Collective oscillations in disordered neural networks

We investigate the onset of collective oscillations in a network of pulse-coupled leaky-integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous to that arising in the Kuramoto model for a finite number N of oscillators [O.V. Popovych at al., Phys. Rev. E 71} 065201(R) (2005)]. In fact, the maximum Lyapunov exponent turns out to scale to zero for N going to infinite, with an exponent that is different for the two types of disorder. In the thermodynamic limit, the random-network dynamics reduces to that of a fully homogenous system with a suitably scaled coupling strength. Moreover, we show that the Lyapunov spectrum of the periodically collective state scales to zero as 1/N^2, analogously to the scaling found for the `splay state'.Comment: 8.5 Pages, 12 figures, submitted to Physical Review

Use of source apportionment model for designing acid deposition mitigating strategies in Massachusetts

The Commonwealth of Massachusetts promulgated an Act limiting S2 emissions from large sources that burn fuel at a rate greater than or equal to 100 million Btu (MBtu) of fuel input per hour. The Act requires that by 1995 the average emission rate at such facilities be less than or equal to 1.2 lb SO2 per MBtu fuel input. Because of their size, almost all power plants in Massachusetts could be subject to emission reductions. Since the average 1980-1982 annual emission rate of Massachusetts power plants was 1.84 lb S02/MBtu ("base case"), the Act requires the annual average emission rate of power plants to diminish by 35%. We use a source apportionment model to estimate the wet sulfate deposition to typical sensitive Massachusetts receptors from Massachusetts power plants, separately for the summer (April-September) and winter (October-March) half-years. We find that the summer wet deposition is about twice the winter deposition, although summer and winter SO2 emissions are approximately equal. Therefore, to reduce sulfate deposition, t is more effective to reduce emissions in the summer months rather than in winter. Using the seasonal source apportionment model we find that an annual wet deposition reduction equal to that resulting from the Act could be accomplished if only summer emission rates were reduced to 0.86 lb SO /MBtu, with winter emission rates remaining at 1.84 lb S02/MBtu. The resulging annual average emission rate is 1.35 lb SO /MBtu, 27% less than the base value. As 1980-1982 average annual emissions rom power plants amounted to 270,000 tons of SO annually, a summer emission control program would save about 21,000 tons of S emission reduction without sacrificing wet deposition protection. Te summer emission reduction could be acomplished by substituting lower sulfur content fuels, including natural gas, for higher sulfur content fuels.New England Power Company under the Electric Utility Program at the Energy Laborator

Ground-level ozone in eastern North America : its formation and transport

Ozone (Os), a natural component of the troposphere, is augmented by photochemical processes involving manmade emissions of nitrogen oxides (NOx) and volatile organic compounds (VOCs). Sufficiently high concentrations of ozone are detrimental to the respiratory system. Ozone exposure also reduces crop yields and damages forests. This study attempts to explain the underlying factors which contribute to observed ozone levels.Long range transport models of three species - NOx, VOCs and ozone - are developed for eastern North America. The seasonally averaged models include the essential physical and chemical processes in a relatively simple framework. NOx and VOCs are treated as primary species, i.e., they are modeled from their introduction into the atmosphere to their point of removal. Detailed emission inventories serve as input to the precursor models. Ozone is considered a secondary species because it is not directly emitted. Rather, its production is assumed to be a function of ambient NO, and VOCs levels.Measured concentrations, available for NO 2 and ozone, are compared with model predictions and aid in determining adjustable model parameters. Predicted NOx concentrations are consistent with rural observations but underestimate sites influenced by nearby sources at which the long range assumptions break down. Local models which properly treat proximate sources account for the discrepancy. The VOCs model, having no measurements for verification, adopts parameters consistent with the NOx model and known chemical properties. Both biogenic and manmade emissions contribute to ambient VOCs levels. Biogenic emissions are found to be more important over most of ENA; anthropogenic sources of VOCs are dominant only in urban areas.Consistent with empirical patterns, the ozone model predicts small regional gradients and hence a limited dependence on NOx and VOCs precursors. The natural background component is determined to be two-thirds of average ozone levels. Regional transport is significant; ozone lifetimes are estimated to be of the order of a day. The high background level and insensitivity to precursors suggests that significant reductions of average ozone concentrations will be difficult to achieve

