Carlo Cattani

Gani Aldashev

Shengyong Chen

Mathematical Problems in Engineering

English

Cattani, Carlo

Chen, Shengyong

Aldashev, Gani

Repository of the University of Namur

Information and modeling in complexity 2013

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Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013, Article ID 797368, 2 pageshttp://dx.doi.org/10.1155/2013/797368EditorialInformation and Modeling in Complexity 2013Carlo Cattani,1 Shengyong Chen,2 and Gani Aldashev31 Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy2 School of Computer Science, Zhejiang University of Technology, Hangzhou 310023, China3Department of Economics, University of Namur, Rempart de la Vierge 8, 5000 Namur, BelgiumCorrespondence should be addressed to Carlo Cattani; ccattani@unisa.itReceived 5 August 2013; Accepted 5 August 2013Copyright © 2013 Carlo Cattani et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Recent research in engineering systems builds theories rep-resented by mathematical models that aim at understandingfundamental questions of spatial structure, self-organization,environmental interaction, behavior, and development.Thus,researchers and engineers are increasingly facing the chal-lenge of dealing with complexity in practical applications thatare based on efficient mathematical models.The topics that deal with these issues can be dividedinto two parts: (i) development of general mathematicalmethods/models and (ii) specific applications in particulardomains.The focus of this issue on topics of information andmodeling complexity is both on themathematicalmodels andthe engineering applications in complex systems. Moreover,we are interested in both new theoretical developments andthe studies of practical implementation concerning model-ing, complexity, fractals, statistics, and signal extraction andtransformation.Complex systems, such as living systems, are often main-tained by information flows. Signals extract such informationfrom the complex phenomena being measured. Such signalsare typically a time series having both a regular and a randomcomponent. Solutions of the arising mathematical problemsattempt to map general principles for modeling how thecomplex systems operate. This area is a burgeoning fieldof research due to both the practical significance of theapplications and the general scientific importance.Further to the 63 submissions in 2012, the special issuereceives 94 new submissions in 2013. After a rigorous reviewprocess, 36 papers, that is, a 38.3% acceptance rate, whichrepresent a good panel in the related new development,are selected in the journal, with the topics being connectedwith modeling of complex systems, computational issuesin dynamical systems, signal processing of complex infor-mation, complexity and parameters, entropy, multifractality,Hurst exponent, correlation, power spectrum, and practicalapplications.In the category of modeling, M. Scalia et al. study theJohnson noise in biological matter, L. Wu et al. propose acontextual hierarchical part-driven conditional random fieldmodel for object category detection, and M. Li and W. Zhaoinvestigate on 1 over 𝑓 noise. L. Zhu et al. propose a bilayerresource model for cloud manufacturing services. L. Wu etal. study the inverse 1-median problem on tree networks withvariable real edge lengths. L. Luo et al. present maximumvariance hashing via column generation. J. Hu et al. show theadaptive multilevel kernel machine for scenic classification.X. Duan et al. propose a Shannon-Runge-Kutta-Gill methodfor convection-diffusion equations. H. Ma et al. presentstrong list edge coloring of subcubic graphs. J. Leng etal. construct bivariate nonseparable compactly supportedorthogonal wavelets. Z.-W. Li et al. propose a dynamicallyweighted clique evolution model in clique networks. B.Nouhi et al. study chaotic charged system search with afeasible-based method for constraint optimization problems.L. Huang et al. propose a dynamics-based stranded-crowdmodel for evacuation in building bottlenecks. E. G. Bakhoumand C. Toma make modeling transitions in complex systemsby multiplicative effect of temporal patterns extracted fromsignal flows.On computational issues, M. Aktas and E. Agcakocastudy the impact of the HMCFRP ratio on the strengtheningof steel composite I-beams. M. Li represents a smoothedspectrum estimate with the Cauchy integral. S. Liu et al.show approximation slack scaling for structural support2 Mathematical Problems in Engineeringvector machines in scene depth analysis. C. Biscarini et al.make detailed simulation of complex hydraulic problemswith macroscopic and mesoscopic mathematical methods.D. Sendrescu proposes parameter identification of anaerobicwastewater treatment bioprocesses using particle swarmoptimization. M. Chen et al. construct a cloud computingplatform for an onlinemodel library system. Z. Lu et al. studynormality of Ethernet traffic at large time scales. X. Huanget al. propose a marching cubes algorithm for fast modelingof human face by incremental data fusion. P.-G. Popescu etal. present new inequalities between information measuresof network information content. X. Xu et al. give a hybriddiscrete differential evolution algorithm for lot splitting withcapacity constraints in flexible job scheduling. H. Pan et al.review recent modeling for deformable body and motionanalysis. K. Guo et al. propose a differential and statisticalapproach to partial model matching. J. Zhang et al. proposea multiobjective quantum evolutionary algorithm for thevehicle routing problem with customer satisfaction.On practical applications, Z. Lu et al. give stationaritytesting of accumulated Ethernet traffic. Y. Niu et al. work onairborne infrared and visible image fusion for target percep-tion based on target region segmentation and discrete wavelettransform. F. Su et al. identify adaptive color features inimage for object tracking. D. Zhang et al. show humanmodeladaptation for multiview markerless motion capture. Y.-S.Juang et al. make fast texture synthesis in adaptive waveletpacket trees. F.-H. Cheng and T.-Y. Sung merge static anddynamic depth cues with optical-flow recovery for creatingstereo videos. A. Marucci et al. study energy efficiency of agreenhouse for the conservation of forestry biodiversity. H.Cai et al. propose entropy-based maximally stable extremalregions for robust feature detection. C. B. Guure and N. A.Ibrahim use Bayesian analysis of the survival function andfailure rate of Weibull distribution with censored data.Nevertheless, this special issue is not intended to consti-tute a complete compendium on the topic, but it does offerthe reader an opportunity to appreciate the possibilities andthe progress in the research area. It can be seen that althoughsome models and solutions become available, most problemsremain open and research is highly active in this field. We areaware of the present and upcoming research progress in thefield.AcknowledgmentsAs guest editors of this special issue, wewould like to thank allthe authors for their valuable contributions and the refereesfor their thorough reviews and helpful comments on thepapers.Carlo CattaniShengyong ChenGani AldashevSubmit your manuscripts athttp://www.hindawi.comHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014MathematicsJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Mathematical Problems in EngineeringHindawi Publishing Corporationhttp://www.hindawi.comDifferential EquationsInternational Journal ofVolume 2014Applied MathematicsJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Probability and StatisticsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Journal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Mathematical PhysicsAdvances inComplex AnalysisJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014OptimizationJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014CombinatoricsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014International Journal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Operations ResearchAdvances inJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Function SpacesAbstract and Applied AnalysisHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014International Journal of Mathematics and Mathematical SciencesHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014AlgebraDiscrete Dynamics in Nature and SocietyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Decision SciencesAdvances inDiscrete MathematicsJournal ofHindawi Publishing Corporationhttp://www.hindawi.comVolume 2014 Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Stochastic AnalysisInternational Journal of

