Mean-field Techniques Research Articles

Mean-field framework for performance evaluation of push–pull gossip protocols

Gossip protocols are designed to operate in very large, decentralised networks. A node in such a network bases its decision to interact (gossip) with another node on its partial view of the global system. Because of the size of these networks, analysis of gossip protocols is mostly done using simulations, but these tend to be expensive in computation time and memory consumption. We employ mean-field analysis techniques for the evaluation of gossip protocols. Nodes in the network are represented by small identical stochastic processes. Joining all nodes would result in an enormous stochastic process. If the number of nodes goes to infinity, however, mean-field analysis allows us to replace this intractably large stochastic process by a small deterministic process. This process approximates the behaviour of very large gossip networks, and can be evaluated using simple matrix-vector multiplications.

Analysis of Television and Cinema Productions using Mean Field Models

Television and cinema productions have a critical influence in today's economy, but performance evaluation techniques are rarely used in these contexts. Both kind of productions share a similar key feature: the spectator. It is in fact the final user who determines the success of a production by deciding to spend his or her money for it. In this paper we use Mean Field techniques to model the behavior of the users, of the production and of the distribution. We use Generalized Stochastic Petri Nets as an upper level formalism to simplify the description of the proposed models. Finally we present comparisons with real data (where available) to prove the validity of the Mean Field approach.

Input-dependent switching of inhibitory configurations in neural networks

Event Abstract Back to Event Input-dependent switching of inhibitory configurations in neural networks Alex D. Reyes1* 1 New York University , United States The responses of neurons during a stimulus depend on the summed excitatory (E) and inhibitory (I) synaptic inputs. Shifts in the E-I balance cause both qualitative and quantitative changes in the neuronal firing patterns. How the E and I inputs scale with stimuli is yet unclear. An important determinant is the network architecture, broadly classified either as the lateral inhibitory network (LIN) where the I inputs to a neuron are more broadly tuned than the E inputs, or the co-tuned network (CON) where the E and I inputs co-vary for the entire stimulus range. E and I scale with input differently in each configuration to produce complementary sets of responses, suggesting that both may be needed to account for the diverse stimulus-evoked firing behavior. Here I show that a single E-I network transitions seamlessly between LIN and CON when the amplitude and spatial extent of the input to the network changes. Simulations were performed with a 2D network (10000 E cells; 2000 I cells) of Adaptive exponential integrate and fire neurons adjusted to reproduce the firing of pyramidal cells, and fast spiking and low threshold spiking interneurons. The patterns of connections between E and I cells were based on experimental data obtained from paired recordings in an in vitro slice preparation. Synaptic barrages (200 ms duration) were delivered to each cell; the number of barrages was adjusted so that the mean input was Gaussian distributed (parameterized by amplitude A and standard deviation S) in space. When the input was narrow (small S), the network was configured as LIN. E cells tended to fire tonically, and exhibited side-band inhibition. As the input broadened, the network switched to CON. The neurons tended to fire phasically and exhibited no sideband inhibition. To characterize quantitatively the variation of E-I balance and firing in the A-S space, mean field techniques were used to calculate the population activity of the neurons in the network. This yielded relations that describe how the widths and amplitude of excitatory and inhibitory inputs and the associated firing patterns change with the magnitude and spatial distribution of the input. Physiologically, the Gaussian input may represent tuning to stimuli such as tone frequency in the auditory system or disc location in the visual system; A may vary with stimulus intensity while S with bandwidth or disc diameter. The changes in firing that occur with increasing the bandwidth/diameter of auditory/visual stimulus are reproduced by tracing appropriate trajectories in the A and S space. That the LIN and CON configurations are not hardwired into the network has important implications. The ability to switch between configurations provides potentially a mechanism for modulating the response of the network to a variety of inputs and behavioral states. Additionally, many of the heterogeneous firing and receptive field properties that had been postulated to arise from different network configurations may in fact be due to transitions within a single network that are triggered perhaps by changes in the stimulus characteristics or state of the animal. Conference: Computational and Systems Neuroscience 2010, Salt Lake City, UT, United States, 25 Feb - 2 Mar, 2010. Presentation Type: Oral Presentation Topic: Oral presentations Citation: Reyes AD (2010). Input-dependent switching of inhibitory configurations in neural networks. Front. Neurosci. Conference Abstract: Computational and Systems Neuroscience 2010. doi: 10.3389/conf.fnins.2010.03.00003 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 17 Feb 2010; Published Online: 17 Feb 2010. * Correspondence: Alex D Reyes, New York University, New York, United States, reyes@cns.nyu.edu Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Alex D Reyes Google Alex D Reyes Google Scholar Alex D Reyes PubMed Alex D Reyes Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Protein−Ligand Docking Using Mutually Orthogonal Latin Squares (MOLSDOCK)

