Hamiltonian field theoryIn theoretical physics, Hamiltonian field theory is the field-theoretic analogue to classical Hamiltonian mechanics. It is a formalism in classical field theory alongside Lagrangian field theory. It also has applications in quantum field theory. The Hamiltonian for a system of discrete particles is a function of their generalized coordinates and conjugate momenta, and possibly, time. For continua and fields, Hamiltonian mechanics is unsuitable but can be extended by considering a large number of point masses, and taking the continuous limit, that is, infinitely many particles forming a continuum or field.
Binomial distributionIn probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability ). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.
Maximum entropy probability distributionIn statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. According to the principle of maximum entropy, if nothing is known about a distribution except that it belongs to a certain class (usually defined in terms of specified properties or measures), then the distribution with the largest entropy should be chosen as the least-informative default.
Poisson distributionIn probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson ('pwɑːsɒn; pwasɔ̃). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.
Hamiltonian vector fieldIn mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named after the physicist and mathematician Sir William Rowan Hamilton, a Hamiltonian vector field is a geometric manifestation of Hamilton's equations in classical mechanics. The integral curves of a Hamiltonian vector field represent solutions to the equations of motion in the Hamiltonian form.
Marginal distributionIn probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. This contrasts with a conditional distribution, which gives the probabilities contingent upon the values of the other variables. Marginal variables are those variables in the subset of variables being retained.
Prior probabilityA prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable.
Data integrationData integration involves combining data residing in different sources and providing users with a unified view of them. This process becomes significant in a variety of situations, which include both commercial (such as when two similar companies need to merge their databases) and scientific (combining research results from different bioinformatics repositories, for example) domains. Data integration appears with increasing frequency as the volume (that is, big data) and the need to share existing data explodes.
Enterprise integrationEnterprise integration is a technical field of enterprise architecture, which is focused on the study of topics such as system interconnection, electronic data interchange, product data exchange and distributed computing environments. It is a concept in enterprise engineering to provide the relevant information and thereby enable communication between people, machines and computers and their efficient co-operation and co-ordination.
Semantic integrationSemantic integration is the process of interrelating information from diverse sources, for example calendars and to do lists, email archives, presence information (physical, psychological, and social), documents of all sorts, contacts (including social graphs), search results, and advertising and marketing relevance derived from them. In this regard, semantics focuses on the organization of and action upon information by acting as an intermediary between heterogeneous data sources, which may conflict not only by structure but also context or value.
Nuclear proliferationNuclear proliferation is the spread of nuclear weapons, fissionable material, and weapons-applicable nuclear technology and information to nations not recognized as "Nuclear Weapon States" by the Treaty on the Non-Proliferation of Nuclear Weapons, commonly known as the Non-Proliferation Treaty or NPT. Proliferation has been opposed by many nations with and without nuclear weapons, as governments fear that more countries with nuclear weapons will increase the possibility of nuclear warfare (up to and including the so-called countervalue targeting of civilians with nuclear weapons), de-stabilize international or regional relations, or infringe upon the national sovereignty of nation states.
Set theorySet theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.
