Related papers: A Study on a New Method of Dynamic Aperture Enlarg…
We study an expansion method for high-dimensional parabolic PDEs which constructs accurate approximate solutions by decomposition into solutions to lower-dimensional PDEs, and which is particularly effective if there are a low number of…
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…
Projected Gradient Ascent (PGA) is the most commonly used optimization scheme in machine learning and operations research areas. Nevertheless, numerous studies and examples have shown that the PGA methods may fail to achieve the tight…
A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…
Determining a model for the time scaling of the dynamic aperture of a circular accelerator is a topic of strong interest and intense research efforts in accelerator physics. The motivation arises in the possibility of finding a method to…
Polynomial convergence bounds are considered for left, right, and split preconditioned GMRES. They include the cases of Weighted and Deflated GMRES for a linear system Ax = b. In particular, the case of positive definite A is considered.…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
Use of resonant light forces opens up a unique approach to high-volume sorting of microspherical resonators with much higher uniformity of resonances compared to that in coupled-cavity structures obtained by the best semiconductor…
The growth dynamics of rigid biopolymers, consisting of $N$ parallel protofilaments, is investigated theoretically using simple approximate models. In our approach, the structure of a polymer's growing end and lateral interactions between…
We examine directed spanners through flow-based linear programming relaxations. We design an $\~O(n^{2/3})$-approximation algorithm for the directed $k$-spanner problem that works for all $k\geq 1$, which is the first sublinear…
Recently, there has been an increasing interest in using tools from dynamical systems to analyze the behavior of simple optimization algorithms such as gradient descent and accelerated variants. This paper strengthens such connections by…
Static analysis by abstract interpretation aims at automatically proving properties of computer programs. To do this, an over-approximation of program semantics, defined as the least fixpoint of a system of semantic equations, must be…
This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…
In this article, we propose a new dimensionality-independent and gradient-free sampler, called Geometric Optics Approximation Sampling, which is based on the reflector antenna system. The core idea is to construct a reflecting surface that…
We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this…
This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications.…
We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix…
We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…
We investigate depoissonization, the problem of recovering asymptotics of sequence coefficients from their exponential generating function. Classical approaches rely on complex-analytic growth conditions, but here we develop real-variable…