arXiv subjects

Tian Xu

Publications and source records attributed to Tian Xu.

50 records · Page 3Linked to original sources

arXiv2021

Proca equation and vector field quantization in rotating system

A strong background field will change the vacuum structure and the proper basis of a system drastically in both classical and quantum mechanics, e.g. the Landau levels in a background magnetic field. The situation is the same for the rotating case. In such a system the usual set of plane-wave states would no longer be suitable as a starting point of perturbation. Alternatively and straightforwardly in a rapidly and globally rotating system, it is better to reformulate the perturbation computation in principle. In this work we will complete the first step for the spin-1 field, which includes solving the Proca equation in present of a background rotation and complete its canonical quantization. It will be shown that because of the symmetry the eigen states are actually the same as the ones of Maxwell equations in cylindrical coordinate. The propagator as well as the near-central approximation will be obtained by considering the vorticity areas are so small in the relativistic QGP.

hep-th↗

arXiv2021

Generating Multi-scale Maps from Remote Sensing Images via Series Generative Adversarial Networks

Considering the success of generative adversarial networks (GANs) for image-to-image translation, researchers have attempted to translate remote sensing images (RSIs) to maps (rs2map) through GAN for cartography. However, these studies involved limited scales, which hinders multi-scale map creation. By extending their method, multi-scale RSIs can be trivially translated to multi-scale maps (multi-scale rs2map translation) through scale-wise rs2map models trained for certain scales (parallel strategy). However, this strategy has two theoretical limitations. First, inconsistency between various spatial resolutions of multi-scale RSIs and object generalization on multi-scale maps (RS-m inconsistency) increasingly complicate the extraction of geographical information from RSIs for rs2map models with decreasing scale. Second, as rs2map translation is cross-domain, generators incur high computation costs to transform the RSI pixel distribution to that on maps. Thus, we designed a series strategy of generators for multi-scale rs2map translation to address these limitations. In this strategy, high-resolution RSIs are inputted to an rs2map model to output large-scale maps, which are translated to multi-scale maps through series multi-scale map translation models. The series strategy avoids RS-m inconsistency as inputs are high-resolution large-scale RSIs, and reduces the distribution gap in multi-scale map generation through similar pixel distributions among multi-scale maps. Our experimental results showed better quality multi-scale map generation with the series strategy, as shown by average increases of 11.69%, 53.78%, 55.42%, and 72.34% in the structural similarity index, edge structural similarity index, intersection over union (road), and intersection over union (water) for data from Mexico City and Tokyo at zoom level 17-13.

cs.CV↗

arXiv2020

Machine learning spatio-temporal epidemiological model to evaluate Germany-county-level COVID-19 risk

As the COVID-19 pandemic continues to ravage the world, it is of critical significance to provide a timely risk prediction of the COVID-19 in multi-level. To implement it and evaluate the public health policies, we develop a framework with machine learning assisted to extract epidemic dynamics from the infection data, in which contains a county-level spatiotemporal epidemiological model that combines a spatial Cellular Automaton (CA) with a temporal Susceptible-Undiagnosed-Infected-Removed (SUIR) model. Compared with the existing time risk prediction models, the proposed CA-SUIR model shows the multi-level risk of the county to the government and coronavirus transmission patterns under different policies. This new toolbox is first utilized to the projection of the multi-level COVID-19 prevalence over 412 Landkreis (counties) in Germany, including t-day-ahead risk forecast and the risk assessment to the travel restriction policy. As a practical illustration, we predict the situation at Christmas where the worst fatalities are 34.5 thousand, effective policies could contain it to below 21 thousand. Such intervenable evaluation system could help decide on economic restarting and public health policies making in pandemic.

physics.soc-ph↗

arXiv2020

Error Bounds of Imitating Policies and Environments

Imitation learning trains a policy by mimicking expert demonstrations. Various imitation methods were proposed and empirically evaluated, meanwhile, their theoretical understanding needs further studies. In this paper, we firstly analyze the value gap between the expert policy and imitated policies by two imitation methods, behavioral cloning and generative adversarial imitation. The results support that generative adversarial imitation can reduce the compounding errors compared to behavioral cloning, and thus has a better sample complexity. Noticed that by considering the environment transition model as a dual agent, imitation learning can also be used to learn the environment model. Therefore, based on the bounds of imitating policies, we further analyze the performance of imitating environments. The results show that environment models can be more effectively imitated by generative adversarial imitation than behavioral cloning, suggesting a novel application of adversarial imitation for model-based reinforcement learning. We hope these results could inspire future advances in imitation learning and model-based reinforcement learning.