The theoretical prediction of the association of a flexible ligand with a protein receptor requires efficient sampling of the conformational space of the ligand. Several docking methodologies are currently available. We have proposed a docking technique that performs well at low computational cost. The method uses mutually orthogonal Latin squares to efficiently sample the docking space. A variant of the mean field technique is used to analyze this sample to arrive at the optimum. The method has been previously applied to search through both the conformational space of a peptide as well its docking space. Here we extend this method to simultaneously identify both the low energy conformation as well as a high scoring docking mode for the small organic ligand molecules. Application of the method to 45 protein-ligand complexes, in which the number of rotatable torsions varies from 2 to 19, and comparisons with AutoDock 4.0, showed that the method works well.

On modeling product advertisement in social networks

Advertising via social networks is receiving more attention these days. Given a fixed investment (e.g., free samples), a company needs to find out the final probability that users will purchase the product. In this paper we characterize and model various influence mechanisms that govern the word-of-mouth spread of advertisements in large social networks. We use the local mean field (LMF) technique to analyze large scale networks wherein states of nodes can be changed by various influence mechanisms. Extensive simulations are carried out to validate the accuracy of our model, and the results also provide insights on designing advertising strategies.

Multideterminant assessment of mean-field methods for the description of electron transfer in the weak-coupling regime

Multideterminant calculations have been performed on model systems to emphasize the role of many-body effects in the general description of charge quantization experiments. We show numerically and derive analytically that a closed-shell ansatz, the usual ingredient of mean-field methods, does not properly describe the steplike electron-transfer characteristic in weakly coupled systems. With the multideterminant results as a benchmark, we have evaluated the performance of common ab initio mean-field techniques, such as Hartree-Fock (HF) and density-functional theory (DFT) with local and hybrid exchange-correlation functionals, with a special focus on spin-polarization effects. For HF and hybrid DFT, a qualitatively correct open-shell solution with distinct steps in the electron-transfer behavior can be obtained with a spin-unrestricted (i.e., spin-polarized) ansatz although this solution differs quantitatively from the multideterminant reference. We also discuss the relationship between the electronic eigenvalue gap and the onset of charge transfer for both HF and DFT and relate our findings to recently proposed practical schemes for calculating the addition energies in the Coulomb blockade regime for single-molecule junctions from closed-shell DFT within the local-density approximation.

Transition fromγ-rigid toγ-soft dynamics in the interacting boson model: Quasicriticality and quasidynamical symmetry

We study the transition from the {gamma}-rigid to {gamma}-soft collective nuclear dynamics across the Casten triangle of the interacting boson model using mean-field techniques and confront the description with the exact diagonalization. We inspect the domain of validity of the SU(3) quasidynamical symmetry inside the Casten triangle and reveal critical behavior within the low-lying excited spectrum due to a degeneracy of {beta} and {gamma} vibrations.

Dynamical formation and interaction of bright solitary waves and solitons in the collapse of Bose–Einstein condensates with attractive interactions

We model the dynamics of formation of multiple, long-lived, bright solitary waves (BSWs) in the collapse of Bose–Einstein condensates with attractive interactions as studied in the experiment of Cornish et al (2006 Phys. Rev. Lett. 96 170401). We use both mean-field and approximate quantum field simulation techniques. While a number of separated wave packets form as observed in the experiment, they do not have a repulsive π phase difference as has been previously inferred. We observe that the inclusion of quantum fluctuations causes soliton dynamics to be predominantly repulsive in one-dimensional (1D) simulations independent of their initial relative phase. However, indicative 3D simulations do not show a similar effect. In contrast, in 3D quantum noise has a negative impact on BSW lifetimes. Finally, we show that condensate oscillations, after the collapse, may serve to deduce three-body recombination rates.

Master-equation analysis of accelerating networks

In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous efforts at analyzing their degree distributions have employed mean-field techniques. By contrast, we show that it is possible to apply a master-equation approach to such network development. We provide full time-dependent expressions for the evolution of the degree distributions for the canonical situations of random and preferential attachment in networks undergoing constant acceleration. These results are in excellent agreement with results obtained from simulations. We note that a growing nonequilibrium network undergoing constant acceleration with random attachment is equivalent to a classical random graph, bridging the gap between nonequilibrium and classical equilibrium networks.

