arXiv subjects

Yi Lai

Publications and source records attributed to Yi Lai.

15 recordsLinked to original sources

arXiv2026

Vibe Coding for Visualization Implementation: An Empirical Study of Practices and Challenges

Data visualization is essential for data analysis and communication, yet creating expressive visualizations remains labor-intensive. Recent AI-driven ``vibe coding'' tools enable users to generate visualizations through natural language interaction, lowering the barrier to entry. However, visualization implementation requires precise alignment between user intent and visual representation, which may differ from general software development practices. We present an empirical study with 16 participants of varying expertise to examine how users employ vibe coding tools for visualization implementation. Participants completed two visualization tasks and a semi-structured interview. Our findings characterize the diverse practices users adopt across prompting, evaluation, and iteration, and surface the challenges they encounter throughout the process.

cs.HC↗

arXiv2025

Classification of ancient cylindrical mean curvature flows and the Mean Convex Neighborhood Conjecture

We resolve the Mean Convex Neighborhood Conjecture for mean curvature flows in all dimensions and for all types of cylindrical singularities. Specifically, we show that if the tangent flow at a singular point is a multiplicity-one cylinder, then in a neighborhood of that point the flow is mean-convex, its time-slices arise as level sets of a continuous function, and all nearby tangent flows are cylindrical. Moreover, we establish a canonical neighborhood theorem near such points, which characterizes the flow via local models. We also obtain a more uniform version of the Mean Convex Neighborhood Conjecture, which only requires closeness to a cylinder at some initial time and yields a quantitative version of this structural description. Our proof relies on a complete classification of ancient, asymptotically cylindrical flows. We prove that any such flow is non-collapsed, convex, rotationally symmetric, and belongs to one of three canonical families: ancient ovals, the bowl soliton, or the flying wing translating solitons. Central to our method is a refined asymptotic analysis and a novel \emph{leading mode condition,} together with a new ``induction over thresholds'' argument. In addition, our approach provides a full parameterization of the space of asymptotically cylindrical flows and gives a new proof of the existence of flying wing solitons. Our method is independent of prior work and, together with our prequel paper, this work is largely self-contained.

math.DG↗

arXiv2025

The PDE-ODI principle and cylindrical mean curvature flows

We introduce a new approach for analyzing ancient solutions and singularities of mean curvature flow that are locally modeled on a cylinder. Its key ingredient is a general mechanism, called the \emph{PDE--ODI principle}, which converts a broad class of parabolic differential equations into systems of ordinary differential inequalities. This principle bypasses many delicate analytic estimates used in previous work, and yields asymptotic expansions to arbitrarily high order. As an application, we establish the uniqueness of the bowl soliton times a Euclidean factor among ancient, cylindrical flows with dominant linear mode. This extends previous results on this problem to the most general setting and is made possible by the stronger asymptotic control provided by our analysis. In the other case, when the quadratic mode dominates, we obtain a complete asymptotic expansion to arbitrary polynomial order, which will form the basis for a subsequent paper. Our framework also recovers and unifies several classical results. In particular, we give new proofs of the uniqueness of tangent flows (due to Colding-Minicozzi) and the rigidity of cylinders among shrinkers (due to Colding-Ilmanen-Minicozzi) by reducing both problems to a single ordinary differential inequality, without using the {\L}ojasiewicz-Simon inequality. Our approach is independent of prior work and the paper is largely self-contained.

math.DG↗

arXiv2025

Higher-dimensional flying wing Steady Ricci Solitons

For any $n\geq 4$, we construct an $(n-2)$-parameter family of steady gradient Ricci solitons with non-negative curvature operator and prescribed by the eigenvalues of Ricci tensor at a critical point of the soliton potential. Among them lies an $(n-3)$-parameter subfamily of non-collapsed solitons. These solitons generalized the flying wings constructed by the second named author and produced new examples of steady gradient Ricci solitons with non-negative curvature operator for $n\geq 4$. Our approach is based on constructing continuous families of Ricci flows smoothing emanating from continuous families of spherical polyhedra which still preserves symmetry. This is built upon a new stability result of Ricci flows with scaling invariant estimates. As another application of the method, we prove the stability of asymptotically conical expanding solitons constructed by Deruelle under $L^\infty$ perturbation of links. In particular, the $C^0$-convergence of smooth links implies the smooth convergence of the expanding solitons.

