Phase synchronization in brain networks derived from correlation between probabilities of recurrences in functional MRI data

It is increasingly being recognized that resting state brain connectivity derived from functional magnetic resonance imaging (fMRI) data is an important marker of brain function both in healthy and clinical populations. Though linear correlation has been extensively used to characterize brain connectivity, it is limited to detecting first order dependencies. In this study, we propose a framework where in phase synchronization (PS) between brain regions is characterized using a new metric ``correlation between probabilities of recurrence'' (CPR) and subsequent graph-theoretic analysis of the ensuing networks. We applied this method to resting state fMRI data obtained from human subjects with and without administration of propofol anesthetic. Our results showed decreased PS during anesthesia and a biologically more plausible community structure using CPR rather than linear correlation. We conclude that CPR provides an attractive nonparametric method for modeling interactions in brain networks as compared to standard correlation for obtaining physiologically meaningful insights about brain function.

Comprehensive investigations on DNa center dot center dot center dot A (D = H/F) complexes show why `sodium bonding' is not commonly observed

A comprehensive study of D-Na center dot center dot center dot A (D = H/F) complexes has been done using advanced ab initio and atoms in molecule (AIM) theoretical analyses. The correlation between electron density at bond critical point and binding energy gives a distinguishing feature for hydrogen bonding, different from the `electrostatic complexes' formed by LiD and NaD. Moreover, the LiD/NaD dimers have both linear and anti-parallel minima, as expected for electrostatic dipole-dipole interactions. The HF dimer has a quasi-linear minimum and the anti-parallel structure is a saddle point. Clearly, characterizing hydrogen bonding as `nothing but electrostatic interaction between two dipoles' is grossly in error.

Generalized eigenvalue decomposition of the field autocorrelation in correlation diffusion of photons in turbid media

We propose a novel numerical method based on a generalized eigenvalue decomposition for solving the diffusion equation governing the correlation diffusion of photons in turbid media. Medical imaging modalities such as diffuse correlation tomography and ultrasound-modulated optical tomography have the (elliptic) diffusion equation parameterized by a time variable as the forward model. Hitherto, for the computation of the correlation function, the diffusion equation is solved repeatedly over the time parameter. We show that the use of a certain time-independent generalized eigenfunction basis results in the decoupling of the spatial and time dependence of the correlation function, thus allowing greater computational efficiency in arriving at the forward solution. Besides presenting the mathematical analysis of the generalized eigenvalue problem on the basis of spectral theory, we put forth the numerical results that compare the proposed numerical method with the standard technique for solving the diffusion equation.

Nonquadratic penalization improves near-infrared diffuse optical tomography

A new approach that can easily incorporate any generic penalty function into the diffuse optical tomographic image reconstruction is introduced to show the utility of nonquadratic penalty functions. The penalty functions that were used include quadratic (l(2)), absolute (l(1)), Cauchy, and Geman-McClure. The regularization parameter in each of these cases was obtained automatically by using the generalized cross-validation method. The reconstruction results were systematically compared with each other via utilization of quantitative metrics, such as relative error and Pearson correlation. The reconstruction results indicate that, while the quadratic penalty may be able to provide better separation between two closely spaced targets, its contrast recovery capability is limited, and the sparseness promoting penalties, such as l(1), Cauchy, and Geman-McClure have better utility in reconstructing high-contrast and complex-shaped targets, with the Geman-McClure penalty being the most optimal one. (C) 2013 Optical Society of America

Structure-property correlation in BaO-TiO2-B2O3 glasses: glass stability, optical, hydrophobic, and dielectric properties

Glasses in the x(BaO-TiO2)-B2O3 (x = 0.25, 0.5, 0.75, and 1 mol.) system were fabricated via the conventional melt-quenching technique. Thermal stability and glass-forming ability as determined by differential thermal analysis (DTA) were found to increase with increasing BaO-TiO2 (BT) content. However, there was no noticeable change in the glass transition temperature (T-g). This was attributed to the active participation of TiO2 in the network formation especially at higher BT contents via the conversion of the TiO6 structural units into TiO4 units, which increased the connectivity and resulted in an increase in crystallization temperature. Dielectric and optical properties at room temperature were studied for all the glasses under investigation. Interestingly, these glasses were found to be hydrophobic. The results obtained were correlated with different structural units and their connectivity in the glasses.

