domain: math info

text:
Gauthier Quesnel
email: gauthier.quesnel@toulouse.inra.fr

Ronan Trépos

A Package System for Maintaining Large Model Distributions in VLE Software

Keywords: Packages, Package System Manager, Distribution, Discrete Event Modeling and Simulation

The Modeling and Simulation (M&S) is becoming a central activity in order to build, study and analyze new systems. To improve activities of M&S, we need to develop collaborative technologies. In this context, we develop the application software Virtual Laboratory Environment (VLE) to model, simulate and analyze dynamic systems. VLE is based on the Discrete Event System specification (DEVS) formalism, a widely recognized specification for modeling and simulating discrete events systems. The main features of the DEVS formalism are a modular and hierarchical approach of the M&S and a relative simplicity to develop the simulation algorithms. Researchers and engineers from different comunities used VLE to develop and study models. However, the modelers need to share source code in order to reuse, couple and combine models. It is not sufficient because they are not helped for maintenance and version upgrades issues. In this paper we present a package system manager that greatly helps modelers to publish source code, binary code, exchange models, data and software application in VLE.

I. INTRODUCTION

The Modeling and Simulation (M&S) is becoming a central activity in order to build, study and analyze new systems. M&S allow researchers, engineers and grant students to study the behavior of systems through virtual representation. Thus, M&S is increasingly used in industrial and research fields such as environment, agronomy, manufacturing, bio-medical systems. However, the cost of M&S activities increases with the complexity of models and the amount of communications between stakeholders (e.g., sub-domain experts, simulator users, simulator engineers, and final system users). To address the increasing costs of M&S activities, collaborative technologies must be introduced to support these activities.

Since 2003, we develop the M&S software environment called VLE [START_REF] Quesnel | The Virtual Laboratory Environment -An operational framework for multi-modelling, simulation and analysis of complex dynamical systems[END_REF]. VLE is based on the Discrete Event System Specification (DEVS) [START_REF] Zeigler | Theory of modeling and simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems[END_REF]. This formalism comes from the Theory of Modeling and Simulation (TMS) defined by Zeigler [START_REF] Zeigler | Theory of modeling and simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems[END_REF]. The TMS tends to be as general as possible. It addresses major issues of computer sciences from artificial intelligence to model design and distributed simulations. TMS aims to develop a formal and operational framework for the specification of dynamical systems. Indeed, it has been shown that classical or timed automaton, discrete time systems, Petri net and state charts can be considered as DEVS subformalisms. Even, continuous systems can be approximated using DEVS numerical solvers. Thus, the DEVS formalism can be candidate to be a common denominator for multimodeling [START_REF] Vangheluwe | An introduction to multi-paradigm modelling and simulation[END_REF].

Today, VLE is used by many researchers, engineers, technicians in agronomic, environmental, transport and manufacturing research fields. They develop models, run simulations, analyze and optimize simulations. Modelers write many models with VLE. However, they have difficulties to use or reuse models or data from other users or from other research fields. In this paper, we propose to develop a package system to improve the sharing of models, data, source code and binary code between users of VLE. This project provides (i) packages to distribute models, data or source code (ii), tools to install, uninstall and build repositories and (iii) a workflow to update and maintain all the packages. This paper is divided into five parts. In the first part, we explain the context of this work. In second part, we present the package, package system and workflow to build distribution. In third part, we show the first results of our work. We talk about the package systems and the returns of the users in the fifth part. Finally, we conclude this paper with conclusion and perspective.

II. CONTEXT

VLE is a modeling and simulation environment based on the DEVS formalism. VLE provides several software programs to develop atomic and coupled models networks, atomic models behavior, runs simulations and analyze results.

In order to build a collaborative environment for exchange or reuse of scientific knowledge between users of VLE, we have defined several tasks: (i) improve the usability of the DEVS formalism (ii) develop an integrated development environment (IDE), (iii) develop tutorials and training, (iv) develop small software programs that link VLE with major statistical and optimization tools.

A. DEVS implementation

The VLE software is an implementation of the DEVS formalism. VLE is set of software programs and software libraries developed in C++. The C++ was chosen because of (i) multi-paradigm (object-oriented programming and metaprogramming) (ii) general-purpose programming language and (iii) compiled features. VLE implements the DSDE [START_REF] Barros | Dynamic Structure Multiparadigm Modeling and Simulation[END_REF] abstract algorithms. DSDE allows building dynamic structure DEVS models. As CD++ [START_REF] Wainer | Cd++: a toolkit to define discrete-event models[END_REF], ADEVS [START_REF] Nutaro | Building Software for Simulation: Theory and Algorithms, with Applications in C++[END_REF] or POWERDEVS [START_REF] Bergero | PowerDEVS: a tool for hybrid system modeling and real-time simulation[END_REF], VLE provides C++ interfaces to develop atomic models. Thus, to develop atomic model, modelers develop C++ class that inherits this interface. The listing 1 shows a simplified representation (without constructor, destructor, and other members) of the C++ class Dynamics. The Dynamics class permits to develop atomic model behavior. The five first functions represent the DSDE interface in VLE. The last function is a specific feature of VLE allowing observation of the state of an atomic model regardless of the simulation time. In VLE framework, each subclass of Dynamics must be compiled into a shared library. Developers of atomic DEVS models can share or reuse their models by exchanging C++ source code or binary code. However, this class and the formalism DEVS is not adapted for many modelers. Thus, we decide to add different modeling formalisms in VLE.

To develop models that change the structure of the model during the simulation, modelers develop C++ classes that inherits the class Executive. This class has the same interface as the previous Dynamics class. However, it offers some functions to manipulate the structure of the model (add and delete models, connections).

B. Modeling formalism

Modelers are not fluent with the DEVS formalism and they prefer using mathematical formalisms as ordinary differential equation or automaton. So, rather than force them to translate their models in the DEVS formalism, VLE proposes a set of modeling formalism to perform the development of model without knowledge of the DEVS formalism. These modeling formalisms are developed as subclasses of Dynamics.

Listing 2: E.g. API of the Euler extension.

1 Class Euler: public Dynamics { 2 public: 3 virtual double compute(const Time& time); 4 }; For example, the listing 2 shows the class Euler. This class proposes a numerical solver of ordinary differential equation (ODE). Users of Euler are not expected to manipulate directly DEVS formalism. Only one method is necessary to declare ODEs variables and to compute their gradients.

With VLE, modelers can develop their models with several modeling formalism. From ODE numerical solver, finite state automaton, cellular automaton etc. These modeling formalisms are developed using a DEVS BUS. In VLE framework, modeling formalisms are sub-classes of the Dynamics class (See listing 1. Modelers must inherit the modeling formalism class to develop atomic model. As for Dynamics, developers can share or reuse their multi-models by exchanging C++ source code or binary code.

C. Integrated Development Environment

VLE provided C++ classes to develop DEVS atomic models from modeling formalisms classes or from basic DEVS atomic model class. However, to model the DEVS models, modelers need to define a hierarchical networks of models. In order to simplify the use and the reuse of the C++ classes, the structure of the model is stored into a classical XML application. The XML application describes (i) the structure of the models, (ii) the parameters to initialize atomic models and (iii) the atomic models to observe. VLE proposes the software program GVLE to perform the edition of this XML application. GVLE is also an IDE to write C++ classes and to develop and compile shared library. For the users of the VLE environment, GVLE is certainly the most important application software.

D. Extra Software Programs

Statistical methods for parameter estimation, validation and sensitivity analysis are necessary for implementing and analyzing agro-ecosystem models [START_REF] Wallach | Working with dynamic crop models: evaluation, analysis, parameterization, and applications[END_REF]. VLE provides a package rvle that links VLE to the statistical language R [START_REF]R: A Language and Environment for Statistical Computing[END_REF] in order to perform models calibration and exploration.

Therefore, we proposed a web-oriented tool, designed to develop web applications around the models implemented on the environment. This tool is based on the development of a specific package: PyVLE that enables the use of VLE from Python applications. This package provides a set of functions that enable the management of VLE simulations from Python scripts.

We present, in this section, three options to improve collaborative aspects in the VLE environment. However these steps are not sufficient to address the problem of exchanging and reusing models. To address this problem, we propose a solution based on the packaging of models. Moreover, this solution greatly improves collaboration between users.

III. METHODS

VLE now offers a wide range of programs and libraries. Each of these components help to share expertise between researchers and other users. However, the exchange of models or data between modelers is still one major issue. If a modeler wants to reuse a model, it needs to copy, install, compile the source code of the model to reuse. New questions arise. How to take into account the evolution of the imported model ? The same problems have been resolved by the Free Open Source Software (FOSS) community and Linux distributions as Debian or RedHat. They develop package system manager such as apt-get or yum. In this paper, we propose to add a package system manager to VLE to improve the collaboration between users of VLE.

