Eighth Workshopon

Mathematical Modellingof

Environmental and Life Sciences Problems

Constanta, October 21–24, 2010

ROMANIAN ACADEMY“Gheorghe Mihoc - Caius Iacob” Institute of Mathematical Statistics and

Applied MathematicsDepartment of Applied Mathematics

Bucharest, Romania

“OVIDIUS” UNIVERSITYFaculty of Mathematics and InformaticsResearch Center of Applied Mathematics

Constanta, Romania

sponsored by

BITDEFENDER Bucharest

Scientific Prof. Dr. Dorel HomentcovschiCommittee Acad. Marius Iosifescu

Prof. Dr. Alexandru MoregaProf. Dr. Ulrich RudeProf. Dr. Christoph SchnorrProf. Dr. Harry Vereeken

Organizing Prof. Dr. Marius CraciunCommittee Dr. Stelian Ion

Dr. Gabriela MarinoschiProf. Dr. Constantin Popa

Conference Dr. Elena PelicanSecretariat Dr. Aurelian Nicola

CONFERENCE PROGRAMME

THURSDAY OCTOBER 21

16.00-19.00 Registration

FRIDAY OCTOBER 22

9.00-10.00 Opening ceremony10.00-11.00 Invited lectures11.00-11.15 Coffee break11.15-12.15 Invited lectures12.15-15.00 Lunch break and visit at Maritime University15.00-16.00 Lectures16.00-16.15 Coffee break16.15-17.15 Lectures17.15-17.30 Coffee break17.30-18.00 Public lecture19.00-23.00 Banquet

SATURDAY OCTOBER 23

9.00-10.00 Invited lectures10.00-10.15 Coffee break10.15-11.15 Invited lectures11.15-11.30 Coffee break11.30-12.30 Lectures12.30-12.45 Coffee break12.45-13.45 Lectures13.45-14.00 Closing ceremony

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Lectures schedule

FRIDAY OCTOBER 22

10.00-12.15 Invited lecturesModerators Gabriela Marinoschi, Olivian Simionescu-Panait1 Florin Gh. Filip

Building Decision Support Systems2 Gabriela Marinoschi

Numerical approach to the population dynamics model———————-Coffee break———————

3 Stelian IonExploratory data analysis tools

4 A.M. Morega, A.A. Dobre and M. MoregaComputational Domains out of Medical Imaging Reconstruction for MoreRealistic, Patient-Related Numerical Simulations in Medical Physics

15.00-18.00 LecturesModerators Alexadru Morega, Adrian Carabineanu5 Alexei Leahu and Carmen Lupu

EM algorithm for zero truncated binomially mixed exponential (EB) dis-tribution

6 Stefan V. StefanescuApplying Monte Carlo simulation techniques in biology

7 Mihaela PricopConvergence analysis of penalized maximum likelihood estimators for lin-ear inverse problems with Poisson noise

———————-Coffee break———————8 Adrian Carabineanu

An Inverse method for the Study of the Seepage from Earthen Channels9 Stefan-Gicu Cruceanu and Dorin Marinescu

Cellular exclusion algorithm for parameter estimation with applicationsin biology models

10 M. Sammany, E. Pelican, and H. Al- NajarApproximating Functions of Vertical Atmospheric Temperature ProfilesRetrieved from the Solutions of Fredholm First Kind Integral Equation

———————-Coffee break———————11 Neculai Andrei

Public lecture: The science metamorphoses

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SATURDAY OCTOBER 23

9.00-11.15 Invited lecturesModerators Stelian Ion, Constantin Popa12 Dirk Breitenreicher, Jan Lellmann, Stefania Petra, Christoph

SchnorrCompressed Sensing and Sparse Representation: Theory and Applications

13 Emil Oanta and Cornel PanaitAdvanced Modeling of an Internal Combustion Engine Structural Problem

———————-Coffee break———————14 Gheorghe Juncu, Aurelian Nicola, Constantin Popa

Iterative methods for the numerical solution of the multicomponent masstransfer equations

15 Olivian Simionescu-PanaitElectromechanics of solid continua subject to a bias

11.30-13.45 LecturesModerators Neculai Andrei, Stefan Stefanescu

———————-Coffee break———————16 Danut Argintaru and Eliodor Constantinescu

Global Analysis and Cluster Algorithm for Jet Studies17 Mioara Alina Nicolaie

EM -algorithm: parameter estimation method in different approaches tocompeting risks data with missing causes of failure

