Related papers: Exploring the Potential Energy Landscape Over a La…
In this paper, we examine the structure of systems that are weighted homogeneous for several systems of weights, and how it impacts the computation of Gr\"obner bases. We present several linear algebra algorithms for computing Gr\"obner…
Chordal structure and bounded treewidth allow for efficient computation in numerical linear algebra, graphical models, constraint satisfaction and many other areas. In this paper, we begin the study of how to exploit chordal structure in…
This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the…
Spectral methods include a family of algorithms related to the eigenvectors of certain data-generated matrices. In this work, we are interested in studying the geometric landscape of the eigendecomposition problem in various spectral…
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods…
Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases,…
Particles interacting with short-ranged potentials have attracted increasing interest, partly for their ability to model mesoscale systems such as colloids interacting via DNA or depletion. We consider the free energy landscape of such…
We apply the computational methodology of phase retrieval to the problem of folding heteropolymers. The ground state fold of the polymer is defined by the intersection of two sets in the configuration space of its constituent monomers: a…
The low-temperature driven or thermally activated motion of several condensed matter systems is often modeled by the dynamics of interfaces (co-dimension-1 elastic manifolds) subject to a random potential. Two characteristic quantitative…
In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers. Some known results are reproved and some new results are obtained.
We derive a fluctuation theorem for generalized work distributions, related to bijective mappings of the phase spaces of two physical systems, and use it to derive a two-sided constraint maximum likelihood estimator of their free energy…
We present a unified approach to the problems of reconstruction of large-scale structure distribution in the universe and determination of the underlying power spectrum. These have often been treated as two separate problems and different…
This paper is concerned with linear algebra based methods for solving exactly polynomial systems through so-called Gr\"obner bases, which allow one to compute modulo the polynomial ideal generated by the input equations. This is a topical…
We present a novel Monte Carlo algorithm which enhances equilibrization of low-temperature simulations and allows sampling of configurations over a large range of energies. The method is based on a non-Boltzmann probability weight factor…
Understanding the feasible power flow region is of central importance to power system analysis. In this paper, we propose a geometric view of the power system loadability problem. By using rectangular coordinates for complex voltages, we…
We show that various formulations (e.g., dual and Kullback-Csiszar iterations) of estimation of maximum entropy (ME) models can be transformed to solving systems of polynomial equations in several variables for which one can use celebrated…
We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior.…
We introduce a unified framework to compute the solution space properties of a broad class of combinatorial optimization problems. These properties include finding one of the optimum solutions, counting the number of solutions of a given…
We describe a provably complete algorithm for the generation of a tight, possibly exact superset of all combinatorially distinct simple n-facet polytopes in R^d, along with their graphs, f-vectors, and face lattices. The technique applies…
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their…