Effects of Diversity on Multi-agent Systems: Minority Games

We consider a version of large population games whose agents compete for resources using strategies with adaptable preferences. The games can be used to model economic markets, ecosystems or distributed control. Diversity of initial preferences of strategies is introduced by randomly assigning biases to the strategies of different agents. We find that diversity among the agents reduces their maladaptive behavior. We find interesting scaling relations with diversity for the variance and other parameters such as the convergence time, the fraction of fickle agents, and the variance of wealth, illustrating their dynamical origin. When diversity increases, the scaling dynamics is modified by kinetic sampling and waiting effects. Analyses yield excellent agreement with simulations.Comment: 41 pages, 16 figures; minor improvements in content, added references; to be published in Physical Review

Temporal decorrelation of collective oscillations in neural networks with local inhibition and long-range excitation

We consider two neuronal networks coupled by long-range excitatory interactions. Oscillations in the gamma frequency band are generated within each network by local inhibition. When long-range excitation is weak, these oscillations phase-lock with a phase-shift dependent on the strength of local inhibition. Increasing the strength of long-range excitation induces a transition to chaos via period-doubling or quasi-periodic scenarios. In the chaotic regime oscillatory activity undergoes fast temporal decorrelation. The generality of these dynamical properties is assessed in firing-rate models as well as in large networks of conductance-based neurons.Comment: 4 pages, 5 figures. accepted for publication in Physical Review Letter

How well can we estimate the information carried in neuronal responses from limited samples?

It is difficult to extract the information carried by neuronal responses about a set of stimuli because limited data samples result in biased estimates. Recently two improved procedures have been developed to calculate information from experimental results: a binning-and-correcting procedure and a neural network procedure. We have used data produced from a model of the spatiotemporal receptive fields of parvocellular and magnocellular lateral geniculate neurons to study the performance of these methods as a function of the number of trials used. Both procedures yield accurate results for one-dimensional neuronal codes. They can also be used to produce a reasonable estimate of the extra information in a three-dimensional code, in this instance, within 0.05-0.1 bit of the asymptotically calculated value - about 10% of the total transmitted information. We believe that this performance is much more accurate than previous procedures

Polyharmonic approximation on the sphere

The purpose of this article is to provide new error estimates for a popular type of SBF approximation on the sphere: approximating by linear combinations of Green's functions of polyharmonic differential operators. We show that the $L_p$ approximation order for this kind of approximation is $\sigma$ for functions having $L_p$ smoothness $\sigma$ (for $\sigma$ up to the order of the underlying differential operator, just as in univariate spline theory). This is an improvement over previous error estimates, which penalized the approximation order when measuring error in $L_p$, p>2 and held only in a restrictive setting when measuring error in $L_p$, p<2.Comment: 16 pages; revised version; to appear in Constr. Appro

Shift in critical temperature for random spatial permutations with cycle weights

We examine a phase transition in a model of random spatial permutations which originates in a study of the interacting Bose gas. Permutations are weighted according to point positions; the low-temperature onset of the appearance of arbitrarily long cycles is connected to the phase transition of Bose-Einstein condensates. In our simplified model, point positions are held fixed on the fully occupied cubic lattice and interactions are expressed as Ewens-type weights on cycle lengths of permutations. The critical temperature of the transition to long cycles depends on an interaction-strength parameter $\alpha$. For weak interactions, the shift in critical temperature is expected to be linear in $\alpha$ with constant of linearity $c$. Using Markov chain Monte Carlo methods and finite-size scaling, we find $c = 0.618 \pm 0.086$. This finding matches a similar analytical result of Ueltschi and Betz. We also examine the mean longest cycle length as a fraction of the number of sites in long cycles, recovering an earlier result of Shepp and Lloyd for non-spatial permutations.Comment: v2 incorporated reviewer comments. v3 removed two extraneous figures which appeared at the end of the PDF