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.

Mass Distribution Studies in Effervescent Sprays

An experimental study on liquid mass distribution in effervescent sprays using water and air as working fluids is presented in this paper. Optical patternation and techniques of image processing are employed for analyzing the spray. The flow regime inside the effervescent atomizer largely dictates the mass distribution patterns. The patterns are seen to vary from concentrated, poorly atomized liquid lumps to uniformly distributed, fine droplets as the flow regime changes from bubbly flow to annular flow. A large variety of instantaneous spray patterns are observed in bubbly flow regime indicating a highly unsteady atomization process. However, relatively better consistency in spray patterns is observed at higher gas flow rates. Thus, the degree of unsteadiness gradually diminishes as gas flow rate is increased. The axial evolution of the spray in annular mode shows good mixing of liquid and gas across the interface.

Flexibility in Food Extraction Techniques in Urban Free-Ranging Bonnet Macaques, Macaca radiata

Non-human primate populations, other than responding appropriately to naturally occurring challenges, also need to cope with anthropogenic factors such as environmental pollution, resource depletion, and habitat destruction. Populations and individuals are likely to show considerable variations in food extraction abilities, with some populations and individuals more efficient than others at exploiting a set of resources. In this study, we examined among urban free-ranging bonnet macaques, Macaca radiata (a) local differences in food extraction abilities, (b) between-individual variation and within-individual consistency in problem-solving success and the underlying problem-solving characteristics, and (c) behavioral patterns associated with higher efficiency in food extraction. When presented with novel food extraction tasks, the urban macaques having more frequent exposure to novel physical objects in their surroundings, extracted food material from PET bottles and also solved another food extraction task (i.e., extracting an orange from a wire mesh box), more often than those living under more natural conditions. Adults solved the tasks more frequently than juveniles, and females more frequently than males. Both solution-technique and problem-solving characteristics varied across individuals but remained consistent within each individual across the successive presentations of PET bottles. The macaques that solved the tasks showed lesser within-individual variation in their food extraction behavior as compared to those that failed to solve the tasks. A few macaques appropriately modified their problem-solving behavior in accordance with the task requirements and solved the modified versions of the tasks without trial-and-error learning. These observations are ecologically relevant - they demonstrate considerable local differences in food extraction abilities, between-individual variation and within-individual consistency in food extraction techniques among free-ranging bonnet macaques, possibly affecting the species' local adaptability and resilience to environmental changes.

Structural Investigations on the Compositional Anomalies in Lanthanum Zirconate System Synthesized by Coprecipitation Method

The study set out to investigate the compositional inconsistency in lanthanum zirconate system revealed the presence of nonstoichiometry in lanthanum zirconate powders when synthesized by coprecipitation route. X-ray diffraction (XRD) and high-resolution transmission electron microscopy (HRTEM) investigations confirmed the depletion of La3+ ions in the system. Analysis using Vegard's law showed the La/Zr mole ratio in the sample to be around 0.45. An extra step of ultrasonication, introduced during the washing stage followed by the coprecipitation reaction, ensured the formation of stoichiometric La2Zr2O7. Noteworthy is also the difference between crystal sizes in the samples prepared by with and without ultrasonication step. This difference has been explained in light of the formation of individual nuclei and their scope of growth within the precipitate core. The differential scanning calorimetry (DSC) analyses revealed that optimum pH for the synthesis of La2Zr2O7 is about 11. The ultrasonication step was pivotal in assuring consistency in mixing and composition for the lanthanum zirconate powders.

Quantitative Strain and Compositional Studies of InxGa1-xAs Epilayer in a GaAs-based pHEMT Device Structure by TEM Techniques

In GaAs-based pseudomorphic high-electron mobility transistor device structures, strain and composition of the InxGa1 (-) As-x channel layer are very important as they influence the electronic properties of these devices. In this context, transmission electron microscopy techniques such as (002) dark-field imaging, high-resolution transmission electron microscopy (HRTEM) imaging, scanning transmission electron microscopy-high angle annular dark field (STEM-HAADF) imaging and selected area diffraction, are useful. A quantitative comparative study using these techniques is relevant for assessing the merits and limitations of the respective techniques. In this article, we have investigated strain and composition of the InxGa1 (-) As-x layer with the mentioned techniques and compared the results. The HRTEM images were investigated with strain state analysis. The indium content in this layer was quantified by HAADF imaging and correlated with STEM simulations. The studies showed that the InxGa1 (-) As-x channel layer was pseudomorphically grown leading to tetragonal strain along the 001] growth direction and that the average indium content (x) in the epilayer is similar to 0.12. We found consistency in the results obtained using various methods of analysis.

Investigation of Annealing Induced Yttria Segregation in Sputtered Yttria-Stabilized Zirconia Thin Films

8mol% yttria-stabilized zirconia (8YSZ) is an extensively studied solid electrolyte. But there is no consistency in the reported ionic conductivity values of 8YSZ thin films. Interfacial segregation in YSZ thin films can affect its ionic conductivity by locally altering the surface chemistry. This article presents the effects of annealing temperature and film thickness on free surface yttria segregation behavior in 8YSZ thin film by Angle Resolved XPS and its influence on the ionic conductivity of sputtered 8YSZ thin films. Surface yttria concentration of about 32, 20, and 9mol% have been found in 40nm 8YSZ films annealed at 1273, 1173, and 1073K, respectively. Yttria segregation is found to increase with increase in annealing temperature and film thickness. Ionic conductivities of 0.23, 0.16, and 0.08Scm(-1) are observed at 923K for 40nm 8YSZ films annealed at 1073, 1173, and 1273K, respectively. The decrease in conductivity with increase in annealing temperature is attributed to the increased yttria segregation with annealing. Neither segregation nor film thickness is found to affect the activation energy of oxygen ion conduction. Target purity is found to play a key role in determining free surface yttria segregation in 8YSZ thin films.

