A First Taste of Quantum Gravity Effects: Deforming Phase Spaces with the Heisenberg Double

We present a well-defined framework to deform the phase spaces of classical particles. These new phase spaces, called Heisenberg doubles, provide a laboratory to probe the effects of quantum gravity. In particular, they allow us to equip momentum space with a non-abelian group structure by the introduction of a single deformation parameter. In order to connect Heisenberg doubles with classical phase spaces we begin with a review of Hamiltonian systems, symmetries and conservation laws in the classical framework. Next, we provide a comprehensive review of the theory behind Poisson-Lie groups, including Lie bialgebras and the construction of the Drinfeld double. Lastly, we build the Heisenberg double from Poisson-Lie group components. We then identify the Heisenberg double as a deformation of the cotangent bundle of Lie groups and extend many of the notions of classical Hamiltonian systems to this new picture with Poisson-Lie symmetries. As an example, we look at a new presentation of the deformed rotator

Nonlinear Model Predictive Control Reduction Strategies for Real-time Optimal Control

This thesis presents a variety of strategies to accelerate the turnaround times (TATs) of nonlinear and hybrid model predictive controllers (MPCs). These strategies are unified by the themes of symbolic computing, nonlinear model reduction and automotive control. The first contribution of this thesis is a new MPC problem formulation, called symbolic single shooting (symSS), that leverages the power of symbolic computing to generate an optimization problem of minimal dimension. This formulation is counter to the recent trend of introducing and exploiting sparsity of the MPC optimization problem for tailored solvers to exploit. We make use of this formulation widely in this thesis. The second contribution of this thesis is a novel application of proper orthogonal decomposition (POD) to MPC. In this strategy we construct a dimensionally-reduced optimization problem by restricting the problem Lagrangian to a subspace. This subspace is found by running simulations offline from which we extract the important solution features. Using this restricted Lagrangian we are able to reduce the problem dimension dramatically, thus simplifying the linear solve. This leads to TAT accelerations of more than two times with minimal controller degradation. The third contribution of this thesis is an informed move blocking strategy. This strategy exploits the features extracted in the restricted Lagrangian subspace to derive a sequence of increasingly blocked move blocking strategies. These move blocking strategies can then be used to reduce the dimension of the optimization problem in a sparse manner, leading to even greater acceleration of the controller TAT . The fourth contribution of this thesis is a new quasi-Newton method for MPC. This method utilizes ideas similar to singular perturbation-based model reduction to truncate the expression for the problem Hessian at the symbolic level. For nonlinear systems with a modest Lipschitz constant, we can identify the timestep as a `small' parameter about which we can do a perturbative expansion of the Lagrangian and its derivatives. Truncating to first order in the timestep, we are able to find a good approximation of the Hessian leading to TAT acceleration. The fifth contribution of this thesis is controller integration strategy based on nested MPCs. Using the symSS formulation we can construct an explicit model of a controlled plant that includes the full model as well as the MPC's action. This form of the controlled plant model allows us to generate exact derivatives so that fast solvers can be used for real time application. We focus here on the problem of planning and motion control integration for autonomous vehicles but this strategy can be extended for other problems that require accurate models of a controlled plant. The sixth contribution of this thesis is a strategy to handle integer controls in MPC based on a few reasonable assumptions: our predictions over the horizon are almost perfect and the future is inevitable. These assumptions enforce a degree of continuity, in the integer controls, between solutions over different timesteps that allow us to mitigate chatter and enforce a hard upper bound on solution complexity. This strategy constrains the integer solution of one timestep to be related to that of the previous timestep. Our results show that this strategy provides acceptable control performance while achieving TATs that are orders of magnitude smaller than those for conventional MINLP-based methods, thereby opening the door to new real-time applications of hybrid MPC

Improving model predictive controller turnaround time using restricted Lagrangians

We present a new application of proper orthogonal decomposition (POD) to optimal control. By restricting the Lagrangian of an optimal control problem to a suitable affine subspace, we can achieve a reduction in computational cost leading to faster turnaround times with minimal degradation in controller performance. An explicit algorithm for nonlinear model predictive control (NMPC) reduction using POD is presented along with some initial error analysis. To the best of our knowledge, this is the first time such an approach has been presented. We applied this approach to the control of a vehicle during a double lane change maneuver using NMPC and achieved 2 times faster turnaround times with excellent controller performance. This reduction approach for the development of real-time optimal controls is very promising and introduces some new research directions.This work was supported by Natural Sciences and Engineering Research Council of Canada (NSERC), the Toyota Motor Corporation and MaplesoftTM.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142387/1/2017_IEEE.pd

