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Xin Zhou

Publications and source records attributed to Xin Zhou.

At least 361 records · Page 20Linked to original sources
arXiv2020

Multiplicity one for min-max theory in compact manifolds with boundary and its applications

We prove the multiplicity one theorem for min-max free boundary minimal hypersurfaces in compact manifolds with boundary of dimension between 3 and 7 for generic metrics. To approach this, we develop existence and regularity theory for free boundary hypersurface with prescribed mean curvature, which includes the regularity theory for minimizers, compactness theory, and a generic min-max theory with Morse index bounds. As applications, we construct new free boundary minimal hypersurfaces in the unit balls in Euclidean spaces and self-shrinkers of the mean curvature flows with arbitrarily large entropy.

math.DG↗
arXiv2020

TGK-Planner: An Efficient Topology Guided Kinodynamic Planner for Autonomous Quadrotors

In this paper, we propose a lightweight yet effective Topology Guided Kinodynamic planner (TGK-Planner) for quadrotor aggressive flights with limited onboard computing resources. The proposed system follows the traditional hierarchical planning workflow, with novel designs to improve the robustness and efficiency in both the pathfinding and trajectory optimization sub-modules. Firstly, we propose the topology guided graph, which roughly captures the topological structure of the environment and guides the state sampling of a sampling-based kinodynamic planner. In this way, we significantly improve the efficiency of finding a safe and dynamically feasible trajectory. Then, we refine the smoothness and continuity of the trajectory in an optimization framework, which incorporates the homotopy constraint to guarantee the safety of the trajectory. The optimization program is formulated as a sequence of quadratic programmings (QPs) and can be iteratively solved in a few milliseconds. Finally, the proposed system is integrated into a fully autonomous quadrotor and validated in various simulated and real-world scenarios. Benchmark comparisons show that our method outperforms state-of-the-art methods with regard to efficiency and trajectory quality. Moreover, we will release our code as an open-source package.

cs.RO↗
arXiv2020

Electric circuit model of microwave optomechanics

We report on the generic classical electric circuit modeling that describes standard single-tone microwave optomechanics. Based on a parallel RLC circuit in which a mechanical oscillator acts as a movable capacitor, derivations of analytical expressions are presented, including key features such as the back-action force, the input-output expressions, and the spectral densities associated, all in the classical regime. These expressions coincide with the standard quantum treatment performed in optomechanics when the occupation number of both cavity and mechanical oscillator are large. Besides, the derived analytics transposes optical elements and properties into electronics terms, which is mandatory for quantitative measurement and design purposes. Finally, the direct comparison between the standard quantum treatment and the classical model addresses the bounds between quantum and classical regimes, highlighting the features which are truly quantum, and those which are not.

quant-ph↗
arXiv2020

Cross Copy Network for Dialogue Generation

In the past few years, audiences from different fields witness the achievements of sequence-to-sequence models (e.g., LSTM+attention, Pointer Generator Networks, and Transformer) to enhance dialogue content generation. While content fluency and accuracy often serve as the major indicators for model training, dialogue logics, carrying critical information for some particular domains, are often ignored. Take customer service and court debate dialogue as examples, compatible logics can be observed across different dialogue instances, and this information can provide vital evidence for utterance generation. In this paper, we propose a novel network architecture - Cross Copy Networks(CCN) to explore the current dialog context and similar dialogue instances' logical structure simultaneously. Experiments with two tasks, court debate and customer service content generation, proved that the proposed algorithm is superior to existing state-of-art content generation models.

cs.CL↗
arXiv2020

Using Neural Architecture Search for Improving Software Flaw Detection in Multimodal Deep Learning Models

Software flaw detection using multimodal deep learning models has been demonstrated as a very competitive approach on benchmark problems. In this work, we demonstrate that even better performance can be achieved using neural architecture search (NAS) combined with multimodal learning models. We adapt a NAS framework aimed at investigating image classification to the problem of software flaw detection and demonstrate improved results on the Juliet Test Suite, a popular benchmarking data set for measuring performance of machine learning models in this problem domain.

