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Yuan Gao

Publications and source records attributed to Yuan Gao.

At least 505 records · Page 28Linked to original sources
arXiv2019

Large time behavior, bi-Hamiltonian structure and kinetic formulation for complex Burgers equation

We prove the existence and uniqueness of positive analytical solutions with positive initial data to the mean field equation (the Dyson equation) of the Dyson Brownian motion through the complex Burgers equation with a force term on the upper half complex plane. These solutions converge to a steady state given by Wigner's semicircle law. A unique global weak solution with nonnegative initial data to the Dyson equation is obtained and some explicit solutions are given by Wigner's semicircle laws. We also construct a bi-Hamiltonian structure for the system of the real and imaginary components of the complex Burgers equation (coupled Burgers system). We establish a kinetic formulation for the coupled Burgers system and prove the existence and uniqueness of entropy solutions. The coupled Burgers system in Lagrangian variable naturally leads to two interacting particle systems: Fermi-Pasta-Ulam-Tsingou model with nearest-neighbor interactions, and Calogero-Moser model. These two particle systems yield the same Lagrangian dynamics in the continuum limit.

math.AP↗
arXiv2019

Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects

We study a $4$th order PDE with a $2$nd order correction that is a modification of one suggested by Peter Smereka using the tools of Krug et al (Z. Phys. B., 1994). First, we provide a non-rigorous derivation of the full model derived with a quadratic interaction potential using the rates and methods of the last author with Jonathan Weare (PRE, 2013). Then, we prove the existence of a global in time weak solution by regularizing the equation in a way that allows us to apply the tools of Bernis-Friedman (JDE, 1990). The methods developed here can be applied to a large number of $4$th order degenerate models. In an appendix, we also discuss the global smooth solution with small data in the Weiner algebra framework following recent developments using tools of the second author with Robert Strain (IFB, 2018).

math.AP↗
arXiv2019

Accurate Protein Structure Prediction by Embeddings and Deep Learning Representations

Proteins are the major building blocks of life, and actuators of almost all chemical and biophysical events in living organisms. Their native structures in turn enable their biological functions which have a fundamental role in drug design. This motivates predicting the structure of a protein from its sequence of amino acids, a fundamental problem in computational biology. In this work, we demonstrate state-of-the-art protein structure prediction (PSP) results using embeddings and deep learning models for prediction of backbone atom distance matrices and torsion angles. We recover 3D coordinates of backbone atoms and reconstruct full atom protein by optimization. We create a new gold standard dataset of proteins which is comprehensive and easy to use. Our dataset consists of amino acid sequences, Q8 secondary structures, position specific scoring matrices, multiple sequence alignment co-evolutionary features, backbone atom distance matrices, torsion angles, and 3D coordinates. We evaluate the quality of our structure prediction by RMSD on the latest Critical Assessment of Techniques for Protein Structure Prediction (CASP) test data and demonstrate competitive results with the winning teams and AlphaFold in CASP13 and supersede the results of the winning teams in CASP12. We make our data, models, and code publicly available.

q-bio.BM↗
arXiv2019

Impact-Aware Online Motion Planning for Fully-Actuated Bipedal Robot Walking

The ability to track a general walking path with specific timing is crucial to the operational safety and reliability of bipedal robots for avoiding dynamic obstacles, such as pedestrians, in complex environments. This paper introduces an online, full-body motion planner that generates the desired impact-aware motion for fully-actuated bipedal robotic walking. The main novelty of the proposed planner lies in its capability of producing desired motions in real-time that respect the discrete impact dynamics and the desired impact timing. To derive the proposed planner, a full-order hybrid dynamic model of fully-actuated bipedal robotic walking is presented, including both continuous dynamics and discrete lading impacts. Next, the proposed impact-aware online motion planner is introduced. Finally, simulation results of a 3-D bipedal robot are provided to confirm the effectiveness of the proposed online impact-aware planner. The online planner is capable of generating full-body motion of one walking step within 0.6 second, which is shorter than a typical bipedal walking step.

