Self-Organized Criticality and Thermodynamic formalism

We introduce a dissipative version of the Zhang's model of Self-Organized Criticality, where a parameter allows to tune the local energy dissipation. We analyze the main dynamical features of the model and relate in particular the Lyapunov spectrum with the transport properties in the stationary regime. We develop a thermodynamic formalism where we define formal Gibbs measure, partition function and pressure characterizing the avalanche distributions. We discuss the infinite size limit in this setting. We show in particular that a Lee-Yang phenomenon occurs in this model, for the only conservative case. This suggests new connexions to classical critical phenomena.Comment: 35 pages, 15 Figures, submitte

Hierarchical modularity in human brain functional networks

The idea that complex systems have a hierarchical modular organization originates in the early 1960s and has recently attracted fresh support from quantitative studies of large scale, real-life networks. Here we investigate the hierarchical modular (or "modules-within-modules") decomposition of human brain functional networks, measured using functional magnetic resonance imaging (fMRI) in 18 healthy volunteers under no-task or resting conditions. We used a customized template to extract networks with more than 1800 regional nodes, and we applied a fast algorithm to identify nested modular structure at several hierarchical levels. We used mutual information, 0 < I < 1, to estimate the similarity of community structure of networks in different subjects, and to identify the individual network that is most representative of the group. Results show that human brain functional networks have a hierarchical modular organization with a fair degree of similarity between subjects, I=0.63. The largest 5 modules at the highest level of the hierarchy were medial occipital, lateral occipital, central, parieto-frontal and fronto-temporal systems; occipital modules demonstrated less sub-modular organization than modules comprising regions of multimodal association cortex. Connector nodes and hubs, with a key role in inter-modular connectivity, were also concentrated in association cortical areas. We conclude that methods are available for hierarchical modular decomposition of large numbers of high resolution brain functional networks using computationally expedient algorithms. This could enable future investigations of Simon's original hypothesis that hierarchy or near-decomposability of physical symbol systems is a critical design feature for their fast adaptivity to changing environmental conditions

Mesoscale dynamics on the Sun's surface from HINODE observations

Aims: The interactions of velocity scales on the Sun's surface, from granulation to supergranulation are still not understood, nor are their interaction with magnetic fields. We thus aim at giving a better description of dynamics in the mesoscale range which lies between the two scales mentioned above. Method: We analyse a 48h high-resolution time sequence of the quiet Sun photosphere at the disk center obtained with the Solar Optical Telescope onboard Hinode. The observations, which have a field of view of 100 \arcsec$\times$ 100 \arcsec, typically contain four supergranules. We monitor in detail the motion and evolution of granules as well as those of the radial magnetic field. Results: This analysis allows us to better characterize Trees of Fragmenting Granules issued from repeated fragmentation of granules, especially their lifetime statistics. Using floating corks advected by measured velocity fields, we show their crucial role in the advection of the magnetic field and in the build up of the network. Finally, thanks to the long duration of the time series, we estimate that the turbulent diffusion coefficient induced by horizontal motion is approximately $430 \mathrm{km}^2 \mathrm{s}^{-1}$. Conclusions: These results demonstrate that the long living families contribute to the formation of the magnetic network and suggest that supergranulation could be an emergent length scale building up as small magnetic elements are advected and concentrated by TFG flows. Our estimate for the magnetic diffusion associated with this horizontal motion might provide a useful input for mean-field dynamo models.Comment: to appear in A&A - 8 pages, 13 figures (degraded quality) - Full resolution version available @ http://www.ast.obs-mip.fr/users/rincon/hinode_roudier_aa09.pd

Efficient C-Phase gate for single-spin qubits in quantum dots

Two-qubit interactions are at the heart of quantum information processing. For single-spin qubits in semiconductor quantum dots, the exchange gate has always been considered the natural two-qubit gate. The recent integration of magnetic field or g-factor gradients in coupled quantum dot systems allows for a one-step, robust realization of the controlled phase (C-Phase) gate instead. We analyze the C-Phase gate durations and fidelities that can be obtained under realistic conditions, including the effects of charge and nuclear field fluctuations, and find gate error probabilities of below 10-4, possibly allowing fault-tolerant quantum computation.Comment: 5 pages, 3 figure

Rfx6 Maintains the Functional Identity of Adult Pancreatic β Cells.

