Ayşe Erzan

Finite q-differences and the discrete renormalization group

Abstract The finite q -difference operator lends itself naturally to describing systems with exact discrete dilatation symmetry, such as hierarchical lattices. We express the homogeneity relation obeyed by the free energy in terms of the q -difference operator and integrate it to obtain the exact expression for the free energy. The site free energy distribution is multifractal, due to the topological nonuniformity of the hierarchical lattice. The Tsallis generalized entropy function provides a prescription for restoring the extensivity of the free energy.

Slow regions percolate near glass transition

Abstract:A nanosecond scale in situ probe reveals that a bulk linear polymer undergoes a sharp phase transition as a function of the degree of conversion, as it nears the glass transition. The scaling behaviour is in the same universality class as percolation. The exponents γ and β are found to be 1.7±0.1 and 0.41±0.01 in agreement with the best percolation results in three dimensions.

The Information Coded in the Yeast Response Elements Accounts for Most of the Topological Properties of Its Transcriptional Regulation Network.

The regulation of gene expression in a cell relies to a major extent on transcription factors, proteins which recognize and bind the DNA at specific binding sites (response elements) within promoter regions associated with each gene. We present an information theoretic approach to modeling transcriptional regulatory networks, in terms of a simple “sequence-matching” rule and the statistics of the occurrence of binding sequences of given specificity in random promoter regions. The crucial biological input is the distribution of the amount of information coded in these cognate response elements and the length distribution of the promoter regions. We provide an analysis of the transcriptional regulatory network of yeast Saccharomyces cerevisiae, which we extract from the available databases, with respect to the degree distributions, clustering coefficient, degree correlations, rich-club coefficient and the k-core structure. We find that these topological features are in remarkable agreement with those predicted by our model, on the basis of the amount of information coded in the interaction between the transcription factors and response elements.

Random model for RNA interference yields scale free network

Abstract.We introduce a random bit-string model of post-transcriptional genetic regulation based on sequence matching. The model spontaneously yields a scale free network with power law scaling with

Evolutionary route to diploidy and sex

\gamma = -1

Testing A Hypothesis For The Evolution Of Sex

and also exhibits log-periodic behaviour. The in-degree distribution is much narrower, and exhibits a pronounced peak followed by a Gaussian distribution. The network is of the smallest world type, with the average minimum path length independent of the size of the network, as long as the network consists of one giant cluster. The percolation threshold depends on the system size.

Content-based networks: A pedagogical overview

By using a bit-string model of evolution, we find a successful route to diploidy and sex in simple organisms. Allowing the sexually reproducing diploid individuals to also perform mitosis, as they do in a haploid-diploid cycle, leads to the complete takeover of the population by sexual diploids. This mechanism is so robust that even the accidental conversion and pairing of only two diploids give rise to a sexual population.

Strategies for the evolution of sex.

An asexual set of primitive bacteria is simulated with a bit-string Penna model with a Fermi function for survival. A recent hypothesis by Jan, Stauffer, and Moseley on the evolution of sex from asexual cells as a strategy for trying to escape the effects of deleterious mutations is checked. This strategy is found to provide a successful scenario for the evolution of a stable macroscopic sexual population.

Dynamics of content-based networks

Complex interactions call for the sharing of information between different entities. In a recent paper, we introduced a combinatoric model which concretizes this idea via a string-matching rule. The model was shown to lend itself to analysis regarding certain topological features of the network. In this paper, we will introduce a statistical physics description of this network in terms of a Potts model. We will give an explicit mean-field treatment of a special case that has been proposed as a model for gene regulatory networks, and derive closed-form expressions for the topological coefficients. Simulations of the hidden variable network are then compared with numerically integrated results.

Content-based network model with duplication and divergence

We find that the hypothesis made by Jan, Stauffer, and Moseley [Theory Biosci. 119, 166 (2000)] for the evolution of sex, namely, a strategy devised to escape extinction due to too many deleterious mutations, is sufficient but not necessary for the successful evolution of a steady state population of sexual individuals within a finite population. Simply allowing for a finite probability for conversion to sex in each generation also gives rise to a stable sexual population, in the presence of an upper limit on the number of deleterious mutations per individual. For large values of this probability, we find a phase transition to an intermittent, multistable regime. On the other hand, in the limit of extremely slow drive, another transition takes place to a different steady state distribution, with fewer deleterious mutations within the population.