Search results for: covering approximation space
1911 Definable Subsets in Covering Approximation Spaces
Authors: Xun Ge, Zhaowen Li
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Covering approximation spaces is a class of important generalization of approximation spaces. For a subset X of a covering approximation space (U, C), is X definable or rough? The answer of this question is uncertain, which depends on covering approximation operators endowed on (U, C). Note that there are many various covering approximation operators, which can be endowed on covering approximation spaces. This paper investigates covering approximation spaces endowed ten covering approximation operators respectively, and establishes some relations among definable subsets, inner definable subsets and outer definable subsets in covering approximation spaces, which deepens some results on definable subsets in approximation spaces.Keywords: Covering approximation space, covering approximation operator, definable subset, inner definable subset, outer definable subset.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12711910 On an Open Problem for Definable Subsets of Covering Approximation Spaces
Authors: Mei He, Ying Ge, Jingyu Qian
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Let (U;D) be a Gr-covering approximation space (U; C) with covering lower approximation operator D and covering upper approximation operator D. For a subset X of U, this paper investigates the following three conditions: (1) X is a definable subset of (U;D); (2) X is an inner definable subset of (U;D); (3) X is an outer definable subset of (U;D). It is proved that if one of the above three conditions holds, then the others hold. These results give a positive answer of an open problem for definable subsets of covering approximation spaces.Keywords: Covering approximation space, covering approximation operator, definable subset, inner definable subset, outer definable subset.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11351909 Some Separations in Covering Approximation Spaces
Authors: Xun Ge, Jinjin Li, Ying Ge
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Adopting Zakowski-s upper approximation operator C and lower approximation operator C, this paper investigates granularity-wise separations in covering approximation spaces. Some characterizations of granularity-wise separations are obtained by means of Pawlak rough sets and some relations among granularitywise separations are established, which makes it possible to research covering approximation spaces by logical methods and mathematical methods in computer science. Results of this paper give further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.Keywords: Rough set, covering approximation space, granularitywise separation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16691908 Some Algebraic Properties of Universal and Regular Covering Spaces
Authors: Ahmet Tekcan
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Let X be a connected space, X be a space, let p : X -→ X be a continuous map and let (X, p) be a covering space of X. In the first section we give some preliminaries from covering spaces and their automorphism groups. In the second section we derive some algebraic properties of both universal and regular covering spaces (X, p) of X and also their automorphism groups A(X, p).
Keywords: covering space, universal covering, regular covering, fundamental group, automorphism group.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20011907 Covering-based Rough sets Based on the Refinement of Covering-element
Authors: Jianguo Tang, Kun She, William Zhu
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Covering-based rough sets is an extension of rough sets and it is based on a covering instead of a partition of the universe. Therefore it is more powerful in describing some practical problems than rough sets. However, by extending the rough sets, covering-based rough sets can increase the roughness of each model in recognizing objects. How to obtain better approximations from the models of a covering-based rough sets is an important issue. In this paper, two concepts, determinate elements and indeterminate elements in a universe, are proposed and given precise definitions respectively. This research makes a reasonable refinement of the covering-element from a new viewpoint. And the refinement may generate better approximations of covering-based rough sets models. To prove the theory above, it is applied to eight major coveringbased rough sets models which are adapted from other literature. The result is, in all these models, the lower approximation increases effectively. Correspondingly, in all models, the upper approximation decreases with exceptions of two models in some special situations. Therefore, the roughness of recognizing objects is reduced. This research provides a new approach to the study and application of covering-based rough sets.Keywords: Determinate element, indeterminate element, refinementof covering-element, refinement of covering, covering-basedrough sets.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13131906 Approximation to the Hardy Operator on Topological Measure Spaces
Authors: Kairat T. Mynbaev, Elena N. Lomakina
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We consider a Hardy type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion and bounds for its approximation numbers. Previously bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness have been found earlier but our approach is different in that we use domain partitions for all problems under consideration.
Keywords: Approximation numbers, boundedness and compactness, multidimensional Hardy operator, Hausdorff topological space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 731905 Structure of Covering-based Rough Sets
Authors: Shiping Wang, Peiyong Zhu, William Zhu
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Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringbased rough sets through down-sets and up-sets. In this way, one can investigate covering-based rough sets from algebraic and topological points of view.
Keywords: Covering, poset, down-set, lattice, topological space, topological base.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18341904 Comparison between Beta Wavelets Neural Networks, RBF Neural Networks and Polynomial Approximation for 1D, 2DFunctions Approximation
Authors: Wajdi Bellil, Chokri Ben Amar, Adel M. Alimi
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This paper proposes a comparison between wavelet neural networks (WNN), RBF neural network and polynomial approximation in term of 1-D and 2-D functions approximation. We present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D functions approximation. Our purpose is to approximate an unknown function f: Rn - R from scattered samples (xi; y = f(xi)) i=1....n, where first, we have little a priori knowledge on the unknown function f: it lives in some infinite dimensional smooth function space and second the function approximation process is performed iteratively: each new measure on the function (xi; f(xi)) is used to compute a new estimate f as an approximation of the function f. Simulation results are demonstrated to validate the generalization ability and efficiency of the proposed Beta wavelet network.