cs.RO↗
arXiv2019

Learning Socially Appropriate Robot Approaching Behavior Toward Groups using Deep Reinforcement Learning

Deep reinforcement learning has recently been widely applied in robotics to study tasks such as locomotion and grasping, but its application to social human-robot interaction (HRI) remains a challenge. In this paper, we present a deep learning scheme that acquires a prior model of robot approaching behavior in simulation and applies it to real-world interaction with a physical robot approaching groups of humans. The scheme, which we refer to as Staged Social Behavior Learning (SSBL), considers different stages of learning in social scenarios. We learn robot approaching behaviors towards small groups in simulation and evaluate the performance of the model using objective and subjective measures in a perceptual study and a HRI user study with human participants. Results show that our model generates more socially appropriate behavior compared to a state-of-the-art model.

cs.RO↗
arXiv2019

Fast Adaptation with Meta-Reinforcement Learning for Trust Modelling in Human-Robot Interaction

In socially assistive robotics, an important research area is the development of adaptation techniques and their effect on human-robot interaction. We present a meta-learning based policy gradient method for addressing the problem of adaptation in human-robot interaction and also investigate its role as a mechanism for trust modelling. By building an escape room scenario in mixed reality with a robot, we test our hypothesis that bi-directional trust can be influenced by different adaptation algorithms. We found that our proposed model increased the perceived trustworthiness of the robot and influenced the dynamics of gaining human's trust. Additionally, participants evaluated that the robot perceived them as more trustworthy during the interactions with the meta-learning based adaptation compared to the previously studied statistical adaptation model.

cs.RO↗
arXiv2019

Mathematical validation of the Peierls--Nabarro model for edge dislocations

In this paper, we perform mathematical validation of the Peierls--Nabarro (PN) models, which are multiscale models of dislocations that incorporate the detailed dislocation core structure. We focus on the static and dynamic PN models of an edge dislocation. In a PN model, the total energy includes the elastic energy in the two half-space continua and a nonlinear potential energy across the slip plane, which is always infinite. We rigorously establish the relationship between the PN model in the full space and the reduced problem on the slip plane in terms of both governing equations and energy variations. The shear displacement jump is determined only by the reduced problem on the slip plane while the displacement fields in the two half spaces are determined by linear elasticity. We establish the existence and sharp regularities of classical solutions in Hilbert space. For both the reduced problem and the full PN model, we prove that a static solution is a global minimizer in perturbed sense. We also show that there is a unique classical, global in time solution of the dynamic PN model.

math.AP↗
arXiv2019

Long time behavior of dynamic solution to Peierls--Nabarro dislocation model

In this paper we study the relaxation process of Peierls-Nabarro dislocation model, which is a gradient flow with singular nonlocal energy and double well potential describing how the materials relax to its equilibrium with the presence of a dislocation. We prove the dynamic solution to Peierls-Nabarro model will converge exponentially to a shifted steady profile which is uniquely determined.

math.AP↗
arXiv2019

Variational Properties of Matrix Functions via the Generalized Matrix-Fractional Function

We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which such functions are closed and proper as well as formulas for the ready computation of both their conjugates and subdifferentials. Special attention is given to support and indicator functions. Particular instances yield all weighted Ky Fan norms and squared gauges on $\mathbb R^{n\times m}$, and as an example we show that all variational Gram functions are representable as squares of gauges. Other instances yield weighted sums of the Frobenius and nuclear norms. The scope of applications is large and the range of variational properties and insight is fascinating and fundamental. An important byproduct of these representations is that they lay the foundation for a smoothing approach to many matrix functions on the interior of the domain of the GMF function, which opens the door to a range of unexplored optimization methods.

