Search results for: stochastic approximation

Authors: Vinai K. Singh

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For reducing impulsive noise without degrading image contours, median filtering is a powerful tool. In multiband images as for example colour images or vector fields obtained by optic flow computation, a vector median filter can be used. Vector median filters are defined on the basis of a suitable distance, the best performing distance being the Euclidean. Euclidean distance is evaluated by using the Euclidean norms which is quite demanding from the point of view of computation given that a square root is required. In this paper an optimal piece-wise linear approximation of the Euclidean norm is presented which is applied to vector median filtering.

Keywords: euclidean norm, quasi euclidean norm, vector median filtering, applied mathematics

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Authors: B. Bouadjemi, S. Bentata, W. Benstaali, A. Abbad, T. Lantri, A. Zitouni

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The purpose of this study was to investigate the structural,electronic and magnetic properties of the cubic praseodymium oxides perovskites PrMnO3. It includes our calculations based on the use of the density functional theory (DFT) with both generalized gradient approximation (GGA) and GGA+U approaches, The spin polarized electronic band structures and densities of states aswellas the integer value of the magnetic moment of the unit cell (6 μB) illustrate that PrMnO3 is half-metallic ferromagnetic. The study shows that the robust half-metallicity makes the cubic PrMnO3 a promising candidate for application in spintronics.

Keywords: Perovskite, DFT, electronic properties, Magnetic moment, half-metallic

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Authors: Tatyana Rybitskaya, Alexandr Starostenko, Kseniya Ryabchenko

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Collector ring (CR) of FAIR project is a large acceptance storage ring and field quality plays a major role in the magnet design. The CR will use normal conducting dipole magnets. There will be 24 H-type sector magnets with a maximum field value of 1.6 T. The integrated over the length of the magnet field quality as a function of radius is ∆B.l/B.l = ±1x10⁻⁴. Below 1.6 T the value ∆B.l/B.l can be higher with a linear approximation up to ±2.5x10⁻⁴ at the field level of 0.8 T. An iron-dominated magnet with required field quality is produced with standard technology as the quality is dominated by the yoke geometry.

Keywords: conventional magnet, iron yoke dipole, harmonic terms, particle accelerators

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Authors: A. Zitouni, S. Bentata, B. Bouadjemi, T. Lantri, W. Benstaali, A. Zoubir, S. Cherid, A. Sefir

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The structural, electronic, and magnetic properties of transition metal Co and Mn doped zinc-blende semiconductor CdTe were calculated using the density functional theory (DFT) with both generalized gradient approximation (GGA). We have analyzed the structural parameters, charge and spin densities, total and partial densities of states. We find that the Co and Mn doped zinc blende CdTe show half-metallic behavior with a total magnetic moment of 6.0 and 10.0 µB, respectively.The results obtained, make the Co and Mn doped CdTe a promising candidate for application in spintronics.

Keywords: first-principles, half-metallic, diluted magnetic semiconductor, magnetic moment

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Authors: Johannes J. Schneider, Mathias S. Weyland, Peter Eggenberger Hotz, William D. Jamieson, Oliver Castell, Alessia Faggian, Rudolf M. Füchslin

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Agglomerations of polydisperse systems of spherical particles are created in computer simulations using a simplified stochastic-hydrodynamic model: Particles sink to the bottom of the cylinder, taking into account gravity reduced by the buoyant force, the Stokes friction force, the added mass effect, and random velocity changes. Two types of particles are considered, with one of them being able to create connections to neighboring particles of the same type, thus forming a network within the agglomeration at the bottom of a cylinder. Decreasing the fraction of these particles, a percolation transition occurs. The critical regime is determined by investigating the maximum cluster size and the percolation susceptibility.

