arXiv subjects

Jiaqi Yang

Publications and source records attributed to Jiaqi Yang.

At least 109 records · Page 6Linked to original sources

arXiv2023

Raman Enhancement in Bowtie-Shaped Aperture-Particle Hybrid Nanostructures Fabricated with DNA-Assisted Lithography

We report on efficient surface-enhanced Raman spectroscopy (SERS) supporting substrates, which are based on DNA-assisted lithography (DALI) and a layered configuration of materials. In detail, we used nanoscopic DNA origami bowtie templates to form hybrid nanostructures consisting of aligned silver bowtie-shaped particles and apertures of similar shape in a silver film. We hypothesized that this particular geometry could facilitate a four-fold advantage in Raman enhancement compared to common particle-based SERS substrates, and further, we verified these hypotheses experimentally and by finite difference time domain simulations. In summary, our DALI-fabricated hybrid structures suppress the background emission, allow emission predominantly from the areas of high field enhancement, and support additional resonances associated with the nanoscopic apertures. Finally, these nanoapertures also enhance the fields associated with the resonances of the underlying bowtie particles. The versatility and parallel nature of our DNA origami-based nanofabrication scheme and all of the above-mentioned features of the hybrid structures therefore make our optically resonant substrates attractive for various SERS-based applications.

cond-mat.mtrl-sci↗

arXiv2022

iQuery: Instruments as Queries for Audio-Visual Sound Separation

Current audio-visual separation methods share a standard architecture design where an audio encoder-decoder network is fused with visual encoding features at the encoder bottleneck. This design confounds the learning of multi-modal feature encoding with robust sound decoding for audio separation. To generalize to a new instrument: one must finetune the entire visual and audio network for all musical instruments. We re-formulate visual-sound separation task and propose Instrument as Query (iQuery) with a flexible query expansion mechanism. Our approach ensures cross-modal consistency and cross-instrument disentanglement. We utilize "visually named" queries to initiate the learning of audio queries and use cross-modal attention to remove potential sound source interference at the estimated waveforms. To generalize to a new instrument or event class, drawing inspiration from the text-prompt design, we insert an additional query as an audio prompt while freezing the attention mechanism. Experimental results on three benchmarks demonstrate that our iQuery improves audio-visual sound source separation performance.

cs.CV↗

arXiv2022

Constrained large solutions to Leray's problem in a distorted strip with the Navier-slip boundary condition

In this paper, we will solve the Leray's problem for the stationary Navier-Stokes system in a 2D infinite distorted strip with the Navier-slip boundary condition. The existence, uniqueness, regularity and asymptotic behavior of the solution will be investigated. Moreover, we discuss how the friction coefficient affects the well-posedness of the solution. Due to the validity of the Korn's inequality, all constants in each a priori estimate are independent of the friction coefficient. The main novelty is the total flux of the velocity can be relatively large (proportional to the {\it slip length}) when the friction coefficient of the Navier-slip boundary condition is small, which is essentially different from the 3D case.

math.AP↗

arXiv2022

Revisiting Some Common Practices in Cooperative Multi-Agent Reinforcement Learning

Many advances in cooperative multi-agent reinforcement learning (MARL) are based on two common design principles: value decomposition and parameter sharing. A typical MARL algorithm of this fashion decomposes a centralized Q-function into local Q-networks with parameters shared across agents. Such an algorithmic paradigm enables centralized training and decentralized execution (CTDE) and leads to efficient learning in practice. Despite all the advantages, we revisit these two principles and show that in certain scenarios, e.g., environments with a highly multi-modal reward landscape, value decomposition, and parameter sharing can be problematic and lead to undesired outcomes. In contrast, policy gradient (PG) methods with individual policies provably converge to an optimal solution in these cases, which partially supports some recent empirical observations that PG can be effective in many MARL testbeds. Inspired by our theoretical analysis, we present practical suggestions on implementing multi-agent PG algorithms for either high rewards or diverse emergent behaviors and empirically validate our findings on a variety of domains, ranging from the simplified matrix and grid-world games to complex benchmarks such as StarCraft Multi-Agent Challenge and Google Research Football. We hope our insights could benefit the community towards developing more general and more powerful MARL algorithms. Check our project website at https://sites.google.com/view/revisiting-marl.

cs.AI↗

arXiv2022

Provable Model-based Nonlinear Bandit and Reinforcement Learning: Shelve Optimism, Embrace Virtual Curvature