Keywords: Beta wavelets networks, RBF neural network, training algorithms, MSE, 1-D, 2D function approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19011903 Best Co-approximation and Best Simultaneous Co-approximation in Fuzzy Normed Spaces
Authors: J. Kavikumar, N. S. Manian, M.B.K. Moorthy
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The main purpose of this paper is to consider the t-best co-approximation and t-best simultaneous co-approximation in fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets.
Keywords: Fuzzy best co-approximation, fuzzy quotient spaces, proximinality, Chebyshevity, best simultaneous co-approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16001902 Localising Gauss's Law and the Electric Charge Induction on a Conducting Sphere
Authors: Sirapat Lookrak, Anol Paisal
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Space debris has numerous manifestations including ferro-metalize and non-ferrous. The electric field will induce negative charges to split from positive charges inside the space debris. In this research, we focus only on conducting materials. The assumption is that the electric charge density of a conducting surface is proportional to the electric field on that surface due to Gauss's law. We are trying to find the induced charge density from an external electric field perpendicular to a conducting spherical surface. An object is a sphere on which the external electric field is not uniform. The electric field is, therefore, considered locally. The localised spherical surface is a tangent plane so the Gaussian surface is a very small cylinder and every point on a spherical surface has its own cylinder. The electric field from a circular electrode has been calculated in near-field and far-field approximation and shown Explanation Touchless manoeuvring space debris orbit properties. The electric charge density calculation from a near-field and far-field approximation is done.
Keywords: Near-field approximation, far-field approximation, localized Gauss’s law, electric charge density.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3671901 Searching the Efficient Frontier for the Coherent Covering Location Problem
Authors: Felipe Azocar Simonet, Luis Acosta Espejo
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In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).Keywords: Coherent covering location problem, efficient frontier, Lagrangian relaxation, data envelopment analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7931900 An Empirical Validation of the Linear- Hyperbolic Approximation of the I-V Characteristic of a Solar Cell Generator
Authors: A. A. Penin
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An empirical linearly-hyperbolic approximation of the I - V characteristic of a solar cell is presented. This approximation is based on hyperbolic dependence of a current of p-n junctions on voltage for large currents. Such empirical approximation is compared with the early proposed formal linearly-hyperbolic approximation of a solar cell. The expressions defining laws of change of parameters of formal approximation at change of a photo current of family of characteristics are received. It allows simplifying a finding of parameters of approximation on actual curves, to specify their values. Analytical calculation of load regime for linearly - hyperbolic model leads to quadratic equation. Also, this model allows to define soundly a deviation from the maximum power regime and to compare efficiency of regimes of solar cells with different parameters.
Keywords: a solar cell generator, I − V characteristic, p − n junction, approximation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14031899 Heuristic Set-Covering-Based Postprocessing for Improving the Quine-McCluskey Method
Authors: Miloš Šeda
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Finding the minimal logical functions has important applications in the design of logical circuits. This task is solved by many different methods but, frequently, they are not suitable for a computer implementation. We briefly summarise the well-known Quine-McCluskey method, which gives a unique procedure of computing and thus can be simply implemented, but, even for simple examples, does not guarantee an optimal solution. Since the Petrick extension of the Quine-McCluskey method does not give a generally usable method for finding an optimum for logical functions with a high number of values, we focus on interpretation of the result of the Quine-McCluskey method and show that it represents a set covering problem that, unfortunately, is an NP-hard combinatorial problem. Therefore it must be solved by heuristic or approximation methods. We propose an approach based on genetic algorithms and show suitable parameter settings.
Keywords: Boolean algebra, Karnaugh map, Quine-McCluskey method, set covering problem, genetic algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27851898 River Flow Prediction Using Nonlinear Prediction Method
Authors: N. H. Adenan, M. S. M. Noorani
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River flow prediction is an essential to ensure proper management of water resources can be optimally distribute water to consumers. This study presents an analysis and prediction by using nonlinear prediction method involving monthly river flow data in Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The phase space reconstruction involves the reconstruction of one-dimensional (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. Revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) have been employed to compare prediction performance for nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show the prediction results using nonlinear prediction method is better than ARIMA and SVM. Therefore, the result of this study could be used to develop an efficient water management system to optimize the allocation water resources.
