A family of Runge-Kutta based explicit methods for rotational dynamics

The present paper develops a family of explicit algorithms for rotational dynamics and presents their comparison with several existing methods. For rotational motion the configuration space is a non-linear manifold, not a Euclidean vector space. As a consequence the rotation vector and its time derivatives correspond to different tangent spaces of rotation manifold at different time instants. This renders the usual integration algorithms for Euclidean space inapplicable for rotation. In the present algorithms this problem is circumvented by relating the equation of motion to a particular tangent space. It has been accomplished with the help of already existing relation between rotation increments which belongs to two different tangent spaces. The suggested method could in principle make any integration algorithm on Euclidean space, applicable to rotation. However, the present paper is restricted only within explicit Runge-Kutta enabled to handle rotation. The algorithms developed here are explicit and hence computationally cheaper than implicit methods. Moreover, they appear to have much higher local accuracy and hence accurate in predicting any constants of motion for reasonably longer time. The numerical results for solutions as well as constants of motion, indicate superior performance by most of our algorithms, when compared to some of the currently known algorithms, namely ALGO-C1, STW, LIEMID[EA], MCG, SUBCYC-M.

Multicomponent solids of lamotrigine with some selected coformers and their characterization by thermoanalytical, spectroscopic and X-ray diffraction methods

The present study investigates the structural and pharmaceutical properties of different multicomponent crystalline forms of lamotrigine (LTG) with some pharmaceutically acceptable coformers viz. nicotinamide (1), acetamide (2), acetic acid (3), 4-hydroxy-benzoic acid (4) and saccharin (5). The structurally homogeneous phases were characterized in the solid state by DSC/TGA, FT-IR and XRD (powder and single crystal structure analysis) as well as in the solution phase. Forms 1 and 2 were found to be cocrystal hydrate and cocrystal, respectively, while in forms 3, 4 and 5, proton transfer was observed from coformer to drug. The enthalpy of formation of multicomponent crystals from their components was determined from the enthalpy of solution of the cocrystals and the components separately. Higher exothermic values of the enthalpy of formation for molecular complexes 3, 4 and 5 suggest these to be more stable than 1 and 2. The solubility was measured in water as well as in phosphate buffers of varying pH. The salt solvate 3 exhibited the highest solubility of the drug in water as well as in buffers over the pH range 7-3 while the cocrystal hydrate 1 showed the maximum solubility in a buffer of pH 2. A significant lowering of the dosage profile of LTG was observed for 1, 3 and 5 in the animal activity studies on mice.

A comparison of three methods for downscaling daily precipitation in the Punjab region

Many downscaling techniques have been developed in the past few years for projection of station-scale hydrological variables from large-scale atmospheric variables simulated by general circulation models (GCMs) to assess the hydrological impacts of climate change. This article compares the performances of three downscaling methods, viz. conditional random field (CRF), K-nearest neighbour (KNN) and support vector machine (SVM) methods in downscaling precipitation in the Punjab region of India, belonging to the monsoon regime. The CRF model is a recently developed method for downscaling hydrological variables in a probabilistic framework, while the SVM model is a popular machine learning tool useful in terms of its ability to generalize and capture nonlinear relationships between predictors and predictand. The KNN model is an analogue-type method that queries days similar to a given feature vector from the training data and classifies future days by random sampling from a weighted set of K closest training examples. The models are applied for downscaling monsoon (June to September) daily precipitation at six locations in Punjab. Model performances with respect to reproduction of various statistics such as dry and wet spell length distributions, daily rainfall distribution, and intersite correlations are examined. It is found that the CRF and KNN models perform slightly better than the SVM model in reproducing most daily rainfall statistics. These models are then used to project future precipitation at the six locations. Output from the Canadian global climate model (CGCM3) GCM for three scenarios, viz. A1B, A2, and B1 is used for projection of future precipitation. The projections show a change in probability density functions of daily rainfall amount and changes in the wet and dry spell distributions of daily precipitation. Copyright (C) 2011 John Wiley & Sons, Ltd.

Methods for Automatic Evaluation of Sentence Extract Summaries

This paper describes three novel techniques to automatically evaluate sentence extract summaries. Two of these techniques called FuSE and DeFuSE evaluate the quality of the generated extract summary based on the degree of similarity to the model summary. They use a fuzzy set theoretic basis to generate a match score. DeFuSE is an enhancement to FuSE and uses WordNet based hypernymy structures to detect similarity between sentences at abstracted levels. The third technique focuses on quantifying the quality of an extract summary based on the difficulty in generating such a summary. Advantages of these techniques are described with examples.

A New Iterative FIR Filter for Image and Video Restoration

Image and video filtering is a key image-processing task in computer vision especially in noisy environment. In most of the cases the noise source is unknown and hence possess a major difficulty in the filtering operation. In this paper we present an error-correction based learning approach for iterative filtering. A new FIR filter is designed in which the filter coefficients are updated based on Widrow-Hoff rule. Unlike the standard filter the proposed filter has the ability to remove noise without the a priori knowledge of the noise. Experimental result shows that the proposed filter efficiently removes the noise and preserves the edges in the image. We demonstrate the capability of the proposed algorithm by testing it on standard images infected by Gaussian noise and on a real time video containing inherent noise. Experimental result shows that the proposed filter is better than some of the existing standard filters

A relook at Reissner's theory of plates in bending

Shear deformation and higher order theories of plates in bending are (generally) based on plate element equilibrium equations derived either through variational principles or other methods. They involve coupling of flexure with torsion (torsion-type) problem and if applied vertical load is along one face of the plate, coupling even with extension problem. These coupled problems with reference to vertical deflection of plate in flexure result in artificial deflection due to torsion and increased deflection of faces of the plate due to extension. Coupling in the former case is eliminated earlier using an iterative method for analysis of thick plates in bending. The method is extended here for the analysis of associated stretching problem in flexure.

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.