5,417 research outputs found
The Number of Different Binary Functions Generated by NK-Kauffman Networks and the Emergence of Genetic Robustness
We determine the average number , of \textit{NK}-Kauffman
networks that give rise to the same binary function. We show that, for , there exists a connectivity critical value such that () for and
for . We find that is not a
constant, but scales very slowly with , as . 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
Recommended from our members
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 . 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 , at which the average number of damaged nodes ,
after a large number of dynamical updates, is independent of . Based on
marginal damage spreading, we determine the critical connectivity
for finite at the SP limit and show that it
systematically deviates from , 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
On the Robustness of NK-Kauffman Networks Against Changes in their Connections and Boolean Functions
NK-Kauffman networks {\cal L}^N_K are a subset of the Boolean functions on N
Boolean variables to themselves, \Lambda_N = {\xi: \IZ_2^N \to \IZ_2^N}. To
each NK-Kauffman network it is possible to assign a unique Boolean function on
N variables through the function \Psi: {\cal L}^N_K \to \Lambda_N. The
probability {\cal P}_K that \Psi (f) = \Psi (f'), when f' is obtained through f
by a change of one of its K-Boolean functions (b_K: \IZ_2^K \to \IZ_2), and/or
connections; is calculated. The leading term of the asymptotic expansion of
{\cal P}_K, for N \gg 1, turns out to depend on: the probability to extract the
tautology and contradiction Boolean functions, and in the average value of the
distribution of probability of the Boolean functions; the other terms decay as
{\cal O} (1 / N). In order to accomplish this, a classification of the Boolean
functions in terms of what I have called their irreducible degree of
connectivity is established. The mathematical findings are discussed in the
biological context where, \Psi is used to model the genotype-phenotype map.Comment: 17 pages, 1 figure, Accepted in Journal of Mathematical Physic
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