Detection and description of non-linear interdependence in normal multichannel human EEG data

Objectives: This study examines human scalp electroencephalographic (EEG) data for evidence of non-linear interdependence between posterior channels. The spectral and phase properties of those epochs of EEG exhibiting non-linear interdependence are studied. Methods: Scalp EEG data was collected from 40 healthy subjects. A technique for the detection of non-linear interdependence was applied to 2.048 s segments of posterior bipolar electrode data. Amplitude-adjusted phase-randomized surrogate data was used to statistically determine which EEG epochs exhibited non-linear interdependence. Results: Statistically significant evidence of non-linear interactions were evident in 2.9% (eyes open) to 4.8% (eyes closed) of the epochs. In the eyes-open recordings, these epochs exhibited a peak in the spectral and cross-spectral density functions at about 10 Hz. Two types of EEG epochs are evident in the eyes-closed recordings; one type exhibits a peak in the spectral density and cross-spectrum at 8 Hz. The other type has increased spectral and cross-spectral power across faster frequencies. Epochs identified as exhibiting non-linear interdependence display a tendency towards phase interdependencies across and between a broad range of frequencies. Conclusions: Non-linear interdependence is detectable in a small number of multichannel EEG epochs, and makes a contribution to the alpha rhythm. Non-linear interdependence produces spatially distributed activity that exhibits phase synchronization between oscillations present at different frequencies. The possible physiological significance of these findings are discussed with reference to the dynamical properties of neural systems and the role of synchronous activity in the neocortex. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra

New arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the “best fit” model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A- (“cheap”) and B- (“expensive”) that are used after their proper calibration for the measuring of the same substance (corundum a-Al2O3). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) - X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to “ideal” experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the IM in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal “filling”) are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposes.

Non-linear time series models

The last three decades have seen quite dramatic changes the way we modeled time dependent data. Linear processes have been in the center stage in modeling time series. As far as the second order properties are concerned, the theory and the methodology are very adequate.However, there are more and more evidences that linear models are not sufficiently flexible and rich enough for modeling purposes and that failure to account for non-linearities can be very misleading and have undesired consequences.

Plasma Polymerised Organic Thin Films-A Study on the Structural, Electrical and Nonlinear Optical Properties for Possible Applications

