Codes with Locality for Two Erasures

In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, we mean recovery via a single parity-check equation associated with small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan et al, in which recovery from a single erasure is considered. By studying the generalized Hamming weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Turan graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from 2 erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case.

An Improved Outer Bound on the Storage-Repair-Bandwidth Tradeoff of Exact-Repair Regenerating Codes

While the tradeoff between the amount of data stored and the repair bandwidth of an (n, k, d) regenerating code has been characterized under functional repair (FR), the case of exact repair (ER) remains unresolved. It is known that there do not exist ER codes which lie on the FR tradeoff at most of the points. The question as to whether one can asymptotically approach the FR tradeoff was settled recently by Tian who showed that in the (4, 3, 3) case, the ER region is bounded away from the FR region. The FR tradeoff serves as a trivial outer bound on the ER tradeoff. In this paper, we extend Tian's results by establishing an improved outer bound on the ER tradeoff which shows that the ER region is bounded away from the FR region, for any (n; k; d). Our approach is analytical and builds upon the framework introduced earlier by Shah et. al. Interestingly, a recently-constructed, layered regenerating code is shown to achieve a point on this outer bound for the (5, 4, 4) case. This represents the first-known instance of an optimal ER code that does not correspond to a point on the FR tradeoff.

A Modified Sum-Product Algorithm over Graphs with Isolated Short Cycles

We investigate into the limitations of the sum-product algorithm in the probability domain over graphs with isolated short cycles. By considering the statistical dependency of messages passed in a cycle of length 4, we modify the update equations for the beliefs at the variable and check nodes. We highlight an approximate log domain algebra for the modified variable node update to ensure numerical stability. At higher signal-to-noise ratios (SNR), the performance of decoding over graphs with isolated short cycles using the modified algorithm is improved compared to the original message passing algorithm (MPA).

Wall-mode instability in plane shear flow of viscoelastic fluid over a deformable solid

The linear stability analysis of a plane Couette flow of an Oldroyd-B viscoelastic fluid past a flexible solid medium is carried out to investigate the role of polymer addition in the stability behavior. The system consists of a viscoelastic fluid layer of thickness R, density rho, viscosity eta, relaxation time lambda, and retardation time beta lambda flowing past a linear elastic solid medium of thickness HR, density rho, and shear modulus G. The emphasis is on the high-Reynolds-number wall-mode instability, which has recently been shown in experiments to destabilize the laminar flow of Newtonian fluids in soft-walled tubes and channels at a significantly lower Reynolds number than that for flows in rigid conduits. For Newtonian fluids, the linear stability studies have shown that the wall modes become unstable when flow Reynolds number exceeds a certain critical value Re c which scales as Sigma(3/4), where Reynolds number Re = rho VR/eta, V is the top-plate velocity, and dimensionless parameter Sigma = rho GR(2)/eta(2) characterizes the fluid-solid system. For high-Reynolds-number flow, the addition of polymer tends to decrease the critical Reynolds number in comparison to that for the Newtonian fluid, indicating a destabilizing role for fluid viscoelasticity. Numerical calculations show that the critical Reynolds number could be decreased by up to a factor of 10 by the addition of small amount of polymer. The critical Reynolds number follows the same scaling Re-c similar to Sigma(3/4) as the wall modes for a Newtonian fluid for very high Reynolds number. However, for moderate Reynolds number, there exists a narrow region in beta-H parametric space, corresponding to very dilute polymer solution (0.9 less than or similar to beta < 1) and thin solids (H less than or similar to 1.1), in which the addition of polymer tends to increase the critical Reynolds number in comparison to the Newtonian fluid. Thus, Reynolds number and polymer properties can be tailored to either increase or decrease the critical Reynolds number for unstable modes, thus providing an additional degree of control over the laminar-turbulent transition.

