arXiv subjects

Haotian Wu

Publications and source records attributed to Haotian Wu.

At least 73 records · Page 4Linked to original sources

arXiv2022

Vision Transformer for Adaptive Image Transmission over MIMO Channels

This paper presents a vision transformer (ViT) based joint source and channel coding (JSCC) scheme for wireless image transmission over multiple-input multiple-output (MIMO) systems, called ViT-MIMO. The proposed ViT-MIMO architecture, in addition to outperforming separation-based benchmarks, can flexibly adapt to different channel conditions without requiring retraining. Specifically, exploiting the self-attention mechanism of the ViT enables the proposed ViT-MIMO model to adaptively learn the feature mapping and power allocation based on the source image and channel conditions. Numerical experiments show that ViT-MIMO can significantly improve the transmission quality cross a large variety of scenarios, including varying channel conditions, making it an attractive solution for emerging semantic communication systems.

cs.IT↗

arXiv2022

The modified Kähler-Ricci flow, II

We improve the understanding of both finite time and infinite time singularities of the modified Kähler-Ricci flow as initiated by the second author of this paper in [26]. This is done by relating the modified Kähler-Ricci flow with the recent studies on the classic Kähler-Ricci flow and the degenerate complex Monge-Ampère equation.

math.DG↗

arXiv2022

GGViT:Multistream Vision Transformer Network in Face2Face Facial Reenactment Detection

Detecting manipulated facial images and videos on social networks has been an urgent problem to be solved. The compression of videos on social media has destroyed some pixel details that could be used to detect forgeries. Hence, it is crucial to detect manipulated faces in videos of different quality. We propose a new multi-stream network architecture named GGViT, which utilizes global information to improve the generalization of the model. The embedding of the whole face extracted by ViT will guide each stream network. Through a large number of experiments, we have proved that our proposed model achieves state-of-the-art classification accuracy on FF++ dataset, and has been greatly improved on scenarios of different compression rates. The accuracy of Raw/C23, Raw/C40 and C23/C40 was increased by 24.34%, 15.08% and 10.14% respectively.

cs.CV↗

arXiv2022

Channel-Adaptive Wireless Image Transmission with OFDM

We present a learning-based channel-adaptive joint source and channel coding (CA-JSCC) scheme for wireless image transmission over multipath fading channels. The proposed method is an end-to-end autoencoder architecture with a dual-attention mechanism employing orthogonal frequency division multiplexing (OFDM) transmission. Unlike the previous works, our approach is adaptive to channel-gain and noise-power variations by exploiting the estimated channel state information (CSI). Specifically, with the proposed dual-attention mechanism, our model can learn to map the features and allocate transmission-power resources judiciously based on the estimated CSI. Extensive numerical experiments verify that CA-JSCC achieves state-of-the-art performance among existing JSCC schemes. In addition, CA-JSCC is robust to varying channel conditions and can better exploit the limited channel resources by transmitting critical features over better subchannels.

cs.IT↗

arXiv2022

The second Robin eigenvalue in non-compact rank-1 symmetric spaces

In this paper, we prove a quantitative spectral inequality for the second Robin eigenvalue in non-compact rank-1 symmetric spaces. In particular, this shows that for bounded domains in non-compact rank-1 symmetric spaces, the geodesic ball maximises the second Robin eigenvalue among domains of the same volume, with negative Robin parameter in the regime connecting the first nontrivial Neumann and Steklov eigenvalues. This result generalises the work of Freitas and Laugesen in the Euclidean setting [FL21] as well as our previous work in the hyperbolic space [LWW20].

