Boris Melnikov
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Special Generation of Random Graphs and Statistical Study of Some of Their Invariants Open
In this paper, we generate random graphs for a specific area, namely, models of real communication networks. We propose a method that determines the “best” invariant; the corresponding basic algorithm is as follows. For the generated set o…
Special Generation of Random Graphs and Statistical Study of Some of Their Invariants Open
With random graph generation, most of the previously described algorithms were not related to graphs arising in any particular subject area, so in this paper we generate random graphs for a specific area, namely, models of real communicati…
Mathematical Modeling of Increasing the Level of Safety Using the Traveling Salesman Problem Open
Due to the extremely high cost of creating and operating manned spacecraft, the cost of losses in accidents and failures of aviation and rocket and space technology, as well as due to the significant costs of designing future manned spacec…
The Inconsistency of the Algorithms of Jaro–Winkler and Needleman–Wunsch Applied to DNA Chain Similarity Results Open
There are many different algorithms for calculating the distances between DNA chains. Different algorithms for determining such distances give different results. This paper does not consider issues related to which of the classical algorit…
New algorithms for restoring DNA matrix and their statistical study Open
In the proposed paper, we continue to consider various heuristics for reconstructing distance matrices between DNA sequences; as before, we prefer to consider mitochondrial DNA. In the paper, we apply new heuristics. First, every time we r…
On some algorithms for comparing models of femtosecond laser radiation propagation in a medium with gold nanorods Open
The study of the features of the nonlinear optical interaction of laser radiation with various media is currently widely studied, including by mathematical modeling methods. In particular, the interaction of the laser pulse with the medium…
Application of Paired Correlation Algorithms for the Distance Matrices Between DNA Chains Open
Authors:This paper is a continuation of some previous works by the authors. We consider various algorithms for calculating distances between genomes of similar species (we use primarily mitochondrial DNA, mtDNA) and various distance matric…
On separability of semigroups: application to models of physics and discrete optimization Open
Nilpotent semigroups are used in various fields of physics to model processes like system decay in quantum mechanics, state transitions in statistical mechanics, and simplifying dynamical systems. They also assist in optimizing control pro…
On the Knowledge-Based Study of All Semilattices of Waterloo Automaton Open
The aim is to study the set of subsets of grids of Waterloo automaton and the set of covering automata defined by the grid subsets. The study was carried out using the library for working with nondeterministic finite automata NFALib implem…
On the Application of Some Decision-Making Algorithms in Discrete Optimization Problems Open
The relevance of the subject area under consideration is due to the need to effectively solve discrete optimization problems that arise in the process of analyzing high-dimensional communication networks. Namely, the article examines decis…
On the Application of Heuristics of the TSP for the Task of Restoring the DNA Matrix Open
The traveling salesman problem (TSP) is a well-known optimization problem that seeks to find the shortest possible route that visits a set of points and returns to the starting point. In this paper, we apply some heuristics of the TSP for …
On Some Properties of Maximal Prefix Codes and Machine Learning for Automata Open
In this paper we study the prefix codes and application of prefix codes for problem of machine learning for deterministic finite state automaton. We give an example for the problem of constructing an inverse morphism, also parameterized by…
On an Invariant of Tournament Digraphs Open
To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successful implementations of …
On the “Onion Husk” Algorithm for Approximate Solution of the Traveling Salesman Problem Open
The paper describes some implementation aspects of an algorithm for approximate solution of the traveling salesman problem based on the construction of convex closed contours on the initial set of points ("cities") and their subsequent com…
On Some Properties of Graph of Prefix Code Open
We investigate decomposition of codes and finite languages. A prime decomposition is a decomposition of a code or languages into a concatenation of nontrivial prime codes or languages. A code is prime if it cannot be decomposed into at lea…
Some more on restoring distance matrices between DNA chains: reliability coefficients Open
This article is a description of the continuation of previous research by the authors related to the restoration of distance matrices. The main difficulty that arises with such a recovery is that it is impossible to use conventional techni…
Some General Heuristics in the Traveling Salesman Problem and the Problem of Reconstructing the DNA Chain Distance Matrix Open
With all their differences, the two problems under consideration, namely the traveling salesman problem and the problem of restoring the DNA chain distance matrix, have a lot in common. This generality primarily consists in the following. …
Pseudogeometric version of the traveling salesman problem: application in quantum physics models and a heuristic variant of point placement Open
The geometric version of the traveling salesman problem (TSP) has been extensively studied, leading to the development of various approaches for solving its special cases. However, these algorithms often fall short when applied to problems…
Greedy and branches-and-boundaries methods for the optimal choice of a subset of vertices in a large communication network Open
The problems of the proposed paper are generated by the actual tasks of communication networks. The development of communication resources is accompanied by an increase in the dimension of existing communication networks, for which the usu…
An Algorithm for the Inverse Problem of Matrix Processing: DNA Chains, Their Distance Matrices and Reconstructing Open
We continue to consider one of the cybernetic methods in biology related to the study of DNA chains. Exactly, we are considering the problem of reconstructing the distance matrix for DNA chains. Such a matrix is formed on the basis of any …
On Some Problems of Extracting the Root from a Given Finite Language Open
Based on the standard definition of the product (concatenation), the natural non-negative degree of the language is introduced. Root extraction is the reverse operation to it, and it can be defined in several different ways. Despite the si…
A Program Study of the Union of Semilattices on the Set of Subsets of Grids of Waterloo Language Open
The aim is to study the set of subsets of grids of the Waterloo language from the point of view of abstract algebra and graph theory. The study was conducted using the library for working with transition graphs of nondeterministic finite a…
An inverse problem for matrix processing: an improved algorithm for restoring the distance matrix for DNA chains Open
We consider one of the cybernetic methods in biology related to the study of DNA chains. Namely, we are considering the problem of reconstructing the distance matrix for DNA chains. Such a matrix is formed on the basis of any of the possib…
An approach for obtaining estimation of stability of large communication network taking into account its dependent paths Open
The physical data layer transmits bits over physical communication channels, such as coaxial cable or twisted pair. That is, it is this level that directly transmits data. At this level, the characteristics of electrical signals that trans…
Pseudoatuomata for generalized regular expressions Open
The definition of generalized non-deterministic finite automata is given and of their languages, an algorithm for checking whether a word belongs to a given language.
A polynomial algorithm for constructing a finite automaton for determining the equality of infinite iterations of two finite languages Open
In this paper, we continue the topic related to the special binary relation on the set of formal languages (considered primarily on the set of iterations of nonempty finite languages); this is so called equivalence relation at infinity. W…