arXiv subjects

Fei Tao

Publications and source records attributed to Fei Tao.

At least 19 recordsLinked to original sources

arXiv2026

Graph Weldings Associated with Functions in Zygmund, $\mathrm{BMO}$, $\mathrm{VMO}$, and $H^{1/2}$

Let $f\colon \mathbb{R}\to\mathbb{R}$ be a continuous function. We define the graph welding associated with $f$ as the homeomorphism \[ \varphi = G^{-1}\circ F\colon \mathbb{R}\to\mathbb{R}. \] Here, $F(x)=x+if(x)$ parametrizes the graph of $f$, and $G$ is a conformal mapping from the upper half-plane $\mathbb{H}$ onto one of the two domains bounded by the graph of $f$, admitting a continuous extension to $\mathbb{R}$. In this paper, we investigate how the regularity of the graph function $f$ influences the analytic properties of the associated graph welding $\varphi$. In particular, under certain assumptions that $f$ within Zygmund, $\mathrm{BMO}$, $\mathrm{VMO}$, and Hardy spaces, we establish results on absolute continuity, quasisymmetry, symmetry, strong quasisymmetry, strong symmetry, and the Weil--Petersson property of the associated graph welding $\varphi$. These results clarify the interplay between the regularity of graph functions, the geometry of graph curves, and the boundary behavior of conformal mappings.

math.CV↗

arXiv2026

Boundary Characterizations of Little Bloch and $\mathrm{VMOA}$ Functions on the Half-Plane

We extend Pommerenke's characterizations of boundary curves of conformal mappings in terms of the little Bloch and $\mathrm{VMOA}$ conditions from the unit disk $\mathbb{D}$ to the upper half-plane $\mathbb{H}$. Let $G\colon \mathbb{H}\to\Omega$ be a conformal mapping onto an unbounded quasidisk $\Omega$ with $G(\infty)=\infty$, and let $g\colon \mathbb{R}\to\Gamma=\partial\Omega$ be its boundary extension. In the non-compact setting, the Euclidean smallness on the boundary curve is not necessarily comparable to the smallness of the parameter on $\mathbb{R}$. To overcome this difficulty, we use relative versions of the asymptotic conformality and the asymptotic smoothness with respect to the parametrization $g$. We prove that $\log G'\in B_0(\mathbb{H})$ is equivalent to the asymptotic conformality of $\Gamma$ relative to $g$, and also to the asymptotic symmetry of the embedding $g$. We further prove that $\log G'\in \mathrm{VMOA}(\mathbb{H})$ is equivalent to the asymptotic smoothness of $\Gamma$ relative to $g$, and also to the asymptotic smoothness of $g$. These results provide half-plane analogues of Pommerenke's theorems and clarify the role of the parametrization in the unbounded case.

math.CV↗

arXiv2026

2026 Roadmap on Artificial Intelligence and Machine Learning for Smart Manufacturing

The evolution of artificial intelligence (AI) and machine learning (ML) is reshaping smart manufacturing by providing new capabilities for efficiency, adaptability, and autonomy across industrial value chains. However, the deployment of AI and ML in industrial settings still faces critical challenges, including the complexity of industrial big data, effective data management, integration with heterogeneous sensing and control systems, and the demand for trustworthy, explainable, and reliable operation in high-stakes industrial environments. In this roadmap, we present a comprehensive perspective on the foundations, applications, and emerging directions of AI and ML in smart manufacturing. It is structured in three parts. The first highlights the foundations and trends that frame the evolution of AI in smart manufacturing. The second focuses on key topics where AI is already enabling advances, including industrial big data analytics, advanced sensing and perception, autonomous systems, additive and laser-based manufacturing, digital twins, robotics, supply chain and logistics optimization, and sustainable manufacturing. The third section explores non-traditional ML approaches that are opening new frontiers, such as physics-informed AI, generative AI, semantic AI, advanced digital twins, explainable AI, RAMS, data-centric metrology, LLMs, and foundation models for highly connected and complex manufacturing systems. By identifying both opportunities and remaining barriers across these areas, this roadmap outlines the advances needed in methods, integration strategies, and industrial adoption. We hope this roadmap will serve as a guide for researchers, engineers, and practitioners to accelerate innovation, align academic and industrial priorities, and ensure that AI-driven smart manufacturing delivers reliable, sustainable, and scalable impact for the future of manufacturing ecosystems.

