{m}}{\partial x_{2}^{m}}}\phi (x_{1},a_{2},...,x_{n})={\frac {\partial ^{m}}{\partial x_{2}^{m}}}\phi (x_{1},b_{2},...,x_{n}),} . .
Multivariate adaptive regression splines Generalized cross validation Multivariate_adaptive_regression_splines > The model building process > The backward pass > Generalized cross validation We penalize flexibility because models that are too flexible will model the specific realization of noise in the data instead of just the systematic structure of the data. Generalized cross-validation is so named because it uses a formula to approximate the error that would be determined by leave-one-out validation. It is just an approximation but works well in practice. GCVs were introduced by Craven and Wahba and extended by Friedman for MARS.
Heliotrope (building) Water usage and natural waste management Heliotrope_(building) > Water usage and natural waste management In order to limit water usage, a gray water circuit (for washing dishes and clothes) is used.Wastewater is purified in a vegetated cascade pond outside the edifice and it also collects rainwater. Natural waste and excrement are dry composted in the structure as well.
Design for Six Sigma Similarities with other methods Design_for_Six_Sigma > Similarities with other methods Arguments about what makes DFSS different from Six Sigma demonstrate the similarities between DFSS and other established engineering practices such as probabilistic design and design for quality. In general Six Sigma with its DMAIC roadmap focuses on improvement of an existing process or processes. DFSS focuses on the creation of new value with inputs from customers, suppliers and business needs.
Kidney transplantation Kidney-pancreas transplant Renal_transplantation > Kidney-pancreas transplant The cells are then injected through a catheter into the recipient and they generally lodge in the liver. The recipient still needs to take immunosuppressants to avoid rejection, but no surgery is required. Most people need two or three such injections, and many are not completely insulin-free.
Wetterich equation Applications Wetterich_equation > Applications The method was applied to numerous problems in physics, e.g.: In statistical field theory, FRG provided a unified picture of phase transitions in classical linear O ( N ) {\displaystyle O(N)} -symmetric scalar theories in different dimensions d {\displaystyle d} , including critical exponents for d = 3 {\displaystyle d=3} and the Berezinskii–Kosterlitz–Thouless phase transition for d = 2 {\displaystyle d=2} , N = 2 {\displaystyle N=2} . In gauge quantum field theory, FRG was used, for instance, to investigate the chiral phase transition and infrared properties of QCD and its large-flavor extensions. In condensed matter physics, the method proved to be successful to treat lattice models (e.g. the Hubbard model or frustrated magnetic systems), repulsive Bose gas, BEC/BCS crossover for two-component Fermi gas, Kondo effect, disordered systems and nonequilibrium phenomena. Application of FRG to gravity provided arguments in favor of nonperturbative renormalizability of quantum gravity in four spacetime dimensions, known as the asymptotic safety scenario. In mathematical physics FRG was used to prove renormalizability of different field theories.
Data deduplication Drawbacks and concerns Data_deduplication > Drawbacks and concerns One method for deduplicating data relies on the use of cryptographic hash functions to identify duplicate segments of data. If two different pieces of information generate the same hash value, this is known as a collision. The probability of a collision depends mainly on the hash length (see birthday attack). Thus, the concern arises that data corruption can occur if a hash collision occurs, and additional means of verification are not used to verify whether there is a difference in data, or not.
Protein precipitation Energetics involved in salting out Protein_precipitation > Methods > Salting out > Energetics involved in salting out Salting out is a spontaneous process when the right concentration of the salt is reached in solution. The hydrophobic patches on the protein surface generate highly ordered water shells. This results in a small decrease in enthalpy, ΔH, and a larger decrease in entropy, ΔS, of the ordered water molecules relative to the molecules in the bulk solution. The overall free energy change, ΔG, of the process is given by the Gibbs free energy equation: Δ G = Δ H − T Δ S .
Congestion collapse TCP/IP congestion avoidance Congestion_collapse > Mitigation > TCP/IP congestion avoidance The TCP congestion avoidance algorithm is the primary basis for congestion control on the Internet.Problems occur when concurrent TCP flows experience tail-drops, especially when bufferbloat is present. This delayed packet loss interferes with TCP's automatic congestion avoidance. All flows that experience this packet loss begin a TCP retrain at the same moment – this is called TCP global synchronization.
Infinite game Determinacy from elementary considerations Determinacy > Determinacy from elementary considerations If player I cannot do this, then it means player II had a winning strategy from the beginning. On the other hand, if player I can play in this way, then I must win, because the game will be over after some finite number of moves, and player I can't have lost at that point.