The GeneMANIA prediction server: biological network integration for gene prioritization and predicting gene function

GeneMANIA (http://www.genemania.org) is a flexible, user-friendly web interface for generating hypotheses about gene function, analyzing gene lists and prioritizing genes for functional assays. Given a query list, GeneMANIA extends the list with functionally similar genes that it identifies using available genomics and proteomics data. GeneMANIA also reports weights that indicate the predictive value of each selected data set for the query. Six organisms are currently supported (Arabidopsis thaliana, Caenorhabditis elegans, Drosophila melanogaster, Mus musculus, Homo sapiens and Saccharomyces cerevisiae) and hundreds of data sets have been collected from GEO, BioGRID, Pathway Commons and I2D, as well as organism-specific functional genomics data sets. Users can select arbitrary subsets of the data sets associated with an organism to perform their analyses and can upload their own data sets to analyze. The GeneMANIA algorithm performs as well or better than other gene function prediction methods on yeast and mouse benchmarks. The high accuracy of the GeneMANIA prediction algorithm, an intuitive user interface and large database make GeneMANIA a useful tool for any biologist

Adjunctive rifampicin for Staphylococcus aureus bacteraemia (ARREST): a multicentre, randomised, double-blind, placebo-controlled trial.

BACKGROUND: Staphylococcus aureus bacteraemia is a common cause of severe community-acquired and hospital-acquired infection worldwide. We tested the hypothesis that adjunctive rifampicin would reduce bacteriologically confirmed treatment failure or disease recurrence, or death, by enhancing early S aureus killing, sterilising infected foci and blood faster, and reducing risks of dissemination and metastatic infection. METHODS: In this multicentre, randomised, double-blind, placebo-controlled trial, adults (≥18 years) with S aureus bacteraemia who had received ≤96 h of active antibiotic therapy were recruited from 29 UK hospitals. Patients were randomly assigned (1:1) via a computer-generated sequential randomisation list to receive 2 weeks of adjunctive rifampicin (600 mg or 900 mg per day according to weight, oral or intravenous) versus identical placebo, together with standard antibiotic therapy. Randomisation was stratified by centre. Patients, investigators, and those caring for the patients were masked to group allocation. The primary outcome was time to bacteriologically confirmed treatment failure or disease recurrence, or death (all-cause), from randomisation to 12 weeks, adjudicated by an independent review committee masked to the treatment. Analysis was intention to treat. This trial was registered, number ISRCTN37666216, and is closed to new participants. FINDINGS: Between Dec 10, 2012, and Oct 25, 2016, 758 eligible participants were randomly assigned: 370 to rifampicin and 388 to placebo. 485 (64%) participants had community-acquired S aureus infections, and 132 (17%) had nosocomial S aureus infections. 47 (6%) had meticillin-resistant infections. 301 (40%) participants had an initial deep infection focus. Standard antibiotics were given for 29 (IQR 18-45) days; 619 (82%) participants received flucloxacillin. By week 12, 62 (17%) of participants who received rifampicin versus 71 (18%) who received placebo experienced treatment failure or disease recurrence, or died (absolute risk difference -1·4%, 95% CI -7·0 to 4·3; hazard ratio 0·96, 0·68-1·35, p=0·81). From randomisation to 12 weeks, no evidence of differences in serious (p=0·17) or grade 3-4 (p=0·36) adverse events were observed; however, 63 (17%) participants in the rifampicin group versus 39 (10%) in the placebo group had antibiotic or trial drug-modifying adverse events (p=0·004), and 24 (6%) versus six (2%) had drug interactions (p=0·0005). INTERPRETATION: Adjunctive rifampicin provided no overall benefit over standard antibiotic therapy in adults with S aureus bacteraemia. FUNDING: UK National Institute for Health Research Health Technology Assessment

Aorta-right atrial fistula: an unusual complication of ascending aortic dissection

Ascending aortic dissection complicated by aorta-right atrial fistula is a very rare occurrence. The patient may present with atypical clinical findings such as a continuous murmur or atrioventricular block, making the diagnosis difficult. Surgical repair is straightforward unless the correct diagnosis is missed, in which case there may be difficulties during the initial period of cardiopulmonary bypass. This report deals with the successful management of a 67-year-old man with this condition