math.DG↗

arXiv2025

Convergence of Ricci flow and long-time existence of Harmonic map heat flow

For an ancient Ricci flow asymptotic to a compact integrable shrinker, or a Ricci flow developing a finite-time singularity modelled on the shrinker, we establish the long-time existence of a harmonic map heat flow between the Ricci flow and the shrinker for all times. This provides a global parabolic gauge for the Ricci flow and implies the uniqueness of the tangent flow without modulo any diffeomorphisms. We present two main applications: First, we construct and classify all ancient Ricci flows asymptotic to any compact integrable shrinker, showing that they converge exponentially. Second, we obtain the optimal convergence rate at singularities modelled on the shrinker, characterized by the first negative eigenvalue of the stability operator for the entropy. In particular, we show that any Ricci flow developing a round $\mathbb S^n$ singularity converges at least at the rate $(-t)^{\frac{n+1}{n-1}}$.

math.DG↗

arXiv2025

SCOPE-DTI: Semi-Inductive Dataset Construction and Framework Optimization for Practical Usability Enhancement in Deep Learning-Based Drug Target Interaction Prediction

Deep learning-based drug-target interaction (DTI) prediction methods have demonstrated strong performance; however, real-world applicability remains constrained by limited data diversity and modeling complexity. To address these challenges, we propose SCOPE-DTI, a unified framework combining a large-scale, balanced semi-inductive human DTI dataset with advanced deep learning modeling. Constructed from 13 public repositories, the SCOPE dataset expands data volume by up to 100-fold compared to common benchmarks such as the Human dataset. The SCOPE model integrates three-dimensional protein and compound representations, graph neural networks, and bilinear attention mechanisms to effectively capture cross domain interaction patterns, significantly outperforming state-of-the-art methods across various DTI prediction tasks. Additionally, SCOPE-DTI provides a user-friendly interface and database. We further validate its effectiveness by experimentally identifying anticancer targets of Ginsenoside Rh1. By offering comprehensive data, advanced modeling, and accessible tools, SCOPE-DTI accelerates drug discovery research.

cs.LG↗

arXiv2025

3-Manifolds with positive scalar curvature and bounded geometry

We show that a complete contractible 3-manifold with positive scalar curvature and bounded geometry must be $\mathbb R^3$. We also show that an open handlebody of genus larger than 1 does not admit complete metrics with positive scalar curvature and bounded geometry. Our results rely on the maximal weak solution to inverse mean curvature flow due to the third-named author.

math.DG↗

arXiv2024

Tokensome: Towards a Genetic Vision-Language GPT for Explainable and Cognitive Karyotyping

Automatic karyotype analysis is often defined as a visual perception task focused solely on chromosomal object-level modeling. This definition has led most existing methods to overlook componential and holistic information, significantly constraining model performance. Moreover, the lack of interpretability in current technologies hinders clinical adoption. In this paper, we introduce Tokensome, a novel vision-language model based on chromosome tokenization for explainable and cognitive karyotyping. Tokensome elevates the method from the conventional visual perception layer to the cognitive decision-making layer. This elevation enables the integration of domain knowledge and cognitive reasoning via knowledge graphs and LLMs, markedly enhancing model's explainability and facilitating abnormality detection.

