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Optimal experimental design is a well studied field in applied science and engineering. Techniques for estimating such a design are commonly used within the framework of parameter estimation. Nonetheless, in recent years parameter…
Given a dataset of points in a metric space and an integer $k$, a diversity maximization problem requires determining a subset of $k$ points maximizing some diversity objective measure, e.g., the minimum or the average distance between two…
Microplastics contamination is one of the most rapidly growing research topics. However, monitoring microplastics contamination in the environment presents both logistical and statistical challenges, particularly when constrained resources…
Most statistical software packages implement numerical strategies for computation of maximum likelihood estimates in random effects models. Little is known, however, about the algebraic complexity of this problem. For the one-way layout…
Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for…
Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box…
This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
Mixed Hamming packings are considered: the maximal cardinality given a minimum codeword Hamming distance of mixed codes is addressed via mixed integer programming models. Adopting the concept of contact graph from classical continuous…
Motion planning in the presence of multiple dynamic obstacles is an important research problem from the perspective of autonomous vehicles as well as space-constrained multi-robot work environment. In this paper, we address the motion…
We leverage proof techniques Fourier analysis and an existing result in coding theory to derive new bounds for the problem of non-interactive simulation of binary random variables. Previous bounds in the literature were derived by applying…
In sequential experiments, subjects become available for the study over a period of time, and covariates are often measured at the time of arrival. We consider the setting where the sample size is fixed but covariate values are unknown…
Maximum diversity problems arise in many practical settings from facility location to social networks, and constitute an important class of NP-hard problems in combinatorial optimization. There has been a growing interest in these problems…
Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their…
Over the past few decades, neuroscience experiments have become increasingly complex and naturalistic. Experimental design has in turn become more challenging, as experiments must conform to an ever-increasing diversity of design…
The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would permit multi-parameter…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
Minimax optimization has been central in addressing various applications in machine learning, game theory, and control theory. Prior literature has thus far mainly focused on studying such problems in the continuous domain, e.g.,…
Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…
Mechanistic mathematical models of biological systems usually contain a number of unknown parameters whose values need to be estimated from available experimental data in order for the models to be validated and used to make quantitative…