CVT and XOR are two binary operations together used to calculate the sum of two non-negative integers on using a recursive mechanism. In this present study the convergence behaviors of this recursive mechanism has been captured through a tree like st
ructure named as CVT-XOR Tree. We have analyzed how to identify the parent nodes, leaf nodes and internal nodes in the CVT-XOR Tree. We also provide the parent information, depth information and the number of children of a node in different CVT-XOR Trees on defining three different matrices. Lastly, one observation is made towards very old Mathematical problem of Goldbach Conjecture.
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.
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 i
n 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 stabilit
y 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.
Intricate comparison between two given tertiary structures of proteins is as important as the comparison of their functions. Several algorithms have been devised to compute the similarity and dissimilarity among protein structures. But, these algorit
hms compare protein structures by structural alignment of the protein backbones which are usually unable to determine precise differences. In this paper, an attempt has been made to compute the similarities and dissimilarities among 3D protein structures using the fundamental mathematical morphology operations and fractal geometry which can resolve the problem of real differences. In doing so, two techniques are being used here in determining the superficial structural (global similarity) and local similarity in atomic level of the protein molecules. This intricate structural difference would provide insight to Biologists to understand the protein structures and their functions more precisely.
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where only one affi
ne Boolean function belongs to each class. Two different methods are proposed to achieve this classification. The first method is a recursive procedure that uses the Cartesian product of sets starting from the set of 1-variable Boolean function and in the second method classification is achieved through a set of invariant bit positions with respect to an affine function belonging to that class. The invariant bit positions also provide information concerning the size and symmetry properties of the classes/sub-classes, such that the members of classes/sub-classes satisfy certain similar properties.
This paper presents a spatial encryption technique for secured transmission of data in networks. The algorithm is designed to break the ciphered data packets into multiple data which are to be packaged into a spatial template. A secure and efficient
mechanism is provided to convey the information that is necessary for obtaining the original data at the receiver-end from its parts in the packets. An authentication code (MAC) is also used to ensure authenticity of every packet.
Ligands for only two human olfactory receptors are known. One of them, OR1D2, binds to Bourgeonal [Malnic B, Godfrey P-A, Buck L-B (2004) The human olfactory receptor gene family. Proc. Natl. Acad. Sci U. S. A. 101: 2584-2589 and Erratum in: Proc Nat
l Acad Sci U. S. A. (2004) 101: 7205]. OR1D2, OR1D4 and OR1D5 are three full length olfactory receptors present in an olfactory locus in human genome. These receptors are more than 80% identical in DNA sequences and have 108 base pair mismatches among them. We have used L-system mathematics and have been able to show a closely related subfamily of OR1D2, OR1D4 and OR1D5.
In this paper we have defined one function that has been used to construct different fractals having fractal dimensions between 1.58 and 2. Also, we tried to calculate the amount of increment of fractal dimension in accordance with the base of the nu
mber systems. Further, interestingly enough, these very fractals could be a frame of lyrics for the musicians, as we know that the fractal dimension of music is around 1.65 and varies between a high of 1.68 and a low of 1.60. Further, at the end we conjecture that the switching from one music fractal to another is nothing but enhancing a constant amount fractal dimension which might be equivalent to a kind of different sets of musical notes in various orientations.
In this paper we have used one 2 variable Boolean function called Rule 6 to define another beautiful transformation named as Extended Rule-6. Using this function we have explored the algebraic beauties and its application to an efficient Round Robin
Tournament (RRT) routine for 2k (k is any natural number) number of teams. At the end, we have thrown some light towards any number of teams of the form nk where n, k are natural numbers.
