Error, Confidence, and Cost in Engineering Computations

The questions that one should answer in engineering computations - deterministic, probabilistic/randomized, as well as heuristic - are (i) how good the computed results/outputs are and (ii) how much the cost in terms of amount of computation and the amount of storage utilized in getting the outputs is. The absolutely errorfree quantities as well as the completely errorless computations done in a natural process can never be captured by any means that we have at our disposal. While the computations including the input real quantities in nature/natural processes are exact, all the computations that we do using a digital computer or are carried out in an embedded form are never exact. The input data for such computations are also never exact because any measuring instrument has inherent error of a fixed order associated with it and this error, as a matter of hypothesis and not as a matter of assumption, is not less than 0.005 per cent. Here by error we imply relative error bounds. The fact that exact error is never known under any circumstances and any context implies that the term error is nothing but error-bounds. Further, in engineering computations, it is the relative error or, equivalently, the relative error-bounds (and not the absolute error) which is supremely important in providing us the information regarding the quality of the results/outputs. Another important fact is that inconsistency and/or near-consistency in nature, i.e., in problems created from nature is completely nonexistent while in our modelling of the natural problems we may introduce inconsistency or near-inconsistency due to human error or due to inherent non-removable error associated with any measuring device or due to assumptions introduced to make the problem solvable or more easily solvable in practice. Thus if we discover any inconsistency or possibly any near-inconsistency in a mathematical model, it is certainly due to any or all of the three foregoing factors. We do, however, go ahead to solve such inconsistent/near-consistent problems and do get results that could be useful in real-world situations. The talk considers several deterministic, probabilistic, and heuristic algorithms in numerical optimisation, other numerical and statistical computations, and in PAC (probably approximately correct) learning models. It highlights the quality of the results/outputs through specifying relative error-bounds along with the associated confidence level, and the cost, viz., amount of computations and that of storage through complexity. It points out the limitation in error-free computations (wherever possible, i.e., where the number of arithmetic operations is finite and is known a priori) as well as in the usage of interval arithmetic. Further, the interdependence among the error, the confidence, and the cost is discussed.

Antimicrobial Properties of Nanostructured TiO2 Plus Fe Additive Thin Films Synthesized by a Cost-Effective Sol-Gel Process

We prepared thin films composed of pure TiO2 or TiO2 with an Fe additive (at concentrations of 0.2-0.8 wt%) via a simple and cost effective sol gel process, and tested their antifungal properties (against Candida albicans (MTCC-1637), Candida tropicalis (MTCC-184), Candida parapsilosis (MTCC-2509), and Candida glabrata (MTCC-3019) and antibacterial properties (against Staphylococcus faecalis (NCIM-2604) Staphylococcus epidermidis (NCIM-2493), Staphylococcus aureus (NCIL-2122), and Bacillus subtilis (NCIM-2549)). The films were deposited on glass and Si substrates and subjected to annealing at 400 degrees C for 3 h in ambient air. The film structural and morphological properties were investigated by X-ray photoelectron spectroscopy profilometry and scanning electron microscopy, respectively. Antifungal and antibacterial tests were conducted using the drop test method. Among the species examined, Candida albicans (MTCC-1637), and Staphylococcus aureus (NCIL-2122) showed complete colony formation inhibition after exposure for 4 h for the TiO2 loaded with 0.8 wt% Fe thin films. These results indicate that increasing the Fe concentration increased the antimicrobial activity, with complete inhibition of colony formation after 4 h exposure.

Optical, electrical and structural characterization of ZnO:Al thin films prepared by a low cost sol-gel method

ZnO:Al thin films were prepared on glass and silicon substrates by the sol-gel spin coating method. The x-ray diffraction (XRD) results showed that a polycrystalline phase with a hexagonal structure appeared after annealing at 400 degrees C for 1 h. The transmittance increased from 91 to about 93% from pure ZnO films to ZnO film doped with 1 wt% Al and then decreased for 2 wt% Al. The optical band gap energy increased as the doping concentration was increased from 0.5 wt% to 1 wt% Al. The metal oxide semiconductor (MOS) capacitors were fabricated using ZnO films deposited on silicon (100) substrates and electrical properties such as current versus voltage (I-V) and capacitance versus voltage (C-V) characteristics were studied. The electrical resistivity decreased and the leakage current increased with an increase of annealing temperature. The dielectric constant was found to be 3.12 measured at 1 MHz. The dissipation value for the film annealed at 300 degrees C was found to be 3.1 at 5 V. (C) 2011 Elsevier Ltd. All rights reserved.

