arXiv subjects

Yuan Zhou

Publications and source records attributed to Yuan Zhou.

At least 181 records · Page 10Linked to original sources

arXiv2023

A Rademacher type theorem for Hamiltonians $H(x,p)$ and application to absolute minimizers

We establish a Rademacher type theorem involving Hamiltonians $H(x,p)$ under very weak conditions in both of Euclidean and Carnot-Carathéodory spaces. In particular,$H(x,p)$ is assumed to be only measurable in the variable $x$, and to be quasiconvex and lower-semicontinuous in the variable $p$. Without the lower-semicontinuity in the variable $p$, we provide a counter example showing the failure of such a Rademacher type theorem. Moreover, by applying such a Rademacher type theorem we build up an existence result of absolute minimizers for the corresponding $L^\infty$-functional. These improve or extend several known results in the literature.

math.CA↗

arXiv2023

FLYOVER: A Model-Driven Method to Generate Diverse Highway Interchanges for Autonomous Vehicle Testing

It has become a consensus that autonomous vehicles (AVs) will first be widely deployed on highways. However, the complexity of highway interchanges becomes the bottleneck for deploying AVs. An AV should be sufficiently tested under different highway interchanges, which is still challenging due to the lack of available datasets containing diverse highway interchanges. In this paper, we propose a model-driven method, FLYOVER, to generate a dataset consisting of diverse interchanges with measurable diversity coverage. First, FLYOVER proposes a labeled digraph to model the topology of an interchange. Second, FLYOVER takes real-world interchanges as input to guarantee topology practicality and extracts different topology equivalence classes by classifying the corresponding topology models. Third, for each topology class, FLYOVER identifies the corresponding geometrical features for the ramps and generates concrete interchanges using k-way combinatorial coverage and differential evolution. To illustrate the diversity and applicability of the generated interchange dataset, we test the built-in traffic flow control algorithm in SUMO and the fuel-optimization trajectory tracking algorithm deployed to Alibaba's autonomous trucks on the dataset. The results show that except for the geometrical difference, the interchanges are diverse in throughput and fuel consumption under the traffic flow control and trajectory tracking algorithms, respectively.

cs.RO↗

arXiv2022

On-chip single-mode thin film lithium niobate laser based on Sagnac loop reflectors

We demonstrate an on-chip single-mode Er3+-doped thin film lithium niobate (Er: TFLN) laser which consists of a Fabry-Pérot (FP) resonator based on Sagnac loop reflectors (SLRs). The fabricated Er: TFLN laser has a footprint of 6.5 mmx1.5 mm with a loaded quality (Q) factor of 1.6x105 and a free spectral range (FSR) of 63 pm. We generate the single-mode laser around 1550-nm wavelength with a maximum output power of 44.7 μW and a slope efficiency of 0.18 %.

physics.optics↗

arXiv2022

The Circular Velocity Curve of the Milky Way from 5 to 25 kpc using luminous red giant branch star

We present a sample of 254,882 luminous red giant branch (LRGB) stars selected from the APOGEE and LAMOST surveys. By combining photometric and astrometric information from the 2MASS and Gaia surveys, the precise distances of the sample stars are determined by a supervised machine learning algorithm: the gradient boosted decision trees. To test the accuracy of the derived distances, member stars of globular clusters (GCs) and open clusters (OCs) are used. The tests by cluster member stars show a precision of about 10 per cent with negligible zero-point offsets, for the derived distances of our sample stars. The final sample covers a large volume of the Galactic disk(s) and halo of $0<R<30$ kpc and $|Z|\leqslant15$ kpc. The rotation curve (RC) of the Milky Way across radius of $5\lesssim R\lesssim25$ kpc have been accurately measured with $\sim$ 54,000 stars of the thin disk population selected from the LRGB sample. The derived RC shows a weak decline along $R$ with a gradient of $-1.83\pm0.02$ $({\rm stat.}) \pm 0.07$ $({\rm sys.})$ km s$^{-1}$ kpc$^{-1}$, in excellent agreement with the results measured by previous studies. The circular velocity at the solar position, yielded by our RC, is $234.04\pm0.08$ $({\rm stat.}) \pm 1.36$ $({\rm sys.})$ km s$^{-1}$, again in great consistent with other independent determinations. From the newly constructed RC, as well as constraints from other data, we have constructed a mass model for our Galaxy, yielding a mass of the dark matter halo of $M_{\rm{200}}$ = ($8.05\pm1.15$)$\times$10$^{11} \rm{M_\odot}$ with a corresponding radius of $R_{\rm{200}}$ = $192.37\pm9.24$ kpc and a local dark matter density of $0.39\pm0.03$ GeV cm$^{-3}$.