Information and Modeling in Complexity 2013

CATTANI, Carlo

Archivio della Ricerca - Università di Salerno

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2012, Article ID 868413, 3 pagesdoi:10.1155/2012/868413EditorialInformation and Modeling in ComplexityCarlo Cattani,1 Shengyong Chen,2 and Gani Aldashev31 Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy2 Department of Computer Science, Zhejiang University of Technology, 310023 Hangzhou, China3 Department of Economics, University of Namur, Rempart de la Vierge 8, 5000 Namur, BelgiumCorrespondence should be addressed to Carlo Cattani, ccattani@unisa.itReceived 13 February 2012; Accepted 13 February 2012Copyright q 2012 Carlo Cattani et al. This is an open access article distributed under the CreativeCommons Attribution License, which permits unrestricted use, distribution, and reproduction inany medium, provided the original work is properly cited.1. Overview of the IssueCurrent research in engineering systems builds theories represented by mathematicalmodels that aim at understanding fundamental questions of systems’ spatial structure,self-organization, environmental interaction, behaviour, and development. Thus, engineersare increasingly facing the challenge of dealing with complexity in advanced engineeringapplications that are based on efficient mathematical models.The topics that deal with these issues can be divided into two large parts: (i)development of general mathematical methods/models, and (ii) specific applications inparticular domains.The focus of this issue on topics of information and modeling complexity is both onthe mathematical models and the engineering applications in complex systems. Moreover,we are interested in both new theoretical developments and the studies of practicalimplementation concerning modeling, complexity, fractals, statistics, and signal extractionand transformation.The complexity theory is the analysis of complex systems, which can be approachedfrom many different points of view. Mathematically it refers to nonlinear dynamical systemswhich are very sensitive to initial conditions, in a such way that a small perturbation of thesecould have unpredictable consequences on the evolution equations. Moreover the futurebehaviour or long-term prediction of the system cannot be fully determined, so that theuniqueness of the solution fails. Complex systems were also related to chaotic systems andto chaos dynamics. Common sense reasoning might lead one to believe that complexity andchaos should be considered as the same characteristic of the state of disorder. However, thesetwo concepts should not be confused, since they refer to different questions. A chaotic system2 Mathematical Problems in Engineeringis a disordered state which follows from the strong dependence on initial conditions, fromthe existence of some attractors and dense periodic orbits. The strong dependence on initial-boundary conditions means that a small variation thereof, from one initial state to anothervery close, could lead to some different future orbits. In other words, the time evolutionfor two very close states is divergent in future. Sometime a state of disorder can be alsoconsidered as a random state. In other words, one can hardly understand from observedexperimental data if they come from the evolution of a chaotic system or if they are simply acollection of random values. Frequency analysis, wavelet analysis, power spectrum method,information theory, entropy, and fractal dimension are expedient tools which enable us toanalyze data trying to single out some deterministic time series by removing what can beconsidered a pure random process.A key issue in all fields of complexity is the signal extraction and processing. In fact,signals extract such information from the complex phenomena being measured; therefore,the signal analysis can be used to study the complex phenomena. However, a main difficultycomes from the fact that signals are typically some time series having both a regular anda random component. Separating these two components is the essence of signal extractionproblem.Randomness, multifractality and chaos are also epitomizing features of complexity. Acomplex system can be also considered as a chaotic system, in the sense that it can be sensitiveto initial conditions, that its evolution could be also disturbed by some random noise andthat it shows some noninteger dimensions typical of fractals. However, a complex system ischaracterized by some more interesting features, such as a multiparametric dependence orself-organizing multiscale activity. Indeed, being a multidisciplinary topic, complexity doesnot have a unique definition. We can roughly define complexity as one of the following three:(1) scale transition from a micro- to macroscale, such that a disordered set ofindividuals behaves as sole entity;(2) the analysis of a unique entity resulting from the interaction of many parts;(3) transition from disorder to organization.It is clear that a special