arXiv subjects

Teng Huang

Publications and source records attributed to Teng Huang.

At least 37 records · Page 2Linked to original sources

arXiv2022

Auto-Focus Contrastive Learning for Image Manipulation Detection

Generally, current image manipulation detection models are simply built on manipulation traces. However, we argue that those models achieve sub-optimal detection performance as it tends to: 1) distinguish the manipulation traces from a lot of noisy information within the entire image, and 2) ignore the trace relations among the pixels of each manipulated region and its surroundings. To overcome these limitations, we propose an Auto-Focus Contrastive Learning (AF-CL) network for image manipulation detection. It contains two main ideas, i.e., multi-scale view generation (MSVG) and trace relation modeling (TRM). Specifically, MSVG aims to generate a pair of views, each of which contains the manipulated region and its surroundings at a different scale, while TRM plays a role in modeling the trace relations among the pixels of each manipulated region and its surroundings for learning the discriminative representation. After learning the AF-CL network by minimizing the distance between the representations of corresponding views, the learned network is able to automatically focus on the manipulated region and its surroundings and sufficiently explore their trace relations for accurate manipulation detection. Extensive experiments demonstrate that, compared to the state-of-the-arts, AF-CL provides significant performance improvements, i.e., up to 2.5%, 7.5%, and 0.8% F1 score, on CAISA, NIST, and Coverage datasets, respectively.

cs.CV↗

arXiv2022

On harmonic symmetries for locally conformally Kähler manifolds

In this article, we study harmonic symmetries on the compact locally conformally Kähler manifold $M$ of $dim_{\mathbb{C}}=n$. The space of harmonic symmetries is a subspace of harmonic differential forms which defined by the kernel of a certain Laplacian-type operator $\square$. We observe that the spaces $\ker(\square)\capΩ^{l}=\{0\}$ for any $|l-n|\geq2$ and $\kerΔ_{\bar{\partial}}\cap P^{k,n-1-k}\cap\ker(i_{θ^{\sharp}})\cong\ker(\square^{k,n-1-k})$, $\kerΔ_{\bar{\partial}}\cap P^{k,n-k}\cong\ker(\square^{k,n-k})$. Furthermore, suppose that $M$ is a Vaisman manifold, we prove that (i) $α$ is $(n-1)$-form in $\ker(\square)$ if only if $α$ is a transversally harmonic and transversally effective $\mathcal{V}$-foliate form; (ii) $α$ is a $(p,n-p)$-form in $\ker(\square^{p,n-p})$ if only if there are two forms $β_{1}\in\mathcal{S}^{p-1,n-p}$ and $β_{2}\in\mathcal{S}^{p,n-p-1}$ such that $α=θ^{1,0}\wedgeβ_{1}+θ^{0,1}\wedgeβ_{2}$.

math.DG↗

arXiv2021

Towards fully ab initio simulation of atmospheric aerosol nucleation

Atmospheric aerosol nucleation contributes to more than half of cloud condensation nuclei globally. The emissions, properties and concentrations of atmospheric aerosols or aerosol precursors could respond significantly to climate change. Despite the importance for climate, the detailed nucleation mechanisms are still poorly understood. The ultimate goal of theoretical understanding aerosol nucleation is to simulate nucleation in ambient condition, hindered by lack of accurate reactive force field. Here we propose the reactive force field for nucleation systems with good size scalability based on deep neural network. The huge computational costs from direct molecular dynamics in ambient conditions are surmounted by bridging the simulation in the limited box with cluster kinetics, facilitating the aerosol nucleation simulation to be fully ab initio. We found that the acid-base formation rates previously based on hard sphere collision rate constants tend to be underestimated up to several times. These findings show that the widely recognized acid-base nucleation observed in the CLOUD (Cosmics Leaving OUtdoor Droplets) chamber experiments, pristine and polluted environments should be revisited to considering the contribution of collision enhancement. Besides, the framework here is transferable to other nucleation systems, potentially boosting the nucleation parameterizations accuracy generally to effectively advance the climate model predictions reliability.

physics.atm-clus↗

arXiv2021

A compactness theorem for stable flat $SL(2,\mathbb{C})$ connections on $3$-folds

Let $Y$ be a closed $3$-manifold such that all flat $SU(2)$-connections on $Y$ are $non$-$degenerate$. In this article, we prove a Uhlenbeck-type compactness theorem on $Y$ for stable flat $SL(2,\mathbb{C})$ connections satisfying an $L^{2}$-bound for the real curvature. Combining the compactness theorem and a previous result in \cite{Huang}, we prove that the moduli space of the stable flat $SL(2,\mathbb{C})$ connections is disconnected under certain technical assumptions.

