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In this paper we consider space-time codes where the code-words are restricted to either real or quaternion matrices. We prove two separate diversity-multiplexing gain trade-off (DMT) upper bounds for such codes and provide a criterion for…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
Symmetry is the essential element of lifted inference that has recently demon- strated the possibility to perform very efficient inference in highly-connected, but symmetric probabilistic models models. This raises the question, whether…
For integers $1 < k < d-1$ and $r \ge k+2$, we establish new lower bounds on the maximum number of points in $[n]^d$ such that no $r$ lie in a $k$-dimensional affine (or linear) subspace. These bounds improve on earlier results of…
Shifted combinatorial optimization is a new nonlinear optimization framework, which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. It captures well studied and…
We investigate the use of order $2$ digital nets for quasi-Monte Carlo quadrature of nonperiodic functions with bounded mixed second derivative over the cube. By using the so-called tent transform and its mapping properties we inherit error…
We revisit the fundamental problem of learning with distribution shift, in which a learner is given labeled samples from training distribution $D$, unlabeled samples from test distribution $D'$ and is asked to output a classifier with low…
Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC…
Choosing the optimization algorithm that performs best on a given machine learning problem is often delicate, and there is no guarantee that current state-of-the-art algorithms will perform well across all tasks. Consequently, the more…
Computer simulations serve as powerful tools for scientists and engineers to gain insights into complex systems. Less costly than physical experiments, computer experiments sometimes involve large number of trials. Conventional design…
The scope of this paper is two-fold. First, to present to the researchers in combinatorics an interesting implementation of permutations avoiding generalized patterns in the framework of discrete-time dynamical systems. Indeed, the orbits…
Using the formal languages Schoonschip and Form, we have developed general codes that are able to carry out all the algebraic manipulations needed to perform analytic lattice calculations, starting from the elementary building blocks…
Performative learning addresses the increasingly pervasive situations in which algorithmic decisions may induce changes in the data distribution as a consequence of their public deployment. We propose a novel view in which these…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
We investigate quasi-Monte Carlo (QMC) integration over the $s$-dimensional unit cube based on rank-1 lattice point sets in weighted non-periodic Sobolev spaces $\mathcal{H}(K_{\alpha,\boldsymbol{\gamma},s}^{\mathrm{sob}})$ and their…
Rapid progress in representation learning has led to a proliferation of embedding models, and to associated challenges of model selection and practical application. It is non-trivial to assess a model's generalizability to new, candidate…
About ten years ago, a paper proposed the first integer linear programming formulation for the constrained two-dimensional guillotine cutting problem (with unlimited cutting stages). Since, six other formulations followed, five of them in…
We consider a class of "filtered" schemes for first order time dependent Hamilton-Jacobi equations and prove a general convergence result for this class of schemes. A typical filtered scheme is obtained mixing a high-order scheme and a…
Lattice studies of spontaneous supersymmetry breaking suffer from a sign problem that in principle can be evaded through novel methods enabled by quantum computing. Focusing on lower-dimensional lattice systems with more modest resource…
We consider first-passage percolation on the $d$ dimensional cubic lattice for $d \geq 2$; that is, we assign independently to each edge $e$ a nonnegative random weight $t_e$ with a common distribution and consider the induced random graph…