feature of complex system is the organization or self-organization arising from a chaotic-random state. However, there are still some open debateson a clear definition of organization. We can assume for organization the meaning ofpredictable, in the sense that there exists a dynamical system able to describe the evolutionof the complex system when it is organized. The transition from disorder to organization isstill unclear. Many models propose the emergence of order as the scale transition from themicroscale, where each individual is characterized by its own activity, to a macroscale wheremore individuals agree on a unique strategy, which could be different from the usual activityat the microscale.Self-organizing complex systems are often/essentially maintained by informationflows, thus implying the quantification of information. Fundamental tools of signalprocessing have been recently developed from the elementary topics of compression data,storing and communicating data into more broad applications of information theory suchas neurobiology, Internet networks, language processing, quantum computing, data mining,and many more. Any information flow is characterized by a measure, originally given byShannon, related to uncertainty and disorder in the flow. Shannon entropy is the mostpopular tool to give a measure of the uncertainty in predicting the evolution of a stochasticvariable. More outcomes have a variable, the higher is the entropy, so that this measure canMathematical Problems in Engineering 3be also taken as the measure of randomness: the higher is the entropy, the more random is thevariable evolution. Many alternative definitions of the Shannon entropy have been recentlyproposed starting from the Kolmogorov-Sinai entropy, Rényi entropy, topological entropy,and so forth.The theory of complexity applied to advanced engineering systems requires subtle andefficient mathematical models obtained by developing classical tools for complex systems.The increasing demand for engineering systems able to handle complex phenomena isnowadays pushing scholar’s investigations in all directions of knowledge, such as medicalbiological and visual systems, environment, optimisation, structural complexity, advancedcomposite material, vibrations, social science, economy, Internet architecture, and processingin networks.The analysis of general principles that lie behind these problems in so many differentfields, transversally across different specific applications is the area of highly active research.Solutions of the arising mathematical problems attempt to map general principles formodeling how the complex systems operate. This area is a burgeoning field of research dueto both the practical significance of the applications and the general scientific importance.From the current states and trends in the issue and related topics of informationand modelling in complexity, although some solutions and models become available, mostproblems remains open and research is highly active in this field. In the near future, we expectmany more contributions that will address all of the key aspects raised above, in particular,the development of general mathematical methods and models, analyses of practical signal-extraction problems, and applications in the study of self-organizing problems in socialsciences.Carlo CattaniShengyong ChenGani AldashevSubmit your manuscripts athttp://www.hindawi.com OperationsResearchAdvances inHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Mathematical Problems in EngineeringAbstract and Applied AnalysisHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013ISRN Applied MathematicsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Hindawi Publishing Corporationhttp://www.hindawi.comVolume 2013International Journal ofCombinatoricsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Journal of Function Spaces and ApplicationsInternational Journal of Mathematics and Mathematical SciencesHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013ISRN GeometryHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Discrete Dynamics in Nature and SocietyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Hindawi Publishing Corporationhttp://www.hindawi.comVolume 2013Advances inMathematical PhysicsISRN AlgebraHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013ProbabilityandStatisticsJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013ISRN Mathematical AnalysisHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Journal ofApplied MathematicsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013 Advances inDecisionSciencesHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2013Stochastic AnalysisInternational Journal ofHindawi Publishing Corporation http://www.hindawi.com Volume 2013The Scientific World JournalHindawi Publishing Corporationhttp://www.hindawi.com Volume 2013ISRN Discrete Mathematics Hindawi Publishing Corporationhttp://www.hindawi.comDifferential EquationsInternational Journal ofVolume 2013