A Markov Decision Theoretic Approach to Pilot Allocation and Receive Antenna Selection

This paper considers antenna selection (AS) at a receiver equipped with multiple antenna elements but only a single radio frequency chain for packet reception. As information about the channel state is acquired using training symbols (pilots), the receiver makes its AS decisions based on noisy channel estimates. Additional information that can be exploited for AS includes the time-correlation of the wireless channel and the results of the link-layer error checks upon receiving the data packets. In this scenario, the task of the receiver is to sequentially select (a) the pilot symbol allocation, i.e., how to distribute the available pilot symbols among the antenna elements, for channel estimation on each of the receive antennas; and (b) the antenna to be used for data packet reception. The goal is to maximize the expected throughput, based on the past history of allocation and selection decisions, and the corresponding noisy channel estimates and error check results. Since the channel state is only partially observed through the noisy pilots and the error checks, the joint problem of pilot allocation and AS is modeled as a partially observed Markov decision process (POMDP). The solution to the POMDP yields the policy that maximizes the long-term expected throughput. Using the Finite State Markov Chain (FSMC) model for the wireless channel, the performance of the POMDP solution is compared with that of other existing schemes, and it is illustrated through numerical evaluation that the POMDP solution significantly outperforms them.

Narrowband signal detection techniques in shallow ocean by acoustic vector sensor array

This paper presents the formulation and performance analysis of four techniques for detection of a narrowband acoustic source in a shallow range-independent ocean using an acoustic vector sensor (AVS) array. The array signal vector is not known due to the unknown location of the source. Hence all detectors are based on a generalized likelihood ratio test (GLRT) which involves estimation of the array signal vector. One non-parametric and three parametric (model-based) signal estimators are presented. It is shown that there is a strong correlation between the detector performance and the mean-square signal estimation error. Theoretical expressions for probability of false alarm and probability of detection are derived for all the detectors, and the theoretical predictions are compared with simulation results. It is shown that the detection performance of an AVS array with a certain number of sensors is equal to or slightly better than that of a conventional acoustic pressure sensor array with thrice as many sensors.

Pattern-growth based frequent serial episode discovery

Frequent episode discovery is a popular framework for pattern discovery from sequential data. It has found many applications in domains like alarm management in telecommunication networks, fault analysis in the manufacturing plants, predicting user behavior in web click streams and so on. In this paper, we address the discovery of serial episodes. In the episodes context, there have been multiple ways to quantify the frequency of an episode. Most of the current algorithms for episode discovery under various frequencies are apriori-based level-wise methods. These methods essentially perform a breadth-first search of the pattern space. However currently there are no depth-first based methods of pattern discovery in the frequent episode framework under many of the frequency definitions. In this paper, we try to bridge this gap. We provide new depth-first based algorithms for serial episode discovery under non-overlapped and total frequencies. Under non-overlapped frequency, we present algorithms that can take care of span constraint and gap constraint on episode occurrences. Under total frequency we present an algorithm that can handle span constraint. We provide proofs of correctness for the proposed algorithms. We demonstrate the effectiveness of the proposed algorithms by extensive simulations. We also give detailed run-time comparisons with the existing apriori-based methods and illustrate scenarios under which the proposed pattern-growth algorithms perform better than their apriori counterparts. (C) 2013 Elsevier B.V. All rights reserved.

A matroidal framework for network-error correcting codes

Matroidal networks were introduced by Dougherty et al. and have been well studied in the recent past. It was shown that a network has a scalar linear network coding solution if and only if it is matroidal associated with a representable matroid. The current work attempts to establish a connection between matroid theory and network-error correcting codes. In a similar vein to the theory connecting matroids and network coding, we abstract the essential aspects of network-error correcting codes to arrive at the definition of a matroidal error correcting network. An acyclic network (with arbitrary sink demands) is then shown to possess a scalar linear error correcting network code if and only if it is a matroidal error correcting network associated with a representable matroid. Therefore, constructing such network-error correcting codes implies the construction of certain representable matroids that satisfy some special conditions, and vice versa.

Antenna selection for time-varying channels based on slepian subspace projections

Single receive antenna selection (AS) allows single-input single-output (SISO) systems to retain the diversity benefits of multiple antennas with minimum hardware costs. We propose a single receive AS method for time-varying channels, in which practical limitations imposed by next-generation wireless standards such as training, packetization and antenna switching time are taken into account. The proposed method utilizes low-complexity subspace projection techniques spanned by discrete prolate spheroidal (DPS) sequences. It only uses Doppler bandwidth knowledge, and does not need detailed correlation knowledge. Results show that the proposed AS method outperforms ideal conventional SISO systems with perfect CSI but no AS at the receiver and AS using the conventional Fourier estimation/prediction method. A closed-form expression for the symbol error probability (SEP) of phase-shift keying (MPSK) with symbol-by-symbol receive AS is derived.