SummaryIncreasing evidence suggests that loss of β cell characteristics may cause insulin secretory deficiency in diabetes, but the underlying mechanisms remain unclear. Here, we show that Rfx6, whose mutation leads to neonatal diabetes in humans, is essential to maintain key features of functionally mature β cells in mice. Rfx6 loss in adult β cells leads to glucose intolerance, impaired β cell glucose sensing, and defective insulin secretion. This is associated with reduced expression of core components of the insulin secretion pathway, including glucokinase, the Abcc8/SUR1 subunit of KATP channels and voltage-gated Ca2+ channels, which are direct targets of Rfx6. Moreover, Rfx6 contributes to the silencing of the vast majority of “disallowed” genes, a group usually specifically repressed in adult β cells, and thus to the maintenance of β cell maturity. These findings raise the possibility that changes in Rfx6 expression or activity may contribute to β cell failure in humans

Non-universal transmission phase behaviour of a large quantum dot

The electron wave function experiences a phase modification at coherent transmission through a quantum dot. This transmission phase undergoes a characteristic shift of $\pi$ when scanning through a Coulomb-blockade resonance. Between successive resonances either a transmission phase lapse of $\pi$ or a phase plateau is theoretically expected to occur depending on the parity of the corresponding quantum dot states. Despite considerable experimental effort, this transmission phase behaviour has remained elusive for a large quantum dot. Here we report on transmission phase measurements across such a large quantum dot hosting hundreds of electrons. Using an original electron two-path interferometer to scan the transmission phase along fourteen successive resonances, we observe both phase lapses and plateaus. Additionally, we demonstrate that quantum dot deformation alters the sequence of transmission phase lapses and plateaus via parity modifications of the involved quantum dot states. Our findings set a milestone towards a comprehensive understanding of the transmission phase of quantum dots.Comment: Main paper: 18 pages, 5 figures, Supplementary materials: 8 pages, 4 figure

Detection of single electron spin resonance in a double quantum dot

Spin-dependent transport measurements through a double quantum dot are a valuable tool for detecting both the coherent evolution of the spin state of a single electron as well as the hybridization of two-electron spin states. In this paper, we discuss a model that describes the transport cycle in this regime, including the effects of an oscillating magnetic field (causing electron spin resonance) and the effective nuclear fields on the spin states in the two dots. We numerically calculate the current flow due to the induced spin flips via electron spin resonance and we study the detector efficiency for a range of parameters. The experimental data are compared with the model and we find a reasonable agreement.Comment: 7 pages, 5 figures. To be published in Journal of Applied Physics, proceedings ICPS 200

Modular and Hierarchically Modular Organization of Brain Networks

Brain networks are increasingly understood as one of a large class of information processing systems that share important organizational principles in common, including the property of a modular community structure. A module is topologically defined as a subset of highly inter-connected nodes which are relatively sparsely connected to nodes in other modules. In brain networks, topological modules are often made up of anatomically neighboring and/or functionally related cortical regions, and inter-modular connections tend to be relatively long distance. Moreover, brain networks and many other complex systems demonstrate the property of hierarchical modularity, or modularity on several topological scales: within each module there will be a set of sub-modules, and within each sub-module a set of sub-sub-modules, etc. There are several general advantages to modular and hierarchically modular network organization, including greater robustness, adaptivity, and evolvability of network function. In this context, we review some of the mathematical concepts available for quantitative analysis of (hierarchical) modularity in brain networks and we summarize some of the recent work investigating modularity of structural and functional brain networks derived from analysis of human neuroimaging data