Time and Energy Complexity of Distributed Computation of a Class of Functions in Wireless Sensor Networks

We consider a scenario in which a wireless sensor network is formed by randomly deploying n sensors to measure some spatial function over a field, with the objective of computing a function of the measurements and communicating it to an operator station. We restrict ourselves to the class of type-threshold functions (as defined in the work of Giridhar and Kumar, 2005), of which max, min, and indicator functions are important examples: our discussions are couched in terms of the max function. We view the problem as one of message-passing distributed computation over a geometric random graph. The network is assumed to be synchronous, and the sensors synchronously measure values and then collaborate to compute and deliver the function computed with these values to the operator station. Computation algorithms differ in (1) the communication topology assumed and (2) the messages that the nodes need to exchange in order to carry out the computation. The focus of our paper is to establish (in probability) scaling laws for the time and energy complexity of the distributed function computation over random wireless networks, under the assumption of centralized contention-free scheduling of packet transmissions. First, without any constraint on the computation algorithm, we establish scaling laws for the computation time and energy expenditure for one-time maximum computation. We show that for an optimal algorithm, the computation time and energy expenditure scale, respectively, as Theta(radicn/log n) and Theta(n) asymptotically as the number of sensors n rarr infin. Second, we analyze the performance of three specific computation algorithms that may be used in specific practical situations, namely, the tree algorithm, multihop transmission, and the Ripple algorithm (a type of gossip algorithm), and obtain scaling laws for the computation time and energy expenditure as n rarr infin. In particular, we show that the computation time for these algorithms scales as Theta(radicn/lo- g n), Theta(n), and Theta(radicn log n), respectively, whereas the energy expended scales as , Theta(n), Theta(radicn/log n), and Theta(radicn log n), respectively. Finally, simulation results are provided to show that our analysis indeed captures the correct scaling. The simulations also yield estimates of the constant multipliers in the scaling laws. Our analyses throughout assume a centralized optimal scheduler, and hence, our results can be viewed as providing bounds for the performance with practical distributed schedulers.

Geometric quantum computation using fictitious spin-1/2 subspaces of strongly dipolar coupled nuclear spins

Geometric phases have been used in NMR to implement controlled phase shift gates for quantum-information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement controlled phase shift gates in strongly coupled systems by using nonadiabatic geometric phases, obtained by evolving the magnetization of fictitious spin-1/2 subspaces, over a closed loop on the Bloch sphere. The dynamical phase accumulated during the evolution of the subspaces is refocused by a spin echo pulse sequence and by setting the delay of transition selective pulses such that the evolution under the homonuclear coupling makes a complete 2 pi rotation. A detailed theoretical explanation of nonadiabatic geometric phases in NMR is given by using single transition operators. Controlled phase shift gates, two qubit Deutsch-Jozsa algorithm, and parity algorithm in a qubit-qutrit system have been implemented in various strongly dipolar coupled systems obtained by orienting the molecules in liquid crystal media.

Computation-Based Reliability Analysis in Real Time Applications

Reliability analysis for computing systems in aerospace applications must account for actual computations the system performs in the use environment. This paper introduces a theoretical nonhomogeneous Markov model for such applications.

An efficient reduction algorithm for computation of interconnect delay variability for statistical timing analysis in clock tree planning

In this paper, we propose a novel and efficient algorithm for modelling sub-65 nm clock interconnect-networks in the presence of process variation. We develop a method for delay analysis of interconnects considering the impact of Gaussian metal process variations. The resistance and capacitance of a distributed RC line are expressed as correlated Gaussian random variables which are then used to compute the standard deviation of delay Probability Distribution Function (PDF) at all nodes in the interconnect network. Main objective is to find delay PDF at a cheaper cost. Convergence of this approach is in probability distribution but not in mean of delay. We validate our approach against SPICE based Monte Carlo simulations while the current method entails significantly lower computational cost.

In-Network Computation in Random Wireless Networks: A PAC Approach to Constant Refresh Rates with Lower Energy Costs

We propose a method to compute a probably approximately correct (PAC) normalized histogram of observations with a refresh rate of Theta(1) time units per histogram sample on a random geometric graph with noise-free links. The delay in computation is Theta(root n) time units. We further extend our approach to a network with noisy links. While the refresh rate remains Theta(1) time units per sample, the delay increases to Theta(root n log n). The number of transmissions in both cases is Theta(n) per histogram sample. The achieved Theta(1) refresh rate for PAC histogram computation is a significant improvement over the refresh rate of Theta(1/log n) for histogram computation in noiseless networks. We achieve this by operating in the supercritical thermodynamic regime where large pathways for communication build up, but the network may have more than one component. The largest component however will have an arbitrarily large fraction of nodes in order to enable approximate computation of the histogram to the desired level of accuracy. Operation in the supercritical thermodynamic regime also reduces energy consumption. A key step in the proof of our achievability result is the construction of a connected component having bounded degree and any desired fraction of nodes. This construction may also prove useful in other communication settings on the random geometric graph.

Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces

This paper presents an algorithm for generating the Interior Medial Axis Transform (iMAT) of 3D objects with free-form boundaries. The algorithm proposed uses the exact representation of the part and generates an approximate rational spline description of the iMAT. The algorithm generates the iMAT by a tracing technique that marches along the object's boundary. The level of approximation is controlled by the choice of the step size in the tracing procedure. Criteria based on distance and local curvature of boundary entities are used to identify the junction points and the search for these junction points is done in an efficient way. The algorithm works for multiply-connected objects as well. Results of the implementation are provided. (C) 2010 Elsevier Ltd. All rights reserved.

