An analogue of the logistic map in two dimensions

This is a sequel to our earlier work on the modulated logistic map. Here, we first show that the map comes under the universality class of Feigenbaum. We then give evidence for the fact that our model can generate strange attractors in the unit square for an uncountable number of parameter values in the range μ∞<μ<1. Numerical plots of the attractor for several values of μ are given and the self-similar structure is explicity shown in one case. The fractal and information dimensions of the attractors for many values of μ are shown to be greater than one and the variation in their structure is analysed using the two Lyapunov exponents of the system. Our results suggest that the map can be considered as an analogue of the logistic map in two dimensions and may be useful in describing certain higher dimensional chaotic phenomena.

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.

DNA Sequence Representation methods

DNA sequence representation methods are used to denote a gene structure effectively and help in similarities/dissimilarities analysis of coding sequences. Many different kinds of representations have been proposed in the literature. They can be broadly classified into Numerical, Graphical, Geometrical and Hybrid representation methods. DNA structure and function analysis are made easy with graphical and geometrical representation methods since it gives visual representation of a DNA structure. In numerical method, numerical values are assigned to a sequence and digital signal processing methods are used to analyze the sequence. Hybrid approaches are also reported in the literature to analyze DNA sequences. This paper reviews the latest developments in DNA Sequence representation methods. We also present a taxonomy of various methods. A comparison of these methods where ever possible is also done

Content Based Image Retrieval System for Malayalam Handwritten Characters

Content Based Image Retrieval is one of the prominent areas in Computer Vision and Image Processing. Recognition of handwritten characters has been a popular area of research for many years and still remains an open problem. The proposed system uses visual image queries for retrieving similar images from database of Malayalam handwritten characters. Local Binary Pattern (LBP) descriptors of the query images are extracted and those features are compared with the features of the images in database for retrieving desired characters. This system with local binary pattern gives excellent retrieval performance

Using Neural Network Classifier Support Vector Machine Regression for the prediction of Melting Point of Drug – like compounds

In our study we use a kernel based classification technique, Support Vector Machine Regression for predicting the Melting Point of Drug – like compounds in terms of Topological Descriptors, Topological Charge Indices, Connectivity Indices and 2D Auto Correlations. The Machine Learning model was designed, trained and tested using a dataset of 100 compounds and it was found that an SVMReg model with RBF Kernel could predict the Melting Point with a mean absolute error 15.5854 and Root Mean Squared Error 19.7576

Hybrid Background Subtraction in Video using Bi-level CodeBook Model

Detection of Objects in Video is a highly demanding area of research. The Background Subtraction Algorithms can yield better results in Foreground Object Detection. This work presents a Hybrid CodeBook based Background Subtraction to extract the foreground ROI from the background. Codebooks are used to store compressed information by demanding lesser memory usage and high speedy processing. This Hybrid method which uses Block-Based and Pixel-Based Codebooks provide efficient detection results; the high speed processing capability of block based background subtraction as well as high Precision Rate of pixel based background subtraction are exploited to yield an efficient Background Subtraction System. The Block stage produces a coarse foreground area, which is then refined by the Pixel stage. The system’s performance is evaluated with different block sizes and with different block descriptors like 2D-DCT, FFT etc. The Experimental analysis based on statistical measurements yields precision, recall, similarity and F measure of the hybrid system as 88.74%, 91.09%, 81.66% and 89.90% respectively, and thus proves the efficiency of the novel system.

Content Based Video Retrieval using SURF Descriptor

This paper presents a Robust Content Based Video Retrieval (CBVR) system. This system retrieves similar videos based on a local feature descriptor called SURF (Speeded Up Robust Feature). The higher dimensionality of SURF like feature descriptors causes huge storage consumption during indexing of video information. To achieve a dimensionality reduction on the SURF feature descriptor, this system employs a stochastic dimensionality reduction method and thus provides a model data for the videos. On retrieval, the model data of the test clip is classified to its similar videos using a minimum distance classifier. The performance of this system is evaluated using two different minimum distance classifiers during the retrieval stage. The experimental analyses performed on the system shows that the system has a retrieval performance of 78%. This system also analyses the performance efficiency of the low dimensional SURF descriptor.

Performance Study of an Improved Legendre Moment Descriptor as Region-Based Shape Descriptor

This paper reports a novel region-based shape descriptor based on orthogonal Legendre moments. The preprocessing steps for invariance improvement of the proposed Improved Legendre Moment Descriptor (ILMD) are discussed. The performance of the ILMD is compared to the MPEG-7 approved region shape descriptor, angular radial transformation descriptor (ARTD), and the widely used Zernike moment descriptor (ZMD). Set B of the MPEG-7 CE-1 contour database and all the datasets of the MPEG-7 CE-2 region database were used for experimental validation. The average normalized modified retrieval rate (ANMRR) and precision- recall pair were employed for benchmarking the performance of the candidate descriptors. The ILMD has lower ANMRR values than ARTD for most of the datasets, and ARTD has a lower value compared to ZMD. This indicates that overall performance of the ILMD is better than that of ARTD and ZMD. This result is confirmed by the precision-recall test where ILMD was found to have better precision rates for most of the datasets tested. Besides retrieval accuracy, ILMD is more compact than ARTD and ZMD. The descriptor proposed is useful as a generic shape descriptor for content-based image retrieval (CBIR) applications