On definable ff-generic groups and minimal flows in pp-adically closed fields

Let $X$ be a definable group definable over a small model $M_0$. Recall that a global type $p$ on $X$ is definable $f$-generic over $M_0$ if every left translate of $p$ is definable over $M_0$. We call $p$ strongly $f$-generic over $M_0$ if every left translate of $p$ does not fork over $M_0$. Let $H$ be a group definable over the field ${\mathbb Q}_p$ of $p$-adic numbers admitting global definable $f$-generic types over ${\mathbb Q}_p$. We show that $H$ has unboundedly many global weakly generic types iff there is a global type $r$ on $H$ which is strongly $f$-generic over ${\mathbb Q}_p$ and a ${\mathbb Q}_p$-definable function $\theta$ such that $\theta(r)$ is finitely satisfiable in ${\mathbb Q}_p$. Recall that the $\mu$-type $\mu(x)$ on $H$ is the partial type consisting of the formulas over ${\mathbb Q}_p$ which define open neighborhoods of the identity of $H$. We show that every global weakly generic type $r$ on $H$ is $\mu$-invariant: For any $\epsilon\models \mu$ and $a\models r$, we have $\epsilon\cdot a\models r$. Let $G$ be groups definable over ${\mathbb Q}_p$ such that $H$ is a normal subgroup of $G$ and $G/H$ is a definably compact group. Then we show that the weakly generic types on $G$ coincide with almost periodic types $G$ iff $G$ has boundedly many global weakly generic types

On minimal flows and definable amenability in some distal NIP theories

We study the definable topological dynamics $(G(M), S_G(M))$ of a definable group acting on its type space, where $M$ is either an $o$-minimal structure or a $p$-adically closed field, and $G$ a definable amenable group. We focus on the problem raised by Neweslki of whether weakly generic types coincide with almost periodic types, showing that the answer is positive when $G$ has boundedly many global weakly generic types. We also give two "minimal counterexamples" where $G$ has unboundedly many global weakly generic types, extending the main results of "On minimal flows, definably amenable groups, and o-minimality" to a more general context

A Real-time Nonlinear Model Predictive Controller for Yaw Motion Optimization of Distributed Drive Electric Vehicles

This paper proposes a real-time nonlinear model predictive control (NMPC) strategy for direct yaw moment control (DYC) of distributed drive electric vehicles (DDEVs). The NMPC strategy is based on a control-oriented model built by integrating a single track vehicle model with the Magic Formula (MF) tire model. To mitigate the NMPC computational cost, the continuation/generalized minimal residual (C/GMRES) algorithm is employed and modified for real-time optimization. Since the traditional C/GMRES algorithm cannot directly solve the inequality constraint problem, the external penalty method is introduced to transform inequality constraints into an equivalently unconstrained optimization problem. Based on the Pontryagin’s minimum principle (PMP), the existence and uniqueness for solution of the proposed C/GMRES algorithm are proven. Additionally, to achieve fast initialization in C/GMRES algorithm, the varying predictive duration is adopted so that the analytic expressions of optimally initial solutions in C/GMRES algorithm can be derived and gained. A Karush-Kuhn-Tucker (KKT) condition based control allocation method distributes the desired traction and yaw moment among four independent motors. Numerical simulations are carried out by combining CarSim and Matlab/Simulink to evaluate the effectiveness of the proposed strategy. Results demonstrate that the real-time NMPC strategy can achieve superior vehicle stability performance, guarantee the given safety constraints, and significantly reduce the computational efforts

Bridging Adversarial and Nonstationary Multi-armed Bandit

In the multi-armed bandit framework, there are two formulations that are commonly employed to handle time-varying reward distributions: adversarial bandit and nonstationary bandit. Although their oracles, algorithms, and regret analysis differ significantly, we provide a unified formulation in this paper that smoothly bridges the two as special cases. The formulation uses an oracle that takes the best-fixed arm within time windows. Depending on the window size, it turns into the oracle in hindsight in the adversarial bandit and dynamic oracle in the nonstationary bandit. We provide algorithms that attain the optimal regret with the matching lower bound

A Computationally Efficient Path Following Control Strategy of Autonomous Electric Vehicles with Yaw Motion Stabilization

his paper proposes a computationally efficient path following control strategy of autonomous electric vehicles (AEVs) with yaw motion stabilization. First, the nonlinear control-oriented model including path following model, single track vehicle model, and Magic Formula tire model, are constructed. To handle the stability constraints with ease, the nonlinear model predictive control (NMPC) technique is applied for path following issue. Here NMPC control problem is reasonably established with the constraints of vehicle sideslip angle, yaw rate, steering angle, lateral position error, and Lyapunov stability. To mitigate the online calculation burden, the continuation/ generalized minimal residual (C/GMRES) algorithm is adopted. The deadzone penalty functions are employed for handling the inequality constraints and holding the smoothness of solution. Moreover, the varying predictive duration is utilized in this paper so as to fast gain the good initial solution by numerical algorithm. Finally, the simulation validations are carried out, which yields that the proposed strategy can achieve desirable path following and vehicle stability efficacy, while greatly reducing the computational burden compared with the NMPC controllers by active set algorithm or interior point algorithm

Present-day kinematics and seismic potential of the Ganzi-Yushu fault, eastern Tibetan plateau, constrained from InSAR

