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Anoosha, P.,Sakthivel, R.,Michael Gromiha, M. Elsevier Science Publishers B.V 2016 Biochimica et biophysica acta Vol.1862 No.2
Somatic mutations developed with missense, silent, insertions and deletions have varying effects on the resulting protein and are one of the important reasons for cancer development. In this study, we have systematically analysed the effect of these mutations at protein level in 41 different cancer types from COSMIC database on different perspectives: (i) Preference of residues at the mutant positions, (ii) probability of substitutions, (iii) influence of neighbouring residues in driver and passenger mutations, (iv) distribution of driver and passenger mutations around hotspot site in five typical genes and (v) distribution of silent and missense substitutions. We observed that R→H substitution is dominant in drivers followed by R→Q and R→C whereas E→K has the highest preference in passenger mutations. A set of 17 mutations including R→Y, W→A and V→R are specific to driver mutations and 31 preferred substitutions are observed only in passenger mutations. These frequencies of driver mutations vary across different cancer types and are selective to specific tissues. Further, driver missense mutations are mainly surrounded with silent driver mutations whereas the passenger missense mutations are surrounded with silent passenger mutations. This study reveals the variation of mutations at protein level in different cancer types and their preferences in cancer genes and provides new insights for understanding cancer mutations and drug development.
EXISTENCE RESULTS FOR SEMILINEAR DIFFERENTIAL EQUATIONS
Sakthivel, R.,Choi, Q.H.,Jung, T. Korean Mathematical Society 2002 대한수학회지 Vol.39 No.5
In this paper we prove the existence of mild soultions for semilinear differential equations in a Banach space. The results are obtained by using the semigroup theory and the Schaefer fixed point theorem. An example is provided to illustrate the theory.
Design of state estimator for bidirectional associative memory neural networks with leakage delays
Sakthivel, R.,Vadivel, P.,Mathiyalagan, K.,Arunkumar, A.,Sivachitra, M. Elsevier science 2015 Information sciences Vol.296 No.-
This paper considers the issue of state estimation for a class of bidirectional associative memory (BAM) neural networks. More precisely, the BAM model is considered with mixed delays which includes a constant delay in the leakage term, time-varying discrete delay and constant distributed delay. By constructing a novel Lyapunov-Krasovskii functional (LKF) together with free-weighting matrix technique, a new delay dependent sufficient condition is derived to estimate the neuron states through available output measurements such that, for all admissible delay bounds, the resulting estimation error system is globally asymptotically stable. Also it is assumed that the derivative of time delay is not necessarily zero or less than one. Further the derived conditions are formulated in terms of a set of linear matrix inequalities (LMIs) which can be easily solved by using some standard numerical packages. Finally a numerical example with simulation result is presented to show the effectiveness of the proposed theory. The result reveals that the leakage delays have a destabilizing influence on the system and they cannot be ignored.
On the approximate controllability of semilinear fractional differential systems
Sakthivel, R.,Ren, Yong,Mahmudov, N.I. Elsevier 2011 COMPUTERS & MATHEMATICS WITH APPLICATIONS - Vol.62 No.3
<P><B>Abstract</B></P><P>Fractional differential equations have wide applications in science and engineering. In this paper, we consider a class of control systems governed by the semilinear fractional differential equations in Hilbert spaces. By using the semigroup theory, the fractional power theory and fixed point strategy, a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems. The results are established under the assumption that the associated linear system is approximately controllable. Further, we extend the result to study the approximate controllability of fractional systems with nonlocal conditions. An example is provided to illustrate the application of the obtained theory.</P>
Dissipativity based repetitive control for switched stochastic dynamical systems
Sakthivel, R.,Saravanakumar, T.,Kaviarasan, B.,Marshal Anthoni, S. Elsevier [etc.] 2016 Applied Mathematics and Computation Vol.291 No.-
<P>This paper addresses the issues of dissipativity analysis and repetitive control synthesis for a class of switched stochastic dynamical systems with time-varying delay. By using the lifting technique, the considered one dimensional model is converted into a continuous-discrete stochastic two dimensional delayed model to describe the control and learning actions of the repetitive controller. By employing stochastic system theory together with Lyapunov function technique, a new set of sufficient conditions in terms of linear matrix inequalities (LMIs) is established such that the switched stochastic system in two dimensional delayed model is mean square asymptotically stable and (Q, S, R)-dissipative. Then, the desired repetitive controller is designed by solving a convex optimization problem established in terms of LMIs. More precisely, repetitive controllers with H-infinity, passivity and mixed H-infinity and passivity performances can be obtained as the special cases for the considered system. Finally, numerical examples are provided to demonstrate the effectiveness and potential of the developed design technique. (C) 2016 Elsevier Inc. All rights reserved.</P>