18 Stefan-Gicu Cruceanu and Ana Maria RaducanArclength continuation to determine equilibrium points in dynamical sys-tems

———————-Coffee break———————19 A.M. Morega, A.A. Dobre, M.C. Ipate, M. Morega

Electrical Activity of the Heart by Numerical Simulation20 Anca Veronica Ion and Stelian Ion

Cellular automaton model of the soil erosion21 Dumitru Popescu

The modeling of the first cycle of a pulsatory lipid vesicle

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Abstracts

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Global Analysis and Cluster Algorithm for Jet Studiesby

Danut Argintaru and Eliodor Constantinescu

The hierarhical jet-finder algorithm “weight center method” is used to ev-idence nuclear matter jets in light-ion induced reactions at 4.5 A GeV/c.The shape of the events, expressed through the sphericity tensor and itsassociated quantities: sphericity, acoplanarity and flow angle is correlatedwith the different jet-classes: singlejet events, two-jet events, etc. The jetstructure of the events and their shapes are indications about the particleproduction mechanisms. The experiments have been performed in the frameof the SKM 200 Collaboration from JINR Dubna.

Compressed Sensing and Sparse Representation: Theory andApplications

byDirk Breitenreicher, Jan Lellmann, Stefania Petra, Christoph

Schnorr

Finding the sparsest solution of an underdetermined system is intimatelylinked to a subject called compressed sensing. This new sampling theory wasrecently proposed by Terry Tao, Emmanuel Candes, Justin Romberg andDavid Donoho. It is about acquiring a sparse signal in the most efficientway possible (subsampling) with the help of an adequate linear operator .The main theoretical findings in this field have mostly centered on1) the design and number of the linear measurements necessary for acquiringthe sparse signal and2) the attendant nonlinear reconstruction techniques needed to reconstructthese signals.In other words, once a signal is known to be sparse in a specific basis, one ofthe main challenge is to find the linear operator (producing the compressedmeasurements) and the respective nonlinear solver that reconstructs theoriginal full signal. Solving this type of system does not involve solving aleast-square problem but usually involves the use of l1 minimization.The same technique is used to implement the astounding single pixel cameraat Rice. We sketch further applications: tomographical particle image recon-struction, face recognition and sparse template-based shape representationfor image segmentation.

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An Inverse method for the Study of the Seepage from EarthenChannels

byAdrian Carabineanu

The free boundary problem of the seepage from a channel is treated as aconformal mapping problem which is investigated by means of Levi-Civita’smethod. For various values of the coefficients of the series expansion ofLevi-Civita’s functions one obtains various contours of the channel.

Arclength continuation to determine equilibrium points in dynamicalsystems

byStefan-Gicu Cruceanu and Ana Maria Raducan

In modeling with dynamical system of ordinary differential equations (ODEs),dx

dt= F (λ, x), one often has to study and describe the behavior of phase

portraits under changes in the parameter λ. The values of λ for which thisbehavior changes qualitatively are called bifurcations. In this paper, we areconsidering the problem of computing the solution branches for a nonlinearsystem of equations F (λ, x) = 0 using an arclength continuation algorithm.These branches are the equilibrium solutions and our proposed algorithmcan handle special points where a natural method using parametrizationwith respect to λ will have difficulties.

Cellular exclusion algorithm for parameter estimation withapplications in biology models

byStefan-Gicu Cruceanu and Dorin Marinescu

We are considering a class of biological phenomena described by ordinarydifferential equations (ODEs). The problem we focus on consists of deter-mining the best parameters fitting a given set of observable data. In thisarticle, we report on a new method to find the global minima of the costfunction associated to this problem.

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Building Decision Support Systemsby

Florin Gh. Filip

This paper aims at reviewing several aspects concerning the process of de-signing and constructing DSS( decision support systems), a particular classof information systems meant to help the knowledge workers to make andtake effective decisions for the complex problems that really count. By tak-ing into account various approaches, the paper describes the basic steps ofthe building process. The usage of rapid prototyping is recommended to-gether with the main ISO standards in the field. The usage of MADM (multi-attribute decision making) in choosing the appropriate pieces of soft-ware is described. Several methods for evaluating the project and elementson the integration of the DSS in the enterprise and its global informationsystem are finally given.

Cellular automaton model of the soil erosionby

Anca Veronica Ion and Stelian Ion

The cellular automata models of the soil erosion by rainfall are character-ized by very complex transition functions. It is so because the transitionfunction must simulate the dynamical coupled processes of rainfall, rainoff,infiltration and sediment transport by water moving. Some existing modelsare reviewed and a new one is proposed.

