Lattice-Gas Cellular Automata In Modeling Biological Pattern Formation

There are several phenomena present in the physical world which can be defined or predicted by specific models. Cellular automata are basic mathematical models for characterization of natural systems by generating simple components and their local interactions. These models are specified on simple updating rules yet demonstrate complex behavior of physical phenomena. Besides this, lattice-gas cellular automata models go one step further and differ from cellular automata by having split updating rule into two parts as collision and propagation. In this study, the goal is to analyze hexagonal lattice-gas cellular automata with single cell type by using agent-based modeling and simulate the model with NetLogo to observe pattern formation. The model examination is focused on the two parameters for stability analysis. The results show that if there is a pattern formation in the model, the system is unstable, and if the patches are smaller and lighter patches, it is stable. Furthermore, the analysis for the choice of particle density and adhesion coefficient displayed that they are the main decision-mechanisms for general structure

Making dynamic modelling effective in economics

Mathematics has been extremely effective in physics, but not in economics beyond finance. To establish economics as science we should follow the Galilean method and try to deduce mathematical models of markets from empirical data, as has been done for financial markets. Financial markets are nonstationary. This means that 'value' is subjective. Nonstationarity also means that the form of the noise in a market cannot be postulated a priroi, but must be deduced from the empirical data. I discuss the essence of complexity in a market as unexpected events, and end with a biological speculation about market growth.Economics; fniancial markets; stochastic process; Markov process; complex systems

Spatiotemporal modeling and model restructuration approaches in studies of intracellular signalling pathways

The main focus of the research is to understand the complex phenomena of cell transduction pathways and cell biology in a single cell. Mathematical modeling and experimental evaluation are widely used approaches for this kind of research. Firstly, A multiscale framework for protein-protein interaction has been established using Brownian dynamics algorithm. Sit specific feature, steric collision, diffusion, co-localization and complex formation with time and space has been included in this spatial modeling framework. By implementation of the time adaptive feature in this framework, the computation time reduces in an order of magnitude compared with traditional modeling framework. This multiscale Brownian framework has been used for the investigation FcεRI aggregation which is an important signaling pathway for immune cells. Using the spatial modeling framework, FcεRI aggregation in the presence of trivalent antigen showed consistent results with current experimental studies. Secondly, the rule-based modeling approach is an excellent way of performing large biochemical network modeling for a single cell as it considers the site-specific features. However, the major difficulty of rule-based modeling approach is combinatorial complexity. In this study, model restructuring approaches have been applied to overcome this problem for cell signaling pathway modeling. These mechanistic modeling approaches are very effective to model large network of signaling pathways together without compromising the accuracy. Finally, Cell size dependent cellular uptake study carried out using confocal microscopy and flow cytometer. To understand the particle uptake behavior with time and steady state condition, reaction-diffusion and kinetics model has been developed in these work. After a detailed analysis of experimental data and models, it showed that total particle uptake is increasing with cell size, however, particle flux is reducing in larger cells --Abstract, page iv

Prion crystalization model and its application to recognition pattern

This paper introduces APA (?Artificial Prion Assembly?): a pattern recognition system based on artificial prion crystalization. Specifically, the system exhibits the capability to classify patterns according to the resulting prion self- assembly simulated with cellular automata. Our approach is inspired in the biological process of proteins aggregation, known as prions, which are assembled as amyloid fibers related with neurodegenerative disorders

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Mathematical Biology

Mathematical biology is a fast growing field of research, which on one hand side faces challenges resulting from the enormous amount of data provided by experimentalists in the recent years, on the other hand new mathematical methods may have to be developed to meet the demand for explanation and prediction on how specific biological systems function

Space-Time Continuous Models of Swarm Robotic Systems: Supporting Global-to-Local Programming

A generic model in as far as possible mathematical closed-form was developed that predicts the behavior of large self-organizing robot groups (robot swarms) based on their control algorithm. In addition, an extensive subsumption of the relatively young and distinctive interdisciplinary research field of swarm robotics is emphasized. The connection to many related fields is highlighted and the concepts and methods borrowed from these fields are described shortly