math.DG↗

arXiv2022

A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup: II

In previous work [GIKW21], we have presented evidence from numerical simulations that the Type-II singularities of mean curvature flow (MCF) of rotationally-symmetric, complete, noncompact embedded hypersurfaces constructed in [IW19, IWZ21] are stable. More precisely, it is shown in that paper that for small rotationally-symmetric perturbations of initial embeddings near the "tip", numerical simulations of MCF of such initial embeddings develop the same Type-II singularities with the same "bowl soliton" blowup behaviors in a neighborhood of the singularity. It is also shown in that work that for small rotationally-symmetric perturbations of the initial embeddings that are sufficiently far away from the tip, MCF develops Type-I "neckpinch" singularities. In this work, we again use numerical simulations to show that MCF subject to initial perturbations that are not rotationally symmetric behaves asymptotically like it does for rotationally-symmetric perturbations. In particular, if we impose sinusoidal angular dependence on the initial embeddings, we find that for perturbations near the tip, evolutions by MCF asymptotically lose their angular dependence -- becoming round -- and develop Type-II bowl soliton singularities. As well, if we impose sinusoidal angular dependence on the initial embeddings for perturbations sufficiently far from the tip, the angular dependence again disappears as Type-I neckpinch singularities develop. The numerical analysis carried out in this work is an adaptation of the "overlap" method introduced in [GIKW21] and permits angular dependence.

math.DG↗

arXiv2022

A High-Performance Customer Churn Prediction System based on Self-Attention

Customer churn prediction is a challenging domain of research that contributes to customer retention strategy. The predictive performance of existing machine learning models, which are often adopted by churn communities, appear to be at a bottleneck, partly due to models' poor feature extraction capability. Therefore, a novel algorithm, a hybrid neural network with self-attention enhancement (HNNSAE), is proposed in this paper to improve the efficiency of feature screening and feature extraction, consequently improving the model's predictive performance. This model consists of three main blocks. The first block is the entity embedding layer, which is employed to process the categorical variables transformed into 0-1 code. The second block is the feature extractor, which extracts the significant features through the multi-head self-attention mechanism. In addition, to improve the feature extraction effect, we stack the residual connection neural network on multi-head self-attention modules. The third block is a classifier, which is a three-layer multilayer perceptron. This work conducts experiments on publicly available dataset related to commercial bank customers. The result demonstrates that HNNSAE significantly outperforms the other Individual Machine Learning (IML), Ensemble Machine Learning (EML), and Deep Learning (DL) methods tested in this paper. Furthermore, we compare the performance of the feature extractor proposed in this paper with that of other three feature extractors and find that the method proposed in this paper significantly outperforms other methods. In addition, four hypotheses about model prediction performance and overfitting risk are tested on the publicly available dataset.

cs.LG↗

arXiv2022

Cyclic Arbitrage in Decentralized Exchanges

Decentralized Exchanges (DEXes) enable users to create markets for exchanging any pair of cryptocurrencies. The direct exchange rate of two tokens may not match the cross-exchange rate in the market, and such price discrepancies open up arbitrage possibilities with trading through different cryptocurrencies cyclically. In this paper, we conduct a systematic investigation on cyclic arbitrages in DEXes. We propose a theoretical framework for studying cyclic arbitrage. With our framework, we analyze the profitability conditions and optimal trading strategies of cyclic transactions. We further examine exploitable arbitrage opportunities and the market size of cyclic arbitrages with transaction-level data of Uniswap V2. We find that traders have executed 292,606 cyclic arbitrages over eleven months and exploited more than 138 million USD in revenue. However, the revenue of the most profitable unexploited opportunity is persistently higher than 1 ETH (4,000 USD), which indicates that DEX markets may not be efficient enough. By analyzing how traders implement cyclic arbitrages, we find that traders can utilize smart contracts to issue atomic transactions and the atomic implementations could mitigate users' financial loss in cyclic arbitrage from the price impact.

q-fin.TR↗

arXiv2021

A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup

We present a numerical study of the local stability of mean curvature flow of rotationally symmetric, complete noncompact hypersurfaces with Type-II curvature blowup. Our numerical analysis employs a novel overlap method that constructs "numerically global" (i.e., with spatial domain arbitrarily large but finite) flow solutions with initial data covering analytically distinct regions. Our numerical results show that for certain prescribed families of perturbations, there are two classes of initial data that lead to distinct behaviors under mean curvature flow. Firstly, there is a "near" class of initial data which lead to the same singular behaviour as an unperturbed solution; in particular, the curvature at the tip of the hypersurface blows up at a Type-II rate no slower than $(T-t)^{-1}$. Secondly, there is a "far" class of initial data which lead to solutions developing a local Type-I nondegenerate neckpinch under mean curvature flow. These numerical findings further suggest the existence of a "critical" class of initial data which conjecturally lead to mean curvature flow of noncompact hypersurfaces forming local Type-II degenerate neckpinches with the highest curvature blowup rate strictly slower than $(T-t)^{-1}$.

