Multigrid algorithms for symmetric discontinuous Galerkin methods on graded meshes

We study a class of symmetric discontinuous Galerkin methods on graded meshes. Optimal order error estimates are derived in both the energy norm and the L 2 norm, and we establish the uniform convergence of V-cycle, F-cycle and W-cycle multigrid algorithms for the resulting discrete problems. Numerical results that confirm the theoretical results are also presented.

NMR methods for fast data acquisition

NMR spectroscopy has witnessed tremendous advancements in recent years with the development of new methodologies for structure determination and availability of high-field strength spectrometers equipped with cryogenic probes. Supported by these advancements, a new dimension in NMR research has emerged which aims to increase the speed with data is collected and analyzed. Several novel methodologies have been proposed in this direction. This review focuses on the principles on which these different approaches are based with an emphasis on G-matrix Fourier transform NMR spectroscopy.

Prototype learning methods for online handwriting recognition

In this paper, we study different methods for prototype selection for recognizing handwritten characters of Tamil script. In the first method, cumulative pairwise- distances of the training samples of a given class are used to select prototypes. In the second method, cumulative distance to allographs of different orientation is used as a criterion to decide if the sample is representative of the group. The latter method is presumed to offset the possible orientation effect. This method still uses fixed number of prototypes for each of the classes. Finally, a prototype set growing algorithm is proposed, with a view to better model the differences in complexity of different character classes. The proposed algorithms are tested and compared for both writer independent and writer adaptation scenarios.

Five-stage Milstein methods for SDEs

In this paper, we consider the problem of computing numerical solutions for Ito stochastic differential equations (SDEs). The five-stage Milstein (FSM) methods are constructed for solving SDEs driven by an m-dimensional Wiener process. The FSM methods are fully explicit methods. It is proved that the FSM methods are convergent with strong order 1 for SDEs driven by an m-dimensional Wiener process. The analysis of stability (with multidimensional Wiener process) shows that the mean-square stable regions of the FSM methods are unbounded. The analysis of stability shows that the mean-square stable regions of the methods proposed in this paper are larger than the Milstein method and three-stage Milstein methods.

Comparison of the degree of creativity in the design outcomes using different design methods

This work analyses the influence of several design methods on the degree of creativity of the design outcome. A design experiment has been carried out in which the participants were divided into four teams of three members, and each team was asked to work applying different design methods. The selected methods were Brainstorming, Functional Analysis, and SCAMPER method. The `degree of creativity' of each design outcome is assessed by means of a questionnaire offered to a number of experts and by means of three different metrics: the metric of Moss, the metric of Sarkar and Chakrabarti, and the evaluation of innovative potential. The three metrics share the property of measuring the creativity as a combination of the degree of novelty and the degree of usefulness. The results show that Brainstorming provides more creative outcomes than when no method is applied, while this is not proved for SCAMPER and Functional Analysis.

On maximum entropy and minimum KL-divergence optimization by Grobner basis methods

In this paper we study constrained maximum entropy and minimum divergence optimization problems, in the cases where integer valued sufficient statistics exists, using tools from computational commutative algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. We give an implicit description of maximum entropy models by embedding them in algebraic varieties for which we give a Grobner basis method to compute it. In the cases of minimum KL-divergence models we show that implicitization preserves specialization of prior distribution. This result leads us to a Grobner basis method to embed minimum KL-divergence models in algebraic varieties. (C) 2012 Elsevier Inc. All rights reserved.

Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data

Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called `early warning signals', and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.

Simple and efficient methods for discrimination of chiral diacids and chiral alpha-methyl amines

The three-component chiral derivatization protocols have been developed for H-1, C-13 and F-19 NMR spectroscopic discrimination of chiral diacids by their coordination and self-assembly with optically active (R)-alpha-methylbenzylamine and 2-formylphenylboronic acid or 3-fluoro-2-formylmethylboronic acid. These protocols yield a mixture of diastereomeric imino-boronate esters which are identified by the well-resolved diastereotopic peaks with significant chemical shift differences ranging up to 0.6 and 2.1 ppm in their corresponding H-1 and F-19 NMR spectra, without any racemization or kinetic resolution, thereby enabling the determination of enantiopurity. A protocol has also been developed for discrimination of chiral alpha-methyl amines, using optically pure trans-1,2-cyclohexanedicarboxylic acid in combination with 2-formylphenylboronic acid or 3-fluoro-2-fluoromethylboronic acid. The proposed strategies have been demonstrated on large number of chiral diacids and chiral alpha-methyl amines.