Information and Modeling in Complexity

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2012, Article ID 868413, 3 pagesdoi:10.1155/2012/868413EditorialInformation and Modeling in ComplexityCarlo Cattani,1 Shengyong Chen,2 and Gani Aldashev31 Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy2 Department of Computer Science, Zhejiang University of Technology, 310023 Hangzhou, China3 Department of Economics, University of Namur, Rempart de la Vierge 8, 5000 Namur, BelgiumCorrespondence should be addressed to Carlo Cattani, ccattani@unisa.itReceived 13 February 2012; Accepted 13 February 2012Copyright q 2012 Carlo Cattani et al. This is an open access article distributed under the CreativeCommons Attribution License, which permits unrestricted use, distribution, and reproduction inany medium, provided the original work is properly cited.1. Overview of the IssueCurrent research in engineering systems builds theories represented by mathematicalmodels that aim at understanding fundamental questions of systems’ spatial structure,self-organization, environmental interaction, behaviour, and development. Thus, engineersare increasingly facing the challenge of dealing with complexity in advanced engineeringapplications that are based on eﬃcient mathematical models.The topics that deal with these issues can be divided into two large parts: idevelopment of general mathematical methods/models, and ii specific applications inparticular domains.The focus of this issue on topics of information and modeling complexity is both onthe mathematical models and the engineering applications in complex systems. Moreover,we are interested in both new theoretical developments and the studies of practicalimplementation concerning modeling, complexity, fractals, statistics, and signal extractionand transformation.The complexity theory is the analysis of complex systems, which can be approachedfrom many diﬀerent points of view. Mathematically it refers to nonlinear dynamical systemswhich are very sensitive to initial conditions, in a such way that a small perturbation of thesecould have unpredictable consequences on the evolution equations. Moreover the futurebehaviour or long-term prediction of the system cannot be fully determined, so that theuniqueness of the solution fails. Complex systems were also related to chaotic systems andto chaos dynamics. Common sense reasoning might lead one to believe that complexity andchaos should be considered as the same characteristic of the state of disorder. However, thesetwo concepts should not be confused, since they refer to diﬀerent questions. A chaotic system2 Mathematical Problems in Engineeringis a disordered state which follows from the strong dependence on initial conditions, fromthe existence of some attractors and dense periodic orbits. The strong dependence on initial-boundary conditions means that a small variation thereof, from one initial state to anothervery close, could lead to some diﬀerent future orbits. In other words, the time evolutionfor two very close states is divergent in future. Sometime a state of disorder can be alsoconsidered as a random state. In other words, one can hardly understand from observedexperimental data if they come from the evolution of a chaotic system or if they are simply acollection of random values. Frequency analysis, wavelet analysis, power spectrum method,information theory, entropy, and fractal dimension are expedient tools which enable us toanalyze data trying to single out some deterministic time series by removing what can beconsidered a pure random process.A key issue in all fields of complexity is the signal extraction and processing. In fact,signals extract such information from the complex phenomena being measured; therefore,the signal analysis can be used to study the complex phenomena. However, a main diﬃcultycomes from the fact that signals are typically some time series having both a regular anda random component. Separating these two components is the essence of signal extractionproblem.Randomness, multifractality and chaos are also epitomizing features of complexity. Acomplex system can be also considered as a chaotic system, in the sense that it can be sensitiveto initial conditions, that its evolution could be also disturbed by some random noise andthat it shows some noninteger dimensions typical of fractals. However, a complex system ischaracterized by some more interesting features, such as a multiparametric dependence orself-organizing multiscale activity. Indeed, being a multidisciplinary topic, complexity doesnot have a unique definition. We can roughly define complexity as one of the following three:1 scale transition from a micro- to macroscale, such that a disordered set ofindividuals behaves as sole entity;2 the analysis of a unique entity resulting from the interaction of many parts;3 transition from disorder to organization.It is clear that a special feature of complex system