Invariant density for a class of initial distributions under quadratic mapping

For the discrete-time quadratic map xt+1=4xt(1-xt) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.

Invariant Characterization of Neural Systems

It is shown that the invariant integral, viz., the Kolmogorov second entropy, is eminently suited to characterize EEG quantitatively. The estimation obtained for a "clinically normal" brain is compared with a previous result obtained from the EEG of a person under epileptic seizure.

Form-invariant bivariate weighted models

In this paper the class of continuous bivariate distributions that has form-invariant weighted distribution with weight function w(x1, x2) ¼ xa1 1 xa2 2 is identified. It is shown that the class includes some well known bivariate models. Bayesian inference on the parameters of the class is considered and it is shown that there exist natural conjugate priors for the parameters

State-of-the-Art: Transformation Invariant Descriptors

As the popularity of digital videos increases, a large number illegal videos are being generated and getting published. Video copies are generated by performing various sorts of transformations on the original video data. For effectively identifying such illegal videos, the image features that are invariant to various transformations must be extracted for performing similarity matching. An image feature can be its local feature or global feature. Among them, local features are powerful and have been applied in a wide variety of computer vision aplications .This paper focuses on various recently proposed local detectors and descriptors that are invariant to a number of image transformations.

Significance of Time Scales in Nonlinear Dynamical Analysis of Electroencephalogram Signals

We propose to show in this paper, that the time series obtained from biological systems such as human brain are invariably nonstationary because of different time scales involved in the dynamical process. This makes the invariant parameters time dependent. We made a global analysis of the EEG data obtained from the eight locations on the skull space and studied simultaneously the dynamical characteristics from various parts of the brain. We have proved that the dynamical parameters are sensitive to the time scales and hence in the study of brain one must identify all relevant time scales involved in the process to get an insight in the working of brain.

Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.

Biochemical & Pharmacological evaluation of liver oils of selected deep sea sharks and chimaeras of the Indian EEZ

With a seacoast of 8,1 18 km, an exclusive economic zone (EEZ) of 2 million square km, and with an area of about 30,000 square km under aquaculture, lndia produces close to six million tonnes of fish, over 4 per cent of the world fish production. While the marine waters upto 50m depth have been fully exploited, those beyond, remain unexplored. There is an ever increasing demand for fishery resources as food. The coastal fishery resources of the country are dwindling at a rapid pace and it becomes highly imperative that we search for alternate fishery resources for food. The option we have is to hunt for marine fishery resources. Studies pertaining to proximate composition, amino acid and fatty acid composition are essential to understand the nutraceutical values of these deep sea fishery resources. The present study was aimed to carry out proximate composition of deep sea fishery resources obtained during cruises onboard the FORV Sarise Sampada, to identify fishery resources which have appreciable lipid content and thereby analyse the bioactive potentials of marine lipids, to study the amino acid profile of these fishery resources, to understand the contents of SPA, MUFA and PUFA and to calculate the n3/n6 fatty acid contents. Though the presence of nutraceuticals was identified in the marine fishery resources their use as potential food resources deserve further investigation. So the study were carried out to calculate the hepatosomatic indices of sharks & chimaeras and conduct biochemical characterisation of liver oils of Apristurus indicus, Cenlrophorus scalprams, Centroselachus crepidater, Neoharriotta raleighana, and Harriotta pinnata obtained during cruises onboard the FORV Sugar Sampada.Therapeutic use of shark liver oil is evident from its use for centuries as a remedy to heal wounds and fight flu (Neil er al. 2006). Japanese seamen called it 'samedava' or "cure all". Shark liver oil is being promoted worldwide as a dietary supplement to boost the immune system, fight infections, to treat cancer and to lessen the side effects of conventional cancer treatment. These days more emphasis is laid on the nutritive benefits of shark liver oils especially on the omega 3 polyunsaturated fatty acids ( PUFAs) (Anandan er al. 2007) and alkylglycerols (AKGs) (Pugliese er al. I998) contained in them due to the high rise of inflammatory disorders such as arthritis, asthma and neurodegenerative diseases like Alzheimer’s, Parkinson’s and Schizophrenia. So the present study also evaluate the pharmacological properties with respect to analgesic, anti-inflammatory, anti pyretic and anti-ulcer effects of four different liver oils of sharks belonging to the Indian EEZ and to identify the components of oil responsible for these activities.The analgesic and anti-inflammatory activities of liver oils from Neoharriotra raleighana (NR), Centrosymnus crepidater (CC), Apristurus indicus (AI), and Centrophorus sculpratus (CS) sharks caught from the Arabian Sea and the Indian Ocean were compared. The main objectives also include determination of the cholesterol lowering effects of liver oils of Neoharriotra raleighana (NR) and Centrophorus sculpratus (CS) on the high fat diet induced dyslipidemia and to compare the impact of four isolipidemic diets, on levels of serum diagnostic marker enzymes, on lipid profile of blood and liver and antioxidant status of heart in male Albino rats. And also to study the efficacy of Centrophorus sculpratus (CS) liver oil against Complete Freund’s Adjuvant-induced arthritis and to compare the anti-inflammatory activity of this oil with a traditionally used anti-inflammatory substance gingerol (oleoresin extracted from ginger.). The results of the present study indicated that both (Centrophorus sculpratus liver oils as well as gingerol extracts proved to be effective natural remedies against CFA-induced arthritis in Albino rats.

