arXiv subjects

Ming Wang

Publications and source records attributed to Ming Wang.

108 records · Page 6Linked to original sources

arXiv2022

GaitGL: Learning Discriminative Global-Local Feature Representations for Gait Recognition

Existing gait recognition methods either directly establish Global Feature Representation (GFR) from original gait sequences or generate Local Feature Representation (LFR) from several local parts. However, GFR tends to neglect local details of human postures as the receptive fields become larger in the deeper network layers. Although LFR allows the network to focus on the detailed posture information of each local region, it neglects the relations among different local parts and thus only exploits limited local information of several specific regions. To solve these issues, we propose a global-local based gait recognition network, named GaitGL, to generate more discriminative feature representations. To be specific, a novel Global and Local Convolutional Layer (GLCL) is developed to take full advantage of both global visual information and local region details in each layer. GLCL is a dual-branch structure that consists of a GFR extractor and a mask-based LFR extractor. GFR extractor aims to extract contextual information, e.g., the relationship among various body parts, and the mask-based LFR extractor is presented to exploit the detailed posture changes of local regions. In addition, we introduce a novel mask-based strategy to improve the local feature extraction capability. Specifically, we design pairs of complementary masks to randomly occlude feature maps, and then train our mask-based LFR extractor on various occluded feature maps. In this manner, the LFR extractor will learn to fully exploit local information. Extensive experiments demonstrate that GaitGL achieves better performance than state-of-the-art gait recognition methods. The average rank-1 accuracy on CASIA-B, OU-MVLP, GREW and Gait3D is 93.6%, 98.7%, 68.0% and 63.8%, respectively, significantly outperforming the competing methods. The proposed method has won the first prize in two competitions: HID 2020 and HID 2021.

cs.CV↗

arXiv2022

Improved lower bounds of analytic radius for the Benjamin-Bona-Mahony equation

This paper is devoted to the spatial analyticity of the solution of the BBM equation on the real line with an analytic initial data. It is shown that the analytic radius has a lower bound like $t^{-\frac{2}{3}}$ as time $t$ goes to infinity, which is an improvement of previous results. The main new ingredient is a higher order almost conservation law in analytic spaces. This is proved by introducing an equivalent analytic norm with smooth symbol and establishing some algebra identities of higher order polynomials.

math.AP↗

arXiv2021

Machine Learning for Real-Time, Automatic, and Early Diagnosis of Parkinson's Disease by Extracting Signs of Micrographia from Handwriting Images

Parkinson's disease (PD) is debilitating, progressive, and clinically marked by motor symptoms. As the second most common neurodegenerative disease in the world, it affects over 10 million lives globally. Existing diagnoses methods have limitations, such as the expense of visiting doctors and the challenge of automated early detection, considering that behavioral differences in patients and healthy individuals are often indistinguishable in the early stages. However, micrographia, a handwriting disorder that leads to abnormally small handwriting, tremors, dystonia, and slow movement in the hands and fingers, is commonly observed in the early stages of PD. In this work, we apply machine learning techniques to extract signs of micrographia from drawing samples gathered from two open-source datasets and achieve a predictive accuracy of 94%. This work also sets the foundations for a publicly available and user-friendly web portal that anyone with access to a pen, printer, and phone can use for early PD detection.

cs.LG↗

arXiv2021

Analyticity and observability for fractional heat equation on $\mathbb{R}^n$

In this paper, we study quantitative spatial analytic bounds and unique continuation inequalities of solutions for fractional heat equations with an analytic lower order term on the whole space. At first, we show that the solution has a uniform positive analytic radius for all time, and the solution enjoys a log-type ultra-analytic bound if the coefficient is ultra-analytic. Second, we prove a Hölder type interpolation inequality on a thick set, with an explicit dependence on the analytic radius of coefficient. Finally, by the telescoping series method, we establish an observability inequality from a thick set. As a byproduct of the proof, we obtain observability inequalities in weighted spaces from a thick set for the classical heat equation with a lower order term.

math.AP↗

arXiv2021

Short term minutes-time scale temporal variation statistics of sodium layer dynamics

