Codes With Local Regeneration and Erasure Correction

Regenerating codes and codes with locality are two coding schemes that have recently been proposed, which in addition to ensuring data collection and reliability, also enable efficient node repair. In a situation where one is attempting to repair a failed node, regenerating codes seek to minimize the amount of data downloaded for node repair, while codes with locality attempt to minimize the number of helper nodes accessed. This paper presents results in two directions. In one, this paper extends the notion of codes with locality so as to permit local recovery of an erased code symbol even in the presence of multiple erasures, by employing local codes having minimum distance >2. An upper bound on the minimum distance of such codes is presented and codes that are optimal with respect to this bound are constructed. The second direction seeks to build codes that combine the advantages of both codes with locality as well as regenerating codes. These codes, termed here as codes with local regeneration, are codes with locality over a vector alphabet, in which the local codes themselves are regenerating codes. We derive an upper bound on the minimum distance of vector-alphabet codes with locality for the case when their constituent local codes have a certain uniform rank accumulation property. This property is possessed by both minimum storage regeneration (MSR) and minimum bandwidth regeneration (MBR) codes. We provide several constructions of codes with local regeneration which achieve this bound, where the local codes are either MSR or MBR codes. Also included in this paper, is an upper bound on the minimum distance of a general vector code with locality as well as the performance comparison of various code constructions of fixed block length and minimum distance.

Effect of amplitude correlations on coherence in the local field potential

Neural activity across the brain shows both spatial and temporal correlations at multiple scales, and understanding these correlations is a key step toward understanding cortical processing. Correlation in the local field potential (LFP) recorded from two brain areas is often characterized by computing the coherence, which is generally taken to reflect the degree of phase consistency across trials between two sites. Coherence, however, depends on two factors-phase consistency as well as amplitude covariation across trials-but the spatial structure of amplitude correlations across sites and its contribution to coherence are not well characterized. We recorded LFP from an array of microelectrodes chronically implanted in the primary visual cortex of monkeys and studied correlations in amplitude across electrodes as a function of interelectrode distance. We found that amplitude correlations showed a similar trend as coherence as a function of frequency and interelectrode distance. Importantly, even when phases were completely randomized between two electrodes, amplitude correlations introduced significant coherence. To quantify the contributions of phase consistency and amplitude correlations to coherence, we simulated pairs of sinusoids with varying phase consistency and amplitude correlations. These simulations confirmed that amplitude correlations can significantly bias coherence measurements, resulting in either over-or underestimation of true phase coherence. Our results highlight the importance of accounting for the correlations in amplitude while using coherence to study phase relationships across sites and frequencies.

Isotropic finite volume discretization

Finite volume methods traditionally employ dimension by dimension extension of the one-dimensional reconstruction and averaging procedures to achieve spatial discretization of the governing partial differential equations on a structured Cartesian mesh in multiple dimensions. This simple approach based on tensor product stencils introduces an undesirable grid orientation dependence in the computed solution. The resulting anisotropic errors lead to a disparity in the calculations that is most prominent between directions parallel and diagonal to the grid lines. In this work we develop isotropic finite volume discretization schemes which minimize such grid orientation effects in multidimensional calculations by eliminating the directional bias in the lowest order term in the truncation error. Explicit isotropic expressions that relate the cell face averaged line and surface integrals of a function and its derivatives to the given cell area and volume averages are derived in two and three dimensions, respectively. It is found that a family of isotropic approximations with a free parameter can be derived by combining isotropic schemes based on next-nearest and next-next-nearest neighbors in three dimensions. Use of these isotropic expressions alone in a standard finite volume framework, however, is found to be insufficient in enforcing rotational invariance when the flux vector is nonlinear and/or spatially non-uniform. The rotationally invariant terms which lead to a loss of isotropy in such cases are explicitly identified and recast in a differential form. Various forms of flux correction terms which allow for a full recovery of rotational invariance in the lowest order truncation error terms, while preserving the formal order of accuracy and discrete conservation of the original finite volume method, are developed. Numerical tests in two and three dimensions attest the superior directional attributes of the proposed isotropic finite volume method. Prominent anisotropic errors, such as spurious asymmetric distortions on a circular reaction-diffusion wave that feature in the conventional finite volume implementation are effectively suppressed through isotropic finite volume discretization. Furthermore, for a given spatial resolution, a striking improvement in the prediction of kinetic energy decay rate corresponding to a general two-dimensional incompressible flow field is observed with the use of an isotropic finite volume method instead of the conventional discretization. (C) 2014 Elsevier Inc. All rights reserved.

