Properties of molecules in tunnel junctions

Molecular tunnel junctions involve studying the behaviour of a single molecule sandwiched between metal leads. When a molecule makes contact with electrodes, it becomes open to the environment which can heavily influence its properties, such as electronegativity and electron transport. While the most common computational approaches remain to be single particle approximations, in this thesis it is shown that a more explicit treatment of electron interactions can be required. By studying an open atomic chain junction, it is found that including electron correlations corrects the strong lead-molecule interaction seen by the ΔSCF approximation, and has an impact on junction I − V properties. The need for an accurate description of electronegativity is highlighted by studying a correlated model of hexatriene-di-thiol with a systematically varied correlation parameter and comparing the results to various electronic structure treatments. The results indicating an overestimation of the band gap and underestimation of charge transfer in the Hartree-Fock regime is equivalent to not treating electron-electron correlations. While in the opposite limit, over-compensating for electron-electron interaction leads to underestimated band gap and too high an electron current as seen in DFT/LDA treatment. It is emphasised in this thesis that correcting electronegativity is equivalent to maximising the overlap of the approximate density matrix to the exact reduced density matrix found at the exact many-body solution. In this work, the complex absorbing potential (CAP) formalism which allows for the inclusion metal electrodes into explicit wavefunction many-body formalisms is further developed. The CAP methodology is applied to study the electron state lifetimes and shifts as the junction is made open.

Analysing energy detector diversity receivers for spectrum sensing

The analysis of energy detector systems is a well studied topic in the literature: numerous models have been derived describing the behaviour of single and multiple antenna architectures operating in a variety of radio environments. However, in many cases of interest, these models are not in a closed form and so their evaluation requires the use of numerical methods. In general, these are computationally expensive, which can cause difficulties in certain scenarios, such as in the optimisation of device parameters on low cost hardware. The problem becomes acute in situations where the signal to noise ratio is small and reliable detection is to be ensured or where the number of samples of the received signal is large. Furthermore, due to the analytic complexity of the models, further insight into the behaviour of various system parameters of interest is not readily apparent. In this thesis, an approximation based approach is taken towards the analysis of such systems. By focusing on the situations where exact analyses become complicated, and making a small number of astute simplifications to the underlying mathematical models, it is possible to derive novel, accurate and compact descriptions of system behaviour. Approximations are derived for the analysis of energy detectors with single and multiple antennae operating on additive white Gaussian noise (AWGN) and independent and identically distributed Rayleigh, Nakagami-m and Rice channels; in the multiple antenna case, approximations are derived for systems with maximal ratio combiner (MRC), equal gain combiner (EGC) and square law combiner (SLC) diversity. In each case, error bounds are derived describing the maximum error resulting from the use of the approximations. In addition, it is demonstrated that the derived approximations require fewer computations of simple functions than any of the exact models available in the literature. Consequently, the regions of applicability of the approximations directly complement the regions of applicability of the available exact models. Further novel approximations for other system parameters of interest, such as sample complexity, minimum detectable signal to noise ratio and diversity gain, are also derived. In the course of the analysis, a novel theorem describing the convergence of the chi square, noncentral chi square and gamma distributions towards the normal distribution is derived. The theorem describes a tight upper bound on the error resulting from the application of the central limit theorem to random variables of the aforementioned distributions and gives a much better description of the resulting error than existing Berry-Esseen type bounds. A second novel theorem, providing an upper bound on the maximum error resulting from the use of the central limit theorem to approximate the noncentral chi square distribution where the noncentrality parameter is a multiple of the number of degrees of freedom, is also derived.

Neonatal EEG classification using atomic decomposition

The electroencephalogram (EEG) is an important noninvasive tool used in the neonatal intensive care unit (NICU) for the neurologic evaluation of the sick newborn infant. It provides an excellent assessment of at-risk newborns and formulates a prognosis for long-term neurologic outcome.The automated analysis of neonatal EEG data in the NICU can provide valuable information to the clinician facilitating medical intervention. The aim of this thesis is to develop a system for automatic classification of neonatal EEG which can be mainly divided into two parts: (1) classification of neonatal EEG seizure from nonseizure, and (2) classifying neonatal background EEG into several grades based on the severity of the injury using atomic decomposition. Atomic decomposition techniques use redundant time-frequency dictionaries for sparse signal representations or approximations. The first novel contribution of this thesis is the development of a novel time-frequency dictionary coherent with the neonatal EEG seizure states. This dictionary was able to track the time-varying nature of the EEG signal. It was shown that by using atomic decomposition and the proposed novel dictionary, the neonatal EEG transition from nonseizure to seizure states could be detected efficiently. The second novel contribution of this thesis is the development of a neonatal seizure detection algorithm using several time-frequency features from the proposed novel dictionary. It was shown that the time-frequency features obtained from the atoms in the novel dictionary improved the seizure detection accuracy when compared to that obtained from the raw EEG signal. With the assistance of a supervised multiclass SVM classifier and several timefrequency features, several methods to automatically grade EEG were explored. In summary, the novel techniques proposed in this thesis contribute to the application of advanced signal processing techniques for automatic assessment of neonatal EEG recordings.