The brightness and height of the sodium laser guide star of adaptive optics could vary significantly due to the temporal dynamics of sodium column density and the mean height of sodium layer. To measure these dynamics, an independent sodium Lidar is a necessity. Without such an instrument, it is almost impossible to discern the cause of the brightness variation of laser guide star from the sodium layer's dynamics or other factors from the laser itself. For applications such as characterizing the performance of sodium laser for sodium laser guide star generation, minutes scale short term statistics of the sodium layers' abundance and height is extremely helpful for estimating the contribution of sodium layer's variation to the variation of laser guide star's brightness. In this paper, we analyzed our previous measurement of sodium layer dynamics that has been gathered in two winters, and presented the temporal variation statistics of sodium column density and mean height within minute time scale based on our measurements.

astro-ph.IM↗

arXiv2021

Analyses of Laser Propagation Noises for TianQin Gravitational Wave Observatory Based on the Global Magnetosphere MHD Simulations

TianQin is a proposed space-borne gravitational wave (GW) observatory composed of three identical satellites orbiting around the geocenter with a radius of $10^5$ km. It aims at detecting GWs in the frequency range of 0.1 mHz -- 1 Hz. The detection of GW relies on the high precision measurement of optical path length at $10^{-12}$~m level. The dispersion of space plasma can lead to the optical path difference (OPD, $Δl$) along the propagation of laser beams between any pair of satellites. Here, we study the OPD noises for TianQin. The Space Weather Modeling Framework is used to simulate the interaction between the Earth magnetosphere and solar wind. From the simulations, we extract the magnetic field and plasma parameters on the orbits of TianQin at four relative positions of the satellite constellation in the Earth magnetosphere. We calculate the OPD noise for single link, Michelson combination, and Time-Delay Interferometry (TDI) combinations ($α$ and $X$). For single link and Michelson interferometer, the maxima of $|Δl|$ are on the order of 1 pm. For the TDI combinations, these can be suppressed to about 0.004 and 0.008 pm for $α$ and $X$. The OPD noise of the Michelson combination is colored in the concerned frequency range; while the ones for the TDI combinations are approximately white. Furthermore, we calculate the ratio of the equivalent strain of the OPD noise to that of TQ, and find that the OPD noises for the TDI combinations can be neglected in the most sensitive frequency range of TQ.

astro-ph.SR↗

arXiv2020

Analyses of residual accelerations for TianQin based on the global MHD simulation

TianQin is a proposed space-based gravitational wave observatory. It is designed to detect the gravitational wave signals in the frequency range of 0.1 mHz -- 1 Hz. At a geocentric distance of $10^5$ km, the plasma in the earth magnetosphere will contribute as the main source of environmental noises. Here, we analyze the acceleration noises that are caused by the magnetic field of space plasma for the test mass of TianQin. The real solar wind data observed by the Advanced Composition Explorer are taken as the input of the magnetohydrodynamic simulation. The Space Weather Modeling Framework is used to simulate the global magnetosphere of the earth, from which we obtain the plasma and magnetic field parameters on the detector's orbits. We calculate the time series of the residual accelerations and the corresponding amplitude spectral densities on these orbit configurations. We find that the residual acceleration produced by the interaction between the TM's magnetic moment induced by the space magnetic field and the spacecraft magnetic field ($\bm{a}_{\rm M1}$) is the dominant term, which can approach $10^{-15}$ m/s$^2$/Hz$^{1/2}$ at $f \approx$ 0.2 mHz for the nominal values of the magnetic susceptibility ($χ_{\rm m} = 10^{-5}$) and the magnetic shielding factor ($ξ_{\rm m} = 10$) of the test mass. The ratios between the amplitude spectral density of the acceleration noise caused by the space magnetic field and the preliminary goal of the inertial sensor are 0.38 and 0.08 at 1 mHz and 10 mHz, respectively. We discuss the further reduction of this acceleration noise by decreasing $χ_{\rm m}$ and/or increasing $ξ_{\rm m}$ in the future instrumentation development for TianQin.

astro-ph.IM↗

arXiv2020

A Robust Consistent Information Criterion for Model Selection based on Empirical Likelihood

Conventional likelihood-based information criteria for model selection rely on the distribution assumption of data. However, for complex data that are increasingly available in many scientific fields, the specification of their underlying distribution turns out to be challenging, and the existing criteria may be limited and are not general enough to handle a variety of model selection problems. Here, we propose a robust and consistent model selection criterion based upon the empirical likelihood function which is data-driven. In particular, this framework adopts plug-in estimators that can be achieved by solving external estimating equations, not limited to the empirical likelihood, which avoids potential computational convergence issues and allows versatile applications, such as generalized linear models, generalized estimating equations, penalized regressions and so on. The formulation of our proposed criterion is initially derived from the asymptotic expansion of the marginal likelihood under variable selection framework, but more importantly, the consistent model selection property is established under a general context. Extensive simulation studies confirm the out-performance of the proposal compared to traditional model selection criteria. Finally, an application to the Atherosclerosis Risk in Communities Study illustrates the practical value of this proposed framework.

