Signatures of Higher Functions of Brain Dynamics in Electroencephalogram: A Nonlinear Analysis

The brain with its highly complex structure made up of simple units,imterconnected information pathways and specialized functions has always been an object of mystery and sceintific fascination for physiologists,neuroscientists and lately to mathematicians and physicists. The stream of biophysicists are engaged in building the bridge between the biological and physical sciences guided by a conviction that natural scenarios that appear extraordinarily complex may be tackled by application of principles from the realm of physical sciences. In a similar vein, this report aims to describe how nerve cells execute transmission of signals ,how these are put together and how out of this integration higher functions emerge and get reflected in the electrical signals that are produced in the brain.Viewing the E E G Signal through the looking glass of nonlinear theory, the dynamics of the underlying complex system-the brain ,is inferred and significant implications of the findings are explored.

Scaling relations in the Lyapunov exponents of one dimensional maps

We establish numerically the validity of Huberman-Rudnick scaling relation for Lyapunov exponents during the period doubling route to chaos in one dimensional maps. We extend our studies to the context of a combination map. where the scaling index is found to be different.

Study on period search methods of variable stars: Application to ASAS and CRTS databases

Study on variable stars is an important topic of modern astrophysics. After the invention of powerful telescopes and high resolving powered CCD’s, the variable star data is accumulating in the order of peta-bytes. The huge amount of data need lot of automated methods as well as human experts. This thesis is devoted to the data analysis on variable star’s astronomical time series data and hence belong to the inter-disciplinary topic, Astrostatistics. For an observer on earth, stars that have a change in apparent brightness over time are called variable stars. The variation in brightness may be regular (periodic), quasi periodic (semi-periodic) or irregular manner (aperiodic) and are caused by various reasons. In some cases, the variation is due to some internal thermo-nuclear processes, which are generally known as intrinsic vari- ables and in some other cases, it is due to some external processes, like eclipse or rotation, which are known as extrinsic variables. Intrinsic variables can be further grouped into pulsating variables, eruptive variables and flare stars. Extrinsic variables are grouped into eclipsing binary stars and chromospheri- cal stars. Pulsating variables can again classified into Cepheid, RR Lyrae, RV Tauri, Delta Scuti, Mira etc. The eruptive or cataclysmic variables are novae, supernovae, etc., which rarely occurs and are not periodic phenomena. Most of the other variations are periodic in nature. Variable stars can be observed through many ways such as photometry, spectrophotometry and spectroscopy. The sequence of photometric observa- xiv tions on variable stars produces time series data, which contains time, magni- tude and error. The plot between variable star’s apparent magnitude and time are known as light curve. If the time series data is folded on a period, the plot between apparent magnitude and phase is known as phased light curve. The unique shape of phased light curve is a characteristic of each type of variable star. One way to identify the type of variable star and to classify them is by visually looking at the phased light curve by an expert. For last several years, automated algorithms are used to classify a group of variable stars, with the help of computers. Research on variable stars can be divided into different stages like observa- tion, data reduction, data analysis, modeling and classification. The modeling on variable stars helps to determine the short-term and long-term behaviour and to construct theoretical models (for eg:- Wilson-Devinney model for eclips- ing binaries) and to derive stellar properties like mass, radius, luminosity, tem- perature, internal and external structure, chemical composition and evolution. The classification requires the determination of the basic parameters like pe- riod, amplitude and phase and also some other derived parameters. Out of these, period is the most important parameter since the wrong periods can lead to sparse light curves and misleading information. Time series analysis is a method of applying mathematical and statistical tests to data, to quantify the variation, understand the nature of time-varying phenomena, to gain physical understanding of the system and to predict future behavior of the system. Astronomical time series usually suffer from unevenly spaced time instants, varying error conditions and possibility of big gaps. This is due to daily varying daylight and the weather conditions for ground based observations and observations from space may suffer from the impact of cosmic ray particles. Many large scale astronomical surveys such as MACHO, OGLE, EROS, xv ROTSE, PLANET, Hipparcos, MISAO, NSVS, ASAS, Pan-STARRS, Ke- pler,ESA, Gaia, LSST, CRTS provide variable star’s time series data, even though their primary intention is not variable star observation. Center for Astrostatistics, Pennsylvania State University is established to help the astro- nomical community with the aid of statistical tools for harvesting and analysing archival data. Most of these surveys releases the data to the public for further analysis. There exist many period search algorithms through astronomical time se- ries analysis, which can be classified into parametric (assume some underlying distribution for data) and non-parametric (do not assume any statistical model like Gaussian etc.,) methods. Many of the parametric methods are based on variations of discrete Fourier transforms like Generalised Lomb-Scargle peri- odogram (GLSP) by Zechmeister(2009), Significant Spectrum (SigSpec) by Reegen(2007) etc. Non-parametric methods include Phase Dispersion Minimi- sation (PDM) by Stellingwerf(1978) and Cubic spline method by Akerlof(1994) etc. Even though most of the methods can be brought under automation, any of the method stated above could not fully recover the true periods. The wrong detection of period can be due to several reasons such as power leakage to other frequencies which is due to finite total interval, finite sampling interval and finite amount of data. Another problem is aliasing, which is due to the influence of regular sampling. Also spurious periods appear due to long gaps and power flow to harmonic frequencies is an inherent problem of Fourier methods. Hence obtaining the exact period of variable star from it’s time series data is still a difficult problem, in case of huge databases, when subjected to automation. As Matthew Templeton, AAVSO, states “Variable star data analysis is not always straightforward; large-scale, automated analysis design is non-trivial”. Derekas et al. 2007, Deb et.al. 2010 states “The processing of xvi huge amount of data in these databases is quite challenging, even when looking at seemingly small issues such as period determination and classification”. It will be beneficial for the variable star astronomical community, if basic parameters, such as period, amplitude and phase are obtained more accurately, when huge time series databases are subjected to automation. In the present thesis work, the theories of four popular period search methods are studied, the strength and weakness of these methods are evaluated by applying it on two survey databases and finally a modified form of cubic spline method is intro- duced to confirm the exact period of variable star. For the classification of new variable stars discovered and entering them in the “General Catalogue of Vari- able Stars” or other databases like “Variable Star Index“, the characteristics of the variability has to be quantified in term of variable star parameters.

