Study of motion around a static black hole in Einstein and Lovelock gravity

We study motion around a static Einstein and pure Lovelock black hole in higher dimensions. It is known that in higher dimensions bound orbits exist only for a pure Lovelock black hole in all even dimensions, D = 2N + 2, where N is the degree of Lovelock polynomial action. In particular, we compute periastron shift and light bending, and the latter is given by one of the transverse spatial components of the Riemann curvature tensor. We also consider the pseudo-Newtonian potentials and Kruskal coordinates.

Novel Transmit Precoding Methods for Rayleigh Fading Multiuser TDD-MIMO Systems With CSIT and No CSIR

In this paper, we present novel precoding methods for multiuser Rayleigh fading multiple-input-multiple-output (MIMO) systems when channel state information (CSI) is available at the transmitter (CSIT) but not at the receiver (CSIR). Such a scenario is relevant, for example, in time-division duplex (TDD) MIMO communications, where, due to channel reciprocity, CSIT can be directly acquired by sending a training sequence from the receiver to the transmitter(s). We propose three transmit precoding schemes that convert the fading MIMO channel into a fixed-gain additive white Gaussian noise (AWGN) channel while satisfying an average power constraint. We also extend one of the precoding schemes to the multiuser Rayleigh fading multiple-access channel (MAC), broadcast channel (BC), and interference channel (IC). The proposed schemes convert the fading MIMO channel into fixed-gain parallel AWGN channels in all three cases. Hence, they achieve an infinite diversity order, which is in sharp contrast to schemes based on perfect CSIR and no CSIT, which, at best, achieve a finite diversity order. Further, we show that a polynomial diversity order is retained, even in the presence of channel estimation errors at the transmitter. Monte Carlo simulations illustrate the bit error rate (BER) performance obtainable from the proposed precoding scheme compared with existing transmit precoding schemes.

B-Spline potential function for maximum a-posteriori image reconstruction in fluorescence microscopy

An iterative image reconstruction technique employing B-Spline potential function in a Bayesian framework is proposed for fluorescence microscopy images. B-splines are piecewise polynomials with smooth transition, compact support and are the shortest polynomial splines. Incorporation of the B-spline potential function in the maximum-a-posteriori reconstruction technique resulted in improved contrast, enhanced resolution and substantial background reduction. The proposed technique is validated on simulated data as well as on the images acquired from fluorescence microscopes (widefield, confocal laser scanning fluorescence and super-resolution 4Pi microscopy). A comparative study of the proposed technique with the state-of-art maximum likelihood (ML) and maximum-a-posteriori (MAP) with quadratic potential function shows its superiority over the others. B-Spline MAP technique can find applications in several imaging modalities of fluorescence microscopy like selective plane illumination microscopy, localization microscopy and STED. (C) 2015 Author(s).

Simulations using meshfree methods

In this paper, attempt is made to solve a few problems using the Polynomial Point Collocation Method (PPCM), the Radial Point Collocation Method (RPCM), Smoothed Particle Hydrodynamics (SPH), and the Finite Point Method (FPM). A few observations on the accuracy of these methods are recorded. All the simulations in this paper are three dimensional linear elastostatic simulations, without accounting for body forces.

Robust design of multiple trailing edge flaps for helicopter vibration reduction: A multi-objective bat algorithm approach

The objective of this study is to determine an optimal trailing edge flap configuration and flap location to achieve minimum hub vibration levels and flap actuation power simultaneously. An aeroelastic analysis of a soft in-plane four-bladed rotor is performed in conjunction with optimal control. A second-order polynomial response surface based on an orthogonal array (OA) with 3-level design describes both the objectives adequately. Two new orthogonal arrays called MGB2P-OA and MGB4P-OA are proposed to generate nonlinear response surfaces with all interaction terms for two and four parameters, respectively. A multi-objective bat algorithm (MOBA) approach is used to obtain the optimal design point for the mutually conflicting objectives. MOBA is a recently developed nature-inspired metaheuristic optimization algorithm that is based on the echolocation behaviour of bats. It is found that MOBA inspired Pareto optimal trailing edge flap design reduces vibration levels by 73% and flap actuation power by 27% in comparison with the baseline design.

