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We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…
A code over a finite alphabet is called locally recoverable (LRC code) if every symbol in the encoding is a function of a small number (at most r) other symbols. A family of linear LRC codes that generalize the classic construction of…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
We experimentally evaluate the practical state-of-the-art in graph bipartization (Odd Cycle Transversal), motivated by recent advances in near-term quantum computing hardware and the related embedding problems. We assemble a preprocessing…
Unitary error bases have a great number of applications across quantum information and quantum computation, and are fundamentally linked to quantum teleportation, dense coding and quantum error correction. Werner's combinatorial…
We provide a gentle introduction, aimed at non-experts, to Borel combinatorics that studies definable graphs on topological spaces. This is an emerging field on the borderline between combinatorics and descriptive set theory with deep…
Combinatorial algorithms are widely used for decision-making and knowledge discovery, and it is important to ensure that their output remains stable even when subjected to small perturbations in the input. Failure to do so can lead to…
The purpose of this note is to give an exposition of some interesting combinatorics and convex geometry concepts that appear in algebraic geometry in relation to counting the number of solutions of a system of polynomial equations in…
After initial release of a machine learning algorithm, the model can be fine-tuned by retraining on subsequently gathered data, adding newly discovered features, or more. Each modification introduces a risk of deteriorating performance and…
We use and adapt the Borsuk-Ulam Theorem from topology to derive limitations on list-replicable and globally stable learning algorithms. We further demonstrate the applicability of our methods in combinatorics and topology. We show that,…
We study iterations of two classical constructions, the evolutes and involutes of plane curves, and we describe the limiting behavior of both constructions on a class of smooth curves with singularities given by their support functions.…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
We propose a method for generating rule sets as global and local explanations for tree-ensemble learning methods using Answer Set Programming (ASP). To this end, we adopt a decompositional approach where the split structures of the base…
Techniques involving factorization are found in a wide range of applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the…
We consider Abel maps for regular smoothing of nodal curves with values in the Esteves compactified Jacobian. In general, these maps are just rational, and an interesting question is to find an explicit resolution. We translate this problem…
A permutation graph is a graph whose edges are given by inversions of a permutation. We study the Abelian sandpile model (ASM) on such graphs. We exhibit a bijection between recurrent configurations of the ASM on permutation graphs and the…
The cryptanalysis of various cipher problems can be formulated as NP-Hard combinatorial problem. Solving such problems requires time and/or memory requirement which increases with the size of the problem. Techniques for solving…
We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the…
The ancestral sequence reconstruction problem is the inference, back in time, of the properties of common sequence ancestors from measured properties of contemporary populations. Standard algorithms for this problem assume independent…
The solving of scientific and practical application connected with conducting of satellite experiments and measurement demand analysis of geometric and physic conditions according to different kind of models. This is forced in connect of…