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This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…

Entropy-based (M_N) moment closures for kinetic equations are defined by a constrained optimization problem that must be solved at every point in a space-time mesh, making it important to solve these optimization problems accurately and…

We introduce and investigate binary $(k,k)$-designs -- combinatorial structures which are related to binary orthogonal arrays. We derive general linear programming bound and propose as a consequence a universal bound on the minimum possible…

Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…

We prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints as it has been proposed by Liberti in 2007. The new conditions…

This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or…

New exact string solutions in non-constant background fields are found and it is shown that some of them are compatible with the boundary conditions for the open string - D-brane system. Extension of the constraint algebra is proposed and…

A lossy compression algorithm for binary redundant memoryless sources is presented. The proposed scheme is based on sparse graph codes. By introducing a nonlinear function, redundant memoryless sequences can be compressed. We propose a…

Identifying the dynamic precompensator that renders a nonlinear control system feedback linearizable is a challenging problem. Researchers have explored the problem -- dynamic feedback linearization -- and produced existence conditions and…

Convex geometries form a subclass of closure systems with unique criticals, or $UC$-systems. We show that the $F$-basis introduced in [1] for $UC$-systems, becomes optimum in convex geometries, in two essential parts of the basis: right…

Although the representation of the real numbers in terms of a base and a set of digits has a long history, new questions arise even in simple situations. This paper concerns binary radix systems, i.e., positional number systems with digits…

In this thesis, a detailed study shows that closed itemsets and minimal generators play a key role for concisely representing both frequent itemsets and association rules. These itemsets structure the search space into equivalence classes…

Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…

In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…

This paper investigates the a-posteriori analysis of Branch-and-Bound~(BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible…

Given an unweighted graph $G$, the *minimum $r$-dominating set problem* asks for the smallest-cardinality subset $S$ such that every vertex in $G$ is within radius $r$ of some vertex in $S$. While the $r$-dominating set problem on planar…

We study monotone extension problems in the general framework of dual systems, without assuming separation. The paper develops a compact target-set formulation that includes multivalued operators as a special case and allows the initial set…

We discuss charged black-hole solutions to the equations of motion of the string-loop-corrected effective action. At the string-tree level, these solutions provide backgrounds for the "chiral null model". The effective action contains…

Given a $d$-dimensional array $A$, an update operation adds a given constant $C$ to each element within a continuous sub-array of $A$. A query operation computes the sum of all the elements within a continuous sub-array of $A$. The…

Constrained Horn Clauses (CHCs) have conventionally been used as a low-level representation in formal verification. Most existing solvers use a diverse set of specialized techniques, including direct state space traversal or…