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Chih-Wei Chen

Publications and source records attributed to Chih-Wei Chen.

16 recordsLinked to original sources
arXiv2026

Designing Proactive Thought Partners for Writing

Writing involves diverse cognitive activities, from ideation to revision, and writers' needs vary across individuals and moments. Proactive AI promises to provide the right support at the right time, yet existing proactive tools largely focus on generic textual assistance, such as autocomplete. This paper studies the design space of proactive thought partners: AI agents that proactively offer customizable, higher-level cognitive support during writing. We instantiated this concept in a technology probe and deployed it with 16 participants for one week. The probe allows users to create partners by configuring their roles and proactivity. As users write, relevant partners take the initiative at appropriate moments to offer suggestions. Our findings show that participants configured proactive support through prospective planning, used suggestions for both idea generation and self-monitoring, and valued lightweight visual representations alongside non-directive rhetorical framing for non-intrusive interventions. We derive implications for designing proactive writing assistants around customization, timing, engagement, and representation.

cs.HC↗
arXiv2025

Convergence of Hessian estimator from random samples on a manifold with boundary

A common method for estimating the Hessian operator from random samples on a low-dimensional manifold involves locally fitting a quadratic polynomial. Although widely used, it is unclear if this estimator introduces bias, especially in complex manifolds with boundaries and nonuniform sampling. Rigorous theoretical guarantees of its asymptotic behavior have been lacking. We show that, under mild conditions, this estimator asymptotically converges to the Hessian operator, with nonuniform sampling and curvature effects proving negligible, even near boundaries. Our analysis framework simplifies the intensive computations required for direct analysis.

math.ST↗
arXiv2021

A new locally linear embedding scheme in light of Hessian eigenmap

We provide a new interpretation of Hessian locally linear embedding (HLLE), revealing that it is essentially a variant way to implement the same idea of locally linear embedding (LLE). Based on the new interpretation, a substantial simplification can be made, in which the idea of "Hessian" is replaced by rather arbitrary weights. Moreover, we show by numerical examples that HLLE may produce projection-like results when the dimension of the target space is larger than that of the data manifold, and hence one further modification concerning the manifold dimension is suggested. Combining all the observations, we finally achieve a new LLE-type method, which is called tangential LLE (TLLE). It is simpler and more robust than HLLE.

stat.ML↗
arXiv2020

The Unsupervised Method of Vessel Movement Trajectory Prediction

In real-world application scenarios, it is crucial for marine navigators and security analysts to predict vessel movement trajectories at sea based on the Automated Identification System (AIS) data in a given time span. This article presents an unsupervised method of ship movement trajectory prediction which represents the data in a three-dimensional space which consists of time difference between points, the scaled error distance between the tested and its predicted forward and backward locations, and the space-time angle. The representation feature space reduces the search scope for the next point to a collection of candidates which fit the local path prediction well, and therefore improve the accuracy. Unlike most statistical learning or deep learning methods, the proposed clustering-based trajectory reconstruction method does not require computationally expensive model training. This makes real-time reliable and accurate prediction feasible without using a training set. Our results show that the most prediction trajectories accurately consist of the true vessel paths.

cs.CV↗
arXiv2019

$C_0$-positivity and a classification of closed three-dimensional CR torsion solitons

A closed CR 3-manifold is said to have $C_{0}$-positive pseudohermitian curvature if $(W+C_{0}Tor)(X,X)>0$ for any $0\neq X\in T_{1,0}(M)$. We discover an obstruction for a closed CR 3-manifold to possess $C_{0}$-positive pseudohermitian curvature. We classify closed three-dimensional CR Yamabe solitons according to $C_{0}$-positivity and $C_{0}$-negativity whenever $C_{0}=1$ and the potential function lies in the kernel of Paneitz operator. Moreover, we show that any closed three-dimensional CR torsion soliton must be the standard Sasakian space form. At last, we discuss the persistence of $C_{0}$-positivity along the CR torsion flow starting from a pseudo-Einstein contact form.