This proposed thesis is entitled “Plasma Polymerised Organic Thin Films: A study on the Structural, Electrical, and Nonlinear Optical Properties for Possible Applications. Polymers and polymer based materials find enormous applications in the realm of electronics and optoelectronics. They are employed as both active and passive components in making various devices. Enormous research activities are going on in this area for the last three decades or so, and many useful contributions are made quite accidentally. Conducting polymers is such a discovery, and eversince the discovery of conducting polyacetylene, a new branch of science itself has emerged in the form of synthetic metals. Conducting polymers are useful materials for many applications like polymer displays, high density data storage, polymer FETs, polymer LEDs, photo voltaic devices and electrochemical cells. With the emergence of molecular electronics and its potential in finding useful applications, organic thin films are receiving an unusual attention by scientists and engineers alike. This is evident from the vast literature pertaining to this field appearing in various journals. Recently, computer aided design of organic molecules have added further impetus to the ongoing research activities in this area. Polymers, especially, conducting polymers can be prepared both in the bulk and in the thinfilm form. However, many applications necessitate that they are grown in the thin film form either as free standing or on appropriate substrates. As far as their bulk counterparts are concerned, they can be prepared by various polymerisation techniques such as chemical routes and electrochemical means. A survey of the literature reveals that polymers like polyaniline, polypyrrole, polythiophene, have been investigated with a view to studying their structural electrical and optical properties. Among the various alternate techniques employed for the preparation of polymer thin films, the method of plasma polymerisation needs special attention in this context. The technique of plasma polymerisation is an inexpensive method and often requires very less infra structure. This method includes the employment of ac, rf, dc, microwave and pulsed sources. They produce pinhole free homogeneous films on appropriate substrates under controlled conditions. In conventional plasma polymerisation set up, the monomer is fed into an evacuated chamber and an ac/rf/dc/ w/pulsed discharge is created which enables the monomer species to dissociate, leading to the formation of polymer thin films. However, it has been found that the structure and hence the properties exhibited by plasma polymerized thin films are quite different from that of their counterparts produced by other thin film preparation techniques such as electrochemical deposition or spin coating. The properties of these thin films can be tuned only if the interrelationship between the structure and other properties are understood from a fundamental point of view. So very often, a through evaluation of the various properties is a pre-requisite for tailoring the properties of the thin films for applications. It has been found that conjugation is a necessary condition for enhancing the conductivity of polymer thin films. RF technique of plasma polymerisation is an excellent tool to induce conjugation and this modifies the electrical properties too. Both oxidative and reductive doping can be employed to modify the electrical properties of the polymer thin films for various applications. This is where organic thin films based on polymers scored over inorganic thin films, where in large area devices can be fabricated with organic semiconductors which is difficult to achieve by inorganic materials. For such applications, a variety of polymers have been synthesized such as polyaniline, polythiophene, polypyrrole etc. There are newer polymers added to this family every now and then. There are many virgin areas where plasma polymers are yet to make a foray namely low-k dielectrics or as potential nonlinear optical materials such as optical limiters. There are also many materials which are not been prepared by the method of plasma polymerisation. Some of the materials which are not been dealt with are phenyl hydrazine and tea tree oil. The advantage of employing organic extracts like tea tree oil monomers as precursors for making plasma polymers is that there can be value addition to the already existing uses and possibility exists in converting them to electronic grade materials, especially semiconductors and optically active materials for photonic applications. One of the major motivations of this study is to synthesize plasma polymer thin films based on aniline, phenyl hydrazine, pyrrole, tea tree oil and eucalyptus oil by employing both rf and ac plasma polymerisation techniques. This will be carried out with the objective of growing thin films on various substrates such as glass, quartz and indium tin oxide (ITO) coated glass. There are various properties namely structural, electrical, dielectric permittivity, nonlinear optical properties which are to be evaluated to establish the relationship with the structure and the other properties. Special emphasis will be laid in evaluating the optical parameters like refractive index (n), extinction coefficient (k), the real and imaginary components of dielectric constant and the optical transition energies of the polymer thin films from the spectroscopic ellipsometric studies. Apart from evaluating these physical constants, it is also possible to predict whether a material exhibit nonlinear optical properties by ellipsometric investigations. So further studies using open aperture z-scan technique in order to evaluate the nonlinear optical properties of a few selected samples which are potential nonlinear optical materials is another objective of the present study. It will be another endeavour to offer an appropriate explanation for the nonlinear optical properties displayed by these films. Doping of plasma polymers is found to modify both the electrical conductivity and optical properties. Iodine is found to modify the properties of the polymer thin films. However insitu iodine doping is tricky and the film often looses its stability because of the escape of iodine. An appropriate insitu technique of doping will be developed to dope iodine in to the plasma polymerized thin films. Doping of polymer thin films with iodine results in improved and modified optical and electrical properties. However it requires tools like FTIR and UV-Vis-NIR spectroscopy to elucidate the structural and optical modifications imparted to the polymer films. This will be attempted here to establish the role of iodine in the modification of the properties exhibited by the films

Ultrasonic measurement of the elastic properties of benzoyl glycine single crystals

Certain organic crystals are found to possess high non- linear optical coefficients,often one to two orders of magnitude higher than those of the well known inorganic non-linear optical materials.Benzoyl glycine is one such crystal whose optical second-harmonic generation efficiency is much higher than that of potassium dihydrogen phosphate. Single crystals of benzoyl glycine are grown by solvent evaporation technique using N,N-dimethyl formamide as the solvent.All the nine second-order elastic stiffness constants of this orthorhombic crystal are determined from ultrasonic wave velocity measurements employing the pulse echo overlap technique.The anisotropy of elastic wave propagation in this crystal is demonstrated by plotting the phase velocity, slowness,Young's modulus and linear compressibility surfaces along symmetry planes.The volume compressibility, bulk modulus and relevant Poisson's ratios are also determined. Variation of the diagonal elastic stiffness constants with temperature over a limited range are measured and reported.

