arXiv subjects

Xuan Liu

Publications and source records attributed to Xuan Liu.

At least 127 records · Page 7Linked to original sources

arXiv2021

A Value-Function-based Interior-point Method for Non-convex Bi-level Optimization

Bi-level optimization model is able to capture a wide range of complex learning tasks with practical interest. Due to the witnessed efficiency in solving bi-level programs, gradient-based methods have gained popularity in the machine learning community. In this work, we propose a new gradient-based solution scheme, namely, the Bi-level Value-Function-based Interior-point Method (BVFIM). Following the main idea of the log-barrier interior-point scheme, we penalize the regularized value function of the lower level problem into the upper level objective. By further solving a sequence of differentiable unconstrained approximation problems, we consequently derive a sequential programming scheme. The numerical advantage of our scheme relies on the fact that, when gradient methods are applied to solve the approximation problem, we successfully avoid computing any expensive Hessian-vector or Jacobian-vector product. We prove the convergence without requiring any convexity assumption on either the upper level or the lower level objective. Experiments demonstrate the efficiency of the proposed BVFIM on non-convex bi-level problems.

math.OC↗

arXiv2021

Adaptive Epidemic Forecasting and Community Risk Evaluation of COVID-19

Pandemic control measures like lock-down, restrictions on restaurants and gatherings, social-distancing have shown to be effective in curtailing the spread of COVID-19. However, their sustained enforcement has negative economic effects. To craft strategies and policies that reduce the hardship on the people and the economy while being effective against the pandemic, authorities need to understand the disease dynamics at the right geo-spatial granularity. Considering factors like the hospitals' ability to handle the fluctuating demands, evaluating various reopening scenarios, and accurate forecasting of cases are vital to decision making. Towards this end, we present a flexible end-to-end solution that seamlessly integrates public health data with tertiary client data to accurately estimate the risk of reopening a community. At its core lies a state-of-the-art prediction model that auto-captures changing trends in transmission and mobility. Benchmarking against various published baselines confirm the superiority of our forecasting algorithm. Combined with the ability to extend to multiple client-specific requirements and perform deductive reasoning through counter-factual analysis, this solution provides actionable insights to multiple client domains ranging from government to educational institutions, hospitals, and commercial establishments.

cs.CY↗

arXiv2021

Cross-lingual Text Classification with Heterogeneous Graph Neural Network

Cross-lingual text classification aims at training a classifier on the source language and transferring the knowledge to target languages, which is very useful for low-resource languages. Recent multilingual pretrained language models (mPLM) achieve impressive results in cross-lingual classification tasks, but rarely consider factors beyond semantic similarity, causing performance degradation between some language pairs. In this paper we propose a simple yet effective method to incorporate heterogeneous information within and across languages for cross-lingual text classification using graph convolutional networks (GCN). In particular, we construct a heterogeneous graph by treating documents and words as nodes, and linking nodes with different relations, which include part-of-speech roles, semantic similarity, and document translations. Extensive experiments show that our graph-based method significantly outperforms state-of-the-art models on all tasks, and also achieves consistent performance gain over baselines in low-resource settings where external tools like translators are unavailable.

cs.CL↗

arXiv2021

Learning Contact-aware CPG-based Locomotion in a Soft Snake Robot

In this paper, we present a model-free learning-based control scheme for the soft snake robot to improve its contact-aware locomotion performance in a cluttered environment. The control scheme includes two cooperative controllers: A bio-inspired controller (C1) that controls both the steering and velocity of the soft snake robot, and an event-triggered regulator (R2) that controls the steering of the snake in anticipation of obstacle contacts and during contact. The inputs from the two controllers are composed as the input to a Matsuoka CPG network to generate smooth and rhythmic actuation inputs to the soft snake. To enable stable and efficient learning with two controllers, we develop a game-theoretic process, fictitious play, to train C1 and R2 with a shared potential-field-based reward function for goal tracking tasks. The proposed approach is tested and evaluated in the simulator and shows significant improvement of locomotion performance in the obstacle-based environment comparing to two baseline controllers.

cs.RO↗

arXiv2021

Bilinear Strichartz's type estimates in Besov spaces with application to inhomogeneous nonlinear biharmonic Schrödinger equation