This paper studies model-based bandit and reinforcement learning (RL) with nonlinear function approximations. We propose to study convergence to approximate local maxima because we show that global convergence is statistically intractable even for one-layer neural net bandit with a deterministic reward. For both nonlinear bandit and RL, the paper presents a model-based algorithm, Virtual Ascent with Online Model Learner (ViOlin), which provably converges to a local maximum with sample complexity that only depends on the sequential Rademacher complexity of the model class. Our results imply novel global or local regret bounds on several concrete settings such as linear bandit with finite or sparse model class, and two-layer neural net bandit. A key algorithmic insight is that optimism may lead to over-exploration even for two-layer neural net model class. On the other hand, for convergence to local maxima, it suffices to maximize the virtual return if the model can also reasonably predict the size of the gradient and Hessian of the real return.

cs.LG↗

arXiv2022

Stability of a point charge for the repulsive Vlasov-Poisson system

We consider solutions of the repulsive Vlasov-Poisson system which are a combination of a point charge and a small gas, i.e.\ measures of the form $δ_{(\mathcal{X}(t),\mathcal{V}(t))}+μ^2d{\bf x}d{\bf v}$ for some $(\mathcal{X}, \mathcal{V}):\mathbb{R}\to\mathbb{R}^6$ and a small gas distribution $μ:\mathbb{R}\to L^2_{{\bf x},{\bf v}}$, and study asymptotic dynamics in the associated initial value problem. If initially suitable moments on $μ_0=μ(t=0)$ are small, we obtain a global solution of the above form, and the electric field generated by the gas distribution $μ$ decays at an almost optimal rate. Assuming in addition boundedness of suitable derivatives of $μ_0$, the electric field decays at an optimal rate and we derive a modified scattering dynamics for the motion of the point charge and the gas distribution. Our proof makes crucial use of the Hamiltonian structure. The linearized system is transport by the Kepler ODE, which we integrate exactly through an asymptotic action-angle transformation. Thanks to a precise understanding of the associated kinematics, moment and derivative control is achieved via a bootstrap analysis that relies on the decay of the electric field associated to $μ$. The asymptotic behavior can then be deduced from the properties of Poisson brackets in asymptotic action coordinates.

math.AP↗

arXiv2022

On Leray's problem in an infinite-long pipe with the Navier-slip boundary condition

The original Leray's problem concerns the well-posedness of weak solutions to the steady incompressible Navier-Stokes equations in a distorted pipe, which approach to the Poiseuille flow subject to the no-slip boundary condition at spacial infinity. In this paper, the same problem with the Navier-slip boundary condition instead of the no-slip boundary condition, is addressed. Due to the complexity of the boundary condition, some new ideas, presented as follows, are introduced to handle the extra difficulties caused by boundary terms. First, the Poiseuille flow in the semi-infinite straight pipe with the Navier-slip boundary condition will be introduced, which will be served as the asymptotic profile of the solution to the generalized Leray's problem at spacial infinity. Second, a solenoidal vector function defined in the whole pipe, satisfying the Navier-slip boundary condition, having the designated flux and equalling to the Poiseuille flow at large distance, will be carefully constructed. This plays an important role in reformulating our problem. Third, the energy estimates depend on a combined $L^2$ estimate of the gradient and the stress tensor of the velocity.

math.AP↗

arXiv2022

VECtor: A Versatile Event-Centric Benchmark for Multi-Sensor SLAM

Event cameras have recently gained in popularity as they hold strong potential to complement regular cameras in situations of high dynamics or challenging illumination. An important problem that may benefit from the addition of an event camera is given by Simultaneous Localization And Mapping (SLAM). However, in order to ensure progress on event-inclusive multi-sensor SLAM, novel benchmark sequences are needed. Our contribution is the first complete set of benchmark datasets captured with a multi-sensor setup containing an event-based stereo camera, a regular stereo camera, multiple depth sensors, and an inertial measurement unit. The setup is fully hardware-synchronized and underwent accurate extrinsic calibration. All sequences come with ground truth data captured by highly accurate external reference devices such as a motion capture system. Individual sequences include both small and large-scale environments, and cover the specific challenges targeted by dynamic vision sensors.

cs.RO↗

arXiv2022

Phasic Self-Imitative Reduction for Sparse-Reward Goal-Conditioned Reinforcement Learning

It has been a recent trend to leverage the power of supervised learning (SL) towards more effective reinforcement learning (RL) methods. We propose a novel phasic approach by alternating online RL and offline SL for tackling sparse-reward goal-conditioned problems. In the online phase, we perform RL training and collect rollout data while in the offline phase, we perform SL on those successful trajectories from the dataset. To further improve sample efficiency, we adopt additional techniques in the online phase including task reduction to generate more feasible trajectories and a value-difference-based intrinsic reward to alleviate the sparse-reward issue. We call this overall algorithm, PhAsic self-Imitative Reduction (PAIR). PAIR substantially outperforms both non-phasic RL and phasic SL baselines on sparse-reward goal-conditioned robotic control problems, including a challenging stacking task. PAIR is the first RL method that learns to stack 6 cubes with only 0/1 success rewards from scratch.

