The interplay between microscopic and mesoscopic structures in complex networks

Understanding a complex network's structure holds the key to understanding its function. The physics community has contributed a multitude of methods and analyses to this cross-disciplinary endeavor. Structural features exist on both the microscopic level, resulting from differences between single node properties, and the mesoscopic level resulting from properties shared by groups of nodes. Disentangling the determinants of network structure on these different scales has remained a major, and so far unsolved, challenge. Here we show how multiscale generative probabilistic exponential random graph models combined with efficient, distributive message-passing inference techniques can be used to achieve this separation of scales, leading to improved detection accuracy of latent classes as demonstrated on benchmark problems. It sheds new light on the statistical significance of motif-distributions in neural networks and improves the link-prediction accuracy as exemplified for gene-disease associations in the highly consequential Online Mendelian Inheritance in Man database. © 2011 Reichardt et al.

Pair breaking and bound states in disordered superconductors

We study the effects of inhomogeneous pairing interactions and impurities in short-coherence-length superconductors. Within the Born approximation, the effects of pairing disorder and magnetic impurities are identical. The T-matrices for pairing disorder sites with and without an impurity give rise to bound states within the BCS (Bardeen-Cooper-Schrieffer) gap, consistent with scanning tunnelling microscopy results on Bi2Sr2CaCu2O8+δ with Zn or Ni impurities.

Granular superconductors:from the nonlinear σ model to the Bose-Hubbard description

We modify a nonlinear σ model (NLσM) for the description of a granular disordered system in the presence of both the Coulomb repulsion and the Cooper pairing. We show that under certain controlled approximations the action of this model is reduced to the Ambegaokar-Eckern-Schön (AES) action, which is further reduced to the Bose-Hubbard (or “dirty-boson”) model with renormalized coupling constants. We obtain an effective action which is more general than the AES one but still simpler than the full NLσM action. This action can be applied in the region of parameters where the reduction to the AES or the Bose-Hubbard model is not justified. This action may lead to a different picture of the superconductor-insulator transition in two-dimensional systems.

Nonlinear σ model for disordered superconductors

We suggest a variant of the nonlinear σ model for the description of disordered superconductors. The main distinction from existing models lies in the fact that the saddle point equation is solved nonperturbatively in the superconducting pairing field. It allows one to use the model both in the vicinity of the metal-superconductor transition and well below its critical temperature with full account for the self-consistency conditions. We show that the model reproduces a set of known results in different limiting cases, and apply it for a self-consistent description of the proximity effect at the superconductor-metal interface.

A new approach to neuroimaging with magnetoencephalography

We discuss the application of beamforming techniques to the field of magnetoencephalography (MEG). We argue that beamformers have given us an insight into the dynamics of oscillatory changes across the cortex not explored previously with traditional analysis techniques that rely on averaged evoked responses. We review several experiments that have used beamformers, with special emphasis on those in which the results have been compared to those observed in functional magnetic resonance imaging (fMRI) and on those studying induced phenomena. We suggest that the success of the beamformer technique, despite the assumption that there are no linear interactions between the mesoscopic local field potentials across distinct cortical areas, may tell us something of the balance between functional integration and segregation in the human brain. What is more, MEG beamformer analysis facilitates the study of these complex interactions within cortical networks that are involved in both sensory-motor and cognitive processes. © 2005 Wiley-Liss, Inc.

Fluctuation-induced traffic congestion in heterogeneous networks

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analyzing network failures caused by hardware faults or overload, where the network reaction was modeled as rerouting of traffic away from failed or congested elements. Here we model another type of the network reaction to congestion - a sharp reduction of the input traffic rate through congested routes which occurs on much shorter time scales. We consider the onset of congestion in the Internet where local mismatch between demand and capacity results in traffic losses and show that it can be described as a phase transition characterized by strong non-Gaussian loss fluctuations at a mesoscopic time scale. The fluctuations, caused by noise in input traffic, are exacerbated by the heterogeneous nature of the network manifested in a scale-free load distribution. They result in the network strongly overreacting to the first signs of congestion by significantly reducing input traffic along the communication paths where congestion is utterly negligible. © Copyright EPLA, 2012.

Universal duality in a Luttinger liquid coupled to a generic environment

We study a Luttinger liquid (LL) coupled to a generic environment consisting of bosonic modes with arbitrary density-density and current-current interactions. The LL can be either in the conducting phase and perturbed by a weak scatterer or in the insulating phase and perturbed by a weak link. The environment modes can also be scattered by the imperfection in the system with arbitrary transmission and reflection amplitudes. We present a general method of calculating correlation functions under the presence of the environment and prove the duality of exponents describing the scaling of the weak scatterer and of the weak link. This duality holds true for a broad class of models and is sensitive to neither interaction nor environmental modes details, thus it shows up as the universal property. It ensures that the environment cannot generate new stable fixed points of the renormalization group flow. Thus, the LL always flows toward either conducting or insulating phase. Phases are separated by a sharp boundary which is shifted by the influence of the environment. Our results are relevant, for example, for low-energy transport in (i) an interacting quantum wire or a carbon nanotube where the electrons are coupled to the acoustic phonons scattered by the lattice defect; (ii) a mixture of interacting fermionic and bosonic cold atoms where the bosonic modes are scattered due to an abrupt local change of the interaction; (iii) mesoscopic electric circuits.

Stabilization of self-assembled alumina mesophases

An efficient route to stabilize alumina mesophases derived from evaporation-induced self-assembly is reported after investigating various aspects in-depth: influence of the solvent (EtOH, s-BuOH, and t-BuOH) on the textural and structural properties of the mesophases based on aluminum tri-sec-butoxide (ATSB), synthesis reproducibility, role of nonvolatile acids, and the crystallization and thermal stability of the crystalline counterparts. Mesophase specific surface area and pore uniformity depend notably on the solvent; s-BuOH yields the highest surface area and pore uniformity. The optimal mesophase synthesis is reproducible with standard deviations in the textural parameters below 5%. The most pore-uniform mesophases from the three solvents were thermally activated at 1023 K to crystallize them into γ-alumina. The s-BuOH mesophase is remarkably thermally stable, retaining the mesoscopic wormhole order with 300 m2/g (0.45 cm3/g) and an increased acidic site density. These features are not obtained with EtOH or t-BuOH, where agglomerated γ-Al2O3 crystallites are formed with lower surface areas and broader pore size distributions. This was rationalized by the increase of the hydrolysis rate using EtOH and t-BuOH. t-BuOH dehydrates under the synthesis conditions or reacts with HCl, situations that increase the water concentration and rate of hydrolysis. It was found that EtOH exchanges rapidly, producing a highly reactive Al-ethoxide, thus enhancing the hydrolysis rate as well. Particle heterogeneity with random packing of fibrous and wormhole morphologies, attributed to the high hydrolysis rate, was observed for mesophases derived from both solvents. Such a low particle coordination favors coarsening with enlargement of the pore size distribution upon thermal treatment, explaining the lower thermal stability. Controlled hydrolysis and formation of low-polymerized Al species in s-BuOH are possibly responsible for the adequate assembly onto the surfactant. This was verified by the formation of a regular distribution of relatively size-uniform nanoparticles in the mesophase; high particle coordination prevents coarsening, favors densification, and maintains a relatively uniform pore size distribution upon thermal treatment. The acid removal in the evaporation is another key factor to promote network condensation in this route. © 2013 American Chemical Society.

Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett. 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.