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.

Computer Networks Security Models - A New Approach for Denial-of-Services Attacks Mitigation

Computer networks are a critical factor for the performance of a modern company. Managing networks is as important as managing any other aspect of the company’s performance and security. There are many tools and appliances for monitoring the traffic and analyzing the network flow security. They use different approaches and rely on a variety of characteristics of the network flows. Network researchers are still working on a common approach for security baselining that might enable early watch alerts. This research focuses on the network security models, particularly the Denial-of-Services (DoS) attacks mitigation, based on a network flow analysis using the flows measurements and the theory of Markov models. The content of the paper comprises the essentials of the author’s doctoral thesis.

Calculation of Reliability Characteristics for Regenerative Models

If a regenerative process is represented as semi-regenerative, we derive formulae enabling us to calculate basic characteristics associated with the first occurrence time starting from corresponding characteristics for the semi-regenerative process. Recursive equations, integral equations, and Monte-Carlo algorithms are proposed for practical solving of the problem.

Improved Hybrid Model of HMM/GMM for Speech Recognition

In this paper, we propose a speech recognition engine using hybrid model of Hidden Markov Model (HMM) and Gaussian Mixture Model (GMM). Both the models have been trained independently and the respective likelihood values have been considered jointly and input to a decision logic which provides net likelihood as the output. This hybrid model has been compared with the HMM model. Training and testing has been done by using a database of 20 Hindi words spoken by 80 different speakers. Recognition rates achieved by normal HMM are 83.5% and it gets increased to 85% by using the hybrid approach of HMM and GMM.

Построение Логико-Вероятностных Моделей Временных Рядов с Использованием Цепей Маркова

The method of logic and probabilistic models constructing for multivariate heterogeneous time series is offered. There are some important properties of these models, e.g. universality. In this paper also discussed the logic and probabilistic models distinctive features in comparison with hidden Markov processes. The early proposed time series forecasting algorithm is tested on applied task.

An Overview of Modelling Bulgarian Wildland Fire Behaviour by Application of a Mathematical Game Method and WRF-Fire Models

This paper presents the main achievements of the author’s PhD dissertation. The work is dedicated to mathematical and semi-empirical approaches applied to the case of Bulgarian wildland fires. After the introductory explanations, short information from every chapter is extracted to cover the main parts of the obtained results. The methods used are described in brief and main outcomes are listed. ACM Computing Classification System (1998): D.1.3, D.2.0, K.5.1.

Single-Server Queueing System with Markov-Modulated Arrivals and Service Times

Key words: Markov-modulated queues, waiting time, heavy traffic.

On the Lp-Norm Regression Models for Estimating Value-at-Risk

Analysis of risk measures associated with price series data movements and its predictions are of strategic importance in the financial markets as well as to policy makers in particular for short- and longterm planning for setting up economic growth targets. For example, oilprice risk-management focuses primarily on when and how an organization can best prevent the costly exposure to price risk. Value-at-Risk (VaR) is the commonly practised instrument to measure risk and is evaluated by analysing the negative/positive tail of the probability distributions of the returns (profit or loss). In modelling applications, least-squares estimation (LSE)-based linear regression models are often employed for modeling and analyzing correlated data. These linear models are optimal and perform relatively well under conditions such as errors following normal or approximately normal distributions, being free of large size outliers and satisfying the Gauss-Markov assumptions. However, often in practical situations, the LSE-based linear regression models fail to provide optimal results, for instance, in non-Gaussian situations especially when the errors follow distributions with fat tails and error terms possess a finite variance. This is the situation in case of risk analysis which involves analyzing tail distributions. Thus, applications of the LSE-based regression models may be questioned for appropriateness and may have limited applicability. We have carried out the risk analysis of Iranian crude oil price data based on the Lp-norm regression models and have noted that the LSE-based models do not always perform the best. We discuss results from the L1, L2 and L∞-norm based linear regression models. ACM Computing Classification System (1998): B.1.2, F.1.3, F.2.3, G.3, J.2.

Lp Microlocal Supercritical Markov Branching Processes with Non-Homogeneous Poisson Immigration

2010 Mathematics Subject Classification: 60J80.