Location Area Planning Using Simulated Annealing With A New Solution Representation

Location area planning problem is to partition the cellular/mobile network into location areas with the objective of minimizing the total cost. This partitioning problem is a difficult combinatorial optimization problem. In this paper, we use the simulated annealing with a new solution representation. In our method, we can automatically generate different number of location areas using Compact Index (CI) to obtain the optimal/best partitions. We compare the results obtained in our method with the earlier results available in literature. We show that our methodology is able to perform better than earlier methods.

Fragment Finder 2.0: a computing server to identify structurally similar fragments

Fragment Finder 2.0 is a web-based interactive computing server which can be used to retrieve structurally similar protein fragments from 25 and 90% nonredundant data sets. The computing server identifies structurally similar fragments using the protein backbone C alpha angles. In addition, the identified fragments can be superimposed using either of the two structural superposition programs, STAMP and PROFIT, provided in the server. The freely available Java plug-in Jmol has been interfaced with the server for the visualization of the query and superposed fragments. The server is the updated version of a previously developed search engine and employs an in-house-developed fast pattern matching algorithm. This server can be accessed freely over the World Wide Web through the URL http://cluster.physics.iisc.ernet.in/ff/.

Low cost calibrated mechanical noisemaker for hearing screening of neonates in resource constrained settings

Background & objectives: There is a need to develop an affordable and reliable tool for hearing screening of neonates in resource constrained, medically underserved areas of developing nations. This study valuates a strategy of health worker based screening of neonates using a low cost mechanical calibrated noisemaker followed up with parental monitoring of age appropriate auditory milestones for detecting severe-profound hearing impairment in infants by 6 months of age. Methods: A trained health worker under the supervision of a qualified audiologist screened 425 neonates of whom 20 had confirmed severe-profound hearing impairment. Mechanical calibrated noisemakers of 50, 60, 70 and 80 dB (A) were used to elicit the behavioural responses. The parents of screened neonates were instructed to monitor the normal language and auditory milestones till 6 months of age. This strategy was validated against the reference standard consisting of a battery of tests - namely, auditory brain stem response (ABR), otoacoustic emissions (OAE) and behavioural assessment at 2 years of age. Bayesian prevalence weighted measures of screening were calculated. Results: The sensitivity and specificity was high with least false positive referrals for. 70 and 80 dB (A) noisemakers. All the noisemakers had 100 per cent negative predictive value. 70 and 80 dB (A) noisemakers had high positive likelihood ratios of 19 and 34, respectively. The probability differences for pre- and post- test positive was 43 and 58 for 70 and 80 dB (A) noisemakers, respectively. Interpretation & conclusions: In a controlled setting, health workers with primary education can be trained to use a mechanical calibrated noisemaker made of locally available material to reliably screen for severe-profound hearing loss in neonates. The monitoring of auditory responses could be done by informed parents. Multi-centre field trials of this strategy need to be carried out to examine the feasibility of community health care workers using it in resource constrained settings of developing nations to implement an effective national neonatal hearing screening programme.

Carbon Nanotube based Composite Fibers for Strain Sensing, Signal Processing and Computing

Carbon nanotubes dispersed in polymer matrix have been aligned in the form of fibers and interconnects and cured electrically and by UV light. Conductivity and effective semiconductor tunneling against reverse to forward bias field have been designed to have differentiable current-voltage response of each of the fiber/channel. The current-voltage response is a function of the strain applied to the fibers along axial direction. Biaxial and shear strains are correlated by differentiating signals from the aligned fibers/channels. Using a small doping of magnetic nanoparticles in these composite fibers, magneto-resistance properties are realized which are strong enough to use the resulting magnetostriction as a state variable for signal processing and computing. Various basic analog signal processing tasks such as addition, convolution and filtering etc. can be performed. These preliminary study shows promising application of the concept in combined analog-digital computation in carbon nanotube based fibers. Various dynamic effects such as relaxation, electric field dependent nonlinearities and hysteresis on the output signals are studied using experimental data and analytical model.

