The Treewidth of MDS and Reed-Muller Codes

The constraint complexity of a graphical realization of a linear code is the maximum dimension of the local constraint codes in the realization. The treewidth of a linear code is the least constraint complexity of any of its cycle-free graphical realizations. This notion provides a useful parameterization of the maximum-likelihood decoding complexity for linear codes. In this paper, we show the surprising fact that for maximum distance separable codes and Reed-Muller codes, treewidth equals trelliswidth, which, for a code, is defined to be the least constraint complexity (or branch complexity) of any of its trellis realizations. From this, we obtain exact expressions for the treewidth of these codes, which constitute the only known explicit expressions for the treewidth of algebraic codes.

On the structure of analytic vectors for the Schrodinger representation

This article deals with the structure of analytic and entire vectors for the Schrodinger representations of the Heisenberg group. Using refined versions of Hardy's theorem and their connection with Hermite expansions we obtain very precise representation theorems for analytic and entire vectors.

On maximum entropy and minimum KL-divergence optimization by Grobner basis methods

In this paper we study constrained maximum entropy and minimum divergence optimization problems, in the cases where integer valued sufficient statistics exists, using tools from computational commutative algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. We give an implicit description of maximum entropy models by embedding them in algebraic varieties for which we give a Grobner basis method to compute it. In the cases of minimum KL-divergence models we show that implicitization preserves specialization of prior distribution. This result leads us to a Grobner basis method to embed minimum KL-divergence models in algebraic varieties. (C) 2012 Elsevier Inc. All rights reserved.

Strain induced phase transition in CdSe nanowires: Effect of size and temperature

Using all-atom molecular dynamics simulation, we have studied the effect of size and temperature on the strain induced phase transition of wurtzite CdSe nanowires. The wurtzite structure transforms into a five-fold coordinated structure under uniaxial strain along the c axis. Our results show that lower temperature and smaller size of the nanowires stabilize the five-fold coordinated phase which is not a stable structure in bulk CdSe. High reversibility of this transformation with a very small heat loss will make these nanowires suitable for building efficient nanodevices. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4734990]

Solid State and Solution Mediated Multistep Sequential Transformations in Metal-Organic Coordination Networks

Sequential transformation in a family of metal-organic framework compounds has been investigated employing both a solid-state as well as a solution mediated route. The compounds, cobalt oxy-bis(benzoate) and manganese oxybis(benzoate) having a two-dimensional structure, were reacted with bipyridine forming cobalt oxy-bis(benzoate)-4,4'-bipyridine and manganese oxy-bis(benzoate)-4,4'-bipyridine, respectively. The bipyridine containing compounds appear to form sequentially through stable intermediates. For the cobalt system, the transformation from a two-dimensional compound, Co(H2O)(2)(OBA)] (OBA = 4,4'-oxy-bis(benzoate)), I, to two different three-dimensional compounds, Co(bpy)(OBA)]center dot bpy, II, (bpy = 4,4'-bipyridine) and Co(bpy)(0.5)(OBA)], III, and reversibility between II and III have been investigated. In the manganese system, transformation from a two-dimensional compound, Mn(H2O)(2)(OBA)], Ia, to two different three-dimensional compounds, Mn (bpy)(OBA)]center dot bpy, Ha and Ha to Mn(bpy)(0.5)(OBA)], Ilia, has been investigated. It has also been possible to identify intermediate products during these transformation reactions. The possible pathways for the formation of the compounds were postulated.

Application of Artificial Neural Networks and Particle Swarm Optimization for the Management of Groundwater Resources

Ground management problems are typically solved by the simulation-optimization approach where complex numerical models are used to simulate the groundwater flow and/or contamination transport. These numerical models take a lot of time to solve the management problems and hence become computationally expensive. In this study, Artificial Neural Network (ANN) and Particle Swarm Optimization (PSO) models were developed and coupled for the management of groundwater of Dore river basin in France. The Analytic Element Method (AEM) based flow model was developed and used to generate the dataset for the training and testing of the ANN model. This developed ANN-PSO model was applied to minimize the pumping cost of the wells, including cost of the pipe line. The discharge and location of the pumping wells were taken as the decision variable and the ANN-PSO model was applied to find out the optimal location of the wells. The results of the ANN-PSO model are found similar to the results obtained by AEM-PSO model. The results show that the ANN model can reduce the computational burden significantly as it is able to analyze different scenarios, and the ANN-PSO model is capable of identifying the optimal location of wells efficiently.

