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.

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.

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.

Farm Programmes of Electronic Media: A Comparative Study of Audience Perception in Kerala

Farm communication and extension programs are vital part of the farm development attempts. Electronic media plays a major role in farm extension activities. Kerala, the consumer state, which was a complete agricultural state in pre-independence period, is the sprouting land of agricultural extension and publication activities in print media. Later AIR (All India Radio) farm programs and farm broadcasting of Doordarshan enriched the role of electronic media in farm extension activities. The media saturated southern state of India received this new electronic media farm communication revolution whole heartedly. However, after 1990, Kerala witnessed a flood of private T V channels and currently there are 24 channels in this regional language, named Malayalam. All major news and entertainment channels are broadcasting farm programs. Farm programs of AIR and Doordarshan, broadcasted in Malayalam language, have been well accepted to the farmers‘ in Kerala. However, post-independence period, witnessed the formation of Kerala state in Indian Union and the first ballot-elected communist Government started its administration. After the land reform bills, the state witnessed a gradual decrease in agricultural production. Even if it is not reflected much in the attitude and practices of farm community and farm broadcast of traditional electronic broadcasting, a change is observable after the post-liberalization era of India. Private Television channels, which were focused on entertainment value of programs, started broadcasting farm programs and the parameters of program production went through certain changes. In this situation, there is ample relevance for a study about the farm programs of electronic media in terms of a comparative study of audience perception. The study is limited in the state of Kerala as it is the most media saturated state in India. The study analyzes the rate, nature and scope of adoption of farming methods transmitted through electronic media (T.V. and Radio) in Malayalam language.All kinds of Farm programs including comprehensive program serials, success stories, seasonal cropping methods, experts opinion, been analyzed on the basis of the following objectives.  To find whether propagating new farm methods through farm programs in electronic media or the availability of adequate infrastructure and economic factors make a farmer to adopt a new farming method.  To find which electronic media has more influence on farmers to adopt agricultural programs.  To find which form of electronic media gets better feedback from farmers  To find out whether the programs of T.V. or Radio is more acceptable to farmers than the print media.  To find whether farmers gets the message through their preferred medium for the message. The researcher recorded opinions from a panel of agricultural officers, farm Information officers, agro extension researchers and experts. According to their opinions and guidelines, a pilot study is designed and conducted in Kanjikuzhy Panchayath, in Alappuzha district, Kerala. The Panchayath is selected by considering its ideal nature of being the sample for a social Science research. Besides, the nature of farming in the Panchayath, which devoid of the cultivation of cash crops also supported its sample value. As per the observations from the pilot study, researcher confirmed the Triangulation method as the methodology of research. The questionnaire survey, being the primary part contained 42 Questions with 6 independent and 32 dependent variables. The survey is conducted among 400 respondents in Idukki, Alappuzha and Pathanamthitta districts considering geographical differences and distribution of different types of crops. The response from a total of 360 respondents, 120 from each district, finally selected for tabulation and data analysis.The data analysis, based on percentage analysis, along with the results from focus group discussion among a selected group of 20 farmers, together produced the results as follows. Farmers, who are the audience of farm programs, have a very serious approach towards the medium. They are maintaining a critical point of view towards the content of the programs. Farmers are reasonably aware about the financial side of the programs and the monitory aspirations of both private and Government owned Television channels. Even though, the farmers are not aware on the technical terminology and jargons, they have ideas about success stories, program serials and they are even informed about channels are not maintaining an audience research section like AIR. Though the farmers accept Doordarshan as the credential source of farm information and methods, they are inclined to the entertainment value of programs too. They prefer to have more entertainment value for the programs of Doordarshan. Surprisingly, they have very solid suggestions on even about the shots which add entertainment value to the farm broadcasting methods of Doordarshan. Farmers are very much aware about the fact that media is just an instrument for inspiration and persuasion. They strongly believe that the source of information and new methods is agricultural research and an effective change happens only when there are adequate infrastructure and marketing facilities, along with the proper support from Government agricultural guideline and support systems like Krishi Bhavans. They strongly believe that media alone cannot create any magic in increasing agricultural production. Farmers are pointing out the lack of response to the feedback and queries of farmers on farming methods, as an evidence for the difference in levels of commitment of Government and private owned Television channels.Farmers are still perceiving AIR farm programs are far more committed to farmers and farming than any other electronic medium. However, they are seriously lacking Radio receivers with medium wave reception facility. Farmers perceive that the farming methods on new crops are more adoptable than the farming methods of traditional crops in both private and Government owned Television channels. There are multiple factors behind this observation from farmers. Farmers changed in terms of viewing habits and they prefer success stories, which are totally irrelevant and they even think that such stories encourage people to go for farming and they opined that such stories are good sources of inspiration. However, they are all very much sure about the importance and particular about the presence of entertainment factor even in farm programs. Farmers expect direct interaction of any expert of the new farming method to implement the method in their agriculture practices. Though introduction of a new idea in the T.V. is acceptable, farmers need the direct instruction of expert on field to start implementing the new farming practices Farmers still have an affinity towards print media reports and agricultural pages and they have complaints to print media on the removal of agricultural information pages from news papers. They prefer the reports in print media as it facilitates them to collect and refer articles when they need it. Farmers are having an eye of doubt about the credibility of farm programs by private T.V. channels. Even if they prefer private Television channels for listening and adopting new farming methods and other farm information, they scrutinize programs to know whether they are sponsored programs by agrochemical or agro-fertilizer manufacturer.

