Communication in networks with hierarchical branching

We present a simple model of communication in networks with hierarchical branching. We analyze the behavior of the model from the viewpoint of critical systems under different situations. For certain values of the parameters, a continuous phase transition between a sparse and a congested regime is observed and accurately described by an order parameter and the power spectra. At the critical point the behavior of the model is totally independent of the number of hierarchical levels. Also scaling properties are observed when the size of the system varies. The presence of noise in the communication is shown to break the transition. The analytical results are a useful guide to forecasting the main features of real networks.

Light scattering from suspensions under external gradients

We analyze the light-scattering spectrum of a suspension in a viscoelastic fluid under density and velocity gradients. When a density gradient is present, the dynamic structure factor exhibits universality in the sense that its expression depends only on the reduced frequency and the reduced density gradient. For a velocity gradient, however, the universality breaks down. In this last case we have found a transition point from one to three characteristic frequencies in the spectrum, which is governed by the value of the external gradient. The presence of the viscoelastic time scales introduces a shift in the ``critical¿¿ point.

Absence of epidemic threshold in scale free networks with degree correlations

Random scale-free networks have the peculiar property of being prone to the spreading of infections. Here we provide for the susceptible-infected-susceptible model an exact result showing that a scale-free degree distribution with diverging second moment is a sufficient condition to have null epidemic threshold in unstructured networks with either assortative or disassortative mixing. Degree correlations result therefore irrelevant for the epidemic spreading picture in these scale-free networks. The present result is related to the divergence of the average nearest neighbors degree, enforced by the degree detailed balance condition.

Generalized Onsager symmetry

Onsager's symmetry theorem for transport near equilibrium is extended in two directions. A corresponding symmetry is obtained for linear transport near nonequilibrium stationary states, and the class of transport laws is extended to include nonlocality in both space and time. The results are formally exact and independent of any specific model for the nonequilibrium state.

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

Precursor phenomena in frustrated systems

To understand the origin of the dynamical transition, between high-temperature exponential relaxation and low-temperature nonexponential relaxation, that occurs well above the static transition in glassy systems, a frustrated spin model, with and without disorder, is considered. The model has two phase transitions, the lower being a standard spin glass transition (in the presence of disorder) or fully frustrated Ising (in the absence of disorder), and the higher being a Potts transition. Monte Carlo results clarify that in the model with (or without) disorder the precursor phenomena are related to the Griffiths (or Potts) transition. The Griffiths transition is a vanishing transition which occurs above the Potts transition and is present only when disorder is present, while the Potts transition which signals the effect due to frustration is always present. These results suggest that precursor phenomena in frustrated systems are due either to disorder and/or to frustration, giving a consistent interpretation also for the limiting cases of Ising spin glass and of Ising fully frustrated model, where also the Potts transition is vanishing. This interpretation could play a relevant role in glassy systems beyond the spin systems case.

Phenomenological approach to nonlinear Langevin equations

In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models

Modelling diffusion of innovations in a social network

A simple model of diffusion of innovations in a social network with upgrading costs is introduced. Agents are characterized by a single real variable, their technological level. According to local information, agents decide whether to upgrade their level or not, balancing their possible benefit with the upgrading cost. A critical point where technological avalanches display a power-law behavior is also found. This critical point is characterized by a macroscopic observable that turns out to optimize technological growth in the stationary state. Analytical results supporting our findings are found for the globally coupled case.

Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium

In this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n ? N) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime, we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function.

Asymmetric Little spin-Glass model

We study the static properties of the Little model with asymmetric couplings. We show that the thermodynamics of this model coincides with that of the Sherrington-Kirkpatrick model, and we compute the main finite-size corrections to the difference of the free energy between these two models and to some clarifying order parameters. Our results agree with numerical simulations. Numerical results are presented for the symmetric Little model, which show that the same conclusions are also valid in this case.

Evidence of a critical time in constrained Kinetic Ising models

We study the relaxational dynamics of the one-spin facilitated Ising model introduced by Fredrickson and Andersen. We show the existence of a critical time which separates an initial regime in which the relaxation is exponentially fast and aging is absent from a regime in which relaxation becomes slow and aging effects are present. The presence of this fast exponential process and its associated critical time is in agreement with some recent experimental results on fragile glasses.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

Compositional influence on the electrical performance of zinc indium tin oxide transparent thin-film transistors

In this work, zinc indium tin oxide layers with different compositions are used as the active layer of thin film transistors. This multicomponent transparent conductive oxide is gaining great interest due to its reduced content of the scarce indium element. Experimental data indicate that the incorporation of zinc promotes the creation of oxygen vacancies. In thin-film transistors this effect leads to a higher threshold voltage values. The field-effect mobility is also strongly degraded, probably due to coulomb scattering by ionized defects. A post deposition annealing in air reduces the density of oxygen vacancies and improves the fieldeffect mobility by orders of magnitude. Finally, the electrical characteristics of the fabricated thin-film transistors have been analyzed to estimate the density of states in the gap of the active layers. These measurements reveal a clear peak located at 0.3 eV from the conduction band edge that could be attributed to oxygen vacancies.