Keywords: binary system, maximum cluster size, percolation, polydisperse

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Authors: Benjamin Sonnenreich

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Brittle fracture failure probability is best described using a stochastic approach which is based on the 'weakest link concept' and the connection between a microstructure and macroscopic fracture scale. A general theoretical and experimental framework is presented to predict the uniaxial strength distribution according to independent uniaxial test data. The framework takes as input the applied stresses, the geometry, the materials, the defect distributions and the relevant random variables from uniaxial test results and gives as output an overall failure probability that can be used to improve the reliability of practical designs. Additionally, the method facilitates comparisons of strength data from several sources, uniaxial tests, and sample geometries.

Keywords: brittle fracture, strength distribution, uniaxial, weakest link concept

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Authors: Iftikhar U. Sikder

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This paper illustrates an application of granular computing approach, namely rough set theory in data mining. The paper outlines the formalism of granular computing and elucidates the mathematical underpinning of rough set theory, which has been widely used by the data mining and the machine learning community. A real-world application is illustrated, and the classification performance is compared with other contending machine learning algorithms. The predictive performance of the rough set rule induction model shows comparative success with respect to other contending algorithms.

Keywords: concept approximation, granular computing, reducts, rough set theory, rule induction

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Authors: Takuya Suzuki, Atsushi Shirai, Takashi Seki

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Acupuncture therapy is one of the treatments in traditional Chinese medicine. Recently, some reports have shown the effectiveness of acupuncture. However, its full acceptance has been hindered by the lack of understanding on mechanism of the therapy. Acupuncture applied to Zusanli (ST-36) enhances blood flow volume in superior mesenteric artery (SMA), yielding peripheral vascular resistance – regulated blood flow of SMA dominated by the parasympathetic system and inhibition of sympathetic system. In this study, a lumped-parameter approximation model of blood flow in the systemic arteries was developed. This model was extremely simple, consisting of the aorta, carotid arteries, arteries of the four limbs and SMA, and their peripheral vascular resistances. Here, the individual artery was simplified to a tapered tube and the resistances were modelled by a linear resistance. We numerically investigated contribution of the peripheral vascular resistance of SMA to the systemic blood distribution using this model. In addition to the upstream end of the model, which correlates with the left ventricle, two types of boundary condition were applied; mean left ventricular pressure which correlates with blood pressure (BP) and mean cardiac output which corresponds to cardiac index (CI). We examined it to reproduce the experimentally obtained hemodynamic change, in terms of the ratio of the aforementioned hemodynamic parameters from their initial values before the acupuncture, by regulating the peripheral vascular resistances and the upstream boundary condition. First, only the peripheral vascular resistance of SMA was changed to show contribution of the resistance to the change in blood flow volume in SMA, expecting reproduction of the experimentally obtained change. It was found, however, this was not enough to reproduce the experimental result. Then, we also changed the resistances of the other arteries together with the value given at upstream boundary. Here, the resistances of the other arteries were changed simultaneously in the same amount. Consequently, we successfully reproduced the hemodynamic change to find that regulation of the upstream boundary condition to the value experimentally obtained after the stimulation is necessary for the reproduction, though statistically significant changes in BP and CI were not observed in the experiment. It is generally known that sympathetic and parasympathetic tones take part in regulation of whole the systemic circulation including the cardiac function. The present result indicates that stimulation to ST-36 could induce vasodilation of peripheral circulation of SMA and vasoconstriction of that of other arteries. In addition, it implies that experimentally obtained small changes in BP and CI induced by the acupuncture may be involved in the therapeutic response.

Keywords: acupuncture, hemodynamics, lumped-parameter approximation, modeling, systemic vascular resistance

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Authors: R. Ouafi, F. Ouafi

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We study the problem of cutting a rectangular material entity into smaller sub-entities of trapezoidal forms with minimum waste of the material. This problem will be denoted TCP (Trapezoidal Cutting Problem). The TCP has many applications in manufacturing processes of various industries: pipe line design (petro chemistry), the design of airfoil (aeronautical) or cuts of the components of textile products. We introduce an orthogonal build to provide the optimal horizontal and vertical homogeneous strips. In this paper we develop a general heuristic search based upon orthogonal build. By solving two one-dimensional knapsack problems, we combine the horizontal and vertical homogeneous strips to give a non orthogonal cutting pattern.