Exploratory data analysis toolsby

Stelian Ion

In this lecture we review some mathematical tools to analyze ecologicaldata. We focus on cluster analysis, linear regression analysis and graphicalmethods. Cluster analysis is the organization of a collection of objects intocluster based on similarity. The clustering process involves the followingsteps: object representation, object proximity, grouping step, validation ofthe clusters.As any clustering algorithm produces a cluster structure, is fundamental to

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know if the structure is valid or not and how many clusters are there. Weaddress this problems by considering the cophenetic correlation coefficient,statistical significance of the cophenetic index and the stable associationwith respect to the number of the species in the ecological data matrix.A mathematical issue on multiple linear regression is to estimate the param-eters in the linear regression disposing on a set of the measurements of thevariables in the model. We discuss the bootstrap and jackknife resamplingtechniques in view to estimate the parameters, covariance matrix and con-fidence interval.The graphical methods are strongly recommended by the ecology practition-ers. The visualization of data in their both aspects, space and time distri-bution can uncover the underlying structure, tendency or detect anomalies.We present a graphical visualization method that can be used to study theplants associations.

Iterative methods for the numerical solution of the multicomponentmass transfer equations

byGheorghe Juncu, Aurelian Nicola, Constantin Popa

The mass transfer (diffusion) in multicomponent mixtures is of centralrelevance in nature and industrial processes. Its modeling and simulationare crucial aspects in engineering sciences. For these reasons, the need ofaccurate and efficient numerical schemes to solve the diffusion–convection–reaction equations modeling transport in multicomponent systems is wellrecognized.From a general point of view, two formalisms describe the multicomponentdiffusion: the first one has been proposed by Maxwell and Stefan, whereasthe second is based on the Fick law of diffusion. The two formulations arefully equivalent. In this work, the generalized Fick approach was considered.The aim of the present work is to analyze the numerical performances ofthe preconditioned conjugate gradient algorithms (CGLS and GMRES) insolving multicomponent mass transfer equations. The test problems arelinear diffusion-reaction equations and linear convection-diffusion equations.The mathematical model equations were discretized with the central finitedifference scheme. Left and right preconditioning with block LU (Cholesky)and block incomplete LU (Cholesky) decomposition of the discrete blockLaplace operator was tested. The influence of the preconditioning on themesh behavior of the convergence rate was studied. The numerical results

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obtained show very satisfactory numerical performances.We may conclude that, for linear 2D multicomponent diffusion equations,the preconditioned conjugate gradient algorithm should be an attractivenumerical alternative. The extension of the present work to the nonlinearmulticomponent diffusion equations will be a challenge for the near futurework

EM algorithm for zero truncated binomially mixed exponential (EB)distribution

byAlexei Leahu and Carmen Lupu

In this paper we consider zero truncated binomially mixed exponential (EB)distribution. It is shown that in the conditions of the Poisson’s Limit The-orem this distribution may by approximated by exponential distributionmixed with zero truncated Poisson (EP) distribution. We apply EM algo-rithm to estimate parameters of EB distribution.Key words: Mixing; Zero truncated binomial and Poisson distributions;Exponential distribution; Life time distribution; EM algorithm.

Numerical approach to the population dynamics modelby

Gabriela Marinoschi

The basic linear model for describing an age structured population spread-ing in a limited habitat is considered with the purpose of investigate anapproximation procedure based on parabolic regularization.

Computational Domains out of Medical Imaging Reconstruction forMore Realistic, Patient-Related Numerical Simulations in Medical

Physicsby

A.M. Morega, A.A. Dobre and M. Morega

Numerical simulation has recently reached the stage where the computa-tional domains may satisfactorily provide the realism of anatomic domains

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and structures. Consequently, more insightful studies may be conducted toinvestigate the finer details of medical physics problems such as the hemo-dynamics of arterial flow, the electrical activity of the heart, the structuralmechanics of the skeletal system. Realistic, patient related computationaldomains are obtained by using contemporary software tools for image-basedreconstruction in conjunction with computer aided design (CAD) packages.The outcome, more realistic computational domains, is usable in modelingcomplex, numerical simulations in medical physics. This paper presents ex-amples of numerical simulations of hemodynamic flows, with and withoutinteraction with the vessels and the muscular embedding tissue; bioelectricfield mapping, action potential propagation in a heart; and structural anal-ysis of the skeletal system.The computational domains are constructed out of CT/MRI DICOM medi-cal image sets (that provide patient related anatomic details) by using Sim-pleware and, when requested (e.g., in the study of the femoral prosthesis),Solidworks CAD.First, we discuss numerical simulation results for the structural analysiscarried on in prototyping a femoral implant. The computational domainis obtained from CT scans. Next, we consider the blood flow in arterialbifurcations and the induced wall vessels deformation. The computationaldomain is based on angio-MRI images. The results evidence the influenceof large displacements, the hyperelastic behavior of the tissues.Finally, we present the computational domain of a human heart used inthe study of the action potential propagation. The action potential (colormap) is computed for different moments. The model is useful in the studyof arrhythmias, or inverse ECG problems.