Influence of Sn doping on structural, optical and electrical properties of ZnO thin films prepared by cost effective sol-gel process

Tin (Sn) doped zinc oxide (ZnO) thin films were synthesized by sol-gel spin coating method using zinc acetate di-hydrate and tin chloride di-hydrate as the precursor materials. The films were deposited on glass and silicon substrates and annealed at different temperatures in air ambient. The agglomeration of grains was observed by the addition of Sn in ZnO film with an average grain size of 60 nm. The optical properties of the films were studied using UV-VIS-NIR spectrophotometer. The optical band gap energies were estimated at different concentrations of Sn. The MOS capacitors were fabricated using Sn doped ZnO films. The capacitance-voltage (C-V), dissipation vs. voltage (D-V) and current-voltage (I-V) characteristics were studied and the electrical resistivity and dielectric constant were estimated. The porosity and surface area of the films were increased with the doping of Sn which makes these films suitable for opto-electronic applications. (C) 2012 Elsevier B.V. All rights reserved.

Polymer thin film structures for ultra-low cost biosensing

Reflectance change due to binding of molecules on thin film structures has been exploited for bio-molecular sensing by several groups due to its potential in the development of sensitive, low cost, easy to fabricate, large area sensors with high multiplexing capabilities. However, all of these sensing platforms have been developed using traditional semiconductor materials and processing techniques, which are expensive. This article presents a method to fabricate disposable thin film reflectance biosensors using polymers, such as polycarbonate, which are 2-3 orders of magnitude cheaper than conventional semiconductor and dielectric materials and can be processed by alternate low cost methods, leading to significant reduction in consumable costs associated with diagnostic biosensing. (C) 2011 Elsevier GmbH. All rights reserved.

Computing Reeb Graphs as a Union of Contour Trees

The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. This paper describes a fast algorithm to compute the Reeb graph of a piecewise-linear (PL) function defined over manifolds and non-manifolds. The key idea in the proposed approach is to maximally leverage the efficient contour tree algorithm to compute the Reeb graph. The algorithm proceeds by dividing the input into a set of subvolumes that have loop-free Reeb graphs using the join tree of the scalar function and computes the Reeb graph by combining the contour trees of all the subvolumes. Since the key ingredient of this method is a series of union-find operations, the algorithm is fast in practice. Experimental results demonstrate that it outperforms current generic algorithms by a factor of up to two orders of magnitude, and has a performance on par with algorithms that are catered to restricted classes of input. The algorithm also extends to handle large data that do not fit in memory.

Relay Selection for Geographical Forwarding in Sleep-Wake Cycling Wireless Sensor Networks

Our work is motivated by geographical forwarding of sporadic alarm packets to a base station in a wireless sensor network (WSN), where the nodes are sleep-wake cycling periodically and asynchronously. We seek to develop local forwarding algorithms that can be tuned so as to tradeoff the end-to-end delay against a total cost, such as the hop count or total energy. Our approach is to solve, at each forwarding node enroute to the sink, the local forwarding problem of minimizing one-hop waiting delay subject to a lower bound constraint on a suitable reward offered by the next-hop relay; the constraint serves to tune the tradeoff. The reward metric used for the local problem is based on the end-to-end total cost objective (for instance, when the total cost is hop count, we choose to use the progress toward sink made by a relay as the reward). The forwarding node, to begin with, is uncertain about the number of relays, their wake-up times, and the reward values, but knows the probability distributions of these quantities. At each relay wake-up instant, when a relay reveals its reward value, the forwarding node's problem is to forward the packet or to wait for further relays to wake-up. In terms of the operations research literature, our work can be considered as a variant of the asset selling problem. We formulate our local forwarding problem as a partially observable Markov decision process (POMDP) and obtain inner and outer bounds for the optimal policy. Motivated by the computational complexity involved in the policies derived out of these bounds, we formulate an alternate simplified model, the optimal policy for which is a simple threshold rule. We provide simulation results to compare the performance of the inner and outer bound policies against the simple policy, and also against the optimal policy when the source knows the exact number of relays. Observing the good performance and the ease of implementation of the simple policy, we apply it to our motivating problem, i.e., local geographical routing of sporadic alarm packets in a large WSN. We compare the end-to-end performance (i.e., average total delay and average total cost) obtained by the simple policy, when used for local geographical forwarding, against that obtained by the globally optimal forwarding algorithm proposed by Kim et al. 1].