Studies in molecular mechanics using spectroscopic data exact force field and bond in homogeneity

This thesis deals with some studies in molecular mechanic using spectroscopic data. It includes an improvement in the parameter technique for the evaluation of exact force fields, the introduction of a new and simple algebraic method for the force field calculation and a study of asymmetric variation of bonding forces along a bond.

Some problems in set topology relating group of homeomorphisms and order

In this thesis we investigate some problems in set theoretical topology related to the concepts of the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms. This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention

“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.

Development of Techniques for the Automatic Extraction and Grade Detection of Glioma Tumors from Conventional Brain Magnetic Resonant Images

Cerebral glioma is the most prevalent primary brain tumor, which are classified broadly into low and high grades according to the degree of malignancy. High grade gliomas are highly malignant which possess a poor prognosis, and the patients survive less than eighteen months after diagnosis. Low grade gliomas are slow growing, least malignant and has better response to therapy. To date, histological grading is used as the standard technique for diagnosis, treatment planning and survival prediction. The main objective of this thesis is to propose novel methods for automatic extraction of low and high grade glioma and other brain tissues, grade detection techniques for glioma using conventional magnetic resonance imaging (MRI) modalities and 3D modelling of glioma from segmented tumor slices in order to assess the growth rate of tumors. Two new methods are developed for extracting tumor regions, of which the second method, named as Adaptive Gray level Algebraic set Segmentation Algorithm (AGASA) can also extract white matter and grey matter from T1 FLAIR an T2 weighted images. The methods were validated with manual Ground truth images, which showed promising results. The developed methods were compared with widely used Fuzzy c-means clustering technique and the robustness of the algorithm with respect to noise is also checked for different noise levels. Image texture can provide significant information on the (ab)normality of tissue, and this thesis expands this idea to tumour texture grading and detection. Based on the thresholds of discriminant first order and gray level cooccurrence matrix based second order statistical features three feature sets were formulated and a decision system was developed for grade detection of glioma from conventional T2 weighted MRI modality.The quantitative performance analysis using ROC curve showed 99.03% accuracy for distinguishing between advanced (aggressive) and early stage (non-aggressive) malignant glioma. The developed brain texture analysis techniques can improve the physician’s ability to detect and analyse pathologies leading to a more reliable diagnosis and treatment of disease. The segmented tumors were also used for volumetric modelling of tumors which can provide an idea of the growth rate of tumor; this can be used for assessing response to therapy and patient prognosis.

