arXiv subjects

Abdul S. Jarrah

Publications and source records attributed to Abdul S. Jarrah.

4 recordsLinked to original sources

arXiv2009

Parameter estimation for Boolean models of biological networks

Boolean networks have long been used as models of molecular networks and play an increasingly important role in systems biology. This paper describes a software package, Polynome, offered as a web service, that helps users construct Boolean network models based on experimental data and biological input. The key feature is a discrete analog of parameter estimation for continuous models. With only experimental data as input, the software can be used as a tool for reverse-engineering of Boolean network models from experimental time course data.

q-bio.MN↗

arXiv2008

Stabilizing and Destabilizing Effects of Embedding 3-node Subgraphs on State Space of Boolean Networks

We demonstrate the effects of embedding subgraphs using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical properties of network embedded seven different subgraphs including feedback and feedforward subgraphs, we found that complexity of the state space that increases with longer length of attractors and greater number of attractors is reduced for networks with more feedforward subgraphs. In addition, feedforward subgraphs can also provide higher mutual information with lower entropy in a temporal program of gene expression. Networks with other six subgraphs show opposite effects on dynamics of the networks, is roughly consistent with Thomas's conjecture. These results suggest that feedforward subgraphs are one of the favorable local structures in biological complex networks.

nlin.CG↗

arXiv2008

On the algebraic geometry of polynomial dynamical systems

This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks. It is shown that several problems relating to their structure and dynamics, as well as control theory, can be formulated and solved in the language of algebraic geometry.

math.AG↗

arXiv2007

A mathematical formalism for agent-based modeling

Many complex systems can be modeled as multiagent systems in which the constituent entities (agents) interact with each other. The global dynamics of such a system is determined by the nature of the local interactions among the agents. Since it is difficult to formally analyze complex multiagent systems, they are often studied through computer simulations. While computer simulations can be very useful, results obtained through simulations do not formally validate the observed behavior. Thus, there is a need for a mathematical framework which one can use to represent multiagent systems and formally establish their properties. This work contains a brief exposition of some known mathematical frameworks that can model multiagent systems. The focus is on one such framework, namely that of finite dynamical systems. Both, deterministic and stochastic versions of this framework are discussed. The paper contains a sampling of the mathematical results from the literature to show how finite dynamical systems can be used to carry out a rigorous study of the properties of multiagent systems and it is shown how the framework can also serve as a universal model for computation.

cs.MA↗