A. Package system

The package system must provide several features. Many of these characteristics are the same as in the Linux distribution such as Debian or Redhat [START_REF] Boender | Improving the quality of gnu/linux distributions[END_REF]. The solution proposed in this paper is largely inspired by the works of the FOSS community, but adapted and restricted to the M&S in VLE environment.

Thus, a package is an archive of sources, data and documentation files with a description file. The description file describes the name, the version, the dependence to the version of VLE and three lists of packages that define the dependencies to build the package, the dependencies to run the package and the conflict dependencies. example, the weather package in agronomic sytem, as no running dependence while the list to build the package contains the modeling formalism difference equation. We categorize the package:

• Model package provides models (atomic or coupled) and contains source code and binary code of the models, data and documentation.

• Formalism package contains a modeling formalism source, headers (to use as a subclass), binary code, data and documentation. • Data package contains only data.

• Meta package contains only a description file with the list of dependency. The format of the package is showed in listing 3. A package is a directory or an archive that allows the construction of model package, modeling formalism package, data package or meta package. The data directory stores input, exp stores the simulation experiments (the XML application), src stores the code sources of the models, test stores the unit test. VLE builds the plugins and lib directories to store respectively the compiled atomic models and the shared library from modeling formalism.

B. Description file

To define a package for VLE, users need to define a description file Description.txt. This description file exists in classical Linux distribution as Debian [START_REF] Krafft | The Debian System: Concepts and Techniques[END_REF] or in R [START_REF]R: A Language and Environment for Statistical Computing[END_REF]. In this file, Two fields are necessary. A package name and a version. The package name must be unique in the distribution. The version number follows a strict representation. Indeed, in Debian [START_REF] Krafft | The Debian System: Concepts and Techniques[END_REF] or RedHat package system, the version number is a string and it complicates the package systems. For the VLE community, we restrict the package version. The version must respects the regular expression: Listing 4: Package version in regular expression.

1 [0-9]+\.[0-9]+\.[0-9]+\-[0-9].
For example, a package can have version a 1.0.0-0 or 1.2.3-7. The third numbers define the version of the package. The last number defines the repository and integrator of the repository version. Integrator can correct package and release a package.

The VLE environment provides C++ development libraries. Thus, we define a policy to ensure stable API and ABI and allows developers to correctly reference VLE's API and ABI.

Listing 5: VLE version in regular expression.

1 [0-9]+\.[0-9]+\.[0-9]+\-[a-Z0-9]+
The first two numbers correspond to the major and the minor version. These numbers define the stable version of VLE. The patch version number, the third number, defines the number of release for the stable version of VLE. We ensure stable API and ABI for the all stable version of VLE. For example, the weather package compiled with VLE 1.0.0 needs to be updated and compiled to add compatibility with the VLE 1.1 while for VLE 1.0.7, the model is already compatible.

C. Distribution

Packaging the models is the first step of building a package system. The next steps are to develop tools and methods to build a distribution of all available packages. A distribution allows users to install and uninstall packages from a distant repository.

A distribution is a finite set of packages rules. Each package rule is a tuple of the form (p, B, D, C) where p is a package, B is a set a dependency build clauses, D is a set of dependency clauses for p. C is a set of conflict clauses for p. the dependency build clauses and dependency clauses must be present to compile and use the package p.

Each dependency clauses or dependency build clauses is a disjunction of packages p 1 |...|p k . A dependency clause requires that some packages from the set {p 1 , ..., p k } be present. Conflict clause requires that package p not present in order to install the package p. Thus, a valid installation is a subset of the packages in the distribution. For example, a set of packages from the distribution installed on a machine of the user community. To ensure functioning of the machine we require that installation profile of the machine be valid. A installation profile is valid if dependency clauses and conflict clauses are satisfied. A valid installation profile for a distribution in one that satisfies the dependency and conflict clauses of each package rule of the distribution.

• A dependency clause p 1 |...|p k for package p is valid iff either p is not installed and some packages in the set {p 1 , ..., p k } are present in the profile. • A conflict clause is valid iff either p is not installed and p is not installed. The package system have two critical problem.

• To install the new package p given a distribution R and an installation profile P , the package system has to check if there is a profile P containing p such that P ∪ P is a valid installation profile for R. • It may happen that a new package p cannot be installed because it is in conflict with some packages already installed on the machine. In this case, we must first uninstall some packages before attempting to install p. The task of the package system is then to identify a set of packages P such that p can be installed on P -P To address these two problems, we can use a satisfiability problem (SAT) solver as proposed in the OPIUM package manager [START_REF] Tucker | Opium: Optimal package install/uninstall manager[END_REF].

D. Distribution Workflow

The task of maintaining a package repository is difficult. It requires to take into account the evolution of all packages over the time, address the error reports from users, developers and the quality assurance (QA) teams. The figure 2 shows the workflow of the distribution. The distribution workflow needs the development of tools to automatize as much of this work as possible.

The role of the QA teams of the distribution is to coordinate bug filling, tracking the absence of maintainers, development of tools, running systematic checks on the entire archive and publishing. Thus, we provide several scripts to automatize the workflow.

IV. RESULTS

In March 2012, the package system manager is not completely available for an every day use. Several model packages begin to convert into the package format. The following modeling formalism have been converted into packages:

• Difference-Equation is a set of class to develop models with recurrence relation i.e. equation that recursively defines a sequence. • CellDEVS is a class to develop cellular automaton [START_REF] Wainer | Application of the Cell-DEVS paradigm for cell spaces modelling and simulation[END_REF].

• CellQSS is a subclass of the CellDEVS to solve numerically partial differential equation. • Output is a set of plug-ins to write output of simulation in different file format.

• Examples is a set of examples that use the previous packages.

In this section we show the construction of a model based on several packages. The goal is to optimize the sowing date of maize according to a stochastic weather generator and an agent decision making.

The basic crop model uses the FSA and Difference-Equation modeling formalism. The first one is used to model maize stage (sowing, harvesting). The second one is used in several atomic models to model the processes of the maize model (Leaf Area Index (LAI), intercepted Photo-synthetically Active Radiation (PAR) and biomass). The maize model need to be coupled with a weather model that sends temperature and rain daily. The maize-agent package introduced a model that inherits of the Agent modeling formalism. This model permits to define tasks such as sowing, harvesting, irrigating, fertilization. In another package, we couple a pseudo random number generator (Mersene Twister [START_REF] Matsumoto | Mersene twister: A 623-dimensionally equidistributed uniform pseudorandom number generator[END_REF]) PRNG and the weather model to build a weather generator. Finally, we define a package maize-optim that combine class from an optimization package and the maize-agent to build the complete model. Fig. 3: An example of package dependencies with an agronomic model.

V. DISCUSSION

For now, the package system is operational and packages can be downloaded and installed from a server. Only the dependence system is not implemented. The tools to perform integration of the distribution are also not yet available.

The use of package seems to simplify the construction of complex models by aggregating atomic models and data from other packages. However, we note that many modelers use modeling formalism package and generic model packages such as the weather or the glue packages. Users do not prefer to create dependency with final package.

We think it is not related to the package systems, but to VLE functioning and to the design model. Indeed, developing a generic dynamic model is complicated. In DEVS and VLE, a model can be seen as a black box in Systems Approach or systemic world view. Events, from another models, can perturb the model any time. These perturbations can arrive in an unexpected state or transport malformed data. Considering these events, developing a robust model becomes a long task. Modelers prefer to use generic models with robust designs.

VI. CONCLUSION

In this paper we define a package system management for the VLE modeling and simulation environment. The package system enables to share data, models source code and shared libraries. It allows the use and the reuse models developed by another users in VLE community. It improves the global quality of the model and simplify the maintenance of the models. However, the package system needs to have computer engineers (i) to perform release of the distribution and (ii) to integrate and maintain package of the community. For now, the package system begins to work perfectly but there are still missing features such as the checking of packages dependencies.

Unfortunately, the package system proposed in this paper depends on the VLE software and its specification. However, we adapt the package systems to VLE requirements. For example, an atomic model must be compiled into shared library or into a plug-in before running a simulation. Thus, we need to define a package system that can compile C++ source code.

In this paper, we focus the package system to the development of the behaviour of atomic modes. However, it may also be necessary to help modelers to build hierarchy of models from the package system. For now, we provide only a way to export sub-classes of the Executive class (which allows drastic changes in the structure of the model). In future development, we want to develop the possibility to import and export some part of structures of models from another package.

Fig. 1 :

 1 Fig. 1: The IDE of VLE: on the left of the picture, GVLE shows the current opened package. On the right, GVLE shows the content of the current experiment. In the middle, the current coupled model.

Listing 3 :

 3 A part of the structure of a package in VLE

Listing 6 :

 6 The description file of the model package is a text file 1 Source: weather-gen 2 Version: 1.0.0-0 3 Section: agronomic 4 Maintainer: quesnel@users.sourceforge.net 5 Homepage: http://www.vle-project.org 6 Build-Depends: vle (>= 1.0), 7 differential-equation (>= 1.0) 8 Depends: weather (= 1.2.3), output-file (>= 1.0) 9 Conflicts: 10 Description: A weather generator.The description file of the listing 6 shows the weather-gen (weather-generator) package. This package is built with 1.0. It recommends the package weather in version 1.2.3 and the package file in version greater than 1.0.

