The Number of Different Binary Functions Generated by NK-Kauffman Networks and the Emergence of Genetic Robustness

We determine the average number $\vartheta (N, K)$, of \textit{NK}-Kauffman networks that give rise to the same binary function. We show that, for $N \gg 1$, there exists a connectivity critical value $K_c$ such that $\vartheta(N,K) \approx e^{\phi N}$ ($\phi > 0$) for $K < K_c$ and $\vartheta(N,K) \approx 1$ for $K > K_c$. We find that $K_c$ is not a constant, but scales very slowly with $N$, as $K_c \approx \log_2 \log_2 (2N / \ln 2)$. The problem of genetic robustness emerges as a statistical property of the ensemble of \textit{NK}-Kauffman networks and impose tight constraints in the average number of epistatic interactions that the genotype-phenotype map can have.Comment: 4 figures 18 page

Phase transition in a class of non-linear random networks

We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical connectivity k = 2. Also, we show that both, pairwise correlation and complexity measures are maximized in dynamically critical networks. These results are in good agreement with the previously reported studies on random Boolean networks and random threshold networks, and show once again that critical networks provide an optimal coordination of diverse behavior.Comment: 9 pages, 3 figures, revised versio

The Role of the Brain in the Pathogenesis and Physiology of Polycystic Ovary Syndrome (PCOS).

Polycystic ovary syndrome (PCOS) is a common reproductive endocrine disorder, affecting at least 10% of women of reproductive age. PCOS is typically characterized by the presence of at least two of the three cardinal features of hyperandrogenemia (high circulating androgen levels), oligo- or anovulation, and cystic ovaries. Hyperandrogenemia increases the severity of the condition and is driven by increased luteinizing hormone (LH) pulse secretion from the pituitary. Indeed, PCOS women display both elevated mean LH levels, as well as an elevated frequency of LH pulsatile secretion. The abnormally high LH pulse frequency, reflective of a hyperactive gonadotropin-releasing hormone (GnRH) neural circuit, suggests a neuroendocrine basis to either the etiology or phenotype of PCOS. Several studies in preclinical animal models of PCOS have demonstrated alterations in GnRH neurons and their upstream afferent neuronal circuits. Some rodent PCOS models have demonstrated an increase in GnRH neuron activity that correlates with an increase in stimulatory GABAergic innervation and postsynaptic currents onto GnRH neurons. Additional studies have identified robust increases in hypothalamic levels of kisspeptin, another potent stimulator of GnRH neurons. This review outlines the different brain and neuroendocrine changes in the reproductive axis observed in PCOS animal models, discusses how they might contribute to either the etiology or adult phenotype of PCOS, and considers parallel findings in PCOS women

The phase transition in random catalytic sets

The notion of (auto) catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems. Here we study catalytic random networks with respect to the final outcome diversity of products. We show that an analytical treatment of this longstanding problem is possible by mapping the problem onto a set of non-linear recurrence equations. The solution of these equations show a crucial dependence of the final number of products on the initial number of products and the density of catalytic production rules. For a fixed density of rules we can demonstrate the existence of a phase transition from a practically unpopulated regime to a fully populated and diverse one. The order parameter is the number of final products. We are able to further understand the origin of this phase transition as a crossover from one set of solutions from a quadratic equation to the other.Comment: 7 pages, ugly eps files due to arxiv restriction

Damage Spreading and Criticality in Finite Random Dynamical Networks

We systematically study and compare damage spreading at the sparse percolation (SP) limit for random boolean and threshold networks with perturbations that are independent of the network size $N$. This limit is relevant to information and damage propagation in many technological and natural networks. Using finite size scaling, we identify a new characteristic connectivity $K_s$, at which the average number of damaged nodes $\bar d$, after a large number of dynamical updates, is independent of $N$. Based on marginal damage spreading, we determine the critical connectivity $K_c^{sparse}(N)$ for finite $N$ at the SP limit and show that it systematically deviates from $K_c$, established by the annealed approximation, even for large system sizes. Our findings can potentially explain the results recently obtained for gene regulatory networks and have important implications for the evolution of dynamical networks that solve specific computational or functional tasks.Comment: 4 pages, 4 eps figure

Self-organized Networks of Competing Boolean Agents

A model of Boolean agents competing in a market is presented where each agent bases his action on information obtained from a small group of other agents. The agents play a competitive game that rewards those in the minority. After a long time interval, the poorest player's strategy is changed randomly, and the process is repeated. Eventually the network evolves to a stationary but intermittent state where random mutation of the worst strategy can change the behavior of the entire network, often causing a switch in the dynamics between attractors of vastly different lengths.Comment: 4 pages, 3 included figures. Some text revision and one new figure added. To appear in PR

Distinguishing scalar from pseudoscalar Higgs production at the LHC

In this letter we examine the production channels for the scalar or pseudoscalar Higgs plus two jets at the CERN Large Hadron Collider (LHC). We identify possible signals for distinguishing between a scalar and a pseudoscalar Higgs boson.Comment: 7 pages, REVTeX4, 4 eps figures. Figure 1 and 4 replaced. Typos corrected, additional reference adde

Robustness of Transcriptional Regulation in Yeast-like Model Boolean Networks

We investigate the dynamical properties of the transcriptional regulation of gene expression in the yeast Saccharomyces Cerevisiae within the framework of a synchronously and deterministically updated Boolean network model. By means of a dynamically determinant subnetwork, we explore the robustness of transcriptional regulation as a function of the type of Boolean functions used in the model that mimic the influence of regulating agents on the transcription level of a gene. We compare the results obtained for the actual yeast network with those from two different model networks, one with similar in-degree distribution as the yeast and random otherwise, and another due to Balcan et al., where the global topology of the yeast network is reproduced faithfully. We, surprisingly, find that the first set of model networks better reproduce the results found with the actual yeast network, even though the Balcan et al. model networks are structurally more similar to that of yeast.Comment: 7 pages, 4 figures, To appear in Int. J. Bifurcation and Chaos, typos were corrected and 2 references were adde

Network growth models and genetic regulatory networks

We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new links, allowing for the possibility that input and output links from a newly created node may have different probabilities of survival. We find some counterintuitive trends as parameters are varied, including the broadening of indegree distribution when the probability for retaining input links is decreased. We also find that both the scaling of transcription factors with genome size and the measured degree distributions for genes in yeast can be reproduced by the growth algorithm if and only if a special seed is used to initiate the process.Comment: 8 pages with 7 eps figures; uses revtex4. Added references, cleaner figure