math.DG↗

arXiv2020

Minimum Potential Energy of Point Cloud for Robust Global Registration

In this paper, we propose a novel minimum gravitational potential energy (MPE)-based algorithm for global point set registration. The feature descriptors extraction algorithms have emerged as the standard approach to align point sets in the past few decades. However, the alignment can be challenging to take effect when the point set suffers from raw point data problems such as noises (Gaussian and Uniformly). Different from the most existing point set registration methods which usually extract the descriptors to find correspondences between point sets, our proposed MPE alignment method is able to handle large scale raw data offset without depending on traditional descriptors extraction, whether for the local or global registration methods. We decompose the solution into a global optimal convex approximation and the fast descent process to a local minimum. For the approximation step, the proposed minimum potential energy (MPE) approach consists of two main steps. Firstly, according to the construction of the force traction operator, we could simply compute the position of the potential energy minimum; Secondly, with respect to the finding of the MPE point, we propose a new theory that employs the two flags to observe the status of the registration procedure. The method of fast descent process to the minimum that we employed is the iterative closest point algorithm; it can achieve the global minimum. We demonstrate the performance of the proposed algorithm on synthetic data as well as on real data. The proposed method outperforms the other global methods in terms of both efficiency, accuracy and noise resistance.

cs.CV↗

arXiv2020

On the second Robin eigenvalue of the Laplacian

We study the Robin eigenvalue problem for the Laplace-Beltrami operator on Riemannian manifolds. Our first result is a comparison theorem for the second Robin eigenvalue on geodesic balls in manifolds whose sectional curvatures are bounded from above. Our second result asserts that geodesic balls in nonpositively curved space forms maximize the second Robin eigenvalue among bounded domains of the same volume.

math.DG↗

arXiv2020

An upper bound for the first nonzero Steklov eigenvalue

Let $(M^n,g)$ be a complete simply connected $n$-dimensional Riemannian manifold with curvature bounds $\operatorname{Sect}_g\leq κ$ for $κ\leq 0$ and $\operatorname{Ric}_g\geq(n-1)Kg$ for $K\leq 0$. We prove that for any bounded domain $Ω\subset M^n$ with diameter $d$ and Lipschitz boundary, if $Ω^*$ is a geodesic ball in the simply connected space form with constant sectional curvature $κ$ enclosing the same volume as $Ω$, then $σ_1(Ω) \leq C σ_1(Ω^*)$, where $σ_1(Ω)$ and $ σ_1(Ω^*)$ denote the first nonzero Steklov eigenvalues of $Ω$ and $Ω^*$ respectively, and $C=C(n,κ, K, d)$ is an explicit constant. When $κ=K$, we have $C=1$ and recover the Brock-Weinstock inequality, asserting that geodesic balls uniquely maximize the first nonzero Steklov eigenvalue among domains of the same volume, in Euclidean space and the hyperbolic space.

math.DG↗

arXiv2020

On the precise asymptotics of Type-IIb solutions to mean curvature flow

In this paper, we study the precise asymptotics of noncompact Type-IIb solutions to the mean curvature flow. Precisely, for each real number $γ>0$, we construct mean curvature flow solutions, in the rotationally symmetric class, with the following precise asymptotics as $t\nearrow\infty$: (1) The highest curvature concentrates at the tip of the hypersurface (an umbilical point) and blows up at the Type-IIb rate $(2t+1)^{(γ-1)/2}$. (2) In a neighbourhood of the tip, the Type-IIb blow-up of the solution converges to a translating soliton known as the bowl soliton. (3) Near spatial infinity, the hypersurface has a precise growth rate depending on $γ$.

