Mean Squared Residue Based Biclustering Algorithms for the Analysis of Gene Expression Data

Computational Biology is the research are that contributes to the analysis of biological data through the development of algorithms which will address significant research problems.The data from molecular biology includes DNA,RNA ,Protein and Gene expression data.Gene Expression Data provides the expression level of genes under different conditions.Gene expression is the process of transcribing the DNA sequence of a gene into mRNA sequences which in turn are later translated into proteins.The number of copies of mRNA produced is called the expression level of a gene.Gene expression data is organized in the form of a matrix. Rows in the matrix represent genes and columns in the matrix represent experimental conditions.Experimental conditions can be different tissue types or time points.Entries in the gene expression matrix are real values.Through the analysis of gene expression data it is possible to determine the behavioral patterns of genes such as similarity of their behavior,nature of their interaction,their respective contribution to the same pathways and so on. Similar expression patterns are exhibited by the genes participating in the same biological process.These patterns have immense relevance and application in bioinformatics and clinical research.Theses patterns are used in the medical domain for aid in more accurate diagnosis,prognosis,treatment planning.drug discovery and protein network analysis.To identify various patterns from gene expression data,data mining techniques are essential.Clustering is an important data mining technique for the analysis of gene expression data.To overcome the problems associated with clustering,biclustering is introduced.Biclustering refers to simultaneous clustering of both rows and columns of a data matrix. Clustering is a global whereas biclustering is a local model.Discovering local expression patterns is essential for identfying many genetic pathways that are not apparent otherwise.It is therefore necessary to move beyond the clustering paradigm towards developing approaches which are capable of discovering local patterns in gene expression data.A biclusters is a submatrix of the gene expression data matrix.The rows and columns in the submatrix need not be contiguous as in the gene expression data matrix.Biclusters are not disjoint.Computation of biclusters is costly because one will have to consider all the combinations of columans and rows in order to find out all the biclusters.The search space for the biclustering problem is 2 m+n where m and n are the number of genes and conditions respectively.Usually m+n is more than 3000.The biclustering problem is NP-hard.Biclustering is a powerful analytical tool for the biologist.The research reported in this thesis addresses the problem of biclustering.Ten algorithms are developed for the identification of coherent biclusters from gene expression data.All these algorithms are making use of a measure called mean squared residue to search for biclusters.The objective here is to identify the biclusters of maximum size with the mean squared residue lower than a given threshold. All these algorithms begin the search from tightly coregulated submatrices called the seeds.These seeds are generated by K-Means clustering algorithm.The algorithms developed can be classified as constraint based,greedy and metaheuristic.Constarint based algorithms uses one or more of the various constaints namely the MSR threshold and the MSR difference threshold.The greedy approach makes a locally optimal choice at each stage with the objective of finding the global optimum.In metaheuristic approaches particle Swarm Optimization(PSO) and variants of Greedy Randomized Adaptive Search Procedure(GRASP) are used for the identification of biclusters.These algorithms are implemented on the Yeast and Lymphoma datasets.Biologically relevant and statistically significant biclusters are identified by all these algorithms which are validated by Gene Ontology database.All these algorithms are compared with some other biclustering algorithms.Algorithms developed in this work overcome some of the problems associated with the already existing algorithms.With the help of some of the algorithms which are developed in this work biclusters with very high row variance,which is higher than the row variance of any other algorithm using mean squared residue, are identified from both Yeast and Lymphoma data sets.Such biclusters which make significant change in the expression level are highly relevant biologically.

