A Bayesian Spatial Mixture Model for FMRI Analysis

We develop, implement and study a new Bayesian spatial mixture model (BSMM). The proposed BSMM allows for spatial structure in the binary activation indicators through a latent thresholded Gaussian Markov random field. We develop a Gibbs (MCMC) sampler to perform posterior inference on the model parameters, which then allows us to assess the posterior probabilities of activation for each voxel. One purpose of this article is to compare the HJ model and the BSMM in terms of receiver operating characteristics (ROC) curves. Also we consider the accuracy of the spatial mixture model and the BSMM for estimation of the size of the activation region in terms of bias, variance and mean squared error. We perform a simulation study to examine the aforementioned characteristics under a variety of configurations of spatial mixture model and BSMM both as the size of the region changes and as the magnitude of activation changes.

Services for Satellite Data Processing

Data processing services for Meteosat geostationary satellite are presented. Implemented services correspond to the different levels of remote-sensing data processing, including noise reduction at preprocessing level, cloud mask extraction at low-level and fractal dimension estimation at high-level. Cloud mask obtained as a result of Markovian segmentation of infrared data. To overcome high computation complexity of Markovian segmentation parallel algorithm is developed. Fractal dimension of Meteosat data estimated using fractional Brownian motion models.

Detecting Precipitation Climate Changes: An Approach Based on a Stochastic Daily Precipitation Model

2002 Mathematics Subject Classification: 62M10.

A Test of Association between Qualitative Trait and a Set of SNPs

2000 Mathematics Subject Classification: 62P10, 92D10, 92D30, 62F03

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

Electronic Education in the Field of Electrical Engineering Disciplines. Combined Didactic Interactive Program System

At present in the educational process of electrical engineering disciplines electronic learning program, providing control over reproductive educational-cognitive activity (the decision of standard problems) and universal modeling program systems, for instance Electronics Workbench, giving a chance of organizing productive, in particular research activity are basically used. However universal modeling program systems can not provide auto control over educational-cognitive activity because of the absence of the feedback with students. The combined didactic interactive program system, providing the closed directed auto control over both the reproductive and productive heuristic educational-cognitive activity of the student is offered.

Domain Modeling to Support Anti-cyber Crime Education

This paper describes an approach to a computer-based learning of educational material. We define a model for the class of subjects of our interest - teaching of investigation and prevention of computer crimes, (those including both theoretical and practical issues). From this model, specific content outlines can be derived as subclasses and then instanced into actual domains. The last step consists in generating interactive documents, which use the instanced domain. Students can explore these documents through a web browser. Thus, an interactive learning scenario is created. This approach allows reusing and adapting the contents to a variety of situations, students and teaching purposes.

On the Structure of Spatial Branching Processes

The paper is a contribution to the theory of branching processes with discrete time and a general phase space in the sense of [2]. We characterize the class of regular, i.e. in a sense sufficiently random, branching processes (Φk) k∈Z by almost sure properties of their realizations without making any assumptions about stationarity or existence of moments. This enables us to classify the clans of (Φk) into the regular part and the completely non-regular part. It turns out that the completely non-regular branching processes are built up from single-line processes, whereas the regular ones are mixtures of left-tail trivial processes with a Poisson family structure.

Discrete Models of Time-Fractional Diffusion in a Potential Well

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.

Mathematical Modeling for Studying Microbial Processes – Some Examples

Mathematical modeling may have different purposes in chemical and biochemical engineering sciences. One of them is to confirm or to reject kinetic models for certain processes, or to evaluate the importance of some transport phenomena on the net chemical or biochemical reaction rate. In the present paper different microbial processes are considered and modeled for evaluation of kinetic constants for batch and continuous processes accomplished by free and immobilized microbial cells. The practical examples are from the field of wastewater treatment and biosynthesis of products, like enzymes, lactic acid, gluconic acid, etc. By the aid of mathematical modeling the kinetics and the type of inhibition are specified for microbial wastewater denitrification and biodegradation of halogenated hydrocarbons. The importance of free and immobilized cells and their separate contribution to the overall microbial process is also evaluated for some fermentation processes: gluconic acid production, dichloroethane biodegradation, lactic acid fermentation and monochloroacetic acid biodegradation.

Robust Parametric Estimation of Branching Processes with a Random Number of Ancestors

2000 Mathematics Subject Classification: 60J80.

Branching Processes in Autoregressive Random Environment

2000 Mathematics Subject Classification: 60J80, 60K05.

A New Class of Processes for Formalizing and Generalizing Individual-Based Models: The Semi-Semi-Markov Processes

2000 Mathematics Subject Classification: 60K15, 60K20, 60G20,60J75, 60J80, 60J85, 60-08, 90B15.

A Note on the Extinction Problem for Controlled Multitype Branching Processes

2000 Mathematics Subject Classification: 60J80, 60J10.

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.