Compound Poisson distributionIn probability theory, a compound Poisson distribution is the probability distribution of the sum of a number of independent identically-distributed random variables, where the number of terms to be added is itself a Poisson-distributed variable. The result can be either a continuous or a discrete distribution. Suppose that i.e., N is a random variable whose distribution is a Poisson distribution with expected value λ, and that are identically distributed random variables that are mutually independent and also independent of N.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Stochastic processIn probability theory and related fields, a stochastic (stəˈkæstɪk) or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule.
Los Angeles TimesThe Los Angeles Times is a daily newspaper that started publishing in Los Angeles in 1881. Based in the Los Angeles County city of El Segundo since 2018, it is the sixth-largest newspaper by circulation in the United States, as well as the largest newspaper in the western United States. Owned by Patrick Soon-Shiong and published by the Times Mirror Company, the paper has won more than 40 Pulitzer Prizes. In the 19th century, the paper developed a reputation for civic boosterism and opposition to labor unions, the latter of which led to the bombing of its headquarters in 1910.
Bayesian inferenceBayesian inference (ˈbeɪziən or ˈbeɪʒən ) is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law.
Times SquareTimes Square is a major commercial intersection, tourist destination, entertainment hub, and neighborhood in Midtown Manhattan, New York City, United States. It is formed by the junction of Broadway, Seventh Avenue, and 42nd Street. Together with adjacent Duffy Square, Times Square is a bowtie-shaped plaza five blocks long between 42nd and 47th Streets. Times Square is brightly lit by numerous digital billboards and advertisements as well as businesses offering 24/7 service.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
The New York TimesThe New York Times (NYT) is a daily newspaper based in New York City with a worldwide readership reported in 2022 to comprise 740,000 paid print subscribers, and 8.6 million paid digital subscribers. Founded in 1851 as the New-York Daily Times, it is published by The New York Times Company. The Times has won 132 Pulitzer Prizes, the most of any newspaper, and has long been regarded as a national "newspaper of record". For print, it is ranked 17th in the world by circulation and 3rd in the United States.
Upper and lower boundsIn mathematics, particularly in order theory, an upper bound or majorant of a subset S of some preordered set (K, ≤) is an element of K that is greater than or equal to every element of S. Dually, a lower bound or minorant of S is defined to be an element of K that is less than or equal to every element of S. A set with an upper (respectively, lower) bound is said to be bounded from above or majorized (respectively bounded from below or minorized) by that bound.
Jordan normal formIn linear algebra, a Jordan normal form, also known as a Jordan canonical form (JCF), is an upper triangular matrix of a particular form called a Jordan matrix representing a linear operator on a finite-dimensional vector space with respect to some basis. Such a matrix has each non-zero off-diagonal entry equal to 1, immediately above the main diagonal (on the superdiagonal), and with identical diagonal entries to the left and below them. Let V be a vector space over a field K.