Keywords: River flow, nonlinear prediction method, phase space, local linear approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23441897 Evolutionary Search Techniques to Solve Set Covering Problems
Authors: Darwin Gouwanda, S. G. Ponnambalam
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Set covering problem is a classical problem in computer science and complexity theory. It has many applications, such as airline crew scheduling problem, facilities location problem, vehicle routing, assignment problem, etc. In this paper, three different techniques are applied to solve set covering problem. Firstly, a mathematical model of set covering problem is introduced and solved by using optimization solver, LINGO. Secondly, the Genetic Algorithm Toolbox available in MATLAB is used to solve set covering problem. And lastly, an ant colony optimization method is programmed in MATLAB programming language. Results obtained from these methods are presented in tables. In order to assess the performance of the techniques used in this project, the benchmark problems available in open literature are used.Keywords: Set covering problem, genetic algorithm, ant colony optimization, LINGO.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36111896 A Model to Study the Effect of Na+ ions on Ca2+diffusion under Rapid Buffering Approximation
Authors: Vikas Tewari, K.R. Pardasani
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Calcium is very important for communication among the neurons. It is vital in a number of cell processes such as secretion, cell movement, cell differentiation. To reduce the system of reactiondiffusion equations of [Ca2+] into a single equation, two theories have been proposed one is excess buffer approximation (EBA) other is rapid buffer approximation (RBA). The RBA is more realistic than the EBA as it considers both the mobile and stationary endogenous buffers. It is valid near the mouth of the channel. In this work we have studied the effects of different types of buffers on calcium diffusion under RBA. The novel thing studied is the effect of sodium ions on calcium diffusion. The model has been made realistic by considering factors such as variable [Ca2+], [Na+] sources, sodium-calcium exchange protein(NCX), Sarcolemmal Calcium ATPase pump. The proposed mathematical leads to a system of partial differential equations which has been solved numerically to study the relationships between different parameters such as buffer concentration, buffer disassociation rate, calcium permeability. We have used Forward Time Centred Space (FTCS) approach to solve the system of partial differential equations.Keywords: rapid buffer approximation, sodium-calcium exchangeprotein, Sarcolemmal Calcium ATPase pump, buffer disassociationrate, forward time centred space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14991895 Monthly River Flow Prediction Using a Nonlinear Prediction Method
Authors: N. H. Adenan, M. S. M. Noorani
Abstract:
River flow prediction is an essential tool to ensure proper management of water resources and the optimal distribution of water to consumers. This study presents an analysis and prediction by using nonlinear prediction method with monthly river flow data for Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The reconstruction of phase space involves the reconstruction of one-dimension (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. The revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) was employed to compare prediction performance for the nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show that the prediction results using the nonlinear prediction method are better than ARIMA and SVM. Therefore, the results of this study could be used to develop an efficient water management system to optimize the allocation of water resources.
Keywords: River flow, nonlinear prediction method, phase space, local linear approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19491894 Particle Swarm Optimization and Quantum Particle Swarm Optimization to Multidimensional Function Approximation
Authors: Diogo Silva, Fadul Rodor, Carlos Moraes
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This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9611893 An Improved Prediction Model of Ozone Concentration Time Series Based On Chaotic Approach
Authors: N. Z. A. Hamid, M. S. M. Noorani
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This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly Ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.
Keywords: Chaotic approach, phase space, Cao method, local linear approximation method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17651892 A Model to Study the Effect of Excess Buffers and Na+ Ions on Ca2+ Diffusion in Neuron Cell
Authors: Vikas Tewari, Shivendra Tewari, K. R. Pardasani
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Calcium is a vital second messenger used in signal transduction. Calcium controls secretion, cell movement, muscular contraction, cell differentiation, ciliary beating and so on. Two theories have been used to simplify the system of reaction-diffusion equations of calcium into a single equation. One is excess buffer approximation (EBA) which assumes that mobile buffer is present in excess and cannot be saturated. The other is rapid buffer approximation (RBA), which assumes that calcium binding to buffer is rapid compared to calcium diffusion rate. In the present work, attempt has been made to develop a model for calcium diffusion under excess buffer approximation in neuron cells. This model incorporates the effect of [Na+] influx on [Ca2+] diffusion,variable calcium and sodium sources, sodium-calcium exchange protein, Sarcolemmal Calcium ATPase pump, sodium and calcium channels. The proposed mathematical model leads to a system of partial differential equations which have been solved numerically using Forward Time Centered Space (FTCS) approach. The numerical results have been used to study the relationships among different types of parameters such as buffer concentration, association rate, calcium permeability.
