Related papers: Algorithms for Combinatorial Systems: Well-Founded…
Well-structured systems, aka WSTSs, are computational models where the set of possible configurations is equipped with a well-quasi-ordering which is compatible with the transition relation between configurations. This structure supports…
The reconstruction of broad resonances is important for understanding the dynamics of heavy ion collisions. However, large combinatorial background makes this objective very challenging. In this work an innovative iterative method which…
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
Inspired by numerical homotopy methods we propose a combinatorial homotopy algorithm for finding all isolated solutions to a tropical polynomial systems of n tropical polynomials in n variables. In particular, a tropicalisation of the…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…
It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs…
The multiplicative Newton-like method developed by the author et al. is extended to the situation where the dynamics is restricted to the orthogonal group. A general framework is constructed without specifying the cost function. Though the…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
We begin a systematic study of the enumerative combinatorics of mixed succession rules, which are succession rules such that, in the associated generating tree, the nodes are allowed to produce their sons at several different levels…
We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collection of Newton polytopes. This…
In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
In materials science, the challenge of rapid prototyping materials with desired properties often involves extensive experimentation to find suitable microstructures. Additionally, finding microstructures for given properties is typically an…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
We devise a unified framework for the design of canonization algorithms. Using hereditarily finite sets, we define a general notion of combinatorial objects that includes graphs, hypergraphs, relational structures, codes, permutation…
Three-graded root systems can be arranged into nested sequences. One exceptional sequence provides a natural means to recover some structures and symmetries familiar in the context of particle physics.