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The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often,…
We show how to use extended word series in the reduction of continuous and discrete dynamical systems to normal form and in the computation of formal invariants of motion in Hamiltonian systems. The manipulations required involve complex…
Computed Tomography (CT) is an imaging technique where information about an object are collected at different angles (called projections or scans). Then the cross-sectional image showing the internal structure of the slice is produced by…
We study multidimensional configurations (infinite words) and subshifts of low pattern complexity using tools of algebraic geometry. We express the configuration as a multivariate formal power series over integers and investigate the setup…
Semidefinite programs (SDPs) -- some of the most useful and versatile optimization problems of the last few decades -- are often pathological: the optimal values of the primal and dual problems may differ and may not be attained. Such SDPs…
We propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired…
In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
The aim of this paper is to present a unified theory of many Kato type representation theorems in terms of solvable forms on Hilbert spaces. In particular, for some sesquilinear forms $\Omega$ on a dense domain $\mathcal{D}$ one looks for…
We present new methods and results for constructing optimal Kobon triangle arrangements. First, we introduce a compact table notation for describing arrangements of pseudolines, enabling the representation and analysis of complex cases,…
Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…
We explore methods for constructing normal forms of indecomposable quiver representations. The first part of the paper develops homological tools for recursively constructing families of indecomposable representations from indecomposables…
We study the representation of systems S of linear equations over the two-element field (aka xor- or parity-constraints) via conjunctive normal forms F (boolean clause-sets). First we consider the problem of finding an "arc-consistent"…
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…
Nowadays, the field computed tomography (CT) encompasses a large variety of settings, ranging from nanoscale to meter-sized objects imaged by different kinds of radiation in various acquisition modes. This experimental diversity challenges…
By connecting the LU factorization and the Gram-Schmidt orthogonalization without any normalization, closed-forms for the coefficients of the ordinary least squares estimates are presented. Instead of using matrix inversion explicitly, each…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
We propose an end-to-end approach for Answer Set Programming (ASP) and linear algebraically compute stable models satisfying given constraints. The idea is to implement Lin-Zhao's theorem together with constraints directly in vector spaces…
This paper introduces a novel tangential-normal ($t$-$n$) decomposition for finite element differential forms, presenting a new framework for constructing bases in finite element exterior calculus. The main contribution is the development…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…