Statistical Methods for Accelerated Life Testing with Particular Reference to Resin Impregnated Paper Bushings

Electrical failure of insulation is known to be an extremal random process wherein nominally identical pro-rated specimens of equipment insulation, at constant stress fail at inordinately different times even under laboratory test conditions. In order to be able to estimate the life of power equipment, it is necessary to run long duration ageing experiments under accelerated stresses, to acquire and analyze insulation specific failure data. In the present work, Resin Impregnated Paper (RIP) a relatively new insulation system of choice used in transformer bushings, is taken as an example. The failure data has been processed using proven statistical methods, both graphical and analytical. The physical model governing insulation failure at constant accelerated stress has been assumed to be based on temperature dependent inverse power law model.

Efficient Methods for Robust Classification Under Uncertainty in Kernel Matrices

In this paper we study the problem of designing SVM classifiers when the kernel matrix, K, is affected by uncertainty. Specifically K is modeled as a positive affine combination of given positive semi definite kernels, with the coefficients ranging in a norm-bounded uncertainty set. We treat the problem using the Robust Optimization methodology. This reduces the uncertain SVM problem into a deterministic conic quadratic problem which can be solved in principle by a polynomial time Interior Point (IP) algorithm. However, for large-scale classification problems, IP methods become intractable and one has to resort to first-order gradient type methods. The strategy we use here is to reformulate the robust counterpart of the uncertain SVM problem as a saddle point problem and employ a special gradient scheme which works directly on the convex-concave saddle function. The algorithm is a simplified version of a general scheme due to Juditski and Nemirovski (2011). It achieves an O(1/T-2) reduction of the initial error after T iterations. A comprehensive empirical study on both synthetic data and real-world protein structure data sets show that the proposed formulations achieve the desired robustness, and the saddle point based algorithm outperforms the IP method significantly.

Modified Newton, rank-1 Broyden update and rank-2 BFGS update methods in helicopter trim: A comparative study

Nonlinear equations in mathematical physics and engineering are solved by linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For strongly nonlinear problems, the solution obtained in the iterative process can diverge due to numerical instability. As a result, the application of numerical simulation for strongly nonlinear problems is limited. Helicopter aeroelasticity involves the solution of systems of nonlinear equations in a computationally expensive environment. Reliable solution methods which do not need Jacobian calculation at each iteration are needed for this problem. In this paper, a comparative study is done by incorporating different methods for solving the nonlinear equations in helicopter trim. Three different methods based on calculating the Jacobian at the initial guess are investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Review of trend detection methods and their application to detect temperature changes in India

Present study performs the spatial and temporal trend analysis of annual, monthly and seasonal maximum and minimum temperatures (t(max), t(min)) in India. Recent trends in annual, monthly, winter, pre-monsoon, monsoon and post-monsoon extreme temperatures (t(max), t(min)) have been analyzed for three time slots viz. 1901-2003,1948-2003 and 1970-2003. For this purpose, time series of extreme temperatures of India as a whole and seven homogeneous regions, viz. Western Himalaya (WH), Northwest (NW), Northeast (NE), North Central (NC), East coast (EC), West coast (WC) and Interior Peninsula (IP) are considered. Rigorous trend detection analysis has been exercised using variety of non-parametric methods which consider the effect of serial correlation during analysis. During the last three decades minimum temperature trend is present in All India as well as in all temperature homogeneous regions of India either at annual or at any seasonal level (winter, pre-monsoon, monsoon, post-monsoon). Results agree with the earlier observation that the trend in minimum temperature is significant in the last three decades over India (Kothawale et al., 2010). Sequential MK test reveals that most of the trend both in maximum and minimum temperature began after 1970 either in annual or seasonal levels. (C) 2012 Elsevier B.V. All rights reserved.

Assessment of the Relationships Among Design Methods, Design Activities, and Creativity

This paper presents an experimental study that was conducted to compare the results obtained from using different design methods (brainstorming (BR), functional analysis (FA), and SCAMPER) in design processes. The objectives of this work are twofold. The first was to determine whether there are any differences in the length of time devoted to the different types of activities that are carried out in the design process, depending on the method that is employed; in other words, whether the design methods that are used make a difference in the profile of time spent across the design activities. The second objective was to analyze whether there is any kind of relationship between the time spent on design process activities and the degree of creativity in the solutions that are obtained. Creativity evaluation has been done by means of the degree of novelty and the level of resolution of the designed solutions using creative product semantic scale (CPSS) questionnaire. The results show that there are significant differences between the amounts of time devoted to activities related to understanding the problem and the typology of the design method, intuitive or logical, that are used. While the amount of time spent on analyzing the problem is very small in intuitive methods, such as brainstorming and SCAMPER (around 8-9% of the time), with logical methods like functional analysis practically half the time is devoted to analyzing the problem. Also, it has been found that the amount of time spent in each design phase has an influence on the results in terms of creativity, but results are not enough strong to define in which measure are they affected. This paper offers new data and results on the distinct benefits to be obtained from applying design methods. DOI: 10.1115/1.4007362]