Fig. 2 :

 2 Fig. 2: Major flow of the VLE package system.

  Listing 1: E.g API of the Dynamics class in VLE.

	1 class Dynamics {
	2 public:
	3 virtual Time timeAdvance() const;
	4 virtual void internalTransition(const Time& time);
	5 virtual void externalTransition(const Time& time,
	6	const ExternalEventList& lst);
	7 virtual void output(const Time& time,
	8	ExternalEventList& out) const;
	9 virtual void confluentTransition(const Time& time,
	10	const ExternalEventList& lst);
	11 virtual Value * observation(
	12	const ObservationEvent& event) const;
	13 }


est destinée au dépôt

Large-scale phenotyping of genetic resources for agronomic traits is useful to structure collections, identify valuable progenitors, and define core-collections for association studies. Plant diseases are one of the main threats for crop production, and resistant genitors are constantly needed for breeding. Many traits such as partial resistance to Phytophthora capsici in pepper (Capsicum spp.) exhibit a continuous range of responses evolving over time, and large collections are difficult to reliably assess for quantitative traits. To phenotype a pepper collection of 1186 lines for P. capsici resistance, we measured 6 variables along a 21 day-time-course post inoculation. By a Self-Organizing Map multivariate analysis, an undemanding clustering method that locates lines and weights variables on a precise map, we defined 10 clusters of distinct resistance levels. The most resistant one gathers 7.5% of the collection, including 6 well-known genitors, confirming the relative rarity of resistance. Other clusters highlight distinction between early and late resistances. Resistant lines originate mostly from C. annuum, and a majority of C. pubescens lines were resistant. Our results reveal that resistance phenotype is highly frequent in Asia, a secondary centre of diversification of pepper. We are now constructing a trait-specific core-collection and achieving an association study by sequencing strategic positions on a locus of interest to detect candidate SNPs.

  Contribution to phenomics for quantitative disease resistance in a germplasm collection of Capsicum spp.: a multivariate analysis by self-organizing map Melissa Cantet, Guillaume Marie, Anne-Marie Sage-Palloix, Anne Massire, Alain Palloix, Véronique Lefebvre To cite this version: Melissa Cantet, Guillaume Marie, Anne-Marie Sage-Palloix, Anne Massire, Alain Palloix, et al.. Contribution to phenomics for quantitative disease resistance in a germplasm collection of Capsicum spp.: a multivariate analysis by self-organizing map. 9. Solanaceae Conference (SOL2012), Aug 2012, Neuchâtel, Switzerland. 250 p. hal-02745281 Contribution to phenomics for quantitative disease resistance in a germplasm collection of capsicum spp.: a multivariate analysis by self-organizing map Mélissa Cantet, Guillaume Marie, Anne-Marie Sage-Palloix, Anne Massire, Alain Palloix and Véronique Lefebvre INRA, Avignon, France


Angel G Angelov

Maroussia Slavtchova-Bojkova

Keywords: Bienaymé-Galton-Watson branching process, offspring mean, Bayesian estimation, reproduction number, Metropolis-Hastings algorithm Monte Carlo method, multidimensional integration, scrambled Sobol sequences, randomized algorithms long horizon risk, ARMA-GARCH fit, volatility clustering, heavy tails, tempered stable distribution k-sample problem, multi-sample, nonparametric

We consider Bayesian method for estimating the basic reproductio n number, having data on the reported cases of an infectious disease on a weekly base. The number of infected individuals is modeled by a singletype Bienaymé-Galton-Watson branching process, which is quite useful, since the basic reproduction number is represented by the offspring mean of the branching process, see [1]. We are using the Metropolis-Hastings algorithm to simulate the posterior distribution . The described method is demonstrated on real data of mumps in Bulgaria. The presentation is based on [2].

Quasilinear structures in stochastic arithmetic

Rene Alt 1 , Roumen Anguelov 2,3 , Jean-Luc Lamotte 1 , Svetoslav Markov 21 Laboratoire Informatique Paris 6, Université Pierre et Marie Curie 2 Dept. Mathematics and Applied Mathematics, Univertity of Pretoria 3 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences Stochastic arithmetic has been developed as a model for computing with imprecise numbers. In this model, numbers are represented by independent Gaussian variables with known mean value and standard deviationand are called stochastic numbers. The algebraic properties of stochastic numbers has already been studied by several authors. In most real-life problems the variables are not independent and a direct application of the model to estimate the standard deviation on the result of a numerical computation leads to some overestimation of the correct value. In this work "quasilinear" algebraic structures based on standard stochastic arithmetic are studied and new arithmetic operations, called "inner stochastic addition and subtraction" are introduced from abstract algebraic considerations. They are stochastic analogues to the inner interval addition and subtraction used in interval arithmetic. The algebraic properties of these operations and the involved algebraic structures are also studied. Then it is shown that these inner operations allows the computation with non independent variables and the connection with the correlation coefficient of the variables is developed. The corresponding methodology for the practical application of the new structures in relation to problems analogous to "dependency problems" in interval arithmetic is given and some numerical experiments showing the interest of these new operations are presented.

Differentiable Approximation by Solutions of Newton Equations Driven by Fractional Brownian Motion

Haidar Al-Talibi

Linnaeus University

We study the scaling limit of Fractional Ornstein-Uhlenbeck processes with drift when the scaling parameter in front of the noise and the drift tends to infinity. The Gaussian nature of the Ornstein-Uhlenbeck processes driven by Fractional Brownian motion is exploited. The Girsanov theorem for Fractional Brownian motion is also used in order to show weak convergence when including nonlinear drift.

Monitoring infectious diseases through discrete-time branching processes

A System for Test Analyses and Diagnostics (TAD)

Dimitar Atanasov 1 , Vessela Stoimenova 2 *
1 New Bulgarian University, Bulgaria 2 Sofia University and Bulgarian Academy of Sciences Evaluation of cognitive abilities by test assessment is a common practice in education as well as in other fields of psychometrics. A lot of specialized software is developed in order to address the needs of applied researchers in the field of cognitive assessment. Usually these applications are based on specific theoretical assumptions and are based on a given methodology. The application, presented here explores different types of test assessment principles. The classical estimators of test properties are accessible as well as IRT and LSDM models.

The application has a graphical user interface with interactive menus and intuitive behaviour. Written in MATLAB, it can be compiled for different platforms. The package is licensed as free for educational and noncommercial usage.

Analysis of Cognitive Attributes Under the Graded Response Model in the Framework of Item Response Theory

Dimitar V. Atanasov 1 , Dimiter M. Dimitrov 2

1 New Bulgarian University, Bulgaria 2 George Mason University, USA

The existing approaches to analysis and validation of latent cognitive attributes that underlie responses on test items deal with binary (1/0) scored items. In many situations of educational and psychological measurement, however, the item scoring is polytomous (e.g., 0, 1, 2, or 3 scores on a 4category item). The grading response model (GRM; Samejima, 1969) is widely used and efficient approach to analysis of polytomous items in the framework of item response theory. The GRM, known also as "cumulative logit model", allows the estimation of probabilities for a person to score at or higher than a specified item category, conditioned on person and item parameters.the person's score on the trait measured by the test, item discrimination, and difficulties of item categories defined as the trait needed to have 50% chances of responding at or higher than the specified category. The purpose of this paper is to propose an approach to analyzing latent cognitive attributes that underlie persons' responses on polytomous items calibrated under the GRM. The results of such analysis can help educators and psychologists to better understand the cognitive operations and processes that underlie the chances of person to be identified as, say, successful in a particular area or being at a certain level of anxiety, depression or other psychological states.

The idea behind the proposed approach is to adapt the least squares distance model for cognitive diagnosis (LSDM; Dimitrov, 2007;Dimitrov & Atanasov, 2012), which works with binary scored items, for use with polytomous items calibrated with the GRM. In its original use, the LSDM uses estimates of the binary item parameters under a specific item-response theory (IRT) model to provide estimates of the probability of a person to process correctly any cognitive attribute given the person's location on the IRT logit scale. Under the proposed approach, the LSDM uses the GRM calibration of person and item parameters to produce probability curves of cognitive attributes for dichotomizations which, say in the case of 4-category items (0, 1, 2, 3), relate to the following GRM probabilities: P(0 versus 123), P(01 versus 23), and P(012 versus 3). In the general case of m+ 1 categories (0, 1, . . . , m), there will be m attribute probability curves (APCs) for each cognitive attribute across the IRT logit scale of persons' trait scores. The information provided by such APCs can be very useful for the validation of the initial set of hypothesized cognitive attributes and understanding their role under different cutting scores for criterion testing or diagnostic of psychological states and behaviors in education and psychology.