Mechanical advantage device Pulleys Mechanical_advantage_device > Pulleys Consider a pulley attached to a weight being lifted. A rope passes around it, with one end attached to a fixed point above, e.g. a barn roof rafter, and a pulling force is applied upward to the other end with the two lengths parallel.
Item tree analysis Summary Item_tree_analysis Other typical examples are questionnaires where the items are statements to which subjects can agree (1) or disagree (0). Depending on the content of the items it is possible that the response of a subject to an item j determines her or his responses to other items. It is, for example, possible that each subject who agrees to item j will also agree to item i. In this case we say that item j implies item i (short i → j {\displaystyle i\rightarrow j} ). The goal of an ITA is to uncover such deterministic implications from the data set D.
Bold hypothesis Brief explanation Bold_hypothesis > Brief explanation " In Popper's philosophy of science, scientific statements are always provisional, they have limits of application, and they could always be wrong. If a statement cannot even in principle be proved wrong, it cannot be a scientific statement.
Eddy saturation and eddy compensation Formation of eddies and overturning response Eddy_saturation_and_eddy_compensation > Formation of eddies and overturning response Dynamics in the Southern Ocean are dominated by two cells with opposing rotation, each is forced by surface buoyancy fluxes. Via isopycnals, tracers are transferred from the deep to the surface. Isopycnal slopes are key for determining the depth of the global Pycnocline, and where water mass outcrops are. Therefore, isopycnals play an important role in the interaction with the atmosphere.
Algorithm selection Boolean satisfiability problem (and other hard combinatorial problems) Algorithm_selection > Examples > Boolean satisfiability problem (and other hard combinatorial problems) A well-known application of algorithm selection is the Boolean satisfiability problem. Here, the portfolio of algorithms is a set of (complementary) SAT solvers, the instances are Boolean formulas, the cost metric is for example average runtime or number of unsolved instances. So, the goal is to select a well-performing SAT solver for each individual instance. In the same way, algorithm selection can be applied to many other N P {\displaystyle {\mathcal {NP}}} -hard problems (such as mixed integer programming, CSP, AI planning, TSP, MAXSAT, QBF and answer set programming). Competition-winning systems in SAT are SATzilla, 3S and CSHC
Sedimentary basin Mechanics of formation Sedimentary_basins > Mechanics of formation Sedimentary basins form as a result of regional subsidence of the lithosphere, mostly as a result of a few geodynamic processes.
Viral meningitis Signs and symptoms Viral_meningitis > Signs and symptoms Viral meningitis characteristically presents with fever, headache and neck stiffness. Fever is the result of cytokines released that affect the thermoregulatory (temperature control) neurons of the hypothalamus. Cytokines and increased intracranial pressure stimulate nociceptors in the brain that lead to headaches. Neck stiffness is the result of inflamed meninges stretching due to flexion of the spine.
Symmetry of diatomic molecules Rotational spectrum Symmetry_of_diatomic_molecules > Observable consequences > Rotational spectrum In the electric dipole approximation the transition amplitude for emission or absorption of radiation can be shown to be proportional to the vibronic matrix element of the component of the electric dipole operator D {\displaystyle D} along the molecular axis. This is the permanent electric dipole moment. In homonuclear diatomic molecules, the permanent electric dipole moment vanishes and there is no pure rotation spectrum (but see N.B.
Glossary of areas of mathematics E Glossary_of_areas_of_mathematics > E Experimental mathematics an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns. Exterior algebra Exterior calculus Extraordinary cohomology theory Extremal combinatorics a branch of combinatorics, it is the study of the possible sizes of a collection of finite objects given certain restrictions. Extremal graph theory a branch of mathematics that studies how global properties of a graph influence local substructure.
Chelsea Bridge Design and construction Chelsea_Bridge > New Chelsea Bridge > Design and construction The horizontal stresses are absorbed by stiffening girders in the deck itself and the suspension cables are not anchored to the ground, relieving stress on the abutments which are built on soft and unstable London clay. The piers of the new bridge were built on the site of the old bridge's piers, and are built of concrete, faced with granite above the low-water point. Each side of the bridge has a single suspension cable, each made up of 37 7⁄8-inch (23mm) diameter wire ropes bundled to form a hexagonal cable.
Resistant statistic Speed-of-light data Breakdown_point > Examples > Speed-of-light data Thus, if the mean is intended as a measure of the location of the center of the data, it is, in a sense, biased when outliers are present. Also, the distribution of the mean is known to be asymptotically normal due to the central limit theorem. However, outliers can make the distribution of the mean non-normal even for fairly large data sets. Besides this non-normality, the mean is also inefficient in the presence of outliers and less variable measures of location are available.
