Related papers: A note on minimization of rational surfaces obtain…
Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover…
Structural optimization (topology, shapes, sizing) is an important tool for facilitating the emergence of new concepts in structural design. Normally, topology optimization is carried out at the early stage of design and then shape and…
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…
We present an algorithm that covers any given rational ruled surface with two rational parametrizations. In addition, we present an algorithm that transforms any rational surface parametrization into a new rational surface parametrization…
We develop a martingale approximation framework yielding quantitative maximal large deviations estimates for invertible dynamical systems. From suitable decay of correlations, we deduce these estimates and, as an application, we obtain…
We study discrete surface breathers in two-dimensional lattices of inductively-coupled split-ring resonators with capacitive nonlinearity. We consider both Hamiltonian and dissipative systems and analyze the properties of the modes…
Analytical approach to SLAM problem was introduced in the recent years. In our work we investigate the method numerically with the motivation of using the algorithm in a real hardware experiments. We perform a robustness test of the…
Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for…
This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of variational Runge-Kutta discretizations is…
We prove that every log crepant birational morphism between log terminal surfaces is decomposed into log-flopping type divisorial contraction morphisms and log blow-downs. Repeating these two kinds of contractions we reach a minimal log…
We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this,…
We develop a new method to construct explicit, regular minimal surfaces in Euclidean space that are defined on the entire complex plane with controlled geometry. More precisely we show that for a large class of planar curves $(x(t), y(t))$…
A rational map with good reduction in the field $\mathbb{Q}\_p$ of $p$-adic numbers defines a $1$-Lipschitz dynamical system on the projective line $\mathbb{P}^1(\mathbb{Q}\_p)$ over $\mathbb{Q}\_p$. The dynamical structure of such a system…
A method is presented, which allows to sample directly low-temperature configurations of glassy systems, like spin glasses. The basic idea is to generate ground states and low lying excited configurations using a heuristic algorithm. Then,…
The spatial components of the autocorrelation function of noninteracting dipoles are analytically obtained in terms of rotational Brownian motion on the surface of a unit sphere using multi-level jumping formalism based on Debye's…
Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random quadrangulation of this surface with $n$ faces and boundary component lengths of order $\sqrt n$ or of lower order. Endow this…
For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a…
We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving…
Smooth real cubic surfaces are birationally trivial (over $\R$) if and only if their real locus is connected or, equivalently, if and only if they have two skew real lines or two skew complex conjugate lines. In such a case a…
We prove that if the bicanonical map of a minimal surface of general type S with p_{g}=q=1 and K^2=8 is non birational, then it is a double cover onto a rational surface. An application of this theorem is the complete classification of…