stat.ME↗

arXiv2020

Characterizations of stabilizable sets for some parabolic equations in $\mathbb{R}^n$

We consider the parabolic type equation in $\mathbb{R}^n$: \begin{align}\label{equ-0} (\partial_t+H)y(t,x)=0,\,\,\, (t,x)\in (0,\infty)\times\mathbb{R}^n;\;\; \quad y(0,x)\in L^2(\mathbb{R}^n), \end{align} where $H$ can be one of the following operators: (i) a shifted fractional Laplacian; (ii) a shifted Hermite operator; (iii) the Schrödinger operator with some general potentials. We call a subset $E\subset \mathbb{R}^n$ as a stabilizable set for the above equation, if there is a linear bounded operator $K$ on $L^2(\mathbb{R}^n)$ so that the semigroup $\{e^{-t(H-χ_EK)}\}_{t\geq 0}$ is exponentially stable. (Here, $χ_E$ denotes the characteristic function of $E$, which is treated as a linear operator on $L^2(\mathbb{R}^n)$.) This paper presents different geometric characterizations of the stabilizable sets for the above equation with different $H$. In particular, when $H$ is a shifted fractional Laplacian, $E\subset \mathbb{R}^n$ is a stabilizable set if and only if $E\subset \mathbb{R}^n$ is a thick set, while when $H$ is a shifted Hermite operator, $E\subset \mathbb{R}^n$ is a stabilizable set for if and only if $E\subset \mathbb{R}^n$ is a set of positive measure. Our results, together with the results on the observable sets for the above equation obtained in \cite{AB,Ko,Li,M09}, reveal such phenomena: for some $H$, the class of stabilizable sets contains strictly the class of observable sets, while for some other $H$, the classes of stabilizable sets and observable sets coincide. Besides, this paper gives some sufficient conditions on the stabilizable sets for the above equation where $H$ is the Schrödinger operator with some general potentials.

math.AP↗

arXiv2020

Observable sets, potentials and Schrödinger equations

We characterize observable sets for 1-dim Schrödinger equations in $\mathbb{R}$: $i \partial_t u = (-\partial_x^2+x^{2m})u$ (with $m\in \mathbb{N}:=\{0,1,\dots\}$). More precisely, we obtain what follows: First, when $m=0$, $E\subset\mathbb{R}$ is an observable set at some time if and only if it is thick, namely, there is $γ>0$ and $L>0$ so that $$ \left|E \bigcap [x, x+ L]\right|\geq γL\;\;\mbox{for each}\;\;x\in \mathbb{R}; $$ Second, when $m=1$ ($m\geq 2$ resp.), $E$ is an observable set at some time (at any time resp. ) if and only if it is weakly thick, namely $$ \varliminf_{x \rightarrow +\infty} \frac{|E\bigcap [-x, x]|}{x} >0. $$ From these, we see how potentials $x^{2m}$ affect the observability (including the geometric structures of observable sets and the minimal observable time). Besides, we obtain several supplemental theorems for the above results, in particular, we find that a half line is an observable set at time $T>0$ for the above equation with $m=1$ if and only if $T>\fracπ{2}$.

math.OC↗

arXiv2019

Empirical-likelihood-based criteria for model selection on marginal analysis of longitudinal data with dropout missingness

Longitudinal data are common in clinical trials and observational studies, where missing outcomes due to dropouts are always encountered. Under such context with the assumption of missing at random, the weighted generalized estimating equations (WGEE) approach is widely adopted for marginal analysis. Model selection on marginal mean regression is a crucial aspect of data analysis, and identifying an appropriate correlation structure for model fitting may also be of interest and importance. However, the existing information criteria for model selection in WGEE have limitations, such as separate criteria for the selection of marginal mean and correlation structures, unsatisfactory selection performance in small-sample set-ups and so on. In particular, there are few studies to develop joint information criteria for selection of both marginal mean and correlation structures. In this work, by embedding empirical likelihood into the WGEE framework, we propose two innovative information criteria named a joint empirical Akaike information criterion (JEAIC) and a joint empirical Bayesian information criterion (JEBIC), which can simultaneously select the variables for marginal mean regression and also correlation structure. Through extensive simulation studies, these empirical-likelihood-based criteria exhibit robustness, flexibility, and outperformance compared to the other criteria including the weighted quasi-likelihood under the independence model criterion, the missing longitudinal information criterion and the joint longitudinal information criterion. In addition, we provide a theoretical justification of our proposed criteria, and present two real data examples in practice for further illustration.