cs.LG↗

arXiv2020

Investigating Bias and Fairness in Facial Expression Recognition

Recognition of expressions of emotions and affect from facial images is a well-studied research problem in the fields of affective computing and computer vision with a large number of datasets available containing facial images and corresponding expression labels. However, virtually none of these datasets have been acquired with consideration of fair distribution across the human population. Therefore, in this work, we undertake a systematic investigation of bias and fairness in facial expression recognition by comparing three different approaches, namely a baseline, an attribute-aware and a disentangled approach, on two well-known datasets, RAF-DB and CelebA. Our results indicate that: (i) data augmentation improves the accuracy of the baseline model, but this alone is unable to mitigate the bias effect; (ii) both the attribute-aware and the disentangled approaches fortified with data augmentation perform better than the baseline approach in terms of accuracy and fairness; (iii) the disentangled approach is the best for mitigating demographic bias; and (iv) the bias mitigation strategies are more suitable in the existence of uneven attribute distribution or imbalanced number of subgroup data.

cs.CV↗

arXiv2020

Strongly localized semiclassical states for nonlinear Dirac equations

We study semiclassical states of the nonlinear Dirac equation \[ -i\hbar\partial_tψ= ic\hbar\sum_{k=1}^3α_k\partial_kψ- mc^2βψ- M(x)ψ+ f(|ψ|)ψ,\quad t\in\mathbb{R},\ x\in\mathbb{R}^3, \] where $V$ is a bounded continuous potential function and the nonlinear term $f(|ψ|)ψ$ is superlinear, possibly of critical growth. Our main result deals with standing wave solutions that concentrate near a critical point of the potential. Standard methods applicable to nonlinear Schrödinger equations, like Lyapunov-Schmidt reduction or penalization, do not work, not even for the homogeneous nonlinearity $f(s)=s^p$. We develop a variational method for the strongly indefinite functional associated to the problem.

math.AP↗

arXiv2020

A variational analysis of the spinorial Yamabe equation on product manifolds

This work is devoted to the analysis of the Yamabe problem on Spin manifolds and some applications to CMC immersions. Despite the efforts of many authors, very little is known on the existence of Yamabe metrics on general Spin manifolds. Motivated to bubbling phenomena for the Riemannian problem and recent multiplicity results in this setting, we investigate special spinorial Yamabe metrics on product manifolds developing a bubbling analysis which has independent interest in the present setting.

math.AP↗

arXiv2020

Blow-up profile for spinorial Yamabe type equation on $S^m$

Motivated by recent progress on a spinorial analogue of the Yamabe problem in the geometric literature, we study a conformally invariant spinor field equation on the $m$-sphere, $m\geq2$. Via variational methods, we study analytic aspects of the associated energy functional, culminating in a blow-up analysis.

math.DG↗

arXiv2019

On Value Discrepancy of Imitation Learning

Imitation learning trains a policy from expert demonstrations. Imitation learning approaches have been designed from various principles, such as behavioral cloning via supervised learning, apprenticeship learning via inverse reinforcement learning, and GAIL via generative adversarial learning. In this paper, we propose a framework to analyze the theoretical property of imitation learning approaches based on discrepancy propagation analysis. Under the infinite-horizon setting, the framework leads to the value discrepancy of behavioral cloning in an order of O((1-γ)^{-2}). We also show that the framework leads to the value discrepancy of GAIL in an order of O((1-γ)^{-1}). It implies that GAIL has less compounding errors than behavioral cloning, which is also verified empirically in this paper. To the best of our knowledge, we are the first one to analyze GAIL's performance theoretically. The above results indicate that the proposed framework is a general tool to analyze imitation learning approaches. We hope our theoretical results can provide insights for future improvements in imitation learning algorithms.

cs.LG↗

arXiv2019

A spinorial analogue of the Brezis-Nirenberg theorem involving the critical Sobolev exponent

