International Journal of Mathematical Models and Methods in Applied Sciences

ISSN: 1998-0140
Volume 13, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of NAUN Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

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Volume 13, 2019

Title of the Paper: 2D Filters with Elliptical and Circular Frequency Response based on Digital Prototypes


Author: Radu Matei

Pages: 149-153

Abstract: In this work an analytical design procedure is proposed for a class of two-dimensional recursive filters, having a frequency response of elliptical or circular shape. The design method relies on efficient digital filter prototypes, to which a specific complex frequency mapping is applied. This allows obtaining directly the transfer function of the desired 2D filter, in a factored form. In the proposed design some accurate approximations are used, like Chebyshev-Padé method, but no global optimization algorithm. Finally the 2D filter matrices are derived, as a convolution of smaller size matrices, an advantage in implementation. The filter results adjustable, its coefficients depending explicitly on the specified orientation and bandwidth. As the design examples show, the obtained 2D filters have an accurate shape, with very low distortions even near the margins of frequency plane and are efficient, of good selectivity and relatively low complexity.

Title of the Paper: Seismic Safety of the Calabria Hospitals and Road Networks


Author: Alessandra Fiore, Ivo Vanzi, Camillo Nuti, Rita Greco, Davide Lavorato, Cristoforo Demartino, Bruno Briseghella

Pages: 141-148

Abstract: This paper shows a model to assess the seismic safety of a regional network system consisting of hospitals connected by roads. The main aim is the evaluation of the system safety. A specific indicator, namely the time taken to be cured for persons injured by the earthquake, is introduced to evaluate the system efficiency. The model takes into account the real road network. The proposed methodology can be so summarized: i) given a seismic event, for each hospital of the system the number of available beds is calculated; ii) it is assumed that casualties leave from each municipality to reach the nearest not full hospital, up to its actual capacity; iii) the average time taken by each casualty to reach the nearest hospital is evaluated. The above analysis allows to clearly identify which hospitals or roads should be strengthened in order to better face seismic emergencies and more precisely in order to avoid people to face unacceptable traveling times for reaching the nearest not full hospital. The efficacy of the proposed methodology is shown with reference to the highly seismic Italian region of Calabria, where Castrovillari, Reggio Calabria and Locri result to be the most vulnerable urban centres.

Title of the Paper: An Alternative DCA-based Approach for Reduced-Rank Multitask Linear Regression with Covariance Estimation


Author: Hoai An Le Thi, Vinh Thanh Ho, Tao Pham Dinh

Pages: 135-140

Abstract: We investigate a nonconvex, nonsmooth optimization approach based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) for the reduced-rank multitask linear regression problem with covariance estimation. The objective is to model the linear relationship between a multitask response and more explanatory variables by estimating a low-rank coefficient matrix and a covariance matrix. The problem is formulated as minimizing the constrained negative log-likelihood function of these two matrix variables. Then, we consider a reformulation of this problem which takes the form of a partial DC program i.e. it is a standard DC program for each variable when fixing the other variable. Next, an alternative version of DCA scheme is developed. Numerical results on synthetic multitask linear regression datasets and benchmark real datasets show the efficiency of our approach in comparison with the existing alternating/joint methods.

Title of the Paper: Unsupervised Anomaly Isolation for Condition Monitoring Systems


Author: Emad Ali, Jürgen Weber

Pages: 129-134

Abstract: This paper deals with the problem of modelling and monitoring the fault-free states of an industrial process without a complete knowledge about the entire machine components. The aim thereby is to automatically detect the deviations in performance as fault symptoms. For that type of data-based modelling, the algorithms of clustering are selected with emphasis on the computational load and application complexity. Kohonen neural networks (self-organizing maps) are found suitable for the task due to the ability to efficiently operate on high dimensional data and because of their robustness against uncertainties. They reveal drawbacks from the perspective of identifying the deviating variable in the input space. A novel structure is designed to solve this dilemma by combining multi one dimensional domains and their statistical relationships, where Kohonen and Bayesian algorithms would be directly applicable. The structure is introduced and applied to simulate the human supervisors in the way of learning normal operation and hence, attempts to automatically identify the deviating variable in high amount of data. An example application is proposed for detecting the wear degradation fault in a real electrohydraulic drive that widely used in many industrial machines. The algorithm can be realized locally or integrated remotely in cloud architectures.

