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Yes / The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the non-distributivity of the lattice of subspaces, there are various levels of independence, from pairwise independence up to (full) independence. Pairwise totalness, totalness and other intermediate concepts are also introduced, which roughly express that the subspaces overlap strongly among themselves, and they cover the full Hilbert space. A duality between independence and totalness, that involves orthocomplementation (logical NOT operation), is discussed. Another approach to independence is also studied, using Rota’s formalism on independent partitions of the Hilbert space. This is used to define informational independence, which is proved to be equivalent to independence. As an application, the pentagram (used in discussions on contextuality) is analysed using these concepts.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 80-84). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph.D.)--Victoria University of Wellington, 2007. / "Version 1.1, 16 August 2007 (including corrections)" Includes bibliographical references.

Quantum systems with finite Hilbert space are considered. Position and mo- mentum states and their relation through a Fourier transform, displacement in the position-momentum phase-space, and symplectic transformations are introduced and their properties are studied. Symplectic Sp(2l;Zp) trans- formations in l-partite finite system are explicit constructed. The general method is applied to bi-partite and tri-partite systems. The effect of these transformations on the correlations is discussed. Entanglement calculations between the subsystems in a bi-partite system and a tri-partite system are presented. The effect of measurements is also studied.

Yes / Coherent subspaces spanned by a finite number of coherent states are introduced, in a quantum system with Hilbert space that has odd prime dimension d. The set of all coherent subspaces is partitioned into equivalence classes, with d 2 subspaces in each class. The corresponding coherent projectors within an equivalence class, have the 'closure under displacements property' and also resolve the identity. Different equivalence classes provide different granularisation of the Hilbert space, and they form a partial order 'coarser' (and 'finer'). In the case of a two-dimensional coherent subspace spanned by two coherent states, the corresponding projector (of rank 2) is different than the sum of the two projectors to the subspaces related to each of the two coherent states. We quantify this with 'non-addditivity operators' which are a measure of quantum interference in phase space, and also of the non-commutativity of the projectors. Generalized Q and P functions of density matrices, which are based on coherent projectors in a given equivalence class, are introduced. Analogues of the Lorenz values and the Gini index (which are popular quantities in mathematical economics) are used here to quantify the inequality in the distribution of the Q function of a quantum state, within the granular structure of the Hilbert space. A comparison is made between Lorenz values and the Gini index for the cases of coarse and also fine granularisation of the Hilbert space. Lorenz values require an ordering of the d 2 values of the Q function of a density matrix, and this leads to the ranking permutation of a density matrix, and to comonotonic density matrices (which have the same ranking permutation). The Lorenz values are a superadditive function and the Gini index is a subadditive function (they are both additive quantities for comonotonic density matrices). Various examples demonstrate these ideas.

With the recent interest in single fraction Stereotactic Body Radiation Therapy and the emerging prominence of the Rapid Arc radiotherapy technique capable of delivering a fast and accurate treatment, the in-field primary dose and out-of-field dose assessments are becoming increasingly important. Currently, full physics Monte Carlo calculations for dose calculations have been regarded as a ‘gold standard’ for dose assessments of the target and OAR (organ at risk). However, these Monte Carlo calculations require very long computation times. The current treatment planning methods provide shorter calculation times, but issues such as heterogeneities and model-based parameter calculations cause challenges and affect dose calculation accuracy. This thesis describes a new and fast dose estimation method leveraging parallel computing called EDK-SN, “Electron Dose Kernel-Discrete Ordinates”. This new method uses hybrid electron dose kernels driven by linear Boltzmann (discrete ordinates) photon transport method to carry out dose calculations. The method has proven effective for fast and accurate computations of out-of-field whole body dose calculations benchmarked to Monte Carlo with isotropic monoenergetic photon sources. This thesis accomplishes adaptation of clinical Varian phase space data for use with general Monte Carlo codes including MCNP, and mapping accurate phase space data into the application of optimized EDK-SN dose calculation method with a 15-year-old patient phantom. The EDK-SN method with improved source term modeling is demonstrated to fall within accuracy of the measured golden beam data for a clinical water phantom.

Quantum systems with finite Hilbert space are considered. Position and mo- mentum states and their relation through a Fourier transform, displacement in the position-momentum phase-space, and symplectic transformations are introduced and their properties are studied. Symplectic Sp(2l;Zp) trans- formations in l-partite finite system are explicit constructed. The general method is applied to bi-partite and tri-partite systems. The effect of these transformations on the correlations is discussed. Entanglement calculations between the subsystems in a bi-partite system and a tri-partite system are presented. The effect of measurements is also studied.

A Thesis submitted to The University of Arizona College of Medicine - Phoenix in partial fulfillment of the requirements for the Degree of Doctor of Medicine. / Obstructive sleep apnea (OSA) is a condition characterized by upper airway obstruction during sleep causing intermittent hypoxia and nighttime awakening. It is a common condition in the United States that is often undiagnosed. It is a significant risk factor for decreased daytime productivity, quality of life, cardiovascular disease, and death. The current gold standard for diagnosis of OSA is laboratory‐based polysomnography (PSG). While PSG is necessary for the diagnosis and monitoring of OSA, many patients have limited access to PSG due to wait times at PSG laboratories or economic or geographic limitations. Portable sleep monitoring has been studied as a possible solution for patients who do not have access to timely PSG. This study aimed to use the Zephyr BioHarness 3, a chest‐worn physical activity monitor that records movement and physiologic data in real‐time, to detect apnea events in patients with suspected OSA undergoing single‐night laboratory PSG. Twenty patients underwent single‐night laboratory‐based PSG while simultaneously wearing the Zephyr BioHarness 3. The Zephyr BioHarness 3 data was analyzed using three methods. First, apnea events were identified in 10‐second windows of Zephyr data via support vector machine, logistic regression, and neural network (sensitivity = 76.0 ± 0.3%, specificity = 62.7 ± 0.2%, accuracy = 63.7 ± 0.1%). Second, apnea events were identified using the mean, median, and variance of the 10‐second windows (sensitivity = 72.3 ± 0.3%, specificity = 69.4 ± 0.1%), accuracy 69.6 ± 0.1%). Third, apnea events were identified using phase‐space transformation of the Zephyr BioHarness 3 data (sensitivity = 76.9 ± 0.3%, specificity = 77.9 ± 0.1 %, accuracy = 77.9 ± 0.1%). The Zephyr BioHarness shows initial promise as a possible OSA screening tool for patients suspected of OSA but who lack access to timely laboratory‐based PSG.

Voltage flicker limitation of electric utilities has been discussed in the past three decades. Arc furnace is one of the most disturbing loads that cause flicker problems in the power network. If displeasing flicker levels are predictable, then corrective solution such as static var compensation or furnace controls could be developed in cooperation between the utility and the customer. In the past, the electric fluctuations in the arc furnace voltage have been proven to be chaotic in nature. This thesis proposes a phase space approach based on nonlinearity chaotic techniques to analyze and predict voltage flicker. The determination of the phase space dimension and the application of Lyapunov exponent for flicker prediction are described. Test results have shown that accurate prediction results are obtainable for short term flicker prediction based on chaos theory.