Investigation of Offences against National Security

The study is a close scrutiny of the process of investigation of offences in India along with an analysis of powers and functions of the investigating agency. The offences, which are prejudicial to sovereignty, integrity and security of the nation or to its friendly relations with foreign states, are generally called the offences against national security. Offences against national security being prejudicial to the very existence of the nation and its legal system, is a heinous and terrible one. As early as 1971 the Law Commission of India had pointed out the need of treating the offences relating to national security and their perpetrators on a totally different procedural footing. The recommendation that, all the offences coming under the said category ought to be brought under the purview of a single enactment so as to confront such offences effectively. The discrepancies in and inadequacies of the criminal justice system in India as much as they are related to the investigations of the offences against national security are examined and the reforms are also suggested. The quality of criminal justice is closely linked with the caliber of the prosecution system and many of the acquittals in courts can be ascribed not only to poor investigations but also to poor quality of prosecution.

Development of Best Practices for Ship Recycling Processes

Ship recycling has been considered as the best means to dispose off an obsolete ship. The current state of art of technology combined with the demands of sustainable developments from the global maritime industrial sector has modified the status of erstwhile ‘ship breaking’ involving ship scrap business to a modern industry undertaking dismantling of ships and recycling/reusing the dismantled products in a supply chain of pre owned product market by following the principles of recycling. Industries will have to formulate a set of best practices and blend them with the engineering activities for producing better quality products, improving the productivity and for achieving improved performances related to sustainable development. Improved performance by industries in a sustainable development perspective is accomplished only by implementing the 4E principles, ie.,. ecofriendliness, engineering efficiency, energy conservation and ergonomics in their core operations. The present study has done a comprehensive investigation into various ship recycling operations for formulating a set of best practices.Being the ultimate life cycle stage of a ship, ship recycling activities incorporate certain commercial procedures well in advance to facilitate the objectives of dismantling and recycling/reusing of various parts of the vessel. Thorough knowledge regarding these background procedures in ship recycling is essential for examining and understanding the industrial business operations associated with it. As a first step, the practices followed in merchant shipping operations regarding the decision on decommissioning have been and made available in the thesis. Brief description about the positioning methods and important preparations for the most feasible ship recycling method ie.,. beach method have been provided as a part of the outline of the background information. Available sources of guidelines, codes and rules & regulations for ship recycling have been compiled and included in the discussion.Very brief summary of practices in major ship recycling destinations has been prepared and listed for providing an overview of the global ship recycling activities. The present status of ship recycling by treating it as a full fledged engineering industry has been brought out to establish the need for looking into the development of the best practices. Major engineering attributes of ship as a unique engineering product and the significant influencing factors on her life cycle stage operations have been studied and added to the information base on ship recycling. Role of ship recycling industry as an important player in global sustainable development efforts has been reviewed by analysing the benefits of ship recycling. A brief synopsis on the state of art of ship recycling in major international ship recycling centres has also been incorporated in the backdrop knowledgebase generation on ship recycling processes.Publications available in this field have been reviewed and classified into five subject categories viz., Infrastructure for recycling yards and methods of dismantling, Rules regarding ship recycling activities, Environmental and safety aspects of ship recycling, Role of naval architects and ship classification societies, Application of information technology and Demand forecasting. The inference from the literature survey have been summarised and recorded. Noticeable observations in the inference include need of creation of a comprehensive knowledgebase on ship recycling and its effective implementation in the industry and the insignificant involvement of naval architects and shipbuilding engineers in ship recycling industry. These two important inferences and the message conveyed by them have been addressed with due importance in the subsequent part of the present study.As a part of the study the importance of demand forecasting in ship recycling has been introduced and presented. A sample input for ship recycling data for implementation of computer based methods of demand forecasting has been presented in this section of the thesis.The interdisciplinary nature of engineering processes involved in ship recycling has been identified as one of the important features of this industry. The present study has identified more than a dozen major stake holders in ship recycling having their own interests and roles. It has also been observed that most of the ship recycling activities is carried out in South East Asian countries where the beach based ship recycling is done in yards without proper infrastructure support. A model of beach based ship recycling has been developed and the roles, responsibilities and the mutual interactions of the elements of the system have been documented as a part of the study Subsequently the need of a generation of a wide knowledgebase on ship recycling activities as pointed out by the literature survey has been addressed. The information base and source of expertise required to build a broad knowledgebase on ship recycling operations have been identified and tabulated. Eleven important ship recycling processes have been identified and a brief sketch of steps involved in these processes have been examined and addressed in detail. Based on these findings, a detailed sequential disassembly process plan of ship recycling has been prepared and charted. After having established the need of best practices in ship recycling initially, the present study here identifies development of a user friendly expert system for ship recycling process as one of the constituents of the proposed best practises. A user friendly expert system has been developed for beach based ship recycling processes and is named as Ship Recycling Recommender (SRR). Two important functions of SRR, first one for the ‘Administrators’, the stake holders at the helm of the ship recycling affairs and second one for the ‘Users’, the stake holders who execute the actual dismantling have been presented by highlighting the steps involved in the execution of the software. The important output generated, ie.,. recommended practices for ship dismantling processes and safe handling information on materials present onboard have been presented with the help of ship recycling reports generated by the expert system. A brief account of necessity of having a ship recycling work content estimation as part of the best practices has been presented in the study. This is supported by a detailed work estimation schedule for the same as one of the appendices.As mentioned earlier, a definite lack of involvement of naval architect has been observed in development of methodologies for improving the status of ship recycling industry. Present study has put forward a holistic approach to review the status of ship recycling not simply as end of life activity of all ‘time expired’ vessels, but as a focal point of integrating all life cycle activities. A new engineering design philosophy targeting sustainable development of marine industrial domain, named design for ship recycling has been identified, formulated and presented. A new model of ship life cycle has been proposed by adding few stages to the traditional life cycle after analysing their critical role in accomplishing clean and safe end of life and partial dismantling of ships. Two applications of design for ship recycling viz, recyclability of ships and her products and allotment of Green Safety Index for ships have been presented as a part of implementation of the philosophy in actual practice.