math.DG↗
arXiv2018

Volume bounds of the Ricci flow on closed manifolds

Let $\{g(t)\}_{t\in [0,T)}$ be the solution of the Ricci flow on a closed Riemannian manifold $M^n$ with $n\geq 3$. Without any assumption, we derive lower volume bounds of the form ${\rm Vol}_{g(t)}\geq C (T-t)^{\frac{n}{2}}$, where $C$ depends only on $n$, $T$ and $g(0)$. In particular, we show that $${\rm Vol}_{g(t)} \geq e^{ Tλ-\frac{n}{2}} \left(\frac{4}{(A(λ-r)+4B)T}\right)^{\frac{n}{2}}\left(T-t\right)^{\frac{n}{2}},$$ where $r:=\inf_{\|ϕ\|_2^2=1} \int_M Rϕ^2 \ d{\rm vol}_{g(0)}$, $λ:=\inf_{\|ϕ\|_2^2=1} \int_M 4|\nablaϕ|^2+Rϕ^2\ d{\rm vol}_{g(0)}$ and $A,B$ are Sobolev constants of $(M,g(0))$. This estimate is sharp in the sense that it is achieved by the unit sphere with scalar curvature $R_{g(0)}=n(n-1)$ and $A=\frac{4}{n(n-2)}ω_n^{-\frac{2}{n}}$, $B=\frac{n-1}{n-2}ω_n^{-\frac{2}{n}}$. On the other hand, if the diameter satisfies ${\rm diam}_{g(t)}\leq c_1\sqrt{T-t}$ and there exist a point $x_0\in M$ such that $R(x_0,t)\leq c_2(T-t)^{-1}$, then we have ${\rm Vol}_{g(t)}\leq C (T-t)^{\frac{n}{2}}$ for all $t>\frac{T}{2}$, where $C$ depends only on $c_1,c_2,n,T$ and $g(0)$.

math.DG↗
arXiv2018

Shi-type estimates of the Ricci flow based on Ricci curvature

We construct a uniform local bound of curvature operator from local bounds of Ricci curvature and injectivity radius among all $n$-dimensional Ricci flows. Thus new compactness theorems for the Ricci flow and Ricci solitons are derived. In particular, we show that every Ricci flow with $|Ric|\leq K$ must satisfy $|Rm|\leq Ct^{-1}$ for all $t\in (0,T]$, where $C$ depends only on the dimension $n$ and $T$ depends on $K$ and the injectivity radius $inj_{g(t)}$. In the second part of this paper, we discuss the behavior of Ricci curvature and its derivative when the injectivity radius is thoroughly unknown. In particular, another Shi-type estimate for Ricci curvature is derived when the derivative of Ricci curvature is controlled by the derivative of scalar curvature.

math.DG↗
arXiv2017

Level set flow in 3D steady gradient Ricci solitons

Let $(M^3, g, f)$ be a nontrivial 3-dimensional steady gradient Ricci soliton. If the scalar curvature $R$ satisfies $c_1r^{-b}\leq R\leq c_2r^{-a}$ for some $a\in(0,1], b\geq a$, and $c_1,c_2>0$, then the umbilical ratio of the level sets of $f$ satisfies $\frac{2|A|^2-H^2}{H^2}\in O(r^{6a-\frac{8a^2}{b}})\cap O(r^{2b-4a})$.

math.DG↗
arXiv2016

Classical and Quantum Szilard Engine under Generalized Uncertainty Principle Effect

We studied the Szilard engine under the effect of generalized uncertainty principle (GUP). In the classical Szilard engine, the work done by the engine is reduced by the GUP effect via a modified ideal gas law. In the quantum Szilard engine, the correction comes from the shifted eigen energy due to the nonlinear momentum dependence. We studied its effect on both bosonic and fermionic molecules.