astro-ph.GA↗

arXiv2022

Few-shot Learning with Global Relatedness Decoupled-Distillation

Despite the success that metric learning based approaches have achieved in few-shot learning, recent works reveal the ineffectiveness of their episodic training mode. In this paper, we point out two potential reasons for this problem: 1) the random episodic labels can only provide limited supervision information, while the relatedness information between the query and support samples is not fully exploited; 2) the meta-learner is usually constrained by the limited contextual information of the local episode. To overcome these problems, we propose a new Global Relatedness Decoupled-Distillation (GRDD) method using the global category knowledge and the Relatedness Decoupled-Distillation (RDD) strategy. Our GRDD learns new visual concepts quickly by imitating the habit of humans, i.e. learning from the deep knowledge distilled from the teacher. More specifically, we first train a global learner on the entire base subset using category labels as supervision to leverage the global context information of the categories. Then, the well-trained global learner is used to simulate the query-support relatedness in global dependencies. Finally, the distilled global query-support relatedness is explicitly used to train the meta-learner using the RDD strategy, with the goal of making the meta-learner more discriminative. The RDD strategy aims to decouple the dense query-support relatedness into the groups of sparse decoupled relatedness. Moreover, only the relatedness of a single support sample with other query samples is considered in each group. By distilling the sparse decoupled relatedness group by group, sharper relatedness can be effectively distilled to the meta-learner, thereby facilitating the learning of a discriminative meta-learner. We conduct extensive experiments on the miniImagenet and CIFAR-FS datasets, which show the state-of-the-art performance of our GRDD method.

cs.CV↗

arXiv2022

Topological states in a dimerized system with staggered magnetic fluxes

The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner states gather at corners in the two-dimensional first-order and second-order topological insulators, respectively. Here, we report two kinds of topological states hosting anomalous bulk-boundary correspondence in the extended two-dimensional dimerized lattice with staggered flux threading. At $\frac{1}{2}$-filling, we observe isolated corner states with no fractional charge as well as metallic near-edge states in the $\mathcal{C}=2$ Chern insulator states. At $\frac{1}{4}$-filling, we find a $\mathcal{C}=0$ topologically nontrivial state, where the robust edge states are well localized along edges but bypass corners. These robust topological insulating states significantly differ from both conventional Chern insulators and usual high-order topological insulators.

cond-mat.mes-hall↗

arXiv2022

Almost Optimal Batch-Regret Tradeoff for Batch Linear Contextual Bandits

We study the optimal batch-regret tradeoff for batch linear contextual bandits. For any batch number $M$, number of actions $K$, time horizon $T$, and dimension $d$, we provide an algorithm and prove its regret guarantee, which, due to technical reasons, features a two-phase expression as the time horizon $T$ grows. We also prove a lower bound theorem that surprisingly shows the optimality of our two-phase regret upper bound (up to logarithmic factors) in the \emph{full range} of the problem parameters, therefore establishing the exact batch-regret tradeoff. Compared to the recent work \citep{ruan2020linear} which showed that $M = O(\log \log T)$ batches suffice to achieve the asymptotically minimax-optimal regret without the batch constraints, our algorithm is simpler and easier for practical implementation. Furthermore, our algorithm achieves the optimal regret for all $T \geq d$, while \citep{ruan2020linear} requires that $T$ greater than an unrealistically large polynomial of $d$. Along our analysis, we also prove a new matrix concentration inequality with dependence on their dynamic upper bounds, which, to the best of our knowledge, is the first of its kind in literature and maybe of independent interest.