Keywords: cognitive diagnosis modeling, graded response model, item response theory.

Stationary solution for the stochastic equation of a viscous gas in one spatial dimension

Azzedine Benchettah, Rym Benseghir

University of Badji Mokhtar, Annaba, Algeria

The study focuses on the discredited stochastic equation of a viscous gas using lagrangian coordinates. Applying Ito's formula to a suitably chosen functional allows us to obtain an a priori estimate which gives us both the existence and uniqueness of the global stochastic solution. Indeed, we first start by proving the existence and uniqueness of the local deterministic solution. Then, by introducing an adequate stopping time, we prove the existence and uniqueness of the local stochastic solution. Finally, the a priori estimate allows us to prove the existence uniqueness of the stochastic global solution. Now, concerning the existence of an invariant measure, we get the assumptions of the Hasminski's theorem which allows us to obtain the existence of a stationary solution.

Keywords: Ito's formula, stationary solution, discretization, Hasminski's theorem.

Invariant measure for the stochastic equation of a barotropic viscous gas in one spatial dimension

Rym Benseghir, Azzedine Benchettah

University of Badji mokhtar, Annaba, Algeria

This work is concerned with the stochastic equation of a barotropic viscous gas in one spatial dimension. The application of Ito's formula in an infinite dimensional space to a suitably chosen functional allows us to analyze the behavior of the solution, i.e., obtaining an estimate of energy. This estimate, because of the low regularity of the space, does not allow us to demonstrate the existence of an invariant measure. Inspired by the Vishik program, by Galerkin's approximation, we thus obtain an estimate that allows us to demonstrate on the one hand, the existence of an invariant measure and on the other, the global stochastic solution of the approximate system. Finally, by passage to the limit and applying the Krylov-Bogoliubov theorem, we obtain an invariant measure for our system of equation.

Keywords: Ito's formula, Invariant measure, Galerkin approximation.

Calibration weighting of the complex random sample with incomplete realization

Wieslawa Dabala

Public Opinion Research Centre, Warsaw

Population was divided into strata. Two-stage sampling scheme was used in sample selection. Primary sampling units (psus) were chosen with application Hartley-Rao scheme. Secondary sampling units (ssus) were selected from previously sampled psus using simple sampling without replacement. Probabilities of selecting units of population were not equal. The response rates in strata were different and less than 80%. In effect the realized sample size was smaller than the size after sampling. Estimation of the basic population parameters comprised:

-adjustments by weights with using selection probabilities, -calibration with using auxiliary variables.

In practice, the estimation of variance of estimators was carried out with simplified methods.

Keywords: applications of representative method in survey researches

Classification of texts' authorship using a regression model on compressed data

Diana Dackova, Plamen Mateev

Faculty of Mathematics and Informatics, Sofia University "St. Kliment Ohridski"

An algorithm for text authorship identification is proposed. The procedure is based on the Kolmogorov complexity and uses regression models on the length of the compressed texts. The classification employs the regression parameters estimates. Different combinations of compressor parameters and the preliminary processing on the data are examined using prose texts of a few English classics. An EM-type algorithm is proposed to obtain the maximum likelihood estimator for the offspring distribution in multitype branching processes, when the process is not observable in the sense of the whole tree, but only as the "generation" at given moment in time. A method is presented to do this in the class of branching processes with terminal types and the results for processes with one nonterminal type, generating binary family trees are discussed. Bayesian statistical analysis for controlled branching processes is developed, considering a non-parametric offspring distribution and control distribution belonging to the power series family, depending on a single parameter, called control parameter. Mainly, inferences on the offspring distribution (and on its main moments) and on the control parameter are considered as well as on the rate of growth of the process. We tackle the problem from a Bayesian perspective using Markov chain Monte Carlo (MCMC) and approximate Bayesian computation (ABC) approaches. Moreover the inference on posterior predictive distributions for as yet unobserved generations is also considered. The graphical depiction of such probabilities along the IRT logit scale for a given cognitive attribute is referred to its attribute probability curve (APC). The purpose of this paper is to propose a LSDM-based probabilistic approach to comparing groups on cognitive attributes. Such groups can be defined, for example, by gender or different treatment conditions (say, experimental and control groups) in educational or psychological research. The proposed approach can be generally described as follows. First, estimates of the test ability scores of the persons from the groups being compared are obtained by fitting an appropriate IRT model to the sample data (binary item scores, 1 = true, 0 = false). Second, the APCs of attributes that underlie the success on test items are obtained through the use of the LSDM. Third, these APCs are described analytically by fitting them to the 3-parameted logistic (3PL) model in IRT using the Curve Fitting Toolbox in MATLAB (MathWorks, Inc., 2010). Fourth, using this 3PL model of cognitive attributes, the probability for each person to process correctly a given attribute (i.e., the person's attribute score) is obtained as a function of the test ability score of that person on the IRT logit scale. Fifth, the obtained attribute scores for the persons in the study sample are used with an appropriate statistical method for group comparison (e.g., t-test, ANOVA, ANCOVA, and so forth). The results from group comparisons on latent cognitive attributes will provide a valuable feedback to educators and psychologists for improving assessment, teaching strategies, and curriculum development in targeted areas of learning, teaching, and behavioral intervention.

Keywords

Keywords

Keywords: cognitive diagnosis modeling, item response theory, assessment.

Efficient Monte Carlo Approaches for Evaluating Integrals with Applications to Sensitivity Studies

Ivan Dimov, Rayna Georgieva, Sofiya Ivanovska An advanced Monte Carlo approachfor multidimensional integration proposedin an earlier work by the authors [1] is studied. This algorithmis based on a special kind of randomization of low discrepancy ΛΠ τ Sobol sequences. It is proved that this algorithm has an optimal rate of convergence for functions with continuous and bounded first derivatives in terms of probability and mean square error. Its efficiency is analyzed and a comparison with randomized quasi-Monte Carlo algorithms [2] is done.

The Monte Carlo algorithms under consideration are applied to sensitivity studies of chemical species concentrations calculatedby the Unified Danish Eulerian Model to some chemical rate reactions. Similar analysis isperformed to the emissions of the most important airpollutants. Reliable variance-based algorithms for global sensitivity analysis [3] are used. Theoretical study, aswell as,numerical experiments are performedin order to analyse efficiency of various variance reduction techniques for computing small sensitivity indices. Conclusions about applicability and efficiency of the algorithms under consideration are drawn.

On the optimization of a finite source retrial queue

Velika Dragieva

Sofia University of Forestry

The paper considers a finite retrial queue with one reliable server, exponential repeated attempts and exponential service times. It continues previous works on this topic and the main goal is optimization of the system performance. Assuming control of the service intensity, we obtain values, minimizing the most probable orbit size. The problem of a cost function minimization in some special cases is studied also.

Keywords: finite queueing systems, retrial queues.

Asymptotic behavior of central order statistics under monotone normalization

A. Gacovska Smirnov, 1949, derived four limit types of distributions for linearly normalized central order statistics, c.o.s. , under the weak convergence. In this paper, we investigate the asymptotic behavior of c.o.s. under monotone normalization. The explicit forms of the limit distributions are obtained using regular norming sequences of mappings from the group of max-automorphisms and the solutions are found of two functional equations which characterize the possible nondegenerate limit of the k-th upper order statistic with central rank.

Keywords: Keywords: K-th upper order statistic, Central rank, Monotone normalization, Regular norming sequence Statistical Tests for Randomness -Integration, Parameterization, Improvements

Jordan Genoff

Technical University of Sofia at Plovdiv

Testing a stream of values for randomness is not a straightforward task. It is accomplished by adopting various assumptions that embody the randomness hypothesis in different instrumental ways. This is the reason for the existence of a large variety of different procedures for randomness testing. This paper presents: a comprehensive survey on the currently known tests for randomness, a new implementation framework, a parametric interface to each of the tests, so its features can be optimally exploited in different applications, some improvements for some of the tests. A free public access to the implementation source code is announced.

Keywords: statistical test for randomness.

Implementation of EM algorithm for maximum likelihood estimation of joint model of one ordinal and one continuous outcome

Denitsa Grigorova

Faculty of Mathematics and Informatics, Sofia University Estimation of probit model for one ordinal and one continuous outcome based on maximum likelihood estimation is numerically intensive procedure especially when we have repeated measures on subjects. We consider an implementation of the EM algorithm proposed by Kawakatsu and Largey [1] for finding the maximum likelihood estimates for cross-sectional data. The algorithm is realized in the free software environment for statistical computing and graphics R. We present simulations for examination of the performance of the algorithm. An advantage of the presented algorithm is the possiblility of extention to random effects models for longitudinal outcomes.

Keywords: EM algorithm, probit model, free software environment for statistical computing and graphics R.

