Related papers: Exploring the Potential Energy Landscape Over a La…
We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply…
Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for…
A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…
We investigate arithmetic, geometric and combinatorial properties of symmetric edge polytopes. We give a complete combinatorial description of their facets. By combining Gr\"obner basis techniques, half-open decompositions and methods for…
The value of graph-based big data can be unlocked by exploring the topology and metrics of the networks they represent, and the computational approaches to this exploration take on many forms. The use-case of performing global computations…
Recent studies of concentrated solid solutions have highlighted the role of varied solute interactions in the determination of a wide variety of mesoscale properties. These solute interactions emerge as spatial fluctuations in potential…
Dark energy is often assumed to be composed by a single scalar field. The background cosmic expansion is not sufficient to determine whether this is true or not. We study multi-field scalar-tensor models with a general dark matter source…
We develop a mathematical model for the energy landscape of polyhedral supramolecular cages recently synthesized by self-assembly [Sun et al., Science 2010]. Our model includes two essential features of the experiment: (i) geometry of the…
In this paper we study the set of rational solutions of equations defined by power sums symmetric polynomials with coefficients in a finite field. We do this by means of applying a methodology which relies on the study of the geometry of…
In the probabilistic approach to quantum many-body systems, the ground-state energy is the solution of a nonlinear scalar equation written either as a cumulant expansion or as an expectation with respect to a probability distribution of the…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
We develop two local energy methods for distributed parameter port-Hamiltonian (pH) systems on one-dimensional spatial domains. The methods are applied to derive a characterization of exponential stability directly in terms of the energy…
Assuming sufficiently many terms of a n-dimensional table defined over a field are given, we aim at guessing the linear recurrence relations with either constant or polynomial coefficients they satisfy. In many applications, the table terms…
Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector…
We present a generative model that amortises computation for the field and potential around e.g.~gravitational or electromagnetic sources. Exact numerical calculation has either computational complexity $\mathcal{O}(M\times{}N)$ in the…
Differential equations may possess coefficients that vary on a spectrum of scales. Because coefficients are typically multiplicative in real space, they turn into convolution operators in spectral space, mixing all wavenumbers. However, in…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
In this paper, we present that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. Quotient space can be considered as mathematically-defined phenotype space in the evolutionary…
We study measures and point configurations optimizing energies based on multivariate potentials. The emphasis is put on potentials defined by geometric characteristics of sets of points, which serve as multi-input generalizations of the…
We establish a unified theoretical framework that connects classical orthogonal polynomial systems to matrix Lyapunov equations through the fundamental physics of energy dissipation in stochastic dynamical systems. Starting from the energy…