Surfaces of Bounded Mean Curvature In Riemannian Manifolds

Consider a sequence of closed, orientable surfaces of fixed genus g in a Riemannian manifold M with uniform upper bounds on the norm of mean curvature and area. We show that on passing to a subsequence, we can choose parametrisations of the surfaces by inclusion maps from a fixed surface of the same genus so that the distance functions corresponding to the pullback metrics converge to a pseudo-metric and the inclusion maps converge to a Lipschitz map. We show further that the limiting pseudo-metric has fractal dimension two. As a corollary, we obtain a purely geometric result. Namely, we show that bounds on the mean curvature, area and genus of a surface F subset of M, together with bounds on the geometry of M, give an upper bound on the diameter of F. Our proof is modelled on Gromov's compactness theorem for J-holomorphic curves.

Effect of longitudinal surface curvature on boundary layers

We consider here the higher order effect of moderate longitudinal surface curvature on steady, two-dimensional, incompressible laminar boundary layers. The basic partial differential equations for the problem, derived by the method of matched asymptotic expansions, are found to possess similarity solutions for a family of surface curvatures and pressure gradients. The similarity equations obtained by this anaylsis have been solved numerically on a computer, and show a definite decrease in skin friction when the surface has convex curvature in all cases including zero pressure gradient. Typical velocity profiles and some relevant boundary-layer characteristics are tabulated, and a critical comparison with previous work is given.

Subspace Based Speech Enhancement Using Gaussian Mixture Model

Traditional subspace based speech enhancement (SSE)methods use linear minimum mean square error (LMMSE) estimation that is optimal if the Karhunen Loeve transform (KLT) coefficients of speech and noise are Gaussian distributed. In this paper, we investigate the use of Gaussian mixture (GM) density for modeling the non-Gaussian statistics of the clean speech KLT coefficients. Using Gaussian mixture model (GMM), the optimum minimum mean square error (MMSE) estimator is found to be nonlinear and the traditional LMMSE estimator is shown to be a special case. Experimental results show that the proposed method provides better enhancement performance than the traditional subspace based methods.Index Terms: Subspace based speech enhancement, Gaussian mixture density, MMSE estimation.

Low Complexity Wideband LSFQuantization Using GMM of Uncorrelated Gaussian Mixtures

We develop a Gaussian mixture model (GMM) based vector quantization (VQ) method for coding wideband speech line spectrum frequency (LSF) parameters at low complexity. The PDF of LSF source vector is modeled using the Gaussian mixture (GM) density with higher number of uncorrelated Gaussian mixtures and an optimum scalar quantizer (SQ) is designed for each Gaussian mixture. The reduction of quantization complexity is achieved using the relevant subset of available optimum SQs. For an input vector, the subset of quantizers is chosen using nearest neighbor criteria. The developed method is compared with the recent VQ methods and shown to provide high quality rate-distortion (R/D) performance at lower complexity. In addition, the developed method also provides the advantages of bitrate scalability and rate-independent complexity.

Finite Signal-set Capacity of Two-user Gaussian Multiple Access Channel

The capacity region of a two-user Gaussian Multiple Access Channel (GMAC) with complex finite input alphabets and continuous output alphabet is studied. When both the users are equipped with the same code alphabet, it is shown that, rotation of one of the user’s alphabets by an appropriate angle can make the new pair of alphabets not only uniquely decodable, but will result in enlargement of the capacity region. For this set-up, we identify the primary problem to be finding appropriate angle(s) of rotation between the alphabets such that the capacity region is maximally enlarged. It is shown that the angle of rotation which provides maximum enlargement of the capacity region also minimizes the union bound on the probability of error of the sumalphabet and vice-verse. The optimum angle(s) of rotation varies with the SNR. Through simulations, optimal angle(s) of rotation that gives maximum enlargement of the capacity region of GMAC with some well known alphabets such as M-QAM and M-PSK for some M are presented for several values of SNR. It is shown that for large number of points in the alphabets, capacity gains due to rotations progressively reduce. As the number of points N tends to infinity, our results match the results in the literature wherein the capacity region of the Gaussian code alphabet doesn’t change with rotation for any SNR.

Source-channel coding for Gaussian sources over a Gaussian multiple access channel

We consider the problem of distributed joint source-channel coding of correlated Gaussian sources over a Gaussian Multiple Access Channel (MAC). There may be side information at the encoders and/or at the decoder. First we specialize a general result in [16] to obtain sufficient conditions for reliable transmission over a Gaussian MAC. This system does not satisfy the source channel separation. Thus, next we study and compare three joint source channel coding schemes available in literature.

Cramer-Rao bounds for source localization in shallow ocean with generalized Gaussian noise

Localization of underwater acoustic sources is a problem of great interest in the area of ocean acoustics. There exist several algorithms for source localization based on array signal processing.It is of interest to know the theoretical performance limits of these estimators. In this paper we develop expressions for the Cramer-Rao-Bound (CRB) on the variance of direction-of-arrival(DOA) and range-depth estimators of underwater acoustic sources in a shallow range-independent ocean for the case of generalized Gaussian noise. We then study the performance of some of the popular source localization techniques,through simulations, for DOA/range-depth estimation of underwater acoustic sources in shallow ocean by comparing the variance of the estimators with the corresponding CRBs.

