SE(3) Koopman-MPC: Data-driven Learning and Control of Quadrotor UAVs

In this paper, we propose a novel data-driven approach for learning and control of quadrotor UAVs based on the Koopman operator and extended dynamic mode decomposition (EDMD). Building observables for EDMD based on conventional methods like Euler angles (to represent orientation) is known to involve singularities. To address this issue, we employ a set of physics-informed observables based on the underlying topology of the nonlinear system. We use rotation matrices to directly represent the orientation dynamics and obtain a lifted linear representation of the nonlinear quadrotor dynamics in the SE(3) manifold. This EDMD model leads to accurate prediction and can be generalized to several validation sets. Further, we design a linear model predictive controller (MPC) based on the proposed EDMD model to track agile reference trajectories. Simulation results show that the proposed MPC controller can run as fast as 100 Hz and is able to track arbitrary reference trajectories with good accuracy. Implementation details can be found in \url{https://github.com/sriram-2502/KoopmanMPC_Quadrotor}

Effect of Activation of the GLT-1 Transporter by a Beta-Lactam Antibiotic on Serotonin-Induced Scratching Behavior in Mice

Glutamate is believed to be the predominant excitatory neurotransmitter in the networks responsible for itch-related behavior. Beta-lactam antibiotics were shown to exert neuroprotective effects by increasing expression of the glutamate transporter GLT-1. We observed whether repeated administration of the beta-lactam antibiotic ceftriaxone suppresses serotonin-induced itch-related behavior (similarly to its effect on pain transmission) in mice. Chronic, but not acute, ceftriaxone introductions reduced the number of serotonin-induced scratches; dihydrokainic acid, a selective GLT-1 transporter inhibitor, partly but significantly abolished this effect of ceftriaxone. Our findings suggest that GLT-1 activation by beta-lactam antibiotics looks promising for the treatment of chronic itch.Як вважають, глутамат є основним збуджуючим нейротрансмітером у нейронних мережах, відповідальних за поведінкові моторні прояви при почутті свербіжу. β-лактамні антибіотики мають нейропротективні властивості, оскільки забезпечують посилену експресію глутаматного транспортера GLT-1. Ми з’ясовували, чи здатне повторне введення β-лактамного антибіотика цефтриаксону пригнічувати викликані ін’єкціями серотоніну поведінкові моторні прояви (чухальні рухи), пов’язані з індукцією почуття свербіжу (подібно до впливу цього агента на біль) у мишей. Хронічні (але не поодинокі) введення цефтриаксону викликали зменшення кількості рухів чухання. Селективний блокатор транспортера GLT-1 дигідрокаїнова кислота частково, але істотно перешкоджала цьому ефекту цефтриаксону. Наші спостереження дають підстави вважати, що активація GLT-1 β-лактамними антибіотиками є перспективним підходом у лікуванні хронічного свербіжу

Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity

We define a class of deformations in W^1,p(\u3a9,R^n), p>n 121, with positive Jacobian that do not exhibit cavitation. We characterize that class in terms of the non-negativity of the topological degree and the equality between the distributional determinant and the pointwise determinant of the gradient. Maps in this class are shown to satisfy a property of weak monotonicity, and, as a consequence, they enjoy an extra degree of regularity. We also prove that these deformations are locally invertible; moreover, the neighbourhood of invertibility is stable along a weak convergent sequence in W^1,p, and the sequence of local inverses converges to the local inverse. We use those features to show weak lower semicontinuity of functionals defined in the deformed configuration and functionals involving composition of maps. We apply those results to prove existence of minimizers in some models for nematic elastomers and magnetoelasticity

Is aspirin effective in women undergoing in vitro fertilization (IVF)? Results from an individual patient data meta-analysis (IPD MA)

BACKGROUND Aspirin is believed to improve the outcome of IVF, but previous conventional meta-analyses on the subject are conflicting. Therefore, we performed a meta-analysis with individual patient data (IPD MA) of randomized clinical trials (RCTs) on the subject. METHODS A systematic literature search was conducted to identify RCTs assessing the effectiveness of aspirin in IVF. Authors were asked to share their original data. In a one step meta-analytic approach, the treatment effect of aspirin was estimated with odds ratios (ORs) and 95% confidence intervals (CIs) using logistic regression, based on the intention to treat principle. RESULTS Ten studies fulfilled the inclusion criteria. Authors of six studies provided IPD, including 1119 patients (562 placebo and 557 aspirin). There were 160 clinical pregnancies in the aspirin (28.8%) and 179 (31.9%) in the placebo group [OR 0.86, 95% CI (0.69–1.1)]. There were 129 ongoing pregnancies in the aspirin (23.6%) and 147 in the placebo group (26.7%) [OR 0.85, 95% CI (0.65–1.1)]. Whereas the conventional meta-analysis limited to studies that could provide IPD showed an OR of 0.89 (95% CI 0.69–1.2), the conventional meta-analysis limited to the eight studies of which method of randomization could be confirmed showed an OR of 0.94 (95% CI 0.76–1.17) and the conventional meta-analysis including all 10 eligible RCTs identified with our search changed the OR to 1.07 (95% CI 0.81–1.41). This difference in direction of effect, derived from the studies not able to share IPD of which quality of randomization could not be confirmed. CONCLUSIONS Aspirin does not improve pregnancy rates after IVF.E. Groeneveld, K.A. Broeze, M.J. Lambers, M. Haapsamo, K. Dirckx, B.C. Schoot, B. Salle, C.I. Duvan, R. Schats, B.W. Mol, and P.G.A. Hompes, for the IPD MARIA study grou

Structural Role of Uracil DNA Glycosylase for the Recognition of Uracil in DNA Duplexes. Clues from Atomistic Simulations

In the \ufb01rst stage of the base excision repair pathway the enzyme uracil DNA glycosylase (UNG) recognizes and excises uracil (U) from DNA \ufb01laments. U repair is believed to occur via a multistep base-\ufb02ipping process, through which the damaged U base is initially detected and then engulfed into the enzyme active site, where it is cleaved. The subtle recognition mechanism by which UNG discriminates between U and the other similar pyrimidine nucleobases is still a matter of active debate. Detailed structural information on the di\ufb00erent steps of the base-\ufb02ipping pathway may provide insights on it. However, to date only two intermediates have been trapped crystallographically thanks to chemical modi\ufb01cations of the target and/or of its complementary base. Here, we performed force-\ufb01eld based molecular dynamics (MD) simulations to explore the structural and dynamical properties of distinct UNG/dsDNA adducts, containing A:U, A:T, G:U, or G:C base pairs, at di\ufb00erent stages of the base-\ufb02ipping pathway. Our simulations reveal that if U is present in the DNA sequence a shortlived extra-helical (EH) intermediate exists. This is stabilized by a water-mediated H-bond network, which connects U with His148, a residue pointed out by mutational studies to play a key role for U recognition and catalysis. Moreover, in this EH intermediate, UNG induces a remarkable overall axis bend to DNA. We believe this aspect may facilitate the \ufb02ipping of U, with respect to other similar nucleobases, in the latter part of the base-extrusion process. In fact, a large DNA bend has been demonstrated to be associated with a lowering of the free energy barrier for base-\ufb02ipping. A detailed comparison of our results with partially \ufb02ipped intermediates identi\ufb01ed crystallographically or computationally for other base-\ufb02ipping enzymes allows us to validate our results and to formulate hypothesis on the recognition mechanism of UNG. Our study provides a \ufb01rst ground for a detailed understanding of the UNG repair pathway, which is necessary to devise new pharmaceutical strategies for targeting DNA-related pathologies