The Closest Substring Problem is one of the most important problems in the field of computational biology. It is stated as follows: given a set of t sequences s1; s2; : : : st over an alphabet , and two integers k; d with d k, can one find a string s of length k and, for all i = 1; 2; : : : ; t, substrings oi of si, all of length k, such that d(s; oi) d (for all i = 1; 2; : : : ; t)? (here, d(:...

Constructing a (signed) distance field and contouring its zero level set are two important steps in many surface reconstruction methods. While most high-quality distance transforms compute the distance to the surface as well as the closest point on it, the contouring step typically uses only the distance and omits the closest point information. Our novel closest point contouring algorithm (CPC)...

For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields ...

We show that for those lattices of Voronoi’s first kind with known obtuse superbasis, a closest lattice point can be computed in O(n) operations where n is the dimension of the lattice. To achieve this a series of relevant lattice vectors that converges to a closest lattice point is found. We show that the series converges after at most n terms. Each vector in the series can be efficiently comp...

The fine line is explored between the application of closest connection principle as a general gap-filling conflict laws rule and solution related issue based on rules contained in customs recognized Russian Federation. In absence custom, unambiguously accordance with paragraph 1 Art. 1186 Civil Code Federation, author offers to refer 2 same article. This proposal justified by complexity format...

In this semitutorial paper, a comprehensive survey of closest point search methods for lattices without a regular structure is presented. The existing search strategies are described in a unified framework, and differences between them are elucidated. An efficient closest point search algorithm, based on the Schnorr–Euchner variation of the Pohst method, is implemented. Given an arbitrary point...