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We show that computing the Tutte polynomial of a linear matroid of dimension $k$ on $k^{O(1)}$ points over a field of $k^{O(1)}$ elements requires $k^{\Omega(k)}$ time unless the \#ETH---a counting extension of the Exponential Time…
Oriented matroids (often called order types) are combinatorial structures that generalize point configurations, vector configurations, hyperplane arrangements, polyhedra, linear programs, and directed graphs. Oriented matroids have played a…
We introduce the notion of an online matroid embedding, which is an algorithm for mapping an unknown matroid that is revealed in an online fashion to a larger-but-known matroid. We establish the existence of such an embedding for binary…
Since the seminal paper of Hendrycks et al. arXiv:1610.02136, Post-hoc deep Out-of-Distribution (OOD) detection has expanded rapidly. As a result, practitioners working on safety-critical applications and seeking to improve the robustness…
In this paper, several row and column orthogonal projection methods are proposed for solving matrix equation $AXB=C$, where the matrix $A$ and $B$ are full rank or rank deficient and equation is consistent or not. These methods are…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…
Advection-dominated problems are predominantly noticed in nature, engineering systems, and various industrial processes. Traditional linear compression methods, such as proper orthogonal decomposition (POD) and reduced basis (RB) methods…
In the domain of machine learning, the assumption that training and test data share the same distribution is often violated in real-world scenarios, requiring effective out-of-distribution (OOD) detection. This paper presents a novel OOD…
Many combinatorial properties of a point set in the plane are determined by the set of possible partitions of the point set by a line. Their essential combinatorial properties are well captured by the axioms of oriented matroids. In fact,…
Research in explorable uncertainty addresses combinatorial optimization problems where there is partial information about the values of numeric input parameters, and exact values of these parameters can be determined by performing costly…
Detecting image correspondences by feature matching forms the basis of numerous computer vision applications. Several detectors and descriptors have been presented in the past, addressing the efficient generation of features from interest…
Fast matrix multiplication is one of the most fundamental problems in algorithm research. The exponent of the optimal time complexity of matrix multiplication is usually denoted by $\omega$. This paper discusses new ideas for improving the…
We consider a scalar wave propagation in harmonic regime modelled by Helmholtz equation with heterogeneous coefficients. Using the Multi-Trace Formalism (MTF), we propose a new variant of the Optimized Schwarz Method (OSM) that can…
Additive combinatorics asks for lower bounds on sumsets and restricted sumsets over finite fields. Central examples are the Cauchy-Davenport theorem and the Erd\H{o}s-Heilbronn conjecture. In this note, we develop Das's linear algebraic…
We present an enhanced version of the parametric nonlinear reduced order model for shape imperfections in structural dynamics we studied in a previous work [1]. The model is computed intrusively and with no training using information about…
Electronic structure methods that exploit nonorthogonal Slater determinants face the challenge of efficiently computing nonorthogonal matrix elements. In a recent publication, H. G. A. Burton, J. Chem. Phys. 154, 144109 (2021), I introduced…
We present a formal analysis, in Isabelle/HOL, of optimisation algorithms for matroids, which are useful generalisations of combinatorial structures that occur in optimisation, and greedoids, which are a generalisation of matroids. Although…
We characterize the algorithmic dimensions (i.e., the lower and upper asymptotic densities of information) of infinite binary sequences in terms of the inability of learning functions having an algorithmic constraint to detect patterns in…
Embeddings of high-dimensional data are widely used to explore data, to verify analysis results, and to communicate information. Their explanation, in particular with respect to the input attributes, is often difficult. With linear projects…
Bayesian nonparametric methods are naturally suited to the problem of out-of-distribution (OOD) detection. However, these techniques have largely been eschewed in favor of simpler methods based on distances between pre-trained or learned…