Estimation of Brown Bears' Population in Rhodope Mountains

Todor Gurov, Emanoul Atanassov, Ruslan Serbezov, Nikolai Spassov

Institute of Information and Communication Technologies, Bulgarian Academy of Sciences

The brown bear (Ursus arctos) is the most widespread bear in the world. It can be found across Europe, Asia and North America in habitats ranging from forests to dry deserts and tundra. Despite its adaptability, the species is protected in Bulgaria. That is why it is important to estimate habitat use and population dynamics of brown bears in the country. In this work we study the population of brown bears in Rhodopa Mountains by using statistical approaches, using data received from the monitoring that was carried out in Autumn 2011. Recommendations regarding the obtained estimators and the necessary sample sizes are presented, as well as some ways to improve data collection during future monitoring.

Keywords: statistical approach, estimator, data analysis, population

Inverse methods in econometrics: the infinite-dimensional HP-filter

Astrid Hilbert

Hiba Nassar, Linnaeus University, Sweden

Inverse methods have recently been successfully introduced into nonparametric time series econometrics. Non-parametric models in general allow for more flexibility. The Hodrick Prescott filter is to be seen is this context as a method to determine a trend for a given time series. The work aims to extend the applicability of inverse methods, when the number of parameters is very large, i.e. can be assumed to be infinite.

On a test in age-dependent branching processes with non-homogeneous immigration

Ollivier Hyrien 1 , Craig Jordan 1 , Nikolay Yanev We consider a class of age-dependent branching processes with nonhomogeneous Poisson immigration, and investigate the asymptotic behaviour of its moments. We propose a test of the assumption that the immigration rate is constant. The construction of the test rests on the asymptotic behavior of the coefficient of variation for the population size, which is shown to converge to a strictly positive constant when immigration is time-homogeneous. The proposed test does not require the formulation of a specific process, making it robust to modeling assumptions. An application to real data on the progression of leukemia suggests that the rate of immigration of cells from other compartments into the blood changes as tumor burden increases.

Keywords: Branching processes, Non-homogeneous Poisson process, Coefficient of variation, Leukemia.

Dynamic Life Insurance Model Based on a Multivariate Point Process

Zvetan G. Ignatov Under the traditional life insurance model, it is usually assumed that the number of insured lives is fixed, their mortality rate is constant and the insurance portfolio is closed for new entrants. In this paper, we relax these limitations of the traditional approach and consider the evolution of a portfolio both in time and age, assuming that new prospects are joining, while some of the current members are leaving. We introduce a new life insurance model in which a two-dimensional point process is used to represent the age and time at entry in the insurance portfolio. A time dependent mortality density function is assumed for the current members. For the purpose we apply the Lee-Carter approach. Our model is dynamic and continuous with respect to age and time. Some quantities of interest, characterizing the portfolio are explicitly derived and their evaluation is considered. The use of the model is illustrated numerically, based on real data from a large insurance company.

Keywords: Non-homogeneous Poisson process, life insurance

A generalized quasi-likelihood estimator for a general class of nonstationary stochastic processes: asymptotic properties and examples

Christine Jacob

Unité de Mathématiques et Informatique Appliquées UR341, INRA, 78350 Jouy-en-Josas, France, christine.jacob@jouy.inra.fr

Let {Z n } be a real nonstationary stochastic process on (Ω, F , P θ 0 ), where θ 0 is a unknown p-dimensionalparameter.

We estimate θ 0 from a single trajectory of the process by a GQLE (Generalized Quasi-LikelihoodEstimator) defined by θ n := argmin

θ n k=1 Ψ k (Z k , θ),
where

Ψ k (x, θ) is F k-1 -measurable, {F n } being an increasing sequence of σ-algebras.
This class of estimators includes many different types of estimators such as weighted conditional least squares estimators, L1-norm estimators and maximum likelihood estimators, and allows missing data,outliers, or infinite first two moments of the process.

We give conditions leading to the strong consistency and the asymptotic normality of the GQLE of θ 0 . The proofs are based on martingales or submartingales properties. Some examples are given.

This work is an extension of Jacob (2010).

Branching processes: from simplistic individualism to collective interaction with the environment -a quick tour through 150 years

Peter Jagers

Chalmers and University of Gothenburg, Sweden Branching processes arose in the 1800's as a theory describing reproduction of independently acting individuals of the simplest possible kind, characterized only by their i.i.d. reproduction numbers. Their XX:th Century history can be viewed as a slow journey towards more and more refined modelling of individual behaviour, encompassing first only splitting individuals like particles or cells, but ultimately all known population theories: individuals can be of various types, their life span distributions can take any forms and reproduction occur in multifarious ways, by splitting or in annual random broods, e.g. Two great challenges remain (for our XXI:st Century). One is that reproduction remains clonal and mating plays no role in the more complex models; interesting work has been done for cases of Galton-Watson type. Another is that matters like resources, and its mirror population size, are not taken into account. Recently, this has been addressed in a sequel of papers by French probabilists working in a birth-and-death tradition and by our Russian-Swedish team, through an extremely simple but lucid discrete time binary splitting process. Together with colleagues from Monash University, I have studied general branching processes, which are supercritical below and subcritical above a so called carrying capacity (of their habitat). What are chances that small such populations grow and come close to the carrying capacity? How long will they stay there? And what will happen to their age-distribution, during the (actually long) time such populations will linger around the carrying capacity?

An Evaluation of the Reliability Systems Using Fuzzy MGLFR Distribution

Ezzatallah Baloui Jamkhaneh

Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran, e_baloui2008@yahoo.com

In this paper we introduced a new four parameter distribution called the modified generalizes linear failure rate (MGLFR) distribution which is a general form and generalizes for some well known and most commonly used distributions in reliability such as exponential, Rayleigh, linear failure rate, generalizes linear failure rate and modified Weibull distribution. We investigated and studied some essential properties of this new distribution. Also we consider the problem of the evaluation of system reliability, in which the lifetimes of components are described using a fuzzy MGLFR distribution. Formula of fuzzy reliability characteristics and their α-cut set are presented. The results can be applied to determining the reliability of real objects in cases where parameters of lifetime variable are a vague numerical type.

Keywords: Fuzzy reliability, fuzzy MGLFR distribution, hazard function.

Weak consistency of t-Hill estimator

Pavlina Jordanova

Faculty of Mathematics and Informatics, Shumen University

The t-Hill estimator for independent data was introduced by Fabian and Stehlik (2009). It estimates the extreme value index of distribution function with regularly varying tail. This paper considers a sample with possibly dependent data. Weak consistency of the t-Hill estimator is derived and it is applied in the infinite moving average model. It is shown that in the case of distributions with RV -α , α > 0 tails contaminated with Pareto noise with parameter 0 < δ < 1, the t-Hill estimator is more robust with respect to large observations than the Hill estimator.

Keywords: Point estimation, Asymptotic properties of estimators.

Stability of Regime-Switching Stochastic Differential Equations

Rafail Khasminskii

Wayne State University, USA

The main result of this talk is the reduction of asymptotic stability problem of stochastic differential equation (SDE) with sufficiently rapid Markovian switching to the well studied analogous problem for the "averaged" SDE without switching. Application to the problem of stabilization by switching and to ordinary differential equation (ODE) with switching are also considered.

A sequential approach to statistical decision making in medical diagnostics

Alexey Kharin

Belarusian State University, Minsk, Belarus

For medical diagnostics, tests results are often available in dynamics [1], so statistical methods may be applied to optimize the decision making procedures.

We propose a mathematical model for the decision making process in medical diagnostics and define two composite hypotheses in the frames of this model. These two hypotheses correspond to the two possible terminal decisions: either the therapy will be successfull for the analyzed patient, or it is not effective in this case and should be replaced.

A sequential statistical test is constructed for the discussed model. For the case of Gaussian data, the test statistic is obtained in the analytic form. The performance characteristics are studied for this test theoretically and illustrated via numerical experiments. Robustness [2], [3] of the constructed test is discussed.

The research is partially supported by the ISTC project No. B-1910.

Keywords: medical diagnostics, decision making, sequential test.

given. We then describe the defined process as a compound birth process. As application we consider the standard risk model which counting process is the Poisson process of order k The ruin probability and some approximations are compared with the corresponding results in the classical risk model.

Existence of global and non-global solutions of an SPDE

Jose Alfredo Lopez-Mimbela In this paper, both global and local sensitivity analysis approaches, in the framework of system identification in mechanized tunneling, are presented. The research in this area is part of the Collaborative Research Center SFB 837 funded by the German Research Foundation (DFG).

In the process of the system identification in mechanized tunneling, a numerical simulation of highly nonlinear problem nature of the geotechnical application with respect to both the physical and geometrical characteristics is carried out; this numerical simulation is computationally expensive. In order to make the identification process as efficient and robust as possible, it is favorable to reduce the number of the parameters to be identified (i.e., the number of numerical simulation runs) by performing an effective sensitivity analysis. With this analysis, the importance of each unknown model parameter with respect to the system response is evaluated such that an effective selection of the dominating model parameters is achieved.