Unconstrained Handwritten Malayalam Character Recognition using Wavelet Transform and Support vector Machine Classifier

This paper presents the application of wavelet processing in the domain of handwritten character recognition. To attain high recognition rate, robust feature extractors and powerful classifiers that are invariant to degree of variability of human writing are needed. The proposed scheme consists of two stages: a feature extraction stage, which is based on Haar wavelet transform and a classification stage that uses support vector machine classifier. Experimental results show that the proposed method is effective

Level Identification of Brain MR Images using Histogram of a LBP variant

Axial brain slices containing similar anatomical structures are retrieved using features derived from the histogram of Local binary pattern (LBP). A rotation invariant description of texture in terms of texture patterns and their strength is obtained with the incorporation of local variance to the LBP, called Modified LBP (MOD-LBP). In this paper, we compare Histogram based Features of LBP (HF/LBP), against Histogram based Features of MOD-LBP (HF/MOD-LBP) in retrieving similar axial brain images. We show that replacing local histogram with a local distance transform based similarity metric further improves the performance of MOD-LBP based image retrieval

Content-Based Image Retrieval of Axial Brain Slices Using a Novel LBP with a Ternary Encoding

Retrieval of similar anatomical structures of brain MR images across patients would help the expert in diagnosis of diseases. In this paper, modified local binary pattern with ternary encoding called modified local ternary pattern (MOD-LTP) is introduced, which is more discriminant and less sensitive to noise in near-uniform regions, to locate slices belonging to the same level from the brain MR image database. The ternary encoding depends on a threshold, which is a user-specified one or calculated locally, based on the variance of the pixel intensities in each window. The variancebased local threshold makes the MOD-LTP more robust to noise and global illumination changes. The retrieval performance is shown to improve by taking region-based moment features of MODLTP and iteratively reweighting the moment features of MOD-LTP based on the user’s feedback. The average rank obtained using iterated and weighted moment features of MOD-LTP with a local variance-based threshold, is one to two times better than rotational invariant LBP (Unay, D., Ekin, A. and Jasinschi, R.S. (2010) Local structure-based region-of-interest retrieval in brain MR images. IEEE Trans. Inf. Technol. Biomed., 14, 897–903.) in retrieving the first 10 relevant images

Content Based Image Retrieval of Brain MR Images across Different Classes

Magnetic Resonance Imaging play a vital role in the decision-diagnosis process of brain MR images. For an accurate diagnosis of brain related problems, the experts mostly compares both T1 and T2 weighted images as the information presented in these two images are complementary. In this paper, rotational and translational invariant form of Local binary Pattern (LBP) with additional gray scale information is used to retrieve similar slices of T1 weighted images from T2 weighted images or vice versa. The incorporation of additional gray scale information on LBP can extract more local texture information. The accuracy of retrieval can be improved by extracting moment features of LBP and reweighting the features based on users’ feedback. Here retrieval is done in a single subject scenario where similar images of a particular subject at a particular level are retrieved, and multiple subjects scenario where relevant images at a particular level across the subjects are retrieved

The Effect of SIFT Features as Content Descriptors in the Context of Automatic Writer Identification in Malayalam Language

The span of writer identification extends to broad domes like digital rights administration, forensic expert decisionmaking systems, and document analysis systems and so on. As the success rate of a writer identification scheme is highly dependent on the features extracted from the documents, the phase of feature extraction and therefore selection is highly significant for writer identification schemes. In this paper, the writer identification in Malayalam language is sought for by utilizing feature extraction technique such as Scale Invariant Features Transform (SIFT).The schemes are tested on a test bed of 280 writers and performance evaluated

Design, Development and Realization of Quadratic Volterra Filters for Selected Applications

The basic concepts of digital signal processing are taught to the students in engineering and science. The focus of the course is on linear, time invariant systems. The question as to what happens when the system is governed by a quadratic or cubic equation remains unanswered in the vast majority of literature on signal processing. Light has been shed on this problem when John V Mathews and Giovanni L Sicuranza published the book Polynomial Signal Processing. This book opened up an unseen vista of polynomial systems for signal and image processing. The book presented the theory and implementations of both adaptive and non-adaptive FIR and IIR quadratic systems which offer improved performance than conventional linear systems. The theory of quadratic systems presents a pristine and virgin area of research that offers computationally intensive work. Once the area of research is selected, the next issue is the choice of the software tool to carry out the work. Conventional languages like C and C++ are easily eliminated as they are not interpreted and lack good quality plotting libraries. MATLAB is proved to be very slow and so do SCILAB and Octave. The search for a language for scientific computing that was as fast as C, but with a good quality plotting library, ended up in Python, a distant relative of LISP. It proved to be ideal for scientific computing. An account of the use of Python, its scientific computing package scipy and the plotting library pylab is given in the appendix Initially, work is focused on designing predictors that exploit the polynomial nonlinearities inherent in speech generation mechanisms. Soon, the work got diverted into medical image processing which offered more potential to exploit by the use of quadratic methods. The major focus in this area is on quadratic edge detection methods for retinal images and fingerprints as well as de-noising raw MRI signals