cs.LG↗

arXiv2022

Characterization of smooth solutions to the Navier-Stokes equations in a pipe with two types of slip boundary conditions

Smooth solutions of the stationary Navier-Stokes equations in an infinitely long pipe, equipped with the Navier-slip or Navier-Hodge-Lions boundary condition, are considered in this paper. Three main results are presented. First, when equipped with the Navier-slip boundary condition, it is shown that, $W^{1,\infty}$ axially symmetric solutions with zero flux at one cross section, must be swirling solutions: $u=(- C x_2, C x_1,0)$, and $x_3-$periodic solutions must be helical solutions: $u=(-C_1x_2,C_1x_1,C_2)$. Second, also equipped with the Navier-slip boundary condition, if the swirl or vertical component of the axially symmetric solution is independent of the vertical variable $x_3$, solutions are also proven to be helical solutions. In the case of the vertical component being independent of $x_3$, the $W^{1,\infty}$ assumption is not needed. In the case of the swirl component being independent of $x_3$, the $W^{1,\infty}$ assumption can be relaxed extensively such that the horizontal radial component of the velocity, $u_r$, can grow exponentially with respect to the distance to the origin. Also, by constructing a counterexample, we show that the growing assumption on $u_r$ is optimal. Third, when equipped with the Navier-Hodge-Lions boundary condition, we can show that if the gradient of the velocity grows sublinearly, then the solution, enjoying the Liouville-type theorem, is a trivial shear flow: $(0,0,C)$.

math.AP↗

arXiv2022

Nearly Minimax Algorithms for Linear Bandits with Shared Representation

We give novel algorithms for multi-task and lifelong linear bandits with shared representation. Specifically, we consider the setting where we play $M$ linear bandits with dimension $d$, each for $T$ rounds, and these $M$ bandit tasks share a common $k(\ll d)$ dimensional linear representation. For both the multi-task setting where we play the tasks concurrently, and the lifelong setting where we play tasks sequentially, we come up with novel algorithms that achieve $\widetilde{O}\left(d\sqrt{kMT} + kM\sqrt{T}\right)$ regret bounds, which matches the known minimax regret lower bound up to logarithmic factors and closes the gap in existing results [Yang et al., 2021]. Our main technique include a more efficient estimator for the low-rank linear feature extractor and an accompanied novel analysis for this estimator.

cs.LG↗

arXiv2022

Unsupervised Learning of 3D Semantic Keypoints with Mutual Reconstruction

Semantic 3D keypoints are category-level semantic consistent points on 3D objects. Detecting 3D semantic keypoints is a foundation for a number of 3D vision tasks but remains challenging, due to the ambiguity of semantic information, especially when the objects are represented by unordered 3D point clouds. Existing unsupervised methods tend to generate category-level keypoints in implicit manners, making it difficult to extract high-level information, such as semantic labels and topology. From a novel mutual reconstruction perspective, we present an unsupervised method to generate consistent semantic keypoints from point clouds explicitly. To achieve this, the proposed model predicts keypoints that not only reconstruct the object itself but also reconstruct other instances in the same category. To the best of our knowledge, the proposed method is the first to mine 3D semantic consistent keypoints from a mutual reconstruction view. Experiments under various evaluation metrics as well as comparisons with the state-of-the-arts demonstrate the efficacy of our new solution to mining semantic consistent keypoints with mutual reconstruction.

cs.CV↗

arXiv2022

A Topology-Attention ConvLSTM Network and Its Application to EM Images

Structural accuracy of segmentation is important for finescale structures in biomedical images. We propose a novel TopologyAttention ConvLSTM Network (TACNet) for 3D image segmentation in order to achieve high structural accuracy for 3D segmentation tasks. Specifically, we propose a Spatial Topology-Attention (STA) module to process a 3D image as a stack of 2D image slices and adopt ConvLSTM to leverage contextual structure information from adjacent slices. In order to effectively transfer topology-critical information across slices, we propose an Iterative-Topology Attention (ITA) module that provides a more stable topology-critical map for segmentation. Quantitative and qualitative results show that our proposed method outperforms various baselines in terms of topology-aware evaluation metrics.