Electrical Activity of the Heart by Numerical Simulationby

A.M. Morega, A.A. Dobre, M.C. Ipate, M. Morega

This paper presents numerical simulation results on the electrical signalpropagation in an excitable tissue that models the electrical activity of theheart, and the transition of this dynamical system under the influence of astrong external stimulus, from periodic oscillatory behavior into a chaoticstate with gradually increasing amplitude of oscillations and decreasing pe-riodicity as described by Ginzburg-Landau equations.The electrical pulses generated by the sinus node trigger the mechanicalcontractions of the cardiac muscle. A number of heart conditions occur

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when the normal steady pulse is disturbed, e.g., the arrhythmia. This pa-per presents simulation results describing the electrical signal propagationin the cardiac tissue based on the FitzHugh-Nagumo and Ginsburg-Landauequations for excitable media.In order to provide for meaningful results, realistic computational domainsare needed, and our approach relies on medical image based reconstruc-tion techniques. The computational domain is constructed out of CT/MRIDICOM medical image sets. Simpleware software is used to segment, label-map, reconstruct, FEM (finite element) mesh, and export the computationaldomain for numerical simulation.The parameters used in the FitzHugh-Nagumo model along with the initialpulse lead to time-dependent excitation, which travels self-entrained aroundthe tissue, without damping.In the Guinzburg-Landau model, the cardiac tissue is characterized also byparameters that describe the properties of the material, and also determinethe existence and nature of the stable solutions.The numerical simulation was carried on by the Galerkin finite element tech-nique, as implemented by.The study may be used in investigating the phenomena that occur in normaland pathological heart conditions.

EM -algorithm: parameter estimation method in different approachesto competing risks data with missing causes of failure

byMioara Alina Nicolaie

Competing risks survival data arise in medical, demographic, industrial con-texts when the individual subjects may experience multiple types of events,such that the occurence of one event precludes the occurence of others. Un-fortunately, infomation on failure/mortality is often not optimal, meaningthat the cause of failure/death is missing or inconclusive.In this paper, we deal with parameter estimation in competing risks datawith missing causes of failure using the EM algorithm. Several approachesto competing risks are considered (the cause specific hazard approach, themixture model of Larson and Dinse, the Fine and Gray model) and com-pared with the existing one (the latent failure time approach, the verticalmodeling). We provide the general likelihood method for each of the aforementioned method and ilustrate the results with simulated data sets.

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Advanced Modeling of an Internal Combustion Engine StructuralProblem

byEmil Oanta and Cornel Pana

An accurate model of a complex phenomenon offers valuable informationwhich can be used for conceiving methods to control the phenomenon andto optimize given processes. A “green” internal combustion engine has tomeet specific requirements, such as: compatibility with the equipment to bepowered, minimum consumption, maximum power, low level of noise andtoxic emissions, predictable behavior in running conditions. One of the di-rections of research involved in the fulfillment of these goals is the stressminimization in the main structure of the engine, i.e. the cylinder block ofthe engine.One can notice the high degree of complexity of the phenomena: dynamicloads, influence of the temperature, elastic supports and others. Consider-ing the main types of models, experimental models, analytical models andnumerical models, it becomes obvious that an accurate model cannot beincluded in one category only.A hybrid model which uses information from all the fields: analytic, exper-imental and numerical is the best choice regarding the method to approachcomplex problems. The results of the distinct studies must be integratedin order to reach an upper level of understanding of the phenomenon andto create an advanced investigation strategy. The only choice regarding theintegration of the information is to conceive a computer based data man-agement method. This means to use computer programming in order toacquire different information, such as: computation of loads, experimentaldata acquisition and reduction. Once the results of the distinct studies arestored as data, they are subjected to complex verification processes whichlead to a high degree of confidence.All these information are used: – to create the particular finite elementmodel;– to calibrate the model;– to check the results by comparing them with the experimental data.Once the finite element model becomes accurate, it can be used for severalstudies, such as:– weight optimization of the structure of the engine; – behavior of the enginein a running condition scenario: deflection of the supports; – evaluation ofstresses in an engine manufactured from a different material.

