Stochastic Algorithms for Discrete Parameter Simulation Optimization

We present two efficient discrete parameter simulation optimization (DPSO) algorithms for the long-run average cost objective. One of these algorithms uses the smoothed functional approximation (SFA) procedure, while the other is based on simultaneous perturbation stochastic approximation (SPSA). The use of SFA for DPSO had not been proposed previously in the literature. Further, both algorithms adopt an interesting technique of random projections that we present here for the first time. We give a proof of convergence of our algorithms. Next, we present detailed numerical experiments on a problem of admission control with dependent service times. We consider two different settings involving parameter sets that have moderate and large sizes, respectively. On the first setting, we also show performance comparisons with the well-studied optimal computing budget allocation (OCBA) algorithm and also the equal allocation algorithm. Note to Practitioners-Even though SPSA and SFA have been devised in the literature for continuous optimization problems, our results indicate that they can be powerful techniques even when they are adapted to discrete optimization settings. OCBA is widely recognized as one of the most powerful methods for discrete optimization when the parameter sets are of small or moderate size. On a setting involving a parameter set of size 100, we observe that when the computing budget is small, both SPSA and OCBA show similar performance and are better in comparison to SFA, however, as the computing budget is increased, SPSA and SFA show better performance than OCBA. Both our algorithms also show good performance when the parameter set has a size of 10(8). SFA is seen to show the best overall performance. Unlike most other DPSO algorithms in the literature, an advantage with our algorithms is that they are easily implementable regardless of the size of the parameter sets and show good performance in both scenarios.

A DCT Based Filtering of Biomedical Images

Image filtering techniques have numerous potential applications in biomedical imaging and image processing. The design of filters largely depends on the a-priori knowledge about the type of noise corrupting the image and image features. This makes the standard filters to be application and image specific. The most popular filters such as average, Gaussian and Wiener reduce noisy artifacts by smoothing. However, this operation normally results in smoothing of the edges as well. On the other hand, sharpening filters enhance the high frequency details making the image non-smooth. An integrated general approach to design filters based on discrete cosine transform (DCT) is proposed in this study for optimal medical image filtering. This algorithm exploits the better energy compaction property of DCT and re-arrange these coefficients in a wavelet manner to get the better energy clustering at desired spatial locations. This algorithm performs optimal smoothing of the noisy image by preserving high and low frequency features. Evaluation results show that the proposed filter is robust under various noise distributions.

Wavelet based spectral finite element modelling and detection of de-lamination in composite beams

In this paper, a model for composite beam with embedded de-lamination is developed using the wavelet based spectral finite element (WSFE) method particularly for damage detection using wave propagation analysis. The simulated responses are used as surrogate experimental results for the inverse problem of detection of damage using wavelet filtering. The WSFE technique is very similar to the fast fourier transform (FFT) based spectral finite element (FSFE) except that it uses compactly supported Daubechies scaling function approximation in time. Unlike FSFE formulation with periodicity assumption, the wavelet-based method allows imposition of initial values and thus is free from wrap around problems. This helps in analysis of finite length undamped structures, where the FSFE method fails to simulate accurate response. First, numerical experiments are performed to study the effect of de-lamination on the wave propagation characteristics. The responses are simulated for different de-lamination configurations for both broad-band and narrow-band excitations. Next, simulated responses are used for damage detection using wavelet analysis.

Modelling and classification of respiratory volume wavefourms

A technique is proposed for classifying respiratory volume waveforms(RVW) into normal and abnormal categories of respiratory pathways. The proposed method transforms the temporal sequence into frequency domain by using an orthogonal transform, namely discrete cosine transform (DCT) and the transformed signal is pole-zero modelled. A Bayes classifier using model pole angles as the feature vector performed satisfactorily when a limited number of RVWs recorded under deep and rapid (DR) manoeuvre are classified.

Discrete control algorithms for a tubular ammonia reactor

The specific objective of this paper is to develop direct digital control strategies for an ammonia reactor using quadratic regulator theory and compare the performance of the resultant control system with that under conventional PID regulators. The controller design studies are based on a ninth order state-space model obtained from the exact nonlinear distributed model using linearization and lumping approximations. The evaluation of these controllers with reference to their disturbance rejection capabilities and transient response characteristics, is carried out using hybrid computer simulation.

Power and Discrete Rate Adaptation for Energy Harvesting Wireless Nodes

Energy Harvesting (EH) nodes, which harvest energy from the environment in order to communicate over a wireless link, promise perpetual operation of a wireless network with battery-powered nodes. In this paper, we address the throughput optimization problem for a rate-adaptive EH node that chooses its rate from a set of discrete rates and adjusts its power depending on its channel gain and battery state. First, we show that the optimal throughput of an EH node is upper bounded by the throughput achievable by a node that is subject only to an average power constraint. We then propose a simple transmission scheme for an EH node that achieves an average throughput close to the upper bound. The scheme's parameters can be made to account for energy overheads such as battery non-idealities and the energy required for sensing and processing. The effect of these overheads on the average throughput is also analytically characterized.

