Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

A Cryptosystem Using the Concepts of Algebraic Geometric Code

Cryptosystem using linear codes was developed in 1978 by Mc-Eliece. Later in 1985 Niederreiter and others developed a modified version of cryptosystem using concepts of linear codes. But these systems were not used frequently because of its larger key size. In this study we were designing a cryptosystem using the concepts of algebraic geometric codes with smaller key size. Error detection and correction can be done efficiently by simple decoding methods using the cryptosystem developed. Approach: Algebraic geometric codes are codes, generated using curves. The cryptosystem use basic concepts of elliptic curves cryptography and generator matrix. Decrypted information takes the form of a repetition code. Due to this complexity of decoding procedure is reduced. Error detection and correction can be carried out efficiently by solving a simple system of linear equations, there by imposing the concepts of security along with error detection and correction. Results: Implementation of the algorithm is done on MATLAB and comparative analysis is also done on various parameters of the system. Attacks are common to all cryptosystems. But by securely choosing curve, field and representation of elements in field, we can overcome the attacks and a stable system can be generated. Conclusion: The algorithm defined here protects the information from an intruder and also from the error in communication channel by efficient error correction methods.

Reinforcement Learning Approaches to Power System Scheduling

One major component of power system operation is generation scheduling. The objective of the work is to develop efficient control strategies to the power scheduling problems through Reinforcement Learning approaches. The three important active power scheduling problems are Unit Commitment, Economic Dispatch and Automatic Generation Control. Numerical solution methods proposed for solution of power scheduling are insufficient in handling large and complex systems. Soft Computing methods like Simulated Annealing, Evolutionary Programming etc., are efficient in handling complex cost functions, but find limitation in handling stochastic data existing in a practical system. Also the learning steps are to be repeated for each load demand which increases the computation time.Reinforcement Learning (RL) is a method of learning through interactions with environment. The main advantage of this approach is it does not require a precise mathematical formulation. It can learn either by interacting with the environment or interacting with a simulation model. Several optimization and control problems have been solved through Reinforcement Learning approach. The application of Reinforcement Learning in the field of Power system has been a few. The objective is to introduce and extend Reinforcement Learning approaches for the active power scheduling problems in an implementable manner. The main objectives can be enumerated as:(i) Evolve Reinforcement Learning based solutions to the Unit Commitment Problem.(ii) Find suitable solution strategies through Reinforcement Learning approach for Economic Dispatch. (iii) Extend the Reinforcement Learning solution to Automatic Generation Control with a different perspective. (iv) Check the suitability of the scheduling solutions to one of the existing power systems.First part of the thesis is concerned with the Reinforcement Learning approach to Unit Commitment problem. Unit Commitment Problem is formulated as a multi stage decision process. Q learning solution is developed to obtain the optimwn commitment schedule. Method of state aggregation is used to formulate an efficient solution considering the minimwn up time I down time constraints. The performance of the algorithms are evaluated for different systems and compared with other stochastic methods like Genetic Algorithm.Second stage of the work is concerned with solving Economic Dispatch problem. A simple and straight forward decision making strategy is first proposed in the Learning Automata algorithm. Then to solve the scheduling task of systems with large number of generating units, the problem is formulated as a multi stage decision making task. The solution obtained is extended in order to incorporate the transmission losses in the system. To make the Reinforcement Learning solution more efficient and to handle continuous state space, a fimction approximation strategy is proposed. The performance of the developed algorithms are tested for several standard test cases. Proposed method is compared with other recent methods like Partition Approach Algorithm, Simulated Annealing etc.As the final step of implementing the active power control loops in power system, Automatic Generation Control is also taken into consideration.Reinforcement Learning has already been applied to solve Automatic Generation Control loop. The RL solution is extended to take up the approach of common frequency for all the interconnected areas, more similar to practical systems. Performance of the RL controller is also compared with that of the conventional integral controller.In order to prove the suitability of the proposed methods to practical systems, second plant ofNeyveli Thennal Power Station (NTPS IT) is taken for case study. The perfonnance of the Reinforcement Learning solution is found to be better than the other existing methods, which provide the promising step towards RL based control schemes for practical power industry.Reinforcement Learning is applied to solve the scheduling problems in the power industry and found to give satisfactory perfonnance. Proposed solution provides a scope for getting more profit as the economic schedule is obtained instantaneously. Since Reinforcement Learning method can take the stochastic cost data obtained time to time from a plant, it gives an implementable method. As a further step, with suitable methods to interface with on line data, economic scheduling can be achieved instantaneously in a generation control center. Also power scheduling of systems with different sources such as hydro, thermal etc. can be looked into and Reinforcement Learning solutions can be achieved.

