Communication structure of cortical networks

Large-scale cortical networks exhibit characteristic topological properties that shape communication between brain regions and global cortical dynamics. Analysis of complex networks allows the description of connectedness, distance, clustering, and centrality that reveal different aspects of how the network's nodes communicate. Here, we focus on a novel analysis of complex walks in a series of mammalian cortical networks that model potential dynamics of information flow between individual brain regions. We introduce two new measures called absorption and driftness. Absorption is the average length of random walks between any two nodes, and takes into account all paths that may diffuse activity throughout the network. Driftness is the ratio between absorption and the corresponding shortest path length. For a given node of the network, we also define four related measurements, namely in-and out-absorption as well as in-and out-driftness, as the averages of the corresponding measures from all nodes to that node, and from that node to all nodes, respectively. We find that the cat thalamo-cortical system incorporates features of two classic network topologies, Erdos-Renyi graphs with respect to in-absorption and in-driftness, and configuration models with respect to out-absorption and out-driftness. Moreover, taken together these four measures separate the network nodes based on broad functional roles (visual, auditory, somatomotor, and frontolimbic).

A study of disorder effects in random (Al(x)Ga(1-x)As)(n)(Al(y)Ga(1-y)As)(m) superlattices embedded in a wide parabolic potential

A photoluminescence (PL) study of the individual electron states localized in a random potential is performed in artificially disordered superlattices embedded in a wide parabolic well. The valence band bowing of the parabolic potential provides a variation of the emission energies which splits the optical transitions corresponding to different wells within the random potential. The blueshift of the PL lines emitted by individual random wells, observed with increasing disorder strength, is demonstrated. The variation of temperature and magnetic field allowed for the behavior of the electrons localized in individual wells of the random potential to be distinguished.

Quantum system under the actions of two counteracting baths: A model for the attenuation-amplification interplay

We analyze the dynamical behavior of a quantum system under the actions of two counteracting baths: the inevitable energy draining reservoir and, in opposition, exciting the system, an engineered Glauber's amplifier. We follow the system dynamics towards equilibrium to map its distinctive behavior arising from the interplay of attenuation and amplification. Such a mapping, with the corresponding parameter regimes, is achieved by calculating the evolution of both the excitation and the Glauber-Sudarshan P function. Techniques to compute the decoherence and the fidelity of quantum states under the action of both counteracting baths, based on the Wigner function rather than the density matrix, are also presented. They enable us to analyze the similarity of the evolved state vector of the system with respect to the original one, for all regimes of parameters. Applications of this attenuation-amplification interplay are discussed.

Delocalization-localization transition of plasmons in random (GaAs)(m)(Al(0.3)Ga(0.7)As)(6) superlattices

The transition of plasmons from propagating to localized state was studied in disordered systems formed in GaAs/AlGaAs superlattices by impurities and by artificial random potential. Both the localization length and the linewidth of plasmons were measured by Raman scattering. The vanishing dependence of the plasmon linewidth on the disorder strength was shown to be a manifestation of the strong plasmon localization. The theoretical approach based on representation of the plasmon wave function in a Gaussian form well accounted for by the obtained experimental data.

Directed Abelian algebras and their application to stochastic models

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma(tau)=3/2). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma(tau)=1.780 +/- 0.005.

Fluorescence spectroscopy for the detection of tongue carcinoma - validation in an animal model

The efficacy of fluorescence spectroscopy to detect squamous cell carcinoma is evaluated in an animal model following laser excitation at 442 and 532 nm. Lesions are chemically induced with a topical DMBA application at the left lateral tongue of Golden Syrian hamsters. The animals are investigated every 2 weeks after the 4th week of induction until a total of 26 weeks. The right lateral tongue of each animal is considered as a control site (normal contralateral tissue) and the induced lesions are analyzed as a set of points covering the entire clinically detectable area. Based on fluorescence spectral differences, four indices are determined to discriminate normal and carcinoma tissues, based on intraspectral analysis. The spectral data are also analyzed using a multivariate data analysis and the results are compared with histology as the diagnostic gold standard. The best result achieved is for blue excitation using the KNN (K-nearest neighbor, a interspectral analysis) algorithm with a sensitivity of 95.7% and a specificity of 91.6%. These high indices indicate that fluorescence spectroscopy may constitute a fast noninvasive auxiliary tool for diagnostic of cancer within the oral cavity. (C) 2008 Society of Photo-Optical Instrumentation Engineers.

