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)

Multidimensional cellular automata and generalization of Fekete's lemma

Fekete's lemma is a well known combinatorial result on number sequences: we extend it to functions defined on $d$-tuples of integers. As an application of the new variant, we show that nonsurjective $d$-dimensional cellular automata are characterized by loss of arbitrarily much information on finite supports, at a growth rate greater than that of the support's boundary determined by the automaton's neighbourhood index.Comment: 6 pages, no figures, LaTeX. Improved some explanations; revised structure; added examples; renamed "hypercubes" into "right polytopes"; added references to Arratia's paper on EJC, Calude's book, Cook's proof of Rule 110 universality, and arXiv paper 0709.117

Integrating a Non-Uniformly Sampled Software Retina with a Deep CNN Model

We present a biologically inspired method for pre-processing images applied to CNNs that reduces their memory requirements while increasing their invariance to scale and rotation changes. Our method is based on the mammalian retino-cortical transform: a mapping between a pseudo-randomly tessellated retina model (used to sample an input image) and a CNN. The aim of this first pilot study is to demonstrate a functional retinaintegrated CNN implementation and this produced the following results: a network using the full retino-cortical transform yielded an F1 score of 0.80 on a test set during a 4-way classification task, while an identical network not using the proposed method yielded an F1 score of 0.86 on the same task. The method reduced the visual data by e×7, the input data to the CNN by 40% and the number of CNN training epochs by 64%. These results demonstrate the viability of our method and hint at the potential of exploiting functional traits of natural vision systems in CNNs

A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications

Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of several researchers over various backgrounds and fields for modelling different physical, natural as well as real-life phenomena. Classically, CAs are uniform. However, non-uniformity has also been introduced in update pattern, lattice structure, neighborhood dependency and local rule. In this survey, we tour to the various types of CAs introduced till date, the different characterization tools, the global behaviors of CAs, like universality, reversibility, dynamics etc. Special attention is given to non-uniformity in CAs and especially to non-uniform elementary CAs, which have been very useful in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin