Statistical properties of first-order bang-bang Pll with nonzero loop delay

A method to solve the stationary state probability is presented for the first-order bang-bang phase-locked loop (BBPLL) with nonzero loop delay. This is based on a delayed Markov chain model and a state How diagram for tracing the state history due to the loop delay. As a result, an eigenequation is obtained, and its closed form solutions are derived for some cases. After obtaining the state probability, statistical characteristics such as mean gain of the binary phase detector and timing error variance are calculated and demonstrated.

Gröbner basis techniques for certain problems in coding and systems theory

There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

Quantum behavior in mesoscopic systems

In this thesis I present the work done during my PhD. The Thesis is divided into two parts; in the first one I present the study of mesoscopic quantum systems whereas in the second one I address the problem of the definition of Markov regime for quantum system dynamics. The first work presented is the study of vortex patterns in (quasi) two dimensional rotating Bose Einstein condensates (BECs). I consider the case of an anisotropy trapping potential and I shall show that the ground state of the system hosts vortex patterns that are unstable. In a second work I designed an experimental scheme to transfer entanglement from two entangled photons to two BECs. This work is meant to propose a feasible experimental set up to bring entanglement from microscopic to macroscopic systems for both the study of fundamental questions (quantum to classical transition) and technological applications. In the last work of the first part another experimental scheme is presented in order to detect coherences of a mechanical oscillator which is assumed to have been previously cooled down to the quantum regime. In this regime in fact the system can rapidly undergo decoherence so that new techniques have to be employed in order to detect and manipulate their states. In the scheme I propose a micro-mechanical oscillator is coupled to a BEC and the detection is performed by monitoring the BEC with a negligible back-action on the cantilever. In the second part of the thesis I give a definition of Markov regime for open quantum dynamics. The importance of such definition comes from both the mathematical description of the system dynamics and from the understanding of the role played by the environment in the evolution of an open system. In the Markov regime the mathematical description can be simplified and the role of the environment is a passive one.

Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Novel ingredients from brewers' spent grain - bioactivity in cell culture model systems and bioactivity retention in fortified food products

Functional food ingredients, with scientifically proven and validated bioactive effects, present an effective means of inferring physiological health benefits to consumers to reduce the risk of certain diseases. The search for novel bioactive compounds for incorporation into functional foods is particularly active, with brewers’ spent grain (BSG, a brewing industry co-product) representing a unique source of potentially bioactive compounds. The DNA protective, antioxidant and immunomodulatory effects of phenolic extracts from both pale (P1 - P4) and black (B1 – B4) BSG were examined. Black BSG extracts significantly (P < 0.05) protected against DNA damage induced by hydrogen peroxide (H2O2) and extracts with the highest total phenolic content (TPC) protected against 3-morpholinosydnonimine hydrochloride (SIN-1)-induced oxidative DNA damage, measured by the comet assay. Cellular antioxidant activity assays were used to measured antioxidant potential in the U937 cell line. Extracts P1 – P3 and B2 - B4 demonstrated significant (P < 0.05) antioxidant activity, measured by the superoxide dismutase (SOD) activity, catalase (CAT) activity and gluatathione (GSH) content assays. Phenolic extracts P2 and P3 from pale BSG possess anti-inflammatory activity measured in concanavalin-A (conA) stimulated Jurkat T cells by an enzyme-linked immunosorbent assay (ELISA); significantly (P < 0.05) reducing production of interleukin-2 (IL-2), interleukin-4 (IL-4, P2 only), interleukin-10 (IL-10) and interferon-γ (IFN-γ). Black BSG phenolic extracts did not exhibit anti-inflammatory effects in vitro. Hydroxycinnamic acids (HA) have previously been shown to be the phenolic acids present at highest concentration in BSG; therefore the HA profile of the phenolic extracts used in this research, the original barley (before brewing) and whole BSG was characterised and quantified using high performance liquid chromatography (HPLC). The concentration of HA present in the samples was in the order of ferulic acid (FA) > p-coumaric acid (p-CA) derivatives > FA derivatives > p-CA > caffeic acid (CA) > CA derivatives. Results suggested that brewing and roasting decreased the HA content. Protein hydrolysates from BSG were also screened for their antioxidant and anti-inflammatory potential. A total of 34 BSG protein samples were tested. Initial analyses of samples A – J found the protein samples did not exert DNA protective effects (except hydrolysate H) or antioxidant effects by the comet and SOD assays, respectively. Samples D, E, F and J selectively reduced IFN-γ production (P < 0.05) in Jurkat T cells, measured using enzyme linked immunosorbent assay (ELISA). Further testing of hydrolysates K – W, including fractionated hydrolysates with molecular weight < 3, < 5 and > 5 kDa, found that higher molecular weight (> 5 kDa) and unfractionated hydrolysates demonstrate greatest anti-inflammatory effects, while fractionated hydrolysates were also shown to have antioxidant activity, by the SOD activity assay. A commercially available yogurt drink (Actimel) and snack-bar and chocolate-drink formulations were fortified with the most bioactive phenolic and protein samples – P2, B2, W, W < 3 kDa, W < 5 kDa, W > 5 kDa. All fortified foods were subjected to a simulated gastrointestinal in vitro digestion procedure and bioactivity retention in the digestates was determined using the comet and ELISA assays. Yogurt fortified with B2 digestate significantly (P < 0.05) protected against H2O2-induced DNA damage in Caco-2 cells. Greatest immunomodulatory activity was demonstrated by the snack-bar formulation, significantly (P < 0.05) reducing IFN-γ production in con-A stimulated Jurkat T cells. Hydrolysate W significantly (P < 0.05) increased the IFN-γ reducing capacity of the snack-bar. Addition of fractionated hydrolysate W < 3 kDa and W < 5 kDa to yogurt also reduced IL-2 production to a greater extent than the unfortified yogurt (P < 0.05).