Statistics of opinion domains of the majority-vote model on a square lattice

The existence of juxtaposed regions of distinct cultures in spite of the fact that people's beliefs have a tendency to become more similar to each other's as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we study an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors' opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size L and that they interact with their nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with L(2) whereas the size of the largest cluster grows with ln L(2). The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model-Axelrod's model-we found that these opinion domains are unstable to the effect of a thermal-like noise.

Covariant Gauge on the Lattice: A New Implementation

We derive a new implementation of linear covariant gauges on the lattice, based on a minimizing functional that can be interpreted as the Hamiltonian of a spin-glass model in a random external magnetic field. We show that our method solves most problems encountered in earlier implementations, mostly related to the no-go condition formulated by Giusti [Nucl. Phys. B498, 331 (1997)]. We carry out tests in the SU(2) case in four space-time dimensions. We also present preliminary results for the transverse gluon propagator at different values of the gauge parameter xi.

Gene Expression Complex Networks: Synthesis, Identification, and Analysis

Thanks to recent advances in molecular biology, allied to an ever increasing amount of experimental data, the functional state of thousands of genes can now be extracted simultaneously by using methods such as cDNA microarrays and RNA-Seq. Particularly important related investigations are the modeling and identification of gene regulatory networks from expression data sets. Such a knowledge is fundamental for many applications, such as disease treatment, therapeutic intervention strategies and drugs design, as well as for planning high-throughput new experiments. Methods have been developed for gene networks modeling and identification from expression profiles. However, an important open problem regards how to validate such approaches and its results. This work presents an objective approach for validation of gene network modeling and identification which comprises the following three main aspects: (1) Artificial Gene Networks (AGNs) model generation through theoretical models of complex networks, which is used to simulate temporal expression data; (2) a computational method for gene network identification from the simulated data, which is founded on a feature selection approach where a target gene is fixed and the expression profile is observed for all other genes in order to identify a relevant subset of predictors; and (3) validation of the identified AGN-based network through comparison with the original network. The proposed framework allows several types of AGNs to be generated and used in order to simulate temporal expression data. The results of the network identification method can then be compared to the original network in order to estimate its properties and accuracy. Some of the most important theoretical models of complex networks have been assessed: the uniformly-random Erdos-Renyi (ER), the small-world Watts-Strogatz (WS), the scale-free Barabasi-Albert (BA), and geographical networks (GG). The experimental results indicate that the inference method was sensitive to average degree k variation, decreasing its network recovery rate with the increase of k. The signal size was important for the inference method to get better accuracy in the network identification rate, presenting very good results with small expression profiles. However, the adopted inference method was not sensible to recognize distinct structures of interaction among genes, presenting a similar behavior when applied to different network topologies. In summary, the proposed framework, though simple, was adequate for the validation of the inferred networks by identifying some properties of the evaluated method, which can be extended to other inference methods.