cs.LG↗

arXiv2022

Near-Optimal Regret Bounds for Multi-batch Reinforcement Learning

In this paper, we study the episodic reinforcement learning (RL) problem modeled by finite-horizon Markov Decision Processes (MDPs) with constraint on the number of batches. The multi-batch reinforcement learning framework, where the agent is required to provide a time schedule to update policy before everything, which is particularly suitable for the scenarios where the agent suffers extensively from changing the policy adaptively. Given a finite-horizon MDP with $S$ states, $A$ actions and planning horizon $H$, we design a computational efficient algorithm to achieve near-optimal regret of $\tilde{O}(\sqrt{SAH^3K\ln(1/δ)})$\footnote{$\tilde{O}(\cdot)$ hides logarithmic terms of $(S,A,H,K)$} in $K$ episodes using $O\left(H+\log_2\log_2(K) \right)$ batches with confidence parameter $δ$. To our best of knowledge, it is the first $\tilde{O}(\sqrt{SAH^3K})$ regret bound with $O(H+\log_2\log_2(K))$ batch complexity. Meanwhile, we show that to achieve $\tilde{O}(\mathrm{poly}(S,A,H)\sqrt{K})$ regret, the number of batches is at least $Ω\left(H/\log_A(K)+ \log_2\log_2(K) \right)$, which matches our upper bound up to logarithmic terms. Our technical contribution are two-fold: 1) a near-optimal design scheme to explore over the unlearned states; 2) an computational efficient algorithm to explore certain directions with an approximated transition model.

cs.LG↗

arXiv2022

Assortment Optimization Under the Multivariate MNL Model

We study an assortment optimization problem under a multi-purchase choice model in which customers choose a bundle of up to one product from each of two product categories. Different bundles have different utilities and the bundle price is the summation of the prices of products in it. For the uncapacitated setting where any set of products can be offered, we prove that this problem is strongly NP-hard. We show that an adjusted-revenue-ordered assortment provides a 1/2-approximation. Furthermore, we develop an approximation framework based on a linear programming relaxation of the problem and obtain a 0.74-approximation algorithm. This approximation ratio almost matches the integrality gap of the linear program, which is proven to be at most 0.75. For the capacitated setting, we prove that there does not exist a constant-factor approximation algorithm assuming the Exponential Time Hypothesis. The same hardness result holds for settings with general bundle prices or more than two categories. Finally, we conduct numerical experiments on randomly generated problem instances. The average approximation ratios of our algorithms are over 99%.

cs.DS↗

arXiv2022

Quantum Interference and Coherent Population Trapping in a Double Quantum Dot

Quantum interference is a natural consequence of wave-particle duality in quantum mechanics, and is widely observed at the atomic scale. One interesting manifestation of quantum interference is coherent population trapping (CPT), first proposed in three-level driven atomic systems and observed in quantum optical experiments. Here, we demonstrate CPT in a gate-defined semiconductor double quantum dot (DQD), with some unique twists as compared to the atomic systems. Specifically, we observe CPT in both driven and non-driven situations. We further show that CPT in a driven DQD could be used to generate adiabatic state transfer. Moreover, our experiment reveals a non-trivial modulation to the CPT caused by the longitudinal driving field, yielding an odd-even effect and a tunable CPT.

cond-mat.mes-hall↗

arXiv2022

First- and second-order gradient couplings to NV centers engineered by the geometric symmetry