Face Recognition using Probabilistic Neural Networks

In this paper we address the problem of face detection and recognition of grey scale frontal view images. We propose a face recognition system based on probabilistic neural networks (PNN) architecture. The system is implemented using voronoi/ delaunay tessellations and template matching. Images are segmented successfully into homogeneous regions by virtue of voronoi diagram properties. Face verification is achieved using matching scores computed by correlating edge gradients of reference images. The advantage of classification using PNN models is its short training time. The correlation based template matching guarantees good classification results

Face Recognition using Probabilistic Neural Networks

n this paper we address the problem of face detection and recognition of grey scale frontal view images. We propose a face recognition system based on probabilistic neural networks (PNN) architecture. The system is implemented using voronoi/ delaunay tessellations and template matching. Images are segmented successfully into homogeneous regions by virtue of voronoi diagram properties. Face verification is achieved using matching scores computed by correlating edge gradients of reference images. The advantage of classification using PNN models is its short training time. The correlation based template matching guarantees good classification results.

Automatic Detection and Classification of Glioma Tumors using Statistical Features

The characterization and grading of glioma tumors, via image derived features, for diagnosis, prognosis, and treatment response has been an active research area in medical image computing. This paper presents a novel method for automatic detection and classification of glioma from conventional T2 weighted MR images. Automatic detection of the tumor was established using newly developed method called Adaptive Gray level Algebraic set Segmentation Algorithm (AGASA).Statistical Features were extracted from the detected tumor texture using first order statistics and gray level co-occurrence matrix (GLCM) based second order statistical methods. Statistical significance of the features was determined by t-test and its corresponding p-value. A decision system was developed for the grade detection of glioma using these selected features and its p-value. The detection performance of the decision system was validated using the receiver operating characteristic (ROC) curve. The diagnosis and grading of glioma using this non-invasive method can contribute promising results in medical image computing

A study on semigroup action on fuzzy subsets, inverse fuzzy automata and related topics

This thesis comprises five chapters including the introductory chapter. This includes a brief introduction and basic definitions of fuzzy set theory and its applications, semigroup action on sets, finite semigroup theory, its application in automata theory along with references which are used in this thesis. In the second chapter we defined an S-fuzzy subset of X with the extension of the notion of semigroup action of S on X to semigroup action of S on to a fuzzy subset of X using Zadeh's maximal extension principal and proved some results based on this. We also defined an S-fuzzy morphism between two S-fuzzy subsets of X and they together form a category S FSETX. Some general properties and special objects in this category are studied and finally proved that S SET and S FSET are categorically equivalent. Further we tried to generalize this concept to the action of a fuzzy semigroup on fuzzy subsets. As an application, using the above idea, we convert a _nite state automaton to a finite fuzzy state automaton. A classical automata determine whether a word is accepted by the automaton where as a _nite fuzzy state automaton determine the degree of acceptance of the word by the automaton. 1.5. Summary of the Thesis 17 In the third chapter we de_ne regular and inverse fuzzy automata, its construction, and prove that the corresponding transition monoids are regular and inverse monoids respectively. The languages accepted by an inverse fuzzy automata is an inverse fuzzy language and we give a characterization of an inverse fuzzy language. We study some of its algebraic properties and prove that the collection IFL on an alphabet does not form a variety since it is not closed under inverse homomorphic images. We also prove some results based on the fact that a semigroup is inverse if and only if idempotents commute and every L-class or R-class contains a unique idempotent. Fourth chapter includes a study of the structure of the automorphism group of a deterministic faithful inverse fuzzy automaton and prove that it is equal to a subgroup of the inverse monoid of all one-one partial fuzzy transformations on the state set. In the fifth chapter we define min-weighted and max-weighted power automata study some of its algebraic properties and prove that a fuzzy automaton and the fuzzy power automata associated with it have the same transition monoids. The thesis ends with a conclusion of the work done and the scope of further study.