DSpace Collection: Volume 4 Number 1
http://hdl.handle.net/10525/1537
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A Solver for ComplexValued Parametric Linear Systems
http://hdl.handle.net/10525/1586
Title: A Solver for ComplexValued Parametric Linear Systems<br/><br/>Authors: Popova, Evgenija; Kolev, Lyubomir; Krämer, Walter<br/><br/>Abstract: This work reports on a new software for solving linear systemsinvolving affinelinear dependencies between complexvalued interval parameters.We discuss the implementation of a parametric residual iterationfor linear interval systems by advanced communication between the systemMathematica and the library CXSC supporting rigorous complex intervalarithmetic. An example of AC electrical circuit illustrates the use of thepresented software.
Fri, 01 Jan 2010 00:00:00 GMT

A New Approach to Fuzzy Arithmetic
http://hdl.handle.net/10525/1585
Title: A New Approach to Fuzzy Arithmetic<br/><br/>Authors: Popov, Antony<br/><br/>Abstract: This work shows an application of a generalized approach forconstructing dilationerosion adjunctions on fuzzy sets. More precisely, operationson fuzzy quantities and fuzzy numbers are considered. By the generalizedapproach an analogy with the well known interval computations couldbe drawn and thus we can define outer and inner operations on fuzzy objects.These operations are found to be useful in the control of bioprocesses,ecology and other domains where data uncertainties exist.
Fri, 01 Jan 2010 00:00:00 GMT

Grid and Simulation of Digital Communication Systems
http://hdl.handle.net/10525/1584
Title: Grid and Simulation of Digital Communication Systems<br/><br/>Authors: Manev, Nikolai<br/><br/>Abstract: The purpose of this paper is to turn researchers' attention tothe use of grid computing for simulating digital communications and its largepotential for decreasing significantly the duration of the experiments and forimproving the statistical representativeness and reliability of the obtainedresults.
Fri, 01 Jan 2010 00:00:00 GMT

Solving Maximum Clique Problem for Protein Structure Similarity
http://hdl.handle.net/10525/1583
Title: Solving Maximum Clique Problem for Protein Structure Similarity<br/><br/>Authors: MalodDognin, Noël; Andonov, Rumen; Yanev, Nicola<br/><br/>Abstract: Computing the similarity between two protein structures isa crucial task in molecular biology, and has been extensively investigated.Many protein structure comparison methods can be modeled as maximumweighted clique problems in specific kpartite graphs, referred here as alignment graphs.In this paper we present both a new integer programming formulationfor solving such clique problems and a dedicated branch and bound algorithm for solving the maximum cardinality clique problem. Both approacheshave been integrated in VAST, a software for aligning protein 3D structureslargely used in the National Center for Biotechnology Information, an original clique solver which uses the well known Bron and Kerbosch algorithm(BK). Our computational results on real protein alignment instances showthat our branch and bound algorithm is up to 116 times faster than BK.
Fri, 01 Jan 2010 00:00:00 GMT

HighOrder Control Variations and SmallTime Local Controllability
http://hdl.handle.net/10525/1582
Title: HighOrder Control Variations and SmallTime Local Controllability<br/><br/>Authors: Krastanov, Mikhail<br/><br/>Abstract: The importance of “control variations” for obtaining local approximationsof the reachable set of nonlinear control systems is well known.Heuristically, if one can construct control variations in all possible directions,then the considered control system is smalltime locally controllable(STLC). Two concepts of control variations of higher order are introducedfor the case of smooth control systems. The relation between these variationsand the smalltime local controllability is studied and a new sufficientSTLC condition is proved.
Fri, 01 Jan 2010 00:00:00 GMT

ComputerAssisted Proofs and Symbolic Computations
http://hdl.handle.net/10525/1581
Title: ComputerAssisted Proofs and Symbolic Computations<br/><br/>Authors: Krämer, Walter<br/><br/>Abstract: We discuss some main points of computerassisted proofs basedon reliable numerical computations. Such socalled selfvalidating numericalmethods in combination with exact symbolic manipulations result in verypowerful mathematical software tools. These tools allow proving mathematicalstatements (existence of a fixed point, of a solution of an ODE, ofa zero of a continuous function, of a global minimum within a given range,etc.) using a digital computer. To validate the assertions of the underlyingtheorems fast finite precision arithmetic is used. The results are absolutelyrigorous.To demonstrate the power of reliable symbolicnumeric computations weinvestigate in some details the verification of very long periodic orbits ofchaotic dynamical systems. The verification is done directly in Maple, e.g.using the Maple Power Tool intpakX or, more efficiently, using the C++class library CXSC.
Fri, 01 Jan 2010 00:00:00 GMT