Analysis of Fluctuations in the Early Universe Using Fokker-Planck Formalism

The thesis begins with a review of basic elements of general theory of relativity (GTR) which forms the basis for the theoretical interpretation of the observations in cosmology. The first chapter also discusses the standard model in cosmology, namely the Friedmann model, its predictions and problems. We have also made a brief discussion on fractals and inflation of the early universe in the first chapter. In the second chapter we discuss the formulation of a new approach to cosmology namely a stochastic approach. In this model, the dynam ics of the early universe is described by a set of non-deterministic, Langevin type equations and we derive the solutions using the Fokker—Planck formalism. Here we demonstrate how the problems with the standard model, can be eliminated by introducing the idea of stochastic fluctuations in the early universe. Many recent observations indicate that the present universe may be approximated by a many component fluid and we assume that only the total energy density is conserved. This, in turn, leads to energy transfer between different components of the cosmic fluid and fluctuations in such energy transfer can certainly induce fluctuations in the mean to factor in the equation of state p = wp, resulting in a fluctuating expansion rate for the universe. The third chapter discusses the stochastic evolution of the cosmological parameters in the early universe, using the new approach. The penultimate chapter is about the refinements to be made in the present model, by means of a new deterministic model The concluding chapter presents a discussion on other problems with the conventional cosmology, like fractal correlation of galactic distribution. The author attempts an explanation for this problem using the stochastic approach.

Identification of models using failure rate and mean residual life of doubly truncated random variables

In this paper, we study the relationship between the failure rate and the mean residual life of doubly truncated random variables. Accordingly, we develop characterizations for exponential, Pareto 11 and beta distributions. Further, we generalize the identities for fire Pearson and the exponential family of distributions given respectively in Nair and Sankaran (1991) and Consul (1995). Applications of these measures in file context of lengthbiased models are also explored

Dominant Mean Percentage Score Factors Of The Consumer Purchase Behaviour Of Passenger Cars

Globalization and liberalization, with the entry of many prominent foreign manufacturers, changed the automobile scenario in India, since early 1990’s. World Leaders in automobile manufacturing such as Ford, General Motors, Honda, Toyota, Suzuki, Hyundai, Renault, Mitsubishi, Benz, BMW, Volkswagen and Nissan set up their manufacturing units in India in joint venture with their Indian counterpart companies, by making use of the Foreign Direct Investment policy of the Government of India, These manufacturers started capturing the hearts of Indian car customers with their choice of technological and innovative product features, with quality and reliability. With the multiplicity of choices available to the Indian passenger car buyers, it drastically changed the way the car purchase scenario in India and particularly in the State of Kerala. This transformed the automobile scene from a sellers’ market to buyers’ market. Car customers started developing their own personal preferences and purchasing patterns, which were hitherto unknown in the Indian automobile segment. The main purpose of this paper is to come up with the identification of possible parameters and a framework development, that influence the consumer purchase behaviour patterns of passenger car owners in the State of Kerala, so that further research could be done, based on the framework and the identified parameters.

ECG Noise Removal using GA tuned Sign-Data Least Mean Square Algorithm

Adaptive filter is a primary method to filter Electrocardiogram (ECG), because it does not need the signal statistical characteristics. In this paper, an adaptive filtering technique for denoising the ECG based on Genetic Algorithm (GA) tuned Sign-Data Least Mean Square (SD-LMS) algorithm is proposed. This technique minimizes the mean-squared error between the primary input, which is a noisy ECG, and a reference input which can be either noise that is correlated in some way with the noise in the primary input or a signal that is correlated only with ECG in the primary input. Noise is used as the reference signal in this work. The algorithm was applied to the records from the MIT -BIH Arrhythmia database for removing the baseline wander and 60Hz power line interference. The proposed algorithm gave an average signal to noise ratio improvement of 10.75 dB for baseline wander and 24.26 dB for power line interference which is better than the previous reported works