cs.CV↗

arXiv2024

A family of K\"ahler flying wing steady Ricci solitons

In $1996$, H.-D. Cao constructed a $U(n)$-invariant steady gradient K\"ahler-Ricci soliton on $\mathbb{C}^{n}$ and asked whether every steady gradient K\"ahler-Ricci soliton of positive curvature on $\mathbb{C}^{n}$ is necessarily $U(n)$-invariant (and hence unique up to scaling). Recently, Apostolov-Cifarelli answered this question in the negative for $n=2$. Here, we construct a family of $U(1)\times U(n-1)$-invariant, but not $U(n)$-invariant, complete steady gradient K\"ahler-Ricci solitons with strictly positive curvature operator on real $(1,\,1)$-forms (in particular, with strictly positive sectional curvature) on $\mathbb{C}^{n}$ for $n\geq3$, thereby answering Cao's question in the negative for $n\geq3$. This family of steady Ricci solitons interpolates between Cao's $U(n)$-invariant steady K\"ahler-Ricci soliton and the product of the cigar soliton and Cao's $U(n-1)$-invariant steady K\"ahler-Ricci soliton. This provides the K\"ahler analog of the Riemannian flying wings construction of Lai. In the process of the proof, we also demonstrate that the almost diameter rigidity of $\mathbb{P}^{n}$ endowed with the Fubini-Study metric does not hold even if the curvature operator is bounded below by $2$ on real $(1,\,1)$-forms.

math.DG↗

arXiv2022

3D flying wings for any asymptotic cones

For every $θ\in(0,π)$, we construct a 3D steady gradient Ricci soliton whose asymptotic cone is a sector with angle $θ$, which is a called 3D flying wing.

math.DG↗

arXiv2022

O(2)-symmetry of 3D steady gradient Ricci solitons

For any 3D steady gradient Ricci soliton with positive curvature, we prove that it must be isometric to the Bryant soliton if it is asymptotic to a ray. Otherwise, it is asymptotic to a sector and hence a flying wing. We show that all 3D flying wings are O(2)-symmetric. Therefore, all 3D steady gradient Ricci solitons are O(2)-symmetric.

math.DG↗

arXiv2020

A family of 3d steady gradient solitons that are flying wings

We find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at infinity. The 3d flying wings are collapsed. For dimension $n\ge 4$, we find a family of $\mathbb{Z}_2\times O(n-1)$-symmetric but non-rotationally symmetric n-dimensional steady gradient solitons with positive curvature operator. We show that these solitons are non-collapsed.

math.DG↗

arXiv2020

A Lean and Highly-automated Model-Based Software Development Process Based on DO-178C/DO-331

The emergence of a global market for urban air mobility and unmanned aerial systems has attracted many startups across the world. These organizations have little training or experience in the traditional processes used in civil aviation for the development of software and electronic hardware. They are also constrained in the resources they can allocate for dedicated teams of professionals to follow these standardized processes. To fill this gap, this paper presents a custom workflow based on a subset of objectives derived from the foundational standards for safety critical software DO-178C/DO-331. The selection of objectives from the standards is based on the importance, degree of automation, and reusability of specific objectives. This custom workflow is intended to establish a lean and highly automated development life cycle resulting in higher quality software with better maintainability characteristics for research and prototype aircraft. It can also be proposed as means of compliance for software of certain applications such as unmanned aircraft systems, urban air mobility and general aviation. By producing the essential set of development and verification artifacts, the custom workflow also provides a scalable basis for potential future certification in compliance with DO-178C/DO-331. The custom workflow is demonstrated in a case study of an Autopilot Manual Disconnection System.

cs.SE↗

arXiv2020

Producing 3d Ricci flows with non-negative Ricci curvature via singular Ricci flows

We extend the concept of singular Ricci flow by Kleiner and Lott from 3d compact manifolds to 3d complete manifolds with possibly unbounded curvature. As an application of the generalized singular Ricci flow, we show that for any 3d complete Riemannian manifold with non-negative Ricci curvature, there exists a smooth Ricci flow starting from it.

math.DG↗

arXiv2018

Ricci flow under local almost non-negative curvature conditions

We find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative number. The curvature conditions we consider include 2-non-negative and weakly $\textnormal{PIC}_1$ cases, of which the results are new. We complete the discussion of the almost preservation problem by Bamler-Cabezas-Rivas-Wilking, and the 2-non-negative case generalizes a result in 3D by Simon-Topping to higher dimensions. As an application, we use the local Ricci flow to smooth a metric space which is the limit of a sequence of manifolds with the almost non-negative curvature conditions, and show that this limit space is bi-H$\ddot{\textnormal{o}}$lder homeomorphic to a smooth manifold.

math.DG↗