A derivative-based sensitivity analysis (local sensitivity analysis) is implemented for the estimation of the system output sensitivity at given base points. Furthermore, a methodology for choosing the best input step size in the numerical estimation of the output derivative with respect to the input parameters is introduced. A major limitation of the derivative-based approach is that it is only informative at the base points, where the derivatives are computed, and it does not investigate the whole space of input parameters. This limitation is of a minor influence in linear systems; however, the geotechnical applications handled in the identification are highly nonlinear.

In order to overcome the locality nature of the derivative-based approach, two other methods, the elementary effect and variance-based sensitivity analysis, which explore the space of the input parameters, are implemented. These methods are categorized within the global sensitivity analysis approach.

In global sensitivity analysis methods the amount of information obtained from the analysis depends on the number and the location of sample points that are taken from the input parameter space. However, the bigger the number of sample points, the higher the computation time of the numerical simulations. Therefore, the elementary effect method tries to identify the most important model parameters in relatively small evaluation points that are well distributed in the parameter space. Whereas, in the variancebased method a significantly big number of evaluation points are needed for the analysis, therefore, a model approximation for the numerical simulation, which is computationally expensive, is unavoidable. Keywords: System identification, numerical simulation, local sensitivity analysis, global sensitivity analysis.

Heavy-Tailed Models for Risk Estimation:

Univariate models

Ivan K. Mitov Head of Quantitative Research, FinAnalytica
The goal of this talk is to present some of the most recent applications of the heavy-tailed models in the field of financial risk modeling and estimation. A brief overview of the stochastic methods employed in the univariate financial variables modeling will be presented. The necessity of each of the components -time-varying volatility, non-Gaussian innovations and changing through time tail parameter will be presented via real market data.

Extremal and additive processes generated by

Pareto distributed random vectors

Kosto V. Mitov Aviation Faculty -National Military University, Pleven, Bulgaria Assume X k = (X 1,k , X 2,k ), k = 1, 2, 3, . . . are i.i.d. random vectors having Pareto distributions P{X 1k > x 1 , X 2k > x 2 } = x 1 c 1 (k) + x 2 c 2 (k) -1 -α , x i ≥ c i (k) ≥ 0, i = 1, 2, . . . .
A series of Bernoulli point processes with non-random time components is defined as follows

N n = {(t nk , X nk ) , k = 1, 2, . . .} := k n , ( X 1k a 1 (n) , X 2k a 2 (n) ) , k = 1, 2, . . . .
The series of point processes defines a sequence of extremal processes

Y n (t) = (Y 1n (t), Y 2n (t)) = k/n≤t X 1k a 1 (n) , X 2k a 2 (n)
and a sequence of additive processes

S n (t) = (S 1 (t), S 2 (t)) = k/n≤t X 1k a 1 (n) , X 1k a 1 (n) .
Some properties the weak limits Y(t), t ≥ 0 and S(t), t ≥ 0 of these two sequences are represented. This is a particular case of the processes studied in [1].

A branching process with immigration in varying environments

Kosto V. Mitov 1 , Edward Omey 2

1 Aviation Faculty -National Military University, Pleven, Bulgaria 2 HUB, Stormstraat 2 -B-1000 Brussels, Belgium

Bienaymé-Galton-Watson branching processes with varying offspring variance and an immigration component are studied in the critical case. The asymptotic formulas for the probability for non-extinction are derived in dependence of the immigration component. Limit theorems are proved too. The investigation of these processes was initiated in [1].

Limit Theorems for Bellman-Harris Branching

Processes with Non-homogeneous Poisson Immigration Kosto V. Mitov 1 , Nickolay M. Yanev 2

1 Aviation Faculty -National Military University, Pleven, Bulgaria 2 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences Bellman-Harris branching processes with non-homogeneous Poisson immigration have been extensively used recently in modeling of cell-proliferation kinetics and the evolution of cancer cells in particular (see e.g. [1], [2].) In the talk we represent some pure theoretical results for these processes depending on the criticality and the intensity of immigration. We have proved the asymptotic of the moments and the probability for visiting the state zero. Several limit theorems are proved too. The obtained results could enlarge the applications of these processes in different areas.

processes with dependence of the number of couples which take part in the reproduction process (progenitor couples). We consider progenitor couples changing, in each generation, in a varying or in a random environment. In both cases, we establish several probabilistic properties and theoretical results. By way of illustration, we provide some simulated examples in population dynamics. Also, we present the software in R that we have developed for its study.

Keywords: Branching processes. Two-sex processes. Population dynamics.

Two-sex branching processes with offspring distribution and random mating depending on the number of females and males in the population

Manuel Mota, Manuel Molina

Department of Mathematics, University of Extremadura, Spain

We introduce a class of two-sex branching processes with offspring distribution and random mating depending on the number of females and males in the population. For such a class of processes, we determine relations among the probability generating functions involved in the probability model and recursive expressions for its main moments. As a consequence of the Markovian properties of the new two-sex model, its duality extinctionexplosion is established. Also, we study its extinction probability, making a distinction between subcritical, critical and supercritical cases.

Keywords: Two-sex branching processes. Population size dependence. Random mating.

The Distribution of Heights of 2-ary Subtrees on Two Types of Galton-Watson Trees

Ljuben R. Mutafchiev

American University in Bulgaria, 2700 Blagoevgrad, Bulgaria and Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences, ljuben@aubg.bg

In the combinatorial theory of trees, a trajectory T of a critical Galton-Watson process starting with a single ancestor, under the hypothesis that its total progeny is equal to n, is called simply generated tree on n vertices (for more details, see [1]). The notion of simply generated trees was introduced by Meir and Moon [5]. For a fixed integer N, 1 ≤ N ≤ n, we consider subtrees of T rooted at the ancestor whose vertices have at least N successors. Let H n,N be the maximum height of the N -ary subtrees of T . Clearly, H n,1 is just the height of T , i.e. the size of the longest path from the root to an end-vertex. For large n, it turns out that the typical order of growth of H n,1 is √ n and the limiting distribution of H n,1 / √ n is the so-called theta distribution. Studies in this direction go back to [6,7,4,3,2]. In the present note, we study H n,2 for two important types of simply generated trees: binary trees on n internal vertices and planted plane (Catalan) trees on n vertices. They correspond to trajectories of conditioned Galton-Watson processes with Bi(2, 1/2) and Ge(1/2) offspring distributions, respectively (Bi and Ge denote the binomial and the geometric probability distribution, respectively). Both cases require an entirely different normalization from that involved in the case N = 1. The method of proof is based on an asymptotic analysis of some nonlinear recurrences for the generating functions of the probabilities P (H n,2 ≥ h), h ≥ 0. The following limit theorems are obtained.

Theorem 1. The maximum height H n,2 of 2-ary subtrees on binary trees with n internal vertices satisfies

lim n→∞ P (H n,2 = h) = 2 -h-1 , h ≥ 0.
Theorem 2. The maximum height H n,2 of 2-ary subtrees on planted plane trees on n vertices satisfies

lim n→∞ P (H n,2 = h) = 2(c h -c h+1 ), h ≥ 0, where c 0 = 1 2 , c 1 = 3 8 , c h = (41)2 h-1 3 r 1,h-1 -2 h-2 3 r 2,h-1 -• • • -(2)3 r h-1,h-1 -(2)3 r h,h (3 2 h -1) 2 , h ≥ 2
and r k,l = l j=k 2 j , 1 ≤ k ≤ l. Numerical computations show that 2(c 0c 1 ) = 0.25, 2(c 1c 2 ) = 0.575625, 2(c 2c 3 ) = 0.169435975 and that P (H n,2 ≥ 3) ≈ 0.005, for planted plane trees.

Parameter Estimation for Tempered Stable Distributions

Metodi Nikolov

Sofia University

The Tempered Stable class of distributions are derived via the multiplication of the Levý measure of the Stable distribution with a particular tempering function. Their usefulness comes in capturing the skewness and heavy tailed-ness of the Stable distribution, while also having a finite variance. In this work, we are concerned with the estimation of parameters of the Tempered Stable distribution, with emphasis given to the Bayesian method of statistical inference.

Minimum Description Length Principle in Model Selection

Bono Nonchev

Sofia University, Faculty of Mathematics and Informatics

In this paper we present the MDL principle in model selection and in particular when discriminating between a model with normal marginal distributions vs a model with Student-t marginal distributions. We offer the analytic formulas for model complexity in those two simple cases and the idea for an optimised numerical approach for the more general case that can be used for the fat-tailed distributions commonly found in econometric time series.

Keywords: Model selection, MDL, AIC, Information criteria, Heterogeneous models, Student-t distribution.

A stochastic model of cell desynchronization

Peter Olofsson

Trinity University

A general (Crump-Mode-Jagers) branching process model is suggested to describe cell cycle desynchronization. Cell cycle phase times are modeled as random variables and random charactierstics are used to count cells in S phase which establishes a formula for the expected fraction of cells in S phase. Our model is compared to data from the literature and is also compared to previously suggested deterministic and stochastic models. The results we obtain serve as testimony to the modeling strength and predicitve powers of general branching process theory.