Modeling non-stationarity in intensity, duration and frequency of extreme rainfall over India

Significant changes are reported in extreme rainfall characteristics over India in recent studies though there are disagreements on the spatial uniformity and causes of trends. Based on recent theoretical advancements in the Extreme Value Theory (EVT), we analyze changes in extreme rainfall characteristics over India using a high-resolution daily gridded (1 degrees latitude x 1 degrees longitude) dataset. Intensity, duration and frequency of excess rain over a high threshold in the summer monsoon season are modeled by non-stationary distributions whose parameters vary with physical covariates like the El-Nino Southern Oscillation index (ENSO-index) which is an indicator of large-scale natural variability, global average temperature which is an indicator of human-induced global warming and local mean temperatures which possibly indicate more localized changes. Each non-stationary model considers one physical covariate and the best chosen statistical model at each rainfall grid gives the most significant physical driver for each extreme rainfall characteristic at that grid. Intensity, duration and frequency of extreme rainfall exhibit non-stationarity due to different drivers and no spatially uniform pattern is observed in the changes in them across the country. At most of the locations, duration of extreme rainfall spells is found to be stationary, while non-stationary associations between intensity and frequency and local changes in temperature are detected at a large number of locations. This study presents the first application of nonstationary statistical modeling of intensity, duration and frequency of extreme rainfall over India. The developed models are further used for rainfall frequency analysis to show changes in the 100-year extreme rainfall event. Our findings indicate the varying nature of each extreme rainfall characteristic and their drivers and emphasize the necessity of a comprehensive framework to assess resulting risks of precipitation induced flooding. (C) 2014 Elsevier B.V. All rights reserved.

Performance evaluation of AR4 Climate Models in simulating daily precipitation over the Indian region using skill scores

The ability of Coupled General Circulation Models (CGCMs) participating in the Intergovernmental Panel for Climate Change's fourth assessment report (IPCC AR4) for the 20th century climate (20C3M scenario) to simulate the daily precipitation over the Indian region is explored. The skill is evaluated on a 2.5A degrees x 2.5A degrees grid square compared with the Indian Meteorological Department's (IMD) gridded dataset, and every GCM is ranked for each of these grids based on its skill score. Skill scores (SSs) are estimated from the probability density functions (PDFs) obtained from observed IMD datasets and GCM simulations. The methodology takes into account (high) extreme precipitation events simulated by GCMs. The results are analyzed and presented for three categories and six zones. The three categories are the monsoon season (JJASO - June to October), non-monsoon season (JFMAMND - January to May, November, December) and for the entire year (''Annual''). The six precipitation zones are peninsular, west central, northwest, northeast, central northeast India, and the hilly region. Sensitivity analysis was performed for three spatial scales, 2.5A degrees grid square, zones, and all of India, in the three categories. The models were ranked based on the SS. The category JFMAMND had a higher SS than the JJASO category. The northwest zone had higher SSs, whereas the peninsular and hilly regions had lower SS. No single GCM can be identified as the best for all categories and zones. Some models consistently outperformed the model ensemble, and one model had particularly poor performance. Results show that most models underestimated the daily precipitation rates in the 0-1 mm/day range and overestimated it in the 1-15 mm/day range.

An Algorithmic Characterization of Polynomial Functions over Z(pn)

In this paper we consider polynomial representability of functions defined over , where p is a prime and n is a positive integer. Our aim is to provide an algorithmic characterization that (i) answers the decision problem: to determine whether a given function over is polynomially representable or not, and (ii) finds the polynomial if it is polynomially representable. The previous characterizations given by Kempner (Trans. Am. Math. Soc. 22(2):240-266, 1921) and Carlitz (Acta Arith. 9(1), 67-78, 1964) are existential in nature and only lead to an exhaustive search method, i.e. algorithm with complexity exponential in size of the input. Our characterization leads to an algorithm whose running time is linear in size of input. We also extend our result to the multivariate case.