math.DG↗

arXiv2021

Hodge theory of holomorphic vector bundle on compact Kähler hyperbolic manifold

Let $E$ be a holomorphic vector bundle over a compact Kähler manifold $(X,ω)$ with negative sectional curvature $sec\leq -K<0$, $Δ_{E}$ be the Chern connection on $E$. In this article we show that if $C:=|[Λ,iΘ(E)]|\leq c_{n}K$, then $(X,E)$ satisfy a family of Chern number inequalities. The main idea in our proof is study the $L^{2}$ $\bar{\partial}_{\tilde{E}}$-harmonic forms on lifting bundle $\tilde{E}$ over the universal covering space $\tilde{X}$. We also observe that there is a closely relationship between the eigenvalue of the Laplace-Beltrami operator $Δ_{\bar{\partial}_{\tilde{E}}}$ and the Euler characteristic of $X$. Precisely, if there is a line bundle $L$ on $X$ such that $χ^{p}(X,L^{\otimes m})$ is not constant for some integers $p\in[0,n]$, then the Euler characteristic of $X$ satisfies $(-1)^{n}χ(X)\geq (n+1)+\lfloor\frac{c_{n}K}{2nC} \rfloor$.

math.DG↗

arXiv2021

On second non-HLC degree of closed symplectic manifold

In this note, we show that for a closed almost-Kähler manifold $(X,J)$ with the almost complex structure $J$ satisfies $\dim\ker P_{J}=b_{2}-1$ the space of de Rham harmonic forms is contained in the space of symplectic-Bott-Chern harmonic forms. In particular, suppose that $X$ is four-dimension, if the self-dual Betti number $b^{+}_{2}=1$, then we prove that the second non-HLC degree measures the gap between the de Rham and the symplectic-Bott-Chern harmonic forms.

math.DG↗

arXiv2021

On $L^{2}$-harmonic forms of complete almost Kähler manifold

In this article, we study the $L^{2}$-harmonic forms on the complete $2n$-dimensional almost Käher manifold $X$. We observe that the $L^{2}$-harmonic forms can decomposition into Lefschetz powers of primitive forms. Therefore we can extend vanishing theorems of $d$(bounded) (resp. $d$(sublinear)) Kähler manifold proved by Gromov (resp. Cao-Xavier, Jost-Zuo) to almost Kählerian case, that is, the spaces of all harmonic $(p,q)$-forms on $X$ vanishing unless $p+q=n$. We also give a lower bound on the spectra of the Laplace operator to sharpen the Lefschetz vanishing theorem on $d$(bounded) case.

math.DG↗

arXiv2021

Template-based Minor Embedding for Adiabatic Quantum Optimization

Quantum Annealing (QA) can be used to quickly obtain near-optimal solutions for Quadratic Unconstrained Binary Optimization (QUBO) problems. In QA hardware, each decision variable of a QUBO should be mapped to one or more adjacent qubits in such a way that pairs of variables defining a quadratic term in the objective function are mapped to some pair of adjacent qubits. However, qubits have limited connectivity in existing QA hardware. This has spurred work on preprocessing algorithms for embedding the graph representing problem variables with quadratic terms into the hardware graph representing qubits adjacencies, such as the Chimera graph in hardware produced by D-Wave Systems. In this paper, we use integer linear programming to search for an embedding of the problem graph into certain classes of minors of the Chimera graph, which we call template embeddings. One of these classes corresponds to complete bipartite graphs, for which we show the limitation of the existing approach based on minimum Odd Cycle Transversals (OCTs). One of the formulations presented is exact, and thus can be used to certify the absence of a minor embedding using that template. On an extensive test set consisting of random graphs from five different classes of varying size and sparsity, we can embed more graphs than a state-of-the-art OCT-based approach, our approach scales better with the hardware size, and the runtime is generally orders of magnitude smaller.

cs.DS↗

arXiv2020

Global perturbation potential function on complete special holonomy manifolds

In this article, we introduce and study the notion of a complete special holonomy manifold $(X,ω)$ which is given by a global perturbation potential function, i.e., there is a function $f$ on $X$ such that $ω'=ω-\mathcal{L}_{\nabla f}ω$ is sufficiently small in $L^{\infty}$-norm. We establish some vanishing theorems on the $L^{2}$ harmonic forms under some conditions on the global perturbation potential function.

math.DG↗

arXiv2020

$L^{2}$-hard Lefschetz complete symplectic manifolds

For a complete symplectic manifold $M^{2n}$, we define the $L^{2}$-hard Lefschetz property on $M^{2n}$. We also prove that the complete symplectic manifold $M^{2n}$ satisfies $L^{2}$-hard Lefschetz property if and only if every class of $L^{2}$-harmonic forms contains a $L^{2}$ symplectic harmonic form. As an application, we get if $M^{2n}$ is a closed symplectic parabolic manifold which satisfies the hard Lefschetz property, then its Euler characteristic satisfies the inequality $(-1)^{n}χ(M^{2n})\geq0$.