cs.AI↗

arXiv2026

CASHEW: Stabilizing Multimodal Reasoning via Iterative Trajectory Aggregation

Vision-language models achieve strong performance across a wide range of multimodal understanding and reasoning tasks, yet their multi-step reasoning remains unstable. Repeated sampling over the same input often produces divergent reasoning trajectories and inconsistent final predictions. To address this, we introduce two complementary approaches inspired by test-time scaling: (1) CASHEW, an inference-time framework that stabilizes reasoning by iteratively aggregating multiple candidate trajectories into higher-quality reasoning traces, with explicit visual verification filtering hallucinated steps and grounding reasoning in visual evidence, and (2) CASHEW-RL, a learned variant that internalizes this aggregation behavior within a single model. CASHEW-RL is trained using Group Sequence Policy Optimization (GSPO) with a composite reward that encourages correct answers grounded in minimal yet sufficient visual evidence, while adaptively allocating reasoning effort based on task difficulty. This training objective enables robust self-aggregation at inference. Extensive experiments on 13 image understanding, video understanding, and video reasoning benchmarks show significant performance improvements, including gains of up to +26.2 percentage points on ScienceQA and +9.1 percentage points on EgoSchema.

cs.CV↗

arXiv2025

Characterization of Asymptotically Smooth Curves

We construct an explicit example of an asymptotically conformal chord-arc curve that fails to be asymptotically smooth. This implies that a function belonging to both the little Bloch space and BMOA does not necessarily lie in VMOA, and that a strongly quasisymmetric homeomorphism which is symmetric is not necessarily strongly symmetric. We also provide a complete characterization of asymptotically smooth curves in terms of asymptotic conformality and uniform approximability.

math.CV↗

arXiv2025

FrameOracle: Learning What to See and How Much to See in Videos

Vision-language models (VLMs) advance video understanding but operate under tight computational budgets, making performance dependent on selecting a small, high-quality subset of frames. Existing frame sampling strategies, such as uniform or fixed-budget selection, fail to adapt to variations in content density or task complexity. To address this, we present FrameOracle, a lightweight, plug-and-play module that predicts both (1) which frames are most relevant to a given query and (2) how many frames are needed. FrameOracle is trained via a curriculum that progresses from weak proxy signals, such as cross-modal similarity, to stronger supervision with FrameOracle-41K, the first large-scale VideoQA dataset with validated keyframe annotations specifying minimal sufficient frames per question. Extensive experiments across five VLMs and six benchmarks show that FrameOracle reduces 16-frame inputs to an average of 10.4 frames without accuracy loss. When starting from 64-frame candidates, it reduces inputs to 13.9 frames on average while improving accuracy by 1.5%, achieving state-of-the-art efficiency-accuracy trade-offs for scalable video understanding.

cs.CV↗

arXiv2025

DMOSpeech 2: Reinforcement Learning for Duration Prediction in Metric-Optimized Speech Synthesis

Diffusion-based text-to-speech (TTS) systems have made remarkable progress in zero-shot speech synthesis, yet optimizing all components for perceptual metrics remains challenging. Prior work with DMOSpeech demonstrated direct metric optimization for speech generation components, but duration prediction remained unoptimized. This paper presents DMOSpeech 2, which extends metric optimization to the duration predictor through a reinforcement learning approach. The proposed system implements a novel duration policy framework using group relative preference optimization (GRPO) with speaker similarity and word error rate as reward signals. By optimizing this previously unoptimized component, DMOSpeech 2 creates a more complete metric-optimized synthesis pipeline. Additionally, this paper introduces teacher-guided sampling, a hybrid approach leveraging a teacher model for initial denoising steps before transitioning to the student model, significantly improving output diversity while maintaining efficiency. Comprehensive evaluations demonstrate superior performance across all metrics compared to previous systems, while reducing sampling steps by half without quality degradation. These advances represent a significant step toward speech synthesis systems with metric optimization across multiple components. The audio samples, code and pre-trained models are available at https://dmospeech2.github.io/.

eess.AS↗

arXiv2024

Global existence and scattering of small data smooth solutions to quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$, II

In our previous paper [Fei Hou, Fei Tao, Huicheng Yin, Global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$, Preprint (2024), arXiv:2405.03242], for the $Q_0$-type quadratic nonlinearities, we have shown the global well-posedness and scattering properties of small data smooth solutions to the quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$. In this paper, we start to solve the global existence problem for the remaining $Q_{\alpha\beta}$-type nonlinearities. By combining these results, we have established the global well-posedness of small solutions on $\mathbb{R}^2\times\mathbb{T}$ for the general 3-D quadratically quasilinear wave systems when the related 2-D null conditions are fulfilled.