math.OC↗
arXiv2019

Deep Generative Learning via Variational Gradient Flow

We propose a general framework to learn deep generative models via \textbf{V}ariational \textbf{Gr}adient Fl\textbf{ow} (VGrow) on probability spaces. The evolving distribution that asymptotically converges to the target distribution is governed by a vector field, which is the negative gradient of the first variation of the $f$-divergence between them. We prove that the evolving distribution coincides with the pushforward distribution through the infinitesimal time composition of residual maps that are perturbations of the identity map along the vector field. The vector field depends on the density ratio of the pushforward distribution and the target distribution, which can be consistently learned from a binary classification problem. Connections of our proposed VGrow method with other popular methods, such as VAE, GAN and flow-based methods, have been established in this framework, gaining new insights of deep generative learning. We also evaluated several commonly used divergences, including Kullback-Leibler, Jensen-Shannon, Jeffrey divergences as well as our newly discovered `logD' divergence which serves as the objective function of the logD-trick GAN. Experimental results on benchmark datasets demonstrate that VGrow can generate high-fidelity images in a stable and efficient manner, achieving competitive performance with state-of-the-art GANs.

cs.LG↗
arXiv2019

NDDR-CNN: Layerwise Feature Fusing in Multi-Task CNNs by Neural Discriminative Dimensionality Reduction

In this paper, we propose a novel Convolutional Neural Network (CNN) structure for general-purpose multi-task learning (MTL), which enables automatic feature fusing at every layer from different tasks. This is in contrast with the most widely used MTL CNN structures which empirically or heuristically share features on some specific layers (e.g., share all the features except the last convolutional layer). The proposed layerwise feature fusing scheme is formulated by combining existing CNN components in a novel way, with clear mathematical interpretability as discriminative dimensionality reduction, which is referred to as Neural Discriminative Dimensionality Reduction (NDDR). Specifically, we first concatenate features with the same spatial resolution from different tasks according to their channel dimension. Then, we show that the discriminative dimensionality reduction can be fulfilled by 1x1 Convolution, Batch Normalization, and Weight Decay in one CNN. The use of existing CNN components ensures the end-to-end training and the extensibility of the proposed NDDR layer to various state-of-the-art CNN architectures in a "plug-and-play" manner. The detailed ablation analysis shows that the proposed NDDR layer is easy to train and also robust to different hyperparameters. Experiments on different task sets with various base network architectures demonstrate the promising performance and desirable generalizability of our proposed method. The code of our paper is available at https://github.com/ethanygao/NDDR-CNN.

cs.CV↗
arXiv2019

Wasserstein-Wasserstein Auto-Encoders

To address the challenges in learning deep generative models (e.g.,the blurriness of variational auto-encoder and the instability of training generative adversarial networks, we propose a novel deep generative model, named Wasserstein-Wasserstein auto-encoders (WWAE). We formulate WWAE as minimization of the penalized optimal transport between the target distribution and the generated distribution. By noticing that both the prior $P_Z$ and the aggregated posterior $Q_Z$ of the latent code Z can be well captured by Gaussians, the proposed WWAE utilizes the closed-form of the squared Wasserstein-2 distance for two Gaussians in the optimization process. As a result, WWAE does not suffer from the sampling burden and it is computationally efficient by leveraging the reparameterization trick. Numerical results evaluated on multiple benchmark datasets including MNIST, fashion- MNIST and CelebA show that WWAE learns better latent structures than VAEs and generates samples of better visual quality and higher FID scores than VAEs and GANs.

cs.LG↗
arXiv2019

Global Strong Solution With BV Derivatives to Singular Solid-on-Solid model With Exponential Nonlinearity

