Backstepping Density Control for Large-Scale Heterogeneous Nonlinear Stochastic Systems

This work studies the problem of controlling the probability density of large-scale stochastic systems, which has applications in various fields such as swarm robotics. Recently, there is a growing amount of literature that employs partial differential equations (PDEs) to model the density evolution and uses density feedback to design control laws which, by acting on individual systems, stabilize their density towards to a target profile. In spite of its stability property and computational efficiency, the success of density feedback relies on assuming the systems to be homogeneous first-order integrators (plus white noise) and ignores higher-order dynamics, making it less applicable in practice. In this work, we present a backstepping design algorithm that extends density control to heterogeneous and higher-order stochastic systems in strict-feedback forms. We show that the strict-feedback form in the individual level corresponds to, in the collective level, a PDE (of densities) distributedly driven by a collection of heterogeneous stochastic systems. The presented backstepping design then starts with a density feedback design for the PDE, followed by a sequence of stabilizing design for the remaining stochastic systems. We present a candidate control law with stability proof and apply it to nonholonomic mobile robots. A simulation is included to verify the effectiveness of the algorithm.

Dislocation induced energy dissipation in a tunable trilayer graphene resonator

In crystalline materials, the creation and modulation of dislocations are often associated with plastic deformation and energy dissipation. Here we report a study on the energy dissipation of a trilayer graphene ribbon resonator. The vibration of the ribbon generates cyclic mechanical loading to the graphene ribbon, during which mechanical energy is dissipated as heat. Measuring the quality factor of the graphene resonator provides a way to evaluate the energy dissipation. The graphene ribbon is integrated with silicon micro actuators, allowing its in-plane tension to be finely tuned. As we gradually increased the tension, we observed, in addition to the well-known resonance frequency increase, a large change in the energy dissipation. We propose that the dominating energy dissipation mechanism shifts over three regions. With small applied tension, the graphene is in elastic region, and the major energy dissipation is through graphene edge folding; as the tension increases, dislocations start to develop in the sample to gradually dominate the energy dissipation; finally, at large enough tension, graphene layers become decoupled and start to slide and cause friction, which induces the more severe energy dissipation. The generation and modulation of dislocations are modeled by molecular dynamics calculation and a method to count the energy loss is proposed and compared to the experiment.

Kerr-Newman-Jacobi geometry and the deflection of charged massive particles

In this paper, we investigate the deflection of a charged particle moving in the equatorial plane of Kerr-Newman spacetime, focusing on weak field limit. To this end, we use the Jacobi geometry, which can be described in three equivalent forms, namely Randers-Finsler metric, Zermelo navigation problem, and $(n+1)$-dimensional stationtary spacetime picture. Based on Randers data and Gauss-Bonnet theorem, we utilize osculating Riemannian manifold method and the generalized Jacobi metric method to study the deflection angle, respectively. In the $(n+1)$-dimensional spacetime picture, the motion of charged particle follows the null geodesic, and thus we use the standard geodesic method to calculate the deflection angle. Three methods lead to the same second-order deflection angle, which is obtained for the first time. The result shows that the black hole spin $a$ affects the deflection of charged particles both gravitationally and magnetically at the leading order (order $mathcal{O}([M]^2/b^2)$). When $qQ/E<2M$, $a$ will decrease (or increase) the deflection of prograde (or retrograde) charged signal. If $qQ/E> 2M$, the opposite happens, and the ray is divergently deflected by the lens. We also showed that the effect of the magnetic charge of the dyonic Kerr-Newman black hole on the deflection angle is independent of the particles charge.

Multimodal Feature Fusion for Video Advertisements Tagging Via Stacking Ensemble

Automated tagging of video advertisements has been a critical yet challenging problem, and it has drawn increasing interests in last years as its applications seem to be evident in many fields. Despite sustainable efforts have been made, the tagging task is still suffered from several challenges, such as, efficiently feature fusion approach is desirable, but under-explored in previous studies. In this paper, we present our approach for Multimodal Video Ads Tagging in the 2021 Tencent Advertising Algorithm Competition. Specifically, we propose a novel multi-modal feature fusion framework, with the goal to combine complementary information from multiple modalities. This framework introduces stacking-based ensembling approach to reduce the influence of varying levels of noise and conflicts between different modalities. Thus, our framework can boost the performance of the tagging task, compared to previous methods. To empirically investigate the effectiveness and robustness of the proposed framework, we conduct extensive experiments on the challenge datasets. The obtained results suggest that our framework can significantly outperform related approaches and our method ranks as the 1st place on the final leaderboard, with a Global Average Precision (GAP) of 82.63%. To better promote the research in this field, we will release our code in the final version.

Entanglement and mixed states of Young tableau states in gauge/gravity correspondence

We use entangled multimode coherent states to produce entangled giant graviton states, in the context of gauge/gravity duality. We make a smeared distribution of the entangled multimode coherent states on the circle, or on the five-sphere, in the higher dimensional view. In gauge/gravity duality, we analyze the superposition of giant graviton states, and the entangled pairs of giant graviton states. We map a class of angular distribution functions to unitary operations on the pairs. We also use Young tableau states to construct cat states and qudit states. Various bipartite quantum states involving Young tableau states are analyzed, including micro-macro entangled states. Mixed states of Young tableau states are generated, by using ensemble mixing using angular distribution functions, and also by going through noisy quantum channels. We then produce mixed entangled pair of giant graviton states, by including interaction with the environment and using noisy quantum channels.