The magnetic fields with the first- and second-order gradient are engineered in several mechanically controlled hybrid systems. The current-carrying nanowires with different geometries can induce a tunable magnetic field gradient because of their geometric symmetries, and therefore develop various couplings to nitrogen-vacancy (NV) centers. For instance, a straight nanowire can guarantee the Jaynes-Cummings (JC) spin-phonon interaction and may indicate a potential route towards the application on quantum measurement. Especially, two parallel straight nanowires can develop the coherent down-conversion spin-phonon interaction through a second-order gradient of the magnetic field, and it can induce a bundle emission of the antibunched phonon pairs via an entirely different magnetic mechanism. Maybe, this investigation is further believed to support NV's future applications in the area of quantum manipulation, quantum sensing, and precision measurement, etc.

cond-mat.mes-hall↗

arXiv2022

Jacobian determinants for (nonlinear) gradient of planar $\infty$-harmonic functions and applications

In dimension 2, we introduce a distributional Jacobian determinant $\det DV_β(Dv)$ for the nonlinear complex gradient $(x_1,x_2)\mapsto |Dv|^β(v_{x_1},-v_{x_2})$ for any $β>-1$, whenever $v\in W^{1,2 }_{\text{loc}}$ and $β|Dv|^{1+β}\in W^{1,2}_{\text{loc}}$. Then for any planar $\infty$-harmonic function $u$, we show that such distributional Jacobian determinant is a nonnegative Radon measure with some quantitative local lower and upper bounds. We also give the following two applications. (i) Applying this result with $β=0$, we develop an approach to build up a Liouville theorem, which improves that of Savin [33]. Precisely, if $u$ is $\infty$-harmonic functions in whole ${\mathbb R}^2$ with $$ \liminf_{R\to\infty}\inf_{c\in\mathbb R}\frac1 {R^3}\int_{B(0,R)}|u(x)-c|\,dx<\infty,$$ then $u=b+a\cdot x$ for some $b\in{\mathbb R}$ and $a\in{\mathbb R}^2$. (ii) Denoting by $u_p$ the $p$-harmonic function having the same nonconstant boundary condition as $u$, we show that $\det DV_β(Du_p) \to \det DV_β(Du)$ as $p\to\infty$ in the weak-$\star$ sense in the space of Radon measure. Recall that $V_β(Du_p)$ is always quasiregular mappings, but $V_β(Du)$ is not in general.

math.AP↗

arXiv2022

Monolithically integrated active passive waveguide array fabricated on thin film lithium niobate using a single continuous photolithography process

We demonstrate a robust low-loss optical interface by tiling passive (i.e., without doping of active ions) thin film lithium niobate (TFLN) and active (i.e., doped with rare earth ions) TFLN substrates for monolithic integration of passive/active lithium niobate photonics. The tiled substrates composed of both active and passive areas allow to pattern the mask of the integrated active passive photonic device at once using a single continuous photolithography process. The interface loss of tiled substrate is measured as low as 0.26 dB. Thanks to the stability provided by this approach, a four-channel waveguide amplifier is realized in a straightforward manner, which shows a net gain of ~5 dB at 1550-nm wavelength and that of ~8 dB at 1530-nm wavelength for each channel. The robust low-loss optical interface for passive/active photonic integration will facilitate large-scale high performance photonic devices which require on-chip light sources and amplifiers.

physics.optics↗

arXiv2022

Electrically driven compact hybrid lithium niobate microring laser

We demonstrate an electrically driven compact hybrid lithium niobate microring laser by butt coupling a commercial 980-nm pump laser diode chip with a high quality Er3+-doped lithium niobate microring chip. Single mode lasing emission at 1531 nm wavelength from the Er3+-doped lithium niobate microring can be observed with the integrated 980-nm laser pumping. The compact hybrid lithium niobate microring laser occupies the chip size of 3 mmx4mmx0.5 mm. The threshold pumping laser power is 6 mW and the threshold current is 0.5 A (operating voltage 1.64 V) in the atmospheric temperature. The spectrum featuring single mode lasing with small linewidth of 0.05 nm is observed. This work explores a robust hybrid lithium niobate microring laser source which has potential applications in coherent optical communication and precision metrology.

