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 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

Cre/lox generation of a novel whole-body Kiss1r KO mouse line recapitulates a hypogonadal, obese, and metabolically-impaired phenotype.

Kisspeptin and its receptor, Kiss1r, act centrally to stimulate reproduction. Recent evidence indicates that kisspeptin is also important for body weight and metabolism, as whole-body Kiss1r KO mice, developed with gene trap technology, display obesity and reduced metabolism. Kiss1r is expressed in brain and multiple peripheral tissues, but it is unknown which is responsible for the metabolic phenotype. Here, we sought to confirm that 1) the metabolic phenotype of the gene trap Kiss1r KOs is due to disruption of kisspeptin signaling and not off-target effects of viral mutagenesis, and 2) the Kiss1r flox line is suitable for creating conditional KOs to study the metabolic phenotype. We used Cre/lox technology (Zp3-Cre/Kiss1r flox) to develop a new global Kiss1r KO ("Kiss1r gKO") to compare with the original gene trap KO phenotype. We confirmed that deleting exon 2 of Kiss1r from the entire body induces hypogonadism in both sexes. Moreover, global deletion of Kiss1r induced obesity in females, but not males, along with increased adiposity and impaired glucose tolerance, similar to the gene trap Kiss1r KOs. Likewise, Kiss1r gKO females had decreased VO2 and VCO2, likely underlying their obesity. These findings support that our previous results in gene trap Kiss1r KOs are due to disrupted kisspeptin signaling, and further highlight a role for Kiss1r signaling in energy expenditure and metabolism besides controlling reproduction. Moreover, given Kiss1r expression in multiple cell-types, our findings indicate that the Kiss1r flox line is viable for future investigations to isolate specific target cells of kisspeptin's metabolic effects

Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring

We study an evolutionary algorithm that locally adapts thresholds and wiring in Random Threshold Networks, based on measurements of a dynamical order parameter. A control parameter $p$ determines the probability of threshold adaptations vs. link rewiring. For any $p < 1$, we find spontaneous symmetry breaking into a new class of self-organized networks, characterized by a much higher average connectivity $\bar{K}_{evo}$ than networks without threshold adaptation ($p =1$). While $\bar{K}_{evo}$ and evolved out-degree distributions are independent from $p$ for $p <1$, in-degree distributions become broader when $p \to 1$, approaching a power-law. In this limit, time scale separation between threshold adaptions and rewiring also leads to strong correlations between thresholds and in-degree. Finally, evidence is presented that networks converge to self-organized criticality for large $N$.Comment: 4 pages revtex, 6 figure

An analytic Approach to Turaev's Shadow Invariant

In the present paper we extend the "torus gauge fixing approach" by Blau and Thompson (Nucl. Phys. B408(1):345--390, 1993) for Chern-Simons models with base manifolds M of the form M= \Sigma x S^1 in a suitable way. We arrive at a heuristic path integral formula for the Wilson loop observables associated to general links in M. We then show that the right-hand side of this formula can be evaluated explicitly in a non-perturbative way and that this evaluation naturally leads to the face models in terms of which Turaev's shadow invariant is defined.Comment: 44 pages, 2 figures. Changes have been made in Sec. 2.3, Sec 2.4, Sec. 3.4, and Sec. 3.5. Appendix C is ne

Graph Invariants of Vassiliev Type and Application to 4D Quantum Gravity

We consider a special class of Kauffman's graph invariants of rigid vertex isotopy (graph invariants of Vassiliev type). They are given by a functor from a category of colored and oriented graphs embedded into a 3-space to a category of representations of the quasi-triangular ribbon Hopf algebra $U_q(sl(2,\bf C))$. Coefficients in expansions of them with respect to $x$ ($q=e^x$) are known as the Vassiliev invariants of finite type. In the present paper, we construct two types of tangle operators of vertices. One of them corresponds to a Casimir operator insertion at a transverse double point of Wilson loops. This paper proposes a non-perturbative generalization of Kauffman's recent result based on a perturbative analysis of the Chern-Simons quantum field theory. As a result, a quantum group analog of Penrose's spin network is established taking into account of the orientation. We also deal with the 4-dimensional canonical quantum gravity of Ashtekar. It is verified that the graph invariants of Vassiliev type are compatible with constraints of the quantum gravity in the loop space representation of Rovelli and Smolin.Comment: 34 pages, AMS-LaTeX, no figures,The proof of thm.5.1 has been improve

Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics

Linearized catalytic reaction equations modeling e.g. the dynamics of genetic regulatory networks under the constraint that expression levels, i.e. molecular concentrations of nucleic material are positive, exhibit nontrivial dynamical properties, which depend on the average connectivity of the reaction network. In these systems the inflation of the edge of chaos and multi-stability have been demonstrated to exist. The positivity constraint introduces a nonlinearity which makes chaotic dynamics possible. Despite the simplicity of such minimally nonlinear systems, their basic properties allow to understand fundamental dynamical properties of complex biological reaction networks. We analyze the Lyapunov spectrum, determine the probability to find stationary oscillating solutions, demonstrate the effect of the nonlinearity on the effective in- and out-degree of the active interaction network and study how the frequency distributions of oscillatory modes of such system depend on the average connectivity.Comment: 11 pages, 5 figure

Colorimetric method for susceptibility testing of voriconazole and other triazoles against Candida species

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72523/1/j.1439-0507.1999.00511.x.pd

Critical Line in Random Threshold Networks with Inhomogeneous Thresholds

We calculate analytically the critical connectivity $K_c$ of Random Threshold Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the results by numerical simulations. We find a super-linear increase of $K_c$ with the (average) absolute threshold $|h|$, which approaches $K_c(|h|) \sim h^2/(2\ln{|h|})$ for large $|h|$, and show that this asymptotic scaling is universal for RTN with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than $h^2$. Interestingly, we find that inhomogeneous distribution of thresholds leads to increased propagation of perturbations for sparsely connected networks, while for densely connected networks damage is reduced; the cross-over point yields a novel, characteristic connectivity $K_d$, that has no counterpart in Boolean networks. Last, local correlations between node thresholds and in-degree are introduced. Here, numerical simulations show that even weak (anti-)correlations can lead to a transition from ordered to chaotic dynamics, and vice versa. It is shown that the naive mean-field assumption typical for the annealed approximation leads to false predictions in this case, since correlations between thresholds and out-degree that emerge as a side-effect strongly modify damage propagation behavior.Comment: 18 figures, 17 pages revte