VictorJuiz/thesis huggingface dataset:
On the variational methods for minimal submanifolds [electronic resource]
Keywords: Mathematics.

In this thesis, we study two problems concerning variational methods for minimal submanifolds. Specifically we consider min-max theory for minimal surfaces. We construct the "saddle point" type critical points for the area functional, and study the geometrical properties of these. In the first part, we consider the mapping problem for the min-max theory. In particular, we prove an existence theorem for min-max minimal surfaces of arbitrary genus g ≥ 2 by variational methods. We show that the min-max critical value for the area functional can be achieved by the bubbling limit of branched minimal surfaces with nodes of genus g together with possibly finitely many branched minimal spheres. We also prove a strong convergence theorem similar to the classical mountain pass lemma. In the second part, we consider the geometric measure theory approach to the min-max theory. We study the shape of the min-max minimal hypersurface constructed by Almgren-Pitts corresponding to the fundamental class of a Riemannian manifold (M, g) of dimension n + 1 with positive Ricci curvature and 2 ≤ n ≤ 6. We characterize the Morse index, area and multiplicity of this min-max hypersurface. Precisely, we show that the min-max hypersurface is either orientable and of index one, or is a double cover of a non-orientable minimal hypersurface with least area among all closed embedded minimal hypersurfaces.
Online self-test, diagnostics, and self-repair for robust system design [electronic resource]
Keywords: Electrical Engineering.

Electronic system malfunctions resulting from hardware failures are a growing concern. For silicon integrated circuits (ICs) with remarkably small geometries, several hardware failure mechanisms that were largely benign in the past are now becoming visible at the system-level. Therefore, a wide range of future electronic systems will require tolerance of hardware failures during their operation. Hardware failures can be broadly classified as permanent or temporary. In this dissertation, we present cost-effective techniques to enable the design of robust systems with built-in resilience to permanent failures, overcoming a major reliability challenge of electronic systems. To tolerate permanent failures in robust systems, three critical activities are involved: detection, localization, and self-repair. Online self-test and diagnostics enable a system to test itself during normal operation to detect and localize permanent failures. We present three new online self-test ideas: 1. A technique called CASP (Concurrent Autonomous chip self-test using Stored test Patterns) which achieves thorough online self-test while incurring minimal area and power cost. 2. Software orchestration techniques that minimize visible system performance impact during online self-test of processor cores. 3. New design principles that minimize system-level performance impact during online self-test of uncore components. Examples of uncore components include cache controllers, memory controllers, and I/O controllers. Although uncore components occupy significant portions of multi-core ICs, very little existing research targets online self-test of these components. We demonstrate the effectiveness of these online self-test ideas using the OpenSPARC T2 design supporting 8 processor cores and 64 hardware threads. The results show that our CASP technique, assisted by software orchestration techniques for processor cores and online self-test design principles for uncore components, achieves very high online test coverage while imposing only 1% area cost, 1% power cost, and 3% performance cost. We also present new self-repair techniques, which are required to keep the system functioning correctly in the presence of failures. Unlike on-chip memories and processor cores, very little attention has been paid to self-repair of uncore components. Naïve redundancy-based techniques impose significant (e.g., 16%) chip-level area costs. We present new techniques that enable cost-effective self-repair of uncore components. For OpenSPARC T2, the chip-level area, power, and performance costs are 7%, 6%, and 5%, respectively, for self-repair of any single faulty component. Our techniques are capable of self-repairing multiple faulty components with graceful degradation of system performance.
Optically controlled magnetic resonance imaging compatible active needle [electronic resource]
Keywords: Mechanical Engineering