Title of the Paper: Chaotic Oscillators as the Pseudo-Random Numbers Generators


Author: Roman Senkerik, Michal Pluhacek, Jakub Janostik, Zuzana Kominkova Oplatkova

Pages: 122-128

Abstract: This paper investigates the utilization of the timecontinuous chaotic system as the chaotic pseudo random number generators. (CPRNGs) Two selected chaotic oscillators are simulated, statistically analyzed and compared within this research study. Complex chaotic systems of interests are well known and widely studied UEDA oscillator and Van der Pol oscillator. Furthermore this paper also shows complex analysis of the influence of sampling rates to the distribution and dynamical sequencing during the generating of pseudo number numbers by means of both studied chaotic systems.

Title of the Paper: Passive Fault Tolerant Control based on Interval Type-2 Fuzzy Controller for Coupled Tank System


Author: Himanshukumar Patel

Pages: 116-121

Abstract: In this paper, a robust controller for a coupled tank level control is proposed in presence of actuator and system component faults. For this purpose, Interval type-2 fuzzy logic control approach (IT2FLC) technique is used to design a controller, named passive Fault Tolerant Interval Type-2 Fuzzy Controller (PFTIT2FLC) based on the robust controller to fault tolerant of coupled tank level control system. The proposed control scheme allows avoiding modeling, reducing the rules number of the fuzzy controller. The simulation results show that the PFIT2FLC can provide good tracking performance, even in presence of actuator and system component faults.

Title of the Paper: Optimization of Airport Passenger Throughput


Author: Linlin Qin, Ling Ou

Pages: 110-115

Abstract: Reducing the passenger waiting time at security checkpoints is key to improving passenger experience. It is known that the process of passengers queuing for identity checks corresponds to the M / M / 1 model in queuing theory, and the process of waiting for baggage and body scanning corresponds to the M / G / 1 model. In this model, the ratio of the common security channels to the number of pre-security channels is an important factor affecting the waiting time. The optimal values for a number of parameters are calculated, including the abovementioned ratio and passengers divestment time. When these important factors exceed the optimal value, the waiting time increase very quickly in the model. Whatmore,the model was optimized , in regards baggage and body security inspection process. We detail the optimized model and the time equation of the process. The Monte Carlo algorithm is used to simulate this process and the results are consistent with the variance. The amount of sensitivity analysis of the model, mainly described the regional cultural differences on the impact of the model. Finally, a concrete solution is put forward to solve the problems caused by such factors

Title of the Paper: Asymptotic Stability by Lyapunov and Assessment of Areas of Attraction of Phase Systems


Author: M. Kalimoldayev

Pages: 103-109

Abstract: In work are investigated asymptotic stability by Lyapunov and assessment of area of an attraction on the basis of the second method of Lyapunov by means of new Lyapunov's function. On the basis of theoretical results received in work computing experiments on concrete examples of electrical power systems, which have shown sufficient efficiency of the offered method for the studied electrical power system are made

Title of the Paper: Applying Software Metrics to RNN for Early Reliability Evaluation


Author: Jie Zhang, Yang Lu, Ke Shi, Chong Xu

Pages: 96-102

Abstract: Reliability engineering implemented early in the development process has a significant impact on improving software quality. It can assist in the design of architecture and guide later testing, which is beyond the scope of traditional reliability models. The structural reliability models are made for this, but most of them remain in the simulation studies because of lack of actual data. In this study, we use software metrics which are collected from actual projects to evaluate the reliability. We use the Recurrent Neural Network to process the metric data to identify defeat-prone classes in one project. A specific strategy is used for aggregating module reliability with the results. Furthermore, we propose a framework which can automatically calculate the overall reliability value by the introduced formal tools. The experimental results of two opensource projects show that reliability analysis at design and development stage can be close to the validity of analysis at test stage through the reasonable application of metric data and related methods.