Modeling data for complications in diabetics using logistic regression K. Prodanova A prospective study of the relationships between complications and genetic markers and complications and some clinical parameters of the patients with diabetes is undertaken. About 200 patients (male and female) are studied. The patient are classified in to five groups subject to type of the diabetes. Data obtained for each patient are type of the complications -macro vascular, retina pathology, neuron pathology and nephrite pathology, 12 clinical parameters and 6 genetic markers. A logistic regression to identify which factors were associated independently with the complications is performed.

Correlated Binomial Model with Applications

Petar Radkov, Leda D. Minkova

Sofia University, Faculty of Mathematics and Informatics

In this paper, we introduce a sequence of dependent Bernoulli trials, which forms a homogeneous Markov chain. Then we define two types of geometric and negative binomial distributions, as well as binomial distribution, related to this sequence. Some properties of the defined distributions are given. Recursion formulas and probability mass functions are derived. An example with data of financial market is given. It is well known that a supercritical Bienyame-Galton-Watson process can be decomposed into a two-type branching process. Type 1 particles form infinite lines of descent and type 2 particles form subcritical branching processes resulting from conditioning on extinction. Particles of type 1 can produce offspring of both types, while the type 2 particles can have offspring only of the same type 2. The remarkable fact that a supercritical branching process conditioned on extinction is again a branching branching though subcritical was recently established in a much more general setting [1]. Although in general the corresponding transformation is not given explicitly, one can find in [1] several examples of explicit results.

In this paper we take up these issues in the framework of the linearfractional branching processes with countably many types, see [2]. We produce a number of calculations providing with a new example of explicit formulae for the decomposition of supercritical branching processes for a special class of Crump-Mode-Jagers processes.

On Supra-Bayesian weighted combination determined by Kerridge inaccuracy and entropy

Vladimíra Sečkárová The contribution deals with the Supra-Bayesian approach to parameter estimation of a discrete random variable's distribution using several information sources. To obtain these estimates, we seek for a posterior distribution of these parameters maximizing the entropy subject to specific constraints. These constraints are represented by Kerridge inaccuracy between information given by each source and the true but unknown distribution. There are a few issues regarding the choice of the value for each constraint and following computation of Lagrange multipliers. Here, we suggest that the entropy of each information source is the answer to the former problem. But the analytical intractability, preventing from direct evaluation of the multipliers and the estimates, is still present. The dificulty is solved by means of numerical optimization, exploiting the properties of the gamma and digamma functions.

Keywords: non-linear optimization, Kerridge inaccuracy, entropy.

On estimation and testing for Pareto tail

Milan Stehlík

Department of Applied Statistics and Econometrics, Johannes Kepler University

Linz, e-mail: Milan.Stehlik@jku.at

If the model underlying the data, is a regularly varying function with index -1/alpha it is usually supposed that the top scaled order statistics are Pareto distributed. [START_REF] Hill | A Simple General Approach to Inference About the Tail of a Distribution[END_REF] derived a procedure of Pareto tail estimation by the MLE. Later on, many authors tried to robustify the Hill estimator, but they still rely on maximum likelihood, e.g. Fraga Alves (2001) has introduced a new lower bound. However, the inuence function of Hill estimator is slowly increasing, but unbounded. Hill procedure is thus no robust and many authors tried to make the original Hill robust (see [START_REF] Beran | On robust tail index estimation[END_REF]Schell, 2010 or Vandewalle et al. 2007). In [START_REF] Fabián | Induced cores and their use in robust parametric estimation[END_REF] a new method of score moment estimators has been proposed. It appeared that these score moment estimators are robust for a heavy tailed distributions (see Stehlík et al. (2010)). In Fabián and Stehlík (2010) we understand "The Hill estimator" as a specific procedure for studying of the tail of Pareto distribution. Instead of implementing "The Hill estimator" procedure, we implement the score moment procedure. For the case of Pareto distribution, the Hill estimator procedure with the score moment estimator has been investigated in [START_REF] Stehlík | Small sample robust testing for Normality against Pareto tails[END_REF] for optimal testing for normality against Pareto tail. Since the score moment estimator is simple, it is easy to implement it to the Hill procedure. In literature, mainly the asymptotical properties of tail estimators are studied. However, in many situations, asymptotics is simplifying the underlying process too much (see e.g. [START_REF] Huisman | Tail-Index Estimates in Small Samples[END_REF]). We may illustrate this fact by a severe bias of the Hill based estimators or by a distributional insensitivity of asymptotical estimators. In many practical situations, such as operational risk assessment, data are sparse (with sample size often bellow 50) and therefore robust estimator with good small sample properties is needed. We will show how to construct a "naturally" robust, distribution sensitive heavy tail estimator and prove its weak consistency together with its good small sample properties. We will illustrate its applications in robust testing for normality against heavy tails. Many open questions remains: these will be also introduced.

Crump-Mode-Jagers Branching Process: Modelling and Application for Human Population P. Trayanov

FMI, Sofia University

Based on Crump-Mode-Jagers branching process theory (see [2]) a methodology for modelling the human population is described and it is shown how the Malthusian parameter can be numerically estimated using this model. We obtain certain characteristics of birth and death in the population which reflect the current demographic status. The interaction of these characteristics determines the rate at which the population is expected to grow or diminish and in this sense the Malthusian parameter plays role as a combined measure for demographic conditions and allows us to compare populations unambiguously. Demographic comparison between Sweden, Greece, Slovenia and Bulgaria is made using the estimated Malthusian parameter and official EUROSTAT data [1]. These results also show whether and how much the economic crisis affects the population growth in these countries. nice and simple mathematical technique for describing processes starting with a single object, which then duplicates and gives 0, 2, or 3 or more descendants. It is called the theory of branching processes. It deals with asexual reproduction and gives methods to calculate the number of existing particles, of various kinds, in future generations, and other questions of this sort. I would like to stress that a corresponding theory for branching with sex, where particles get together, say, at random and then produce offspring, i.e., combination of a binary process of mating and reproduction, is mathematically much more difficult and no exact theory exists as yet." We will discuss processes with mating and, in more detail, some questions about the distribution of the time to extinction.

Branching processes with lattice spatial dynamics and a finite set of particle generation centers

Elena Yarovaya In previous branching random walk models only the time-asymptotic results under fixed spatial coordinates were used. In the situation when the spatial and temporal variables grow jointly it is urgent to know asymptotic behavior of the Green functions of random walk transition probabilities for branching random walks with large deviations. Cranston et al. (J. Funct. Anal., 2009, 256:8) proposed a new approach based on the resolvent analysis of evolutionary operators to study a continuous model of homopolymers on R d with path large deviations for Brownian motion. We use resolvent analysis of the spectrum of a bounded symmetric operator with multi-points potential to investigate branching random walks on Z d with large deviation and several sources of branching. Limit theorems for the Green functions of transition probabilities are obtained. A special attention is paid to the case when the spectrum of the evolution operator of mean numbers of particles contains only one positive isolated eigenvalue. The obtained results expand the previous studies in various directions such as the concept of the front reaction, the structure of the population inside of the front and near to its boundary, and so on.

The research was partly supported by RFBR grant 10-01-00266.

  Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev 25 A, 1113 Sofia, Bulgaria

Keywords:

  Markov sequence, Negative binomial distribution, Correlated Markov binomial distribution Decomposition of supercritical branching processes with countably many types Serik Sagitov, Altynay Shaimerdenova Chalmers U. of Technology, University of Gothenburg and Al-Farabi University

  For this last problem, Monte-Carlo sampling-based and analytic approximations are discussed. The results are illustrated with both simulated and real-data examples. This is a coauthored work with M. González, C. Gutiérrez and R. Martínez.

	or rules, referred to as cognitive attributes, and information about which
	attributes are required for the correct solution of each test item. As the at-
	tributes are hypothesized according to a cognitive theory in the context of
	study, they are latent (hidden) in nature and cannot be measured and scored
	directly. Knowledge about cognitive structures can help test developers,
	psychologists, and educators to better understand the cognitive processes
	of thinking, learning, and performance. The least squares distance model of
	cognitive diagnosis (LSDM; Dimitrov, 2007; Dimitrov & Atanasov, 2012)
	uses estimates of the item parameters under a specific item-response theory
	(IRT) model to provide estimates of the probability of a person to process
	correctly any cognitive attribute given the person's location on the IRT logit
	scale.
	Group Comparisons on Cognitive Attributes Using the Least Squares Distance Model of Cognitive Diagnosis
	Dimiter M. Dimitrov 1 , Dimitar V. Atanasov 2

2 1

 2 University of Rochester 2 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

  1 , Vladimir K. Kaishev 2,3 , Rossen S. Krachunov 3 1 Faculy of Economics, Sofia University, "St.Kliment Ohridski" 2 Cass Business School, City University London 3 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia

  1 , S. Pashkunova 2

	1 Technical University of Sofia
	2 Military Medical Academy

  Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University in Prague, seckarov@karlin.mff.cuni.cz Department of Adaptive Systems, Institute of Information Theory and Automation of the ASCR, Prague

  1 , Stanislav Molchanov 2 1 Moscow State University, Russia 2 The University of North Carolina, USA

* The research was partially supported by appropriated state funds for research allocated to Sofia University (contract No 125/2012), Bulgaria.