An active needle is proposed for the development of magnetic resonance imaging (MRI) guided percutaneous procedures. The needle uses internal laser heating, conducted via optical fibers, of a shape memory alloy (SMA) actuator to produce bending in the distal section of the needle. Active bending of the needle as it is inserted into an organ allows it to reach small targets while overcoming the effects of interactions with surrounding tissue, which can otherwise deflect the needle away from its ideal path. The active section is designed to bend preferentially in one direction under actuation, and is made from SMA for its combination of MR- and bio-compatibility and its superelastic bending properties. A prototype, with a size equivalent to a standard 16 gauge biopsy needle, exhibits significant bending in the air with a tip rotation of more than 10 degree. For this slender, 1.67 mm diameter, MR-compatible active needle, a distributed, side optical actuation method is presented. A prototype, with multiple side heating regions made by chemical etching, demonstrates faster initial response than prototypes that use fiber tip heating for a given optical power. A gold coating captures light that would otherwise be lost and redirects it back to the SMA wire for higher efficiency and greater safety in tissue. A single-ended optical sensor with a gold reflector at the tip is also developed to measure the curvature independently of temperature as a function of optical transmission loss. Preliminary tests with the sensor prototype demonstrate approximately linear response and a repeatable signal, independent of the bending history. The optical sensor is intended for closed-loop control of the bend angle, using a presented opto-thermo-mechanical model. The needle performance was studied in tissue phantoms mimicking human prostate. The experimental results show that this needle can compensate for the usual targeting error during prostate biopsy. For future versions, a more flexible needle design is suggested to increase the steerability and bending speed. In addition, because human tissue works as a large heat sink, resulting in fast heat dissipation from the wire, it is suggested to use a wire with a lower transition temperature. Ideally, the wire should have a transition temperature starting only slightly above body temperature. This modification would also reduce the required optical power. A feasibility study of the fabrication of such a wire is presented, combining the standard annealing technique for coarse tuning with pre-stressing for fine tuning of the transition temperature.
Optimal information collection for dynamic health care policy [electronic resource]
Keywords: Management Science and Engineering.

Mathematical models of health systems and disease can provide important information to decision makers when direct experimentation is impossible, impractical, or unethical, and when there are many possible decision alternatives. When costs or benefits of a medical or health policy decision are in the distant future (perhaps decades away) or are borne by other members of society, mathematical models may be the only practical way to fully evaluate the costs and consequences of policy alternatives. Through modeling, the decision maker can develop a deeper understanding of which factors have the greatest impact on the outcome of interest and explicitly explore decision uncertainty. This dissertation applies and extends the use of mathematical models in the application area of health policy -- specifically to applications of human immunodeficiency virus (HIV) and hepatitis C virus (HCV) screening in injection drug users (IDUs) and the general population.
Optimization methods for regularized high dimensional graphical model selection [electronic resource]
Keywords: Computational and Mathematical Engineering.

Graphical models yield compact representations of the dependencies present in a multivariate random vector via graphs/networks. Nodes in the graph encode random variables in a high dimensional random vector, and the edges represent different types of associations, such as conditional or marginal dependences. Sparse graphical models have been useful for encoding complex multivariate dependencies in ultra high dimensional sample starved settings, where limited sample sizes often only allow for the estimation of sparse graphs. Given the wide applicability of such models, the field has seen several key contributions from a wide spectrum of communities, including the statistics, machine learning, mathematics, computer science, computational mathematics and optimization communities. Despite tremendous efforts, the vast majority of work on graphical model selection for continuous data have been centered around the multivariate Gaussian distribution. This restriction often poses serious shortcomings in various applications. In this thesis we propose a comprehensive methodology for graphical model selection that goes beyond the Gaussian paradigm. In particular, we propose a nested sequence of families of distributions rooted in probability and statistical theory that enrich the Gaussian, so as to yield a a more flexible family. We demonstrate that our proposed class of distributions, the log-concave elliptical family, has deep and interesting structure. Moreover, this family of multivariate distributions are constructed so as to take advantage of convex optimization tools that yield fast algorithms in order to estimate high dimensional partial correlation graphs. We develop rigorous theory to give a firm foundation to our proposed approach, both from optimization and statistical perspectives. Statistical issues such as identifiability, calculation of the Fisher information, consistency and asymptotic normality are considered. Consistent estimation of the additional shape parameters of the log-concave elliptical family in a way that is computationally tractable is carefully developed. From the optimization perspective, first and second order proximal methods are used for maximizing l1 regularized log-concave elliptical likelihoods, and linear and quadratic rates of convergence for these approaches are established. To our knowledge, our endeavour is the only such approach in the literature with established theory that is applicable in moderate or high dimensions. The methodology is illustrated on both real and simulated data to demonstrate its efficacy.
Optimizing patient treatment decisions in an era of rapid technological advances [electronic resource] : models and insights
Keywords: Management Science and Engineering.

