Related papers: Asymptotic optimality of the triangular lattice fo…
We consider n identically prepared qubits and study the asymptotic properties of the joint state \rho^{\otimes n}. We show that for all individual states \rho situated in a local neighborhood of size 1/\sqrt{n} of a fixed state \rho^0, the…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…
We undertake a detailed study of the $L^2$ discrepancy of rational and irrational 2-dimensional lattices either with or without symmetrization. We give a full characterization of lattices with optimal $L^2$ discrepancy in terms of the…
We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the system. Concentrating on configurations with infinitely many…
We consider the range-based localization problem, which involves estimating an object's position by using $m$ sensors, hoping that as the number $m$ of sensors increases, the estimate converges to the true position with the minimum…
We consider the Landau-de Gennes variational problem on a bound\-ed, two dimensional domain, subject to Dirichlet smooth boundary conditions. We prove that minimizers are maximally biaxial near the singularities, that is, their biaxiality…
In this paper, we study the 3D strip packing problem in which we are given a list of 3-dimensional boxes and required to pack all of them into a 3-dimensional strip with length 1 and width 1 and unlimited height to minimize the height used.…
The accurate asymptotic evaluation of marginal likelihood integrals is a fundamental problem in Bayesian statistics. Following the approach introduced by Watanabe, we translate this into a problem of computational algebraic geometry,…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
In materials science, wedge disclinations are defects caused by angular mismatches in the crystallographic lattice. To describe such disclinations, we introduce an atomistic model in planar domains. This model is given by a…
In this paper we present a new version of the second author's factorization theorem for perfect matchings of symmetric graphs. We then use our result to solve four open problems of Propp on the enumeration of trimer tilings on the hexagonal…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
We consider the problem of optimal distribution of a limited amount of conductive material in systems governed by local and non-local scalar diffusion laws. Of particular interest for these problems is the study of the limiting case, which…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
Small heavy particles cannot get attracted into a region of closed streamlines in a non-accelerating frame (Sapsis & Haller 2010). In a rotating system, however, particles can get trapped (Angilella 2010) near vortices. We perform numerical…
We introduce a new algorithm for the simulation of Euclidean dynamical triangulations that mimics the Metropolis-Hastings algorithm, but where all proposed moves are accepted. This rejection-free algorithm allows for the factorization of…
This paper studies a distributed stochastic optimization problem over random networks with imperfect communications subject to a global constraint, which is the intersection of local constraint sets assigned to agents. The global cost…
Filtering in spatially-extended dynamical systems is a challenging problem with significant practical applications such as numerical weather prediction. Particle filters allow asymptotically consistent inference but require infeasibly large…