Keywords: Excess buffer approximation, Na+ influx, sodium calcium exchange protein, sarcolemmal calcium atpase pump, forward time centred space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15801891 Constant Factor Approximation Algorithm for p-Median Network Design Problem with Multiple Cable Types
Authors: Chaghoub Soraya, Zhang Xiaoyan
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This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.Keywords: Approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5781890 Packing and Covering Radii of Linear Error-Block Codes
Authors: Rabiˆı DARITI, El Mamoun SOUIDI
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Linear error-block codes are a natural generalization of linear error correcting codes. The purpose of this paper is to generalize some results on the packing and the covering radii to the error-block case. We study their properties when a code undergoes some specific modifications and combinations with another code. We give a few bounds on the packing and the covering radii of these codes.
Keywords: Linear error-block codes, π-distance, Correction capacity, Packing radius, Covering radius.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21711889 Using the Polynomial Approximation Algorithm in the Algorithm 2 for Manipulator's Control in an Unknown Environment
Authors: Pavel K. Lopatin, Artyom S. Yegorov
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The Algorithm 2 for a n-link manipulator movement amidst arbitrary unknown static obstacles for a case when a sensor system supplies information about local neighborhoods of different points in the configuration space is presented. The Algorithm 2 guarantees the reaching of a target position in a finite number of steps. The Algorithm 2 is reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the Algorithm2 implementation are given.
Keywords: Manipulator, trajectory planning, unknown obstacles.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12241888 Denoising and Compression in Wavelet Domainvia Projection on to Approximation Coefficients
Authors: Mario Mastriani
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We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the approximation subband coefficients (much less noisy). The new algorithm is called Projection Onto Approximation Coefficients (POAC). As a result of this approach, only the approximation subband coefficients and three scalars are stored and/or transmitted to the channel. Besides, with the elimination of the details subbands coefficients, we obtain a bigger compression rate. Experimental results demonstrate that our approach compares favorably to more typical methods of denoising and compression in wavelet domain.
Keywords: Compression, denoising, projections, wavelets.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16061887 A Note on Negative Hypergeometric Distribution and Its Approximation
Authors: S. B. Mansuri
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In this paper, at first we explain about negative hypergeometric distribution and its properties. Then we use the w-function and the Stein identity to give a result on the poisson approximation to the negative hypergeometric distribution in terms of the total variation distance between the negative hypergeometric and poisson distributions and its upper bound.Keywords: Negative hypergeometric distribution, Poisson distribution, Poisson approximation, Stein-Chen identity, w-function.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 30721886 A Comparison of Recent Methods for Solving a Model 1D Convection Diffusion Equation
Authors: Ashvin Gopaul, Jayrani Cheeneebash, Kamleshsing Baurhoo
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In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.
Keywords: Chebyshev Pseudospectral collocation method, convection-diffusion equation, restrictive Taylor approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16651885 The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation
Authors: Yongxin Yuan, Hao Liu
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In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw
Keywords: Inverse problem, Least-squares solution, model updating, Singular value decomposition (SVD), Optimal approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16351884 Approximation Algorithm for the Shortest Approximate Common Superstring Problem
Authors: A.S. Rebaï, M. Elloumi
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The Shortest Approximate Common Superstring (SACS) problem is : Given a set of strings f={w1, w2, ... , wn}, where no wi is an approximate substring of wj, i ≠ j, find a shortest string Sa, such that, every string of f is an approximate substring of Sa. When the number of the strings n>2, the SACS problem becomes NP-complete. In this paper, we present a greedy approximation SACS algorithm. Our algorithm is a 1/2-approximation for the SACS problem. It is of complexity O(n2*(l2+log(n))) in computing time, where n is the number of the strings and l is the length of a string. Our SACS algorithm is based on computation of the Length of the Approximate Longest Overlap (LALO).Keywords: Shortest approximate common superstring, approximation algorithms, strings overlaps, complexities.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14941883 Finite Element Approximation of the Heat Equation under Axisymmetry Assumption
Authors: Raphael Zanella
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This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit time marching. The code is verified by space and time convergence tests using a manufactured solution. An example problem is solved with an axisymmetric formulation and with a 3D formulation. Both formulations lead to the same result but the code based on the axisymmetric formulation is mush faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest of using an axisymmetric formulation when it is possible.
Keywords: Axisymmetric problem, continuous finite elements, heat equation, weak formulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3211882 A Robust LS-SVM Regression
Authors: József Valyon, Gábor Horváth
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In comparison to the original SVM, which involves a quadratic programming task; LS–SVM simplifies the required computation, but unfortunately the sparseness of standard SVM is lost. Another problem is that LS-SVM is only optimal if the training samples are corrupted by Gaussian noise. In Least Squares SVM (LS–SVM), the nonlinear solution is obtained, by first mapping the input vector to a high dimensional kernel space in a nonlinear fashion, where the solution is calculated from a linear equation set. In this paper a geometric view of the kernel space is introduced, which enables us to develop a new formulation to achieve a sparse and robust estimate.Keywords: Support Vector Machines, Least Squares SupportVector Machines, Regression, Sparse approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2051