A constructive mean field analysis of multi population neural networks with random synaptic weights and stochastic inputs

We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the time variations of their membrane potentials. They are coupled by synaptic connections acting on their resulting activity, a nonlinear function of their membrane potential. At the second (mesoscopic) scale, interacting populations of neurons are described individually by similar equations. The equations describing the dynamical and the stationary mean field behaviors are considered as functional equations on a set of stochastic processes. Using this new point of view allows us to prove that these equations are well-posed on any finite time interval and to provide a constructive method for effectively computing their unique solution. This method is proved to converge to the unique solution and we characterize its complexity and convergence rate. We also provide partial results for the stationary problem on infinite time intervals. These results shed some new light on such neural mass models as the one of Jansen and Rit \cite{jansen-rit:95}: their dynamics appears as a coarse approximation of the much richer dynamics that emerges from our analysis. Our numerical experiments confirm that the framework we propose and the numerical methods we derive from it provide a new and powerful tool for the exploration of neural behaviors at different scales.Comment: 55 pages, 4 figures, to appear in "Frontiers in Neuroscience

Sounds of silence: an interview with Rolf de Heer

Rolf de Heer's twelfth feature film, "Dr. Plonk" (starring Nigel Lunghi, Paul Blackwell and Magda Szubanski), premiered on closing night of the 2007 Adelaide Film Festival recently. Already feted as South Australian of the Year, De Heer received the Don Dunstan award on opening night to rapturous applause from his home town crowd. D. Bruno Starrs interviewed Australia's most successful non-mainstream film-maker about the black and white, silent slap-stick comedy three days before its inaugural screening

Approximation by the Dickman distribution and quasi-logarithmic combinatorial structures

Quasi-logarithmic combinatorial structures are a class of decomposable combinatorial structures which extend the logarithmic class considered by Arratia, Barbour and Tavar\'{e} (2003). In order to obtain asymptotic approximations to their component spectrum, it is necessary first to establish an approximation to the sum of an associated sequence of independent random variables in terms of the Dickman distribution. This in turn requires an argument that refines the Mineka coupling by incorporating a blocking construction, leading to exponentially sharper coupling rates for the sums in question. Applications include distributional limit theorems for the size of the largest component and for the vector of counts of the small components in a quasi-logarithmic combinatorial structure.Comment: 22 pages; replaces earlier paper [arXiv:math/0609129] with same title by Bruno Nietlispac

Signal and System Design for Wireless Power Transfer : Prototype, Experiment and Validation

A new line of research on communications and signals design for Wireless Power Transfer (WPT) has recently emerged in the communication literature. Promising signal strategies to maximize the power transfer efficiency of WPT rely on (energy) beamforming, waveform, modulation and transmit diversity, and a combination thereof. To a great extent, the study of those strategies has so far been limited to theoretical performance analysis. In this paper, we study the real over-the-air performance of all the aforementioned signal strategies for WPT. To that end, we have designed, prototyped and experimented an innovative radiative WPT architecture based on Software-Defined Radio (SDR) that can operate in open-loop and closed-loop (with channel acquisition at the transmitter) modes. The prototype consists of three important blocks, namely the channel estimator, the signal generator, and the energy harvester. The experiments have been conducted in a variety of deployments, including frequency flat and frequency selective channels, under static and mobility conditions. Experiments highlight that a channeladaptive WPT architecture based on joint beamforming and waveform design offers significant performance improvements in harvested DC power over conventional single-antenna/multiantenna continuous wave systems. The experimental results fully validate the observations predicted from the theoretical signal designs and confirm the crucial and beneficial role played by the energy harvester nonlinearity.Comment: Accepted to IEEE Transactions on Wireless Communication

Prototyping and Experimentation of a Closed-Loop Wireless Power Transmission with Channel Acquisition and Waveform Optimization

A systematic design of adaptive waveform for Wireless Power Transfer (WPT) has recently been proposed and shown through simulations to lead to significant performance benefits compared to traditional non-adaptive and heuristic waveforms. In this study, we design the first prototype of a closed-loop wireless power transfer system with adaptive waveform optimization based on Channel State Information acquisition. The prototype consists of three important blocks, namely the channel estimator, the waveform optimizer, and the energy harvester. Software Defined Radio (SDR) prototyping tools are used to implement a wireless power transmitter and a channel estimator, and a voltage doubler rectenna is designed to work as an energy harvester. A channel adaptive waveform with 8 sinewaves is shown through experiments to improve the average harvested DC power at the rectenna output by 9.8% to 36.8% over a non-adaptive design with the same number of sinewaves.Comment: accepted for publication in IEEE WPTC 201

Technical and Environmental efficiencies and Best Management Practices in Agriculture

An input distance function (IDF) is estimated to empirically evaluate and analyze the technical and environmental efficiencies of 210 farms located in the Chaudière watershed (Quebec), where water quality problems are particularly acute because of the production of undesirable outputs that are jointly produced with agricultural products. The true IDF is approximated by a flexible translog functional form estimated using a full information maximum likelihood method. Technical and environmental efficiencies are disaggregated across farms and account for spatial variations. Our results show that there is a significant correlation between technical and environmental efficiencies. The IDF is used to compute the cumulative Malmquist productivity index and the Fisher index. The two indices are used to measure changes in technology, profitability, efficiency, and productivity in response to the adoption of 2 selected best management practices (BMPs) whose objective is to reduce water pollution. We found significant differences across BMPs regarding the direction and the magnitude of their effect on profitability, efficiency and productivity.Environmental efficiency, distance function, phosphorus runoff, productivity, profitability, technical efficiency.

Giant anharmonicity suppresses superconductivity in AlH3_3 under pressure

The anharmonic self energy of two zone boundary phonons were computed to lowest order for AlH$_3$ in the $Pm\bar 3n$ structure at 110 GPa. The wavevector and branch index corresponding to these modes are situated in a region of phase space providing most of the electron-phonon coupling. The self energies are found to be very large and the anharmonic contribution to the linewidth of one of the modes studied could be distinguished from the electron-phonon linewidth. It is found that anharmonicity suppresses the electron-phonon coupling parameter $\lambda$, providing a possible explanation for the disagreement between experiment and previous theoretical studies of superconductivity in this system.Comment: 10 pages, 4 figure