hep-th↗
arXiv2015

On Three-dimensional CR Yamabe Solitons

In this paper, we investigate the geometry and classification of three-dimensional CR Yamabe solitons. In the compact case, we show that any 3-dimensional CR Yamabe soliton must have constant Tanaka-Webster scalar curvature; we also obtain a classification under the assumption that their potential functions are in the kernel of the CR Paneitz operator. In the complete case, we obtain a structure theorem on the diffeomorphism types of complete 3-dimensional pseudo-gradient CR Yamabe solitons (shrinking, or steady, or expanding) of vanishing torsion.

math.DG↗
arXiv2015

On the CR Analogue of Reilly Formula and Yau Eigenvalue Conjecture

In this paper, we derive the CR Reilly's formula and its applications to studying of the first eigenvalue estimate for CR Dirichlet eigenvalue problem and embedded p-minimal hypersurfaces. In particular, we obtain the first Dirichlet eigenvalue estimate in a compact pseudohermitian (2n+1)-manifold with boundary and the first eigenvalue estimate of the tangential sublaplacian on closed oriented embedded p-minimal hypersurfaces in a closed pseudohermitian (2n+1)-manifold of vanishing torsion.

math.DG↗
arXiv2015

Very large magnetoresistance in Fe$_{0.28}$TaS$_{2}$ single crystals

Magnetic moments intercalated into layered transition metal dichalcogenides are an excellent system for investigating the rich physics associated with magnetic ordering in a strongly anisotropic, strong spin-orbit coupling environment. We examine electronic transport and magnetization in Fe$_{0.28}$TaS$_{2}$, a highly anisotropic ferromagnet with a Curie temperature $T_{\mathrm{C}} \sim 68.8~$K. We find anomalous Hall data confirming a dominance of spin-orbit coupling in the magnetotransport properties of this material, and a remarkably large field-perpendicular-to-plane MR exceeding 60% at 2 K, much larger than the typical MR for bulk metals, and comparable to state-of-the-art GMR in thin film heterostructures, and smaller only than CMR in Mn perovskites or high mobility semiconductors. Even within the Fe$_x$TaS$_2$ series, for the current $x$ = 0.28 single crystals the MR is nearly $100\times$ higher than that found previously in the commensurate compound Fe$_{0.25}$TaS$_{2}$. After considering alternatives, we argue that the large MR arises from spin disorder scattering in the strong spin-orbit coupling environment, and suggest that this can be a design principle for materials with large MR.

cond-mat.str-el↗
arXiv2014

Thermally Driven Analog of the Barkhausen Effect at the Metal-Insulator Transition in Vanadium Dioxide

The physics of the metal-insulator transition (MIT) in vanadium dioxide remains a subject of intense interest. Because of the complicating effects of elastic strain on the phase transition, there is interest in comparatively strain-free means of examining VO2 material properties. We report contact-free, low-strain studies of the MIT through an inductive bridge approach sensitive to the magnetic response of VO2 powder. Rather than observing the expected step-like change in susceptibility at the transition, we argue that the measured response is dominated by an analog of the Barkhausen effect, due to the extremely sharp jump in the magnetic response of each grain as a function of time as the material is cycled across the phase boundary. This effect suggests that future measurements could access the dynamics of this and similar phase transitions.

cond-mat.str-el↗
arXiv2011

Structure at infinity of expanding gradient Ricci soliton

We study the geometry at infinity of expanding gradient Ricci solitons of dimension greater than two with finite asymptotic curvature ratio without curvature sign assumptions. We mainly prove that they have a cone structure at infinity.

math.DG↗
arXiv2011

Volume estimates and the asymptotic behavior of expanding gradient Ricci solitons

We study the asymptotic volume ratio of non-steady gradient Ricci solitons. Moreover, a local estimate of the volume ratio is obtained for expanding solitons which satisfy $\lim_{dist(O,x)\rightarrow\infty} |Sect|\cdot dist(O,x)^2=0$. Therefore, for such a soliton, we can show that it must have $\mathbb{R}^n$ as one of its tangent cone at infinity. (Here we assume that the soliton is simply connected at infinity, has only one end and $n\geq 3$.)

math.DG↗