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.

Analogous Synaptic Plasticity Profiles Emerge from Disparate Channel Combinations

An open question within the Bienenstock-Cooper-Munro theory for synaptic modification concerns the specific mechanism that is responsible for regulating the sliding modification threshold (SMT). In this conductance-based modeling study on hippocampal pyramidal neurons, we quantitatively assessed the impact of seven ion channels (R- and T-type calcium, fast sodium, delayed rectifier, A-type, and small-conductance calcium-activated (SK) potassium and HCN) and two receptors (AMPAR and NMDAR) on a calcium-dependent Bienenstock-Cooper-Munro-like plasticity rule. Our analysis with R- and T-type calcium channels revealed that differences in their activation-inactivation profiles resulted in differential impacts on how they altered the SMT. Further, we found that the impact of SK channels on the SMT critically depended on the voltage dependence and kinetics of the calcium sources with which they interacted. Next, we considered interactions among all the seven channels and the two receptors through global sensitivity analysis on 11 model parameters. We constructed 20,000 models through uniform randomization of these parameters and found 360 valid models based on experimental constraints on their plasticity profiles. Analyzing these 360 models, we found that similar plasticity profiles could emerge with several nonunique parametric combinations and that parameters exhibited weak pairwise correlations. Finally, we used seven sets of virtual knock-outs on these 360 models and found that the impact of different channels on the SMT was variable and differential. These results suggest that there are several nonunique routes to regulate the SMT, and call for a systematic analysis of the variability and state dependence of the mechanisms underlying metaplasticity during behavior and pathology.

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.

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.

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.

Do carboximide-carboxylic acid combinations form co-crystals? The role of hydroxyl substitution on the formation of co-crystals and eutectics

Carboxylic acids, amides and imides are key organic systems which provide understanding of molecular recognition and binding phenomena important in biological and pharmaceutical settings. In this context, studies of their mutual interactions and compatibility through co-crystallization may pave the way for greater understanding and new applications of their combinations. Extensive co-crystallization studies are available for carboxylic acid/amide combinations, but only a few examples of carboxylic acid/imide co-crystals are currently observed in the literature. The non-formation of co-crystals for carboxylic acid/imide combinations has previously been rationalized, based on steric and computed stability factors. In the light of the growing awareness of eutectic mixtures as an alternative outcome in co-crystallization experiments, the nature of various benzoic acid/cyclic imide combinations is established in this paper. Since an additional functional group can provide sites for new intermolecular interactions and, potentially, promote supramolecular growth into a co-crystal, benzoic acids decorated with one or more hydroxyl groups have been systematically screened for co-crystallization with one unsaturated and two saturated cyclic imides. The facile formation of an abundant number of hydroxybenzoic acid/cyclic carboximide co-crystals is reported, including polymorphic and variable stoichiometry co-crystals. In the cases where co-crystals did not form, the combinations are shown invariably to result in eutectics. The presence or absence and geometric disposition of hydroxyl functionality on benzoic acid is thus found to drive the formation of co- crystals or eutectics for the studied carboxylic acid/imide combinations.

Multicomponent Adducts of Pyridoxine: An Evaluation of the Formation of Eutectics and Molecular Salts

Cocrystallization of pyridoxine (vitamin B6) with several biologically important molecules was undertaken with the intent of successfully designing various hydrogen bonded adducts such as salts, cocrystals, and eutectics. Pyridoxine formed eutectics with isoniazid (an antitubercular drug) and nicotinic acid (vitamin B3) and molecular salts with para-aminobenzoic acid (a bioactive) and saccharin (an artificial sweetener), respectively, in accordance to our design strategy. A salt cocrystal, a precisely conjugate acid-base cocrystal, was obtained for the pyridoxine-para-nitrobenzoic acid combination. The role of supramolecular affinity of hydrogen bonding functional groups and Delta pK(a) differences leading to the formation of above diverse adducts was discussed. This study underpins the need for full-fledged supramolecular compatibility studies of multivitamin/drug combinations toward the development of optimal and/or synergistic combination formulations.

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.

QoS Constrained Optimal Sink and Relay Placement in Planned Wireless Sensor Networks

We are given a set of sensors at given locations, a set of potential locations for placing base stations (BSs, or sinks), and another set of potential locations for placing wireless relay nodes. There is a cost for placing a BS and a cost for placing a relay. The problem we consider is to select a set of BS locations, a set of relay locations, and an association of sensor nodes with the selected BS locations, so that the number of hops in the path from each sensor to its BS is bounded by h(max), and among all such feasible networks, the cost of the selected network is the minimum. The hop count bound suffices to ensure a certain probability of the data being delivered to the BS within a given maximum delay under a light traffic model. We observe that the problem is NP-Hard, and is hard to even approximate within a constant factor. For this problem, we propose a polynomial time approximation algorithm (SmartSelect) based on a relay placement algorithm proposed in our earlier work, along with a modification of the greedy algorithm for weighted set cover. We have analyzed the worst case approximation guarantee for this algorithm. We have also proposed a polynomial time heuristic to improve upon the solution provided by SmartSelect. Our numerical results demonstrate that the algorithms provide good quality solutions using very little computation time in various randomly generated network scenarios.

Near-Optimal Detection Thresholds for Bayesian Spectrum Sensing Under Fading

This paper considers the problem of energy-based, Bayesian spectrum sensing in cognitive radios under various fading environments. Under the well-known central limit theorem based model for energy detection, we derive analytically tractable expressions for near-optimal detection thresholds that minimize the probability of error under lognormal, Nakagami-m, and Weibull fading. For the Suzuki fading case, a generalized gamma approximation is provided, which saves on the computation of an integral. In each case, the accuracy of the theoretical expressions as compared to the optimal thresholds are illustrated through simulations.