Title of the Paper: On a Linearization Method for the Dynamical Systems Associated to Excitable Media Models


Author: Adela Ionescu

Pages: 90-95

Abstract: In the present paper there are presented recent results concerning the behavior of the mixing flow dynamical system. From analytical standpoint, the feedback linearization of this dynamical system issue special interpretations. This technique contains two fundamental nonlinear controller design techniques: input-output linearization and state-space linearization. The approach is usually referred as input-output linearization or feedback linearization and is based on concepts from nonlinear systems theory. The resulting controller includes the inverse of the dynamic model of the process, providing that such an inverse exists. The results will be used for further analysis of 3D mixing flow dynamical system

Title of the Paper: Transient Analysis of a Repairable Single Server Queue with Working Vacations and System Disasters


Author: M.I.G. Suranga Sampath, K. Kalidass, Jicheng Liu

Pages: 82-89

Abstract: This study investigates the repairable single server queue with working vacations and system disasters. The server allows to take a working vacation if there is no any customers in the system. There is a possibility of breakdowns happening in a system. When the system occurs server breakdowns, the server goes to the failure state and all customers in the queue are flushed away. The repairing process starts immediately, when the server comes to the failure state. The explicit expression for system size probabilities of the queueing system is derived in terms of the modified Bessel function of first kind using the probability generating function method, Laplace transform and continued fractions. Additionally, the mean and variance for number of jobs in the system at time t are derived as the performance measures.

Title of the Paper: New Non-Secant Implicit Update Method for Unconstrained Optimization


Author: Issam Moghrabi

Pages: 77-81


Title of the Paper: Subsonic to Supersonic Transition through a Vertical Pipe Bend


Author: Etsuo Morishita

Pages: 70-76

Abstract: It is theoretically possible to accelerate the one- dimensional compressible pipe flow from subsonic to supersonic by the gravity effect through a vertical pipe bend. A viscous one-dimensional compressible pipe flow under gravity effect is first studied analytically. The compressible one-dimensional pipe flow with friction is called Fanno flow and the solution is given by analytical formula. In gas dynamics, the gravity effect is minimal and it is not included in the equations. However, it was shown by the present author that the elevation of a pipe could change the flow conditions in a one-dimensional compressible potential flow under gravity. The sonic condition is reached at the maximum height for an inviscid pipe flow. In this paper, the gravity effect is extended to the viscous one-dimensional pipe flow. Subsonic–supersonic transition is also possible by up and down of a pipe, i.e. through a vertical pipe bend for viscous flows, and it is found that the sonic condition deviates from the peak position of the pipe. The analytical solutions are obtained for the prescribed Mach number distribution. For the given pipe geometry, numerical approach is necessary, and the classical method of characteristics is applied to the problem and compared to the exact analytical solutions.

Title of the Paper: Modeling Systems’ Interactions Type “Stochastic - Determined”


Authors: Stepan V. Mednikov, Vladimir I. Mednikov

Pages: 64-69

Abstract: Publications analysis revealed some disadvantages in enterprises’ interactions modeling. The article is “filling the gap” in modeling of inter-system interaction type “stochastic – determined” by using earlier devised enterprise math model. Main features of catastrophe theory were compared with developed protection theory. Previously unknown dependence of the kinetic energy on the substance viscosity in any of the environment, where force majeure exists, is given. Previously unknown fundamental relationships between the turbulence propensities of this substance and the probability density of the force majeure kinetic energy on these substances’ viscosity. Enterprise resource damage calculation was given; math model of rivalry in commodity market and pertinent indicators of enterprise activity were showed.