X(3872) Production in Relativistic Heavy-Ion Collisions

Heavy ion collisions provide a unique opportunity to study the nature of X(3872) compared with electron-positron and proton-proton (antiproton) collisions. With the abundant charm pairs produced in heavy-ion collisions, the production of multicharm hadrons and molecules can be enhanced by the combination of charm and anticharm quarks in the medium. We investigate the centrality and momentum dependence of X(3872) in heavy-ion collisions via the Langevin equation and instant coalescence model (LICM). When X(3872) is treated as a compact tetraquark state, the tetraquarks are produced via the coalescence of heavy and light quarks near the quantum chromodynamic (QCD) phase transition due to the restoration of the heavy quark potential at $Trightarrow T_c$. In the molecular scenario, loosely bound X(3872) is produced via the coalescence of $D^0$-$bar D^{*0}$ mesons in a hadronic medium after kinetic freeze-out. The phase space distributions of the charm quarks and D mesons in a bulk medium are studied with the Langevin equation, while the coalescence probability between constituent particles is controlled by the Wigner function, which encodes the internal structure of the formed particle. First, we employ the LICM to explain both $D^0$ and $J/psi$ production as a benchmark. Then, we give predictions regarding X(3872) production. We find that the total yield of tetraquark is several times larger than the molecular production in Pb-Pb collisions. Although the geometric size of the molecule is huge, the coalescence probability is small due to strict constraints on the relative momentum between $D^0$ and $bar D^{*0}$ in the molecular Wigner function, which significantly suppresses the molecular yield.

Topological charge and spin pumping in a semiconductor nanowire

The adiabatic topological pumping is proposed by periodically modulating a semiconductor nanowire double-quantum-dot chain. We demonstrate that the quantized charge transport can be achieved by a nontrivial modulation of the quantum-dot well and barrier potentials. When the quantum-dot well potential is replaced by a time-dependent staggered magnetic field, the topological spin pumping can be realized by periodically modulating the barrier potentials and magnetic field. We also demonstrate that in the presence of Rashba spin-orbit interaction, the double-quantum-dot chain can be used to implement the topological spin pumping. However, the pumped spin in this case can have a quantization axis other than the applied magnetic field direction. Moreover, we show that all the adiabatic topological pumping are manifested by the presence of gapless edge states traversing the band gap as a function of time.

The weak decays of $Xi^{()}_{c}toXi$ in the light-front quark model

Without contamination from the final state interactions, the calculation of the branching ratios of semileptonic decays $Xi^{()}_{c}toXi+e^+ u_e$ may provide us more information about the inner structure of charmed baryons. Moreover, by studying those processes, one can better determine the form factors of $Xi_ctoXi$ which can be further applied to relevant estimates. In this work, we use the light-front quark model to carry out the computations where the three-body vertex functions for $Xi_c$ and $Xi$ are employed. To fit the new data of the Belle II, we re-adjust the model parameters and obtain $beta_{s[sq]}=1.07$ GeV which is 2.9 times larger than $beta_{sbar s}=0.366$ GeV. This value may imply that the $ss$ pair in $Xi$ constitutes a more compact subsystem. Furthermore, we also investigate the non-leptonic decays of $Xi^{()}_cto Xi$ which will be experimentally measured soon, so our model would be tested by consistency with the new data.

Distributed Mean-Field Density Estimation for Large-Scale Systems

This work studies how to estimate the mean-field density of large-scale systems in a distributed manner. Such problems are motivated by the recent swarm control technique that uses mean-field approximations to represent the collective effect of the swarm, wherein the mean-field density (and its gradient) is usually used in feedback control design. In the first part, we formulate the density estimation problem as a filtering problem of the associated mean-field partial differential equation (PDE), for which we employ kernel density estimation (KDE) to construct noisy observations and use filtering theory of PDE systems to design an optimal (centralized) density filter. It turns out that the covariance operator of observation noise depends on the unknown density. Hence, we use approximations for the covariance operator to obtain a suboptimal density filter, and prove that both the density estimates and their gradient are convergent and remain close to the optimal one using the notion of input-to-state stability (ISS). In the second part, we continue to study how to decentralize the density filter such that each agent can estimate the mean-field density based on only its own position and local information exchange with neighbors. We prove that the local density filter is also convergent and remains close to the centralized one in the sense of ISS. Simulation results suggest that the (centralized) suboptimal density filter is able to generate convergent density estimates, and the local density filter is able to converge and remain close to the centralized filter.

Feedback Interconnected Mean-Field Estimation and Control

Swarm robotic systems have foreseeable applications in the near future. Recently, there has been an increasing amount of literature that employs mean-field partial differential equations (PDEs) to model the time-evolution of the probability density of swarm robotic systems and uses mean-field feedback to design stable control laws that act on individuals such that their density converges to a target profile. However, it remains largely unexplored considering problems of how to estimate the mean-field density, how the density estimation algorithms affect the control performance, and whether the estimation performance in turn depends on the control algorithms. In this work, we focus on studying the interplay of these algorithms. Specially, we propose new mean-field control laws which use the real-time density and its gradient as feedback, and prove that they are globally input-to-state stable (ISS) to estimation errors. Then, we design filtering algorithms to obtain estimates of the density and its gradient, and prove that these estimates are convergent assuming the control laws are known. Finally, we show that the feedback interconnection of these estimation and control algorithms is still globally ISS, which is attributed to the bilinearity of the mean-field PDE system. An agent-based simulation is included to verify the stability of these algorithms and their feedback interconnection.