Quantization of the Inhomogeneous Bianchi I model:quasi-Heisenberg picture

The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so called quasi-Heisenberg) equations describing explicit evolution of a system. Some particular gauge suitable for quantization is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero scale factor and it is used to construct a space where the quasi-Heisenberg operators act. Spatial discretization as a UV regularization procedure is suggested for the equations of motion.

Low bit-rate speech encoding for digital mobile radio

The need for low bit-rate speech coding is the result of growing demand on the available radio bandwidth for mobile communications both for military purposes and for the public sector. To meet this growing demand it is required that the available bandwidth be utilized in the most economic way to accommodate more services. Two low bit-rate speech coders have been built and tested in this project. The two coders combine predictive coding with delta modulation, a property which enables them to achieve simultaneously the low bit-rate and good speech quality requirements. To enhance their efficiency, the predictor coefficients and the quantizer step size are updated periodically in each coder. This enables the coders to keep up with changes in the characteristics of the speech signal with time and with changes in the dynamic range of the speech waveform. However, the two coders differ in the method of updating their predictor coefficients. One updates the coefficients once every one hundred sampling periods and extracts the coefficients from input speech samples. This is known in this project as the Forward Adaptive Coder. Since the coefficients are extracted from input speech samples, these must be transmitted to the receiver to reconstruct the transmitted speech sample, thus adding to the transmission bit rate. The other updates its coefficients every sampling period, based on information of output data. This coder is known as the Backward Adaptive Coder. Results of subjective tests showed both coders to be reasonably robust to quantization noise. Both were graded quite good, with the Forward Adaptive performing slightly better, but with a slightly higher transmission bit rate for the same speech quality, than its Backward counterpart. The coders yielded acceptable speech quality of 9.6kbps for the Forward Adaptive and 8kbps for the Backward Adaptive.

Neural population coding is optimized by discrete tuning curves

The sigmoidal tuning curve that maximizes the mutual information for a Poisson neuron, or population of Poisson neurons, is obtained. The optimal tuning curve is found to have a discrete structure that results in a quantization of the input signal. The number of quantization levels undergoes a hierarchy of phase transitions as the length of the coding window is varied. We postulate, using the mammalian auditory system as an example, that the presence of a subpopulation structure within a neural population is consistent with an optimal neural code.

Self-similar parabolic optical solitary waves

We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

Self-similar parabolic optical solitary waves

We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

A hierarchy of phase transitions in optimal neuronal coding:from binary to M-ary discrete optimal codes

We have investigated how optimal coding for neural systems changes with the time available for decoding. Optimization was in terms of maximizing information transmission. We have estimated the parameters for Poisson neurons that optimize Shannon transinformation with the assumption of rate coding. We observed a hierarchy of phase transitions from binary coding, for small decoding times, toward discrete (M-ary) coding with two, three and more quantization levels for larger decoding times. We postulate that the presence of subpopulations with specific neural characteristics could be a signiture of an optimal population coding scheme and we use the mammalian auditory system as an example.

Bound dissipative-pulse evolution in the all-normal dispersion fiber laser using a 45° tilted fiber grating

The formation and evolution of bound dissipative pulses in the all-normal dispersion Yb-fiber laser based on a novel 45° tilted fiber grating (TFG) are first investigated both numerically and experimentally. Based on the nonlinear polarization rotation technique, the TFG and two polarization controllers (PCs) are exploited for stable self-started passive mode locking. Numerical results show that the formation of bound-state pulses in the all-normal dispersion region is the progress of soliton shaping through the dispersive waves and follows the soliton energy quantization effect. Theoretical and experimental results demonstrate that the formation mechanism of bound-state pulses can be attributed to the high pump strength and effective filter bandwidth. The obtained bound-state dissipative pulses with quasi-rectangular spectral profile have fixed pulse separation as a function of pump power. © 2013 Astro Ltd.