COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS

The ability to simulate a biological organism by employing a computer is related to the ability of the computer to calculate the behavior of such a dynamical system, or the "computability" of the system.* However, the two questions of computability and simulation are not equivalent. Since the question of computability can be given a precise answer in terms of recursive functions, automata theory and dynamical systems, it will be appropriate to consider it first. The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered. A conjecture is formulated that suggests the possibility of employing an algebraic-topological, "quantum" computer (Baianu, 1971b) for analogous and symbolic simulations of biological systems that may include chaotic processes that are not, in genral, either recursively or digitally computable. Depending on the biological network being modelled, such as the Human Genome/Cell Interactome or a trillion-cell Cognitive Neural Network system, the appropriate logical structure for such simulations might be either the Quantum MV-Logic (QMV) discussed in recent publications (Chiara, 2004, and references cited therein)or Lukasiewicz Logic Algebras that were shown to be isomorphic to MV-logic algebras (Georgescu et al, 2001)

Multiplication cubes and multiplication automata

We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers $p$ and $q$ in base $pq$ to higher dimensional multiplication tessellation systems. We develop the theory of these systems and link different multiplication tessellation systems with each other via macrocube operations that glue cubes in one tessellation system into larger cubes of another tessellation system. The macrocube operations yield topological conjugacies and factor maps between cellular automata performing multiplication by positive numbers in various bases.Comment: 35 pages, 6 figure

Placing large group relations into pedestrian dynamics: psychological crowds in counterflow

Understanding influences on pedestrian movement is important to accurately simulate crowd behaviour, yet little research has explored the psychological factors that influence interactions between large groups in counterflow scenarios. Research from social psychology has demonstrated that social identities can influence the micro-level pedestrian movement of a psychological crowd, yet this has not been extended to explore behaviour when two large psychological groups are co-present. This study investigates how the presence of large groups with different social identities can affect pedestrian behaviour when walking in counterflow. Participants (N = 54) were divided into two groups and primed to have identities as either ‘team A’ or ‘team B’. The trajectories of all participants were tracked to compare the movement of team A when walking alone to when walking in counterflow with team B, based on their i) speed of movement and distance walked, and ii) proximity between participants. In comparison to walking alone, the presence of another group influenced team A to collectively self-organise to reduce their speed and distance walked in order to walk closely together with ingroup members. We discuss the importance of incorporating social identities into pedestrian group dynamics for empirically validated simulations of counterflow scenarios

Modeling growth in biological materials

The biomechanical modeling of growing tissues has recently become an area of intense interest. In particular, the interplay between growth patterns and mechanical stress is of great importance, with possible applications to arterial mechanics, embryo morphogenesis, tumor development, and bone remodeling. This review aims to give an overview of the theories that have been used to model these phenomena, categorized according to whether the tissue is considered as a continuum object or a collection of cells. Among the continuum models discussed is the deformation gradient decomposition method, which allows a residual stress field to develop from an incompatible growth field. The cell-based models are further subdivided into cellular automata, center-dynamics, and vertex-dynamics models. Of these the second two are considered in more detail, especially with regard to their treatment of cell-cell interactions and cell division. The review concludes by assessing the prospects for reconciliation between these two fundamentally different approaches to tissue growth, and by identifying possible avenues for further research. © 2012 Society for Industrial and Applied Mathematics