Artefact detection and removal algorithms for EEG diagnostic systems

The electroencephalogram (EEG) is a medical technology that is used in the monitoring of the brain and in the diagnosis of many neurological illnesses. Although coarse in its precision, the EEG is a non-invasive tool that requires minimal set-up times, and is suitably unobtrusive and mobile to allow continuous monitoring of the patient, either in clinical or domestic environments. Consequently, the EEG is the current tool-of-choice with which to continuously monitor the brain where temporal resolution, ease-of- use and mobility are important. Traditionally, EEG data are examined by a trained clinician who identifies neurological events of interest. However, recent advances in signal processing and machine learning techniques have allowed the automated detection of neurological events for many medical applications. In doing so, the burden of work on the clinician has been significantly reduced, improving the response time to illness, and allowing the relevant medical treatment to be administered within minutes rather than hours. However, as typical EEG signals are of the order of microvolts (μV ), contamination by signals arising from sources other than the brain is frequent. These extra-cerebral sources, known as artefacts, can significantly distort the EEG signal, making its interpretation difficult, and can dramatically disimprove automatic neurological event detection classification performance. This thesis therefore, contributes to the further improvement of auto- mated neurological event detection systems, by identifying some of the major obstacles in deploying these EEG systems in ambulatory and clinical environments so that the EEG technologies can emerge from the laboratory towards real-world settings, where they can have a real-impact on the lives of patients. In this context, the thesis tackles three major problems in EEG monitoring, namely: (i) the problem of head-movement artefacts in ambulatory EEG, (ii) the high numbers of false detections in state-of-the-art, automated, epileptiform activity detection systems and (iii) false detections in state-of-the-art, automated neonatal seizure detection systems. To accomplish this, the thesis employs a wide range of statistical, signal processing and machine learning techniques drawn from mathematics, engineering and computer science. The first body of work outlined in this thesis proposes a system to automatically detect head-movement artefacts in ambulatory EEG and utilises supervised machine learning classifiers to do so. The resulting head-movement artefact detection system is the first of its kind and offers accurate detection of head-movement artefacts in ambulatory EEG. Subsequently, addtional physiological signals, in the form of gyroscopes, are used to detect head-movements and in doing so, bring additional information to the head- movement artefact detection task. A framework for combining EEG and gyroscope signals is then developed, offering improved head-movement arte- fact detection. The artefact detection methods developed for ambulatory EEG are subsequently adapted for use in an automated epileptiform activity detection system. Information from support vector machines classifiers used to detect epileptiform activity is fused with information from artefact-specific detection classifiers in order to significantly reduce the number of false detections in the epileptiform activity detection system. By this means, epileptiform activity detection which compares favourably with other state-of-the-art systems is achieved. Finally, the problem of false detections in automated neonatal seizure detection is approached in an alternative manner; blind source separation techniques, complimented with information from additional physiological signals are used to remove respiration artefact from the EEG. In utilising these methods, some encouraging advances have been made in detecting and removing respiration artefacts from the neonatal EEG, and in doing so, the performance of the underlying diagnostic technology is improved, bringing its deployment in the real-world, clinical domain one step closer.