stat.ML↗
arXiv2020

Molecular Clouds Surrounding Supernova Remnant G43.9+1.6: Associated and Non-associated

Many supernova remnants (SNRs) are considered to evolve in molecular environments, but the associations between SNRs and molecular clouds (MCs) are often unclear. Being aware of such ambiguous case, we report our study on the molecular environment towards the SNR G43.9+1.6 by CO line observations. We investigated the correlations between the SNR and MCs at different velocities, and found two velocity components, i.e. $\sim$5 km s$^{-1}$ and $\sim$50 km s$^{-1}$ velocity components, showing spatial correlations with the remnant. However, no dynamical evidence of disturbance was found for the $\sim$5 km s$^{-1}$ velocity component. At the distance of the $\sim$5 km s$^{-1}$ velocity component, either near or far distance, the derived physical parameters are unreasonable too. We conclude that the SNR is not associated with the $\sim$5 km s$^{-1}$ velocity component, and their spatial correlation is just a chance correlation. For the $\sim$50 km s$^{-1}$ velocity component, dynamical evidence of disturbances, as well as the spatial correlation, indicate that it is associated with the SNR. We found that all the CO spectra extracted from the molecular clumps distributed along the border of the remnant are with broadened components presented, which can be fitted by Gaussian functions. By further analysis, we suggest that the SNR is at a near kinematic distance of about 3.1 kpc.

astro-ph.HE↗
arXiv2020

An Efficient Smoothing Proximal Gradient Algorithm for Convex Clustering

Cluster analysis organizes data into sensible groupings and is one of fundamental modes of understanding and learning. The widely used K-means and hierarchical clustering methods can be dramatically suboptimal due to local minima. Recently introduced convex clustering approach formulates clustering as a convex optimization problem and ensures a globally optimal solution. However, the state-of-the-art convex clustering algorithms, based on the alternating direction method of multipliers (ADMM) or the alternating minimization algorithm (AMA), require large computation and memory space, which limits their applications. In this paper, we develop a very efficient smoothing proximal gradient algorithm (Sproga) for convex clustering. Our Sproga is faster than ADMM- or AMA-based convex clustering algorithms by one to two orders of magnitude. The memory space required by Sproga is less than that required by ADMM and AMA by at least one order of magnitude. Computer simulations and real data analysis show that Sproga outperforms several well known clustering algorithms including K-means and hierarchical clustering. The efficiency and superior performance of our algorithm will help convex clustering to find its wide application.

cs.LG↗
arXiv2020

Mapping Natural Language Instructions to Mobile UI Action Sequences

We present a new problem: grounding natural language instructions to mobile user interface actions, and create three new datasets for it. For full task evaluation, we create PIXELHELP, a corpus that pairs English instructions with actions performed by people on a mobile UI emulator. To scale training, we decouple the language and action data by (a) annotating action phrase spans in HowTo instructions and (b) synthesizing grounded descriptions of actions for mobile user interfaces. We use a Transformer to extract action phrase tuples from long-range natural language instructions. A grounding Transformer then contextually represents UI objects using both their content and screen position and connects them to object descriptions. Given a starting screen and instruction, our model achieves 70.59% accuracy on predicting complete ground-truth action sequences in PIXELHELP.

cs.CL↗
arXiv2020

Local Molecular Gas toward the Aquila Rift Region

We present the results of a ~250 square degrees CO mapping (+26d 4.1x10^5 Msun in the whole region. In fact, the mass of the molecular gas is dominated by the W40 giant molecular cloud (GMC) at ~474 pc (~1.4x10^5 Msun) and the GMC complex G036.0+01.0 at ~560-670 pc (~2.0x10^5 Msun), while the MCs at ~220-260pc have gas masses of 10^2-10^3 Msun. Interestingly, an ~80pc long filamentary MC G044.0-02.5 at a distance of ~404 pc shows a systematic velocity gradient along and perpendicular to the major axis of the filament. The HI gas with the enhanced emission has the similar spatial morphologies and velocity features compared to the corresponding CO structure, indicating that the large-scale converging HI flows are probably responsible for the formation of the MC. Meanwhile, the long filamentary MC consists of many sub-filaments with the lengths ranging from ~0.5 pc to several pc, as well as prevalent networks of filaments in other large-scale local MCs.