Novel Approaches to Biodegradable Polymers: Synthesis and Biodegradation Studies

Biodegradable polymers have opened an emerging area of great interest because they are the ultimate solution for the disposal problems of synthetic polymers used for short time applications in the environmental and biomedical field. The biodegradable polymers available until recently have a number of limitations in terms of strength and dimensional stability. Most of them have processing problems and are also very expensive. Recent developments in biodegradable polymers show that monomers and polymers obtained from renewable resources are important owing to their inherent biodegradability, biocompatibility and easy availability. The present study is, therefore, mostly concemed with the utilization of renewable resources by effecting chemical modification/copolymerization on existing synthetic polymers/natural polymers for introducing better biodegradability and material properties.The thesis describes multiple approaches in the design of new biodegradable polymers: (1) Chemical modification of an existing nonbiodegradable polymer, polyethylene, by anchoring monosaccharides after functionalization to introduce biodegradability. (2) Copolymerization of an existing biodegradable polymer, polylactide, with suitable monomers and/or polymers to tailor their properties to suit the emerging requirements such as (2a) graft copolymerization of lactide onto chitosan to get controlled solvation and biodegradability and (2b) copolymerization of polylactide with cycloaliphatic amide segments to improve upon the thermal properties and processability.

“Development of lymphoid cell culture system from Penaeus monodon and molecular approaches for its transformation

Unveiling the molecular and regulatory mechanisms that prevent in vitro transformation in shrimp remains elusive in the development of continuous cell lines, with an arduous history of over 25 years (Jayesh et al., 2012). Despite presenting challenges to researchers in developing a cell line, the billion dollar aquaculture industry is under viral threat. In addition, the regulatory mechanisms that prevent in vitro transformation and carcinoma in shrimps might provide new leads for the development of anti-ageing and anti-cancer interventions in human (Vogt, 2011) and in higher vertebrates. This highlights the importance of developing shrimp cell lines, to bring out effective prophylactics against shrimp viruses and for understanding the mechanism that induce cancer and ageing in human.. Advances in molecular biology and various gene transfer technologies for immortalization of cells have resulted in the development of hundreds of cell lines from insects and mammals, but yet not a single cell line has been developed from shrimp and other marine invertebrates. With this backdrop, the research described in this thesis attempted to develop molecular tools for induced in vitro transformation in lymphoid cells from Penaeus monodon and for the development of continuous cell lines using conventional and novel technologies to address the problems at cellular and molecular level.

“Improved Feature Extraction and Classification Techniques for Multispectral Brain Magnetic Resonance Images”

Magnetic Resonance Imaging (MRI) is a multi sequence medical imaging technique in which stacks of images are acquired with different tissue contrasts. Simultaneous observation and quantitative analysis of normal brain tissues and small abnormalities from these large numbers of different sequences is a great challenge in clinical applications. Multispectral MRI analysis can simplify the job considerably by combining unlimited number of available co-registered sequences in a single suite. However, poor performance of the multispectral system with conventional image classification and segmentation methods makes it inappropriate for clinical analysis. Recent works in multispectral brain MRI analysis attempted to resolve this issue by improved feature extraction approaches, such as transform based methods, fuzzy approaches, algebraic techniques and so forth. Transform based feature extraction methods like Independent Component Analysis (ICA) and its extensions have been effectively used in recent studies to improve the performance of multispectral brain MRI analysis. However, these global transforms were found to be inefficient and inconsistent in identifying less frequently occurred features like small lesions, from large amount of MR data. The present thesis focuses on the improvement in ICA based feature extraction techniques to enhance the performance of multispectral brain MRI analysis. Methods using spectral clustering and wavelet transforms are proposed to resolve the inefficiency of ICA in identifying small abnormalities, and problems due to ICA over-completeness. Effectiveness of the new methods in brain tissue classification and segmentation is confirmed by a detailed quantitative and qualitative analysis with synthetic and clinical, normal and abnormal, data. In comparison to conventional classification techniques, proposed algorithms provide better performance in classification of normal brain tissues and significant small abnormalities.

