Unitary representationIn mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every g ∈ G. The general theory is well-developed in the case that G is a locally compact (Hausdorff) topological group and the representations are strongly continuous. The theory has been widely applied in quantum mechanics since the 1920s, particularly influenced by Hermann Weyl's 1928 book Gruppentheorie und Quantenmechanik.
École des ponts ParisTechÉcole des Ponts ParisTech (originally called École nationale des ponts et chaussées or ENPC, also nicknamed Ponts) is a university-level institution of higher education and research in the field of science, engineering and technology. Founded in 1747 by Daniel-Charles Trudaine, it is one of the oldest and one of the most prestigious French Grandes Écoles. Historically, its primary mission has been to train engineering officials and civil engineers but the school now offers a wide-ranging education including computer science, applied mathematics, civil engineering, mechanics, finance, economics, innovation, urban studies, environment and transport engineering.
École normale supérieureAn école normale supérieure (ekɔl nɔʁmal sypeʁjœʁ) or ENS is a type of publicly funded higher education institution in France. A portion of the student body, admitted via a highly-selective competitive examination process, are French civil servants and are known as normaliens. ENSes also offers master's degrees, and can be compared to "Institutes for Advanced Studies". They constitute the top level of research-training education in the French university system.
Error functionIn mathematics, the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: Some authors define without the factor of . This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real.
Record labelA record label, or record company, or simply records, is a brand or trademark of music recordings and music videos, or the company that owns it. Sometimes, a record label is also a publishing company that manages such brands and trademarks, coordinates the production, manufacture, distribution, marketing, promotion, and enforcement of copyright for sound recordings and music videos, while also conducting talent scouting and development of new artists, and maintaining contracts with recording artists and their managers.
Gamma functionIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.
Transcendental functionIn mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically. Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions. Formally, an analytic function f (z) of one real or complex variable z is transcendental if it is algebraically independent of that variable.
Linear regressionIn statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.
Segmented regressionSegmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning the various independent variables. Segmented regression is useful when the independent variables, clustered into different groups, exhibit different relationships between the variables in these regions.
Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).
Regression analysisIn statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one or more independent variables (often called 'predictors', 'covariates', 'explanatory variables' or 'features'). The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion.
Independent record labelAn independent record label (or indie label) is a record label that operates without the funding or distribution of major record labels; they are a type of small- to medium-sized enterprise, or SME. The labels and artists are often represented by trade associations in their country or region, which in turn are represented by the international trade body, the Worldwide Independent Network (WIN). Many of the labels started as producers and distributors of specific genres of music, such as jazz music, or represent something new and non-mainstream, such as Elvis Presley in the early days.