Effect of hydrogen on the yielding behavior and shear transformation zone volume in metallic glass ribbons

The effect of hydrogen (H) charging on the shear yield strength (tau(max)) and shear transformation zone volume (Omega) of Ni-Nb-Zr metallic glass ribbons, with varying Zr content, were studied through the first pop-in loads during nanoindentation. Weight gain measurements after H charging and desorption studies were utilized to identify how the total H absorbed during charging is partitioned into mobile and immobile (or trapped) parts. These, in turn, indicate the significant role of H mobility in the amorphous structure on the yielding behavior. In high-Zr alloys, tau(max) increases significantly whereas Omega decreases. In low-Zr alloys, a slight decrease in tau(max) and increase in Omega were noted. These experimental observations are rationalized in terms of the mobility of the absorbed H in the amorphous structure and the possible role of it in the shear transformation zone dynamics during deformation of the metallic glass. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

On the stability of the L-p-norm of the Riemannian curvature tensor

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M where R(g) and dv (g) denote the corresponding Riemannian curvature tensor and volume form and p a (0, a). First we prove that the Riemannian metrics with non-zero constant sectional curvature are strictly stable for for certain values of p. Then we conclude that they are strict local minimizers for for those values of p. Finally generalizing this result we prove that product of space forms of same type and dimension are strict local minimizer for for certain values of p.

Pressure induced manifold enhancement of Li-kinetics in FCC fullerene

The reduction of the diffusion energy barrier for Li in electrodes is one of the required criteria to achieve better performances in Li ion batteries. Using density functional theory based calculations, we report a pressure induced manifold enhancement of Li-kinetics in bulk FCC fullerene. Scanning of the potential energy surface reveals a diffusion path with a low energy barrier of 0.62 eV, which reduces further under the application of hydrostatic pressure. The pressure induced reduction in the diffusion barrier continues till a uniform volume strain of 17.7% is reached. Further enhancement of strain increases the barrier due to the repulsion caused by C-C bond formation between two neighbouring fullerenes. The decrease in the barrier is attributed to the combined effect of charge transfer triggered by the enhanced interaction of Li with the fullerene as well as the change in profile of the local potential, which becomes more attractive for Li. The lowering of the barrier leads to an enhancement of two orders of magnitude in Li diffusivity at room temperature making pressurized bulk fullerene a promising artificial solid electrolyte interface (SEI) for a faster rechargeable battery.

Local Structural and Environmental Factors Define the Efficiency of an RNA Pseudoknot Involved in Programmed Ribosomal Frameshift Process

In programmed -1 ribosomal frameshift, an RNA pseudoknot stalls the ribosome at specific sequence and restarts translation in a new reading frame. A precise understanding of structural characteristics of these pseudoknots and their PRF inducing ability has not been clear to date. To investigate this phenomenon, we have studied various structural aspects of a -1 PRF inducing RNA pseudoknot from BWYV using extensive molecular dynamics simulations. A set of functional and poorly functional forms, for which previous mutational data were available, were chosen for analysis. These structures differ from each other by either single base substitutions or base-pair replacements from the native structure. We have rationalized how certain mutations in RNA pseudoknot affect its function; e.g., a specific base substitution in loop 2 stabilizes the junction geometry by forming multiple noncanonical hydrogen bonds, leading to a highly rigid structure that could effectively resist ribosome-induced unfolding, thereby increasing efficiency. While, a CG to AU pair substitution in stem 1 leads to loss of noncanonical hydrogen bonds between stems and loop, resulting in a less stable structure and reduced PRF inducing ability, inversion of a pair in stem 2 alters specific base-pair geometry that might be required in ribosomal recognition of nucleobase groups, negatively affecting pseudoknot functioning. These observations illustrate that the ability of an RNA pseudoknot to induce -1 PRF with an optimal rate depends on several independent factors that contribute to either the local conformational variability or geometry