Virtually cool ternary content addressable memory

Fast content addressable data access mechanisms have compelling applications in today's systems. Many of these exploit the powerful wildcard matching capabilities provided by ternary content addressable memories. For example, TCAM based implementations of important algorithms in data mining been developed in recent years; these achieve an an order of magnitude speedup over prevalent techniques. However, large hardware TCAMs are still prohibitively expensive in terms of power consumption and cost per bit. This has been a barrier to extending their exploitation beyond niche and special purpose systems. We propose an approach to overcome this barrier by extending the traditional virtual memory hierarchy to scale up the user visible capacity of TCAMs while mitigating the power consumption overhead. By exploiting the notion of content locality (as opposed to spatial locality), we devise a novel combination of software and hardware techniques to provide an abstraction of a large virtual ternary content addressable space. In the long run, such abstractions enable applications to disassociate considerations of spatial locality and contiguity from the way data is referenced. If successful, ideas for making content addressability a first class abstraction in computing systems can open up a radical shift in the way applications are optimized for memory locality, just as storage class memories are soon expected to shift away from the way in which applications are typically optimized for disk access locality.

Simulation of potential and electric field across faulty ceramic disc insulator string

Ceramic/Porcelain insulators are widely used in power transmission lines to provide mechanical support for High voltage conductors in addition to withstand electrical stresses. As a result of lightning, switching or temporary over voltages that could initiate flashover under worst weather conditions, and to operate within interference limits. Given that the useful life in service of the individual insulator elements making up the insulator strings is hard to predict, they must be verified periodically to ensure that adequate line reliability is maintained at all times. Over the years utilities have adopted few methods to detect defective discs in a string, subsequently replacement of the faulty discs are being carried out for smooth operation. But, if the insulator is found to be defective in a string at some location that may not create any changes in the field configuration, there is no need to replace to avoid manpower and cost of replacement. Due to deficiency of electric field data for the existing string configuration, utilities are forced to replace the discs which may not be essentially required. Hence, effort is made in the present work to simulate the potential and electric field along the normal and with faults induced discs in a string up to 765 kV system voltages using Surface Charge Simulation Method (SCSM). A comparison is made between simulated results, experimental and field data and it was found that the computed results are quite acceptable and useful.

A novel Q-learning algorithm with function approximation for constrained Markov decision processes

We present a novel multi-timescale Q-learning algorithm for average cost control in a Markov decision process subject to multiple inequality constraints. We formulate a relaxed version of this problem through the Lagrange multiplier method. Our algorithm is different from Q-learning in that it updates two parameters - a Q-value parameter and a policy parameter. The Q-value parameter is updated on a slower time scale as compared to the policy parameter. Whereas Q-learning with function approximation can diverge in some cases, our algorithm is seen to be convergent as a result of the aforementioned timescale separation. We show the results of experiments on a problem of constrained routing in a multistage queueing network. Our algorithm is seen to exhibit good performance and the various inequality constraints are seen to be satisfied upon convergence of the algorithm.

Tradeoff of average service cost and average delay for the state dependent M/M/1 queue

The optimal tradeoff between average service cost rate and average delay, is addressed for a M/M/1 queueing model with queue-length dependent service rates, chosen from a finite set. We provide an asymptotic characterization of the minimum average delay, when the average service cost rate is a small positive quantity V more than the minimum average service cost rate required for stability. We show that depending on the value of the arrival rate, the assumed service cost rate function, and the possible values of the service rates, the minimum average delay either a) increases only to a finite value, b) increases without bound as log(1/V), or c) increases without bound as 1/V, when V down arrow 0. We apply the analysis to a flow-level resource allocation model for a wireless downlink. We also investigate the asymptotic tradeoff for a sequence of policies which are obtained from an approximate fluid model for the M/M/1 queue.