Computation of restoration of ligand response in the random kinetics of a prostate cancer cell signaling pathway

Mutation and/or dysfunction of signaling proteins in the mitogen activated protein kinase (MAPK) signal transduction pathway are frequently observed in various kinds of human cancer. Consistent with this fact, in the present study, we experimentally observe that the epidermal growth factor (EGF) induced activation profile of MAP kinase signaling is not straightforward dose-dependent in the PC3 prostate cancer cells. To find out what parameters and reactions in the pathway are involved in this departure from the normal dose-dependency, a model-based pathway analysis is performed. The pathway is mathematically modeled with 28 rate equations yielding those many ordinary differential equations (ODE) with kinetic rate constants that have been reported to take random values in the existing literature. This has led to us treating the ODE model of the pathways kinetics as a random differential equations (RDE) system in which the parameters are random variables. We show that our RDE model captures the uncertainty in the kinetic rate constants as seen in the behavior of the experimental data and more importantly, upon simulation, exhibits the abnormal EGF dose-dependency of the activation profile of MAP kinase signaling in PC3 prostate cancer cells. The most likely set of values of the kinetic rate constants obtained from fitting the RDE model into the experimental data is then used in a direct transcription based dynamic optimization method for computing the changes needed in these kinetic rate constant values for the restoration of the normal EGF dose response. The last computation identifies the parameters, i.e., the kinetic rate constants in the RDE model, that are the most sensitive to the change in the EGF dose response behavior in the PC3 prostate cancer cells. The reactions in which these most sensitive parameters participate emerge as candidate drug targets on the signaling pathway. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Decoupled three-dimensional finite element computation of thermoelastic damping using Zener's approximation

We consider three dimensional finite element computations of thermoelastic damping ratios of arbitrary bodies using Zener's approach. In our small-damping formulation, unlike existing fully coupled formulations, the calculation is split into three smaller parts. Of these, the first sub-calculation involves routine undamped modal analysis using ANSYS. The second sub-calculation takes the mode shape, and solves on the same mesh a periodic heat conduction problem. Finally, the damping coefficient is a volume integral, evaluated elementwise. In the only other decoupled three dimensional computation of thermoelastic damping reported in the literature, the heat conduction problem is solved much less efficiently, using a modal expansion. We provide numerical examples using some beam-like geometries, for which Zener's and similar formulas are valid. Among these we examine tapered beams, including the limiting case of a sharp tip. The latter's higher-mode damping ratios dramatically exceed those of a comparable uniform beam.

On Computation of Minimum Distance of Linear Block Codes Above 1/2 Rate Coding

The minimum distance of linear block codes is one of the important parameter that indicates the error performance of the code. When the code rate is less than 1/2, efficient algorithms are available for finding minimum distance using the concept of information sets. When the code rate is greater than 1/2, only one information set is available and efficiency suffers. In this paper, we investigate and propose a novel algorithm to find the minimum distance of linear block codes with the code rate greater than 1/2. We propose to reverse the roles of information set and parity set to get virtually another information set to improve the efficiency. This method is 67.7 times faster than the minimum distance algorithm implemented in MAGMA Computational Algebra System for a (80, 45) linear block code.

Distributed computation of fixed points of infinity-nonexpansive maps

The distributed implementation of an algorithm for computing fixed points of an infinity-nonexpansive map is shown to converge to the set of fixed points under very general conditions.

Fast computation of Legendre and Zernike moments

This paper presents recursive algorithms for fast computation of Legendre and Zernike moments of a grey-level image intensity distribution. For a binary image, a contour integration method is developed for the evaluation of Legendre moments using only the boundary information. A method for recursive calculation of Zernike polynomial coefficients is also given. A square-to-circular image transformation scheme is introduced to minimize the computation involved in Zernike moment functions. The recursive formulae can also be used in inverse moment transforms to reconstruct the original image from moments. The mathematical framework of the algorithms is given in detail, and illustrated with binary and grey-level images.

A current error space vector based hysteresis controller with constant switching frequency and simple online boundary computation for VSI fed IM drive

This paper proposes a simple current error space vector based hysteresis controller for two-level inverter fed Induction Motor (IM) drives. This proposed hysteresis controller retains all advantages of conventional current error space vector based hysteresis controllers like fast dynamic response, simple to implement, adjacent voltage vector switching etc. The additional advantage of this proposed hysteresis controller is that it gives a phase voltage frequency spectrum exactly similar to that of a constant switching frequency space vector pulse width modulated (SVPWM) inverter. In this proposed hysteresis controller the boundary is computed online using estimated stator voltages along alpha and beta axes thus completely eliminating look up tables used for obtaining parabolic hysteresis boundary proposed in. The estimation of stator voltage is carried out using current errors along alpha and beta axes and steady state model of induction motor. The proposed scheme is simple and capable of taking inverter upto six step mode operation, if demanded by drive system. The proposed hysteresis controller based inverter fed drive scheme is simulated extensively using SIMULINK toolbox of MATLAB for steady state and transient performance. The experimental verification for steady state performance of the proposed scheme is carried out on a 3.7kW IM.