math.AP↗

arXiv2024

Conformal weldings in the Loewner equation and Weil--Petersson quasislit-disks

A simple arc $\Gamma = \gamma(0, T]$, growing into the unit disk $\mathbb D$ from its boundary, generates a driving term $\xi$ and a conformal welding $\phi$ through the Loewner differential equation. When $\Gamma$ is the slit of a Weil--Petersson quasislit-disk $\mathbb D\setminus\Gamma$, the Loewner transform and its inverse $\Gamma \leftrightarrow \xi$ have been well understood due to Y. Wang's work. We investigate the maps $\Gamma \leftrightarrow \phi$ in this case, giving a description of $\Gamma$ in terms of $\phi$.

math.CV↗

arXiv2024

Redefinition of Digital Twin and its Situation Awareness Framework Designing Towards Fourth Paradigm for Energy Internet of Things

Traditional knowledge-based situation awareness (SA) modes struggle to adapt to the escalating complexity of today's Energy Internet of Things (EIoT), necessitating a pivotal paradigm shift. In response, this work introduces a pioneering data-driven SA framework, termed digital twin-based situation awareness (DT-SA), aiming to bridge existing gaps between data and demands, and further to enhance SA capabilities within the complex EIoT landscape. First, we redefine the concept of digital twin (DT) within the EIoT context, aligning it with data-intensive scientific discovery paradigm (the Fourth Paradigm) so as to waken EIoT's sleeping data; this contextual redefinition lays the cornerstone of our DT-SA framework for EIoT. Then, the framework is comprehensively explored through its four fundamental steps: digitalization, simulation, informatization, and intellectualization. These steps initiate a virtual ecosystem conducive to a continuously self-adaptive, self-learning, and self-evolving big model (BM), further contributing to the evolution and effectiveness of DT-SA in engineering. Our framework is characterized by the incorporation of system theory and Fourth Paradigm as guiding ideologies, DT as data engine, and BM as intelligence engine. This unique combination forms the backbone of our approach. This work extends beyond engineering, stepping into the domain of data science -- DT-SA not only enhances management practices for EIoT users/operators, but also propels advancements in pattern analysis and machine intelligence (PAMI) within the intricate fabric of a complex system. Numerous real-world cases validate our DT-SA framework.

cs.NI↗

arXiv2024

Global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$

In this paper, we are concerned with the global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on the product space $\mathbb{R}^2\times\mathbb{T}$. These quasilinear wave systems include 3D irrotational potential flow equation of Chaplygin gases, 3D relativistic membrane equation, some 3D quasilinear wave equations which come from the corresponding Lagrangian functionals as perturbations of the Lagrangian densities of linear waves, and nonlinear wave maps system. Through looking for some suitable transformations of unknown functions, the nonlinear wave system can be reduced into a more tractable form. Subsequently, by applying the vector-field method together with the ghost weight technique as well as deriving some kinds of weighted $L^\infty-L^\infty$ and $L^\infty-L^2$ estimates of solution $w$ to the 2D linear wave equation $\Box w=f(t,x)$, the global existence and scattering of small data solutions are established.

math.AP↗

arXiv2024

Generative manufacturing systems using diffusion models and ChatGPT

In this study, we introduce Generative Manufacturing Systems (GMS) as a novel approach to effectively manage and coordinate autonomous manufacturing assets, thereby enhancing their responsiveness and flexibility to address a wide array of production objectives and human preferences. Deviating from traditional explicit modeling, GMS employs generative AI, including diffusion models and ChatGPT, for implicit learning from envisioned futures, marking a shift from a model-optimum to a training-sampling decision-making. Through the integration of generative AI, GMS enables complex decision-making through interactive dialogue with humans, allowing manufacturing assets to generate multiple high-quality global decisions that can be iteratively refined based on human feedback. Empirical findings showcase GMS's substantial improvement in system resilience and responsiveness to uncertainties, with decision times reduced from seconds to milliseconds. The study underscores the inherent creativity and diversity in the generated solutions, facilitating human-centric decision-making through seamless and continuous human-machine interactions.

cs.LG↗

arXiv2023

Almost global solutions of 1D nonlinear Klein-Gordon equations with small weakly decaying initial data

