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

A new approach to partial synchronization in globally coupled rotators

We develop a formalism to analyze the behaviour of pulse--coupled identical phase oscillators with a specific attention devoted to the onset of partial synchronization. The method, which allows describing the dynamics both at the microscopic and macroscopic level, is introduced in a general context, but then the application to the dynamics of leaky integrate-and-fire (LIF) neurons is analysed. As a result, we derive a set of delayed equations describing exactly the LIF behaviour in the thermodynamic limit. We also investigate the weak coupling regime by means of a perturbative analysis, which reveals that the evolution rule reduces to a set of ordinary differential equations. Robustness and generality of the partial synchronization regime is finally tested both by adding noise and considering different force fields.Comment: 5 pages, 3 eps figure

A new test for random number generators: Schwinger-Dyson equations for the Ising model

We use a set of Schwinger-Dyson equations for the Ising Model to check several random number generators. For the model in two and three dimensions, it is shown that the equations are sensitive tests of bias originated by the random numbers. The method is almost costless in computer time when added to any simulation.Comment: 6 pages, 3 figure

Giant Enhancement of Surface Second Harmonic Generation in BaTiO_3 due to Photorefractive Surface Wave Excitation

We report observation of strongly enhanced surface SHG in BaTiO_3 due to excitation of a photorefractive surface electromagnetic wave. Surface SH intensity may reach 10^{-2} of the incident fundamental light intensity. Angular, crystal orientation and polarization dependencies of this SHG are presented. Possible applications of this effect in nonlinear surface spectroscopy are discussed.Comment: 5 pages, 6 figures, submitted to Physical Review Letters on the 3/29/199

Population coding by globally coupled phase oscillators

A system of globally coupled phase oscillators subject to an external input is considered as a simple model of neural circuits coding external stimulus. The information coding efficiency of the system in its asynchronous state is quantified using Fisher information. The effect of coupling and noise on the information coding efficiency in the stationary state is analyzed. The relaxation process of the system after the presentation of an external input is also studied. It is found that the information coding efficiency exhibits a large transient increase before the system relaxes to the final stationary state.Comment: 7 pages, 9 figures, revised version, new figures added, to appear in JPSJ Vol 75, No.

Spatial constancy of attention across eye movements is mediated by the presence of visual objects

Recent studies have shown that attentional facilitation lingers at the retinotopic coordinates of a previously attended position after an eye movement. These results are intriguing, because the retinotopic location becomes behaviorally irrelevant once the eyes have moved. Critically, in these studies participants were asked to maintain attention on a blank location of the screen. In the present study, we examined whether the continuing presence of a visual object at the cued location could affect the allocation of attention across eye movements. We used a trans-saccadic cueing paradigm in which the relevant positions could be defined or not by visual objects (simple square outlines). We find an attentional benefit at the spatiotopic location of the cue only when the object (the placeholder) has been continuously present at that location. We conclude that the presence of an object at the attended location is a critical factor for the maintenance of spatial constancy of attention across eye movements, a finding that helps to reconcile previous conflicting results

Modeling of Spiking-Bursting Neural Behavior Using Two-Dimensional Map

A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation of spikes, bursts of spikes, and restructuring of the map behavior are explained using phase portrait analysis. The dynamics of two coupled maps which model the behavior of two electrically coupled neurons is discussed. Synchronization regimes for spiking and bursting activity of these maps are studied as a function of coupling strength. It is demonstrated that the results of this model are in agreement with the synchronization of chaotic spiking-bursting behavior experimentally found in real biological neurons.Comment: 9 pages, 12 figure

Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators

In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist novel hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.Comment: 4 pages, 4 figure

Noise Induced Coherence in Neural Networks

We investigate numerically the dynamics of large networks of $N$ globally pulse-coupled integrate and fire neurons in a noise-induced synchronized state. The powerspectrum of an individual element within the network is shown to exhibit in the thermodynamic limit ($N\to \infty$) a broadband peak and an additional delta-function peak that is absent from the powerspectrum of an isolated element. The powerspectrum of the mean output signal only exhibits the delta-function peak. These results are explained analytically in an exactly soluble oscillator model with global phase coupling.Comment: 4 pages ReVTeX and 3 postscript figure

Modified Cross-Correlation for Efficient White-Beam Inelastic Neutron Scattering Spectroscopy

We describe a method of white-beam inelastic neutron scattering for improved measurement efficiency. The method consists of matrix inversion and selective extraction. The former is to resolve each incident energy component from the white-beam data, and the latter eliminates contamination by elastic components, which produce strong backgrounds that otherwise obfuscate the inelastic scattering components. In this method, the optimal experimental condition to obtain high efficiency will strongly depend on the specific aim of the individual experiments.Comment: 6 pages, 3 figure