Molecular Approaches For Characterization And Determination Of Pathogenicity Of Vibrios With Special Reference To Vibrio Harveyi From Penaeus Monodon Larval Production Systems

The present study focuses on vibrios especially Vibrio harveyi isolated from shrimp (P. monodon) larval production systems from both east and west coasts during times of mortality. A comprehensive approach has been made to work out their systematics through numerical taxonomy and group them based on RAPD profiling and to segregate the virulent from non- virulent isolates based on the presence of virulent genes as well as their phenotypic expression. The information gathered has helped to develop a simple scheme of identification based on phenotypic characters and segregate the virulent from non virulent strains of V. harveyi.

Algebraic Geometric Codes and their relation to Cryptography using Elliptic Curves

Communication is the process of transmitting data across channel. Whenever data is transmitted across a channel, errors are likely to occur. Coding theory is a stream of science that deals with finding efficient ways to encode and decode data, so that any likely errors can be detected and corrected. There are many methods to achieve coding and decoding. One among them is Algebraic Geometric Codes that can be constructed from curves. Cryptography is the science ol‘ security of transmitting messages from a sender to a receiver. The objective is to encrypt message in such a way that an eavesdropper would not be able to read it. A eryptosystem is a set of algorithms for encrypting and decrypting for the purpose of the process of encryption and decryption. Public key eryptosystem such as RSA and DSS are traditionally being prel‘en‘ec| for the purpose of secure communication through the channel. llowever Elliptic Curve eryptosystem have become a viable altemative since they provide greater security and also because of their usage of key of smaller length compared to other existing crypto systems. Elliptic curve cryptography is based on group of points on an elliptic curve over a finite field. This thesis deals with Algebraic Geometric codes and their relation to Cryptography using elliptic curves. Here Goppa codes are used and the curves used are elliptic curve over a finite field. We are relating Algebraic Geometric code to Cryptography by developing a cryptographic algorithm, which includes the process of encryption and decryption of messages. We are making use of fundamental properties of Elliptic curve cryptography for generating the algorithm and is used here to relate both.

Reinforcement Learning approaches to Economic Dispatch problem

This paper presents Reinforcement Learning (RL) approaches to Economic Dispatch problem. In this paper, formulation of Economic Dispatch as a multi stage decision making problem is carried out, then two variants of RL algorithms are presented. A third algorithm which takes into consideration the transmission losses is also explained. Efficiency and flexibility of the proposed algorithms are demonstrated through different representative systems: a three generator system with given generation cost table, IEEE 30 bus system with quadratic cost functions, 10 generator system having piecewise quadratic cost functions and a 20 generator system considering transmission losses. A comparison of the computation times of different algorithms is also carried out.

Characterization and applications of two protease enzymes obtained by culture dependent and independent approaches from mangrove sediments

Soil community genomics or metagenomics is employed in this study to analyze the evolutionary related - ness of mangrove microbial community. The metagenomic DNA was isolated from mangrove sediment and 16SrDNA was amplified using universal primers. The amplicons were ligated into pTZ57R/T cloning vector and transformed onto E. coli JM109 host cells. The recombinant plasmids were isolated from positive clones and the insert was confirmed by its reamplification. The amplicons were subjected to Amplified Ribosomal DNA Restriction Analysis (ARDRA) using three different tetra cutter restriction enzymes namely Sau3A1, Hha1 and HpaII. The 16SrDNA insert were sequenced and their identity was determined. The sequences were submitted to NCBI database and accession numbers obtained. The phylo - genetic tree was constructed based on Neighbor-Joining technique. Clones belonged to two major phyla of the bacterial domain, namely Firmicutes and Proteobacteria, with members of Firmicutes predominating. The microbial diversity of the mangrove sediment was explored in this manner.