Related papers: Consistency of multidimensional combinatorial subs…
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…
We study the existence of stable matchings when agents have choice correspondences instead of preference relations. We extend the framework of \cite{chambers2017choice} by weakening the path independence assumption. For many-to-many…
Many physical problems involving heterogeneous spatial scales, such as the flow through fractured porous media, the study of fiber-reinforced materials, or the modeling of the small circulation in living tissues -- just to mention a few…
A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical…
Many empirical time series are genuinely symbolic: examples range from link activation patterns in network science, DNA coding or firing patterns in neuroscience to cryptography or combinatorics on words. In some other contexts, the…
In this work, we consider the problem of bounding the values of a covariance function corresponding to a continuous-time stationary stochastic process or signal. Specifically, for two signals whose covariance functions agree on a finite…
A bipartite quantum state (for two systems in any dimensions) can be decomposed as a superposition of many components. For a superposition of more than two components we prove that there is a bound of the entanglement of the superposition…
The study of the structure of translational tilings has captivated mathematicians, scientists, and the general public for centuries and continues to thrive at the crossroads of analysis, combinatorics, dynamics, logic, number theory, and…
Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…
Pattern matching is a powerful tool which is part of many functional programming languages as well as computer algebra systems such as Mathematica. Among the existing systems, Mathematica offers the most expressive pattern matching.…
A visual counterfactual explanation replaces image regions in a query image with regions from a distractor image such that the system's decision on the transformed image changes to the distractor class. In this work, we present a novel…
I investigate a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are…
Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…
In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…
This paper deals with the problem of point-to-point reachability in multi-linear systems. These systems consist of a partition of the Euclidean space into a finite number of regions and a constant derivative assigned to each region in the…
We study decision problems on geometric tilings. First, we study a variant of the Domino problem where square tiles are replaced by geometric tiles of arbitrary shape. We show that this variant is undecidable regardless of the shapes,…
A two-dimensional configuration is a coloring of the infinite grid Z^2 with finitely many colors. For a finite subset D of Z^2, the D-patterns of a configuration are the colored patterns of shape D that appear in the configuration. The…
The $d$-dimensional pattern matching problem is to find an occurrence of a pattern of length $m \times \dots \times m$ within a text of length $n \times \dots \times n$, with $n \ge m$. This task models various problems in text and image…
We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley [GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…
In this study, explicit differential equations representing commutative pairs of some well-known second-order linear time-varying systems have been derived. The commutativity of these systems are investigated by considering 30 second-order…