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1

A Weighted Threshold for Detection of Cancerous miRNA Expressions

Pal J. K., Ray S. S., Pal S.K.

Fundamenta Informaticae

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2013

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Vol. 127, nr 1-4

289--305

EN

MicroRNAs (miRNA) are one kind of non-coding RNA which play many important roles in eukaryotic cell. Investigations on miRNAs show that miRNAs are involved in cancer development in animal body. In this article, a threshold based method to check the condition (normal or cancer) of miRNAs of a given sample/patient, using weighted average distance between the normal and cancer miRNA expressions, is proposed. For each miRNA, the city block distance between two representatives, corresponding to scaled normal and cancer expressions, is obtained. The average of all such distances for different miRNAs is weighted by a factor, to generate the threshold. The weight factor, which is cancer dependent, is determined through an exhaustive search by maximizing the F score during training. In a part of the investigation, a ranking algorithm for cancer specific miRNAs is also discussed. The performance of the proposed method is evaluated in terms of Matthews Correlation Coefficient (MCC) and by plotting points (1 – Specificity vs: Sensitivity) in Receiver Operating Characteristic (ROC) space, besides the F score. Its efficiency is demonstrated on breast, colorectal, melanoma lung, prostate and renal cancer data sets and it is observed to be superior to some of the existing classifiers in terms of the said indices.

2

Application of Adomian Decomposition Method and Variational Iteration Method for the solution of fractional Basset differential equation

Ray S. S.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 4

1163-1167

EN

In this paper, the Adomian decomposition method (ADM) and variational iteration method (VIM) are implemented to obtain an approximate solution for a fractional Basset equation with an arbitrary order […].The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. The approximate solution obtained using the VIM is exactly the same and in good agreement to that obtained by using the ADM.

3

Application of Adomian Decomposition Method and Variational Iteration Method for the solution of a fractional (arbitrary) order differential equation

Ray S. S., Bera R. K.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 4

1169-1173

EN

In this paper, the Adomian decomposition method (ADM) and variational iteration method (VIM) are implemented to obtain an approximate solution to a fractional differential equation with an arbitrary order […]. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions to different types of differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. The approximate solution obtained using the VIM is exactly the same and in good agreement as that obtained by using the ADM.

4

Application of Adomian method on the solution of wave propagation in a linear random non-homogeneous viscoelastic semi-infinite rod

Ray S. S., Bera R. K.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no 1

133-143

EN

The aim of the present problem is to investigate the efficiency of the method of Adomian for the solution of non-linear and complicated differential equation in a random medium. Here the problem is connected with the investigation of the mean and variance of the displacement distribution in a thin linear random non-homogeneous Biot type viscoelastic semi-infinite rod, due to general time-dependent displacement input at the rod. A truncated series solution of the wave problem following the method of Adomian after using the Laplace transform is obtained for small random variations in viscoelastic properties. Three specific cases concerning the probability measure as a function of the continuous type of random variable have been discussed.