In this paper, we consider the well-posedness of the inhomogeneous nonlinear biharmonic Schrödinger equation with spatial inhomogeneity coefficient $K(x)$ behaves like $\left|x\right|^{-b}$ for $0<b<\min \left\{\frac{N}{2},4\right\} $. We show the local well-posedness in the whole $H^s$-subcritical case, with $0<s\le2$. The difficulties of this problem come from the singularity of $K(x)$ and the lack of differentiability of the nonlinear term. To resolve this, we derive the bilinear Strichartz's type estimates for the nonlinear biharmonic Schrödinger equations in Besov spaces.

math.AP↗

arXiv2021

Global solutions for $H^s$-critical nonlinear biharmonic Schrödinger equation

We consider the nonlinear biharmonic Schrödinger equation $$i\partial_tu+(Δ^2+μΔ)u+f(u)=0,\qquad (\text{BNLS})$$ in the critical Sobolev space $H^s(\R^N)$, where $N\ge1$, $μ=0$ or $-1$, $0<s<\min\{\fc N2,8\}$ and $f(u)$ is a nonlinear function that behaves like $λ\left|u\right|^αu$ with $λ\in\mathbb{C},α=\frac{8}{N-2s}$. We prove the existence and uniqueness of the global solutions to (BNLS) for the small initial data.

math.AP↗

arXiv2021

Blockchain for Decentralized Multi-Drone to Combat COVID-19

Currently, drones represent a promising technology for combating Coronavirus disease 2019 (COVID-19) due to the transport of goods, medical supplies to a given target location in the quarantine areas experiencing an epidemic outbreak. Drone missions will increasingly rely on drone collaboration, which requires the drones to reduce communication complexity and be controlled in a decentralized fashion. Blockchain technology becomes a must in industrial applications because it provides decentralized data, accessibility, immutability, and irreversibility. Therefore, Blockchain makes data public for all drones and enables drones to log information concerning world states, time, location, resources, delivery data, and drone relation to all neighbors drones. This paper introduces decentralized independent multi-drones to accomplish the task collaboratively. Improving blockchain with a consensus algorithm can improve network partitioning and scalability in order to combat COVID-19. The multi-drones task is to combat COVID-19 via monitoring and detecting, social distancing, sanitization, data analysis, delivering goods and medical supplies, and announcement while avoiding collisions with one another. We discuss End to End (E2E) delivery application of combination blockchain and multi-drone in combating COVID-19 and beyond future pandemics. Furthermore, the challenges and opportunities of our proposed framework are highlighted.

cs.DC↗

arXiv2021

Local well-posedness and finite time blowup for fourth-order Schrödinger equation with complex coefficient

We consider the fourth-order Schrödinger equation $$ i\partial_tu+Δ^2 u+μΔu+λ|u|^αu=0, $$ where $α>0,μ=\pm1$ or $0$ and $λ\in\mathbb{C}$. Firstly, we prove local well-posedness in $H^4\left(\R^N\right)$ in both $H^4$ subcritical and critical case: $α>0$, $(N-8)α\leq8$. Then, for any given compact set $K\subset\mathbb{R}^N$, we construct $H^4(\R^N)$ solutions that are defined on $(-T, 0)$ for some $T>0$, and blow up exactly on $K$ at $t=0$.

