BRST invariant theory of a generalized 1+1 Dimensional nonlinear sigma model with topological term

We give a generalized Lagrangian density of 1 + 1 Dimensional O( 3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint. N = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter beta originating from the freedom degree of BRST transformation in a general O( 3) nonlinear sigma model, and we gain the general commutation relations of ghost field.

Comparative Performance Measures of Fuzzy ARTMAP, Learned Vector Quantization, and Back Propagation for Handwritten Character Recognition

This article compares the performance of Fuzzy ARTMAP with that of Learned Vector Quantization and Back Propagation on a handwritten character recognition task. Training with Fuzzy ARTMAP to a fixed criterion used many fewer epochs. Voting with Fuzzy ARTMAP yielded the highest recognition rates.

Interaction of additive and quantization noises in digital PLLs

Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions.

Lovelock terms and BRST cohomology

Lovelock terms are polynomial scalar densities in the Riemann curvature tensor that have the remarkable property that their Euler-Lagrange derivatives contain derivatives of the metric of an order not higher than 2 (while generic polynomial scalar densities lead to Euler-Lagrange derivatives with derivatives of the metric of order 4). A characteristic feature of Lovelock terms is that their first nonvanishing term in the expansion g λμ = η λμ + h λμ of the metric around flat space is a total derivative. In this paper, we investigate generalized Lovelock terms defined as polynomial scalar densities in the Riemann curvature tensor and its covariant derivatives (of arbitrarily high but finite order) such that their first nonvanishing term in the expansion of the metric around flat space is a total derivative. This is done by reformulating the problem as a BRST cohomological one and by using cohomological tools. We determine all the generalized Lovelock terms. We find, in fact, that the class of nontrivial generalized Lovelock terms contains only the usual ones. Allowing covariant derivatives of the Riemann tensor does not lead to a new structure. Our work provides a novel algebraic understanding of the Lovelock terms in the context of BRST cohomology. © 2005 IOP Publishing Ltd.

Role of Landau quantization on the neutron-drip transition in magnetar crusts

The role of a strong magnetic field on the neutron-drip transition in the crust of a magnetar is studied. The composition of the crust and the neutron-drip threshold are determined numerically for different magnetic field strengths using the experimental atomic mass measurements from the 2012 Atomic Mass Evaluation complemented with theoretical masses calculated from the Brussels-Montreal Hartree-Fock-Bogoliubov nuclear mass model HFB-24. The equilibrium nucleus at the neutron-drip point is found to be independent of the magnetic field strength. As demonstrated analytically, the neutron-drip density and pressure increase almost linearly with the magnetic field strength in the strongly quantizing regime for which electrons lie in the lowest Landau level. For weaker magnetic fields, the neutron-drip density exhibits typical quantum oscillations. In this case, the neutron-drip density can be either increased by about 14% or decreased by 25% depending on the magnetic field strength. These variations are shown to be almost universal, independently of the nuclear mass model employed. These results may have important implications for the physical interpretation of timing irregularities and quasiperiodic oscillations detected in soft gamma-ray repeaters and anomalous x-ray pulsars, as well as for the cooling of strongly magnetized neutron stars.

Effect of quantization of vibrations on the structural properties of crystals

We study the structural effects produced by the quantization of vibrational degrees of freedom in periodic crystals at zero temperature. To this end we introduce a methodology based on mapping a suitable subspace of the vibrational manifold and solving the Schrödinger equation in it. A number of increasingly accurate approximations ranging from the quasiharmonic approximation (QHA) to the vibrational self-consistent field (VSCF) method and the exact solution are described. A thorough analysis of the approximations is presented for model monatomic and hydrogen-bonded chains, and results are presented for a linear H-F chain where the potential-energy surface is obtained via first-principles electronic structure calculations. We focus on quantum nuclear effects on the lattice constant and show that the VSCF is an excellent approximation, meaning that correlation between modes is not extremely important. The QHA is excellent for covalently bonded mildly anharmonic systems, but it fails for hydrogen-bonded ones. In the latter, the zero-point energy exhibits a nonanalytic behavior at the lattice constant where the H atoms center, which leads to a spurious secondary minimum in the quantum-corrected energy curve. An inexpensive anharmonic approximation of noninteracting modes appears to produce rather good results for hydrogen-bonded chains for small system sizes. However, it converges to the incorrect QHA results for increasing size. Isotope effects are studied for the first-principles H-F chain. We show how the lattice constant and the H-F distance increase with decreasing mass and how the QHA proves to be insufficient to reproduce this behavior.

Systolic array system for vector quantization using transformed sub-band coding.

The use of bit-level systolic arrays in the design of a vector quantized transformed subband coding system for speech signals is described. It is shown how the major components of this system can be decomposed into a small number of highly regular building blocks that interface directly to one another. These include circuits for the computation of the discrete cosine transform, the inverse discrete cosine transform, and vector quantization codebook search.

VLSI architectures for vector quantization

The real time implementation of an efficient signal compression technique, Vector Quantization (VQ), is of great importance to many digital signal coding applications. In this paper, we describe a new family of bit level systolic VLSI architectures which offer an attractive solution to this problem. These architectures are based on a bit serial, word parallel approach and high performance and efficiency can be achieved for VQ applications of a wide range of bandwidths. Compared with their bit parallel counterparts, these bit serial circuits provide better alternatives for VQ implementations in terms of performance and cost. © 1995 Kluwer Academic Publishers.