Related papers: A New Approach to Determine the Minimal Polynomial…
This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from $\{\pm 1\}$ or from $\{0,1\}$, and an unconstrained factor. The research answers fundamental questions about the existence and…
This paper addresses the challenge of identifying a minimal subset of discrete, independent variables that best predicts a binary class. We propose an efficient iterative method that sequentially selects variables based on which one…
The binary Defect Combination Problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular,…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
We propose a method based on minimum-variance polynomial approximation to extract system poles from a data set of samples of the impulse response of a linear system. The method is capable of handling the problem under general conditions of…
Denote the alternating and symmetric groups of degree $n$ by $A_n$ and $S_n$ respectively. Consider a permutation $\sigma\in S_n$ all of whose nontrivial cycles are of the same length. We find the minimal polynomials of $\sigma$ in the…
Universal cycles, such as De Bruijn cycles, are cyclic sequences of symbols that represent every combinatorial object from some family exactly once as a consecutive subsequence. Graph universal cycles are a graph analogue of universal…
Lienard systems are very important mathematical models describing oscillatory processes arising in applied sciences. In this paper, we study polynomial Lienard systems of arbitrary degree on the plane, and develop a new method to obtain a…
In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…
A method for generating irreducible polynomials of degree n over the finite field GF(2) is proposed. The irreducible polynomials are found by solving a system of equations that brings the information on the internal properties of the…
We introduce a new variant of the $k$-deck problem, which in its traditional formulation asks for determining the smallest $k$ that allows one to reconstruct any binary sequence of length $n$ from the multiset of its $k$-length…
The method is based on the preliminary transformation of the traditionally used matrices or adjacency lists in the graph theory into refined projections free from redundant information, and their subsequent use in constructing shortest…
The periodogram is a widely used tool to analyze second order stationary time series. An attractive feature of the periodogram is that the expectation of the periodogram is approximately equal to the underlying spectral density of the time…
For a directed graph $G$, a $t$-identifying code is a subset $S\subseteq V(G)$ with the property that for each vertex $v\in V(G)$ the set of vertices of $S$ reachable from $v$ by a directed path of length at most $t$ is both non-empty and…
This paper deals with the problem of multi-degree reduction of a composite B\'ezier curve with the parametric continuity constraints at the endpoints of the segments. We present a novel method which is based on the idea of using constrained…
Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of perfect matchings via alternating cycles. Namely, we want to find a shortest sequence of perfect matchings which transforms one given…
We study the problems of finding a shortest synchronizing word and its length for a given prefix code. This is done in two different settings: when the code is defined by an arbitrary decoder recognizing its star and when the code is…
It is common in stability analysis to linearize a system and investigate the spectrum of the Jacobian matrix. This approach faces the challenge of determining the matrix spectrum when the coefficients depend on parameters or when the…
Minimal separators in graphs are an important concept in algorithmic graph theory. In particular, many problems that are NP-hard for general graphs are known to become polynomial-time solvable for classes of graphs with a polynomially…
We study problems of reconfiguration of shortest paths in graphs. We prove that the shortest reconfiguration sequence can be exponential in the size of the graph and that it is NP-hard to compute the shortest reconfiguration sequence even…