Norm-conserving diffusion Monte Carlo method and diagrammatic expansion of interacting Drude oscillators: Application to solid xenon

The quantum Drude oscillator (QDO) model, which allows many-body polarization and dispersion to be treated both on an equal footing and beyond the dipole limit, is investigated using two approaches to the linear scaling diffusion Monte Carlo (DMC) technique. The first is a general purpose norm-conserving DMC (NC-DMC) method wherein the number of walkers, $N$, remains strictly constant thereby avoiding the sudden death or explosive growth of walker populations with an error that vanishes as $\mathcal{O}({N}^{\ensuremath{-}1})$ in the absence of weights. As NC-DMC satisfies detailed balance, a phase space can be defined that permits both an exact trajectory weighting and a fast mean-field trajectory weighting technique to be constructed which can eliminate or reduce the population bias, respectively. The second is a many-body diagrammatic expansion for trial wave functions in systems dominated by strong on-site harmonic coupling and a dense matrix of bilinear coupling constants such as the QDO in the dipole limit; an approximate trial function is introduced to treat two-body interactions outside the dipole limit. Using these approaches, high accuracy is achieved in studies of the fcc-solid phase of the highly polarizable atom, xenon, within the QDO model. It is found that 200 walkers suffice to generate converged results for systems as large as 500 atoms. The quality of QDO predictions compared to experiment and the ability to generate these predictions efficiently demonstrate the feasibility of employing the QDO approach to model long-range forces.

Magnetic and metallic state at intermediate HubbardUcoupling in multiorbital models for undoped iron pnictides

Multiorbital Hubbard model Hamiltonians for the undoped parent compounds of the Fe-pnictide superconductors are investigated here using mean-field techniques. For a realistic four-orbital model, our results show the existence of an intermediate Hubbard $U$ coupling regime where the mean-field ground state has a $(\ensuremath{\pi},0)$ antiferromagnetic order, as in neutron-scattering experiments, while remaining metallic due to the phenomenon of band overlaps. The angle-resolved photoemission intensity and Fermi surface of this magnetic and metallic state are discussed. Other models are also investigated, including a two-orbital model where not only the mean-field technique can be used but also the exact diagonalization in small clusters and the variational cluster approximation in the bulk. The combined results of the three techniques point toward the existence of an intermediate-coupling magnetic and metallic state in the two-orbital model, similar to the intermediate-coupling mean-field state of the four-orbital model. We conclude that the state discussed here is compatible with the experimentally known properties of the undoped Fe pnictides.

THE EMISSION OF HEAVY CLUSTERS DESCRIBED IN THE MEAN-FIELD HFB THEORY: THE CASE OF 242Cm

The emission of a nucleus of 34 Si by the parent [Formula: see text] is a process in the diffuse borderline between cluster emission and standard mass asymmetric fission. In this paper we analyze in a microscopic framework such process using the standard mean field techniques used to describe cluster emission. They include Hartree-Fock-Bogoliubov constrained calculations with the Gogny D1S interaction and the octupole moment operator as the collective coordinate to describe the process. Collective masses and all kind of zero point energy corrections are considered which allows for a parameter free estimation of the process' half-life. The agreement with experiment is quite satisfactory.

Enhanced Superconductivity in Superlattices of High-TcCuprates

The electronic properties of multilayers of strongly correlated models for cuprate superconductors are investigated using cluster dynamical mean-field techniques. We focus on combinations of underdoped and overdoped layers and find that the superconducting order parameter in the overdoped layers is enhanced by the proximity effect of the strong pairing scale originating from the underdoped layers. The enhanced order parameter can even exceed the maximum value in uniform systems. This behavior is well reproduced in slave-boson mean-field calculations which also find higher transition temperatures than in the uniform system.

On the origin of the anomalous behaviour of [formula omitted] excitation energies in the neutron-rich Cd isotopes

Recent experimental results obtained using β decay and isomer spectroscopy indicate an unusual behaviour of the energies of the first excited 2 + states in neutron-rich Cd isotopes approaching the N = 82 shell closure. To explain the unexpected trend, changes of the nuclear structure far-off stability have been suggested, namely a quenching of the N = 82 shell gap already in 130Cd, only two proton holes away from doubly magic 132Sn. We study the behaviour of the 2 + energies in the Cd isotopes from N = 50 to N = 82 , i.e. across the entire span of a major neutron shell using modern beyond mean field techniques and the Gogny force. We demonstrate that the observed low 2 + excitation energy in 128Cd close to the N = 82 shell closure is a consequence of the doubly magic character of this nucleus for oblate deformation favoring thereby prolate configurations rather than spherical ones.

