On compact representations of Voronoi cells of lattices

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We study the glass transition by exploring a broad class of kinetic rules that can significantly modify the normal dynamics of supercooled liquids while maintaining thermal equilibrium. Beyond the usual dynamics of liquids, this class includes dynamics in ...

We study the statistical mechanics and the equilibrium dynamics of a system of classical Heisenberg spins with frustrated interactions on a d -dimensional simple hypercubic lattice, in the limit of infinite dimensionality d -> infinity . In the analysis we ...

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

This paper offers a new algorithm to efficiently optimize scheduling decisions for dial-a-ride problems (DARPs), including problem variants considering electric and autonomous vehicles (e-ADARPs). The scheduling heuristic, based on linear programming theor ...

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

We propose an adaptive quantum algorithm to prepare accurate variational time evolved wave functions. The method is based on the projected variational quantum dynamics (pVQD) algorithm, that performs a global optimization with linear scaling in the number ...

In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be sampled using an ...

In a collaboration between Ecole Polytechnique Fédérale de Lausanne (EPFL) and CEA, in the fall of 2020, the experimental Programme d’Étude en Transmission de l’Acier Lourd et ses Eléments (PETALE) was successfully carried out in the CROCUS reactor of EPFL ...

In this paper, we propose an analytical stochastic dynamic programming (SDP) algorithm to address the optimal management problem of price-maker community energy storage. As a price-maker, energy storage smooths price differences, thus decreasing energy arb ...

In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with r ...

A kernel method for estimating a probability density function from an independent and identically distributed sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined b ...

Given a hyperelliptic hyperbolic surface S of genus g >= 2, we find bounds on the lengths of homologically independent loops on S. As a consequence, we show that for any lambda is an element of (0, 1) there exists a constant N(lambda) such that every such ...

In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...

We generalize the class vectors found in neural networks to linear subspaces (i.e., points in the Grassmann manifold) and show that the Grassmann Class Representation (GCR) enables simultaneous improvement in accuracy and feature transferability. In GCR, e ...

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

Collaborative learning algorithms, such as distributed SGD (or D-SGD), are prone to faulty machines that may deviate from their prescribed algorithm because of software or hardware bugs, poisoned data or malicious behaviors. While many solutions have been ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

On compact representations of Voronoi cells of lattices

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Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules

Frustrated magnets in the limit of infinite dimensions: Dynamics and disorder-free glass transition

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

A ride time-oriented scheduling algorithm for dial-a-ride problems

Randomized flexible GMRES with deflated restarting

Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

Adaptive projected variational quantum dynamics

Gibbs sampling the posterior of neural networks

High-Resolution Modeling Without Computation Slowdown for PETALE in CROCUS

Energy Management of Price-Maker Community Energy Storage by Stochastic Dynamic Programming

Dynamical Low-Rank Approximation for Stochastic Differential Equations

From Self-managed Database Systems to Runtime-intelligent Analytics

Density estimation in RKHS with application to Korobov spaces in high dimensions

Short homology bases for hyperelliptic hyperbolic surfaces

Approximation Algorithms for Allocation and Network Design

Get the Best of Both Worlds: Improving Accuracy and Transferability by Grassmann Class Representation

Results on Sparse Integer Programming and Geometric Independent Sets

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Robust Collaborative Learning with Linear Gradient Overhead

Augmented Lagrangian Methods for Provable and Scalable Machine Learning