An Adaptive Conditional Zero-Forcing Decoder With Full-Diversity, Least Complexity and Essentially-ML Performance for STBCs

A low complexity, essentially-ML decoding technique for the Golden code and the three antenna Perfect code was introduced by Sirianunpiboon, Howard and Calderbank. Though no theoretical analysis of the decoder was given, the simulations showed that this decoding technique has almost maximum-likelihood (ML) performance. Inspired by this technique, in this paper we introduce two new low complexity decoders for Space-Time Block Codes (STBCs)-the Adaptive Conditional Zero-Forcing (ACZF) decoder and the ACZF decoder with successive interference cancellation (ACZF-SIC), which include as a special case the decoding technique of Sirianunpiboon et al. We show that both ACZF and ACZF-SIC decoders are capable of achieving full-diversity, and we give a set of sufficient conditions for an STBC to give full-diversity with these decoders. We then show that the Golden code, the three and four antenna Perfect codes, the three antenna Threaded Algebraic Space-Time code and the four antenna rate 2 code of Srinath and Rajan are all full-diversity ACZF/ACZF-SIC decodable with complexity strictly less than that of their ML decoders. Simulations show that the proposed decoding method performs identical to ML decoding for all these five codes. These STBCs along with the proposed decoding algorithm have the least decoding complexity and best error performance among all known codes for transmit antennas. We further provide a lower bound on the complexity of full-diversity ACZF/ACZF-SIC decoding. All the five codes listed above achieve this lower bound and hence are optimal in terms of minimizing the ACZF/ACZF-SIC decoding complexity. Both ACZF and ACZF-SIC decoders are amenable to sphere decoding implementation.

Loop transformations: convexity, pruning, and optimization

High-level loop transformations are a key instrument in mapping computational kernels to effectively exploit the resources in modern processor architectures. Nevertheless, selecting required compositions of loop transformations to achieve this remains a significantly challenging task; current compilers may be off by orders of magnitude in performance compared to hand-optimized programs. To address this fundamental challenge, we first present a convex characterization of all distinct, semantics-preserving, multidimensional affine transformations. We then bring together algebraic, algorithmic, and performance analysis results to design a tractable optimization algorithm over this highly expressive space. Our framework has been implemented and validated experimentally on a representative set of benchmarks running on state-of-the-art multi-core platforms.

On the treewidth of MDS and Reed-Muller codes

The treewidth of a linear code is the least constraint complexity of any of its cycle-free graphical realizations. This notion provides a useful parametrization of the maximum-likelihood decoding complexity for linear codes. In this paper, we compute exact expressions for the treewidth of maximum distance separable codes, and first- and second-order Reed-Muller codes. These results constitute the only known explicit expressions for the treewidth of algebraic codes.

Probing hemoglobin confinement inside submicron silica tubes using synchrotron SAXS and electrochemical response

The configuration of hemoglobin in solution and confined inside silica nanotubes has been studied using synchrotron small angle X-ray scattering and electrochemical activity. Confinement inside submicron tubes of silica aid in preventing protein aggregation, which is vividly observed for unconfined protein in solution. The radius of gyration (R-g) and size polydispersity (p) of confined hemoglobin was found to be lower than that in solution. This was also recently demonstrated in case of confined hemoglobin inside layered polymer capsules. The confined hemoglobin displayed a higher thermal stability with Rg and p showing negligible changes in the temperature range 25-75 degrees C. The differences in configuration between the confined and unconfined protein were reflected in their electrochemical activity. Reversible electrochemical response (from cyclic voltammograms) obtained in case of the confined hemoglobin, in contrary to the observance of only a cathodic response for the unconfined protein, gave direct indication of the differences between the residences of the electroactive heme center in a different orientation compared to that in solution state. The confined Hb showed loss of reversibility only at higher temperatures. The electron transfer coefficient (alpha) and electron transfer rate constant (k(s)) were also different, providing additional evidence regarding structural differences between the unconfined and confined states of hemoglobin. Thus, absence of any adverse effects due to confinement of proteins inside the inorganic matrices such as silica nanotubes opens up new prospects for utilizing inorganic matrices as protein ``encapsulators'', as well as sensors at varying temperatures.