Class of linear time-varying discrete systems

A class of linear time-varying discrete systems is considered, and closed-form solutions are obtained in different cases. Some comments on stability are also included.

Wavelet transform analysis of truncated fringe patterns in 3-D surface profilometry

Wavelet transform analysis of projected fringe pattern for phase recovery in 3-D shape measurement of objects is investigated. The present communication specifically outlines and evaluates the errors that creep in to the reconstructed profiles when fringe images do not satisfy periodicity. Three specific cases that give raise to non-periodicity of fringe image are simulated and leakage effects caused by each one of them are analyzed with continuous complex Morlet wavelet transform. Same images are analyzed with FFT method to make a comparison of the reconstructed profiles with both methods. Simulation results revealed a significant advantage of wavelet transform profilometry (WTP), that the distortions that arise due to leakage are confined to the locations of discontinuity and do not spread out over the entire projection as in the case of Fourier transform profilometry (FTP).

New Insights into Optimal Discrete Rate Adaptation for Average Power Constrained Single and Multi-Node Systems

The throughput-optimal discrete-rate adaptation policy, when nodes are subject to constraints on the average power and bit error rate, is governed by a power control parameter, for which a closed-form characterization has remained an open problem. The parameter is essential in determining the rate adaptation thresholds and the transmit rate and power at any time, and ensuring adherence to the power constraint. We derive novel insightful bounds and approximations that characterize the power control parameter and the throughput in closed-form. The results are comprehensive as they apply to the general class of Nakagami-m (m >= 1) fading channels, which includes Rayleigh fading, uncoded and coded modulation, and single and multi-node systems with selection. The results are appealing as they are provably tight in the asymptotic large average power regime, and are designed and verified to be accurate even for smaller average powers.

Elasto-plastic analysis of jointed rocks using discrete continuum and equivalent continuum approaches

Results from elasto-plastic numerical simulations of jointed rocks using both the equivalent continuum and discrete continuum approaches are presented, and are compared with experimental measurements. Initially triaxial compression tests on different types of rocks with wide variation in the uniaxial compressive strength are simulated using both the approaches and the results are compared. The applicability and relative merits and limitations of both the approaches for the simulation of jointed rocks are discussed. It is observed that both the approaches are reasonably good in predicting the real response. However, the equivalent continuum approach has predicted somewhat higher stiffness values at low strains. Considering the modelling effort involved in case of discrete continuum approach, for problems with complex geometry, it is suggested that a proper equivalent continuum model can be used, without compromising much on the accuracy of the results. Then the numerical analysis of a tunnel in Japan is taken up using the continuum approach. The deformations predicted are compared well against the field measurements and the predictions from discontinuum analysis. (C) 2012 Elsevier Ltd. All rights reserved.

Receive Antenna Selection for Time-Varying Channels Using Discrete Prolate Spheroidal Sequences

Receive antenna selection (AS) has been shown to maintain the diversity benefits of multiple antennas while potentially reducing hardware costs. However, the promised diversity gains of receive AS depend on the assumptions of perfect channel knowledge at the receiver and slowly time-varying fading. By explicitly accounting for practical constraints imposed by the next-generation wireless standards such as training, packetization and antenna switching time, we propose a single receive AS method for time-varying fading channels. The method exploits the low training overhead and accuracy possible from the use of discrete prolate spheroidal (DPS) sequences based reduced rank subspace projection techniques. It only requires knowledge of the Doppler bandwidth, and does not require detailed correlation knowledge. Closed-form expressions for the channel prediction and estimation error as well as symbol error probability (SEP) of M-ary phase-shift keying (MPSK) for symbol-by-symbol receive AS are also derived. It is shown that the proposed AS scheme, after accounting for the practical limitations mentioned above, outperforms the ideal conventional single-input single-output (SISO) system with perfect CSI and no AS at the receiver and AS with conventional estimation based on complex exponential basis functions.

Revisiting Riesz transforms on Heisenberg groups

We characterise higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. Using transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to multiple Hermite and Laguerre expansions.

Capacity region of K-user discrete memoryless interference channels with a mixed strong-very strong interference

The capacity region of the 3-user Gaussian Interference Channel (GIC) with mixed strong-very strong interference was established in [1]. The mixed strong-very strong interference conditions considered in [1] correspond to the case where, at each receiver, one of the interfering signals is strong and the other is very strong. In this paper, we derive the capacity region of K-user (K ≥ 3) Discrete Memoryless Interference Channels (DMICs) with a mixed strong-very strong interference. This corresponds to the case where, at each receiver one of the interfering signals is strong and the other (K - 2) interfering signals are very strong. This includes, as a special case, the 3-user DMIC with mixed strong-very strong interference. The proof is specialized to the 3-user GIC case and hence an alternative derivation for the capacity region of the 3-user GIC with mixed strong-very strong interference is provided.