RECOVERING LOCAL NEURAL TRACT DIRECTIONS AND RECONSTRUCTING NEURAL PATHWAYS IN HIGH ANGULAR RESOLUTION DIFFUSION MRI

Magnetic resonance imaging (MRI) is an imaging technique to visualize internal structures of the body. Diffusion MRI is an MRI modality that measures overall diffusion effect of molecules in vivo and non-invasively. Diffusion tensor imaging (DTI) is an extended technique of diffusion MRI. The major application of DTI is to measure the location, orientation and anisotropy of fiber tracts in white matter. It enables non-invasive investigation of major neural pathways of human brain, namely tractography. As spatial resolution of MRI is limited, it is possible that there are multiple fiber bundles within the same voxel. However, diffusion tensor model is only capable of resolving a single direction. The goal of this dissertation is to investigate complex anatomical structures using high angular resolution diffusion imaging (HARDI) data without any assumption on the parameters. The dissertation starts with a study of the noise distribution of truncated MRI data. The noise is often not an issue in diffusion tensor model. However, in HARDI studies, with many more gradient directions being scanned, the number of repetitions of each gradient direction is often small to restrict total acquisition time, making signal-to-noise ratio (SNR) lower. Fitting complex diffusion models to data with reduced SNR is a major interest of this study. We focus on fitting diffusion models to data using maximum likelihood estimation (MLE) method, in which the noise distribution is used to maximize the likelihood. In addition to the parameters being estimated, we use likelihood values for model selection when multiple models are fit to the same data. The advantage of carrying out model selection after fitting the models is that both the quality of data and the quality of fitting results are taken into account. When it comes to tractography, we extend streamline method by using covariance of the estimated parameters to generate probabilistic tracts according to the uncertainty of local tract orientations

Holographic entropy inequalities and gapped phases of matter

We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the "cyclic inequalities" derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.Comment: 20 pages, 4 figures. v2: section 4 rewritten, where all linear entropy (in)equalities satisfied by area-law systems are derived and an error in their relations to graph theory is correcte

Probing medium-induced jet splitting and energy loss in heavy-ion collisions

The nuclear modification of jet splitting in relativistic heavy-ion collisions at RHIC and the LHC energies is studied based on the higher twist formalism. Assuming coherent energy loss for the two splitted subjets, a non-monotonic jet energy dependence is found for the nuclear modification of jet splitting function: strongest modification at intermediate jet energies whereas weaker modification for larger or smaller jet energies. Combined with the smaller size and lower density of the QGP medium at RHIC than at the LHC, this explains the CMS-STAR groomed jet puzzle -- strong nuclear modification of the momentum sharing $z_g$ distribution at the LHC whereas no obvious modification of the $z_g$ distribution at RHIC. In contrast, the observed nuclear modification pattern of the groomed jet $z_g$ distribution cannot be explained solely by independent energy loss of the two subjets. Our result may be tested in future measurements of groomed jets with lower jet energies at the LHC and larger jet energies at RHIC, for different angular separations between the two subjets.Comment: 10 pages, 12 figure

Towards Bulk Metric Reconstruction from Extremal Area Variations

The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension $d \geq 4$, knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an explicit spacetime metric reconstruction.Comment: 33+4 pages, 7 figures; v2: addressed referee comment

Joint radar-communication waveform designs using signals from multiplexed users

Joint radar-communication designs are exploited in applications where radar and communications systems share the same frequency band or when both radar sensing and information communication functions are required in the same system. Finding a waveform that is suitable for both radar and communication is challenging due to the difference between radar and communication operations. In this paper, we propose a new method of designing dual-functional waveforms for both radar and communication using signals from multiplexed communications users. Specifically, signals from different communications users multiplexed in the time, code or frequency domains across different data bits are linearly combined to generate an overall radar waveform. Three typical radar waveforms are considered. The coefficients of the linear combination are optimized to minimize the mean squared error with or without a constraint on the signal-to-noise ratio (SNR) for the communications signals. Numerical results show that the optimization without SNR constraint can almost perfectly approximate the radar waveform in all the cases considered, giving good dual-functional waveforms for both radar and communication. Also, among different multiplexing techniques, time division multiple access is the best option to approximate the radar waveform, followed by code division multiple access and orthogonal frequency division multiple access

Quantum Circuit Cosmology: The Expansion of the Universe Since the First Qubit

We consider cosmological evolution from the perspective of quantum information. We present a quantum circuit model for the expansion of a comoving region of space, in which initially-unentangled ancilla qubits become entangled as expansion proceeds. We apply this model to the comoving region that now coincides with our Hubble volume, taking the number of entangled degrees of freedom in this region to be proportional to the de Sitter entropy. The quantum circuit model is applicable for at most 140 $e$-folds of inflationary and post-inflationary expansion: we argue that no geometric description was possible before the time $t_1$ when our comoving region was one Planck length across, and contained one pair of entangled degrees of freedom. This approach could provide a framework for modeling the initial state of inflationary perturbations.Comment: v2, minor correction

Fabrication of alginate hydrogel scaffolds and cell viability in calcium-crosslinked alginate hydrogel

Tissue-engineering (TE) is one of the most innovative approaches for tackling many diseases and body parts that need to be replaced, by developing artificial tissues and organs. For this, tissue scaffolds play an important role in various TE applications. A tissue scaffold is a 3D (3D) structure with interconnected pore networks and used to facilitate cell growth and transport of nutrients and wastes while degrading gradually itself. Many fabrication techniques have been developed recently for incorporating living cells into the scaffold fabrication process and among them; dispensing-based rapid prototyping techniques have been drawn considerable attention due to its fast and efficient material processing. This research is aimed at conducting a preliminary study on the dispensing-based biofabrication of 3D cell-encapsulated alginate hydrogel scaffolds. Dispensing-based polymer deposition system was used to fabricate 3D porous hydrogel scaffolds. Sodium alginate was chosen and used as a scaffolding biomaterial. The influences of fabrication process parameters were studied. With knowledge and information gained from this study, 3D hydrogel scaffolds were successfully fabricated. Calcium chloride was employed as crosslinker in order to form hydrogels from alginate solution. The mechanical properties of formed hydrogels were characterized and examined by means of compressive tests. The influences of reagent concentrations, gelation time, and gelation type were studied. A post-fabrication treatment was used and characterized in terms of strengthening the hydrogels formed. In addition, the influence of calcium ions used as crosslinker on cell viability and proliferation during and after the dispensing fabrication process was examined and so was the influence of concentration of calcium solutions and exposing time in both media and alginate hydrogel. The study also showed that the density of encapsulated cells could affect the viscosity of alginate solution. In summary, this thesis presents a preliminary study on the dispensing-based biofabrication of 3D cell-encapsulated alginate hydrogel scaffolds. The results obtained regarding the influence of various factors on the cell viability and scaffold fabrication would form the basis and rational to continue research on fabricating 3D cell-encapsulated scaffolds for specific applications