Chemical revolution John Dalton Chemical_revolution > John Dalton John Dalton was an English chemist who developed the idea of atomic theory of chemical elements. Dalton's atomic theory of chemical elements assumed that each element had unique atoms associated with and specific to that atom. This was in opposition to Lavoisier's definition of elements which was that elements are substances that chemists could not break down further into simpler parts. Dalton's idea also differed from the idea of corpuscular theory of matter, which believed that all atoms were the same, and had been a supported theory since the 17th century.
Cytoplasmic dynein Mitotic spindle positioning Cytoplasmic_dynein > Function > Mitotic spindle positioning When the end of the microtubules become close to the cell membrane, they release a chemical signal that punts the dynein to the other side of the cell. It does this repeatedly so the chromosomes end up in the center of the cell, which is necessary in mitosis. Budding yeast have been a powerful model organism to study this process and has shown that dynein is targeted to plus ends of astral microtubules and delivered to the cell cortex via an offloading mechanism.
Engine efficiency Piston engine Engine_efficiency > External combustion engines > Steam engine > Piston engine Watt's engine operated with steam at slightly above atmospheric pressure. Watt's improvements increased efficiency by a factor of over 2.5. The lack of general mechanical ability, including skilled mechanics, machine tools, and manufacturing methods, limited the efficiency of actual engines and their design until about 1840.Higher-pressured engines were developed by Oliver Evans and Richard Trevithick, working independently.
Zero to the power of zero Current situation Zero_to_the_power_of_zero > History > Current situation Some authors define 00 as 1 because it simplifies many theorem statements. According to Benson (1999), "The choice whether to define 00 is based on convenience, not on correctness. If we refrain from defining 00, then certain assertions become unnecessarily awkward. ... The consensus is to use the definition 00 = 1, although there are textbooks that refrain from defining 00." Knuth (1992) contends more strongly that 00 "has to be 1"; he draws a distinction between the value 00, which should equal 1, and the limiting form 00 (an abbreviation for a limit of f(t)g(t) where f(t), g(t) → 0), which is an indeterminate form: "Both Cauchy and Libri were right, but Libri and his defenders did not understand why truth was on their side." Other authors leave 00 undefined because 00 is an indeterminate form: f(t), g(t) → 0 does not imply f(t)g(t) → 1.There do not seem to be any authors assigning 00 a specific value other than 1.
Power systems Supplies Electric_power_system > Components of power systems > Supplies If the load on the system increases, the generators will require more torque to spin at that speed and, in a steam power station, more steam must be supplied to the turbines driving them. Thus the steam used and the fuel expended directly relate to the quantity of electrical energy supplied. An exception exists for generators incorporating power electronics such as gearless wind turbines or linked to a grid through an asynchronous tie such as a HVDC link — these can operate at frequencies independent of the power system frequency.
Factorial design Example of advantages of factorial experiments Factorial_designs > Advantages of factorial experiments > Example of advantages of factorial experiments In his book, Improving Almost Anything: Ideas and Essays, statistician George Box gives many examples of the benefits of factorial experiments. Here is one. Engineers at the bearing manufacturer SKF wanted to know if changing to a less expensive "cage" design would affect bearing life.
Helminthic therapy Hypotheses Helminthic_therapy > Hypotheses Although the mechanism(s) of autoimmune disease development is(are) not fully understood, there is broad agreement that the majority of autoimmune diseases are caused by inappropriate immunological responses to innocuous antigens; these are generally called the hygiene hypothesis, but exist in several variants. One version proposes that the dysfunction is driven by a branch of the immune system known as the T helper cells (Th or TH). Two other refinements to the hygiene hypothesis exist: The "old friends" hypothesis, and the "microbiome depletion" hypothesis.
Kirchhoff's circuit laws Kirchhoff's voltage law Kirchhoff's_voltage_law > Kirchhoff's voltage law This law, also called Kirchhoff's second law, or Kirchhoff's loop rule, states the following: The directed sum of the potential differences (voltages) around any closed loop is zero. Similarly to Kirchhoff's current law, the voltage law can be stated as: Here, n is the total number of voltages measured.
Modulo (mathematics) Original use Modulo_(mathematics) > Usage > Original use Gauss originally intended to use "modulo" as follows: given the integers a, b and n, the expression a ≡ b (mod n) (pronounced "a is congruent to b modulo n") means that a − b is an integer multiple of n, or equivalently, a and b both leave the same remainder when divided by n. For example: 13 is congruent to 63 modulo 10means that 13 − 63 is a multiple of 10 (equiv., 13 and 63 differ by a multiple of 10).
