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An atlas is a collection of consistent coordinate charts on a manifold, where "consistent" most commonly means that the transition functions of the charts are smooth. As the ...

In discrete percolation theory, bond percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice graph ...

Conway's soldiers, also known as the "solitaire army" game (Berlekamp et al. 1982) or "checker-jumping problem" (Honsberger 1976) is a one-player game played on an infinite ...

The problem in calculus of variations to find the minimal surface of a boundary with specified constraints (usually having no singularities on the surface). In general, there ...

A point process is a probabilistic model for random scatterings of points on some space X often assumed to be a subset of R^d for some d. Oftentimes, point processes describe ...

A sequence of n-tuples that fills n-space more uniformly than uncorrelated random points, sometimes also called a low-discrepancy sequence. Although the ordinary uniform ...

Let G=(V,E) be a finite graph, let Omega be the set Omega={0,1}^E whose members are vectors omega=(omega(e):e in E), and let F be the sigma-algebra of all subsets of Omega. A ...

A ruled surface is a surface that can be swept out by moving a line in space. It therefore has a parameterization of the form x(u,v)=b(u)+vdelta(u), (1) where b is called the ...

The Siegel theta function is a Gamma_n-invariant meromorphic function on the space of all p×p symmetric complex matrices Z=X+iY with positive definite imaginary part. It is ...

A state diagram is a labeled directed graph together with state information that can be used to indicate that certain paths on in a system may be traversed only in a certain ...