Related papers: Minimum relaxation n-body simulations using orthog…

Though one dimensional self-gravitating $N$-body systems have been studied for three decade, the nature of relaxation was still unclear. There were inconsistent results about relaxation time; some initial state relaxed in the time scale…

A recent theorem giving the initial behavior of very short-time fluctuations of particle displacements in classical many-body systems is discussed. It has applications to equilibrium and non-equilibrium systems, one of which is a series…

We consider the global optimization of nonconvex quadratic programs and mixed-integer quadratic programs. We present a family of convex quadratic relaxations which are derived by convexifying nonconvex quadratic functions through…

Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…

In studying the time evolution of isolated many-body quantum systems, a key focus is determining whether the system undergoes relaxation and reaches a steady state at a given point in time. Traditional approaches often rely on specific…

This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…

Dynamical simulations are a fundamental tool for studying the secular evolution of disc galaxies. Even at their maximum resolution, they still follow a limited number of particles and typically resolve scales of the order of a few tens of…

We focus on the estimation of the intensity of a Poisson process in the presence of a uniform noise. We propose a kernel-based procedure fully calibrated in theory and practice. We show that our adaptive estimator is optimal from the oracle…

In this work, the problem of optimizing damper positions in vibrational systems is investigated. The objective is to determine the positions of external dampers in such a way that the influence of the input on the output is minimized. The…

In this contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion in general and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the…

In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…

This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming,…

We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such…

We consider the problem of finding the minimum element in a list of length $N$ using a noisy comparator. The noise is modelled as follows: given two elements to compare, if the values of the elements differ by at least $\alpha$ by some…

In a previous article we developed an approach to the optimal (minimum variance, unbiased) statistical estimation technique for the equilibrium displacement of a damped, harmonic oscillator in the presence of thermal noise. Here, we expand…

We investigate the effectiveness of convex relaxation and nonconvex optimization in solving bilinear systems of equations under two different designs (i.e.$~$a sort of random Fourier design and Gaussian design). Despite the wide…

The Poisson-Boltzmann equation is widely used to model molecular electrostatics; however, it is usually solved in linearised form because the sinh nonlinearity is challenging, limiting its applicability in highly charged systems such as…

Waveform-relaxation methods divide systems of differential equations into subsystems and therefore allow for parallelization across the system. Here we present an application for ODE waveform-relaxation methods in the context of spiking…

Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper…

A novel probabilistic approach for the design of mechanical structures with friction interfaces is proposed. The objective function is defined as the probability that a specified performance measure of the forced vibration response is…