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The Gross–Pitaevskii equation (GPE, named after Eugene P. Gross [1] and Lev Petrovich Pitaevskii [2]) describes the ground state of a quantum system of identical bosons using the Hartree–Fock approximation and the pseudopotential interaction model. A Bose–Einstein condensate (BEC) is a gas of bosons that are in the same quantum state, and ...
Catastrophic cancellation. In numerical analysis, catastrophic cancellation[1][2] is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers. For example, if there are two studs, one long and the other long, and they are measured with a ruler that is ...
The term "Bellman equation" usually refers to the dynamic programming equation (DPE) associated with discrete-time optimization problems. [5] In continuous-time optimization problems, the analogous equation is a partial differential equation that is called the Hamilton–Jacobi–Bellman equation. [6][7] In discrete time any multi-stage ...
Gravitational potential. In classical mechanics, the gravitational potential is a scalar potential associating with each point in space the work (energy transferred) per unit mass that would be needed to move an object to that point from a fixed reference point in the conservative gravitational field. It is analogous to the electric potential ...
Tracing garbage collection. In computer programming, tracing garbage collection is a form of automatic memory management that consists of determining which objects should be deallocated ("garbage collected") by tracing which objects are reachable by a chain of references from certain "root" objects, and considering the rest as "garbage" and ...
Differentiable programming. Differentiable programming is a programming paradigm in which a numeric computer program can be differentiated throughout via automatic differentiation. [1][2][3][4][5] This allows for gradient-based optimization of parameters in the program, often via gradient descent, as well as other learning approaches that are ...
Second-order cone programming. A second-order cone program (SOCP) is a convex optimization problem of the form. where the problem parameters are , and . is the optimization variable. is the Euclidean norm and indicates transpose. [1] The "second-order cone" in SOCP arises from the constraints, which are equivalent to requiring the affine ...
Python is a multi-paradigm programming language. Object-oriented programming and structured programming are fully supported, and many of their features support functional programming and aspect-oriented programming (including metaprogramming [73] and metaobjects). [74] Many other paradigms are supported via extensions, including design by ...