Fluorescence-polarization studies on binding of 4-methylumbelliferyl beta-D-galactopyranoside to Ricinus communis (castor-bean) agglutinin

The binding of Ricinus communis (castor-bean) agglutinin 1 to saccharides was studied by equilibrium dialysis and fluorescence polarization by using the fluorescently labelled sugar 4-methylumbelliferyl beta-D-galactopyranoside. No appreciable change in ligand fluorescence of 4-methylumbelliferyl beta-D-galactopyranoside was considerably polarized on its binding to the lectin. The association constants obtained by Scatchard analysis of equilibrium-dialysis and fluorescence-polarization data do not differ much from each other, and at 25 degrees C, Ka = 2.4 (+/- 0.2) X 10(4)M-1. These values agree reasonably well with that reported in the literature for Ricinus agglutinin 1. The number of binding sites obtained by the different experimental procedures is 1.94 +/- 0.1 per molecule of 120 000 daltons and is equal to the reported value of 2. The consistency in the values of Ka and number of binding sites indicate the absence of additional subsites on Ricinus agglutinin 1 for its specific sugars. In addition, the excellent agreement between the binding parameters obtained by equilibrium dialysis and fluorescence polarization indicate the potential of ligand-fluorescence-polarization measurements in the investigation of lectin-sugar interactions.

Proton NMR and infrared investigations of secondary dithiocarbamate ester: molecular conformation and vibrational assignment of S-methyl N-methyl dithiocarbamate

Rotational isomerism of S-methyl N-methyl dithiocarbamate (MMDTC) has been investigated by means of variable temperature proton NMR and i.r. spectroscopy. The i.r. spectra of MMDTC as neat, solution and at sub-ambient temperatures have been examined. Normal vibrational analysis of all the fundamentals of MMDTC has been carried out, the vibrational assignment has been compared with those of related secondary thioamides to note the consistency in the assignments and to obtain the pattern characteristic of the secondary thioamide vibrations.

An Input Triggered Polymorphic ASIC for H.264 Decoding

This paper reports the design of an input-triggered polymorphic ASIC for H.264 baseline decoder. Hardware polymorphism is achieved by selectively reusing hardware resources at system and module level. Complete design is done using ESL design tools following a methodology that maintains consistency in testing and verification throughout the design flow. The proposed design can support frame sizes from QCIF to 1080p.

18-Bit binary inductive voltage divider for self balancing ac bridge applications

The constructional details of an 18-bit binary inductive voltage divider (IVD) for a.c. bridge applications is described. Simplified construction with less number of windings, interconnection of winding through SPDT solid state relays instead of DPDT relays, improves reliability of IVD. High accuracy for most precision measurement achieved without D/A converters. The checks for self consistency in voltage division shows that the error is less than 2 counts in 2(18).

Probabilistic design of retaining walls.

Retaining walls are one of the important structures in nearshore environment and are generally designed based on deterministic approaches. The present paper focuses on the reliability assessment of cantilever retaining walls with due consideration to the uncertainties in soil parameters. Reliability analysis quantifies the level of reliability associated with designs and the associated risk. It also gives the formalisation of a design situation that is normally recognised by experienced designers and provides a greater level of consistency in design. The results are also examined in terms of a simple cost function. The study shows that sliding mode is the critical failure mode and the consequent failure costs are also higher. The study also shows that provision of shear key results in improved reliability and reduction in expected costs.

The dynamics between forward citations and price of singleton patents

In recent years, business practitioners are seen valuing patents on the basis of the market price that the patent can attract. Researchers have also looked into various patent latent variables and firm variables that influence the price of a patent. Forward citations of a patent are shown to play a role in determining price. Using patent auction price data (of Ocean Tomo now ICAP patent brokerage), we delve deeper into of the role of forward citations. The successfully sold 167 singleton patents form the sample of our study. We found that, it is mainly the right tail of the citation distribution that explains the high prices of the patents falling on the right tail of the price distribution. There is consistency in the literature on the positive correlation between patent prices and forward citations. In this paper, we go deeper to understand this linear relationship through case studies. Case studies of patents with high and low citations are described in this paper to understand why some patents attracted high prices. We look into the role of additional patent latent variables like age, technology discipline, class and breadth of the patent in influencing citations that a patent receives.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Weak consistency of read-only transactions: A tool to improve concurrency in heterogeneous locking protocols

Three different types of consistencies, viz., semiweak, weak, and strong, of a read-only transaction in a schedule s of a set T of transactions are defined and these are compared with the existing notions of consistencies of a read-only transaction in a schedule. We present a technique that enables a user to control the consistency of a read-only transaction in heterogeneous locking protocols. Since the weak consistency of a read-only transaction improves concurrency in heterogeneous locking protocols, the users can help to improve concurrency in heterogeneous locking protocols by supplying the consistency requirements of read-only transactions. A heterogeneous locking protocol P' derived from a locking protocol P that uses exclusive mode locks only and ensures serializability need not be deadlock-free. We present a sufficient condition that ensures the deadlock-freeness of Pprime, when P is deadlock-free and all the read-only transactions in Pprime are two phase.

Least path criterion (LPC) for unique indexing in a two-dimensional decagonal quasilattice

The least path criterion or least path length in the context of redundant basis vector systems is discussed and a mathematical proof is presented of the uniqueness of indices obtained by applying the least path criterion. Though the method has greater generality, this paper concentrates on the two-dimensional decagonal lattice. The order of redundancy is also discussed; this will help eventually to correlate with other redundant but desirable indexing sets.