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.

Optimal Pulse Width Modulation of Voltage-Source Inverter fed Motor Drives with Relaxation of Quarter Wave Symmetry Condition

Optimal switching angles for minimization of total harmonic distortion of line current (I-THD) in a voltage source inverter are determined traditionally by imposing half-wave symmetry (HWS) and quarter-wave symmetry (QWS) conditions on the pulse width modulated waveform. This paper investigates optimal switching angles with QWS relaxed. Relaxing QWS expands the solution space and presents the possibility of improved solutions. The optimal solutions without QWS are shown here to outperform the optimal solutions with QWS over a range of modulation index (M) between 0.82 and 0.94 for a switching frequency to fundamental frequency ratio of 5. Theoretical and experimental results are presented on a 2.3kW induction motor drive.

Optimal Linear Glauber Model

Contrary to the actual nonlinear Glauber model, the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate () in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

Optimal power allocation for protective jamming in wireless networks: A flow based model

We address the problem of passive eavesdroppers in multi-hop wireless networks using the technique of friendly jamming. The network is assumed to employ Decode and Forward (DF) relaying. Assuming the availability of perfect channel state information (CSI) of legitimate nodes and eavesdroppers, we consider a scheduling and power allocation (PA) problem for a multiple-source multiple-sink scenario so that eavesdroppers are jammed, and source-destination throughput targets are met while minimizing the overall transmitted power. We propose activation sets (AS-es) for scheduling, and formulate an optimization problem for PA. Several methods for finding AS-es are discussed and compared. We present an approximate linear program for the original nonlinear, non-convex PA optimization problem, and argue that under certain conditions, both the formulations produce identical results. In the absence of eavesdroppers' CSI, we utilize the notion of Vulnerability Region (VR), and formulate an optimization problem with the objective of minimizing the VR. Our results show that the proposed solution can achieve power-efficient operation while defeating eavesdroppers and achieving desired source-destination throughputs simultaneously. (C) 2015 Elsevier B.V. All rights reserved.

Ultrasound-modulated optical tomography: direct recovery of elasticity distribution from experimentally measured intensity autocorrelation

Based on an ultrasound-modulated optical tomography experiment, a direct, quantitative recovery of Young's modulus (E) is achieved from the modulation depth (M) in the intensity autocorrelation. The number of detector locations is limited to two in orthogonal directions, reducing the complexity of the data gathering step whilst ensuring against an impoverishment of the measurement, by employing ultrasound frequency as a parameter to vary during data collection. The M and E are related via two partial differential equations. The first one connects M to the amplitude of vibration of the scattering centers in the focal volume and the other, this amplitude to E. A (composite) sensitivity matrix is arrived at mapping the variation of M with that of E and used in a (barely regularized) Gauss-Newton algorithm to iteratively recover E. The reconstruction results showing the variation of E are presented. (C) 2015 Optical Society of America

Investigations on Optimal Pulse-Width Modulation to Minimize Total Harmonic Distortion in the Line Current

PWM waveforms with positive voltage transition at the positive zero crossing of the fundamental voltage (type-A) are generally considered for PWM waveform with even number of switching angles per quarter whereas, waveforms with negative voltage transition at the positive zero crossing (type-B) are considered for odd number of switching angles per quarter. Optimal PWM, for minimization of total harmonic distortion of line to line (VWTHD), is generally solved with the aforementioned criteria. This paper establishes that a combination of both types of waveforms gives better performance than any individual type in terms of minimum VWTHD for complete range of modulation index (M). Optimal PWM for minimum VWTHD is solved for PWM waveforms with pulse numbers (P) of 5 and 7. Both type-A and type-B waveforms are found to be better in different ranges of M. The theoretical findings are confirmed through simulation and experimental results on a 3.7 kW squirrel cage induction motor in an open-loop V/f drive. Further, the optimal PWM is analysed from a space vector point of view.

Timing Recovery Algorithms and Architectures for 2-D Magnetic Recording Systems

We investigate the problem of timing recovery for 2-D magnetic recording (TDMR) channels. We develop a timing error model for TDMR channel considering the phase and frequency offsets with noise. We propose a 2-D data-aided phase-locked loop (PLL) architecture for tracking variations in the position and movement of the read head in the down-track and cross-track directions and analyze the convergence of the algorithm under non-separable timing errors. We further develop a 2-D interpolation-based timing recovery scheme that works in conjunction with the 2-D PLL. We quantify the efficiency of our proposed algorithms by simulations over a 2-D magnetic recording channel with timing errors.

Modified Greedy Pursuits for Improving Sparse Recovery

Compressive Sensing (CS) theory combines the signal sampling and compression for sparse signals resulting in reduction in sampling rate. In recent years, many recovery algorithms have been proposed to reconstruct the signal efficiently. Subspace Pursuit and Compressive Sampling Matching Pursuit are some of the popular greedy methods. Also, Fusion of Algorithms for Compressed Sensing is a recently proposed method where several CS reconstruction algorithms participate and the final estimate of the underlying sparse signal is determined by fusing the estimates obtained from the participating algorithms. All these methods involve solving a least squares problem which may be ill-conditioned, especially in the low dimension measurement regime. In this paper, we propose a step prior to least squares to ensure the well-conditioning of the least squares problem. Using Monte Carlo simulations, we show that in low dimension measurement scenario, this modification improves the reconstruction capability of the algorithm in clean as well as noisy measurement cases.

