An essential quantity required to understand the physics of the early Universe is the primordial scalar potential and its statistics. We present an inexpensive all-sky reconstruction of the potential from CMB temperature data as well as an extension including polarization data. Once explicitly having the potential, its statistics and underlying physics can be directly obtained avoiding expensive CMB analyses.

Recent studies have shown that when graphene is placed on a thin hexagonal boron nitride (h-BN) substrate, unlike when it is placed on a typical SiO2 surface, it can closely approach the ideal carrier mobility observed in suspended graphene samples. This study further examines the epitaxial relationship between graphene and h-BN substrate with high-resolution transmission electron microscopy simulation. Virtual monolayer and multilayer stacks of h-BN were produced with a monolayer of graphene on top, on bottom, and in between h-BN layers, in order to study this interface. Once the simulations were performed, the phase contrast image and Moiré pattern created by this heterostack were analyzed for local and global intensity minima and maxima. In addition, h-BN substrate thickness and rotations between h-BN and graphene were probed and analyzed. The simulated images produced in this work will be used to help understand subsequent transmission electron microscopy images and electron energy-loss studies.

Contrast sensitivity is a measure of the ability of an observer to detect contrast signals of particular spatial and temporal frequencies. A formal definition of contrast sensitivity that can be applied to individual linear visual neurons is derived. A neuron is modeled by a contrast transfer function and its modulus, contrast gain, and by a noise power spectrum. The distributions of neural responses to signal and blank presentations are derived, and from these, a definition of contrast sensitivity is obtained. This formal definition may be used to relate the sensitivities of various populations of neurons, and to relate the sensitivities of neurons to that of the behaving animal.

The discharges of ON- and OFF-center X and Y retinal ganglion cells in the presence of stationary patterns or of a uniform field of photopic luminance were recorded from urethane-anesthetized adult cats. The interval statistics and power spectra of these discharges were determined from these discharge records. The patterned stimuli were selected and positioned with respect to a cell's receptive field so as to generate steady discharges that were different in mean discharge rate from that cell's discharge for the diffuse field. The interval statistics of discharges recorded for diffuse or patterned illumination for all cell types can be modeled, approximately, as coming from renewal processes with gamma-distributed intervals. The gamma order of the interval distributions was found to be nearly proportional to the mean discharge rate for X cells, but not for Y cells. Typical values for the gamma orders and their dependence on mean rate for different cell types are given. The same model of a renewal process with gamma-distributed intervals is used to model the measured power spectra and performs well. When the gamma order is proportional to mean rate, the power spectral density at low temporal frequencies is independent of discharge rate. Gamma order was proportional to mean rate for X cells but not for Y cells. Nonetheless, the power spectral densities of both cell types at low frequencies were approximately independent of discharge rate. Hence, noise in this band of frequencies can be considered additive. The consequences of departures from the renewal process and of the gamma order not being proportional to mean rate are considered. The significance of different rates of discharge for signaling is discussed.

Steady discharges were collected from ganglion cells of the magnocellular (MC) and parvocellular (PC) pathways of the macaque while their receptive fields were uniformly illuminated with a 4.7-deg steady yellow light of photopic illuminance. The mean rates, coefficients of variation, interval distributions, serial correlation coefficients, and power spectra of these discharges were determined. The results presented permit one to estimate the noise power in the discharges of macaque ganglion cells and hence determine how visual signals of different amplitudes will be affected by the noise resident in their discharges.

Although there was some small serial correlation in the discharges of both MC- and PC-pathway cells, their discharges can be considered to result from renewal processes with reasonable accuracy. As with the discharges of cat ganglion cells, macaque ganglion cell discharges can be considered to have approximately gamma-distributed intervals. Steady discharges of MC- and PC-pathway cells show considerable overlap in their statistics, although small but significant differences are present.

A spectral theory for stationary random closed sets is developed and provided with a sound mathematical basis. The definition and a proof of the existence of the Bartlett spectrum of a stationary random closed set as well as the proof of a Wiener-Khinchin theorem for the power spectrum are used to two ends. First, well-known second-order characteristics like the covariance can be estimated faster than usual via frequency space. Second, the Bartlett spectrum and the power spectrum can be used as second-order characteristics in frequency space. Examples show that in some cases information about the random closed set is easier to obtain from these characteristics in frequency space than from their real-world counterparts.

The G/G/1 queueing system is studied by means of the regeneration point method, exploiting the concept of busy cycles. Recurrence relations are set-up for the distribution of the queue length at the arrival epochs. The same method is used to obtain the correlation structure of arrivals and departures for the G/M/1 queue.