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1

Algorithms for computations with Sylow 2-subgroups of symetric groups

Olshevska Vita

Silesian Journal of Pure and Applied Mathematics

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2020

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vol. 10, iss. 1

103--120

EN

An algorithm to transform n-levels labeled binary rooted trees into elements from Sylow 2-subgroups of symmetric groups of degree 2n is described. The inverse algorithm that on input permutation from a Sylow 2-subgroup of symmetric groups of degree 2n finds a labeled tree is presented. An algorithm for multiplication of labeled trees that correspond to the multiplication of permutations from the Sylow 2-subgroup is introduced. The complexity and correctness of these algorithms are studied.

2

Detection of ice states from mechanical vibrations using entropy measurements and machine learning algorithms

Mejía Juan C., Quintero Héctor F., Echeverry-Correa Julián D., Romero Carlos A.

Diagnostyka

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2020

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Vol. 21, No. 4

87--94

EN

Entropy measurements are an accessible tool to perform irregularity and uncertainty measurements present in time series. Particularly in the area of signal processing, Multiscale Permutation Entropy (MPE) is presented as a characterization methodology capable of measuring randomness and non-linear dynamics present in non-stationary signals, such as mechanical vibrations. In this article, we present a robust methodology based on MPE for detection of Internal Combustion Engine (ICE) states. The MPE is combined with Principal Component Analysis (PCA) as a technique for visualization and feature selection and KNearest Neighbors (KNN) as a supervised classifier. The proposed methodology is validated by comparing accuracy and computation time with others presented in the literature. The results allow to appreciate a high effectiveness in the detection of failures in bearings (experiment 1) and ICE states (experiment 2) with a low computational consumption.

3

A Novel Image Encryption Scheme Based on Generalized Multi-sawtooth Maps

Ye R.

Fundamenta Informaticae

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2014

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Vol. 133, nr 1

87--104

EN

In this paper, a generalized multi-sawtooth map based image encryption scheme with an efficient permutation-diffusion mechanism is proposed. In the permutation process, a generalized multi-sawtooth map is utilized to generate one chaotic orbit used to get one index order sequence for the permutation of image pixel positions, while in the diffusion process, two generalized multi-sawtooth maps are employed to yield two pseudo-random grey value sequences for a twoway diffusion of pixel grey values. The yielded grey value sequences are not only sensitive to the control parameters and initial conditions of the considered chaotic maps, but also strongly depend on the plain-image processed, therefore the proposed scheme can effectively resist statistical attack, differential attack, known-plaintext as well as chosen-plaintext attack. Experimental results show that the new image encryption scheme has satisfactory security thanks to its large key space and robust permutation-diffusion mechanism, which makes it a potential candidate for designing image encryption schemes.

4

Image encryption using edge diffusion and selective permutations in orthogonal polynomials based transformation domain

Krishnamoorthi R., Sheba Kezia Malarchelvi P. D.

Image Processing & Communications

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2009

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Vol. 14, no 4

13-27

EN

This paper proposes a new image encryption technique in orthogonal polynomials based transformation domain (OPT) with edge diffusion and selective combinational permutations for secure transmission of images. In this technique, we propose the use of the polynomials based edge detection algorithm to decompose the image blocks into edge blocks and non-edge blocks. The edge blocks are first encrypted with a cryptographic algorithm and then a selective combinational permutation is applied over the low frequency coefficients of the edge as well as non-edge blocks in order to reduce the number of bits to be permuted. Then a combinational shuffling of bits, coefficients and blocks are carried out in addition to sign bit encryption. A symmetric key based cryptographically secure pseudo random process controls the entire encryption process. Experimental results reveal that the proposed encryption scheme provides very low encryption PSNRs and security analyses prove that the proposed technique offers effective encryption.

5

Metoda analizy minimów lokalnych do rozwiązywania permutacyjnych problemów optymalizacyjnych

Bożejko W., Rajba P., Wodecki M.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

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2008

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z. 150

19-24

PL

W pracy przedstawiono metodę konstrukcji algorytmów rozwiązywania problemów optymalizacyjnych opartą na analizie minimów lokalnych. Najlepsze cechy tych minimów są dziedziczone przez następną populację rozwiązań. Wykonano eksperymenty obliczeniowe, które potwierdziły efektywność proponowanej metody.

EN

In the paper we present a method of algorithms construction based on analyzing local minima for solving optimization problems. The best properties of these minima are succeeded by a next generation of solutions. Computational experiments, which has been done, affirmed the efficiency of the proposed method.

6

Digraph description of k-interchange technique for optimization over permutations and adaptive algorithm system

Levin M. S.

Foundations of Computing and Decision Sciences

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2001

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Vol. 26, No. 3

225-235

EN

The paper describes a general glance to the use of element exchange techniques for optimization over permutations. A multi-level description of problems is proposed which is a fundamental to understand nature and complexity of optimization problems over permutations (e.g., ordering, scheduling, traveling salesman problem). The description is based on permutation neighborhoods of several kinds (e.g., by improvement of an objective function). Our proposed operational digraph and its kinds can be considered as a way to understand convexity and polynomial solvability for combinatorial optimization problems over permutations. Issues of an analysis of problems and a design of hierarchical heuristics are discussed. The discussion leads to a multi-level adaptive algorithm system which analyzes an individual problem and selects / designs a solving strategy (trajectory).