How can chronically ill patients make the best treatment decisions when there is uncertainty about the costs and effectiveness of new and emerging treatments? We investigate this question by evaluating new medical technologies and interventions focusing on chronic hepatitis C virus (HCV) infection. Chronic HCV affects approximately 3 million Americans and has been historically difficult to treat. New and emerging treatments show great promise in providing better health outcomes, but at a significantly higher cost. Using decision-analytic Markov models, we first examine the cost-effectiveness of various disease monitoring strategies before treatment initiation, and the improved use of a new genetic marker-guided therapy to target HCV treatment to patients. We then investigate the cost-effectiveness of population screening policies to detect and treat the estimated 2 million Americans who are unaware of their chronic HCV infection. Motivated by this applied work, we consider the general theoretical question of how long a patient with a treatable chronic disease should wait for more effective treatments to emerge before undergoing currently available treatment. This decision involves a difficult tradeoff between the deterioration of a patient's health and the magnitude of technological improvement over time. We model the patient-level treatment adoption decision problem as an optimal stopping problem using a discrete-time, finite-horizon Markov Decision Process framework. We present structural properties of the model, analytical results, and a numerical example for chronic HCV treatment. Results of this work can inform both individuals and organizations in making treatment decisions in the presence of rapid medical technology advancement.
Optogenetic dissection of amygdala and extended amygdala circuits in the anxious state [electronic resource]
Keywords: Neurosciences.

Anxiety, a sustained state of apprehension in the absence of a specific and imminent threat, is critical for an organism to survive in an environment with unpredictable risks. In disease states, however, anxiety becomes severely debilitating; anxiety disorders represent the most common psychiatric diseases (28% lifetime prevalence). Despite the high prevalence of anxiety disorders, current treatments are often ineffective and have severe side-effects, such as addiction, pointing to the need for a deeper understanding of anxiety circuits. The amygdala and extended amygdala have long been hypothesized to play a central role in anxiety, but the function of the intra- and inter-connections of the amygdala and extended amygdala circuits are unclear, largely due to the lack of appropriate tools. With the advent of optogenetics, which was pioneered in the Deisseroth lab, and with the evolution of virus- or promoter-based targeting strategies, it is now possible to manipulate a specific circuit element with unprecedented precision and to identify its function in behavior. The first part of this thesis illustrates the application of optogenetics to identify an intra-amygdala circuit element that decreases anxiety. The second part explores the functional circuitry of the bed nucleus of the stria terminalis (BNST), a key component of the extended amygdala. We studied the roles of its input from the amygdala and outputs to the hypothalamus and brainstem areas in the anxious state. Here, the term 'anxious state' is used to emphasize that anxiety is a behavioral state consisting of distinct features, such as behavioral risk-avoidance and changes in respiration rate. We sought to find circuit elements mediating each distinct feature of the anxious state. The data provided by this thesis furthers our understanding of the function and dysfunction of anxiety circuitry. The approach that we employed here for functional circuit mapping may be applicable to the dissection of other behavioral states, such as fear and aggression.
Ordering-based nonlinear solver with adaptive coupling for multiphase flow and transport [electronic resource]
Keywords: Energy Resources Engineering.

The Fully Implicit Method (FIM) is widely used to discretize the nonlinear conservation equations that govern multiphase flow in porous media. Although FIM is unconditionally stable, the nonlinear solver, which is typically based on Newton's method, often fails to converge for large time steps. As the time step size increases, the complexity of the nonlinear coupling increases. In the presence of strong buoyancy in a heterogeneous domain, for example, counter-current flow may be present, and phase-flow reversal - as a function of time or Newton iteration - becomes an issue. It does not take too many interfaces with flow reversal across them to make the nonlinear solver stall. Even when the Newton-based iterative procedure converges, the cost associated with updating all the unknowns simultaneously - everywhere and all the time - can be quite expensive. Conventional sequential-implicit strategies can be used to reduce the cost, but they suffer from severe restrictions on the allowable timestep size. We propose a new nonlinear solution strategy to improve the robustness and efficiency of FIM. Specifically, for each FIM Newton iteration, we update pressure by solving a linear system obtained from the full Jacobian. Then, we construct a directed graph with grid-cells as nodes and phase fluxes at grid-cell interfaces as edges, to identify the counter-current flow regions. After that, we employ a topological ordering that makes it possible to visit the components once, from upstream to downstream. The graph components vary in size from a single cell to multiple `strongly connected' cells. For each component made up of a single cell, we update the saturation nonlinearly. For each component made up of multiple cells (strongly connected region), we perform a simultaneous linear update of both saturation and pressure. The saturation iterates are safeguarded based on `trust regions' of the flux (fractional flow) functions. We compare the new solver with the current state-of-the-art for a wide range of heterogeneous problems with special focus on counter-current flow due to buoyancy. Our results show that the proposed FIM nonlinear solver converges for large time steps, with excellent convergence rates and lower computational cost per iteration compared with standard or safeguarded Newton.
The origins of C4 photosynthesis [electronic resource]
Keywords: Biology.

