Tensor completion in hierarchical tensor representations

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the reconstruction of tensors of low multi-linear rank in recently introduced hierarchical tensor formats from a small number of measurements. Hierarchical tensors are a flexible generalization of the well-known Tucker representation, which have the advantage that the number of degrees of freedom of a low rank tensor does not scale exponentially with the order of the tensor. While corresponding tensor decompositions can be computed efficiently via successive applications of (matrix) singular value decompositions, some important properties of the singular value decomposition do not extend from the matrix to the tensor case. This results in major computational and theoretical difficulties in designing and analyzing algorithms for low rank tensor recovery. For instance, a canonical analogue of the tensor nuclear norm is NP-hard to compute in general, which is in stark contrast to the matrix case. In this book chapter we consider versions of iterative hard thresholding schemes adapted to hierarchical tensor formats. A variant builds on methods from Riemannian optimization and uses a retraction mapping from the tangent space of the manifold of low rank tensors back to this manifold. We provide first partial convergence results based on a tensor version of the restricted isometry property (TRIP) of the measurement map. Moreover, an estimate of the number of measurements is provided that ensures the TRIP of a given tensor rank with high probability for Gaussian measurement maps.Comment: revised version, to be published in Compressed Sensing and Its Applications (edited by H. Boche, R. Calderbank, G. Kutyniok, J. Vybiral

Treatment Outcomes of Patients With Multidrug-Resistant and Extensively Drug-Resistant Tuberculosis According to Drug Susceptibility Testing to First- and Second-line Drugs: An Individual Patient Data Meta-analysis

The clinical validity of drug susceptibility testing (DST) for pyrazinamide, ethambutol, and second-line antituberculosis drugs is uncertain. In an individual patient data meta-analysis of 8955 patients with confirmed multidrug-resistant tuberculosis, DST results for these drugs were associated with treatment outcome

Cabotegravir for HIV Prevention in Cisgender Men and Transgender Women

Background: Safe and effective long-acting injectable agents for preexposure prophylaxis (PrEP) for human immunodeficiency virus (HIV) infection are needed to increase the options for preventing HIV infection. Methods: We conducted a randomized, double-blind, double-dummy, noninferiority trial to compare long-acting injectable cabotegravir (CAB-LA, an integrase strand-transfer inhibitor [INSTI]) at a dose of 600 mg, given intramuscularly every 8 weeks, with daily oral tenofovir disoproxil fumarate-emtricitabine (TDF-FTC) for the prevention of HIV infection in at-risk cisgender men who have sex with men (MSM) and in at-risk transgender women who have sex with men. Participants were randomly assigned (1:1) to receive one of the two regimens and were followed for 153 weeks. HIV testing and safety evaluations were performed. The primary end point was incident HIV infection. Results: The intention-to-treat population included 4566 participants who underwent randomization; 570 (12.5%) identified as transgender women, and the median age was 26 years (interquartile range, 22 to 32). The trial was stopped early for efficacy on review of the results of the first preplanned interim end-point analysis. Among 1698 participants from the United States, 845 (49.8%) identified as Black. Incident HIV infection occurred in 52 participants: 13 in the cabotegravir group (incidence, 0.41 per 100 person-years) and 39 in the TDF-FTC group (incidence, 1.22 per 100 person-years) (hazard ratio, 0.34; 95% confidence interval, 0.18 to 0.62). The effect was consistent across prespecified subgroups. Injection-site reactions were reported in 81.4% of the participants in the cabotegravir group and in 31.3% of those in the TDF-FTC group. In the participants in whom HIV infection was diagnosed after exposure to CAB-LA, INSTI resistance and delays in the detection of HIV infection were noted. No safety concerns were identified. Conclusions: CAB-LA was superior to daily oral TDF-FTC in preventing HIV infection among MSM and transgender women. Strategies are needed to prevent INSTI resistance in cases of CAB-LA PrEP failure

Revitalizing a mature oil play: Strategies for finding and producing unrecovered oil in Frio Fluvial-Deltaic Sandstone Reservoirs of South Texas

The Frio Fluvial-Deltaic Sandstone Play of South Texas is one example of a mature play where reservoirs are being abandoned at high rates, potentially leaving behind significant unrecovered resources in untapped and incompletely drained reservoirs. Nearly 1 billion barrels of oil have been produced from Frio reservoirs since the 1940`s, yet more than 1.6 BSTB of unrecovered mobile oil is estimated to remain in the play. Frio reservoirs of the South Texas Gulf Coast are being studied to better characterize interwell stratigraphic heterogeneity in fluvial-deltaic depositional systems and determine controls on locations and volumes of unrecovered oil. Engineering data from fields throughout the play trend were evaluated to characterize variability exhibited by these heterogeneous reservoirs and were used as the basis for resource calculations to demonstrate a large additional oil potential remaining within the play. Study areas within two separate fields have been selected in which to apply advanced reservoir characterization techniques. Stratigraphic log correlations, reservoir mapping, core analyses, and evaluation of production data from each field study area have been used to characterize reservoir variability present within a single field. Differences in sandstone depositional styles and production behavior were assessed to identify zones with significant stratigraphic heterogeneity and a high potential for containing unproduced oil. Detailed studies of selected reservoir zones within these two fields are currently in progress

Revitalizing a mature oil play: Strategies for finding and producing oil in Frio Fluvial-Deltaic Sandstone reservoirs of South Texas

Domestic fluvial-dominated deltaic (FDD) reservoirs contain more than 30 Billion barrels (Bbbl) of remaining oil, more than any other type of reservoir, approximately one-third of which is in danger of permanent loss through premature field abandonments. The U.S. Department of Energy has placed its highest priority on increasing near-term recovery from FDD reservoirs in order to prevent abandonment of this important strategic resource. To aid in this effort, the Bureau of Economic Geology, The University of Texas at Austin, began a 46-month project in October, 1992, to develop and demonstrate advanced methods of reservoir characterization that would more accurately locate remaining volumes of mobile oil that could then be recovered by recompleting existing wells or drilling geologically targeted infill. wells. Reservoirs in two fields within the Frio Fluvial-Deltaic Sandstone (Vicksburg Fault Zone) oil play of South Texas, a mature play which still contains 1.6 Bbbl of mobile oil after producing 1 Bbbl over four decades, were selected as laboratories for developing and testing reservoir characterization techniques. Advanced methods in geology, geophysics, petrophysics, and engineering were integrated to (1) identify probable reservoir architecture and heterogeneity, (2) determine past fluid-flow history, (3) integrate fluid-flow history with reservoir architecture to identify untapped, incompletely drained, and new pool compartments, and (4) identify specific opportunities for near-term reserve growth. To facilitate the success of operators in applying these methods in the Frio play, geologic and reservoir engineering characteristics of all major reservoirs in the play were documented and statistically analyzed. A quantitative quick-look methodology was developed to prioritize reservoirs in terms of reserve-growth potential

Quick-look assessments to identify optimal CO2 EOR storage sites

Bureau of Economic Geolog

Geologic factors controlling CO2 storage capacity and permanence: case studies based on experience with heterogeneity in oil and gas reservoirs applied to CO2 storage

Bureau of Economic Geolog

Geologic and infrastructure factors for delineating areas for clean coal: examples in Texas, USA

Bureau of Economic Geolog

Measuring permanence of CO2 storage in saline formations: the Frio experiment

Bureau of Economic Geolog