Keywords: combinatorial optimization, cutting problem, heuristic

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Authors: Jing Zhang, Daniel Nikovski

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We propose an approximation algorithm called LINKUMP to compute the Pan Matrix Profile (PMP) under the unnormalized l∞ distance (useful for value-based similarity search) using double-ended queue and linear interpolation. The algorithm has comparable time/space complexities as the state-of-the-art algorithm for typical PMP computation under the normalized l₂ distance (useful for shape-based similarity search). We validate its efficiency and effectiveness through extensive numerical experiments and a real-world anomaly detection application.

Keywords: pan matrix profile, unnormalized euclidean distance, double-ended queue, discord discovery, anomaly detection

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Authors: Francis O. Nwawuru

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The convergence analysis of split monotone inclusion problems and fixed point problems of certain nonlinear mappings are investigated in the setting of real Hilbert spaces. Inertial extrapolation term in the spirit of Polyak is incorporated to speed up the rate of convergence. Under standard assumptions, a strong convergence of the proposed algorithm is established without computing the resolvent operator or involving Yosida approximation method. The stepsize involved in the algorithm does not depend on the spectral radius of the linear operator. Furthermore, applications of the proposed algorithm in solving some related optimization problems are also considered. Our result complements and extends numerous results in the literature.

Keywords: fixedpoint, hilbertspace, monotonemapping, resolventoperators

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Adnan A. Y. Mustafa

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In this paper we present a quick technique to measure the similarity between binary images. The technique is based on a probabilistic mapping approach and is fast because only a minute percentage of the image pixels need to be compared to measure the similarity, and not the whole image. We exploit the power of the Probabilistic Matching Model for Binary Images (PMMBI) to arrive at an estimate of the similarity. We show that the estimate is a good approximation of the actual value, and the quality of the estimate can be improved further with increased image mappings. Furthermore, the technique is image size invariant; the similarity between big images can be measured as fast as that for small images. Examples of trials conducted on real images are presented.

Keywords: big images, binary images, image matching, image similarity

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Authors: Leonard Kabeya Mukeba Yakasham

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The theoretical machinery from singularity theory introduced by Glolubitsky, Stewart, and Schaeffer, to study equivariant bifurcation problem is completed and expanded wile generalized to the multiparameter context. In this setting the finite deterinancy theorem or normal forms, the stability of equivariant bifurcation problem, and the structural stability of universal unfolding are discussed. With Yakam Matrix the solutions are limited for some partial differential equations stochastic nonlinear of the open questions in singularity artificial intelligence for future.

Keywords: equivariant bifurcation, symmetry singularity, equivariant jets and transversality; normal forms, universal unfolding instability, structural stability, artificial intelligence, pdens, yakam matrix

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Authors: Amir T. Payandeh Najafabadi

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This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.

Keywords: ruin probability, compound poisson processes, mixture exponential (hyperexponential) distribution, heavy-tailed distributions

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Authors: Mesias Alfeus, Kirsty Fitzhenry, Alessia Lederer

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The present paper provides empirical studies to estimate defaultable bonds in the South African financial market. The main goal is to estimate the unobservable factors affecting bond yields for South African major banks. The maximum likelihood approach is adopted for the estimation methodology. Extended Kalman filtering techniques are employed in order to tackle the situation that the factors cannot be observed directly. Multi-dimensional Cox-Ingersoll-Ross (CIR)-type factor models are considered. Results show that default risk increased sharply in the South African financial market during COVID-19 and the CIR model with jumps exhibits a better performance.

Keywords: default intensity, unobservable state variables, CIR, α-CIR, extended kalman filtering

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Authors: Tomáš Vyčítal

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In a simulation model of a railway system it is important, besides other crucial algorithms, to have correct behaviour of train overtaking in stochastic conditions. This problem is being addressed in many simulation tools focused on railway traffic, however these are not very human-realistic. The goal of this paper is to create a more human-realistic overtaking decision support system for the use in railway traffic simulations. A fuzzy system has been chosen for this task as fuzzy systems are well-suited for human-like decision making. The fuzzy system designed takes into account timetables, train positions, delays and buffer times as inputs and provides an instruction to overtake or not overtake.