Rapid reduction of GO by hydrogen spill-over mechanism by in situ generated nanoparticles at room temperature and their catalytic performance towards 4-nitrophenol reduction and ethanol oxidation

Here, we report the clean and facile synthesis of Pt and Pd nanoparticles decorated on reduced graphene oxide (rGO) by the simultaneous reduction of graphene oxide (GO) and the metal ions in Mg/acid medium. As-generated Pt and Pd nanoparticles serve as a heterogeneous catalyst for the further reduction of the rGO by the hydrogen spill-over process. The C/O ratio is much higher as compared to the rGO obtained by the reduction of GO by only Mg/acid. Overall, the process is rapid, facile and green that does not require any toxic chemical agent or any rigorous chemical reactions. We perform the catalytic reduction of 4-nitophenol (4-NP) to 4-aminophenol (4-AP) at room temperature by Pd@rGO and Pt@rGO. The reduction is complete within 35 s for Pd@rGO and 60 s for Pt@rGO when 50 mu g of hybrid catalyst is used for 0.5 ml of 1 mM of 4-NP. In case of ethanol oxidation, the current density for Pd@rGO is comparable to commercial Pt/C but is doubled for Pt@rGO. Overall, both structures show highly stable catalytic activity compared to commercial Pt/C. (C) 2014 Elsevier B.V. All rights reserved.

Layered Exact-Repair Regenerating Codes via Embedded Error Correction and Block Designs

A new class of exact-repair regenerating codes is constructed by stitching together shorter erasure correction codes, where the stitching pattern can be viewed as block designs. The proposed codes have the help-by-transfer property where the helper nodes simply transfer part of the stored data directly, without performing any computation. This embedded error correction structure makes the decoding process straightforward, and in some cases the complexity is very low. We show that this construction is able to achieve performance better than space-sharing between the minimum storage regenerating codes and the minimum repair-bandwidth regenerating codes, and it is the first class of codes to achieve this performance. In fact, it is shown that the proposed construction can achieve a nontrivial point on the optimal functional-repair tradeoff, and it is asymptotically optimal at high rate, i.e., it asymptotically approaches the minimum storage and the minimum repair-bandwidth simultaneously.

Structural variations in aromatic 2 pi-electron three-membered rings of the main group elements

Structural variations of different Z pi-aromatic three-membered ring systems of main group elements, especially group 14 and 13 elements as compared to the classical description of cyclopropenyl cation has been reviewed in this article. The structures of heavier analogues as well as group 13 analogues of cyclopropenyl cation showed an emergence of dramatic structural patterns which do not conform, to the general norms of carbon chemistry. Isolobal analogies between the main group fragments have been efficiently used to explain the peculiarities observed in these three-membered ring systems.

THREE-LAYER FLUID FLOW OVER A SMALL OBSTRUCTION ON THE BOTTOM OF A CHANNEL

Many boundary value problems occur in a natural way while studying fluid flow problems in a channel. The solutions of two such boundary value problems are obtained and analysed in the context of flow problems involving three layers of fluids of different constant densities in a channel, associated with an impermeable bottom that has a small undulation. The top surface of the channel is either bounded by a rigid lid or free to the atmosphere. The fluid in each layer is assumed to be inviscid and incompressible, and the flow is irrotational and two-dimensional. Only waves that are stationary with respect to the bottom profile are considered in this paper. The effect of surface tension is neglected. In the process of obtaining solutions for both the problems, regular perturbation analysis along with a Fourier transform technique is employed to derive the first-order corrections of some important physical quantities. Two types of bottom topography, such as concave and convex, are considered to derive the profiles of the interfaces. We observe that the profiles are oscillatory in nature, representing waves of variable amplitude with distinct wave numbers propagating downstream and with no wave upstream. The observations are presented in tabular and graphical forms.

