Construction of Parseval wavelets from redundant filter systems

We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more reference

Local category-specific gamma band responses in the visual cortex do not reflect conscious perception

Which neural processes underlie our conscious experience? One theoretical view argues that the neural correlates of consciousness (NCC) reside in local activity in sensory cortices. Accordingly, local category-specific gamma band responses in visual cortex correlate with conscious perception. However, as most studies manipulated conscious perception by altering the amount of sensory evidence, it is possible that they reflect prerequisites or consequences of consciousness rather than the actual NCC. Here we directly address this issue by developing a new experimental paradigm in which conscious perception is modulated either by sensory evidence or by previous exposure of the images while recording intracranial EEG from the higher-order visual cortex of human epilepsy patients. A clear prediction is that neural processes directly reflecting conscious perception should be present regardless of how it comes about. In contrast, we observed that although subjective reports were modulated both by sensory evidence and by previous exposure, gamma band responses solely reflected sensory evidence. This result contradicts the proposal that local gamma band responses in the higher-order visual cortex reflect conscious perception

Aspects of noncommutative Lorentzian geometry for globally hyperbolic spacetimes

Connes' functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d'Alembert operator and the causal functions of a globally hyperbolic spacetime. As a step of the presented machinery, a proof of the almost-everywhere smoothness of the Lorentzian distance considered as a function of one of the two arguments is given. Afterwards, using a $C^*$-algebra approach, the spacetime causal structure and the Lorentzian distance are generalized into noncommutative structures giving rise to a Lorentzian version of part of Connes' noncommutative geometry. The generalized noncommutative spacetime consists of a direct set of Hilbert spaces and a related class of $C^*$-algebras of operators. In each algebra a convex cone made of self-adjoint elements is selected which generalizes the class of causal functions. The generalized events, called {\em loci}, are realized as the elements of the inductive limit of the spaces of the algebraic states on the $C^*$-algebras. A partial-ordering relation between pairs of loci generalizes the causal order relation in spacetime. A generalized Lorentz distance of loci is defined by means of a class of densely-defined operators which play the r\^ole of a Lorentzian metric. Specializing back the formalism to the usual globally hyperbolic spacetime, it is found that compactly-supported probability measures give rise to a non-pointwise extension of the concept of events.Comment: 43 pages, structure of the paper changed and presentation strongly improved, references added, minor typos corrected, title changed, accepted for publication in Reviews in Mathematical Physic

General Framework for phase synchronization through localized sets

We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another one whenever this event occurs, these observations give rise to a localized set. Our result provides a general and easy way to identify PS, which can also be used to oscillators that possess multiple time scales. We illustrate our approach in networks of chemically coupled neurons. We show that clusters of phase synchronous neurons may emerge before the onset of phase synchronization in the whole network, producing a suitable environment for information exchanging. Furthermore, we show the relation between the localized sets and the amount of information that coupled chaotic oscillator can exchange

Solar Energy

This thesis is about Photovoltaic (PV) cells and its stresses in various directions by calculating the power generated using solar cells under different conditions to improve its efficiency. Our research studies found that using multi-junction cells with larger substrates can increase the efficiency to some extent which in practice is limited to 43 percent. The experiment was conducted using ten solar cells each with an area of 20.9?cm? ^2, where each cell gives 0.5 V and 0.4 A and a 1.25 ? resistor was used. The cells were connected in series. Once, the PV cells were fixed horizontally and the other time tested in tilted position under same outdoor condition. The purpose of testing PV cells was to investigate the efficiency under above mentioned conditions. The data collected from the readings was used in calculation, and we have obtained from the calculations that horizontally fixed cells gave 4.8 percent efficiency whereas tilted cells gave 6.6 percent efficiency. Hence, the ratio showed that fixed cells produced 37.5 percent more power compared to horizontally fixed cells. Our other experiment consisted of testing PV cells under different temperature conditions that was done using a freezer and an oven for temperature variation and a tungsten bulb was used as a light source. The purpose of performing this experiment was to investigate how the efficiency of PV cells is affected under extreme conditions. Part of our thesis was also including studies and analysis of produced energy by the solar panel installed on the roof of BTH building in Karlskrona, Sweden. The data consisted of energy produced from February up to August 2014. The investigation also included finding the highest produced energy during these months. We have found that the highest energy was generated on the 1st of July which was 12.86 kWh. Furthermore, we went deep into investigation of the 1st of July to know exactly which hour of that day the highest energy was produced. The data showed that the highest produced energy was at 12:19 and 13:19 which was 2.03 kWh. Ramzi: +46723231353, +966561993488 Zain Document type: Part of book or chapter of boo

Cosmological perturbations on local systems

We study the effect of cosmological expansion on orbits--galactic, planetary, or atomic--subject to an inverse-square force law. We obtain the laws of motion for gravitational or electrical interactions from general relativity--in particular, we find the gravitational field of a mass distribution in an expanding universe by applying perturbation theory to the Robertson-Walker metric. Cosmological expansion induces an ($\ddot a/a) \vec r$ force where $a(t)$ is the cosmological scale factor. In a locally Newtonian framework, we show that the $(\ddot a/a) \vec r$ term represents the effect of a continuous distribution of cosmological material in Hubble flow, and that the total force on an object, due to the cosmological material plus the matter perturbation, can be represented as the negative gradient of a gravitational potential whose source is the material actually present. We also consider the effect on local dynamics of the cosmological constant. We calculate the perihelion precession of elliptical orbits due to the cosmological constant induced force, and work out a generalized virial relation applicable to gravitationally bound clusters.Comment: 10 page

Positronium S state spectrum: analytic results at O(m alpha^6)

We present an analytic calculation of the O(m alpha^6) recoil and radiative recoil corrections to energy levels of positronium nS states and their hyperfine splitting. A complete analytic formula valid to O(m alpha^6) is given for the spectrum of S states. Technical aspects of the calculation are discussed in detail. Theoretical predictions are given for various energy intervals and compared with experimental results.Comment: 29 pages, revte

Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions

We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a pair of basic realizations of the algebra of N=2 pseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is identified with either a boson-phermion or a boson-abnormal-phermion exchange symmetry. We further establish the physical equivalence (non-equivalence) of phermions (abnormal phermions) with ordinary fermions, describe the underlying Lie algebras, and study multi-particle systems of abnormal phermions. The latter provides a certain bosonization of multi-fermion systems.Comment: 20 pages, to appear in J.Phys.

QED theory of the nuclear recoil effect in atoms

The quantum electrodynamic theory of the nuclear recoil effect in atoms to all orders in \alpha Z is formulated. The nuclear recoil corrections for atoms with one and two electrons over closed shells are considered in detail. The problem of the composite nuclear structure in the theory of the nuclear recoil effect is discussed.Comment: 20 pages, 6 figures, Late