Keywords: decision-making support, fuzzy systems, simulation, railway, transport

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Authors: Yisau Adelaja Odusote, Olakanmi Felix Akinto

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The associative tendency between like atoms in molten Cd-Ga and Cd-In alloy systems has been studied by using the Quasi-Chemical Approximation Model (QCAM). The concentration dependence of the microscopic functions (the concentration-concentration fluctuations in the long-wavelength limits, Scc(0), the chemical short-range order (CSRO) parameter α1 as well as the chemical diffusion) and the mixing properties as the free energy of mixing, GM, enthalpy of mixing and entropy of mixing of the two molten alloys have been determined. Thermodynamic properties of both systems deviate positively from Raoult's law, while the systems are characterized by positive interaction energy. The role of atomic size ratio on the alloying properties was discussed.

Keywords: homo-pairs, interchange energy, enthalpy, entropy, Cd-Ga, Cd-In

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Authors: Olufunke Olufunmilayo Ilemobayo, Barakat. O Abdulazeez

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Profit making among poultry egg farmers has been a challenge to efficient distribution of scarce farm resources over the years, due majorly to low capital base, inefficient management, technical inefficiency, economic inefficiency, thus poultry egg production has moved into an underperformed situation, characterised by low profit margin. Though previous studies focus mainly on broiler production and efficiency of its production, however, paucity of information exist in the areas of profit efficiency in the study area. Hence, determinants of profit efficiency among poultry egg farmers in Ondo State, Nigeria were investigated. A purposive sampling technique was used to obtain primary data from poultry egg farmers in Owo and Akure local government area of Ondo State, through a well-structured questionnaire. socio-economic characteristics such as age, gender, educational level, marital status, household size, access to credit, extension contact, other variables were input and output data like flock size, cost of feeder and drinker, cost of feed, cost of labour, cost of drugs and medications, cost of energy, price of crate of table egg, price of spent layers were variables used in the study. Data were analysed using descriptive statistics, budgeting analysis, and stochastic profit function/inefficiency model. Result of the descriptive statistics shows that 52 per cent of the poultry farmers were between 31-40 years, 62 per cent were male, 90 per cent had tertiary education, 66 per cent were primarily poultry farmers, 78 per cent were original poultry farm owners and 55 per cent had more than 5 years’ work experience. Descriptive statistics on cost and returns indicated that 64 per cent of the return were from sales of egg, while the remaining 36 per cent was from sales of spent layers. The cost of feeding take the highest proportion of 69 per cent of cost of production and cost of medication the lowest (7 per cent). A positive gross margin of N5, 518,869.76, net farm income of ₦ 5, 500.446.82 and net return on investment of 0.28 indicated poultry egg production is profitable. Equipment’s cost (22.757), feeding cost (18.3437), labour cost (136.698), flock size (16.209), drug and medication cost (4.509) were factors that affecting profit efficiency, while education (-2.3143), household size (-18.4291), access to credit (-16.027), and experience (-7.277) were determinant of profit efficiency. Education, household size, access to credit and experience in poultry production were the main determinants of profit efficiency of poultry egg production in Ondo State. Other factors that affect profit efficiency were cost of feeding, cost of labour, flock size, cost of drug and medication, they positively and significantly influenced profit efficiency in Ondo State, Nigeria.

