Related papers: Approximate pushforward designs and image bounds o…
This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
We give a condition on the curvature tensors of Riemannian manifolds that admit Lipschitz approximation by polyhedral metrics with curvature bounded below or above. We show that this condition is also sufficient for the existence of local…
We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance-optimality (A-optimality) criterion,…
We derive optimal statistical and computational complexity bounds for exp-concave stochastic minimization in terms of the effective dimension. For common eigendecay patterns of the population covariance matrix, this quantity is…
We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First we show that the problem of estimating the separation…
A prevalent problem in general state-space models is the approximation of the smoothing distribution of a state, or a sequence of states, conditional on the observations from the past, the present, and the future. The aim of this paper is…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…
Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite…
The approximate coherent state rank is the minimal number of (classical) coherent states required to approximate a continuous-variable bosonic quantum state and directly relates to the classical complexity of simulating bosonic…
We consider the problem of discriminating finite-dimensional quantum processes, also called quantum supermaps, that can consist of multiple time steps. Obtaining the ultimate performance for discriminating quantum processes is of…
We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…
Quasi-states are certain not necessarily linear functionals on the space of continuous functions on a compact Hausdorff space. They were discovered as a part of an attempt to understand the axioms of quantum mechanics due to von Neumann. A…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
We establish the convergence of threshold dynamics-type approximation schemes to propagating fronts evolving according to an anisotropic mean curvature motion in the presence of a forcing term depending on both time and position, thus…
Quantum light is described not only by a quantum state but also by the shape of the electromagnetic modes on which the state is defined. Optical precision measurements often estimate a ``mode parameter'' that determines properties such as…
The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a…
Finite mixture models have long been used across a variety of fields in engineering and sciences. Recently there has been a great deal of interest in quantifying the convergence behavior of the \emph{mixing measure}, a fundamental object…