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Register a new userAnalysis of Boolean Functions based on Interaction Graphs and their influence in System Biology
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Jayanta Kumar Das
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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Interaction graphs provide an important qualitative modeling approach for System Biology. This paper presents a novel approach for construction of interaction graph with the help of Boolean function decomposition. Each decomposition part (Consisting of 2-bits) of the Boolean functions has some important significance. In the dynamics of a biological system, each variable or node is nothing but gene or protein. Their regulation has been explored in terms of interaction graphs which are generated by Boolean functions. In this paper, different classes of Boolean functions with regards to Interaction Graph with biologically significant properties have been adumbrated.
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Boolean networks are used to model biological networks such as gene regulatory networks. Often Boolean networks show very chaotic behavior which is sensitive to any small perturbations.In order to reduce the chaotic behavior and to attain stability in the gene regulatory network,nested canalizing functions(NCF)are best suited NCF and its variants have a wide range of applications in system biology. Previously many work were done on the application of canalizing functions but there were fewer methods to check if any arbitrary Boolean function is canalizing or not. In this paper, by using Karnaugh Map this problem gas been solved and also it has been shown that when the canalizing functions of n variable is given, all the canalizing functions of n+1 variable could be generated by the method of concatenation. In this paper we have uniquely identified the number of NCFs having a particular hamming distance (H.D) generated by each variable x as starting canalizing input. Partially nested canalizing functions of 4 variables have also been studied in this paper. Keywords: Karnaugh Map, Canalizing function, Nested canalizing function, Partially nested canalizing function,concatenation
Boolean networks are used to model biological networks such as gene regulatory networks. Often Boolean networks show very chaotic behaviour which is sensitive to any small perturbations. In order to reduce the chaotic behaviour and to attain stability in the gene regulatory network, nested Canalizing Functions (NCFs) are best suited. NCFs and its variants have a wide range of applications in systems biology. Previously, many works were done on the application of canalizing functions, but there were fewer methods to check if any arbitrary Boolean function is canalizing or not. In this paper, by using Karnaugh Map this problem is solved and also it has been shown that when the canalizing functions of variable is given, all the canalizing functions of variable could be generated by the method of concatenation. In this paper we have uniquely identified the number of NCFs having a particular Hamming Distance (H.D) generated by each variable as starting canalizing input. Partially NCFs of 4 variables has also been studied in this paper.
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : {0,1}^n to {0,1}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps the most basic object of study in theoretical computer science, and Fourier analysis has become an indispensable tool in the field. The topic has also played a key role in several other areas of mathematics, from combinatorics, random graph theory, and statistical physics, to Gaussian geometry, metric/Banach spaces, and social choice theory. The intent of this book is both to develop the foundations of the field and to give a wide (though far from exhaustive) overview of its applications. Each chapter ends with a highlight showing the power of analysis of Boolean functions in different subject areas: property testing, social choice, cryptography, circuit complexity, learning theory, pseudorandomness, hardness of approximation, concrete complexity, and random graph theory. The book can be used as a reference for working researchers or as the basis of a one-semester graduate-level course. The author has twice taught such a course at Carnegie Mellon University, attended mainly by graduate students in computer science and mathematics but also by advanced undergraduates, postdocs, and researchers in adjacent fields. In both years most of Chapters 1-5 and 7 were covered, along with parts of Chapters 6, 8, 9, and 11, and some additional material on additive combinatorics. Nearly 500 exercises are provided at the ends of the books chapters.
With the advancement of the idea of the HVDC grid, it becomes imperative to study the interaction of controller and identification of modes of oscillations. The paper presents the complete model of HVDC grid with detailed modeling of controllers, phase lock loops (PLLs), dc grid and the ac systems. An analytical method combining participation factors and Eigen-sensitivity is proposed to determine the relative stability of the HVDC grid with respect to parameter variations. The paper also proposes the identification of inter-area and controller interaction modes on the basis of the nearest distance between the eigenvalues using the derived sensitivity indices. The critical parameters are varied in a mixed short circuit ratio (SCR) HVDC grid and predictions from the analysis method are confirmed with time-domain simulation in PSCAD simulator
In this paper, we present a novel approach to identify the generators and states responsible for the small-signal stability of power networks. To this end, the newly developed notion of information transfer between the states of a dynamical system is used. In particular, using the concept of information transfer, which characterizes influence between the various states and a linear combination of states of a dynamical system, we identify the generators and states which are responsible for causing instability of the power network. While characterizing influence from state to state, information transfer can also describe influence from state to modes thereby generalizing the well-known notion of participation factor while at the same time overcoming some of the limitations of the participation factor. The developed framework is applied to study the three bus system identifying various cause of instabilities in the system. The simulation study is extended to IEEE 39 bus system.
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