math.AP↗

arXiv2020

Estimation of the Galaxy Quenching Rate in the Illustris Simulation

Quenching is a key topic in exploring the formation and evolution of galaxies. In this work, we study the quenching rate, i.e., the variation in the fraction of quenched galaxies per unit time, of the Illustris-1 simulation. By building the quenched fraction function $f(m,ρ, t)$ of each snapshot in the simulation, we derive an accurate form of quenching rate as $\Re_q=df(m,ρ,t)/dt$. According to the analytic expression of the quenching rate $\Re_q$, we split it into four components: mass quenching, environmental quenching, intrinsic mass quenching and intrinsic environmental quenching. The precise value and evolutions can be given via the formula of $\Re_q$. With this method, we analyze the Illustris-1 simulation. We find that quenched galaxies concentrate around $M_*\simeq10^{11}h^{-1}M_\odot$ and $δ+1\simeq10^{3.5}$ at earlier times, and that the quenching galaxy population slowly shifts to lower stellar mass and lower overdensity regions with time. We also find that mass quenching dominates the quenching process in this simulation, in agreement with some previous analytical models. Intrinsic quenching is the second most important component. Environmental quenching is very weak, because it is possible that the pre- or postprocessing of environments disguises environmental quenching as intrinsic quenching. We find that our method roughly predict the actual quenching rate. It could well predict the actual amount of galaxies quenched by intrinsic quenching. However, it overestimates the amount of mass quenching galaxies and underestimates the amount of environmental quenching. We suggest that the reason is the nonlinearity of the environmental overdensity change and mass growth of the galaxy.

astro-ph.GA↗

arXiv2020

Defending Against Adversarial Attacks in Transmission- and Distribution-level PMU Data

Phasor measurement units (PMUs) provide high-fidelity data that improve situation awareness of electric power grid operations. PMU datastreams inform wide-area state estimation, monitor area control error, and facilitate event detection in real time. As PMU data become more available and increasingly reliable, these devices are found in new roles within control systems, such as remedial action schemes and early warning detection systems. As with other cyber physical systems, maintaining data integrity and security pose a significant challenge for power system operators. In this paper, we present a comprehensive analysis of multiple machine learning techniques to detect malicious data injection within PMU data streams. The two datasets used in this study come from two PMU networks: an inter-university, research-grade distribution network spanning three institutions in the U.S. Pacific Northwest, and a utility transmission network from the Bonneville Power Administration. We implement the detection algorithms with TensorFlow, an open-source software library for machine learning, and the results demonstrate potential for distributing the training workload and achieving higher performance, while maintaining effectiveness in the detection of spoofed data.

eess.SP↗

arXiv2020

A Dielectric Metasurface Optical Chip for the Generation of Cold Atoms

Compact and robust cold atom sources are increasingly important for quantum research, especially for transferring cutting-edge quantum science into practical applications. In this letter, we report on a novel scheme that utilizes a metasurface optical chip to replace the conventional bulky optical elements used to produce a cold atomic ensemble with a single incident laser beam, which is split by the metasurface into multiple beams of the desired polarization states. Atom numbers $~10^7$ and temperatures (about 35 $μ$K) of relevance to quantum sensing are achieved in a compact and robust fashion. Our work highlights the substantial progress towards fully integrated cold atom quantum devices by exploiting metasurface optical chips, which may have great potential in quantum sensing, quantum computing and other areas.

physics.optics↗

arXiv2020

The Multi-Symplectic Lanczos Algorithm and Its Applications to Color Image Processing

Low-rank approximations of original samples are playing more and more an important role in many recently proposed mathematical models from data science. A natural and initial requirement is that these representations inherit original structures or properties. With this aim, we propose a new multi-symplectic method based on the Lanzcos bidiagonalization to compute the partial singular triplets of JRS-symmetric matrices. These singular triplets can be used to reconstruct optimal low-rank approximations while preserving the intrinsic multi-symmetry. The augmented Ritz and harmonic Ritz vectors are used to perform implicit restarting to obtain a satisfactory bidiagonal matrix for calculating the $k$ largest or smallest singular triplets, respectively. We also apply the new multi-symplectic Lanczos algorithms to color face recognition and color video compressing and reconstruction. Numerical experiments indicate their superiority over the state-of-the-art algorithms.

math.NA↗

arXiv2020

Snapshot Interferometric 3D Imaging by Compressive Sensing and Deep Learning

We demonstrate single-shot compressive three-dimensional (3D) $(x, y, z)$ imaging based on interference coding. The depth dimension of the object is encoded into the interferometric spectra of the light field, resulting a $(x, y, λ)$ datacube which is subsequently measured by a single-shot spectrometer. By implementing a compression ratio up to $400$, we are able to reconstruct $1G$ voxels from a 2D measurement. Both an optimization based compressive sensing algorithm and a deep learning network are developed for 3D reconstruction from a single 2D coded measurement. Due to the fast acquisition speed, our approach is able to capture volumetric activities at native camera frame rates, enabling 4D (volumetric-temporal) visualization of dynamic scenes.