Optimal Power Allocation Policies for Low Powered Wireless Communication Systems

We consider optimal average power allocation policies in a wireless channel in the presence of individual delay constraints on the transmitted packets. Power is consumed in transmission of data only. We consider the case when the power used in transmission is a linear function of the data transmitted. The transmission channel may experience multipath fading. We have developed a computationally efficient online algorithm, when there is same hard delay constraint for all packets. Later on, we generalize it to the case when there are multiple real time streams with different hard deadline constraints. Our algorithm uses linear programming and has very low complexity.

Direct Link-Aware Optimal Relay Selection and a Low Feedback Variant for Underlay CR

Cooperative relaying combined with selection has been extensively studied in the literature to improve the performance of interference-constrained secondary users in underlay cognitive radio (CR). We present a novel symbol error probability (SEP)-optimal amplify-and-forward relay selection rule for an average interference-constrained underlay CR system. A fundamental principle, which is unique to average interference-constrained underlay CR, that the proposed rule brings out is that the choice of the optimal relay is affected not just by the source-to-relay, relay-to-destination, and relay-to-primary receiver links, which are local to the relay, but also by the direct source-to-destination (SD) link, even though it is not local to any relay. We also propose a simpler, practically amenable variant of the optimal rule called the 1-bit rule, which requires just one bit of feedback about the SD link gain to the relays, and incurs a marginal performance loss relative to the optimal rule. We analyze its SEP and develop an insightful asymptotic SEP analysis. The proposed rules markedly outperform several ad hoc SD link-unaware rules proposed in the literature. They also generalize the interference-unconstrained and SD link-unaware optimal rules considered in the literature.

Graphene oxide as an optimal candidate material for methane storage

Methane, the primary constituent of natural gas, binds too weakly to nanostructured carbons to meet the targets set for on-board vehicular storage to be viable. We show, using density functional theory calculations, that replacing graphene by graphene oxide increases the adsorption energy of methane by 50%. This enhancement is sufficient to achieve the optimal binding strength. In order to gain insight into the sources of this increased binding, that could also be used to formulate design principles for novel storage materials, we consider a sequence of model systems that progressively take us from graphene to graphene oxide. A careful analysis of the various contributions to the weak binding between the methane molecule and the graphene oxide shows that the enhancement has important contributions from London dispersion interactions as well as electrostatic interactions such as Debye interactions, aided by geometric curvature induced primarily by the presence of epoxy groups. (C) 2015 AIP Publishing LLC.

Energy Harvesting WSNs for Accurately Estimating the Maximum Sensor Reading: Trade-Offs and Optimal Design

Computing the maximum of sensor readings arises in several environmental, health, and industrial monitoring applications of wireless sensor networks (WSNs). We characterize the several novel design trade-offs that arise when green energy harvesting (EH) WSNs, which promise perpetual lifetimes, are deployed for this purpose. The nodes harvest renewable energy from the environment for communicating their readings to a fusion node, which then periodically estimates the maximum. For a randomized transmission schedule in which a pre-specified number of randomly selected nodes transmit in a sensor data collection round, we analyze the mean absolute error (MAE), which is defined as the mean of the absolute difference between the maximum and that estimated by the fusion node in each round. We optimize the transmit power and the number of scheduled nodes to minimize the MAE, both when the nodes have channel state information (CSI) and when they do not. Our results highlight how the optimal system operation depends on the EH rate, availability and cost of acquiring CSI, quantization, and size of the scheduled subset. Our analysis applies to a general class of sensor reading and EH random processes.

A Fast and Fault-Tolerant Distributed Algorithm for Near-Optimal TDMA Scheduling in WSNs

The time division multiple access (TDMA) based channel access mechanisms perform better than the contention based channel access mechanisms, in terms of channel utilization, reliability and power consumption, specially for high data rate applications in wireless sensor networks (WSNs). Most of the existing distributed TDMA scheduling techniques can be classified as either static or dynamic. The primary purpose of static TDMA scheduling algorithms is to improve the channel utilization by generating a schedule of smaller length. But, they usually take longer time to schedule, and hence, are not suitable for WSNs, in which the network topology changes dynamically. On the other hand, dynamic TDMA scheduling algorithms generate a schedule quickly, but they are not efficient in terms of generated schedule length. In this paper, we propose a novel scheme for TDMA scheduling in WSNs, which can generate a compact schedule similar to static scheduling algorithms, while its runtime performance can be matched with those of dynamic scheduling algorithms. Furthermore, the proposed distributed TDMA scheduling algorithm has the capability to trade-off schedule length with the time required to generate the schedule. This would allow the developers of WSNs, to tune the performance, as per the requirement of prevalent WSN applications, and the requirement to perform re-scheduling. Finally, the proposed TDMA scheduling is fault-tolerant to packet loss due to erroneous wireless channel. The algorithm has been simulated using the Castalia simulator to compare its performance with those of others in terms of generated schedule length and the time required to generate the TDMA schedule. Simulation results show that the proposed algorithm generates a compact schedule in a very less time.

A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.