Title of the Paper: High Precision Stochastic Solvers for Large Autonomous Systems of Differential Equations


Author: Flavius Guias

Pages: 60-63

Title of the Paper: Group Consensus Analysis for First Order Collective Model with Spatial Coordinates Coupling


Authors: Fen Nie, Xiaojun Duan, Yicheng Liu

Pages: 52-59

Abstract: In this paper, we studied some consensus and group consensus algorithms for the collective rotating motions of a team of agents, which has been widely studied in different disciplines ranging from physics, networks and engineering. discrete group consensus algorithm when delay are free and consensus algorithm with processing delays are investigated. Based on algebraic matrix theories, graph theories and the properties of Kronecker product, some necessary and sufficient criteria for the consensus and group consensus are derived, where we show that both the eigenvalue distribution of the Laplacian matrix and the Euler angle of the rotation matrix play an important role in achieving group consensus and consensus. Finally, simulation examples are presented to validate the effectiveness of the theoretical results.

Title of the Paper: Comparing Partitions: Shortest Path Length Metrics and Submodularity


Authors: Jyrko Correa-Morris

Pages: 45-51

Abstract: With the recent impetus in the development of generic properties and formal frameworks for understanding and organizing the different clustering methods at a technical level, the interest in measures to compare partitions has risen, specially motivated by the applications these have to averagebased consensus methods, and the various notions of clusterability. In this regard, Shortest Path Length metrics (also known as Minimum Number of Structural Transformations metrics) have been established as one of the great paradigms for the comparison of not only partitions, but of structured data in general. It has been proven that these metrics can encode many of the properties of the primary notion of proximity that the refinement relation endows the lattice of partitions with. On the other hand, another property that has naturally emerges in many mathematical model in combinatorial optimization, economics, machine learning, among others, is submodularity, which has proven to be quite useful from the algorithmic and computational point of view. Motivated by these facts, a question arose: Are there Shortest Path Length metric which are submodular in any of its arguments? In this paper, we prove that there is no shortest path length metric on the lattice of partitions which is submodular in any of their arguments, thus demonstrating that measures such as Mirkin metric and Variation of Information fail to meet this property. We also prove that there are dissimilarity measures that are nonnegative; symmetric; satisfy the triangle inequality; for a chain of partitions, respects the nearness among partitions in the chain (which basically represent the aforementioned primary notion of proximity); and, in addition, are submodular in each of their arguments. These constitute a novel family of measure for comparing partitions with promising attributes.

Title of the Paper: Modeling the Impact of Cyber Threats on an Organization's Information System in the Framework of Cyber-Risk Insurance


Authors: Lukáš Pavlík

Pages: 40-44

Abstract: Many organizations around the world are exposed to cyber risks every day. This has also begun in recent years to react to the insurance market. This paper presents possible approaches to modeling the impact of selected cyber threats on the organization and its information system. The proposed algorithm is divided into two parts. The first one is focused on the pricing of selected parameters. The second part focuses on identifying the most serious cyber threat scenario. The main results are then based on the interaction of cyber threats and predefined parameters and can be implemented in the process of determining insurance coverage. On the basis of the results found, it is possible in the next steps to estimate the amount of insurance cover for each organization. It is also described the possible development of this field in the future.

Title of the Paper: Modeling of Cardiac Arrhythmias and Blockades as the Unity of Fractal and Anti-Fractal Antonyms


Authors: Sergii K. Kulishov

Pages: 35-39

Abstract: Different technologies were used for mathematical modeling of biological rhythms. The purpose of our study is to simulate cardiac arrhythmia and blockade as a unity of opposites, pairs of fractal and anti-fractal antonyms. We proposed and tested algorithms for solving these problems. Our concept is presented in the form of a step-by-step analysis of myocardial electrical instability. The methodology of this analysis: the initiation of electrical instability of the myocardium in a particular case; definition of arrhythmic and blockade types; search for cardiac arrhythmias and conduction components as a unity of opposites, antonyms; selection of basic and additional pairs of antonyms, oxymorons; identification of these pairs; the conversion of these results into fractal and / or anti-fractal antonyms; representation of this data in the form of graphical models. Additional investigations were included the graph theory, topology, convex analysis. The proposed algorithms, graphical models contribute to the understanding of arrhythmogenesis, triggers and resonators of these processes; improving the quality of diagnosis as a prerequisite to correct treatment.