George Mason University, USA

New Bulgarian University, BulgariaThe cognitive structure of a test in education, psychology, and other behavioral fields is typically defined by a set of cognitive operations, processes * The research was supported by the Ministerio de Economía y Competitividad, Junta de Extremadura and the FEDER through the grants MTM2009-13248 and GR10118.

Teodosi Geninski 1 , Ivan Mitov 2 , Svetlozar Rachev 2 , Frank Fabozzi 2 1 Sofia University, Faculty of Mathematics and Informatics 2 FinAnalytica Inc.

Exponential Functionals of Brownian Motion and Explosion Times of a System of Semilinear SPDEs

Ekaterina T. Kolkovska

Centro de Investigacion en Matematicas, Guanajuato, Mexico

We investigate lower and upper bounds for the blowup times of a system of semilinear SPDEs. Under certain conditions on the system parameters, we obtain explicit solutions of a related system of random PDEs, which allows us to use a formula due to Yor to obtain the distribution functions of several explosion times. We also give the Laplace transforms at independent exponential times of related exponential functionals of Brownian motion.

Keywords: Blowup of systems of semi-linear equations, systems of stochastic partial differential equations.

On the Poisson process of order k

Krasimira Kostadinova 1 , Leda Minkova In this notes, we discuss discrete compound distributions, in which the counting distribution is a weighted distribution. The particular case of weighted Poisson counting distribution is analyzed. The over-and underdispersion of these distributions is then discussed. Several forms of compounding distributions and weight functions are then examined in detail.

Keywords: Weighted distribution, compound distributions, over-dispersion, under-dispersion, log-concavity, log.

Heavy-Tailed Models for Risk Estimation:

Dependence structures

Georgi Mitov

Head of Quantitative Product Development, FinAnalytica Inc.

The goal of this talk is to present some of the most recent applications of the heavy-tailed models in the field of financial risk modeling and estimation. A comparison of the methodologies for describing the tail dependence between assets will be examined. The necessity of each of the components -nonlinear and asymmetric dependence will be presented via real market data. Two-sex branching processes are appropriate mathematical models to describe the demographics dynamics in sexually reproducing biological populations. We are especially interested in the study of two-sex branching

Two-sex branching processes depending of the number of progenitor couples in the population

Saddlepoint tests for regression quantiles

Radka Sabolová

Department of Probability and Mathematical Statistics Faculty of Mathematics and Physics Charles University in Prague, Czech Republic, sabolova@karlin.mff.cuni.cz

Quantile regression enables us to study the conditional quantiles of a dependent random variable and therefore offers a more complex view at the behavior of random variables. By appropriate choice of quantile we can study not only conditional median but also behavior in tails and get an idea about variability of studied random variable.

We are particularly interested in the parametric and nonparametric regression quantile tests and will show that extremely accurate approximations for the density of a statistic and for the p-values of a test criterion, even under a very small sample size, yields the saddle-point method. Test statistic is based on the exponent in the saddle-point approximation to the density of the function of M-estimates. Although this statistic is analogous to the log likelihood ratio in the parametric case, the relative error is of order n -1 . In case the distribution of observations in unknown, we will use empirical likelihood statistic.

Combination of simplicity of score function for regression quantile as an M-estimator and asymptotic properties of saddlepoint tests allows us to construct a test statistic with an explicit formula that makes proposed test much easier to use and works very well even under small sample sizes. The precision of the tests will be numerically illustrated.

The work was supported by the grant SVV 265 315.

Keywords: saddlepoint test, regression quantiles, small sample.

Rank tests for the multi-sample location problem

Eugenia Stoimenova

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Nonparametric tests are proposed for the homogeneity of k-samples, where the alternatives of interest are of the form F 1 (x) ≥ . . . ≥ F k (x) for all x with at least one strict inequality. The test statistics are based on the number of precedences and exceedances of each sample with respect to thresholds from the other samples. The tests can be viewed as extension of the two-sample rank tests proposed by [START_REF] Stoimenova | A class of exceedance-type statistics for the two-sample problem[END_REF]. Small sample null distributions are discussed, and the results of a Monte Carlo power study are presented.

Subcritical branching processes in random environment

Vladimir Vatutin

Steklov Mathematical Institute, Moscow

Let Z n , n = 0, 1, . . . be a branching process in random environment specified by iid (random) probability generating functions f 0 (s), f 1 (s), . . . ,

be the associated random walk for such a process. It is known that the set of all subcritical branching processes in random environment may be divided into 4 classes depending on the properties of the distributions of the increments of S n . We give a survey of the recent results dealing with the survival probabilities of the mentioned classes of subcritical branching processes and with the Yaglom type functional limit theorems for the number of particles in such processes given their survival up to a distant moment. These results are obtained in collaboration with V. I. Afanasyev (Steklov Mathematical Institute), C. Boeinghoff, G. Kersting, J. Geiger (Frankfurt), and X. Zehng (Hongkong).

Keywords: branching processes, limit theorems, random walk.

Marginal Densities of the Wishart Distribution

Evelina Veleva

Rousse University "A. Kanchev", Rousse

Wishart distribution arises as the distribution of the sample covariance matrix for a sample from a multivariate normal distribution. We present each subset of covariance coefficients as a special undirected graph. The paper discusses different marginal densities, derived by integration of the Wishart density function.

Keywords: Wishart distribution, positive definite matrix, marginal density, covariance matrix.

Extinction time in branching processes with mating

George Yanev 1 , David Hull 1 , Manuel Mota The study has been taken on a new method for dental prosthetics in which a software for modelling the occlusal curves has been utilized. Measures has been taken on 103 students from the Department of Stomatology in Sofia, at the age of 19-26 years, of which 49 women and 54 men. The kmeans and hierarchical cluster methods has been applied on the same data. The purpose of the study is to help and improve the already existing expert's classification.

Keywords: occlusal curves, kmeans cluster method, hierarchical cluster method.


est destinée au dépôt

Specificity of eIF4E factors towards resistance to potyviruses in Arabidopsis thaliana

Aramata Marena, Caroline Callot, André Moretti, Jean-Luc J.-L. Gallois

To cite this version:

Aramata Marena, Caroline Callot, André Moretti, Jean-Luc J.-L. Gallois. Specificity of eIF4E factors towards resistance to potyviruses in Arabidopsis thaliana.

Specificity of eIF4E factors towards resistance to potyviruses in Arabidopsis thaliana

Aramata MARENA, Caroline CALLOT, André MORETTI et Jean-Luc GALLOIS INRA-UR 1052. Génétique et Amélioration des Fruits et Légumes (GAFL) Domaine St Maurice, CS 60094. F-84143 Montfavet cedex e-mail : jlgallois@avignon.inra.fr

The translational initiation factors eIF4E represent the main resistance to Potyvirus as well as to other families of plant RNA virus. Although those factors are encoded by small multigenic families, it has been shown that each virus can only use specific eIF4E to perfom its cycle in plants. Often, this coincides with the ability of the virus VPg to interact with those host proteins. Using Arabidopsis transgenic approaches, we aimed at better understanding the basis of the virus specificity for eIF4E.

First, we looked at the interaction pattern of the Clover Yellow Vein Virus (ClYVV) VPg with all five Arabidopsis eIF4E proteins and found that it interacts with three of them. However, Arabidopsis mutant studies have shown that only eIF4E1 is necessary to allow ClYVV infection. This suggests that unlike what has been shown for other plants (as pepper and tomato), not only the eIF4E protein sequence but also its gene expression pattern may have a key role in susceptibility, as we investigated by studying various eIF4E overexpressions.

Then we looked at a case in which the same virus can use very different eIF4E in separate species: the Tobacco Etch Virus (TEV) relies on eIF4E1 in tomato and pepper but on its isoform eIFiso4E in Arabidopsis. To see whether this specificity depends on those eIF4E isoforms only, or rather on a more general host protein complex, we over-expressed pepper eIF4E in TEV-resistant Arabidopsis to see whether it can restore host susceptibility to TEV.

As a result from those idiosyncratic eIF4E requirements, broadening the resistance spectrum of plants to viruses may require the inactivation of different eIF4E genes, a process which may be detrimental to the plant development. Indeed, we show that the double mutant eif4e1; eifiso4e is lethal in Arabidopsis. As an alternative, we aimed at creating new resistance alleles in Arabidopsis by mimicking natural -and possibly functional-resistance alleles that have been characterized in other species. We hope this may help developing new resistances alleles to Potyvirus, including in plants species for which none has been described so far.

.