It has been known that if the initial data decay sufficiently fast at space infinity, then 1D Klein-Gordon equations with quadratic nonlinearity admit classical solutions up to time $e^{C/\epsilon^2}$ while $e^{C/\epsilon^2}$ is also the upper bound of the lifespan, where $C>0$ is some suitable constant and $\epsilon>0$ is the size of the initial data. In this paper, we will focus on the 1D nonlinear Klein-Gordon equations with weakly decaying initial data. It is shown that if the $H^s$-Sobolev norm with $(1+|x|)^{1/2+}$ weight of the initial data is small, then the almost global solutions exist; if the initial $H^s$-Sobolev norm with $(1+|x|)^{1/2}$ weight is small, then for any $M>0$, the solutions exist on $[0,\epsilon^{-M}]$. Our proof is based on the dispersive estimate with a suitable $Z$-norm and a delicate analysis on the phase function.

math.AP↗

arXiv2023

Decomposition and characterization of VMO via vanishing Carleson measures

We establish two equivalent characterizations of $\mathrm{VMO}$ in terms of vanishing Carleson measures. First, we show that any $\mathrm{VMO}$ function admits a decomposition into a continuous boundary term and an integral operator associated with a vanishing Carleson measure. Second, motivated by Varopoulos's work on the $\bar{\partial}$-equation, we characterize $\mathrm{VMO}$ via the boundary values of smooth functions whose gradients induce vanishing Carleson measures. As a consequence, we recover the known representation \[ \mathrm{VMO}=\mathrm{VLO}-\mathrm{VLO}, \] thereby providing a new perspective on this decomposition.

math.CV↗

arXiv2023

The partial null conditions and global smooth solutions of the nonlinear wave equations on $\mathbb{R}^d\times\mathbb{T}$ with $d=2,3$

In this paper, we investigate the fully nonlinear wave equations on the product space $\mathbb{R}^3\times\mathbb{T}$ with quadratic nonlinearities and on $\mathbb{R}^2\times\mathbb{T}$ with cubic nonlinearities, respectively. It is shown that for the small initial data satisfying some space-decay rates at infinity, these nonlinear equations admit global smooth solutions when the corresponding partial null conditions hold and while have almost global smooth solutions when the partial null conditions are violated. Our proof relies on the Fourier mode decomposition of the solutions with respect to the periodic direction, the efficient combinations of time-decay estimates for the solutions to the linear wave equations and the linear Klein-Gordon equations, and the global weighted energy estimates. In addition, an interesting auxiliary energy is introduced. As a byproduct, our results can be applied to the 4D irrotational compressible Euler equations of polytropic gases or Chaplygin gases on $\mathbb{R}^3\times\mathbb{T}$, the 3D relativistic membrane equation and the 3D nonlinear membrane equation on $\mathbb{R}^2\times\mathbb{T}$.

math.AP↗

arXiv2022

A description of $A_{\infty }$-weights for VMO

We present a new characterization of Muckenhoupt $A_{\infty}$-weights whose logarithm is in $\operatorname{VMO}(\mathbb{R})$ in terms of vanishing Carleson measures on $\mathbb{R}_+^2$ and vanishing doubling weights on $\mathbb{R}$. This also gives a novel description of strongly symmetric homeomorphisms on the real line by using a geometric quantity.

math.CV↗

arXiv2022

Crystallographic effects on transgranular chloride-induced stress corrosion crack propagation of arc welded austenitic stainless steel

The effect of crystallography on transgranular chloride-induced stress corrosion cracking (TGCISCC) of arc welded 304L austenitic stainless steel is studied on >300 grains along crack paths. Schmid and Taylor factor mismatches across grain boundaries (GBs) reveal that cracks propagate either from a hard to soft grain, which can be explained merely by mechanical arguments, or soft to hard grain. In the latter case, finite element analysis reveals that TGCISCC will arrest at GBs without sufficient mechanical stress, favorable crystallographic orientations, or crack tip corrosion. GB type does not play a significant role in determining TGCISCC cracking behavior nor susceptibility. TGCISCC crack behaviors at GBs are discussed in the context of the competition between mechanical, crystallographic, and corrosion factors.

cond-mat.mtrl-sci↗

arXiv2022

Almost global smooth solutions of the 3D quasilinear Klein-Gordon equations on the product space $\mathbb{R}^{2}\times \mathbb{T}$

In the paper, for the 3D quasilinear Klein-Gordon equation with the small initial data posed on the product space $\mathbb{R}^{2}\times \mathbb{T}$, we focus on the lower bound of the lifespan of the smooth solution. When the size of initial data is bounded by $\varepsilon_0>0$, by the space-time resonance method, it is shown that smooth solution exists up to the time $e^{c_{0}/\varepsilon_{0}^2}$ with $\varepsilon_0$ being sufficiently small and $c_0>0$ being some suitable constant.

math.AP↗