Tricritical transition in the classicalXYmodel on the kagome lattice under local anisotropy

Using mean-field theory and high-resolution Monte Carlo simulation technique based on multihistogram method, we have investigated the critical properties of an antiferromagnetic $XY$ model on the two-dimensional (2D) kagome lattice, with single-ion easy-axes anisotropy. The mean-field theory predicts second-order phase transition from disordered to all-in all-out state for any value of anisotropy for this model. However, Monte Carlo simulations result in first-order transition for small values of anisotropy, which turns to second order with increasing strength of anisotropy, indicating the existence of a tricritical point for this model. The critical exponents, obtained by finite-size scaling methods, show that the transition is in Ising universality class for large values of anisotropy, while the critical behavior of the system deviates from 2D ${\ensuremath{\phi}}^{6}$ model near the tricritical point. This suggests the possibility for existence of another tricritical universality in two dimensions.

Generating multichain configurations of an inhomogeneous melt from the knowledge of single-chain properties

Mean-field techniques provide a rather accurate description of single-chain conformations in spatially inhomogeneous polymer systems containing interfaces or surfaces. Intermolecular correlations, however, are not described by the mean-field approach and information about the distribution of distance between different molecules is lost. Based on the knowledge of the exact equilibrium single-chain properties in contact with solid substrates, we generate multichain configurations that serve as nearly equilibrated starting configurations for molecular dynamics simulations by utilizing the packing algorithm of [Auhl et al., J. Chem. Phys. 119, 12718 (2003)] for spatially inhomogeneous systems, i.e., a thin polymer film confined between two solid substrates. The single-chain conformations are packed into the thin film conserving the single-chain properties and simultaneously minimizing local fluctuations of the density. The extent to which enforcing incompressibility of a dense polymer liquid during the packing process is able to re-establish intermolecular correlations is investigated by monitoring intermolecular correlation functions and the structure function of density fluctuations as a function of the distance from the confining solid substrates.

A new peptide docking strategy using a mean field technique with mutually orthogonal Latin square sampling

The theoretical prediction of the association of a flexible ligand with a protein receptor requires efficient sampling of the conformational space of the ligand. Several docking methodologies are currently available. We propose a new docking technique that performs well at low computational cost. The method uses mutually orthogonal Latin squares to efficiently sample the docking space. A variant of the mean field technique is used to analyze this sample to arrive at the optimum. The method has been previously applied to explore the conformational space of peptides and identify structures with low values for the potential energy. Here we extend this method to simultaneously identify both the low energy conformation as well as a 'high-scoring' docking mode. Application of the method to 56 protein-peptide complexes, in which the length of the peptide ligand ranges from three to seven residues, and comparisons with Autodock 3.05, showed that the method works well.

Quantum phases of bosons in double-well optical lattices

We study the superfluid and insulating phases of bosons in double-well optical lattices, and focus on the specific example of a two-legged ladder, which is currently accessible in experiments. We obtain the zero-temperature phase diagram using both mean-field and time-evolving block decimation techniques. We find that the mean-field approach describes the correct phase boundaries only when the intrachain hopping is sufficiently small in comparison to the on-site repulsion. We show the dependence of the phase diagram on the interchain hopping or tilt between double wells. We find that the Mott-insulator phase at unit filling exhibits a nonmonotonic behavior as a function of the tilt parameter, producing a reentrant phase transition between Mott insulator and superfluid phases. Finally, we determine the critical point separating the insulating and superfluid phases at commensurate fillings, where the Berezinskii-Kosterlitz-Thouless transition occurs.

Magnetocaloric effect in metamagnetic systems

We propose a model to account for the magnetocaloric effect associated with field-driven first-order magnetic transitions. The model is based on an Ising model for the magnetic degrees of freedom which are coupled to lattice vibrations. The coupling is introduced within the framework of a bond proportion model, which assumes that nearest-neighbor pairs of antiparallel and parallel spins have different stiffness. The model is solved by means of a variational mean field technique and it is found that, for strong enough coupling, it displays a field-induced first-order magnetic transition. The magnetocaloric properties are obtained and results are compared with experimental results reported for systems undergoing metamagnetic transitions.

Exploring conformational space using a mean field technique with MOLS sampling

The computational identification of all the low energy structures of a peptide given only its sequence is not an easy task even for small peptides,due to the multiple-minima problem and combinatorial explosion. We have developed an algorithm, called the MOLS technique,that addresses this problem, and have applied it to a number of different aspects of the study of peptide and protein structure. Conformational studies of oligopeptides, including loop sequences in proteins have been carried out using this technique. In general the calculations identified all the folds determined by previous studies,and in addition picked up other energetically favorable structures. The method was also used to map the energy surface of the peptides. In another application, we have combined the MOLS technique, using it to generate a library of low energy structures of an oligopeptide, with a genetic algorithm to predict protein structures. The method has also been applied to explore the conformational space of loops in protein structures.Further, it has been applied to the problem of docking a ligand in its receptor site, with encouraging results.