Inference of gene regulatory networks from time series by Tsallis entropy

Background: The inference of gene regulatory networks (GRNs) from large-scale expression profiles is one of the most challenging problems of Systems Biology nowadays. Many techniques and models have been proposed for this task. However, it is not generally possible to recover the original topology with great accuracy, mainly due to the short time series data in face of the high complexity of the networks and the intrinsic noise of the expression measurements. In order to improve the accuracy of GRNs inference methods based on entropy (mutual information), a new criterion function is here proposed. Results: In this paper we introduce the use of generalized entropy proposed by Tsallis, for the inference of GRNs from time series expression profiles. The inference process is based on a feature selection approach and the conditional entropy is applied as criterion function. In order to assess the proposed methodology, the algorithm is applied to recover the network topology from temporal expressions generated by an artificial gene network (AGN) model as well as from the DREAM challenge. The adopted AGN is based on theoretical models of complex networks and its gene transference function is obtained from random drawing on the set of possible Boolean functions, thus creating its dynamics. On the other hand, DREAM time series data presents variation of network size and its topologies are based on real networks. The dynamics are generated by continuous differential equations with noise and perturbation. By adopting both data sources, it is possible to estimate the average quality of the inference with respect to different network topologies, transfer functions and network sizes. Conclusions: A remarkable improvement of accuracy was observed in the experimental results by reducing the number of false connections in the inferred topology by the non-Shannon entropy. The obtained best free parameter of the Tsallis entropy was on average in the range 2.5 <= q <= 3.5 (hence, subextensive entropy), which opens new perspectives for GRNs inference methods based on information theory and for investigation of the nonextensivity of such networks. The inference algorithm and criterion function proposed here were implemented and included in the DimReduction software, which is freely available at http://sourceforge.net/projects/dimreduction and http://code.google.com/p/dimreduction/.

On the resilience of long cycles in random graphs

In this paper we determine the local and global resilience of random graphs G(n,p) (p >> n(-1)) with respect to the property of containing a cycle of length at least (1 - alpha)n. Roughly speaking, given alpha > 0, we determine the smallest r(g) (G, alpha) with the property that almost surely every subgraph of G = G(n,p) having more than r(g) (G, alpha)vertical bar E(G)vertical bar edges contains a cycle of length at least (1 - alpha)n (global resilience). We also obtain, for alpha < 1/2, the smallest r(l) (G, alpha) such that any H subset of G having deg(H) (v) larger than r(l) (G, alpha) deg(G) (v) for all v is an element of V(G) contains a cycle of length at least (1 - alpha)n (local resilience). The results above are in fact proved in the more general setting of pseudorandom graphs.

A PHASE TRANSITION FOR COMPETITION INTERFACES

We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with probability 1. The behavior of this direction depends on the angle theta of the cone: for theta >= 180 degrees, the direction is deterministic, while for theta < 180 degrees, it is random, and its distribution can be given explicitly in certain cases. We also obtain partial results on the fluctuations of the interface around its asymptotic direction. The evolution of the competition interface in the growth model can be mapped onto the path of a second-class particle in the totally asymmetric simple exclusion process; from the existence of the limiting direction for the interface, we obtain a new and rather natural proof of the strong law of large numbers (with perhaps a random limit) for the position of the second-class particle at large times.

POLLING SYSTEMS WITH PARAMETER REGENERATION, THE GENERAL CASE

We consider a polling model with multiple stations, each with Poisson arrivals and a queue of infinite capacity. The service regime is exhaustive and there is Jacksonian feedback of served customers. What is new here is that when the server comes to a station it chooses the service rate and the feedback parameters at random; these remain valid during the whole stay of the server at that station. We give criteria for recurrence, transience and existence of the sth moment of the return time to the empty state for this model. This paper generalizes the model, when only two stations accept arriving jobs, which was considered in [Ann. Appl. Probab. 17 (2007) 1447-1473]. Our results are stated in terms of Lyapunov exponents for random matrices. From the recurrence criteria it can be seen that the polling model with parameter regeneration can exhibit the unusual phenomenon of null recurrence over a thick region of parameter space.

Random perturbations of stochastic processes with unbounded variable length memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.

Gibbs random graphs on point processes

Consider a discrete locally finite subset Gamma of R(d) and the cornplete graph (Gamma, E), with vertices Gamma and edges E. We consider Gibbs measures on the set of sub-graphs with vertices Gamma and edges E` subset of E. The Gibbs interaction acts between open edges having a vertex in common. We study percolation properties of the Gibbs distribution of the graph ensemble. The main results concern percolation properties of the open edges in two cases: (a) when Gamma is sampled from a homogeneous Poisson process; and (b) for a fixed Gamma with sufficiently sparse points. (c) 2010 American Institute of Physics. [doi:10.1063/1.3514605]