A Note on the Extinction Problem for Controlled Multitype Branching Processes

2000 Mathematics Subject Classification: 60J80, 60J10.

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Simulation and Robust Modifications of Estimates in Branching Processes

This study is focused on the comparison and modification of different estimates arising in the branching processes. Simulations of models with or without migration are put through. Due to the complexity of the computations the algorithms are designed with the language of technical computing MATLAB. Using the simulations, estimates of the o spring mean of the generated processes are calculated. It is well known in the literature that under certain conditions the asymptotic distribution of the estimates is proved to be normal. Using the asymptotic normality a modified method of maximum likelihood is proposed. The aim is to obtain trimmed maximum likelihood estimates based on several sample paths with the same number of generations. Thus in a natural way the observations, inconsistent with the aprior information about the asymptotic normality are excluded from the model. The computation of the standard error allows the comparison of different types of estimates.

Situational Script Management of Business Processes with Changeable Structure

In the presented work the problem of management business-processes with changeable structure is considered and situational based approach to its decision is offered. The approach is based on situational model of management business-process according to which process is represented as a set of situations. The script defining necessary actions is connected with each situation. Management of process is carried out by means of the rules formalizing functional requirements to processes.

Using Inside-Outside Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes

Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are particles of different types. Usually such a process is not observable in the sense of the whole tree, but only as the “generation” at a given moment in time, which consists of the number of particles of every type. This requires an EM-type algorithm to obtain a maximum likelihood (ML) estimate of the parameters of the branching process. Using a version of the inside-outside algorithm for stochastic context-free grammars (SCFG), such an estimate could be obtained for the offspring distribution of the process.

On the Extinction Probability for Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Large Deviations and Branching Processes

These lecture notes are devoted to present several uses of Large Deviation asymptotics in Branching Processes.

Em Estimation of the Offspring Distribution in Mutitype Branching Processes - a Model in Cell Kinetics

2000 Mathematics Subject Classification: 60J80, 60J85, 62P10, 92D25.

Subcritical Randomly Indexed Branching Processes

2000 Mathematics Subject Classification: 60J80, 62P05.

Some Bounds for Almost Absorbing Birth and Death Processes with Catastrophes

2000 Mathematics Subject Classification: 60J27.

Characterization of Schrödinger Processes with Unbounded Potentials

2000 Mathematics Subject Classification: 49L20, 60J60, 93E20

Estimation of the Offspring Mean in a General Single-Type Size-Dependent Branching Process

2000 Mathematics Subject Classification: 60J80, 62F12, 62P10

Problems Connected with the Realisation of State E-governance in the Republic of Bulgaria

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Controlled Multitype Branching Models: Geometric Growth

2000 Mathematics Subject Classi cation: 60J80, 60F25.

Application of the Artificial Intelligence Algorithms with a Cognitive Graphic as a Tool for a System Analysis of Electrophysiological Processes

Summarizing the accumulated experience for a long time in the polyparametric cognitive modeling of different physiological processes (electrocardiogram, electroencephalogram, electroreovasogram and others) and the development on this basis some diagnostics methods give ground for formulating a new methodology of the system analysis in biology. The gist of the methodology consists of parametrization of fractals of electrophysiological processes, matrix description of functional state of an object with a unified set of parameters, construction of the polyparametric cognitive geometric model with artificial intelligence algorithms. The geometry model enables to display the parameter relationships are adequate to requirements of the system approach. The objective character of the elements of the models and high degree of formalization which facilitate the use of the mathematical methods are advantages of these models. At the same time the geometric images are easily interpreted in physiological and clinical terms. The polyparametric modeling is an object oriented tool possessed advances functional facilities and some principal features.