Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 2472 for “"Gaussian"”.
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Gaussian Amicable Pairs
… of one is the other and vice versa. Since the Gaussian integers have many of the properties of the regular integers, we sought to discover whether there exist any pairs of Gaussian integers with the same property. It turns out that they do exist. In fact, some of the normal amicable pairs carry …
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Reliability of a Gaussian channel in the presence of Gaussian feedback
… time, infinite band-width, Additive White Gaussian Noise channel was studied under a peak power constraint, in the presence of a feedback channel that was also a continuous time peak-power constrained infinite bandwidth Additive White Gaussian Noise channel. Motivated by [9], a two phase …
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Gaussian processes:iterative sparse approximations
… Significant research has been devoted to Gaussian processes (GPs) due to their increased flexibility when compared with parametric models. These methods use Bayesian learning, which generally leads to analytically intractable posteriors. This thesis proposes a two-step solution to …
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On Gaussian Multiplicative Chaos
Gaussian multiplicative chaos was first constructed in Kahane's seminal paper in 1985 in an attempt to provide a mathematical foundation for Kolmogorov-Obukhov-Mandelbrot theory of energy dissipation in developed turbulence. It has attracted a lot of attentions from the mathematics community in the …
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Detection of signals corrupted by the combination of Gaussian and Non-Gaussian noise
… abounds with analyses of communications in Gaussian noise, relatively little work has appeared dealing with communications in non-Gaussian noise. In this thesis several digital communication systems disturbed by non-Gaussian noise are analysed. The thesis is divided into two main parts. In …
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Sign Ambiguities of Gaussian Sums
… and Davenport-Hasse} relations, between Gaussian sums, were known. In 1964, H. Hasse conjectured that the norm and Davenport-Hasse relations are the only multiplicative relations connecting the Gaussian sums over $mathbb F_p$. However, in 1966, K. Yamamoto provided a simple counterexample …
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On Self-Similar Gaussian Processes
… a change-of-variable formula for a class of Gaussian processes with a covariance function satisfying minimal regularity and integrability conditions. The existence of the local time and a version of Tanaka's formula are derived. These results are applied to a general class of self-similar …
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Hierarchical Inference in Gaussian Processes
… hierarchical constructions in the context of Gaussian processes. Gaussian processes (GP) are flexible distribution over functions and exemplify the key attributes of probabilistic machine learning. They have the ability to encode a diverse range of statistical structures through the choice of …
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Two-parameter noncommutative Gaussian processes
… to a two-parameter deformation of the classical Gaussian statistics and (2) a two-parameter continuum of non-commutative probability spaces in which to realize these statistics. The framework that emerges has a remarkably rich combinatorial structure and bears upon a number of well-known …
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Smoothed analysis of Gaussian elimination
We present a smoothed analysis of Gaussian elimination, both with partial pivoting and without pivoting. Let A be any matrix and let A be a slight random perturbation of A. We prove that it is unlikely that A has large condition number. Using this result, we prove it is unlikely that A has large …
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Entanglement in a Bipartite Gaussian State
… the loss of entanglement in a two-particle Gaussian system, we couple it to an environment and use the Non-Rotating Wave master equation to study the system's dynamics. We also present a derivation of this equation. We consider two di�fferent types of evolution. Under free evolution we �and …
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Fractional Diffusion in Gaussian Noisy Environment
… the time-fractional diffusion with fractional Gaussian noise. We obtain conditions so that the square integrable solution exists uniquely. Chapter 5 studies the time-fractional diffusion where the Gaussian noise is general in time with space covariance given by fractional, Riesz and Bessel …
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Extreme values of non-Gaussian fields
… the extremal behaviour of log-correlated spatial Gaussian processes has drawn a lot of attention. Among many other results, it is known for the lattice discrete Gaussian free field (DGFF) in $d=2$ as well as for general log-correlated Gaussian fields, that the limiting law of the centred maximum …
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Sparse Gaussian Process Approximations and Applications
… we will investigate methods which use Gaussian processes to represent distributions over functions. Gaussian process models require approximations in order to be practically useful. This thesis focuses on understanding existing approximations and investigating new ones tailored to …
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The Generalised Gaussian Process Convolution Model
This thesis formulates the Generalised Gaussian Process Convolution Model (GGPCM), which is a generalisation of the Gaussian Process Convolution Model presented by Tobar et al. [2015b]. The GGPCM provides a theoretical framework for nonparametric kernel models of multidimensional signals defined on …
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Automatic model construction with Gaussian processes
… and physical dynamics. These models, based on Gaussian processes, can capture many types of statistical structure, such as periodicity, changepoints, additivity, and symmetries. Such structure can be encoded through kernels, which have historically been hand-chosen by experts. We show how to …
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