is the organization or self-organization arising from a chaotic-random state. However, there are still some open debateson a clear definition of organization. We can assume for organization the meaning ofpredictable, in the sense that there exists a dynamical system able to describe the evolutionof the complex system when it is organized. The transition from disorder to organization isstill unclear. Many models propose the emergence of order as the scale transition from themicroscale, where each individual is characterized by its own activity, to a macroscale wheremore individuals agree on a unique strategy, which could be diﬀerent from the usual activityat the microscale.Self-organizing complex systems are often/essentially maintained by informationflows, thus implying the quantification of information. Fundamental tools of signalprocessing have been recently developed from the elementary topics of compression data,storing and communicating data into more broad applications of information theory suchas neurobiology, Internet networks, language processing, quantum computing, data mining,and many more. Any information flow is characterized by a measure, originally given byShannon, related to uncertainty and disorder in the flow. Shannon entropy is the mostpopular tool to give a measure of the uncertainty in predicting the evolution of a stochasticvariable. More outcomes have a variable, the higher is the entropy, so that this measure canMathematical Problems in Engineering 3be also taken as the measure of randomness: the higher is the entropy, the more random is thevariable evolution. Many alternative definitions of the Shannon entropy have been recentlyproposed starting from the Kolmogorov-Sinai entropy, Re´nyi entropy, topological entropy,and so forth.The theory of complexity applied to advanced engineering systems requires subtle andeﬃcient mathematical models obtained by developing classical tools for complex systems.The increasing demand for engineering systems able to handle complex phenomena isnowadays pushing scholar’s investigations in all directions of knowledge, such as medicalbiological and visual systems, environment, optimisation, structural complexity, advancedcomposite material, vibrations, social science, economy, Internet architecture, and processingin networks.The analysis of general principles that lie behind these problems in so many diﬀerentfields, transversally across diﬀerent specific applications is the area of highly active research.Solutions of the arising mathematical problems attempt to map general principles formodeling how the complex systems operate. This area is a burgeoning field of research dueto both the practical significance of the applications and the general scientific importance.From the current states and trends in the issue and related topics of informationand modelling in complexity, although some solutions and models become available, mostproblems remains open and research is highly active in this field. In the near future, we expectmany more contributions that will address all of the key aspects raised above, in particular,the development of general mathematical methods and models, analyses of practical signal-extraction problems, and applications in the study of self-organizing problems in socialsciences.Carlo CattaniShengyong ChenGani AldashevSubmit your manuscripts athttp://www.hindawi.comHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014MathematicsJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Mathematical Problems in EngineeringHindawi Publishing Corporationhttp://www.hindawi.comDifferential EquationsInternational Journal ofVolume 2014Applied MathematicsJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Probability and StatisticsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Journal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Mathematical PhysicsAdvances inComplex AnalysisJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014OptimizationJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014CombinatoricsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014International Journal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Operations ResearchAdvances inJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Function SpacesAbstract and Applied AnalysisHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014International Journal of Mathematics and Mathematical SciencesHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014AlgebraDiscrete Dynamics in Nature and SocietyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Decision SciencesAdvances inDiscrete MathematicsJournal ofHindawi Publishing Corporationhttp://www.hindawi.comVolume 2014 Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Stochastic AnalysisInternational Journal of

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Information and Modeling in Complexity 2013

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