This dissertation describes the physiological advantages and disadvantages conferred by 'Type I' C3-C4 intermediate photosynthesis, how they appear to be related to the ecological distribution of C3-C4 intermediate species, and how these relationships may provide insight to the evolutionary origins of C4 photosynthesis. The primary study system is the genus Flaveria (Asteraceae), a group that is endemic to southwestern North America and contains multiple representatives of C3, C3-C4 intermediate, and NADP-malic enzyme type C4 photosynthesis. A laboratory-based gas exchange study of six of the basal species of Flaveria grown under common conditions finds that, relative to C3 species, 'Type I' C3-C4 intermediate species are characterized by an increase in instantaneous photosynthetic nutrient use-efficiency and a decrease in instantaneous water use-efficiency. The majority of the increase in nutrient use-efficiency appears to derive from refixation of photorespired CO2 in the bundle sheath, and the enhanced resistance of the bundle sheath cell walls that this implies may be the cause of the coincident decrease in water use-efficiency. A field-based study of wild populations of Flaveria chloraefolia ('Type I' C3-C4) finds that their photosynthetic performance is analogous to what was observed in the laboratory and has the potential to confer several ecologically relevant advantages. Since the increase in nutrient use-efficiency conferred by the 'Type I' C3-C4 pathway is probably less than that conferred by the C4 pathway under comparable conditions, this aspect of performance alone does not appear to be sufficient to explain the stable coexistence of C3, C3-C4, and C4 species in an ecological context. However, it might be sufficient to explain the relative advantage of C3-C4 species compared to C3 species in an evolutionary context.
Packet transport mechanisms for data center networks [electronic resource]
Keywords: Electrical Engineering.

Data centers are large facilities that house tens of thousands of interconnected computing and storage servers. In recent years, large investments have been made in massive data centers to support services such as search, social networking, electronic commerce, and cloud computing. This has spurred a lot of interest in the industry and the research community in innovation for reducing costs and improving the performance of data center networks. One of the most crucial components of a data center network (indeed, of any network) is its transport mechanism --- the method by which data is transferred from one server to another. The major goals of a transport mechanism are to transfer data at the highest possible rate and with the lowest latency. In this dissertation, we present measurements from three production clusters with 6000 servers that reveal impairments with today's state-of-the-art Transmission Control Protocol (TCP) in data center environments. The impairments are rooted in TCP's demands on the limited buffer space available in commodity data center switches. We then propose two novel transport mechanisms designed specifically for the data center: DCTCP and HULL. These mechanisms enable the construction of large-scale, high-performance data center networks with very low latency and high bandwidth using commodity switches. DCTCP (for Data Center TCP) uses a simple modification to the TCP congestion control algorithm that allows it to maintain very low queue occupancy (and latency) in data center switches while simultaneously providing high throughput. HULL (for High-bandwidth Ultra-Low Latency) is an architecture that builds on DCTCP to deliver baseline fabric latency (only propagation and switching) by nearly eliminating all queueing from the data center network. We also present a stability analysis of the Quantized Congestion Notification (QCN) algorithm that has been standardized as the IEEE802.1Qau standard for Layer 2 (Ethernet) congestion control.
P-adic Hodge theory in rigid analytic families [electronic resource]
Keywords: Mathematics.

In this thesis, we study p-adic Hodge theory in rigid analytic families. Roughly speaking, p-adic Hodge theory is the study of p-adic representations of p-adic Galois groups. One introduces certain p-adic period rings B, such as B_{HT}, B_{dR}, B_{st}, and B_{cris}, and uses them to define functors D_B(.) from the category of p-adic Galois representations to various categories of linear algebra data. In the first half of this thesis, we study generalizations of these functors to families of p-adic Galois representations with rigid analytic coefficients. We prove that the functors D_{HT}(.) and D_{dR}(.) are coherent sheaves, and we prove that the B-admissible locus is a closed subspace of the base. In the second half of this thesis, we study the linear algebra data which arises from families of potentially semi-stable Galois representations valued in a connected reductive group G. We prove that for any G, the moduli space of linear algebra data is reduced and locally a complete intersection, and we deduce that potentially semi-stable deformation rings are generically smooth and equi-dimensional.