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.

Broadband coaxial cavity resonator for complex permittivity measurements of liquids

A novel cavity perturbation technique using coaxial cavity resonators for the measurement of complex permittivity of liquids is presented. The method employs two types of resonators (Resonator I and Resonator II). Resonator I operates in the frequency range 600 MHz-7 GHz and resonator II operates in the frequency range 4 GHz-14 GHz. The introduction of the capillary tube filled with the sample liquid into the coaxial resonator causes shifts in the resonance frequency and loaded Q-factor of the resonator. The shifts in the resonance frequency and loaded Q-factor are used to determine the real and imaginary parts of the complex permittivity of the sample liquid, respectively. Using this technique, the dielectric parameters of water and nitrobenzene are measured. The results are compared with those obtained using other standard methods. The sources of errors are analyzed.

Some problems of discrete function theory

An attempt is made by the researcher to establish a theory of discrete functions in the complex plane. Classical analysis q-basic theory, monodiffric theory, preholomorphic theory and q-analytic theory have been utilised to develop concepts like differentiation, integration and special functions.

Studies in the geometry of the discrete plane

This thesis is an attempt to initiate the development of a discrete geometry of the discrete plane H = {(qmxo,qnyo); m,n e Z - the set of integers}, where q s (0,1) is fixed and (xO,yO) is a fixed point in the first quadrant of the complex plane, xo,y0 ¢ 0. The discrete plane was first considered by Harman in 1972, to evolve a discrete analytic function theory for geometric difference functions. We shall mention briefly, through various sections, the principle of discretization, an outline of discrete a alytic function theory, the concept of geometry of space and also summary of work done in this thesis

Development of CHH family recombinant hormones and RNAi for induced maturation of Penaeus monodon

About 80 years ago, the neurosecretory eyestalk structures and their role in endocrine regulation was recognized in crustaceans. After the recognition it took half a century to identify the first peptide hormone. Till date a large number of homologous peptides of crustacean hyperglycaemic hormone and moult-inhibiting hormone have been identified, consequently they are called the CHH family hormones. This family comprises of highly multifunctional peptides which according to sequences and precursor structures can be divided into two subfamilies, type-I (CHH/ITP) and II (MIH, MOIH, VIH/GIH) (Webster et al., 2012). The XO-SG complex has been the major site of the two subfamilies. The advent of molecular techniques resulted in the characterization of different precursors of CHH, MIH and GIH; these hormones consist of a signal peptide, but only the preprohormone of CHHs contain a precursor- related peptide (CPRP) located between the signal and the mature hormone (Weidemann et al., 1989; Klein et al., 1993b; De Kleijn and Van Herp, 1995). The essentialities of the gene structure comply with the functions of the CHH family hormones. The CHH family hormone functions are inhibitory as well as stimulatory in the process of reproduction and maturation

Formation of an unusual copper(II) complex from the degradation of a novel tricopper(II) carbohydrazone complex

An unusual copper(II) complex [Cu(L1a)2Cl2] CH3OH H2O H3O+Cl (1a) was isolated from a solution of a novel tricopper(II) complex [Cu3(HL1)Cl2]Cl3 2H2O (1) in methanol, where L1a is 3-(2-pyridyl)triazolo [1,5-a]-pyridine, and characterized with single crystal X-ray diffraction study. The tricopper(II) complex of potential ligand 1,5-bis(di-2-pyridyl ketone) carbohydrazone (H2L1) was synthesized and physicochemically characterized, while the formation of the complex 1a was followed by time-dependant monitoring of the UV–visible spectra, which reveals degradation of ligand backbone as intensity loss of bands corresponding to O?Cu(II) charge transfer

Synthesis, spectral and structural studies of novel binuclear Ni(II) complex of salicylaldehyde 3-azacyclothiosemicarbazone

A novel binuclear Ni(II) complex of salicylaldehyde 3-azacyclothiosemicarbazone (H2L) has been synthesized and characterized by elemental analysis, IR and UV–Vis spectroscopy. The single crystal X-ray structure of the complex shows that bridging occurs through thiolato sulfur and phenolic oxygen atoms. Nickel centers in the complex have square planar and octahedral geometries

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.