On the Parameterized Complexity of Finding Separators with Non-Hereditary Properties

We study the problem of finding small s-t separators that induce graphs having certain properties. It is known that finding a minimum clique s-t separator is polynomial-time solvable (Tarjan in Discrete Math. 55:221-232, 1985), while for example the problems of finding a minimum s-t separator that induces a connected graph or forms an independent set are fixed-parameter tractable when parameterized by the size of the separator (Marx et al. in ACM Trans. Algorithms 9(4): 30, 2013). Motivated by these results, we study properties that generalize cliques, independent sets, and connected graphs, and determine the complexity of finding separators satisfying these properties. We investigate these problems also on bounded-degree graphs. Our results are as follows: Finding a minimum c-connected s-t separator is FPT for c=2 and W1]-hard for any ca parts per thousand yen3. Finding a minimum s-t separator with diameter at most d is W1]-hard for any da parts per thousand yen2. Finding a minimum r-regular s-t separator is W1]-hard for any ra parts per thousand yen1. For any decidable graph property, finding a minimum s-t separator with this property is FPT parameterized jointly by the size of the separator and the maximum degree. Finding a connected s-t separator of minimum size does not have a polynomial kernel, even when restricted to graphs of maximum degree at most 3, unless .

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.

Event-triggered sampling using signal extrema for instantaneous amplitude and instantaneous frequency estimation

Event-triggered sampling (ETS) is a new approach towards efficient signal analysis. The goal of ETS need not be only signal reconstruction, but also direct estimation of desired information in the signal by skillful design of event. We show a promise of ETS approach towards better analysis of oscillatory non-stationary signals modeled by a time-varying sinusoid, when compared to existing uniform Nyquist-rate sampling based signal processing. We examine samples drawn using ETS, with events as zero-crossing (ZC), level-crossing (LC), and extrema, for additive in-band noise and jitter in detection instant. We find that extrema samples are robust, and also facilitate instantaneous amplitude (IA), and instantaneous frequency (IF) estimation in a time-varying sinusoid. The estimation is proposed solely using extrema samples, and a local polynomial regression based least-squares fitting approach. The proposed approach shows improvement, for noisy signals, over widely used analytic signal, energy separation, and ZC based approaches (which are based on uniform Nyquist-rate sampling based data-acquisition and processing). Further, extrema based ETS in general gives a sub-sampled representation (relative to Nyquistrate) of a time-varying sinusoid. For the same data-set size captured with extrema based ETS, and uniform sampling, the former gives much better IA and IF estimation. (C) 2015 Elsevier B.V. All rights reserved.

NON-COERCIVE RICCI FLOW INVARIANT CURVATURE CONES

This note is a study of nonnegativity conditions on curvature preserved by the Ricci flow. We focus on a specific class of curvature conditions which we call non-coercive: These are the conditions for which nonnegative curvature and vanishing scalar curvature does not imply flatness. We show, in dimensions greater than 4, that if a Ricci flow invariant nonnegativity condition is satisfied by all Einstein curvature operators with nonnegative scalar curvature, then this condition is just the nonnegativity of scalar curvature. As a corollary, we obtain that a Ricci flow invariant curvature condition, which is stronger than a nonnegative scalar curvature, cannot be strictly satisfied by curvature operators (other than multiples of the identity) of compact Einstein symmetric spaces. We also investigate conditions which are satisfied by all conformally flat manifolds with nonnegative scalar curvature.

Structures of substrate- and nucleotide-bound propionate kinase from Salmonella typhimurium: substrate specificity and phosphate-transfer mechanism

Kinases are ubiquitous enzymes that are pivotal to many biochemical processes. There are contrasting views on the phosphoryl-transfer mechanism in propionate kinase, an enzyme that reversibly transfers a phosphoryl group from propionyl phosphate to ADP in the final step of non-oxidative catabolism of L-threonine to propionate. Here, X-ray crystal structures of propionate- and nucleotide-bound Salmonella typhimurium propionate kinase are reported at 1.8-2.0 angstrom resolution. Although the mode of nucleotide binding is comparable to those of other members of the ASKHA superfamily, propionate is bound at a distinct site deeper in the hydrophobic pocket defining the active site. The propionate carboxyl is at a distance of approximate to 5 angstrom from the -phosphate of the nucleotide, supporting a direct in-line transfer mechanism. The phosphoryl-transfer reaction is likely to occur via an associative S(N)2-like transition state that involves a pentagonal bipyramidal structure with the axial positions occupied by the nucleophile of the substrate and the O atom between the - and the -phosphates, respectively. The proximity of the strictly conserved His175 and Arg236 to the carboxyl group of the propionate and the -phosphate of ATP suggests their involvement in catalysis. Moreover, ligand binding does not induce global domain movement as reported in some other members of the ASKHA superfamily. Instead, residues Arg86, Asp143 and Pro116-Leu117-His118 that define the active-site pocket move towards the substrate and expel water molecules from the active site. The role of Ala88, previously proposed to be the residue determining substrate specificity, was examined by determining the crystal structures of the propionate-bound Ala88 mutants A88V and A88G. Kinetic analysis and structural data are consistent with a significant role of Ala88 in substrate-specificity determination. The active-site pocket-defining residues Arg86, Asp143 and the Pro116-Leu117-His118 segment are also likely to contribute to substrate specificity.