physics.optics↗

arXiv2022

AACC: Asymmetric Actor-Critic in Contextual Reinforcement Learning

Reinforcement Learning (RL) techniques have drawn great attention in many challenging tasks, but their performance deteriorates dramatically when applied to real-world problems. Various methods, such as domain randomization, have been proposed to deal with such situations by training agents under different environmental setups, and therefore they can be generalized to different environments during deployment. However, they usually do not incorporate the underlying environmental factor information that the agents interact with properly and thus can be overly conservative when facing changes in the surroundings. In this paper, we first formalize the task of adapting to changing environmental dynamics in RL as a generalization problem using Contextual Markov Decision Processes (CMDPs). We then propose the Asymmetric Actor-Critic in Contextual RL (AACC) as an end-to-end actor-critic method to deal with such generalization tasks. We demonstrate the essential improvements in the performance of AACC over existing baselines experimentally in a range of simulated environments.

cs.LG↗

arXiv2022

Physical Backdoor Attacks to Lane Detection Systems in Autonomous Driving

Modern autonomous vehicles adopt state-of-the-art DNN models to interpret the sensor data and perceive the environment. However, DNN models are vulnerable to different types of adversarial attacks, which pose significant risks to the security and safety of the vehicles and passengers. One prominent threat is the backdoor attack, where the adversary can compromise the DNN model by poisoning the training samples. Although lots of effort has been devoted to the investigation of the backdoor attack to conventional computer vision tasks, its practicality and applicability to the autonomous driving scenario is rarely explored, especially in the physical world. In this paper, we target the lane detection system, which is an indispensable module for many autonomous driving tasks, e.g., navigation, lane switching. We design and realize the first physical backdoor attacks to such system. Our attacks are comprehensively effective against different types of lane detection algorithms. Specifically, we introduce two attack methodologies (poison-annotation and clean-annotation) to generate poisoned samples. With those samples, the trained lane detection model will be infected with the backdoor, and can be activated by common objects (e.g., traffic cones) to make wrong detections, leading the vehicle to drive off the road or onto the opposite lane. Extensive evaluations on public datasets and physical autonomous vehicles demonstrate that our backdoor attacks are effective, stealthy and robust against various defense solutions. Our codes and experimental videos can be found in https://sites.google.com/view/lane-detection-attack/lda.

cs.CV↗

arXiv2022

A global second order Sobolev regularity for $p$-Laplacian type equations with variable coefficients in bounded domains

Let $Ω\subset R^n$ be a bounded convex domain with $n\ge2$. Suppose that $A$ is uniformly elliptic and belongs to $W^{1,n}$ when $n\ge 3$ or $W^{1,q}$ for some $q>2$ when $n=2$. For $1<p<\infty$, we build up a global second order regularity estimate $$\|D[|Du|^{p-2} Du]\|_{L^2(Ω)}+\|D[ |\sqrt{A}Du|^{p-2} A Du]\|_{L^2(Ω)} \le C \|f\|_{L^2(Ω)} $$ for inhomogeneous $p$-Laplace type equation \begin{equation} -\mathrm{div}\big(\langle A Du,Du\rangle ^{\frac{p-2}2} A Du\big)=f \quad\rm{in }\ Ω\mbox{ with Dirichlet/Neumann $0$-boundary.} \end{equation} Similar result was also built up for certain bounded Lipschitz domain whose boundary is weakly second order differentiable and satisfies some smallness assumptions.

math.AP↗

arXiv2022

Dynamic Car Dispatching and Pricing: Revenue and Fairness for Ridesharing Platforms

A major challenge for ridesharing platforms is to guarantee profit and fairness simultaneously, especially in the presence of misaligned incentives of drivers and riders. We focus on the dispatching-pricing problem to maximize the total revenue while keeping both drivers and riders satisfied. We study the computational complexity of the problem, provide a novel two-phased pricing solution with revenue and fairness guarantees, extend it to stochastic settings and develop a dynamic (a.k.a., learning-while-doing) algorithm that actively collects data to learn the demand distribution during the scheduling process. We also conduct extensive experiments to demonstrate the effectiveness of our algorithms.

math.OC↗