Complex-k modes of plasmonic chain waveguides

Nanoparticle chain waveguide based on negative-epsilon material is investigated through a generic 3D finite-element Bloch-mode solver which derives complex propagation constant ($k$). Our study starts from waveguides made of non-dispersive material, which not only singles out "waveguide dispersion" but also motivates search of new materials to achieve guidance at unconventional wavelengths. Performances of gold or silver chain waveguides are then evaluated; a concise comparison of these two types of chain waveguides has been previously missing. Beyond these singly-plasmonic chain waveguides, we examine a hetero-plasmonic chain system with interlacing gold and silver particles, inspired by a recent proposal; the claimed enhanced energy transfer between gold particles appears to be a one-sided view of its hybridized waveguiding behavior --- energy transfer between silver particles worsens. Enabled by the versatile numerical method, we also discuss effects of inter-particle spacing, background medium, and presence of a substrate. Our extensive analyses show that the general route for reducing propagation loss of e.g. a gold chain waveguide is to lower chain-mode frequency with a proper geometry (e.g. smaller particle spacing) and background material setting (e.g. high-permittivity background or even foreign nanoparticles). In addition, the possibility of building mid-infrared chain waveguides using doped silicon is commented based on numerical simulation.Comment: 26 pages, many figures, now including "Supplementary Data". Accepted, Journal of Physics Communicatio

Derivation of new and existing discrete-time Kharitonov theorems based on discrete-time reactances

The author first uses a discrete-time reactance approach to give a second proof of existing discrete-time Kharitonov-type results (1979). He then uses the same reactance language to derive a new discrete-time Kharitonov-type theorem which, in some sense, is a very close analog to the continuous-time case. He also points out the relation between discrete-time reactances and the technique of line-spectral pairs (LSP) used in speech compression

Disease Localization in Multilayer Networks

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the SIS and SIR dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasi-stationary state method we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: if the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we verified the barrier effect, i.e., for three-layer configuration, when the layer with the largest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems opening new possibilities for the study of spreading processes.Comment: Revised version. 25 pages and 18 figure

Algebraic graph theory in the analysis of frequency assignment problems

Frequency Assignment Problems (FAPs) arise when transmitters need to be allocated frequencies with the aim of minimizing interference, whilst maintaining an efficient use of the radio spectrum. In this thesis FAPs are seen as generalised graph colouring problems, where transmitters are represented by vertices, and their interactions by weighted edges. Solving FAPs often relies on known structural properties to facilitate algorithms. When no structural information is available explicitly, obtaining it from numerical data is difficult. This lack of structural information is a key underlying motivation for the research work in this thesis. If there are TV transmitters to be assigned, we assume as given an N x N "influence matrix" W with entries Wij representing influence between transmitters i and j. From this matrix we derive the Laplacian matrix L = D—W, where D is a diagonal matrix whose entries da are the sum of all influences working in transmitter i. The focus of this thesis is the study of mathematical properties of the matrix L. We généralisé certain properties of the Laplacian eigenvalues and eigenvectors that hold for simple graphs. We also observe and discuss changes in the shape of the Laplacian eigenvalue spectrum due to modifications of a FAP. We include a number of computational experiments and generated simulated examples of FAPs for which we explicitly calculate eigenvalues and eigenvectors in order to test the developed theoretical results. We find that the Laplacians prove useful in identifying certain types of problems, providing structured approach to reducing the original FAP to smaller size subproblems, hence assisting existing heuristic algorithms for solving frequency assignments. In that sense we conclude that analysis of the Laplacians is a useful tool for better understanding of FAPs

Exploration of the functional consequences of fixational eye movements in the absence of a fovea.

A recent theory posits that ocular drifts of fixational eye movements serve to reformat the visual input of natural images, so that the power of the input image is equalized across a range of spatial frequencies. This "spectral whitening" effect is postulated to improve the processing of high-spatial-frequency information and requires normal fixational eye movements. Given that people with macular disease exhibit abnormal fixational eye movements, do they also exhibit spectral whitening? To answer this question, we computed the power spectral density of movies of natural images translated in space and time according to the fixational eye movements (thus simulating the retinal input) of a group of observers with long-standing bilateral macular disease. Just as for people with normal vision, the power of the retinal input at low spatial frequencies was lower than that based on the 1/f2 relationship, demonstrating spectral whitening. However, the amount of whitening was much less for observers with macular disease when compared with age-matched controls with normal vision. A mediation analysis showed that the eccentricity of the preferred retinal locus adopted by these observers and the characteristics of ocular drifts are important factors limiting the amount of whitening. Finally, we did not find a normal aging effect on spectral whitening. Although these findings alone cannot form a causal link between macular disease and spectral properties of eye movements, they suggest novel potential means of modifying the characteristics of fixational eye movements, which may in turn improve functional vision for people with macular disease

Linear predictive modelling of speech : constraints and line spectrum pair decomposition

In an exploration of the spectral modelling of speech, this thesis presents theory and applications of constrained linear predictive (LP) models. Spectral models are essential in many applications of speech technology, such as speech coding, synthesis and recognition. At present, the prevailing approach in speech spectral modelling is linear prediction. In speech coding, spectral models obtained by LP are typically quantised using a polynomial transform called the Line Spectrum Pair (LSP) decomposition. An inherent drawback of conventional LP is its inability to include speech specific a priori information in the modelling process. This thesis, in contrast, presents different constraints applied to LP models, which are then shown to have relevant properties with respect to root loci of the model in its all-pole form. Namely, we show that LSP polynomials correspond to time domain constraints that force the roots of the model to the unit circle. Furthermore, this result is used in the development of advanced spectral models of speech that are represented by stable all-pole filters. Moreover, the theoretical results also include a generic framework for constrained linear predictive models in matrix notation. For these models, we derive sufficient criteria for stability of their all-pole form. Such models can be used to include a priori information in the generation of any application specific, linear predictive model. As a side result, we present a matrix decomposition rule for Toeplitz and Hankel matrices.reviewe

Adaptive deinterlacing of video sequences using motion data

In this work an efficient motion adaptive deinterlacing method with considerable improvement in picture quality is proposed. A temporal deinterlacing method has a high performance in static images while a spatial method has a better performance in dynamic parts. In the proposed deinterlacing method, a motion adaptive interpolator combines the results of a spatial method and a temporal method based on motion activity level of video sequence. A high performance and low complexity algorithm for motion detection is introduced. This algorithm uses five consecutive interlaced video fields for motion detection. It is able to capture a wide range of motions from slow to fast. The algorithm benefits from a hierarchal structure. It starts with detecting motion in large partitions of a given field. Depending on the detected motion activity level for that partition, the motion detection algorithm might recursively be applied to sub-blocks of the original partition. Two different low pass filters are used during the motion detection to increase the algorithm accuracy. The result of motion detection is then used in the proposed motion adaptive interpolator. The performance of the proposed deinterlacing algorithm is compared to previous methods in the literature. Experimenting with several standard video sequences, the method proposed in this work shows excellent results for motion detection and deinterlacing performance