eess.IV↗

arXiv2022

DEVO: Depth-Event Camera Visual Odometry in Challenging Conditions

We present a novel real-time visual odometry framework for a stereo setup of a depth and high-resolution event camera. Our framework balances accuracy and robustness against computational efficiency towards strong performance in challenging scenarios. We extend conventional edge-based semi-dense visual odometry towards time-surface maps obtained from event streams. Semi-dense depth maps are generated by warping the corresponding depth values of the extrinsically calibrated depth camera. The tracking module updates the camera pose through efficient, geometric semi-dense 3D-2D edge alignment. Our approach is validated on both public and self-collected datasets captured under various conditions. We show that the proposed method performs comparable to state-of-the-art RGB-D camera-based alternatives in regular conditions, and eventually outperforms in challenging conditions such as high dynamics or low illumination.

cs.RO↗

arXiv2021

Going Beyond Linear RL: Sample Efficient Neural Function Approximation

Deep Reinforcement Learning (RL) powered by neural net approximation of the Q function has had enormous empirical success. While the theory of RL has traditionally focused on linear function approximation (or eluder dimension) approaches, little is known about nonlinear RL with neural net approximations of the Q functions. This is the focus of this work, where we study function approximation with two-layer neural networks (considering both ReLU and polynomial activation functions). Our first result is a computationally and statistically efficient algorithm in the generative model setting under completeness for two-layer neural networks. Our second result considers this setting but under only realizability of the neural net function class. Here, assuming deterministic dynamics, the sample complexity scales linearly in the algebraic dimension. In all cases, our results significantly improve upon what can be attained with linear (or eluder dimension) methods.

cs.LG↗

arXiv2021

Future prospects on constraining neutrino cosmology with the Ali CMB Polarization Telescope

We forecast the constraints on the parameters of neutrino physics with the constructions of Cosmic Microwave Background (CMB) temperature, E-mode polarization and lensing spectra for the ground-based Ali Cosmic Microwave Background Polarization Telescope (AliCPT). To implement the forecast calculations, we perform numerical simulations which show that AliCPT would yield the result $σ(N_{\mathrm{eff}})=0.42$ and $σ(M_ν)=0.18$ for the first year observation. Moreover, we investigate how the instrumental parameters, such as noise level, full width at half maxima (FWHM), and sky coverage can affect the constraints on these two parameters. Our forecasting results find that a large aperture telescope with a large sky survey strategy would significant improve the current constraints.

astro-ph.CO↗

arXiv2021

Persistence of Periodic Orbits under State-dependent Delayed Perturbations: Computer-assisted Proofs

A computer-assisted argument is given, which provides existence proofs for periodic orbits in state-dependent delayed perturbations of ordinary differential equations (ODEs). Assuming that the unperturbed ODE has an isolated periodic orbit, we introduce a set of polynomial inequalities whose successful verification leads to the existence of periodic orbits in the perturbed delay equation. We present a general algorithm, which describes a way of computing the coefficients of the polynomials and optimizing their variables so that the polynomial inequalities are satisfied. The algorithm uses the tools of validated numerics together with Chebyshev series expansion to obtain the periodic orbit of the ODE as well as the solution of the variational equations, which are both used to compute rigorously the coefficients of the polynomials. We apply our algorithm to prove the existence of periodic orbits in a state-dependent delayed perturbation of the van der Pol equation.

math.DS↗

arXiv2021

Double periodic viscous flows in infinite space-periodic pipes

We study the motion of an incompressible fluid in an $n+1$-dimensional infinite pipe $\,\La\,$ with an $L$-periodic shape in the $z=x_{n+1}$ direction. We set $\,x=(x_1,x_2,\cdots,x_{n})$, and $z=x_{n+1}$. We denote by $Σ_z$ the cross section of the pipe at the level $z\,,$ and by $v_z$ the $n+1$ component of the velocity. Fluid motion is described by the evolution Stokes or Navier-Stokes equations together with the non-slip boundary condition $\bv=\,0\,$. We look for solutions $\bv(x,z,t)$ with a given, arbitrary, $T-$time periodic total flux $\,\int_{Σ_z} \,v_z(x,z,t)\,dx=g(t)\,,$ which should be simultaneously $T$-periodic with respect to time and $L$-periodic with respect to $z\,.$ We prove existence and uniqueness of the solution to the above problems. The results extend those proved in reference \cite{B-05}, where the cross sections were independent of $z$. The argument is presented through a sequence of steps. We start by considering the linear, stationary, $z-$periodic Stokes problem. Then we study the double periodic evolution Stokes equations, which is the heart of the matter. Finally, we end with the extension to the full Navier-Stokes equations.

math.AP↗