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Volume 25, September

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Math. Comput. Appl., Volume 25, Issue 4 (December 2020) – 10 articles

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Open AccessArticle
Convolutional Neural Network Based Ensemble Approach for Homoglyph Recognition
Math. Comput. Appl. 2020, 25(4), 71; https://doi.org/10.3390/mca25040071 (registering DOI) - 21 Oct 2020
Abstract
Homoglyphs are pairs of visual representations of Unicode characters that look similar to the human eye. Identifying homoglyphs is extremely useful for building a strong defence mechanism against many phishing and spoofing attacks, ID imitation, profanity abusing, etc. Although there is a list [...] Read more.
Homoglyphs are pairs of visual representations of Unicode characters that look similar to the human eye. Identifying homoglyphs is extremely useful for building a strong defence mechanism against many phishing and spoofing attacks, ID imitation, profanity abusing, etc. Although there is a list of discovered homoglyphs published by Unicode consortium, regular expansion of Unicode character scripts necessitates a robust and reliable algorithm that is capable of identifying all possible new homoglyphs. In this article, we first show that shallow Convolutional Neural Networks are capable of identifying homoglyphs. We propose two variations, both of which obtain very high accuracy (99.44%) on our benchmark dataset. We also report that adoption of transfer learning allows for another model to achieve 100% recall on our dataset. We ensemble these three methods to obtain 99.72% accuracy on our independent test dataset. These results illustrate the superiority of our ensembled model in detecting homoglyphs and suggest that our model can be used to detect new homoglyphs when increasing Unicode characters are added. As a by-product, we also prepare a benchmark dataset based on the currently available list of homoglyphs. Full article
(This article belongs to the Section Engineering)
Open AccessFeature PaperArticle
Steady State and 2D Thermal Equivalence Circuit for Winding Heads—A New Modelling Approach
Math. Comput. Appl. 2020, 25(4), 70; https://doi.org/10.3390/mca25040070 - 18 Oct 2020
Viewed by 155
Abstract
The study concerns the winding head thermal design of electrical machines in difficult thermal environments. The new approach is adapted for all basic shapes and solves the thermal behaviour of a random wire layout. The model uses the nodal method but does not [...] Read more.
The study concerns the winding head thermal design of electrical machines in difficult thermal environments. The new approach is adapted for all basic shapes and solves the thermal behaviour of a random wire layout. The model uses the nodal method but does not use the common homogenization method for the winding slot. The layout impact can be precisely studied to find different hotspots. To achieve this a Delaunay triangulation provides the thermal links between adjoining wires in the slot. Voronoï tessellation gives a cutting to estimate thermal conductance between adjoining wires. This thermal behaviour is simulated in cell cutting and it is simplified with the thermal bridge notion to obtain a simple solving of these thermal conductances. The boundaries are imposed on the slot borders with Dirichlet condition. Then solving with many Dirichlet conditions is described. Some results show different possible applications with rectangular and round shapes, one ore many boundaries, different limit condition values and different layouts. The model can be integrated into a larger model that represents the stator to have best results. Full article
(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
Open AccessReview
Convergence versus Divergence Behaviors of Asynchronous Iterations, and Their Applications in Concrete Situations
Math. Comput. Appl. 2020, 25(4), 69; https://doi.org/10.3390/mca25040069 - 16 Oct 2020
Viewed by 183
Abstract
Asynchronous iterations have long been used in distributed computing algorithms to produce calculation methods that are potentially faster than a serial or parallel approach, but whose convergence is more difficult to demonstrate. Conversely, over the past decade, the study of the complex dynamics [...] Read more.
Asynchronous iterations have long been used in distributed computing algorithms to produce calculation methods that are potentially faster than a serial or parallel approach, but whose convergence is more difficult to demonstrate. Conversely, over the past decade, the study of the complex dynamics of asynchronous iterations has been initiated and deepened, as well as their use in computer security and bioinformatics. The first work of these studies focused on chaotic discrete dynamical systems, and links were established between these dynamics on the one hand, and between random or complex behaviours in the sense of the theory of the same name. Computer security applications have focused on pseudo-random number generation, hash functions, hidden information, and various security aspects of wireless sensor networks. At the bioinformatics level, this study of complex systems has allowed an original approach to understanding the evolution of genomes and protein folding. These various contributions are detailed in this review article, which is an extension of the paper “An update on the topological properties of asynchronous iterations” presented during the Sixth International Conference on Parallel, Distributed, GPU and Cloud Computing (Pareng 2019). Full article
Open AccessArticle
In-Plane Free Vibration Analysis of a Scimitar-Type Rotating Curved Beam Using the Adomian Modified Decomposition Method
Math. Comput. Appl. 2020, 25(4), 68; https://doi.org/10.3390/mca25040068 - 15 Oct 2020
Viewed by 146
Abstract
Free in-plane vibrations of a scimitar-type nonprismatic rotating curved beam, with a variable cross-section and increasing sweep along the leading edge, are calculated using an innovative, efficient and accurate solver called the Adomian modified decomposition method (AMDM). The equation of motion includes the [...] Read more.