Local disorder investigation in NiS2-xSex using Raman and Ni K-edge x-ray absorption spectroscopies

We report on Raman and Ni K-edge x-ray absorption investigations of a NiS2-xSex (with x = 0.00, 0.50/0.55, 0.60, and 1.20) pyrite family. The Ni K-edge absorption edge shows a systematic shift going from an insulating phase (x = 0.00 and 0.50) to a metallic phase (x = 0.60 and 1.20). The near-edge absorption features show a clear evolution with Se doping. The extended x-ray absorption fine structure data reveal the evolution of the local structure with Se doping which mainly governs the local disorder. We also describe the decomposition of the NiS2-xSex Raman spectra and investigate the weights of various phonon modes using Gaussian and Lorentzian profiles. The effectiveness of the fitting models in describing the data is evaluated by means of Bayes factor estimation. The Raman analysis clearly demonstrates the disorder effects due to Se alloying in describing the phonon spectra of NiS2-xSex pyrites.

VIRTUAL VIEW SYNTHESIS BY NON-LOCAL MEANS FILTERING USING TEMPORAL DATA

A novel algorithm for Virtual View Synthesis based on Non-Local Means Filtering is presented in this paper. Apart from using the video frames from the nearby cameras and the corresponding per-pixel depth map, this algorithm also makes use of the previously synthesized frame. Simple and efficient, the algorithm can synthesize video at any given virtual viewpoint at a faster rate. In the process, the quality of the synthesized frame is not compromised. Experimental results prove the above mentioned claim. The subjective and objective quality of the synthesized frames are comparable to the existing algorithms.

Local spatial structure of forest biomass and its consequences for remote sensing of carbon stocks

Advances in forest carbon mapping have the potential to greatly reduce uncertainties in the global carbon budget and to facilitate effective emissions mitigation strategies such as REDD+ (Reducing Emissions from Deforestation and Forest Degradation). Though broad-scale mapping is based primarily on remote sensing data, the accuracy of resulting forest carbon stock estimates depends critically on the quality of field measurements and calibration procedures. The mismatch in spatial scales between field inventory plots and larger pixels of current and planned remote sensing products for forest biomass mapping is of particular concern, as it has the potential to introduce errors, especially if forest biomass shows strong local spatial variation. Here, we used 30 large (8-50 ha) globally distributed permanent forest plots to quantify the spatial variability in aboveground biomass density (AGBD in Mgha(-1)) at spatial scales ranging from 5 to 250m (0.025-6.25 ha), and to evaluate the implications of this variability for calibrating remote sensing products using simulated remote sensing footprints. We found that local spatial variability in AGBD is large for standard plot sizes, averaging 46.3% for replicate 0.1 ha subplots within a single large plot, and 16.6% for 1 ha subplots. AGBD showed weak spatial autocorrelation at distances of 20-400 m, with autocorrelation higher in sites with higher topographic variability and statistically significant in half of the sites. We further show that when field calibration plots are smaller than the remote sensing pixels, the high local spatial variability in AGBD leads to a substantial ``dilution'' bias in calibration parameters, a bias that cannot be removed with standard statistical methods. Our results suggest that topography should be explicitly accounted for in future sampling strategies and that much care must be taken in designing calibration schemes if remote sensing of forest carbon is to achieve its promise.

