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When machine learning supports decision-making in safety-critical systems, it is important to verify and understand the reasons why a particular output is produced. Although feature importance calculation approaches assist in…
Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is often difficult to…
Verification and safety assessment of neural network controlled systems (NNCSs) is an emerging challenge. To provide guarantees, verification tools must efficiently capture the interplay between the neural network and the physical system…
We illustrate that numerical solutions of high order finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for some nonconvex conservation laws perform poorly or converge to the entropy solution in a slow speed. The…
Estimating the volume of a convex body is a central problem in convex geometry and can be viewed as a continuous version of counting. We present a quantum algorithm that estimates the volume of an $n$-dimensional convex body within…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…
This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition,…
Volumetry is one of the principal downstream applications of 3D medical image segmentation, for example, to detect abnormal tissue growth or for surgery planning. Conformal Prediction is a promising framework for uncertainty quantification,…
This paper presents an algorithm to maximize the volume of an affine slice through a given semialgebraic set. This slice-volume task is formulated as an infinite-dimensional linear program in continuous functions, inspired by prior work in…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
Bayesian Optimization (BO) is a popular approach to optimizing expensive-to-evaluate black-box functions. Despite the success of BO, its performance may decrease exponentially as the dimensionality increases. A common framework to tackle…
In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…
We study optimal simple second-order cone representations (a particular subclass of second-order cone representations) for weighted geometric means, which turns out to be closely related to minimum mediated sets. Several lower and upper…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
Among the monotone metrics on the (n^{2} - 1)-dimensional convex set of n x n density matrices, as Petz and Sudar have recently elaborated, there are a minimal (Bures) and a maximal one. We examine the proposition that it is physically…
An efficient algorithm to enumerate the vertices of a two-dimensional (2D) projection of a polytope, is presented in this paper. The proposed algorithm uses the support function of the polytope to be projected and enumerated for vertices.…
This paper introduces a high-performance hybrid algorithm, called Hybrid Hypervolume Maximization Algorithm (H2MA), for multi-objective optimization that alternates between exploring the decision space and exploiting the already obtained…
The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT). In the recent past, different algorithms have been proposed for PBO and for MaxSAT,…
Neural network algorithms simulated on standard computing platforms typically make use of high resolution weights, with floating-point notation. However, for dedicated hardware implementations of such algorithms, fixed-point synaptic…