Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem

We prove that the $q$-state Potts antiferromagnet on a lattice of maximum coordination number $r$ exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever $q > 2r$. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for $q \ge 7$), triangular lattice ($q \ge 11$), hexagonal lattice ($q \ge 4$), and Kagom\'e lattice ($q \ge 6$). The proofs are based on the Dobrushin uniqueness theorem.Comment: 32 pages including 3 figures. Self-unpacking file containing the tex file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and eqsection.sty) and the 3 ps file

Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions

The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had significant parameter correlation, but also contained multiple modes. We conclude that the mixture between two K distributions is the most applicable to this dataset.Comment: 15 pages, 7 figures, Accepted to the Journal of the Acoustical Society of Americ

Design of FIR paraunitary filter banks for subband coding using a polynomial eigenvalue decomposition

The problem of paraunitary filter bank design for subband coding has received considerable attention in recent years, not least because of the energy preserving property of this class of filter banks. In this paper, we consider the design of signal-adapted, finite impulse response (FIR), paraunitary filter banks using polynomial matrix EVD (PEVD) techniques. Modifications are proposed to an iterative, time-domain PEVD method, known as the sequential best rotation (SBR2) algorithm, which enables its effective application to the problem of FIR orthonormal filter bank design for efficient subband coding. By choosing an optimisation scheme that maximises the coding gain at each stage of the algorithm, it is shown that the resulting filter bank behaves more and more like the infiniteorder principle component filter bank (PCFB). The proposed method is compared to state-of-the-art techniques, namely the iterative greedy algorithm (IGA), the approximate EVD (AEVD), standard SBR2 and a fast algorithm for FIR compaction filter design, called the window method (WM). We demonstrate that for the calculation of the subband coder, the WM approach offers a low-cost alternative at lower coding gains, while at moderate to high complexity, the proposed approach outperforms the benchmarkers. In terms of run-time complexity, AEVD performs well at low orders, while the proposed algorithm offers a better coding gain than the benchmarkers at moderate to high filter order for a number of simulation scenarios

Efficient Multiband Algorithms for Blind Source Separation

The problem of blind separation refers to recovering original signals, called source signals, from the mixed signals, called observation signals, in a reverberant environment. The mixture is a function of a sequence of original speech signals mixed in a reverberant room. The objective is to separate mixed signals to obtain the original signals without degradation and without prior information of the features of the sources. The strategy used to achieve this objective is to use multiple bands that work at a lower rate, have less computational cost and a quicker convergence than the conventional scheme. Our motivation is the competitive results of unequal-passbands scheme applications, in terms of the convergence speed. The objective of this research is to improve unequal-passbands schemes by improving the speed of convergence and reducing the computational cost. The first proposed work is a novel maximally decimated unequal-passbands scheme.This scheme uses multiple bands that make it work at a reduced sampling rate, and low computational cost. An adaptation approach is derived with an adaptation step that improved the convergence speed. The performance of the proposed scheme was measured in different ways. First, the mean square errors of various bands are measured and the results are compared to a maximally decimated equal-passbands scheme, which is currently the best performing method. The results show that the proposed scheme has a faster convergence rate than the maximally decimated equal-passbands scheme. Second, when the scheme is tested for white and coloured inputs using a low number of bands, it does not yield good results; but when the number of bands is increased, the speed of convergence is enhanced. Third, the scheme is tested for quick changes. It is shown that the performance of the proposed scheme is similar to that of the equal-passbands scheme. Fourth, the scheme is also tested in a stationary state. The experimental results confirm the theoretical work. For more challenging scenarios, an unequal-passbands scheme with over-sampled decimation is proposed; the greater number of bands, the more efficient the separation. The results are compared to the currently best performing method. Second, an experimental comparison is made between the proposed multiband scheme and the conventional scheme. The results show that the convergence speed and the signal-to-interference ratio of the proposed scheme are higher than that of the conventional scheme, and the computation cost is lower than that of the conventional scheme

Locally stationary long memory estimation

There exists a wide literature on modelling strongly dependent time series using a longmemory parameter d, including more recent work on semiparametric wavelet estimation. As a generalization of these latter approaches, in this work we allow the long-memory parameter d to be varying over time. We embed our approach into the framework of locally stationary processes. We show weak consistency and a central limit theorem for our log-regression wavelet estimator of the time-dependent d in a Gaussian context. Both simulations and a real data example complete our work on providing a fairly general approach