Related papers: Optimal configurations of lines and a statistical …
In this paper we provide explicit upper and lower bounds on certain $L^2$ $n$-widths, i.e., best constants in $L^2$ approximation. We further describe a numerical method to compute these $n$-widths approximately, and prove that this method…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
Constellation shaping is a practical and effective technique to improve the performance and the rate adaptivity of optical communication systems. In principle, it could also be used to mitigate the impact of nonlinear effects, possibly…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…
In this paper, we study the problem of optimal topology design in wireless networks equipped with highly-directional transmission antennas. We use the 1-2-1 network model to characterize the optimal placement of two relays that assist the…
Hypothesis testing procedures are developed to assess linear operator constraints in function-on-scalar regression when incomplete functional responses are observed. The approach enables statistical inferences about the shape and other…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
Structured prediction is used in areas such as computer vision and natural language processing to predict structured outputs such as segmentations or parse trees. In these settings, prediction is performed by MAP inference or, equivalently,…
We revisit the problem of searching for a target at an unknown location on a line when given upper and lower bounds on the distance D that separates the initial position of the searcher from the target. Prior to this work, only asymptotic…
We consider the line planning problem in public transportation, under a robustness perspective. We present a mechanism for robust line planning in the case of multiple line pools, when the line operators have a different utility function…
In this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that…
We explore distribution questions for rational maps on the projective line $\mathbb{P}^1$ over $\mathbb{Q}$ within the framework of arithmetic dynamics, drawing analogies to elliptic curves. Specifically, we investigate counting problems…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
We define and study exact, efficient representations of realization spaces Euclidean Distance Constraint Systems (EDCS), which includes Linkages and Frameworks. Each representation corresponds to a choice of Cayley parameters and yields a…
Experimental designs based on the classical D-optimal criterion minimize the volume of the linear-approximation inference regions for the parameters using local sensitivity coefficients. For nonlinear models, these designs can be unreliable…
We study the small-regularisation limit of the entropic optimal transport problem on the line with distance cost. While convergence of entropic minimizers is well understood in the discrete setting and in the case where the cost is…
Our goal is to develop a design framework for multifunctional mechanical metamaterials that can tune their rigidity while optimizing other desired properties. Towards this goal, we first demonstrate that underconstrained central force…
Constraining the maximum likelihood density estimator to satisfy a sufficiently strong constraint, $\log-$concavity being a common example, has the effect of restoring consistency without requiring additional parameters. Since many results…
Image analysis frequently deals with shape estimation and image reconstruction. The ob jects of interest in these problems may be thought of as random sets, and one is interested in finding a representative, or expected, set. We consider a…
We consider maximin and Bayesian $D$-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes…