The exponential function is a mathematical function denoted by or . Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation, but modern definitions allow it to be rigorously extended to all real arguments, including irrational numbers. Its ubiquitous occurrence in pure and applied mathematics led mathematician Walter Rudin to opine that the exponential function is "the most important function in mathematics".
In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. These methods were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta.
In statistics, the logistic model is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables. In regression analysis, logistic regression is estimating the parameters of a logistic model. Formally, in binary logistic regression there is a single binary dependent variable, coded by an indicator variable, where the two values are labeled "0" and "1", while the independent variables can each be a binary variable or a continuous variable. The corresponding probability of the value labeled "1" can vary between 0 and 1, hence the labeling; the function that converts log-odds to probability is the logistic function, hence the name. The unit of measurement for the log-odds scale is called a logit, from logistic unit, hence the alternative names. See § Background and § Definition for formal mathematics, and § Example for a worked example.
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called vertices and each of the related pairs of vertices is called an edge. Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.
Partial least squares regression is a statistical method that bears some relation to principal components regression; instead of finding hyperplanes of maximum variance between the response and independent variables, it finds a linear regression model by projecting the predicted variables and the observable variables to a new space. Because both the X and Y data are projected to new spaces, the PLS family of methods are known as bilinear factor models. Partial least squares discriminant analysis (PLS-DA) is a variant used when the Y is categorical.
In statistics, semiparametric regression includes regression models that combine parametric and nonparametric models. They are often used in situations where the fully nonparametric model may not perform well or when the researcher wants to use a parametric model but the functional form with respect to a subset of the regressors or the density of the errors is not known. Semiparametric regression models are a particular type of semiparametric modelling and, since semiparametric models contain a parametric component, they rely on parametric assumptions and may be misspecified and inconsistent, just like a fully parametric model.
Bootstrapping is any test or metric that uses random sampling with replacement, and falls under the broader class of resampling methods. Bootstrapping assigns measures of accuracy to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods.
POU domain, class 1, transcription factor 1 , also known as POU1F1, is a transcription factor for growth hormone.
Prostaglandin-H2 D-isomerase (PTGDS) is an enzyme that in humans is encoded by the PTGDS gene.
Interleukin 6 receptor (IL6R) also known as CD126 is a type I cytokine receptor.
Endothelin receptor type B, (ET-B) is a protein that in humans is encoded by the EDNRB gene.
Endothelin receptor type A, also known as ETA, is a human G protein-coupled receptor.
Somatostatin receptor type 4 is a protein that in humans is encoded by the SSTR4 gene.
Y-23684 is an anxiolytic drug with a novel chemical structure, which is used in scientific research. It has similar effects to benzodiazepine drugs, but is structurally distinct and so is classed as a nonbenzodiazepine anxiolytic.
Krueppel-like factor 9 is a protein that in humans is encoded by the KLF9 gene. Previously known as Basic Transcription Element Binding Protein 1, Klf9 is part of the Sp1 C2H2-type zinc finger family of transcription factors. Several previous studies showed Klf9-related regulation of animal development, including cell differentiation of B cells, keratinocytes, and neurons. Klf9 is also a key transcriptional regulator for uterine endometrial cell proliferation, adhesion, and differentiation, all factors that are essential during the process of pregnancy and are turned off during tumorigenesis.
Callicarpa kwangtungensis is a species of beautyberry. The tree is introduced in Europe as an ornamental plant. The fruit is light-pink and grows in small clusters. The flowers can range from pink to white. It is endemic to China. The berries are very bitter and inedible for human use. Birds and other wild life won't eat them unless all their food sources are depleted.
In mathematics, the Dedekind numbers are a rapidly growing sequence of integers named after Richard Dedekind, who defined them in 1897. The Dedekind number M(n) is the number of monotone boolean functions of n variables. Equivalently, it is the number of antichains of subsets of an n-element set, the number of elements in a free distributive lattice with n generators, and one more than the number of abstract simplicial complexes on a set with n elements.
Libo County is a county of southern Guizhou province, China, bordering Guangxi to the south. It is under the administration of the Qiannan Buyei and Miao Autonomous Prefecture.