math.DG↗

arXiv2019

Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up. II

We continue the study, initiated by the first two authors in \cite{IW19}, of Type-II curvature blow-up in mean curvature flow of complete noncompact embedded hypersurfaces. In particular, we construct mean curvature flow solutions, in the rotationally symmetric class, with the following precise asymptotics near the "vanishing" time $T$: (1) The highest curvature concentrates at the tip of the hypersurface (an umbilical point) and blows up at the rate $(T-t)^{-1}$. (2) In a neighbourhood of the tip, the solution converges to a translating soliton known as the bowl soliton. (3) Near spatial infinity, the hypersurface approaches a collapsing cylinder at an exponential rate.

math.DG↗

arXiv2017

Robust FCC solute diffusion predictions from ab-initio machine learning methods

We evaluate the performance of four machine learning methods for modeling and predicting FCC solute diffusion barriers. More than 200 FCC solute diffusion barriers from previous density functional theory (DFT) calculations served as our dataset to train four machine learning methods: linear regression (LR), decision tree (DT), Gaussian kernel ridge regression (GKRR), and artificial neural network (ANN). We separately optimize key physical descriptors favored by each method to model diffusion barriers. We also assess the ability of each method to extrapolate when faced with new hosts with limited known data. GKRR and ANN were found to perform the best, showing 0.15 eV cross-validation errors and predicting impurity diffusion in new hosts to within 0.2 eV when given only 5 data points from the host. We demonstrate the success of a combined DFT + data mining approach towards solving materials science challenges and predict the diffusion barrier of all available impurities across all FCC hosts.

cond-mat.mtrl-sci↗

arXiv2017

Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up

We study the phenomenon of Type-II curvature blow-up in mean curvature flows of rotationally symmetric noncompact embedded hypersurfaces. Using analytic techniques based on formal matched asymptotics and the construction of upper and lower barrier solutions enveloping formal solutions with prescribed behavior, we show that for each initial hypersurface considered, a mean curvature flow solution exhibits the following behavior near the "vanishing" time $T$: (1) The highest curvature concentrates at the tip of the hypersurface (an umbilic point), and for each choice of the parameter $γ>1/2$, there is a solution with the highest curvature blowing up at the rate $(T-t)^{-(γ+1/2)}$. (2) In a neighborhood of the tip, the solution converges to a translating soliton which is a higher-dimensional analogue of the "Grim Reaper" solution for the curve-shortening flow. (3) Away from the tip, the flow surface approaches a collapsing cylinder at a characteristic rate dependent on the parameter $γ$.

math.DG↗

arXiv2015

Metrics with non-negative Ricci curvature on convex three-manifolds

We prove that the space of smooth Riemannian metrics on the three-ball with non-negative Ricci curvature and strictly convex boundary is path connected; and, moreover, that the associated moduli space (i.e., modulo orientation-preserving diffeomorphisms of the three-ball) is contractible. As an application, using results of Maximo, Nunes, and Smith [MNS13], we show the existence of properly embedded free boundary minimal annulus on any three-ball with non-negative Ricci curvature and strictly convex boundary.

math.DG↗

arXiv2015

On type-II singularities in Ricci flow on $\mathbb{R}^{N}$

In each dimension $N\geq 3$ and for each real number $λ\geq 1$, we construct a family of complete rotationally symmetric solutions to Ricci flow on $\mathbb{R}^{N}$ which encounter a global singularity at a finite time $T$. The singularity forms arbitrarily slowly with the curvature blowing up arbitrarily fast at the rate $(T-t)^{-(λ+1)}$. Near the origin, blow-ups of such a solution converge uniformly to the Bryant soliton. Near spatial infinity, blow-ups of such a solution converge uniformly to the shrinking cylinder soliton. As an application of this result, we prove that there exist standard solutions of Ricci flow on $\mathbb{R}^N$ whose blow-ups near the origin converge uniformly to the Bryant soliton.

math.DG↗