Bounds on the sum-rate capacity of the Gaussian MIMO X channel

We consider the MIMO X channel (XC), a system consisting of two transmit-receive pairs, where each transmitter communicates with both the receivers. Both the transmitters and receivers are equipped with multiple antennas. First, we derive an upper bound on the sum-rate capacity of the MIMO XC under individual power constraint at each transmitter. The sum-rate capacity of the two-user multiple access channel (MAC) that results when receiver cooperation is assumed forms an upper bound on the sum-rate capacity of the MIMO XC. We tighten this bound by considering noise correlation between the receivers and deriving the worst noise covariance matrix. It is shown that the worst noise covariance matrix is a saddle-point of a zero-sum, two-player convex-concave game, which is solved through a primal-dual interior point method that solves the maximization and the minimization parts of the problem simultaneously. Next, we propose an achievable scheme which employs dirty paper coding at the transmitters and successive decoding at the receivers. We show that the derived upper bound is close to the achievable region of the proposed scheme at low to medium SNRs.

Eigen-profiles of spatio-temporal fragments for adaptive region-based tracking

We propose a novel space-time descriptor for region-based tracking which is very concise and efficient. The regions represented by covariance matrices within a temporal fragment, are used to estimate this space-time descriptor which we call the Eigenprofiles(EP). EP so obtained is used in estimating the Covariance Matrix of features over spatio-temporal fragments. The Second Order Statistics of spatio-temporal fragments form our target model which can be adapted for variations across the video. The model being concise also allows the use of multiple spatially overlapping fragments to represent the target. We demonstrate good tracking results on very challenging datasets, shot under insufficient illumination conditions.

Channel estimation at the transmitter in a reciprocal MIMO spatial multiplexing system

This paper considers the problem of channel estimation at the transmitter in a spatial multiplexing-based Time Division Duplex (TDD) Multiple Input Multiple Output (MIMO) system with perfect CSIR. A novel channel-dependent Reverse Channel Training (RCT) sequence is proposed, using which the transmitter estimates the beamforming vectors for forward link data transmission. This training sequence is designed based on the following two metrics: (i) a capacity lower bound, and (ii) the mean square error in the estimate. The performance of the proposed training scheme is analyzed and is shown to significantly outperform the conventional orthogonal RCT sequence. Also, in the case where the transmitter uses water-filling power allocation for data transmission, a novel RCT sequence is proposed and optimized with respect to the MSE in estimating the transmit covariance matrix.

3D flat holography: entropy and logarithmic corrections

We compute the leading corrections to the Bekenstein-Hawking entropy of the Flat Space Cosmological (FSC) solutions in 3D flat spacetimes, which are the flat analogues of the BTZ black holes in AdS(3). The analysis is done by a computation of density of states in the dual 2D Galilean Conformal Field Theory and the answer obtained by this matches with the limiting value of the expected result for the BTZ inner horizon entropy as well as what is expected for a generic thermodynamic system. Along the way, we also develop other aspects of holography of 3D flat spacetimes.

A fast NMR method for resonance assignments: application to metabolomics

We present a new method for rapid NMR data acquisition and assignments applicable to unlabeled (C-12) or C-13-labeled biomolecules/organic molecules in general and metabolomics in particular. The method involves the acquisition of three two dimensional (2D) NMR spectra simultaneously using a dual receiver system. The three spectra, namely: (1) G-matrix Fourier transform (GFT) (3,2)D C-13, H-1] HSQC-TOCSY, (2) 2D H-1-H-1 TOCSY and (3) 2D C-13-H-1 HETCOR are acquired in a single experiment and provide mutually complementary information to completely assign individual metabolites in a mixture. The GFT (3,2)D C-13, H-1] HSQC-TOCSY provides 3D correlations in a reduced dimensionality manner facilitating high resolution and unambiguous assignments. The experiments were applied for complete H-1 and C-13 assignments of a mixture of 21 unlabeled metabolites corresponding to a medium used in assisted reproductive technology. Taken together, the experiments provide time gain of order of magnitudes compared to the conventional data acquisition methods and can be combined with other fast NMR techniques such as non-uniform sampling and covariance spectroscopy. This provides new avenues for using multiple receivers and projection NMR techniques for high-throughput approaches in metabolomics.

Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition

A new representation of spatio-temporal random processes is proposed in this work. In practical applications, such processes are used to model velocity fields, temperature distributions, response of vibrating systems, to name a few. Finding an efficient representation for any random process leads to encapsulation of information which makes it more convenient for a practical implementations, for instance, in a computational mechanics problem. For a single-parameter process such as spatial or temporal process, the eigenvalue decomposition of the covariance matrix leads to the well-known Karhunen-Loeve (KL) decomposition. However, for multiparameter processes such as a spatio-temporal process, the covariance function itself can be defined in multiple ways. Here the process is assumed to be measured at a finite set of spatial locations and a finite number of time instants. Then the spatial covariance matrix at different time instants are considered to define the covariance of the process. This set of square, symmetric, positive semi-definite matrices is then represented as a third-order tensor. A suitable decomposition of this tensor can identify the dominant components of the process, and these components are then used to define a closed-form representation of the process. The procedure is analogous to the KL decomposition for a single-parameter process, however, the decompositions and interpretations vary significantly. The tensor decompositions are successfully applied on (i) a heat conduction problem, (ii) a vibration problem, and (iii) a covariance function taken from the literature that was fitted to model a measured wind velocity data. It is observed that the proposed representation provides an efficient approximation to some processes. Furthermore, a comparison with KL decomposition showed that the proposed method is computationally cheaper than the KL, both in terms of computer memory and execution time.