In this work, we consider the one dimensional very singular fourth-order equation for solid-on-solid model in attachment-detachment-limit regime with exponential nonlinearity $$h_t = \nabla \cdot (\frac{1}{|\nabla h|} \nabla e^{\frac{δE}{δh}}) =\nabla \cdot (\frac{1}{|\nabla h|}\nabla e^{- \nabla \cdot (\frac{\nabla h}{|\nabla h|})})$$ where total energy $E=\int |\nabla h|$ is the total variation of $h$. Using a logarithmic correction $E=\int |\nabla h|\ln|\nabla h| d x$ and gradient flow structure with a suitable defined functional, we prove the evolution variational inequality solution preserves a positive gradient $h_x$ which has upper and lower bounds but in BV space. We also obtain the global strong solution to the solid-on-solid model which allows an asymmetric singularity $h_{xx}^+$ happens.

math.AP↗
arXiv2018

Solution for Large-Scale Hierarchical Object Detection Datasets with Incomplete Annotation and Data Imbalance

This report demonstrates our solution for the Open Images 2018 Challenge. Based on our detailed analysis on the Open Images Datasets (OID), it is found that there are four typical features: large-scale, hierarchical tag system, severe annotation incompleteness and data imbalance. Considering these characteristics, an amount of strategies are employed, including SNIPER, soft sampling, class-aware sampling (CAS), hierarchical non-maximum suppression (HNMS) and so on. In virtue of these effective strategies, and further using the powerful SENet154 armed with feature pyramid module and deformable ROIalign as the backbone, our best single model could achieve a mAP of 56.9%. After a further ensemble with 9 models, the final mAP is boosted to 62.2% in the public leaderboard (ranked the 2nd place) and 58.6% in the private leaderboard (ranked the 3rd place, slightly inferior to the 1st place by only 0.04 point).

cs.CV↗
arXiv2018

High-dimensional functional time series forecasting: An application to age-specific mortality rates

We address the problem of forecasting high-dimensional functional time series through a two-fold dimension reduction procedure. The difficulty of forecasting high-dimensional functional time series lies in the curse of dimensionality. In this paper, we propose a novel method to solve this problem. Dynamic functional principal component analysis is first applied to reduce each functional time series to a vector. We then use the factor model as a further dimension reduction technique so that only a small number of latent factors are preserved. Classic time series models can be used to forecast the factors and conditional forecasts of the functions can be constructed. Asymptotic properties of the approximated functions are established, including both estimation error and forecast error. The proposed method is easy to implement especially when the dimension of the functional time series is large. We show the superiority of our approach by both simulation studies and an application to Japanese age-specific mortality rates.

stat.ME↗
arXiv2018

Energy Efficient and Fair Resource Allocation for LTE-Unlicensed Uplink Networks: A Two-sided Matching Approach with Partial Information

LTE-Unlicensed (LTE-U) has recently attracted worldwide interest to meet the explosion in cellular traffic data. By using carrier aggregation (CA), licensed and unlicensed bands are integrated to enhance transmission capacity while maintaining reliable and predictable performance. As there may exist other conventional unlicensed band users, such as Wi-Fi users, LTE-U users have to share the same unlicensed bands with them. Thus, an optimized resource allocation scheme to ensure the fairness between LTE-U users and conventional unlicensed band users is critical for the deployment of LTE-U networks. In this paper, we investigate an energy efficient resource allocation problem in LTE-U coexisting with other wireless networks, which aims at guaranteeing fairness among the users of different radio access networks (RANs). We formulate the problem as a multi-objective optimization problem and propose a semi-distributed matching framework with a partial information-based algorithm to solve it. We demonstrate our contributions with simulations in which various network densities and traffic load levels are considered.

cs.IT↗
arXiv2018

Gradient flow approach to an exponential thin film equation: global existence and latent singularity

In this work, we study a fourth order exponential equation, $u_t=Δe^{-Δu},$ derived from thin film growth on crystal surface in multiple space dimensions. We use the gradient flow method in metric space to characterize the latent singularity in global strong solution, which is intrinsic due to high degeneration. We define a suitable functional, which reveals where the singularity happens, and then prove the variational inequality solution under very weak assumptions for initial data. Moreover, the existence of global strong solution is established with regular initial data.

math.AP↗