eess.IV↗

arXiv2020

Large-Scale Beamforming for Massive MIMO via Randomized Sketching

Massive MIMO system yields significant improvements in spectral and energy efficiency for future wireless communication systems. The regularized zero-forcing (RZF) beamforming is able to provide good performance with the capability of achieving numerical stability and robustness to the channel uncertainty. However, in massive MIMO systems, the matrix inversion operation in RZF beamforming becomes computationally expensive. To address this computational issue, we shall propose a novel randomized sketching based RZF beamforming approach with low computational complexity. This is achieved by solving a linear system via randomized sketching based on the preconditioned Richard iteration, which guarantees high quality approximations to the optimal solution. We theoretically prove that the sequence of approximations obtained iteratively converges to the exact RZF beamforming matrix linearly fast as the number of iterations increases. Also, it turns out that the system sum-rate for such sequence of approximations converges to the exact one at a linear convergence rate. Our simulation results verify our theoretical findings.

cs.IT↗

arXiv2020

Learning to Locomote with Deep Neural-Network and CPG-based Control in a Soft Snake Robot

In this paper, we present a new locomotion control method for soft robot snakes. Inspired by biological snakes, our control architecture is composed of two key modules: A deep reinforcement learning (RL) module for achieving adaptive goal-tracking behaviors with changing goals, and a central pattern generator (CPG) system with Matsuoka oscillators for generating stable and diverse locomotion patterns. The two modules are interconnected into a closed-loop system: The RL module, analogizing the locomotion region located in the midbrain of vertebrate animals, regulates the input to the CPG system given state feedback from the robot. The output of the CPG system is then translated into pressure inputs to pneumatic actuators of the soft snake robot. Based on the fact that the oscillation frequency and wave amplitude of the Matsuoka oscillator can be independently controlled under different time scales, we further adapt the option-critic framework to improve the learning performance measured by optimality and data efficiency. The performance of the proposed controller is experimentally validated with both simulated and real soft snake robots.

cs.RO↗

arXiv2019

On a maximal inequality and its application to SDEs with singular drift

In this paper we present a Doob type maximal inequality for stochastic processes satisfying the conditional increment control condition. If we assume, in addition, that the margins of the process have uniform exponential tail decay, we prove that the supremum of the process decays exponentially in the same manner. Then we apply this result to the construction of the almost everywhere stochastic flow to stochastic differential equations with singular time dependent divergence-free drift.

math.PR↗

arXiv2019

Compositional planning in Markov decision processes: Temporal abstraction meets generalized logic composition

In hierarchical planning for Markov decision processes (MDPs), temporal abstraction allows planning with macro-actions that take place at different time scale in form of sequential composition. In this paper, we propose a novel approach to compositional reasoning and hierarchical planning for MDPs under temporal logic constraints. In addition to sequential composition, we introduce a composition of policies based on generalized logic composition: Given sub-policies for sub-tasks and a new task expressed as logic compositions of subtasks, a semi-optimal policy, which is optimal in planning with only sub-policies, can be obtained by simply composing sub-polices. Thus, a synthesis algorithm is developed to compute optimal policies efficiently by planning with primitive actions, policies for sub-tasks, and the compositions of sub-policies, for maximizing the probability of satisfying temporal logic specifications. We demonstrate the correctness and efficiency of the proposed method in stochastic planning examples with a single agent and multiple task specifications.

math.OC↗

arXiv2019

A Validated Physical Model For Real-Time Simulation of Soft Robotic Snakes

In this work we present a framework that is capable of accurately representing soft robotic actuators in a multiphysics environment in real-time. We propose a constraint-based dynamics model of a 1-dimensional pneumatic soft actuator that accounts for internal pressure forces, as well as the effect of actuator latency and damping under inflation and deflation and demonstrate its accuracy a full soft robotic snake with the composition of multiple 1D actuators. We verify our model's accuracy in static deformation and dynamic locomotion open-loop control experiments. To achieve real-time performance we leverage the parallel computation power of GPUs to allow interactive control and feedback.

cs.RO↗