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The paper presents the results of the study of the stresses in the main struc-ture of the 12B165 engine manufactured by MASTER SA, Bucharest, enginewhich is used on military vessels. Several information regarding the researchmethodology are also presenteence.

The modeling of the first cycle of a pulsatory lipid vesicleby

Dumitru Popescu

In this paper I have described the first cycle of the periodical activity of apulsatory unilamellar lipid vesicle. Under some conditions, if an unilamellarlipid vesicle filled with aqueous solution of an impermeable solute is intro-duced into a hypotonic aqueous medium, can become a periodical dynamicdevice. Because of the mechanical tension induced by osmotic flow, thevesicle swells up to critical size, when suddenly a transient pore appears invesicle membrane. A part of the intracellular material leaks out throughthis pore and the liposome membrane relaxes and finally, it recovers. Theswelling begins again and the vesicle experiences o periodical process. Usingthe differential equations of both vesicle and pore dynamics I have calculatedall the parameters characterizing the first cycle of this periodical device. Thesolute concentration at the end of the first cycle may be the initial value forthe starting of the second cycle, and so on.

Convergence analysis of penalized maximum likelihood estimators forlinear inverse problems with Poisson noise

byMihaela Pricop

In this talk we focused on the convergence analysis of a class of penal-ized maximum likelihood estimators for linear inverse problems with Poissonnoise. To fulfill this aim, we study the tail behaviour of the Kullback-Leiblerdistance between independent, Poisson distributed random variables andtheir parameters. Based on this result we derive conditions on the illumina-tion time such that this distance converges to 0 a.s. Under this hypothesisand under some assumptions on the penalization term we show the almostsure convergence of the penalized maximum likelihood estimator towardsthe exact solution as the sample size goes to infinity. We illustrate these

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results by implementing and comparing the quality of the estimators for‖ · ‖L2 , KL(·, ·) and ‖ · ‖BV penalization terms for fluorescence microscopyapplications.

Approximating Functions of Vertical Atmospheric TemperatureProfiles Retrieved from the Solutions of Fredholm First Kind Integral

Equationby

M. Sammany, E. Pelican, and H. Al- Najar

Retrieving vertical atmospheric temperature profiles is an example of in-put identification problem, which requires solving radiative transfer integralequation. In a previous work, we used an artificial neural network (ANN) forsolving this equation for some given sets of observed satellite input-outputmeasurements from the atmospheric levels. In this paper, we approximatethe obtained solutions in our previous work by analytical formulas, usingnumerical methods of curve fitting. Three case studies were considered fordata sets representing infra-red satellite measurements received via threemetrology stations.

Electromechanics of solid continua subject to a biasby

Olivian Simionescu-Panait

In this lecture we review various aspects concerning the electromechanicalbehavior of solid continua subject to a bias, which we published last decade.After deriving the fundamental equations on the dynamics of piezoelectriccrystals subject to initial electromechanical fields, we analyze the followingparticular problems:1. Homogeneous plane wave propagation in isotropic solids, cubic and 6-mmtype crystals subject to initial electromechanical fields.2. Attenuated plane wave propagation in isotropic solids and cubic crystalssubject to initial electromechanical fields.3. Guided wave propagation in monoclinic crystals and isotropic solids sub-ject to initial electromechanical fields.4. Inhomogeneous plane wave propagation in monoclinic crystals subject toinitial electromechanical fields.

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Applying Monte Carlo simulation techniques in biologyby

Stefan V. Stefanescu

The evolution of the molecular populations is generally described by first-order coupled ordinary differential equations. Due to the huge number ofcomputations is very difficult to solve the chemical master equation by usingthe traditional methods. In this paper are applied the tau leap proceduresto accelerate the stochastic simulation of the chemically reacting systems.General multiple coupled stochastic processes are treated too.