stat.ME↗

arXiv2018

Observability on lattice points for heat equations and applications

Observability inequalities on lattice points are established for non-negative solutions of the heat equation with potentials in the whole space. As applications, some controllability results of heat equations are derived by the above-mentioned observability inequalities.

math.OC↗

arXiv2018

Asymptotic observability identity for the heat equation in R^d

We build up an asymptotic observability identity for the heat equation in the whole space. It says that one can approximately recover a solution, through observing it over some countable lattice points in the space and at one time. This asymptotic identity is a natural extension of the well-known Shannon-Whittaker sampling theorem \cite{Shannon,Whittaker}. According to it, we obtain a kind of feedback null approximate controllability for impulsively controlled heat equations. We also obtain a weak asymptotic observability identity with finitely many observation lattice points. This identity holds only for some solutions to the heat equation.

math.AP↗

arXiv2018

$L^p$ estimates for fractional schrodinger operators with kato class potentials

Let $α>0$, $H=(-\triangle)^α+V(x)$, $V(x)$ belongs to the higher order Kato class $K_{2α}(\mathbbm{R}^n)$. For $1\leq p\leq \infty$, we prove a polynomial upper bound of $\|e^{-itH}(H+M)^{-β}\|_{L^p, L^p}$ in terms of time $t$. Both the smoothing exponent $β$ and the growth order in $t$ are almost optimal compared to the free case. The main ingredients in our proof are pointwise heat kernel estimates for the semigroup $e^{-tH}$. We obtain a Gaussian upper bound with sharp coefficient for integral $α$ and a polynomial decay for fractal $α$.

math.AP↗

arXiv2018

New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{-1/4}$ as time $t$ goes to infinity. This improves the works [Selberg, da Silva, Lower bounds on the radius of spatial analyticity for the KdV equation, Annales Henri Poincaré, 2017, 18(3): 1009-1023] and [Tesfahun, Asymptotic lower bound for the radius of spatial analtyicity to solutions of KdV equation, arXiv preprint arXiv:1707.07810, 2017]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the $I-$method.

math.AP↗

arXiv2017

Observable set, observability, interpolation inequality and spectral inequality for the heat equation in $\mathbb{R}^n$

This paper studies connections among observable sets, the observability inequality, the Hölder-type interpolation inequality and the spectral inequality for the heat equation in $\mathbb R^n$. We present a characteristic of observable sets for the heat equation. In more detail, we show that a measurable set in $\mathbb{R}^n$ satisfies the observability inequality if and only if it is $γ$-thick at scale $L$ for some $γ>0$ and $L>0$.We also build up the equivalence among the above-mentioned three inequalities. More precisely, we obtain that if a measurable set $E\subset\mathbb{R}^n$ satisfies one of these inequalities, then it satisfies others. Finally, we get some weak observability inequalities and weak interpolation inequalities where observations are made over a ball.

math.OC↗

arXiv2016

Observability and unique continuation inequalities for the Schrödinger equation

In this paper, we present several observability and unique continuation inequalities for the free Schrödinger equation in the whole space. The observations in these inequalities are made either at two points in time or one point in time. These inequalities correspond to different kinds of controllability for the free Schrödinger equation. We also find that the observability inequality at two points in time is equivalent to the uncertainty principle built up in [18].

math.OC↗

arXiv2015

Quantitative uniqueness of some higher order elliptic equations

We study the quantitative unique continuation property of some higher order elliptic operators. In the case of $P=(-Δ)^m$, where $m$ is a positive integer, we derive lower bounds of decay at infinity for any nontrivial solutions under some general assumptions. Furthermore, in dimension 2, we can obtain essentially sharp lower bounds for some forth order elliptic operators, the sharpness is shown by constructing a Meshkov type example.

math.AP↗