Effects of large-scale deforestation on precipitation in the monsoon regions: Remote versus local effects

In this paper, using idealized climate model simulations, we investigate the biogeophysical effects of large-scale deforestation on monsoon regions. We find that the remote forcing from large-scale deforestation in the northern middle and high latitudes shifts the Intertropical Convergence Zone southward. This results in a significant decrease in precipitation in the Northern Hemisphere monsoon regions (East Asia, North America, North Africa, and South Asia) and moderate precipitation increases in the Southern Hemisphere monsoon regions (South Africa, South America, and Australia). The magnitude of the monsoonal precipitation changes depends on the location of deforestation, with remote effects showing a larger influence than local effects. The South Asian Monsoon region is affected the most, with 18% decline in precipitation over India. Our results indicate that any comprehensive assessment of afforestation/reforestation as climate change mitigation strategies should carefully evaluate the remote effects on monsoonal precipitation alongside the large local impacts on temperatures.

Tailoring local density of optical states to control emission intensity and anisotropy of quantum dots in hybrid photonic-plasmonic templates

We report results of controlled tuning of the local density of states (LDOS) in versatile, flexible, and hierarchical self assembled plasmonic templates. Using 5 nm diameter gold (Au) spherical nanoantenna within a polymer template randomly dispersed with quantum dots, we show how the photoluminescence intensity and lifetime anisotropy of these dots can be significantly enhanced through LDOS tuning. Finite difference time domain simulations corroborate the experimental observations and extend the regime of enhancement to a wider range of geometric and spectral parameters bringing out the versatility of these functional plasmonic templates. It is also demonstrated how the templates act as plasmonic resonators for effectively engineer giant enhancement of the scattering efficiency of these nano antenna embedded in the templates. Our work provides an alternative method to achieve spontaneous emission intensity and anisotropy enhancement with true nanoscale plasmon resonators. (C) 2015 AIP Publishing LLC.

Identification of local variations within secondary structures of proteins

Secondary-structure elements (SSEs) play an important role in the folding of proteins. Identification of SSEs in proteins is a common problem in structural biology. A new method, ASSP (Assignment of Secondary Structure in Proteins), using only the path traversed by the C atoms has been developed. The algorithm is based on the premise that the protein structure can be divided into continuous or uniform stretches, which can be defined in terms of helical parameters, and depending on their values the stretches can be classified into different SSEs, namely -helices, 3(10)-helices, -helices, extended -strands and polyproline II (PPII) and other left-handed helices. The methodology was validated using an unbiased clustering of these parameters for a protein data set consisting of 1008 protein chains, which suggested that there are seven well defined clusters associated with different SSEs. Apart from -helices and extended -strands, 3(10)-helices and -helices were also found to occur in substantial numbers. ASSP was able to discriminate non--helical segments from flanking -helices, which were often identified as part of -helices by other algorithms. ASSP can also lead to the identification of novel SSEs. It is believed that ASSP could provide a better understanding of the finer nuances of protein secondary structure and could make an important contribution to the better understanding of comparatively less frequently occurring structural motifs. At the same time, it can contribute to the identification of novel SSEs. A standalone version of the program for the Linux as well as the Windows operating systems is freely downloadable and a web-server version is also available at .

A Statistical Model of Current Loops and Magnetic Monopoles

We formulate a natural model of loops and isolated vertices for arbitrary planar graphs, which we call the monopole-dimer model. We show that the partition function of this model can be expressed as a determinant. We then extend the method of Kasteleyn and Temperley-Fisher to calculate the partition function exactly in the case of rectangular grids. This partition function turns out to be a square of a polynomial with positive integer coefficients when the grid lengths are even. Finally, we analyse this formula in the infinite volume limit and show that the local monopole density, free energy and entropy can be expressed in terms of well-known elliptic functions. Our technique is a novel determinantal formula for the partition function of a model of isolated vertices and loops for arbitrary graphs.