Decreasing intensity of monsoon low-frequency intraseasonal variability over India

Understanding the changing nature of the intraseasonal oscillatory (ISO) modes of Indian summer monsoon manifested by active and break phase, and their association with extreme rainfall events are necessary for probabilistic estimation of flood-related risks in a warming climate. Here, using ground-based observed rainfall, we define an index to measure the strength of monsoon ISOs and show that the relative strength of the northward-propagating low-frequency ISO (20-60 days) modes have had a significant decreasing trend during the past six decades, possibly attributed to the weakening of large-scale circulation in the region during monsoon season. This reduction is compensated by a gain in synoptic-scale (3-9 days) variability. The decrease in low-frequency ISO variability is associated with a significant decreasing trend in the percentage of extreme events during the active phase of the monsoon. However, this decrease is balanced by significant increasing trends in the percentage of extreme events in the break and transition phases. We also find a significant rise in the occurrence of extremes during early and late monsoon months, mainly over eastern coastal regions. Our study highlights the redistribution of rainfall intensity among periodic (low-frequency) and non-periodic (extreme) modes in a changing climate scenario.

Construction of Singer Subgroup Orbit Codes Based on Cyclic Difference Sets

A recent approach for the construction of constant dimension subspace codes, designed for error correction in random networks, is to consider the codes as orbits of suitable subgroups of the general linear group. In particular, a cyclic orbit code is the orbit of a cyclic subgroup. Hence a possible method to construct large cyclic orbit codes with a given minimum subspace distance is to select a subspace such that the orbit of the Singer subgroup satisfies the distance constraint. In this paper we propose a method where some basic properties of difference sets are employed to select such a subspace, thereby providing a systematic way of constructing cyclic orbit codes with specified parameters. We also present an explicit example of such a construction.

Performance of WRF-Chem over Indian region: Comparison with measurements

The aerosol mass concentrations over several Indian regions have been simulated using the online chemistry transport model, WRF-Chem, for two distinct seasons of 2011, representing the pre-monsoon (May) and post-monsoon (October) periods during the Indo-US joint experiment `Ganges Valley Aerosol Experiment (GVAX)'. The simulated values were compared with concurrent measurements. It is found that the model systematically underestimates near-surface BC mass concentrations as well as columnar Aerosol Optical Depths (AODs) from the measurements. Examining this in the light of the model-simulated meteorological parameters, we notice the model overestimates both planetary boundary layer height (PBLH) and surface wind speeds, leading to deeper mixing and dispersion and hence lower surface concentrations of aerosols. Shortcoming in simulating rainfall pattern also has an impact through the scavenging effect. It also appears that the columnar AODs are influenced by the unrealistic emission scenarios in the model. Comparison with vertical profiles of BC obtained from aircraft-based measurements also shows a systematic underestimation by the model at all levels. It is seen that concentration of other aerosols, viz., dust and sea-salt are closely linked with meteorological conditions prevailing over the region. Dust is higher during pre-monsoon periods due to the prevalence of north-westerly winds that advect dust from deserts of west Asia into the Indo-Gangetic plain. Winds and rainfall influence sea-salt concentrations. Thus, the unrealistic simulation of wind and rainfall leads to model simulated dust and sea-salt also to deviate from the real values; which together with BC also causes underperformance of the model with regard to columnar AOD. It appears that for better simulations of aerosols over Indian region, the model needs an improvement in the simulation of the meteorology.

Non-deterministic transducer models of retransmission protocols over noisy channels

Retransmission protocols such as HDLC and TCP are designed to ensure reliable communication over noisy channels (i.e., channels that can corrupt messages). Thakkar et al. 15] have recently presented an algorithmic verification technique for deterministic streaming string transducer (DSST) models of such protocols. The verification problem is posed as equivalence checking between the specification and protocol DSSTs. In this paper, we argue that more general models need to be obtained using non-deterministic streaming string transducers (NSSTs). However, equivalence checking is undecidable for NSSTs. We present two classes where the models belong to a sub-class of NSSTs for which it is decidable. (C) 2015 Elsevier B.V. All rights reserved.