Faster computation of the Karhunen-Loeve expansion using its domain independence property

The goal of this work is to reduce the cost of computing the coefficients in the Karhunen-Loeve (KL) expansion. The KL expansion serves as a useful and efficient tool for discretizing second-order stochastic processes with known covariance function. Its applications in engineering mechanics include discretizing random field models for elastic moduli, fluid properties, and structural response. The main computational cost of finding the coefficients of this expansion arises from numerically solving an integral eigenvalue problem with the covariance function as the integration kernel. Mathematically this is a homogeneous Fredholm equation of second type. One widely used method for solving this integral eigenvalue problem is to use finite element (FE) bases for discretizing the eigenfunctions, followed by a Galerkin projection. This method is computationally expensive. In the current work it is first shown that the shape of the physical domain in a random field does not affect the realizations of the field estimated using KL expansion, although the individual KL terms are affected. Based on this domain independence property, a numerical integration based scheme accompanied by a modification of the domain, is proposed. In addition to presenting mathematical arguments to establish the domain independence, numerical studies are also conducted to demonstrate and test the proposed method. Numerically it is demonstrated that compared to the Galerkin method the computational speed gain in the proposed method is of three to four orders of magnitude for a two dimensional example, and of one to two orders of magnitude for a three dimensional example, while retaining the same level of accuracy. It is also shown that for separable covariance kernels a further cost reduction of three to four orders of magnitude can be achieved. Both normal and lognormal fields are considered in the numerical studies. (c) 2014 Elsevier B.V. All rights reserved.

MIMO Decode-and-Forward Relay Beamforming for Secrecy with Cooperative Jamming

In this paper, we consider decode-and-forward (DF) relay beamforming for secrecy with cooperative jamming (CJ) in the presence of multiple eavesdroppers. The communication between a source-destination pair is aided by a multiple-input multiple-output (MIMO) relay. The source has one transmit antenna and the destination and eavesdroppers have one receive antenna each. The source and the MIMO relay are constrained with powers P-S and P-R, respectively. We relax the rank-1 constraint on the signal beamforming matrix and transform the secrecy rate max-min optimization problem to a single maximization problem, which is solved by semidefinite programming techniques. We obtain the optimum source power, signal relay weights, and jamming covariance matrix. We show that the solution of the rank-relaxed optimization problem has rank-1. Numerical results show that CJ can improve the secrecy rate.

MIMO Decode-and-Forward Relay Beamforming for Secrecy with Cooperative Jamming

In this paper, we consider decode-and-forward (DF) relay beamforming for secrecy with cooperative jamming (CJ) in the presence of multiple eavesdroppers. The communication between a source-destination pair is aided by a multiple-input multiple-output (MIMO) relay. The source has one transmit antenna and the destination and eavesdroppers have one receive antenna each. The source and the MIMO relay are constrained with powers P-S and P-R, respectively. We relax the rank-1 constraint on the signal beamforming matrix and transform the secrecy rate max-min optimization problem to a single maximization problem, which is solved by semidefinite programming techniques. We obtain the optimum source power, signal relay weights, and jamming covariance matrix. We show that the solution of the rank-relaxed optimization problem has rank-1. Numerical results show that CJ can improve the secrecy rate.

Lateralisation abnormalities in obsessive-compulsive disorder: a line bisection study

Objective Asymmetry in brain structure and function is implicated in the pathogenesis of psychiatric disorders. Although right hemisphere abnormality has been documented in obsessive-compulsive disorder (OCD), cerebral asymmetry is rarely examined. Therefore, in this study, we examined anomalous cerebral asymmetry in OCD patients using the line bisection task. Methods A total of 30 patients with OCD and 30 matched healthy controls were examined using a reliable and valid two-hand line bisection (LBS) task. The comparative profiles of LBS scores were analysed using analysis of covariance. Results Patients with OCD bisected significantly less number of lines to the left and had significant rightward deviation than controls, indicating right hemisphere dysfunction. The correlations observed in this study suggest that those with impaired laterality had more severe illness at baseline. Conclusions The findings of this study indicate abnormal cerebral lateralisation and right hemisphere dysfunction in OCD patients.

Power Allocation in MIMO Wiretap Channel with Statistical CSI and Finite-Alphabet Input

In this paper, we consider the problem of power allocation in MIMO wiretap channel for secrecy in the presence of multiple eavesdroppers. Perfect knowledge of the destination channel state information (CSI) and only the statistical knowledge of the eavesdroppers CSI are assumed. We first consider the MIMO wiretap channel with Gaussian input. Using Jensen's inequality, we transform the secrecy rate max-min optimization problem to a single maximization problem. We use generalized singular value decomposition and transform the problem to a concave maximization problem which maximizes the sum secrecy rate of scalar wiretap channels subject to linear constraints on the transmit covariance matrix. We then consider the MIMO wiretap channel with finite-alphabet input. We show that the transmit covariance matrix obtained for the case of Gaussian input, when used in the MIMO wiretap channel with finite-alphabet input, can lead to zero secrecy rate at high transmit powers. We then propose a power allocation scheme with an additional power constraint which alleviates this secrecy rate loss problem, and gives non-zero secrecy rates at high transmit powers.

ON THE UTILITY OF CANONICAL CORRELATION ANALYSIS FOR DOMAIN ADAPTATION IN MULTI-VIEW HEADPOSE ESTIMATION

The utility of canonical correlation analysis (CCA) for domain adaptation (DA) in the context of multi-view head pose estimation is examined in this work. We consider the three problems studied in 1], where different DA approaches are explored to transfer head pose-related knowledge from an extensively labeled source dataset to a sparsely labeled target set, whose attributes are vastly different from the source. CCA is found to benefit DA for all the three problems, and the use of a covariance profile-based diagonality score (DS) also improves classification performance with respect to a nearest neighbor (NN) classifier.