QuasiMonte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity
http://hdl.handle.net/10525/1580
Title: QuasiMonte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity<br/><br/>Authors: Karaivanova, Aneta<br/><br/>Abstract: We present quasiMonte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations,computing extreme eigenvalues, and matrix inversion. Reformulating theproblems as solving integral equations with a special kernels and domainspermits us to analyze the quasiMonte Carlo methods with bounds fromnumerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. QuasiMonte Carlomethods use quasirandom sequences with the resulting convergence rate fornumerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequencesimproves both the magnitude of the error and the convergence rate of theconsidered Monte Carlo methods. We also analyze the complexity of considered quasiMonte Carlo algorithms and compare them to the complexityof the analogous Monte Carlo and deterministic algorithms.
Fri, 01 Jan 2010 00:00:00 GMT

OneParameter Bifurcation Analysis of Dynamical Systems using Maple
http://hdl.handle.net/10525/1579
Title: OneParameter Bifurcation Analysis of Dynamical Systems using Maple<br/><br/>Authors: Borisov, Milen; Dimitrova, Neli<br/><br/>Abstract: This paper presents two algorithms for oneparameter localbifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities.
Fri, 01 Jan 2010 00:00:00 GMT

A Mathematical Basis for an Interval Arithmetic Standard
http://hdl.handle.net/10525/1578
Title: A Mathematical Basis for an Interval Arithmetic Standard<br/><br/>Authors: Bohlender, Gerd; Kulisch, Ulrich<br/><br/>Abstract: Basic concepts for an interval arithmetic standard are discussedin the paper. Interval arithmetic deals with closed and connected sets of realnumbers. Unlike floatingpoint arithmetic it is free of exceptions. A completeset of formulas to approximate real interval arithmetic on the computeris displayed in section 3 of the paper. The essential comparison relations andlattice operations are discussed in section 6. Evaluation of functions for intervalarguments is studied in section 7. The desirability of variable lengthinterval arithmetic is also discussed in the paper. The requirement to adaptthe digital computer to the needs of interval arithmetic is as old as intervalarithmetic. An obvious, simple possible solution is shown in section 8.
Fri, 01 Jan 2010 00:00:00 GMT

Mathematical Modeling for Studying Microbial Processes – Some Examples
http://hdl.handle.net/10525/1577
Title: Mathematical Modeling for Studying Microbial Processes – Some Examples<br/><br/>Authors: Beschkov, V; Sapundzhiev, T; Petrov, K; Vasileva, E<br/><br/>Abstract: Mathematical modeling may have different purposes in chemical and biochemical engineering sciences. One of them is to confirm or toreject kinetic models for certain processes, or to evaluate the importance ofsome transport phenomena on the net chemical or biochemical reaction rate.In the present paper different microbial processes are considered and modeled for evaluation of kinetic constants for batch and continuous processesaccomplished by free and immobilized microbial cells. The practical examples are from the field of wastewater treatment and biosynthesis of products,like enzymes, lactic acid, gluconic acid, etc.By the aid of mathematical modeling the kinetics and the type of inhibition are specified for microbial wastewater denitrification and biodegradation of halogenated hydrocarbons. The importance of free and immobilized cells and their separate contribution to the overall microbial processis also evaluated for some fermentation processes: gluconic acid production, dichloroethane biodegradation, lactic acid fermentation and monochloroacetic acid biodegradation.
Fri, 01 Jan 2010 00:00:00 GMT

Parameter Identification of a FedBatch Cultivation of S. Cerevisiae using Genetic Algorithms
http://hdl.handle.net/10525/1576
Title: Parameter Identification of a FedBatch Cultivation of S. Cerevisiae using Genetic Algorithms<br/><br/>Authors: Angelova, Maria; Tzonkov, Stoyan; Pencheva, Tania<br/><br/>Abstract: Fermentation processes as objects of modelling and highqualitycontrol are characterized with interdependence and timevarying of processvariables that lead to nonlinear models with a very complex structure. Thisis why the conventional optimization methods cannot lead to a satisfiedsolution. As an alternative, genetic algorithms, like the stochastic globaloptimization method, can be applied to overcome these limitations. Theapplication of genetic algorithms is a precondition for robustness and reaching of a global minimum that makes them eligible and more workable forparameter identification of fermentation models. Different types of geneticalgorithms, namely simple, modified and multipopulation ones, have beenapplied and compared for estimation of nonlinear dynamic model parametersof fedbatch cultivation of S. cerevisiae.
Fri, 01 Jan 2010 00:00:00 GMT

Stochastic Arithmetic Theory and Experiments
http://hdl.handle.net/10525/1575
Title: Stochastic Arithmetic Theory and Experiments<br/><br/>Authors: Alt, René; Lamotte, JeanLuc; Markov, Svetoslav<br/><br/>Abstract: Stochastic arithmetic has been developed as a model for exactcomputing with imprecise data. Stochastic arithmetic provides confidenceintervals for the numerical results and can be implemented in any existingnumerical software by redefining types of the variables and overloading theoperators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and thesolution to linear systems. Several numerical experiments are performedshowing the efficiency of the proposed approach.
Fri, 01 Jan 2010 00:00:00 GMT