Let $(M,\textit{g},σ)$ be a compact Riemannian spin manifold of dimension $m\geq2$, let $\mathbb{S}(M)$ denote the spinor bundle on $M$, and let $D$ be the Atiyah-Singer Dirac operator acting on spinors $ψ:M\to\mathbb{S}(M)$. We study the existence of solutions of the nonlinear Dirac equation with critical exponent \[ Dψ= λψ+ f(|ψ|)ψ+ |ψ|^{\frac2{m-1}}ψ\tag{NLD} \] where $λ\in\mathbb{R}$ and $f(|ψ|)ψ$ is a subcritical nonlinearity in the sense that $f(s)=o\big(s^{\frac2{m-1}}\big)$ as $s\to\infty$. A model nonlinearity is $f(s)=αs^{p-2}$ with $2 0$, even if $λ$ is an eigenvalue of $D$. For some classes of nonlinearities $f$ we also obtain solutions of (NLD) for every $λ\in\mathbb{R}$, except for non-positive eigenvalues. If $m\not\equiv3$ (mod 4) we obtain solutions of (NLD) for every $λ\in\mathbb{R}$, except for a finite number of non-positive eigenvalues. In certain parameter ranges we obtain multiple solutions of (NLD) and (BND), some near the trivial branch, others away from it. The proofs of our results are based on variational methods using the strongly indefinite energy functional associated to (NLD).

math.DG↗

arXiv2018

Deeper Interpretability of Deep Networks

Deep Convolutional Neural Networks (CNNs) have been one of the most influential recent developments in computer vision, particularly for categorization. There is an increasing demand for explainable AI as these systems are deployed in the real world. However, understanding the information represented and processed in CNNs remains in most cases challenging. Within this paper, we explore the use of new information theoretic techniques developed in the field of neuroscience to enable novel understanding of how a CNN represents information. We trained a 10-layer ResNet architecture to identify 2,000 face identities from 26M images generated using a rigorously controlled 3D face rendering model that produced variations of intrinsic (i.e. face morphology, gender, age, expression and ethnicity) and extrinsic factors (i.e. 3D pose, illumination, scale and 2D translation). With our methodology, we demonstrate that unlike human's network overgeneralizes face identities even with extreme changes of face shape, but it is more sensitive to changes of texture. To understand the processing of information underlying these counterintuitive properties, we visualize the features of shape and texture that the network processes to identify faces. Then, we shed a light into the inner workings of the black box and reveal how hidden layers represent these features and whether the representations are invariant to pose. We hope that our methodology will provide an additional valuable tool for interpretability of CNNs.

cs.CV↗

arXiv2014

Localized concentration of semi-classical states for nonlinear Dirac equations

The present paper studies concentration phenomena of semiclassical approximation of a massive Dirac equation with general nonlinear self-coupling: \[ -i\hbarα\cdot\nabla w+aβw+V(x)w=g(|w|)w \,. \] Compared with some existing issues, the most interesting results obtained here are twofold: the solutions concentrating around local minima of the external potential; and the nonlinearities assumed to be either super-linear or asymptotically linear at the infinity. As a consequence one sees that, if there are $k$ bounded domains $Λ_j\subset\mathbb{R}^3$ such that $-a<\min_{Λ_j} V=V(x_j)<\min_{\partialΛ_j}V$, $x_j\inΛ_j$, then the $k$-families of solutions $w_\hbar^j$ concentrates around $x_j$ as $\hbar\to 0$, respectively. The proof relies on variational arguments: the solutions are found as critical points of an energy functional. The Dirac operator has a continuous spectrum which is not bounded from below and above, hence the energy functional is strongly indefinite. A penalization technique is developed here to obtain the desired solutions.

math.AP↗

arXiv2014

On the concentration of semi-classical states for a nonlinear Dirac-Klein-Gordon system

In the present paper, we study the semi-classical approximation of a Yukawa-coupled massive Dirac-Klein-Gordon system with some general nonlinear self-coupling. We prove that for a constrained coupling constant there exists a family of ground states of the semi-classical problem, for all $\hbar$ small, and show that the family concentrates around the maxima of the nonlinear potential as $\hbar\to0$. Our method is variational and relies upon a delicate cutting off technique. It allows us to overcome the lack of convexity of the nonlinearities.

math.AP↗

arXiv2013

A Robust Alternating Direction Method for Constrained Hybrid Variational Deblurring Model

In this work, a new constrained hybrid variational deblurring model is developed by combining the non-convex first- and second-order total variation regularizers. Moreover, a box constraint is imposed on the proposed model to guarantee high deblurring performance. The developed constrained hybrid variational model could achieve a good balance between preserving image details and alleviating ringing artifacts. In what follows, we present the corresponding numerical solution by employing an iteratively reweighted algorithm based on alternating direction method of multipliers. The experimental results demonstrate the superior performance of the proposed method in terms of quantitative and qualitative image quality assessments.

cs.CV↗