wolfram cellular automata are considered and their operation is demonstrated using an example of traffic flow simulation. For the class of one-dimensional elementary cellular automata, the concept of linearity is introduced in the language of Zhegalkin operators. An algorithm for finding linear Zhegalkin operators with multipliers of three variables is presented. The algorithm is implemented in Python.
We found a lower bound on the rank of a square matrix where every entry in the leading diagonal is neither zero nor one and every entry outside the leading diagonal is either zero or one. The rank of this matrix is at least half its order. Under an additional condition, the lower bound is higher by one. This condition means that some auxiliary system of linear equations has no binary solution. Some examples are provided that show that the lower bound can be achieved. This lower bound on the matrix rank allows the problem of finding a binary solution to a system of linear equations with a sufficiently large number of linearly independent equations to be reduced to a similar problem in a smaller number of variables. Restrictions on the existence of a large set of solutions are found, each differing from the binary one by the value of one variable. In addition, we discuss the possibility of certifying the absence of a binary solution to a large system of linear algebraic equations. Estimates of the time required for calculating the matrix rank in the SymPy computer algebra system are also provided. It is shown that the rank of a matrix over the field of residues modulo prime number is calculated faster than it generally takes to calculate the rank of a matrix of the same order over the field of rational numbers.
Different implementations of Clifford algebra: spinors, quaternions, and geometric algebra, are used to describe physical and technical systems. The geometric algebra formalism is a relatively new approach, destined to be used primarily by engineers and applied researchers. In a number of works, the authors examined the implementation of the geometric algebra formalism for computer algebra systems. In this article, the authors extend elliptic geometric algebra to hyperbolic space-time algebra. The results are illustrated by different representations of Maxwell’s equations. Using a computer algebra system, Maxwell’s vacuum equations in the space-time algebra representation are converted to Maxwell’s equations in vector formalism. In addition to practical application, the authors would like to draw attention to the didactic significance of these studies.
In this paper, we continue to consider the problem of recovering the port-Hamiltonian structure for an arbitrary system of differential equations. We complement our previous study on this topic by explaining the choice of machine learning algorithms and discussing some details of their application. We also consider the possibility provided by this approach for a potentially new definition of canonical forms and classification of systems of differential equations.
A method to calculate partial sums of some multiple numerical series arising when searching for the resultant of a polynomial and an entire function is proposed. One can apply a symbolic algorithm that uses recurrent Newton formulas to find power sums of roots included in this formula without finding the very roots of the system. The algorithm that implements the proposed approach to calculate partial sums of multiple numerical series is implemented in Maple. Examples of using this algorithm to find partial sums of some classes of multiple numerical series are given.
Laurent solutions of systems of linear ordinary differential equations with truncated power series as coefficients are considered. The Laurent series in the solutions are also truncated. As a means for constructing such solutions, induced recurrent systems are used; earlier, an algorithm for the case when the induced recurrent system has a nonsingular leading matrix was proposed. For the series in solutions, this algorithm finds the maximum possible number of terms that are invariant with respect to any prolongation of the truncated coefficients of the original system. Results on extending the applicability of the earlier proposed algorithm to the case when the leading matrix is singular using the EG-elimination algorithm as an auxiliary tool. An implementation of the proposed algorithm in the form of a Maple procedure is given and examples of its use are presented.
One of the basic aspects of information flow control in applications is a security policy language. This language should allow one to define security policies for evaluation of environment elements in coherence with higher-level access control rules. Hence, the language is expected to be flexible because there may be different access control paradigms (mandatory, role-based, etc.) implemented at the system level. The application may also have its own specific restrictions. Finally, it is also desirable that the language support declassification (controlled release of information) during computations. Paralocks is one of such languages. This research is devoted to the logical semantics of a modified version of Paralocks implemented in TLA+. Paralocks represents a language basis for the PLIF information flow control platform, which is developed with author’s participation for the analysis of PL/SQL program blocks. It includes proofs of the partial order and lattice defined on a set of security policy expressions.
This paper considers the problem of constructing compartmental models of dynamic systems by using a software package for symbolic calculation written in Julia. The software package is aimed at unifying the formalized construction of compartmental models, taking into account the meaningful description of possible interactions among compartments and the influence of various factors on the evolution of systems. An approach to the development of the instrumental and methodological basis for modeling the dynamic systems the behavior of which can be described by one-step processes is developed. The proposed software package enables the symbolic representation of the differential equations of the model in both stochastic and deterministic cases. It is implemented in Julia and uses the Julia Symbolics computer algebra library. A comparison between the Julia Symbolics tools and some other computer algebra systems is carried out. The application of the developed software package to a compartmental model is considered. The results can be used to solve problems of constructing and studying dynamic models in natural sciences that are represented by one-step processes.
Code comments are an essential part of software documentation. Many software projects suffer from the problem of low-quality comments that are often produced by copy-paste. In case of similar methods, classes, etc. copy-pasted comments with minor modifications are justified. However, in many cases this approach leads to degraded documentation quality and, subsequently, to problematic maintenance and development of the project. In this study, we address the problem of near-duplicate code comments detection, which can potentially improve software documentation. We have conducted a thorough evaluation of traditional string similarity metrics and modern machine learning methods. In our experiment, we use a collection of Javadoc comments from four industrial open-source Java projects. We have found out that LCS (Longest Common Subsequence) is the best similarity algorithm taking into account both quality (Precision 94%, Recall 74%) and performance.
Topology synthesis in integrated design of wireless communication networks is considered. An iterative method has been developed for placing base stations of a broadband network along extended transportation routes. The problem of base station placement is formulated as an extremal problem on a finite set in the form of a special combinatorial model. An algorithm of the branch and bound method (BBM) has been developed to solve this problem. This algorithm serves as the basis for finding a sequence of best variants for the placement of base stations. Numerical calculations confirming the efficiency of the proposed algorithm are described.
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