Free in-plane vibrations of a scimitar-type nonprismatic rotating curved beam, with a variable cross-section and increasing sweep along the leading edge, are calculated using an innovative, efficient and accurate solver called the Adomian modified decomposition method (AMDM). The equation of motion includes the axial force resulting from centrifugal stiffening, and the boundary conditions imposed are those of a cantilever beam, i.e., clamped-free and simple-free. The AMDM allows the governing differential equation to become a recursive algebraic equation suitable for symbolic computation, and, after additional simple mathematical operations, the natural frequencies and corresponding closed-form series solution of the mode shapes are obtained simultaneously. Two main advantages of the application of the AMDM are its fast convergence rate to a solution and its high degree of accuracy. The design shape parameters of the beam, such as transitioning from a straight beam pattern to a curved beam pattern, are investigated. The accuracy of the model is investigated using previously reported investigations and using an innovative error analysis procedure. Full article
(This article belongs to the Section Engineering)
Open AccessArticle
Markov Chain-Based Sampling for Exploring RNA Secondary Structure under the Nearest Neighbor Thermodynamic Model and Extended Applications
Math. Comput. Appl. 2020, 25(4), 67; https://doi.org/10.3390/mca25040067 - 10 Oct 2020
Viewed by 217
Abstract
Ribonucleic acid (RNA) secondary structures and branching properties are important for determining functional ramifications in biology. While energy minimization of the Nearest Neighbor Thermodynamic Model (NNTM) is commonly used to identify such properties (number of hairpins, maximum ladder distance, etc.), it is difficult [...] Read more.
Ribonucleic acid (RNA) secondary structures and branching properties are important for determining functional ramifications in biology. While energy minimization of the Nearest Neighbor Thermodynamic Model (NNTM) is commonly used to identify such properties (number of hairpins, maximum ladder distance, etc.), it is difficult to know whether the resultant values fall within expected dispersion thresholds for a given energy function. The goal of this study was to construct a Markov chain capable of examining the dispersion of RNA secondary structures and branching properties obtained from NNTM energy function minimization independent of a specific nucleotide sequence. Plane trees are studied as a model for RNA secondary structure, with energy assigned to each tree based on the NNTM, and a corresponding Gibbs distribution is defined on the trees. Through a bijection between plane trees and 2-Motzkin paths, a Markov chain converging to the Gibbs distribution is constructed, and fast mixing time is established by estimating the spectral gap of the chain. The spectral gap estimate is obtained through a series of decompositions of the chain and also by building on known mixing time results for other chains on Dyck paths. The resulting algorithm can be used as a tool for exploring the branching structure of RNA, especially for long sequences, and to examine branching structure dependence on energy model parameters. Full exposition is provided for the mathematical techniques used with the expectation that these techniques will prove useful in bioinformatics, computational biology, and additional extended applications. Full article
(This article belongs to the Section Natural Sciences)
Open AccessArticle
Proximal Gradient Method for Solving Bilevel Optimization Problems
Math. Comput. Appl. 2020, 25(4), 66; https://doi.org/10.3390/mca25040066 - 04 Oct 2020
Viewed by 226
Abstract
In this paper, we consider a bilevel optimization problem as a task of finding the optimum of the upper-level problem subject to the solution set of the split feasibility problem of fixed point problems and optimization problems. Based on proximal and gradient methods, [...] Read more.
In this paper, we consider a bilevel optimization problem as a task of finding the optimum of the upper-level problem subject to the solution set of the split feasibility problem of fixed point problems and optimization problems. Based on proximal and gradient methods, we propose a strongly convergent iterative algorithm with an inertia effect solving the bilevel optimization problem under our consideration. Furthermore, we present a numerical example of our algorithm to illustrate its applicability. Full article
Open AccessArticle
Marshall–Olkin Length-Biased Maxwell Distribution and Its Applications
Math. Comput. Appl. 2020, 25(4), 65; https://doi.org/10.3390/mca25040065 - 01 Oct 2020
Viewed by 224
Abstract
It is well established that classical one-parameter distributions lack the flexibility to model the characteristics of a complex random phenomenon. This fact motivates clever generalizations of these distributions by applying various mathematical schemes. In this paper, we contribute in extending the one-parameter length-biased [...] Read more.