Optimization of the Mechanical and Optical Properties of Tunable Optical Sensor Arrays (TOSA) for a Nanospectrometer in the Visible and Near Infrared Spectral Range

Tunable Optical Sensor Arrays (TOSA) based on Fabry-Pérot (FP) filters, for high quality spectroscopic applications in the visible and near infrared spectral range are investigated within this work. The optical performance of the FP filters is improved by using ion beam sputtered niobium pentoxide (Nb2O5) and silicon dioxide (SiO2) Distributed Bragg Reflectors (DBRs) as mirrors. Due to their high refractive index contrast, only a few alternating pairs of Nb2O5 and SiO2 films can achieve DBRs with high reflectivity in a wide spectral range, while ion beam sputter deposition (IBSD) is utilized due to its ability to produce films with high optical purity. However, IBSD films are highly stressed; resulting in stress induced mirror curvature and suspension bending in the free standing filter suspensions of the MEMS (Micro-Electro-Mechanical Systems) FP filters. Stress induced mirror curvature results in filter transmission line degradation, while suspension bending results in high required filter tuning voltages. Moreover, stress induced suspension bending results in higher order mode filter operation which in turn degrades the optical resolution of the filter. Therefore, the deposition process is optimized to achieve both near zero absorption and low residual stress. High energy ion bombardment during film deposition is utilized to reduce the film density, and hence the film compressive stress. Utilizing this technique, the compressive stress of Nb2O5 is reduced by ~43%, while that for SiO2 is reduced by ~40%. Filters fabricated with stress reduced films show curvatures as low as 100 nm for 70 μm mirrors. To reduce the stress induced bending in the free standing filter suspensions, a stress optimized multi-layer suspension design is presented; with a tensile stressed metal sandwiched between two compressively stressed films. The stress in Physical Vapor Deposited (PVD) metals is therefore characterized for use as filter top-electrode and stress compensating layer. Surface micromachining is used to fabricate tunable FP filters in the visible spectral range using the above mentioned design. The upward bending of the suspensions is reduced from several micrometers to less than 100 nm and 250 nm for two different suspension layer combinations. Mechanical tuning of up to 188 nm is obtained by applying 40 V of actuation voltage. Alternatively, a filter line with transmission of 65.5%, Full Width at Half Maximum (FWHM) of 10.5 nm and a stopband of 170 nm (at an output wavelength of 594 nm) is achieved. Numerical model simulations are also performed to study the validity of the stress optimized suspension design for the near infrared spectral range, wherein membrane displacement and suspension deformation due to material residual stress is studied. Two bandpass filter designs based on quarter-wave and non-quarter-wave layers are presented as integral components of the TOSA. With a filter passband of 135 nm and a broad stopband of over 650 nm, high average filter transmission of 88% is achieved inside the passband, while maximum filter transmission of less than 1.6% outside the passband is achieved.

Numerical modelling of two-way propagation of non-linear dispersive waves

We describe and implement a fully discrete spectral method for the numerical solution of a class of non-linear, dispersive systems of Boussinesq type, modelling two-way propagation of long water waves of small amplitude in a channel. For three particular systems, we investigate properties of the numerically computed solutions; in particular we study the generation and interaction of approximate solitary waves.

Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

Electro-optical properties of liquid crystal copolymers and their relationship to structural order

A range of side chain liquid crystal copolymers have been prepared using mesogenic and non-mesogenic units. It is found that high levels of the non-mesogenic moieties may be introduced without completely disrupting the organization of the liquid crystal phase. Incorporation of this comonomer causes a marked reduction in the glass transition temperature (Tg), presumably as a result of enhanced backbone mobility and a corresponding lowering of the nematic transition temperature, thereby restricting the temperature range for stability of the liquid crystal phase. The effect of the interactions between the various components of these side-chain polymers on their electro-optic responses is described. Infrared (i.r.) dichroism measurements have been made to determine the order parameters of the liquid crystalline side-chain polymers. By identifying a certain band (CN stretching) in the i.r. absorption spectrum, the order parameter of the mesogenic groups can be obtained. The temperature and composition dependence of the observed order parameter are related to the liquid crystal phase transitions and to the electro-optic response. It is found that the introduction of the non-mesogenic units into the polymer chain lowers the threshold voltage of the electro-optic response over and above that due to the reduction in the order parameter. The dynamic electro-optic responses are dominated by the temperature-dependent viscosity and evidence is presented for relaxation processes involving the polymer backbone which are on a time scale greater than that for the mesogenic side-chain units.