Algebraic characterization of rainbow connectivity

The use of algebraic techniques to solve combinatorial problems is studied in this paper. We formulate the rainbow connectivity problem as a system of polynomial equations. We first consider the case of two colors for which the problem is known to be hard and we then extend the approach to the general case. We also present a formulation of the rainbow connectivity problem as an ideal membership problem.

Seismic microzonation of a nuclear power plant site with detailed geotechnical, geophysical and site effect studies

This paper highlights the seismic microzonation carried out for a nuclear power plant site. Nuclear power plants are considered to be one of the most important and critical structures designed to withstand all natural disasters. Seismic microzonation is a process of demarcating a region into individual areas having different levels of various seismic hazards. This will help in identifying regions having high seismic hazard which is vital for engineering design and land-use planning. The main objective of this paper is to carry out the seismic microzonation of a nuclear power plant site situated in the east coast of South India, based on the spatial distribution of the hazard index value. The hazard index represents the consolidated effect of all major earthquake hazards and hazard influencing parameters. The present work will provide new directions for assessing the seismic hazards of new power plant sites in the country. Major seismic hazards considered for the evaluation of the hazard index are (1) intensity of ground shaking at bedrock, (2) site amplification, (3) liquefaction potential and (4) the predominant frequency of the earthquake motion at the surface. The intensity of ground shaking in terms of peak horizontal acceleration (PHA) was estimated for the study area using both deterministic and probabilistic approaches with logic tree methodology. The site characterization of the study area has been carried out using the multichannel analysis of surface waves test and available borehole data. One-dimensional ground response analysis was carried out at major locations within the study area for evaluating PHA and spectral accelerations at the ground surface. Based on the standard penetration test data, deterministic as well as probabilistic liquefaction hazard analysis has been carried out for the entire study area. Finally, all the major earthquake hazards estimated above, and other significant parameters representing local geology were integrated using the analytic hierarchy process and hazard index map for the study area was prepared. Maps showing the spatial variation of seismic hazards (intensity of ground shaking, liquefaction potential and predominant frequency) and hazard index are presented in this work.

Boundary perturbations and the Helmholtz equation in three dimensions

We propose an analytic perturbative scheme in the spirit of Lord Rayleigh's work for determining the eigenvalues of the Helmholtz equation in three dimensions inside an arbitrary boundary where the eigenfunction satisfies either the Dirichlet boundary condition or the Neumann boundary condition. Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to the best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schrodinger perturbation theory. The efficacy of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.

Riemann shock tube: 1D normal shocks in air, simulations and experiments

This paper presents numerical simulation of the evolution of one-dimensional normal shocks, their propagation, reflection and interaction in air using a single diaphragm Riemann shock tube and validate them using experimental results. Mathematical model is derived for one-dimensional compressible flow of viscous and conducting medium. Dimensionless form of the mathematical model is used to construct space-time finite element processes based on minimization of the space-time residual functional. The space-time local approximation functions for space-time p-version hierarchical finite elements are considered in higher order GRAPHICS] spaces that permit desired order of global differentiability of local approximations in space and time. The resulting algebraic systems from this approach yield unconditionally positive-definite coefficient matrices, hence ensure unique numerical solution. The evolution is computed for a space-time strip corresponding to a time increment Delta t and then time march to obtain the evolution up to any desired value of time. Numerical studies are designed using recently invented hand-driven shock tube (Reddy tube) parameters, high/low side density and pressure values, high- and low-pressure side shock tube lengths, so that numerically computed results can be compared with actual experimental measurements.