astro-ph.SR↗
arXiv2020

Searching for Molecular Outflows with Support Vector Machines: Dark Cloud Complex in Cygnus

We present a survey of molecular outflows across the dark cloud complex in the Cygnus region, based on 46.75 deg^2 field of CO isotopologues data from Milky Way Imaging Scroll Painting (MWISP) survey. A supervised machine learning algorithm, Support Vector Machine (SVM), is introduced to accelerate our visual assessment of outflow features in the data cube of 12CO and 13CO J = 1-0 emission. A total of 130 outflow candidates are identified, of which 77 show bipolar structures and 118 are new detections. Spatially, these outflows are located inside dense molecular clouds and some of them are found in clusters or in elongated linear structures tracing the underlying gas filament morphology. Along the line of sight, 97, 31, and 2 candidates reside in the Local, Perseus, and Outer arm, respectively. Young stellar objects as outflow drivers are found near most outflows, while 36 candidates show no associated source. The clusters of outflows that we detect are inhomogeneous in their properties; nevertheless, we show that the outflows cannot inject turbulent energy on cloud scales. Instead, at best, they are restricted to affecting the so called "clump" and "core" scales, and this only on short (~0.3 Myr) estimated timescales. Combined with outflow samples in the literature, our work shows a tight outflow mass-size correlation.

astro-ph.SR↗
arXiv2020

Super-biderivations of the contact Lie superalgebra $K(m,n;\underline{t})$

Let $K$ denote the contact Lie superalgebra $K(m,n;\underline{t})$ over a field of characteristic $p>3$, which has a finite $\mathbb{Z}$-graded structure. Let $T_K$ be the canonical torus of $K$, which is an abelian subalgebra of $K_{0}$ and operates on $K_{-1}$ by semisimple endomorphisms. Utilizing the weight space decomposition of $K$ with respect to $T_K$, %we show the action of the skew-symmetric super-biderivation on the elements of $T$ and the contact of $K$. %Moreover, we prove that each skew-symmetric super-biderivation of $K$ is inner.

math.RA↗
arXiv2020

Alternating Minimization Based Trajectory Generation for Quadrotor Aggressive Flight

With much research has been conducted into trajectory planning for quadrotors, planning with spatial and temporal optimal trajectories in real-time is still challenging. In this paper, we propose a framework for generating large-scale piecewise polynomial trajectories for aggressive autonomous flights, with highlights on its superior computational efficiency and simultaneous spatial-temporal optimality. Exploiting the implicitly decoupled structure of the planning problem, we conduct alternating minimization between boundary conditions and time durations of trajectory pieces. In each minimization phase, we leverage the algebraic convenience of the sub-problem to escape poor local minima and achieve the lowest time consumption. Theoretical analysis for the global/local convergence rate of our proposed method is provided. Moreover, based on polynomial theory, an extremely fast feasibility check method is designed for various kinds of constraints. By incorporating the method into our alternating structure, a constrained minimization algorithm is constructed to optimize trajectories on the premise of feasibility. Benchmark evaluation shows that our algorithm outperforms state-of-the-art methods regarding efficiency, optimality, and scalability. Aggressive flight experiments in a limited space with dense obstacles are presented to demonstrate the performance of the proposed algorithm. We release our implementation as an open-source ros-package.

cs.RO↗
arXiv2020

Detailed Proofs of Alternating Minimization Based Trajectory Generation for Quadrotor Aggressive Flight