Fractional order and non-linear system identification algorithms for biomedical applications

We discuss the modelling of dielectric responses of amorphous biological samples. Such samples are commonly encountered in impedance spectroscopy studies as well as in UV, IR, optical and THz transient spectroscopy experiments and in pump-probe studies. In many occasions, the samples may display quenched absorption bands. A systems identification framework may be developed to provide parsimonious representations of such responses. To achieve this, it is appropriate to augment the standard models found in the identification literature to incorporate fractional order dynamics. Extensions of models using the forward shift operator, state space models as well as their non-linear Hammerstein-Wiener counterpart models are highlighted. We also discuss the need to extend the theory of electromagnetically excited networks which can account for fractional order behaviour in the non-linear regime by incorporating nonlinear elements to account for the observed non-linearities. The proposed approach leads to the development of a range of new chemometrics tools for biomedical data analysis and classification.

Polymorphism and optical properties in [NH4][InSe2]

The solvothermal synthesis and characterization of two indium selenides with stoichiometry [NH4][InSe2] is described. Yellow [NH4][InSe2] (1), which exhibits a layered structure, was initially prepared in an aqueous solution of trans-1,4-diaminocyclohexane, and subsequently using a concentrated ammonia solution. A red polymorph of one-dimensional character, [NH4][InSe2] (2), was obtained using 3,5-dimethylpyridine as solvent. [NH4][InSe2] (1) crystallizes in the non-centrosymmetric space group Cc (a=11.5147(6), b=11.3242(6), c=15.9969(9) Å and β=100.354(3)°). The structural motif of the layers is the In4Se10 adamantane unit, composed of four corner-linked InSe4 tetrahedra. These units are linked by their corners, forming [InSe2]− layers which are stacked back to back along the c-direction, and interspaced by [NH4]+cations. The one-dimensional polymorph, (2), crystallizes in the tetragonal space group, I4/mcm (a=8.2519(16), c=6.9059 (14) Å). This structure contains infinite chains of edge-sharing InSe4 tetrahedra separated by [NH4]+ cations.

MAGNETIC FIELD INDUCED NEAR-BAND-GAP OPTICAL PROPERTIES IN EuTe LAYERS

The magnetic response of the near-band-edge optical properties is studied in EuTe layers. In several magneto-optical experiments, the absorption and emission are described as well as the related Stokes shift. Specifically, we present the first experimental report of the photoluminescence excitation (PLE) spectrum in Faraday configuration. The PLE spectra shows to be related with the absorption spectra through the observation of resonance between the excitation light and the zero-field band-gap. A new emission line appears at 1.6 eV at a moderate magnetic field in the photoluminescence (PL) spectra. Furthermore, we examine the absorption and PL red-shift induced by the magnetic field in the light of the d-f exchange interaction energy involved in these processes. Whereas the absorption red-shift shows a quadratic dependence on the field, the PL red-shift shows a linear dependence which is explained by spin relaxation of the excited state.

The electronic and optical properties of sodalite (Na(8)Al(6)Si(6)O(24)Cl(2)) from first principles

This study reports the results of ab initio electronic and optical calculations for pure socialite crystal using the linear augmented plane wave (LAPW) method within density functional theory (DFT). The calculated electronic structure revealed predominantly orbital characters of the valence band and the conduction band, and enabled us to determine the type and the value of the fundamental gap of the compound. The imaginary part of the dielectric tensor, extinction coefficient and refraction index were calculated as functions of the incident radiation wavelength. It is shown that the O 2p states and Na 3s states play the major role in optical transitions as initial and final states, respectively. The absorption spectrum is localized in the ultraviolet range between 40 and 250 nm. Furthermore, we concluded that the material does not absorb radiation in the visible range. (C) 2009 Elsevier Ltd. All rights reserved.

Relation among optical, thermal and thermo-optical properties and niobium concentration in tellurite glasses

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Thermodynamic analysis of a non linear lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)