Title of the Paper: Career Determination using Information Theoretical Measure and It’s Comparison with Distances in IFS and PFS


Authors: A. Mandaliya, M. Sahni, R. Verma

Pages: 28-34

Abstract: In this paper, we have proposed a method to help students of High School to choose a career having multiple options available after High School. It is based on the student’s marks and their Teacher’s perception of their own marks using generalized intuitionistic fuzzy divergence measure. The method is also compared with distance measure using intuitionistic fuzzy sets (IFS) and pythagorean fuzzy sets (PFS). Tables are drawn using the results based on the feedback collected from the student’s perception and their teacher’s perception about their High School result and compared with the table of membership and non-membership values required in each subject versus career written arbitrarily.

Title of the Paper: Using Random Adaptive Grouping for Improving the Performance of Evolutionary Algorithms Solving LSGO Problems


Authors: A. Vakhnin, E. Sopov, E. Semenkin

Pages: 13-27

Abstract: In fact, many modern real-world optimization problems have the great number of variables (more than 1000), which values should be optimized. These problems have been titled as large-scale global optimization (LSGO) problems. Typical LSGO problems can be formulated as the global optimization of a continuous objective function presented by a computational model of «Black-Box» (BB) type. For the BB optimization problem one can request only input and output values. LSGO problems are the challenge for the majority of evolutionary and metaheuristic algorithms. In this paper, we have described details on a new DECC-RAG algorithm based on a random adaptive grouping (RAG) algorithm for the cooperative coevolution framework and the well-known SaNSDE algorithm. We have tuned the number of subcomponents for RAG algorithm and have demonstrated that the proposed DECC-RAG algorithm outperforms some state-of-the-art algorithms with benchmark problems taken from the IEEE CEC’2010 and CEC’2013 competitions on LSGO.

Title of the Paper: Ranking of Teachers based on Feedback from the Students using Multiple Subjects


Authors: M. Sahni, A. Mandaliya, R. Sahni

Pages: 7-12

Abstract: The purpose of this paper is to evaluate the teachers' performance by using the concept of metric. For the evaluation, we have prepared a questionnaire of fifteen questions divided in six categories. An aggregator operator is used to calculate the mean corresponding to different Teacher's and performance evaluation is done for multiple subjects. The overall evaluation is done for the teachers and the ranking is shown in the form of table.

Title of the Paper: Solution of Radiation and Scattering Electromagnetic Problems in Cartesian, Spherical and Cylindrical Coordinates by Green's Function Method


Authors: Sergey Knyazev, Boris Panchenko, Sergey Shabunin

Pages: 1-6

Abstract: The method of Green’s functions for layered magneto-dielectric structures with arbitrary extraneous electric and magnetic currents is described. Application peculiarities of the method for Cartesian, cylindrical and spherical coordinate system are under consideration. The equivalent circuit approach is applied for layered structures description. Transmitting matrices are used for wave propagation modelling in each layer and through boundaries between layers. It is shown that the boundary transmitting matrix for flat and spherical structures is equal to the unit matrix. Different kinds of loads are used for region boundaries modelling. Suggested method with transmitting matrices allows one to develop universal algorithms with common modules for wave propagation, antennas radiation and scattering problems associated with flat, cylindrical and spherical structures of any number of layers, arbitrary permittivity and permeability. As an example, the problem of minimizing the reflection from a perfectly conducting surface with a two-layer cover using the Green’s functions method is considered.