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Authors

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Neculai Andrei Research Institute for Informatics, Center forAdvanced Modeling and Optimization 8-10,Averescu Avenue, Bucharest 1, Romaniae-mail: nandrei@ici.ro

Danut Argintaru Constanta Maritime University, Mircea celBatran str. 104, Constanta, Romaniae-mail: danag@imc.ro

Dirk Breitenreicher Image and Pattern Analysis Group, Depart-ment of Mathematics and Computer Science,University of Heidelberg, Germanye-mail: breitenreicher@math.uni-heidelberg.de

Adrian Carabineanu Faculty of Mathematics and Informatics, Uni-versity of Bucharest, Romania,”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: acara@math.math.unibuc.ro

EliodorConstantinescu

Constanta Maritime University, Mircea celBatran str. 104, Constanta, Romaniae-mail: mirelcon@imc.ro

Stefan Gicu-Cruceanu ”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: gcruceanu@yahoo.com

A.A. Dobre POLITEHNICA University Bucharest,Bucharest 6, Romaniae-mail:

Florin Gh. Filip Romanian Academy of Sciences, Calea Victo-riei 125, 010071 Bucharest, Romaniae-mail: ffilip@acad.ro

Anca Veronica Ion ”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: averionro@yahoo.com

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Stelian Ion ”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: ro diff@yahoo.com

M.C. Ipate POLITEHNICA University Bucharest,Bucharest 6, Romaniae-mail:

Gheorghe Juncu POLITEHNICA University of Bucharest,Catedra Inginerie Chimica, Polizu 1, 78126Bucharest, RomaniaFax: +40 21 345 05 96, Phone: + 40 21 34505 96e-mail: juncugh@netscape.net,juncu@easynet.ro

Alexei Leahu “Ovidius” University of Constantae-mail: aleahu@univ-ovidius.ro

Jan Lellmann Image and Pattern Analysis Group, Depart-ment of Mathematics and Computer Science,University of Heidelberg, Germanye-mail: lellmann@math.uni-heidelberg.de

Carmen Elena Lupu “Ovidius” University of Constantae-mail: celenalupu@yahoo.com

Dorin Marinescu ”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: marinescu.dorin@gmail.com

Gabriela Marinoschi ”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: gabimarinoschi@yahoo.com

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Alexandru Morega POLITEHNICA University Bucharest, De-partment of Bioengineering and Biotechnol-ogy& Department of Electrical Engineering,Bucharest 6, Romania,”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: amm@iem.pub.ro

Mihaela Morega POLITEHNICA University Bucharest, De-partment of Bioengineering and Biotechnol-ogy& Department of Electrical Engineering,Bucharest 6, Romaniae-mail: mihaela@iem.pub.ro

Mioara Alina Nicolaie Faculty of Mathematics and Computer Sci-ence, ”Transilvania” University of Brasov,Romania, Str. Iuliu Maniu nr. 50, Cod postal500091, Brasov,Department of Medical Statistics and Bioin-formatics, Leiden University Medical Centre,Leiden, The Netherlandse-mail: alinanicolae@unitbv

H. Al- Najar Dept. of Mathematics, Faculty of Science,University of Aleppo, Syriae-mail: hamdo1956@yahoo.com

Aurelian Nicola ”Ovidius” University of Constanta, Romaniae-mail: anicola@univ-ovidius.ro

Emil Oanta Constanta Maritime University, 104 Mirceacel Batran, Constanta, Romaniae-mail: eoanta@yahoo.com

Cornel Panait Constanta Maritime University, 104 Mirceacel Batran, Constanta, Romaniae-mail: cornel.panait@gaad.ro

Mihaela Pricop Institut fur Mathematische Stochastik,Universitat Gottingen, Goldschmidtstr. 7,37077, Gottingen, Germanye-mail: pricop@math.uni-goettingen.de

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Elena Pelican “Ovidius” University of Constanta, Facultyof Mathematics and Computer Science,Romaniae-mail: e-mail:epelican@univ-ovidius.ro

Stefania Petra Image and Pattern Analysis Group, Depart-ment of Mathematics and Computer Science,University of Heidelberg, Germanye-mail: petra@math.uni-heidelberg.de

Constantin Popa “Ovidius” University of Constantza, Roma-nia,”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: cpopa@univ-ovidius.ro

Dumitru Popescu ”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: popescu1947@yahoo.com

M. Sammany Dept. of Mathematics, Faculty of Science,University of Aleppo, Syriae-mail: sammanyddr1@hotmail.com

Ana Maria Raducan ”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail:

Christoph Schnorr Image and Pattern Analysis Group, Depart-ment of Mathematics and Computer Science,University of Heidelberg, Germanye-mail: schnoerr@math.uni-heidelberg.de

OlivianSimionescu-Panait

University of Bucharest, Faculty of Mathe-matics and Informaticse-mail: o simionescu@yahoo.com

Stefan V. Stefanescu University of Bucharest, Faculty of Mathe-matics and Informaticse-mail: stefanst@fmi.unibuc.ro

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