Keywords: cost and returns, economic inefficiency, profit margin, technical inefficiency

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Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

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Authors: Mazura Mokhtar, Adibah Shuib, Daud Mohamad

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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: portfolio optimization, mathematical programming, multi-objective programming, solution approaches

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Shuhua Lai, Kairui Chen

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In this paper, we present a fast and efficient mesh coarsening algorithm for 3D triangular meshes. Theis approach can be applied to very complex 3D meshes of arbitrary topology and with millions of vertices. The algorithm is based on the clustering of the input mesh elements, which divides the faces of an input mesh into a given number of clusters for clustering purpose by approximating the Centroidal Voronoi Tessellation of the input mesh. Once a clustering is achieved, it provides us an efficient way to construct uniform tessellations, and therefore leads to good coarsening of polygonal meshes. With proliferation of 3D scanners, this coarsening algorithm is particularly useful for reverse engineering applications of 3D models, which in many cases are dense, non-uniform, irregular and arbitrary topology. Examples demonstrating effectiveness of the new algorithm are also included in the paper.

Keywords: coarsening, mesh clustering, shape approximation, mesh simplification

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Authors: Alluri Swaroopa, L. V. N. Prasad

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Alone with fast urbanization in world, traffic control problem became a big issue in urban construction. Having an efficient and reliable traffic control system is crucial to macro-traffic control. Traffic signal is used to manage conflicting requirement by allocating different sets of mutually compatible traffic movement during distinct time interval. Many approaches have been made proposed to solve this discrete stochastic problem. Recognizing the need to minimize right-of-way impacts while efficiently handling the anticipated high traffic volumes, the proposed alternative system gives effective design. This model allows for increased traffic capacity and reduces delays by eliminating a step in maneuvering through the freeway interchange. The concept proposed in this paper involves construction of bridges and ramps at intersection of four roads to control the vehicular congestion and to prevent traffic breakdown.

Keywords: bridges, junctions, ramps, urban traffic control

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Authors: Ahmed Al-Sultan

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The check-in area of airport terminal is one of the busiest sections at airports at certain periods. The passengers are subjected to queues and delays during the check-in process. These delays and queues are due to constraints in the capacity of service facilities. In this project, the airport terminal is decomposed into several check-in areas. The airport check-in scheduling problem requires both a deterministic (integer programming) and stochastic (simulation) approach. Integer programming formulations are provided to minimize the total number of counters in each check-in area under the realistic constraint that counters for one and the same flight should be adjacent and the desired number of counters remaining in each area should be fixed during check-in operations. By using simulation, the airport system can be modeled to study the effects of various parameters such as number of passengers on a flight and check-in counter opening and closing time.

Keywords: airport terminal, integer programming, scheduling, simulation

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Authors: Bakur Gulua

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In this work, we consider some boundary value problems for the plate. The plate is the elastic material with voids. The state of plate equilibrium is described by the system of differential equations that is derived from three-dimensional equations of equilibrium of an elastic material with voids (Cowin-Nunziato model) by Vekua's reduction method. Its general solution is represented by means of analytic functions of a complex variable and solutions of Helmholtz equations. The problem is solved analytically by the method of the theory of functions of a complex variable.

Keywords: the elastic material with voids, boundary value problems, Vekua's reduction method, a complex variable

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Authors: Norhashidah Hj Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula

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Authors: Ali Safdari-Vaighani

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Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.

Keywords: basket option, jump diffusion, ‎radial basis function, RBF-PUM

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Authors: F. Erdal, E. Dogan, F. E. Uz

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In this study, firefly optimization based optimum design algorithm is presented for the grillage systems. Naming of the algorithm is derived from the fireflies, whose sense of movement is taken as a model in the development of the algorithm. Fireflies’ being unisex and attraction between each other constitute the basis of the algorithm. The design algorithm considers the displacement and strength constraints which are implemented from LRFD-AISC (Load and Resistance Factor Design-American Institute of Steel Construction). It selects the appropriate W (Wide Flange)-sections for the transverse and longitudinal beams of the grillage system among 272 discrete W-section designations given in LRFD-AISC so that the design limitations described in LRFD are satisfied and the weight of the system is confined to be minimal. Number of design examples is considered to demonstrate the efficiency of the algorithm presented.

Keywords: firefly algorithm, steel grillage systems, optimum design, stochastic search techniques

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