Two-User Gaussian Interference Channel with Finite Constellation Input and FDMA

In the two-user Gaussian Strong Interference Channel (GSIC) with finite constellation inputs, it is known that relative rotation between the constellations of the two users enlarges the Constellation Constrained (CC) capacity region. In this paper, a metric for finding the approximate angle of rotation to maximally enlarge the CC capacity is presented. It is shown that for some portion of the Strong Interference (SI) regime, with Gaussian input alphabets, the FDMA rate curve touches the capacity curve of the GSIC. Even as the Gaussian alphabet FDMA rate curve touches the capacity curve of the GSIC, at high powers, with both the users using the same finite constellation, we show that the CC FDMA rate curve lies strictly inside the CC capacity curve for the constellations BPSK, QPSK, 8-PSK, 16-QAM and 64-QAM. It is known that, with Gaussian input alphabets, the FDMA inner-bound at the optimum sum-rate point is always better than the simultaneous-decoding inner-bound throughout the Weak Interference (WI) regime. For a portion of the WI regime, it is shown that, with identical finite constellation inputs for both the users, the simultaneous-decoding inner-bound enlarged by relative rotation between the constellations can be strictly better than the FDMA inner-bound.

Nonlinear dynamic state estimation in instrumented structures with conditionally linear Gaussian substructures

Many problems of state estimation in structural dynamics permit a partitioning of system states into nonlinear and conditionally linear substructures. This enables a part of the problem to be solved exactly, using the Kalman filter, and the remainder using Monte Carlo simulations. The present study develops an algorithm that combines sequential importance sampling based particle filtering with Kalman filtering to a fairly general form of process equations and demonstrates the application of a substructuring scheme to problems of hidden state estimation in structures with local nonlinearities, response sensitivity model updating in nonlinear systems, and characterization of residual displacements in instrumented inelastic structures. The paper also theoretically demonstrates that the sampling variance associated with the substructuring scheme used does not exceed the sampling variance corresponding to the Monte Carlo filtering without substructuring. (C) 2012 Elsevier Ltd. All rights reserved.

q-Gaussian based Smoothed Functional Algorithms for Stochastic Optimization

The q-Gaussian distribution results from maximizing certain generalizations of Shannon entropy under some constraints. The importance of q-Gaussian distributions stems from the fact that they exhibit power-law behavior, and also generalize Gaussian distributions. In this paper, we propose a Smoothed Functional (SF) scheme for gradient estimation using q-Gaussian distribution, and also propose an algorithm for optimization based on the above scheme. Convergence results of the algorithm are presented. Performance of the proposed algorithm is shown by simulation results on a queuing model.

Capacity of fading gaussian channel with an energy harvesting sensor node

Network life time maximization is becoming an important design goal in wireless sensor networks. Energy harvesting has recently become a preferred choice for achieving this goal as it provides near perpetual operation. We study such a sensor node with an energy harvesting source and compare various architectures by which the harvested energy is used. We find its Shannon capacity when it is transmitting its observations over a fading AWGN channel with perfect/no channel state information provided at the transmitter. We obtain an achievable rate when there are inefficiencies in energy storage and the capacity when energy is spent in activities other than transmission.

A constellation power allocation scheme for two-user Gaussian MAC

Constellation Constrained (CC) capacity regions of two-user Gaussian Multiple Access Channels (GMAC) have been recently reported, wherein introducing appropriate rotation between the constellations of the two users is shown to maximally enlarge the CC capacity region. Such a Non-Orthogonal Multiple Access (NO-MA) method of enlarging the CC capacity region is referred to as Constellation Rotation (CR) scheme. In this paper, we propose a novel NO-MA technique called Constellation Power Allocation (CPA) scheme to enlarge the CC capacity region of two-user GMAC. We show that the CPA scheme offers CC sum capacities equal (at low SNR values) or close (at high SNR values) to those offered by the CR scheme with reduced ML decoding complexity for some QAM constellations. For the CR scheme, code pairs approaching the CC sum capacity are known only for the class of PSK and PAM constellations but not for QAM constellations. In this paper, we design code pairs with the CPA scheme to approach the CC sum capacity for 16-QAM constellations. Further, the CPA scheme used for two-user GMAC with random phase offsets is shown to provide larger CC sum capacities at high SNR values compared to the CR scheme.

Speeded up Gaussian mixture model algorithm for background subtraction

Adaptive Gaussian Mixture Models (GMM) have been one of the most popular and successful approaches to perform foreground segmentation on multimodal background scenes. However, the good accuracy of the GMM algorithm comes at a high computational cost. An improved GMM technique was proposed by Zivkovic to reduce computational cost by minimizing the number of modes adaptively. In this paper, we propose a modification to his adaptive GMM algorithm that further reduces execution time by replacing expensive floating point computations with low cost integer operations. To maintain accuracy, we derive a heuristic that computes periodic floating point updates for the GMM weight parameter using the value of an integer counter. Experiments show speedups in the range of 1.33 - 1.44 on standard video datasets where a large fraction of pixels are multimodal.