Behavior of geopolymer concrete exposed to elevated temperatures

The research in the area of geopolymer is gaining momentum during the past 20 years. Studies confirm that geopolymer concrete has good compressive strength, tensile strength, flexural strength, modulus of elasticity and durability. These properties are comparable with OPC concrete.There are many occasions where concrete is exposed to elevated temperatures like fire exposure from thermal processor, exposure from furnaces, nuclear exposure, etc.. In such cases, understanding of the behaviour of concrete and structural members exposed to elevated temperatures is vital. Even though many research reports are available about the behaviour of OPC concrete at elevated temperatures, there is limited information available about the behaviour of geopolymer concrete after exposure to elevated temperatures. A preliminary study was carried out for the selection of a mix proportion. The important variable considered in the present study include alkali/fly ash ratio, percentage of total aggregate content, fine aggregate to total aggregate ratio, molarity of sodium hydroxide, sodium silicate to sodium hydroxide ratio, curing temperature and curing period. Influence of different variables on engineering properties of geopolymer concrete was investigated. The study on interface shear strength of reinforced and unreinforced geopolymer concrete as well as OPC concrete was also carried out. Engineering properties of fly ash based geopolymer concrete after exposure to elevated temperatures (ambient to 800 °C) were studied and the corresponding results were compared with those of conventional concrete. Scanning Electron Microscope analysis, Fourier Transform Infrared analysis, X-ray powder Diffractometer analysis and Thermogravimetric analysis of geopolymer mortar or paste at ambient temperature and after exposure to elevated temperature were also carried out in the present research work. Experimental study was conducted on geopolymer concrete beams after exposure to elevated temperatures (ambient to 800 °C). Load deflection characteristics, ductility and moment-curvature behaviour of the geopolymer concrete beams after exposure to elevated temperatures were investigated. Based on the present study, major conclusions derived could be summarized as follows. There is a definite proportion for various ingredients to achieve maximum strength properties. Geopolymer concrete with total aggregate content of 70% by volume, ratio of fine aggregate to total aggregate of 0.35, NaOH molarity 10, Na2SiO3/NaOH ratio of 2.5 and alkali to fly ash ratio of 0.55 gave maximum compressive strength in the present study. An early strength development in geopolymer concrete could be achieved by the proper selection of curing temperature and the period of curing. With 24 hours of curing at 100 °C, 96.4% of the 28th day cube compressive strength could be achieved in 7 days in the present study. The interface shear strength of geopolymer concrete is lower to that of OPC concrete. Compared to OPC concrete, a reduction in the interface shear strength by 33% and 29% was observed for unreinforced and reinforced geopolymer specimens respectively. The interface shear strength of geopolymer concrete is lower than ordinary Portland cement concrete. The interface shear strength of geopolymer concrete can be approximately estimated as 50% of the value obtained based on the available equations for the calculation of interface shear strength of ordinary portland cement concrete (method used in Mattock and ACI). Fly ash based geopolymer concrete undergoes a high rate of strength loss (compressive strength, tensile strength and modulus of elasticity) during its early heating period (up to 200 °C) compared to OPC concrete. At a temperature exposure beyond 600 °C, the unreacted crystalline materials in geopolymer concrete get transformed into amorphous state and undergo polymerization. As a result, there is no further strength loss (compressive strength, tensile strength and modulus of elasticity) in geopolymer concrete, whereas, OPC concrete continues to lose its strength properties at a faster rate beyond a temperature exposure of 600 °C. At present no equation is available to predict the strength properties of geopolymer concrete after exposure to elevated temperatures. Based on the study carried out, new equations have been proposed to predict the residual strengths (cube compressive strength, split tensile strength and modulus of elasticity) of geopolymer concrete after exposure to elevated temperatures (upto 800 °C). These equations could be used for material modelling until better refined equations are available. Compared to OPC concrete, geopolymer concrete shows better resistance against surface cracking when exposed to elevated temperatures. In the present study, while OPC concrete started developing cracks at 400 °C, geopolymer concrete did not show any visible cracks up to 600 °C and developed only minor cracks at an exposure temperatureof 800 °C. Geopolymer concrete beams develop crack at an early load stages if they are exposed to elevated temperatures. Even though the material strength of the geopolymer concrete does not decrease beyond 600 °C, the flexural strength of corresponding beam reduces rapidly after 600 °C temperature exposure, primarily due to the rapid loss of the strength of steel. With increase in temperature, the curvature at yield point of geopolymer concrete beam increases and thereby the ductility reduces. In the present study, compared to the ductility at ambient temperature, the ductility of geopolymer concrete beams reduces by 63.8% at 800 °C temperature exposure. Appropriate equations have been proposed to predict the service load crack width of geopolymer concrete beam exposed to elevated temperatures. These equations could be used to limit the service load on geopolymer concrete beams exposed to elevated temperatures (up to 800 °C) for a predefined crack width (between 0.1mm and 0.3 mm) or vice versa. The moment-curvature relationship of geopolymer concrete beams at ambient temperature is similar to that of RCC beams and this could be predicted using strain compatibility approach Once exposed to an elevated temperature, the strain compatibility approach underestimates the curvature of geopolymer concrete beams between the first cracking and yielding point.