Correlation of Automorphism Group Size and Topological Properties with Program-size Complexity Evaluations of Graphs and Complex Networks

We show that numerical approximations of Kolmogorov complexity (K) applied to graph adjacency matrices capture some group-theoretic and topological properties of graphs and empirical networks ranging from metabolic to social networks. That K and the size of the group of automorphisms of a graph are correlated opens up interesting connections to problems in computational geometry, and thus connects several measures and concepts from complexity science. We show that approximations of K characterise synthetic and natural networks by their generating mechanisms, assigning lower algorithmic randomness to complex network models (Watts-Strogatz and Barabasi-Albert networks) and high Kolmogorov complexity to (random) Erdos-Renyi graphs. We derive these results via two different Kolmogorov complexity approximation methods applied to the adjacency matrices of the graphs and networks. The methods used are the traditional lossless compression approach to Kolmogorov complexity, and a normalised version of a Block Decomposition Method (BDM) measure, based on algorithmic probability theory.Comment: 15 2-column pages, 20 figures. Forthcoming in Physica A: Statistical Mechanics and its Application

Inverse Dynamical Problems: An Algebraic Formulation Via MP Grammars

Metabolic P grammars are a particular class of multiset rewriting grammars introduced in the MP systems' theory for modelling metabolic processes. In this paper, a new algebraic formulation of inverse dynamical problems, based on MP grammars and Kronecker product, is given, for further motivating the correctness of the LGSS (Log-gain Stoichiometric Stepwise) algorithm, introduced in 2010s for solving dynamical inverse problems in the MP framework. At the end of the paper, a section is included that introduces the problem of multicollinearity, which could arise during the execution of LGSS, and that de nes an algorithm, based on a hierarchical clustering technique, that solves it in a suitable way

Toward a Self-replicating Metabolic P System

This work concerns the synthesis of a "minimal cell' by means of a P system, which is a distributed rewriting system inspired by the structure and the functioning of the biological cell. Specifically, we aim to define a dynamical system which exhibits a steady metabolic evolution, resulting in self-maintenance and self-reproduction. Metabolic P systems represent a class of P systems particularly promising to model a minimal cell in discrete terms, since they have already successfully modeled several metabolisms. The main further step is thus to find a simple way to obtain Metabolic P system self-replication. This paper deals with ideas presented at the BWMC11 (held in Seville, Feb 2011) and opens a new trend in membrane computing, based on computational synthetic biology oriented applications of P systems modeling. The framework is here outlined, and some problems to tackle the synthesis of a minimal cell are discussed. Moreover, an overview of literature and a list of appealing research directions is given, along with several references

Evolution of Metabolic Networks: A Computational Framework

Background: The metabolic architectures of extant organisms share many key pathways such as the citric acid cycle, glycolysis, or the biosynthesis of most amino acids. Several competing hypotheses for the evolutionary mechanisms that shape metabolic networks have been discussed in the literature, each of which finds support from comparative analysis of extant genomes. Alternatively, the principles of metabolic evolution can be studied by direct computer simulation. This requires, however, an explicit implementation of all pertinent components: a universe of chemical reaction upon which the metabolism is built, an explicit representation of the enzymes that implement the metabolism, of a genetic system that encodes these enzymes, and of a fitness function that can be selected for. Results: We describe here a simulation environment that implements all these components in a simplified ways so that large-scale evolutionary studies are feasible. We employ an artificial chemistry that views chemical reactions as graph rewriting operations and utilizes a toy-version of quantum chemistry to derive thermodynamic parameters. Minimalist organisms with simple string-encoded genomes produce model ribozymes whose catalytic activity is determined by an ad hoc mapping between their secondary structure and the transition state graphs that they stabilize. Fitness is computed utilizing the ideas of metabolic flux analysis. We present an implementation of the complete system and first simulation results. Conclusions: The simulation system presented here allows coherent investigations into the evolutionary mechanisms of the first steps of metabolic evolution using a self-consistent toy univers

Membrane Computing as a Modeling Framework. Cellular Systems Case Studies

Membrane computing is a branch of natural computing aiming to abstract computing models from the structure and functioning of the living cell, and from the way cells cooperate in tissues, organs, or other populations of cells. This research area developed very fast, both at the theoretical level and in what concerns the applications. After a very short description of the domain, we mention here the main areas where membrane computing was used as a framework for devising models (biology and bio-medicine, linguistics, economics, computer science, etc.), then we discuss in a certain detail the possibility of using membrane computing as a high level computational modeling framework for addressing structural and dynamical aspects of cellular systems. We close with a comprehensive bibliography of membrane computing applications

Deterministic and stochastic P systems for modelling cellular processes

This paper presents two approaches based on metabolic and stochastic P systems, together with their associated analysis methods, for modelling biological sys- tems and illustrates their use through two case studies.Kingdom's Engineering and Physical Sciences Research Council EP/ E017215/1Biotechnology and Biological Sciences Research Council/United Kingdom BB/D019613/1Biotechnology and Biological Sciences Research Council/United Kingdom BB/F01855X/