Role of academic bodies with special references to the academic programmes in the universities in Kerala

This makes a thorough study of Role of Academic Bodies with Special Reference to the Academic Programmes in the Universities in Kerala. The present study has dealt with the constitution, powers and functions of the authorities of the universities in Kerala, especially the academic bodies which have well-defined powers and function. This thesis gives in detail the role and functions of the academic bodies in the four universities in Kerala, under study: and examines the role-effectiveness of these bodies. To sum up, it can be concluded that the academic bodies in the universities in Kerala do not function as effectively as envisaged in the laws of the universities. They have a maintenance-oriented approach rather than a dynamic one, without thinking in terms of introducing innovations. They need improvement in the various aspects of their constitution, selection of members and their mode of functioning

Model Diagnostics in the presence of measurement error

The problem of using information available from one variable X to make inferenceabout another Y is classical in many physical and social sciences. In statistics this isoften done via regression analysis where mean response is used to model the data. Onestipulates the model Y = µ(X) +ɛ. Here µ(X) is the mean response at the predictor variable value X = x, and ɛ = Y - µ(X) is the error. In classical regression analysis, both (X; Y ) are observable and one then proceeds to make inference about the mean response function µ(X). In practice there are numerous examples where X is not available, but a variable Z is observed which provides an estimate of X. As an example, consider the herbicidestudy of Rudemo, et al. [3] in which a nominal measured amount Z of herbicide was applied to a plant but the actual amount absorbed by the plant X is unobservable. As another example, from Wang [5], an epidemiologist studies the severity of a lung disease, Y , among the residents in a city in relation to the amount of certain air pollutants. The amount of the air pollutants Z can be measured at certain observation stations in the city, but the actual exposure of the residents to the pollutants, X, is unobservable and may vary randomly from the Z-values. In both cases X = Z+error: This is the so called Berkson measurement error model.In more classical measurement error model one observes an unbiased estimator W of X and stipulates the relation W = X + error: An example of this model occurs when assessing effect of nutrition X on a disease. Measuring nutrition intake precisely within 24 hours is almost impossible. There are many similar examples in agricultural or medical studies, see e.g., Carroll, Ruppert and Stefanski [1] and Fuller [2], , among others. In this talk we shall address the question of fitting a parametric model to the re-gression function µ(X) in the Berkson measurement error model: Y = µ(X) + ɛ; X = Z + η; where η and ɛ are random errors with E(ɛ) = 0, X and η are d-dimensional, and Z is the observable d-dimensional r.v.