Robust Savitzky-Golay Filters

Local polynomial approximation of data is an approach towards signal denoising. Savitzky-Golay (SG) filters are finite-impulse-response kernels, which convolve with the data to result in polynomial approximation for a chosen set of filter parameters. In the case of noise following Gaussian statistics, minimization of mean-squared error (MSE) between noisy signal and its polynomial approximation is optimum in the maximum-likelihood (ML) sense but the MSE criterion is not optimal for non-Gaussian noise conditions. In this paper, we robustify the SG filter for applications involving noise following a heavy-tailed distribution. The optimal filtering criterion is achieved by l(1) norm minimization of error through iteratively reweighted least-squares (IRLS) technique. It is interesting to note that at any stage of the iteration, we solve a weighted SG filter by minimizing l(2) norm but the process converges to l(1) minimized output. The results show consistent improvement over the standard SG filter performance.

A hybrid method for stochastic response analysis of a vibrating structure

Response analysis of a linear structure with uncertainties in both structural parameters and external excitation is considered here. When such an analysis is carried out using the spectral stochastic finite element method (SSFEM), often the computational cost tends to be prohibitive due to the rapid growth of the number of spectral bases with the number of random variables and the order of expansion. For instance, if the excitation contains a random frequency, or if it is a general random process, then a good approximation of these excitations using polynomial chaos expansion (PCE) involves a large number of terms, which leads to very high cost. To address this issue of high computational cost, a hybrid method is proposed in this work. In this method, first the random eigenvalue problem is solved using the weak formulation of SSFEM, which involves solving a system of deterministic nonlinear algebraic equations to estimate the PCE coefficients of the random eigenvalues and eigenvectors. Then the response is estimated using a Monte Carlo (MC) simulation, where the modal bases are sampled from the PCE of the random eigenvectors estimated in the previous step, followed by a numerical time integration. It is observed through numerical studies that this proposed method successfully reduces the computational burden compared with either a pure SSFEM of a pure MC simulation and more accurate than a perturbation method. The computational gain improves as the problem size in terms of degrees of freedom grows. It also improves as the timespan of interest reduces.

Parameterized Algorithms and Kernels for 3-Hitting Set with Parity Constraints

The 3-Hitting Set problem involves a family of subsets F of size at most three over an universe U. The goal is to find a subset of U of the smallest possible size that intersects every set in F. The version of the problem with parity constraints asks for a subset S of size at most k that, in addition to being a hitting set, also satisfies certain parity constraints on the sizes of the intersections of S with each set in the family F. In particular, an odd (even) set is a hitting set that hits every set at either one or three (two) elements, and a perfect code is a hitting set that intersects every set at exactly one element. These questions are of fundamental interest in many contexts for general set systems. Just as for Hitting Set, we find these questions to be interesting for the case of families consisting of sets of size at most three. In this work, we initiate an algorithmic study of these problems in this special case, focusing on a parameterized analysis. We show, for each problem, efficient fixed-parameter tractable algorithms using search trees that are tailor-made to the constraints in question, and also polynomial kernels using sunflower-like arguments in a manner that accounts for equivalence under the additional parity constraints.

Lower Bound Axisymmetric Limit Analysis Using Drucker-Prager Yield Cone and Simulation with Mohr-Coulomb Pyramid

This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker-Prager (D-P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D-P yield cone with the Mohr-Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors N-c, N-q and N-gamma have been computed, as a function of phi, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.

Asymptotic Bounds on the Power-Delay Tradeoff for Fading Point-to-Point Links From Geometric Bounds on the Stationary Distribution of the Queue Length

The optimal power-delay tradeoff is studied for a time-slotted independently and identically distributed fading point-to-point link, with perfect channel state information at both transmitter and receiver, and with random packet arrivals to the transmitter queue. It is assumed that the transmitter can control the number of packets served by controlling the transmit power in the slot. The optimal tradeoff between average power and average delay is analyzed for stationary and monotone transmitter policies. For such policies, an asymptotic lower bound on the minimum average delay of the packets is obtained, when average transmitter power approaches the minimum average power required for transmitter queue stability. The asymptotic lower bound on the minimum average delay is obtained from geometric upper bounds on the stationary distribution of the queue length. This approach, which uses geometric upper bounds, also leads to an intuitive explanation of the asymptotic behavior of average delay. The asymptotic lower bounds, along with previously known asymptotic upper bounds, are used to identify three new cases where the order of the asymptotic behavior differs from that obtained from a previously considered approximate model, in which the transmit power is a strictly convex function of real valued service batch size for every fade state.