This technical report provides detailed theoretical analysis of the algorithm used in \textit{Alternating Minimization Based Trajectory Generation for Quadrotor Aggressive Flight}. An assumption is provided to ensure that settings for the objective function are meaningful. What's more, we explore the structure of the optimization problem and analyze the global/local convergence rate of the employed algorithm.

cs.RO↗
arXiv2020

Auto Completion of User Interface Layout Design Using Transformer-Based Tree Decoders

It has been of increasing interest in the field to develop automatic machineries to facilitate the design process. In this paper, we focus on assisting graphical user interface (UI) layout design, a crucial task in app development. Given a partial layout, which a designer has entered, our model learns to complete the layout by predicting the remaining UI elements with a correct position and dimension as well as the hierarchical structures. Such automation will significantly ease the effort of UI designers and developers. While we focus on interface layout prediction, our model can be generally applicable for other layout prediction problems that involve tree structures and 2-dimensional placements. Particularly, we design two versions of Transformer-based tree decoders: Pointer and Recursive Transformer, and experiment with these models on a public dataset. We also propose several metrics for measuring the accuracy of tree prediction and ground these metrics in the domain of user experience. These contribute a new task and methods to deep learning research.

cs.HC↗
arXiv2020

Automatic Business Process Structure Discovery using Ordered Neurons LSTM: A Preliminary Study

Automatic process discovery from textual process documentations is highly desirable to reduce time and cost of Business Process Management (BPM) implementation in organizations. However, existing automatic process discovery approaches mainly focus on identifying activities out of the documentations. Deriving the structural relationships between activities, which is important in the whole process discovery scope, is still a challenge. In fact, a business process has latent semantic hierarchical structure which defines different levels of detail to reflect the complex business logic. Recent findings in neural machine learning area show that the meaningful linguistic structure can be induced by joint language modeling and structure learning. Inspired by these findings, we propose to retrieve the latent hierarchical structure present in the textual business process documents by building a neural network that leverages a novel recurrent architecture, Ordered Neurons LSTM (ON-LSTM), with process-level language model objective. We tested the proposed approach on data set of Process Description Documents (PDD) from our practical Robotic Process Automation (RPA) projects. Preliminary experiments showed promising results.

cs.CL↗
arXiv2019

Searching for Stage-wise Neural Graphs In the Limit

Search space is a key consideration for neural architecture search. Recently, Xie et al. (2019) found that randomly generated networks from the same distribution perform similarly, which suggests we should search for random graph distributions instead of graphs. We propose graphon as a new search space. A graphon is the limit of Cauchy sequence of graphs and a scale-free probabilistic distribution, from which graphs of different number of nodes can be drawn. By utilizing properties of the graphon space and the associated cut-distance metric, we develop theoretically motivated techniques that search for and scale up small-capacity stage-wise graphs found on small datasets to large-capacity graphs that can handle ImageNet. The scaled stage-wise graphs outperform DenseNet and randomly wired Watts-Strogatz networks, indicating the benefits of graphon theory in NAS applications.

cs.LG↗
arXiv2019

Min-max theory for free boundary minimal hypersurfaces II -- General Morse index bounds and applications

For any smooth Riemannian metric on an $(n+1)$-dimensional compact manifold with boundary $(M,\partial M)$ where $3\leq (n+1)\leq 7$, we establish general upper bounds for the Morse index of free boundary minimal hypersurfaces produced by min-max theory in the Almgren-Pitts setting. We apply our Morse index estimates to prove that for almost every (in the $C^\infty$ Baire sense) Riemannan metric, the union of all compact, properly embedded free boundary minimal hypersurfaces is dense in $M$. If $\partial M$ is further assumed to have a strictly mean convex point, we show the existence of infinitely many compact, properly embedded free boundary minimal hypersurfaces whose boundaries are non-empty. Our results prove a conjecture of Yau for generic metrics in the free boundary setting.

math.DG↗