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We formalize the semantics of hybrid systems as sets of hybrid trajectories, including those generated by an hybrid transition system. We study the abstraction of hybrid trajectory semantics for verification, static analysis, and…

In a number of recent papers, the idea of generalized boundaries has found use in fractal and in multiresolution analysis; many of the papers having a focus on specific examples. Parallel with this new insight, and motivated by quantum…

This paper presents methods for using zonotopes and constrained zonotopes to improve the practicality of a wide variety of set-based operations commonly used in control theory. The proposed methods extend the use of constrained zonotopes to…

We propose a methodology for the automatic verification of safety properties of controllers based on dynamical systems, such as those typically used in avionics. In particular, our focus is on proving stability properties of software…

Decidability and synthesis of inductive invariants ranging in a given domain play an important role in many software and hardware verification systems. We consider here inductive invariants belonging to an abstract domain $A$ as defined in…

We present a domain decomposition approach for the simulation of charge transport in heterojunction semiconductors. The problem is characterized by a large variation of primary variables across an interface region of a size much smaller…

Mixed integer set representations, and specifically hybrid zonotopes, have enabled new techniques for reachability and verification of nonlinear and hybrid systems. Mixed-integer sets which have the property that their convex relaxation is…

The classical Painlev\'e equations are so well known that it may come as a surprise to learn that the asymptotic description of its solutions remains incomplete. The problem lies mainly with the description of families of solutions in the…

Multi-domain translation seeks to learn a probabilistic coupling between marginal distributions that reflects the correspondence between different domains. We assume that data from different domains are generated from a shared latent…

Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…

Zonotopes are studied from the point of view of central symmetry and how volumes of facets and the angles between them determine a zonotope uniquely. New proofs are given for theorems of Shephard and McMullen characterizing a zonotope by…

Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…

Infrared and visible image fusion has been developed from vision perception oriented fusion methods to strategies which both consider the vision perception and high-level vision task. However, the existing task-driven methods fail to…

Inner-approximate reachability analysis involves calculating subsets of reachable sets, known as inner-approximations. This analysis is crucial in the fields of dynamic systems analysis and control theory as it provides a reliable…

We present a technique novel in numerical methods. It compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a boundary value problem of a…

Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of…

Scholars often explore literature outside of their home community of study. This exploration process is frequently hampered by field-specific jargon. Past computational work often focuses on supporting translation work by removing jargon…

Neural networks and other machine learning models compute continuous representations, while humans communicate with discrete symbols. Reconciling these two forms of communication is desirable to generate human-readable interpretations or to…

We define a random zonotope in Euclidean space, by adding finitely many random segments, which are independently and identically distributed. For this random polytope, we determine, under a mild assumption on the distribution, the…

The modelling of discrete regulatory networks combines a graph specifying the pairwise influences between the variables of the system, and a parametrisation from which can be derived a discrete transition system. Given the influence graph…