Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression

We study the spatiotemporal dynamics of a two-dimensional excitatory neuronal network with synaptic depression. Coupling between populations of neurons is taken to be nonlocal, while depression is taken to be local and presynaptic. We show that the network supports a wide range of spatially structured oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. The particular form of the oscillations depends on initial conditions and the level of background noise. Given an initial, spatially localized stimulus, activity evolves to a spatially localized oscillating core that periodically emits target waves. Low levels of noise can spontaneously generate several pockets of oscillatory activity that interact via their target patterns. Periodic activity in space can also organize into spiral waves, provided that there is some source of rotational symmetry breaking due to external stimuli or noise. In the high gain limit, no oscillatory behavior exists, but a transient stimulus can lead to a single, outward propagating target wave

Stationary bumps in a piecewise smooth neural field model with synaptic depression

We analyze the existence and stability of stationary pulses or bumps in a one–dimensional piecewise smooth neural field model with synaptic depression. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Synaptic depression dynamically reduces the strength of synaptic weights in response to increases in activity. We show that in the case of a Mexican hat weight distribution, there exists a stable bump for sufficiently weak synaptic depression. However, as synaptic depression becomes stronger, the bump became unstable with respect to perturbations that shift the boundary of the bump, leading to the formation of a traveling pulse. The local stability of a bump is determined by the spectrum of a piecewise linear operator that keeps track of the sign of perturbations of the bump boundary. This results in a number of differences from previous studies of neural field models with Heaviside firing rate functions, where any discontinuities appear inside convolutions so that the resulting dynamical system is smooth. We also extend our results to the case of radially symmetric bumps in two–dimensional neural field models

Linear statistics for zeros of Riemann's zeta function

We consider a smooth counting function of the scaled zeros of the Riemann zeta function, around height T. We show that the first few moments tend to the Gaussian moments, with the exact number depending on the statistic considered

Measurement of induced surface charges, contact potentials, and surface states in GaN by electric force microscopy

We have studied molecular beam epitaxy grown GaN films of both polarities using electric force microscopy to detect sub 1 µm regions of charge density variations associated with GaN extended defects. The large piezoelectric coefficients of GaN together with strain introduced by crystalline imperfections produce variations in piezoelectrically induced electric fields around these defects. The consequent spatial rearrangement of charges can be detected by electrostatic force microscopy and was found to be on the order of the characteristic Debye length for GaN at our dopant concentration. The electric force microscope signal was also found to be a linear function of the contact potential between the metal coating on the tip and GaN. Electrostatic analysis yielded a surface state density of 9.4 ± 0.5 × 10^10 cm – 2 at an energy of 30 mV above the valence band indicating that the GaN surface is unpinned in this case

Wave packet transmission of Bloch electron manipulated by magnetic field

We study the phenomenon of wave packet revivals of Bloch electrons and explore how to control them by a magnetic field for quantum information transfer. It is showed that the single electron system can be modulated into a linear dispersion regime by the "quantized" flux and then an electronic wave packet with the components localized in this regime can be transferred without spreading. This feature can be utilized to perform the high-fidelity transfer of quantum information encoded in the polarization of the spin. Beyond the linear approximation, the re-localization and self-interference occur as the novel phenomena of quantum coherence.Comment: 6 pages, 5 figures, new content adde

Electron diffusion length and lifetime in p-type GaN

We report on electron beam induced current and current–voltage (I–V) measurements on Schottky diodes on p-type doped GaN layers grown by metal organic chemical vapor deposition. A Schottky barrier height of 0.9 eV was measured for the Ti/Au Schottky contact from the I–V data. A minority carrier diffusion length for electrons of (0.2 ± 0.05) µm was measured for the first time in GaN. This diffusion length corresponds to an electron lifetime of approximately 0.1 ns. We attempted to correlate the measured electron diffusion length and lifetime with several possible recombination mechanisms in GaN and establish connection with electronic and structural properties of GaN

Electric force microscopy of induced charges and surface potentials in GaN modified by light and strain

We have studied molecular beam epitaxy grown GaN films using electric force microscopy to detect sub-1 µm regions of electric field gradient and surface potential variations associated with GaN extended defects. The large piezoelectric coefficients of GaN together with strain introduced by crystalline imperfections produce variation in piezoelectrically induced electric fields around these defects. The consequent spatial rearrangement of charges can be detected by electrostatic force microscopy, and can be additionally modified by externally applied strain and illumination. The electron force microscopy signal was found to be a function of the applied tip bias, showed reversal under externally applied strain, and was sensitive to above band gap illumination