Quadratic residue Complexity of finding square roots Least_quadratic_non-residue > Complexity of finding square roots That is, given a number a and a modulus n, how hard is it to tell whether an x solving x2 ≡ a (mod n) exists assuming one does exist, to calculate it?An important difference between prime and composite moduli shows up here. Modulo a prime p, a quadratic residue a has 1 + (a\|p) roots (i.e. zero if a N p, one if a ≡ 0 (mod p), or two if a R p and gcd(a,p) = 1.) In general if a composite modulus n is written as a product of powers of distinct primes, and there are n1 roots modulo the first one, n2 mod the second, ..., there will be n1n2... roots modulo n. The theoretical way solutions modulo the prime powers are combined to make solutions modulo n is called the Chinese remainder theorem; it can be implemented with an efficient algorithm. For example: Solve x2 ≡ 6 (mod 15).
Photodiode arrays Photoconductive mode Photo_transistor > Principle of operation > Photoconductive mode In photoconductive mode the diode is reverse biased, that is, with the cathode driven positive with respect to the anode. This reduces the response time because the additional reverse bias increases the width of the depletion layer, which decreases the junction's capacitance and increases the region with an electric field that will cause electrons to be quickly collected. The reverse bias also creates dark current without much change in the photocurrent. Although this mode is faster, the photoconductive mode can exhibit more electronic noise due to dark current or avalanche effects. The leakage current of a good PIN diode is so low (<1 nA) that the Johnson–Nyquist noise of the load resistance in a typical circuit often dominates.
Diastolic blood pressure Regulation of blood pressure Home_blood_pressure_monitoring > Physiology > Regulation of blood pressure Renin–angiotensin system (RAS): This system is generally known for its long-term adjustment of arterial pressure. This system allows the kidney to compensate for loss in blood volume or drops in arterial pressure by activating an endogenous vasoconstrictor known as angiotensin II. Aldosterone release: This steroid hormone is released from the adrenal cortex in response to activation of the renin-angiotensin system, high serum potassium levels, or elevated adrenocorticotropic hormone (ACTH).
Lamport signature Summary Lamport_signature In cryptography, a Lamport signature or Lamport one-time signature scheme is a method for constructing a digital signature. Lamport signatures can be built from any cryptographically secure one-way function; usually a cryptographic hash function is used. Although the potential development of quantum computers threatens the security of many common forms of cryptography such as RSA, it is believed that Lamport signatures with large hash functions would still be secure in that event.
Colligative property Osmotic pressure Colligative_Properties > Osmotic pressure Two laws governing the osmotic pressure of a dilute solution were discovered by the German botanist W. F. P. Pfeffer and the Dutch chemist J. H. van’t Hoff: The osmotic pressure of a dilute solution at constant temperature is directly proportional to its concentration. The osmotic pressure of a solution is directly proportional to its absolute temperature.These are analogous to Boyle's law and Charles's law for gases. Similarly, the combined ideal gas law, P V = n R T {\displaystyle PV=nRT} , has as an analogue for ideal solutions Π V = n R T i {\displaystyle \Pi V=nRTi} , where Π {\displaystyle \Pi } is osmotic pressure; V is the volume; n is the number of moles of solute; R is the molar gas constant 8.314 J K−1 mol−1; T is absolute temperature; and i is the Van 't Hoff factor.
Francis Galton Model for population stability Francis_Galton > Model for population stability Each group was not centred on the parent's weight, but rather at a weight closer to the population average. Galton called this reversion, as every progeny group was distributed at a value that was closer to the population average than the parent. The deviation from the population average was in the same direction, but the magnitude of the deviation was only one-third as large.
Sodium percarbonate Chemistry Sodium_percarbonate > Chemistry Dissolved in water, sodium percarbonate yields a mixture of hydrogen peroxide (which eventually decomposes to water and oxygen), sodium cations Na+, and carbonate CO2−3. 2 Na 2 CO 3 ⋅ 3 H 2 O 2 ⟶ 3 H 2 O 2 + 4 Na + + 2 CO 3 2 − {\displaystyle {\ce {2Na2CO3*3H2O2 -> 3H2O2 + 4Na+ + 2CO3^2-}}} 2 H 2 O 2 ⟶ 2 H 2 O + O 2 {\displaystyle {\ce {2H2O2 -> 2H2O + O2}}}
Domain objects Kinds of models Domain_objects > Overview > Kinds of models When people exchange business cards, for instance, they only care about the information on the card (its attributes) rather than trying to distinguish between each unique card. Models can also define events (something that happened in the past). A domain event is an event that domain experts care about.
