相关论文: Combinatorial Tools for Regge Calculus

Mesh numbering is a critical issue in Finite Element Methods, as the computational cost of one analysis is highly dependent on the order of the nodes of the mesh. This paper presents some preliminary investigations on the problem of mesh…

In this note we demonstrate that a number of case-heavy combinatorial proofs in the mathematical phylogenetics literature can be proven more compactly using computational support. We use these techniques to also prove several new…

Bilevel optimization is defined as a mathematical program, where an optimization problem contains another optimization problem as a constraint. These problems have received significant attention from the mathematical programming community.…

In general Evolutionary Computation (EC) includes a number of optimization methods inspired by biological mechanisms of evolution. The methods catalogued in this area use the Darwinian principles of life evolution to produce algorithms that…

Evolutionary algorithms have been frequently used for dynamic optimization problems. With this paper, we contribute to the theoretical understanding of this research area. We present the first computational complexity analysis of…

We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method will be investigated.

Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…

Abbreviated Abstract: The objective of Evolutionary Computation is to solve practical problems (e.g. optimization, data mining) by simulating the mechanisms of natural evolution. This thesis addresses several topics related to adaptation…

An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.

This is the final version of the lecture notes of the 23rd Internet Seminar on Evolutionary Equations, see also https://www.mat.tuhh.de/isem23/.

Convergence results are stated for the variational iteration method applied to solve an initial value problem for a system of ordinary differential equations.

A survey of recent progress in three areas of algebraic combinatorics: (1) the Saturation Conjecture for Littlewood-Richardson coefficients, (2) the n! and (n+1)^{n-1} conjectures, and (3) longest increasing subsequences of permutations.

Any practical attempt to solve the Regge equations, these being a large system of non-linear algebraic equations, will almost certainly employ a Newton-Raphson like scheme. In such cases it is essential that efficient algorithms be used…

The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…

In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…

We systematize and analyze some results obtained in Subset Combinatorics of $G$ groups after publications the previous surveys [1-4]. The main topics: the dynamical and descriptive characterizations of subsets of a group relatively their…

A method for constructing evolution equations admitting a master symmetry is proposed. Several examples illustrating the method are presented. It is also noted that for certain evolution equations master symmetries can be useful for…

There have been several modifications of how basic calculus has been taught, but very few of these modifications have considered the computational tools available at our disposal. Here, we present a few tools that are easy to develop and…

In this review, we summarize recent developments in stochastic evolutionary game dynamics of finite populations.

We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest…