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

Robustness and Enhancement of Neural Synchronization by Activity-Dependent Coupling

We study the synchronization of two model neurons coupled through a synapse having an activity-dependent strength. Our synapse follows the rules of Spike-Timing Dependent Plasticity (STDP). We show that this plasticity of the coupling between neurons produces enlarged frequency locking zones and results in synchronization that is more rapid and much more robust against noise than classical synchronization arising from connections with constant strength. We also present a simple discrete map model that demonstrates the generality of the phenomenon.Comment: 4 pages, accepted for publication in PR

'The medical gaze and the watchful eye' : the treatment, prevention and epidemiology of venereal diseases in New South Wales c.1901 - 1925

From Federation in 1901 through the first three decades of the twentieth century there was a perceptible shift in modes of rule in New South Wales (NSW) related to the management of venereal diseases. At the beginning of the twentieth century a medicopenal approach was central. By 1925, persuasion and ‘responsibilisation’ were becoming important modes, and young people rather than ‘case-hardened prostitutes' were assessed as being a ‘venereal’ risk. Framing this period were three important legislative developments which informed, and were informed by, these shifts: the NSW Prisoners Detention Act 1909, the NSW Select Committee into the Prevalence of Venereal Diseases 1915 and the NSW Venereal Diseases Act 1918. At its core this thesis is concerned with examining shifting modes of rule. This thesis closely examines each. I suggest that these modes of rule can be viewed through the lens of biopolitics, and following Foucault, deploy the ‘medical gaze’ and the ‘watchful eye’ as constructs to examine the relationship between the government of self, government of others and government of the state. I use the medical gaze to describe not only the individual venereal patient attending a hospital and the body of the patient diagnosed with syphilis and/or gonorrhoea, but most importantly to describe the power relationship between the medical practitioner, the teaching hospital and the patient. I use the watchful eye in a more overarching way to suggest the suite of techniques and apparatus deployed by government to monitor and regulate the venereal body politic, both the populations perceived to be posing a venereal risk, and populations at risk of venereal infection. In relation to the venereal body and the venereal body politic, I analyse three fundamental aspects of the management of venereal diseases: treatment, prevention and epidemiology. Treatment: Over this period, treatment moved from lock institutions to outpatient clinics. Embodied in this change was a widespread institutional ambivalence towards treating venereal patients. I contend that treatment of venereal diseases was painful, prolonged and punitive precisely because of the moral sickness perceived to be at the iv heart of venereal infection. I track this ambivalence to a systemic fear of institutional ‘venerealisation’, which decreased perceptibly across the period. Closely analysing surviving patient records, I argue that in their conduct, venereal patients were often compliant, conscientious and responsible. Prevention: I argue that preventative approaches to venereal diseases became increasingly complex, and operated in three domains – preventative medicine (diagnosis, treatment and vaccination); public health prevention (notification, isolation and disinfection); and prevention education (social purity campaigns and sex hygiene). An emerging plethora of community-based organisations and campaigns began to shift the sites and practices of power. Epidemiology: I suggest that there was a shift from danger to risk in the conceptualisation of venereal diseases. This shift necessitated a focus on factors affecting populations, as opposed to factors affecting individuals. This in turn led to the deployment of various techniques to monitor the conduct of venereal populations. The NSW Venereal Diseases Act 1918 created two important new venereal categories: the ‘notified person’ and the ‘defaulter,’ both of which came to permeate renditions of venereal patients throughout the 20th century

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

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

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

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

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

Microstructural analysis of sands with varying degrees of internal stability

Internal erosion involves the migration of particles through a geotechnical structure. Internal erosion poses a significant hazard to embankment dams and flood embankments. The fundamental mechanisms operate at the particle scale and a thorough understanding of these mechanisms can inform the filter design and specification process and reduce the hazard that internal erosion is known to pose to many engineered embankment structures. Engineers have long acknowledged the importance of the grain scale interactions, but until recently, explanations of the mechanisms have been purely hypothetical, as direct observation of the internal structure of filters was not possible. Recent research has used the discrete-element method to establish a particle-scale basis for Ke´zdi’s filter internal stability criterion. The discrete-element method can provide significant useful data on soil microstructure, so a discrete-element method model is inherently ideal. This study therefore examines a number of real sand samples with varying degrees of internal stability at the particle scale using high-resolution microcomputed tomography. The correlation between coordination number and internal stability is confirmed, with the coordination number values being significantly higher for the real material