Vitamin K reaction Vitamin K as reversal agent for vitamin K antagonists Vitamin_K_reaction > Treatment > Vitamin K as reversal agent for vitamin K antagonists The intravenous (IV) route of administration has a faster onset of action when compared to the oral and subcutaneous routes, thus IV vitamin K is more appropriate in critical situations. However, the intravenous route of administration of vitamin K still takes hours before the vitamin K dependent coagulation factors can be produced by the liver, thus it requires more time for the body to suspend bleeding. In situations where rapid reversal is necessary for those on warfarin, such as in the case of major hemorrhage or surgery, 4-factor prothrombin complex concentrate (4F-PCC) is used with vitamin K to neutralize the effects of VKAs. 4F-PCC is composed of clotting factors that allow for quick reversal of VKAs, thus it compensates for the slow reversal time of vitamin K when administered together.
Whisper (speech recognition system) Training and capabilities Whisper_(speech_recognition_system) > Training and capabilities Whisper has been trained using semi-supervised learning on 680,000 hours of multilingual and multitask data, of which about one-fifth (117,000 hours) were non-English audio data. Whisper does not outperform models which specialize in the LibriSpeech dataset, although when tested across many datasets, it is more robust and makes 50% fewer errors than other models.Whisper has a differing error rate with respect to transcribing different languages, with a higher word error rate in languages not well-represented in the training data.
127 (number) In mathematics 127_(number) > In mathematics As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also the largest known Mersenne prime exponent for a Mersenne number, 2 127 − 1 {\displaystyle 2^{127}-1} , which is also a Mersenne prime. It was discovered by Édouard Lucas in 1876 and held the record for the largest known prime for 75 years. 2 127 − 1 {\displaystyle 2^{127}-1} is the largest prime ever discovered by hand calculations as well as the largest known double Mersenne prime.
Hypertree network Summary Hypertree_network A hypertree network is a network topology that shares some traits with the binary tree network. It is a variation of the fat tree architecture.A hypertree of degree k depth d may be visualized as a 3-dimensional object whose front view is the top-down complete k-ary tree of depth d and the side view is the bottom-up complete binary tree of depth d.Hypertrees were proposed in 1981 by James R. Goodman and Carlo Sequin.Hypertrees are a choice for parallel computer architecture, used, e.g., in the connection machine CM-5. == References ==
Interchange of limiting operations List of related theorems Interchange_of_limiting_operations > List of related theorems Interchange of limits: Moore-Osgood theorem Interchange of limit and infinite summation: Tannery's theorem Interchange of partial derivatives: Schwarz's theorem Interchange of integrals: Fubini's theorem Interchange of limit and integral: Dominated convergence theorem Vitali convergence theorem Fichera convergence theorem Cafiero convergence theorem Fatou's lemma Monotone convergence theorem for integrals (Beppo Levi's lemma) Interchange of derivative and integral: Leibniz integral rule
Ornstein–Uhlenbeck operator The Laplacian Ornstein–Uhlenbeck_operator > Introduction: the finite-dimensional picture > The Laplacian Consider the gradient operator ∇ acting on scalar functions f: Rn → R; the gradient of a scalar function is a vector field v = ∇f: Rn → Rn. The divergence operator div, acting on vector fields to produce scalar fields, is the adjoint operator to ∇. The Laplace operator Δ is then the composition of the divergence and gradient operators: Δ = d i v ∘ ∇ {\displaystyle \Delta =\mathrm {div} \circ \nabla } ,acting on scalar functions to produce scalar functions. Note that A = −Δ is a positive operator, whereas Δ is a dissipative operator.
Increased urinary frequency Mechanism Increased_urinary_frequency > Mechanism Polyuria in osmotic cases, increases flow amount in the distal nephron where flow rates and velocity are low. The significant pressure increase occurring in the distal nephron takes place particularly in the cortical-collecting ducts. One study from 2008 lays out a hypothesis that hyperglycaemic and osmotic polyuria play roles ultimately in diabetic nephropathy.
Rotation plane Eigenvalues and eigenplanes Rotation_plane > Mathematical properties > Eigenvalues and eigenplanes The planes of rotations for a particular rotation using the eigenvalues. Given a general rotation matrix in n dimensions its characteristic equation has either one (in odd dimensions) or zero (in even dimensions) real roots. The other roots are in complex conjugate pairs, exactly ⌊ n 2 ⌋ , {\displaystyle \left\lfloor {\frac {n}{2}}\right\rfloor ,} such pairs.

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.