In recent years, earthquakes have occurred frequently on the southeastern edge of the Tibetan Plateau, and the seismic hazard is high. However, because of the remote location of the Ganzi-Yushu fault zone, no high-resolution geodetic measurements of this region have been made. The radar line-of-sight deformation field of the Ganzi-Yushu fault was obtained using seven-track ascending and descending Sentinel-A/B interferometric synthetic aperture radar (InSAR) data from 2014 to 2020. Using the InSAR and published Global Navigation Satellite System (GNSS) data, we calculated the 3D deformation field in the study area, investigated the segment-specific fault slip rate, and inverted the fault slip distribution pattern using the steepest descent method. We then evaluated the seismic hazard using the strain rate field and slip deficit rate. The main findings of this study include the following. 1) The slip rate of the Ganzi-Yushu fault gradually increases from 2.5 to 6.8 mm/yr from northwest to southeast. 2) A high-resolution strain rate map shows high-value anomalies in the Yushu and Dangjiang areas. 3) Our comprehensive analysis suggests that the seismic hazard of the Dangjiang and Dengke segments with high slip deficits cannot be ignored

Evidence of spin density waves in La3_3Ni2_2O7−δ_{7-\delta}

The recently discovered superconductivity with critical temperature $T_{c}$ up to 80 K in the Ruddlesden-Popper phases La$_3$Ni$_2$O$_{7-\delta}$ under pressure has drawn great attention. Here we report the positive muon spin relaxation ($\mu^+$SR) study of polycrystalline La$_3$Ni$_2$O$_{7-\delta}$ under ambient pressure. The zero-field $\mu^+$SR experiments reveal the existence of static long range magnetic order in La$_3$Ni$_2$O$_{7-\delta}$, and the the muon spin depolarization spectra are consistent with the spin density wave internal field distribution. The weak transverse field $\mu^+$SR measurements suggest the bulk magnetic transition near $T_{\rm{N}}=148$ K. This is the first research which discovers the existence of the spin density wave in La$_3$Ni$_2$O$_{7-\delta}$ microscopically

Vitamin D Supplementation Enhances the Fixation of Titanium Implants in Chronic Kidney Disease Mice

Vitamin D (Vit D) deficiency is a common condition in chronic kidney disease (CKD) patients that negatively affects bone regeneration and fracture healing. Previous study has shown that timely healing of titanium implants is impaired in CKD. This study aimed to investigate the effect of Vit D supplementation on implant osseointegration in CKD mice. Uremia was induced by 5/6 nephrectomy in C57BL mice. Eight weeks after the second renal surgery, animals were given 1,25(OH)2D3 three times a week intraperitoneally for four weeks. Experimental titanium implants were inserted into the distal end of femurs two weeks later. Serum measurements confirmed decreased 1,25(OH)2D levels in CKD mice, which could be successfully corrected by Vit D injections. Moreover, the hyperparathyroidism observed in CKD mice was also corrected. X-ray examination and histological sections showed successful osseointegration in these mice. Histomorphometrical analysis revealed that the bone-implant contact (BIC) ratio and bone volume (BV/TV) around the implant were significantly increased in the Vit D-supplementation group. In addition, resistance of the implant, as measured by a push-in method, was significantly improved compared to that in the vehicle group. These results demonstrate that Vit D supplementation is an effective approach to improve the fixation of titanium implants in CKD

Middle-Late Jurassic magmatism in the west central Lhasa subterrane, Tibet: Petrology, zircon chronology, elemental and Sr-Nd-Pb-Hf-Mg isotopic geochemistry

Mesozoic magmatic rocks are widespread in the Lhasa terrane, but most of them are of cretaceous age. Because Jurassic rocks are relatively rare and our knowledge on such earlier magmatism in the context of the tectonic setting and evolution is limited. In this study, we focus on the mid-late Jurassic granitoids that occur in the west central Lhasa subterrane. We present the results of a systematic study of these granitoid rocks of tonalite composition together with the hosted mafic magmatic enclaves. We dated 4 representative tonalite samples and 2 enclaves using zircon U-Pb method that gives the age range of 167–154 Ma. All these samples have Sr-Nd-Pb isotopic compositions (87Sr/86Sr = 0.713941–0.718417, εNd(t) = −14 to −9.8, 206Pb/204Pb = 18.806–18.936, 207Pb/204Pb = 15.739–15.764, 208Pb/204Pb = 39.257–39.798) similar to the composition of gneisses from the basement of the Lhasa terrane, suggesting that magmas parental to these mid-late Jurassic granitoids of tonalitic composition are of largely crustal origin, which is also supported by the petrographic observations. Both of the tonalite samples and the mafic enclaves have a wide span of zircon εHf(t) of −15.9 to −0.2 and − 13.8 to −7.4, respectively. These samples also show varying δ26Mg ranging from −0.40 to −0.18, with an average δ26Mg = −0.27 ± 0.06‰ (2SD) that is best understood as representing the Mg composition of the continental crust of the Lhasa terrane. All these observations allow us to conclude that basaltic melts derived from metasomatized mantle were involved in the petrogenesis of these granitoids. Specifically, southward subduction of the Bangong-Nujiang Ocean lithosphere and subsequent slab rollback metasomatized the mantle wedge and the lithospheric mantle above, whose melting produced basaltic magmas. Underplating and intrusion of these basaltic magmas caused crustal melting and generation of granitoid magmas parental to the tonalite and enclaves we study