 Open Access
 Authors : Lakshmi Bharathi S , Dr. Vidya Niranjan , Sudhamshu Mohan S
 Paper ID : IJERTV9IS010132
 Volume & Issue : Volume 09, Issue 01 (January 2020)
 Published (First Online): 20072021
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
State Machine based Framework for Genomic Analysis
1. Lakshmi Bharathi S, 2. Dr. Vidya Niranjan, 3. Sudhamshu Mohan S
Mysore Road, R V Vidyanikethan, Bengaluru 560059, Karnataka, India
INTRODUCTION
The extensibility of Finite State Machines (FSM) to different disciplines viz., networking, compiler design, marketing, etc., is highly appreciated for its optimal and precise solutions to respective problems[12]. The attempt of attributing states of a FSM to biological data, specifically to genes is rarely endeavored because it is very difficult to visualize and represent states and events corresponding to genomic data. This constraint paved the way in looking for a transform using which representable genomic states and events could be realized. The subsequent sections of this paper introduce to such a linear transform thereby the mapping of genes leads to mathematically representable states[17].
METHODOLOGY

Gene Representation
Let = {G1, G2, GN} be the genes present in a genome, where G1, G2,GN are genes. As there we be a really large set of genes present in genome. This representation can lead to a very large set.
Mathematically contains finite set of genes, however large it might be. We can use mathematically convenient representations which are computationally appreciable
= {G1, G2, GN}
General flow of the framework
Where, is impulsive only at kth index where gene is present. In fact, will have a value unity where genek exists and is equal to 0 elsewhere. This throws focus on mathematical representation of nucleotides A T G C.
Bergen and Antoniou proposed a method based on complex representation, parametric window function and STDFT to maximize SNR (Signal to Noise Ratio) to identify coding regions of the genes
A= 0.10+0.12j; T= 0.300.20j;
G=0.450.19j; C=0
Graphical representation of nucleotides

Gene Function
is complex in nature.
which is a Such that leads to a numerical value V which
should be a convergent function.
Where Where, n is the position of nucleotide within a gene
Where, is the arithmetic mean of gene, l is the number of nucleotides within a gene is the mean of the nucleotide
the variance of the nucleotide
So, we will have each gene getting mapped to a number, uniqueness of this value increases with increase in number of parameters, that is if we go for and , the value we get will be more unique.

Representation using Gene Function
can be represented as a righthanded sequence starting from origin till valN.
Similarly, we can also represent the query sequence.
Now we have mathematically representable sequences and numbers which are unique.

Gene Convolution
Genome convolution is the convolution of these sequences
(G)
G1 G2
GN
Reference axis
Here, G1, G2, GN are complex in nature.
Q(G)
G1 G2
Gn
Reference axis
Similarly, Reference gene RG corresponds to some value.
With all these assumptions, we need to find the 1 and 2 Where,
and
1(G) and 2(G) are the resultants obtained by convolving genomic sequence with the query sequence and genomic sequence with the reference sequence.[13]
If 1(G) and 2(G) are of bigger length, we need to use transformation. (1(G), 2(G))
We need to first reduce the feature space of 1(G) and 2(G) using K means algorithm, if the feature space is very large to the best samples.

Scoring Mechanism
Now, scoring mechanism needs to be employed This will be a rectangular matrix of order p*q. pq = (1(G) – 2(G))/
where, is the determinant.
We need to make order (r*r) where R is the LCM(p,q) = We need to make all the remaining entries 0 by appending it everywhere
Now, the determinant needs to be calculated

States (Key Players)
Now try to make the matrix upper/lower triangular or try to diagonalize it (Echelon forms).
The remaining entries now are the key players of our analysis. If the matrix is diagonalizable then analysis becomes easy. Judgement (J) from the key players will be based on the learning methods.
Inputs for learning are
[Principal diagonal elements or Triangular matrix] + [Determinant obtained from matrix] + [Rank of the matrix]Using some machine learning techniques like multilayered perception or SVM we can train some of the inputs. Involving reference genes for a given genome with some of the query sequences (around 3040 samples)
Then by using this binary classifier we can make a decision for a particular analysis.

SVM based Binary Classifier
Training inputs
Output Range
Ref Gene +Genome +Query sequence
Decide on output range of values
II. CONSTRAINTS FOR THE APPLICATION OF THIS METHOD

Gene Representation
To mathematically represent a gene, following parameters need to be decided.

All the nucleotides must be unique i.e., the number corresponding to each nucleotide must be different from others.

These numbers must be linearly independent and should not belong to same linear space.

Orthogonality is the most preferred feature to introduce the uniqueness in the analysis.

Each nucleotide will be a point on complex plane. (Splane in Laplace plane)
Imaginary plane
Gene
Real Plane


Gene Function

It should be convergent

It should be definitive, continuous and differentiable

Periodic and nonperiodic properties need to be studied further


Scoring Mechanism

As this involves finding key players (numbers) that is finding triangular elements or diagonal elements, the values are highly uncorrelated.

Dividing the values by determinant will normalize the values.

APPLICATIONS
This idea could be transformed as a framework for Genomic Analysis, primarily intended to characterize nucleotide, gene, genome and their expressions in a mathematically coherent way.[14] The inherent modularity of this framework ensures to enhance and improve performance of each stage independently. As the crux of the framework is principally derived harnessing the concept of linear systems viz. Convolution, Linear Transformation Cartesian Association, K means Clustering, Discrete Differentiation, Characteristic Equations followed by a training method based on Support Vector Machines, the approach employed is robust, simple, conclusive and reliable.[16]
The tangibility of this approach is derived from the philosophy of Linearization of Sample Space.[13] This novel approach shapes & fits the noncharacterized biological data into a framework where one can apply any of the Linear Discriminative Techniques which are deterministic in nature, thus leading to conclusions which are reliable and specific in nature. [18]

FUTURE SCOPE
As this framework is modular and generic in nature, this could be enhanced and extended to techniques based on Fuzzy Logic, for better decisiveness and quantifiability of conclusions. For huge training data sets a layered approach involving Artificial
intelligencebased approach could be studied. For better characterization of Gene Functions, we can even go for multi parameter based statistical techniques for Modelling, which are based on Curvature based analysis.

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