It is well established that classical one-parameter distributions lack the flexibility to model the characteristics of a complex random phenomenon. This fact motivates clever generalizations of these distributions by applying various mathematical schemes. In this paper, we contribute in extending the one-parameter length-biased Maxwell distribution through the famous Marshall–Olkin scheme. We thus introduce a new two-parameter lifetime distribution called the Marshall–Olkin length-biased Maxwell distribution. We emphasize the pliancy of the main functions, strong stochastic order results and versatile moments measures, including the mean, variance, skewness and kurtosis, offering more possibilities compared to the parental length-biased Maxwell distribution. The statistical characteristics of the new model are discussed on the basis of the maximum likelihood estimation method. Applications to simulated and practical data sets are presented. In particular, for five referenced data sets, we show that the proposed model outperforms five other comparable models, also well known for their fitting skills. Full article
Open AccessArticle
Geometry and Geodesy on the Primary Visual Cortex as a Surface of Revolution
Math. Comput. Appl. 2020, 25(4), 64; https://doi.org/10.3390/mca25040064 - 29 Sep 2020
Viewed by 202
Abstract
Biological mapping of the visual field from the eye retina to the primary visual cortex, also known as occipital area V1, is central to vision and eye movement phenomena and research. That mapping is critically dependent on the existence of cortical [...] Read more.
Biological mapping of the visual field from the eye retina to the primary visual cortex, also known as occipital area V1, is central to vision and eye movement phenomena and research. That mapping is critically dependent on the existence of cortical magnification factors. Once unfolded, V1 has a convex three-dimensional shape, which can be mathematically modeled as a surface of revolution embedded in three-dimensional Euclidean space. Thus, we solve the problem of differential geometry and geodesy for the mapping of the visual field to V1, involving both isotropic and non-isotropic cortical magnification factors of a most general form. We provide illustrations of our technique and results that apply to V1 surfaces with curve profiles relevant to vision research in general and to visual phenomena such as `crowding’ effects and eye movement guidance in particular. From a mathematical perspective, we also find intriguing and unexpected differential geometry properties of V1 surfaces, discovering that geodesic orbits have alternative prograde and retrograde characteristics, depending on the interplay between local curvature and global topology. Full article
(This article belongs to the Section Natural Sciences)
Open AccessArticle
Mathematical Attack of RSA by Extending the Sum of Squares of Primes to Factorize a Semi-Prime
Math. Comput. Appl. 2020, 25(4), 63; https://doi.org/10.3390/mca25040063 - 28 Sep 2020
Viewed by 251
Abstract
The security of RSA relies on the computationally challenging factorization of RSA modulus with being a large semi-prime consisting of two primes for the generation of RSA keys in commonly adopted cryptosystems. The property of both congruent to 1 mod 4, is used [...] Read more.
The security of RSA relies on the computationally challenging factorization of RSA modulus with being a large semi-prime consisting of two primes for the generation of RSA keys in commonly adopted cryptosystems. The property of both congruent to 1 mod 4, is used in Euler’s factorization method to theoretically factorize them. While this caters to only a quarter of the possible combinations of primes, the rest of the combinations congruent to 3 mod 4 can be found by extending the method using Gaussian primes. However, based on Pythagorean primes that are applied in RSA, the semi-prime has only two sums of two squares in the range of possible squares . As becomes large, the probability of finding the two sums of two squares becomes computationally intractable in the practical world. In this paper, we apply Pythagorean primes to explore how the number of sums of two squares in the search field can be increased thereby increasing the likelihood that a sum of two squares can be found. Once two such sums of squares are found, even though many may exist, we show that it is sufficient to only find two solutions to factorize the original semi-prime. We present the algorithm showing the simplicity of steps that use rudimentary arithmetic operations requiring minimal memory, with search cycle time being a factor for very large semi-primes, which can be contained. We demonstrate the correctness of our approach with practical illustrations for breaking RSA keys. Our enhanced factorization method is an improvement on our previous work with results compared to other factorization algorithms and continues to be an ongoing area of our research. Full article
Open AccessEditorial
Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics
Math. Comput. Appl. 2020, 25(4), 62; https://doi.org/10.3390/mca25040062 - 26 Sep 2020
Viewed by 251
Abstract
Nonlinear dynamics takes its origins from physics and applied mathematics [...] Full article
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