math.DG↗

arXiv2020

Vanishing theorems on complete Riemannian manifold with a parallel $1$-form

In this article, we first consider the $L^{2}$ \textit{Morse-Novikov cohomology} on a complete Riemannian manifold $M$ equipped with a parallel $1$-form which includes Vaisman manifold. Based on a vanishing theorem of $L^{2}$ \textit{Morse-Novikov cohomology}, we prove that the $L^{2}$-harmonic forms on $M$ are identically zero.

math.DG↗

arXiv2020

A note on Euler number of locally conformally Kähler manifolds

Let $M^{2n}$ be a compact Riemannian manifold of non-positive (resp. negative) sectional curvature. We call $(M,J,θ)$ a $d$(bounded) locally conformally Kähler manifold if the lifted Lee form $\tildeθ$ on the universal covering space of $M$ is $d$(bounded). We shown that if $M^{2n}$ is homeomorphic to a $d$(bounded) LCK manifold, then its Euler number satisfies the inequality $(-1)^{n}χ(M^{2n})\geq$ (resp. $>$) $0$.

math.DG↗

arXiv2020

On Yang-Mills connections on compact Kähler surfaces

We extend an $L^{2}$-energy gap of Yang-Mills connections on principal $G$-bundles $P$ over a compact Riemannian manfold with a $good$ Riemannian metric to the case of a compact Kähler surface with a $generic$ Kähler metric $g$, which guarantees that all ASD connections on the principal bundle $P$ over $X$ are irreducible.

math.DG↗

arXiv2019

JANOS: An Integrated Predictive and Prescriptive Modeling Framework

Business research practice is witnessing a surge in the integration of predictive modeling and prescriptive analysis. We describe a modeling framework JANOS that seamlessly integrates the two streams of analytics, for the first time allowing researchers and practitioners to embed machine learning models in an optimization framework. JANOS allows for specifying a prescriptive model using standard optimization modeling elements such as constraints and variables. The key novelty lies in providing modeling constructs that allow for the specification of commonly used predictive models and their features as constraints and variables in the optimization model. The framework considers two sets of decision variables; regular and predicted. The relationship between the regular and the predicted variables are specified by the user as pre-trained predictive models. JANOS currently supports linear regression, logistic regression, and neural network with rectified linear activation functions, but we plan to expand on this set in the future. In this paper, we demonstrate the flexibility of the framework through an example on scholarship allocation in a student enrollment problem and provide a numeric performance evaluation.

cs.LG↗

arXiv2019

Some boundedness properties of solutions to the complex Yang-Mills equations on closed $4$-manifolds

In this article, we study the analytical properties of the solutions of the complex Yang-Mills equations on a closed Riemannian four-manifold $X$ with a Riemannian metric $g$. The main result is that if $g$ is $good$ and the connection is an approximate ASD connection, then the extra field has a positive lower {bound}. As an application, we obtain some gap results for Yang-Mills connections and Kapustin-Witten equations.

math.DG↗

arXiv2019

$L^{2}$ vanishing theorem on some Kähler manifolds

Let $E$ be a Hermitian vector bundle over a complete Kähler manifold $(X,ω)$, $\dim_{\mathbb{C}}X=n$, with a $d$(bounded) Kähler form $ω$, $d_{A}$ be a Hermitian connection on $E$. The goal of this article is to study the $L^{2}$-Hodge theory on the vector bundle $E$. We extend the results of Gromov's \cite{Gro} to the Hermitian vector bundle. At last, as an application, we prove a gap result for Yang-Mills connection on the bundle $E$ over $X$.

math.DG↗

arXiv2019

On a topology property for the moduli space of Kapustin-Witten equations

In this article, we study the Kapustin-Witten equations on a closed, simply-connected, four-dimensional manifold which were introduced by Kapustin and Witten. We use the Taubes' compactness theorem in arXiv:1307.6447v4 to prove that if $(A,ϕ)$ is a smooth solution of Kapustin-Witten equations and the connection $A$ is closed to a $generic$ ASD connection $A_{\infty}$, then $(A,ϕ)$ must be a trivial solution. We also prove that the moduli space of the solutions of Kapustin-Witten equations is non-connected if the connections on the compactification of moduli space of ASD connections are all $generic$. At last, we extend the results for the Kapustin-Witten equations to other equations on gauge theory such as the Hitchin-Simpson equations and Vafa-Witten on a compact Kähler surface.

math-ph↗

arXiv2019

Asymptotic behaviour of instantons on Cylinder Manifolds

IIn this article, we study the instanton equation on the cylinder over a closed manifold $X$ which admits non-zero smooth $3$-form $P$ and $4$-form $Q$. Our results are (1) if $X$ is a \textbf{good} manifold, i.e., $P,Q$ satisfying $d\ast_{X}P=d\ast_{X}Q=0$, then the instanton with integrable curvature decays exponentially at the ends, and, (2) if $X$ is a real Killing spinor manifold, i.e., $P,Q$ satisfying $dP=4Q$ and $d\ast_{X}Q=(n-3)\ast_{X}P$, we prove that the solution of instanton equation is trivial under some mild conditions.

math.DG↗