Burst error correction using partial fourier matrices and block sparse representation

There is a strong relation between sparse signal recovery and error control coding. It is known that burst errors are block sparse in nature. So, here we attempt to solve burst error correction problem using block sparse signal recovery methods. We construct partial Fourier based encoding and decoding matrices using results on difference sets. These constructions offer guaranteed and efficient error correction when used in conjunction with reconstruction algorithms which exploit block sparsity.

Experimental analysis of composite single-lap joints using digital image correlation and comparison with theoretical models

The demand for energy efficient, low weight structures has boosted the use of composite structures assembled using increased quantities of structural adhesives. Bonded structures may be subjected to severe working environments such as high temperature and moisture due to which the adhesive gets degraded over a period of time. This reduces the strength of a joint and leads to premature failure. Measurement of strains in the adhesive bondline at any point of time during service may be beneficial as an assessment can be made on the integrity of a joint and necessary preventive actions may be taken before failure. This paper presents an experimental approach of measuring peel and shear strains in the adhesive bondline of composite single-lap joints using digital image correlation. Different sets of composite adhesive joints with varied bond quality were prepared and subjected to tensile load during which digital images were taken and processed using digital image correlation software. The measured peel strain at the joint edge showed a rapid increase with the initiation of a crack till failure of the joint. The measured strains were used to compute the corresponding stresses assuming a plane strain condition and the results were compared with stresses predicted using theoretical models, namely linear and nonlinear adhesive beam models. A similar trend in stress distribution was observed. Further comparison of peel and shear strains also exhibited similar trend for both healthy and degraded joints. Maximum peel stress failure criterion was used to predict the failure load of a composite adhesive joint and a comparison was made between predicted and actual failure loads. The predicted failure loads from theoretical models were found to be higher than the actual failure load for all the joints.

A POSTERIORI ERROR CONTROL OF DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC OBSTACLE PROBLEMS

In this article, we derive an a posteriori error estimator for various discontinuous Galerkin (DG) methods that are proposed in (Wang, Han and Cheng, SIAM J. Numer. Anal., 48: 708-733, 2010) for an elliptic obstacle problem. Using a key property of DG methods, we perform the analysis in a general framework. The error estimator we have obtained for DG methods is comparable with the estimator for the conforming Galerkin (CG) finite element method. In the analysis, we construct a non-linear smoothing function mapping DG finite element space to CG finite element space and use it as a key tool. The error estimator consists of a discrete Lagrange multiplier associated with the obstacle constraint. It is shown for non-over-penalized DG methods that the discrete Lagrange multiplier is uniformly stable on non-uniform meshes. Finally, numerical results demonstrating the performance of the error estimator are presented.

On t-designs and bounds relating query complexity to error resilience in locally correctable codes

An n-length block code C is said to be r-query locally correctable, if for any codeword x ∈ C, one can probabilistically recover any one of the n coordinates of the codeword x by querying at most r coordinates of a possibly corrupted version of x. It is known that linear codes whose duals contain 2-designs are locally correctable. In this article, we consider linear codes whose duals contain t-designs for larger t. It is shown here that for such codes, for a given number of queries r, under linear decoding, one can, in general, handle a larger number of corrupted bits. We exhibit to our knowledge, for the first time, a finite length code, whose dual contains 4-designs, which can tolerate a fraction of up to 0.567/r corrupted symbols as against a maximum of 0.5/r in prior constructions. We also present an upper bound that shows that 0.567 is the best possible for this code length and query complexity over this symbol alphabet thereby establishing optimality of this code in this respect. A second result in the article is a finite-length bound which relates the number of queries r and the fraction of errors that can be tolerated, for a locally correctable code that employs a randomized algorithm in which each instance of the algorithm involves t-error correction.

STOKES' SYSTEM IN A DOMAIN WITH OSCILLATING BOUNDARY: HOMOGENIZATION AND ERROR ANALYSIS OF AN INTERIOR OPTIMAL CONTROL PROBLEM

Homogenization and error analysis of an optimal interior control problem in the framework of Stokes' system, on a domain with rapidly oscillating boundary, are the subject matters of this article. We consider a three dimensional domain constituted of a parallelepiped with a large number of rectangular cylinders at the top of it. An interior control is applied in a proper subdomain of the parallelepiped, away from the oscillating volume. We consider two types of functionals, namely a functional involving the L-2-norm of the state variable and another one involving its H-1-norm. The asymptotic analysis of optimality systems for both cases, when the cross sectional area of the rectangular cylinders tends to zero, is done here. Our major contribution is to derive error estimates for the state, the co-state and the associated pressures, in appropriate functional spaces.