A method for authorship attribution based on function word adjacency networks (WANs) is introduced. Function words are parts of speech that express grammatical relationships between other words but do not carry lexical meaning on their own. In the WANs in this paper, nodes are function words and directed edges stand in…
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23 results for “WANs”
Proposes a graph neural network for traffic forecasting in WANs.
problem Traffic forecasting challenges in WANs due to dynamic and large data volumes.
method Dynamic diffusion convolutional recurrent neural networks for multistep traffic forecasting.
result Significant improvements in forecasting accuracy compared to classical methods.
A classical result of Sampson and Schoen-Yau in 1978 states that every diffeomorphism between compact hyperbolic Riemann surfaces is homotopic to an harmonic diffeomorphism. As conjectured by Schoen in 1993 and partially proved by Wan in 1992 and Tam-Wan in 1995, we prove in this article that this theorem generalizes t…
In this paper, we prove the extensions of Bonnet--Myers' type theorems obtained by Calabi and Cheeger--Gromov--Taylor via Bakry--Emery Ricci curvature, which generalize the results of \cite{FG, Lim1, Wan, Wang, WW, Wu}.
The task of aggregating and denoising crowd-labeled data has gained increased significance with the advent of crowdsourcing platforms and massive datasets. We propose a permutation-based model for crowd labeled data that is a significant generalization of the classical Dawid-Skene model, and introduce a new error metri…
In this paper we prove that if a point in a complete Riemannian manifold is not a cut point of any point whose distance to is , then the injectivity radius of is strictly large than . As a corollary we give a positive answer to a problem raised by Z. Sun and J. Wan.
Study on contracting maps and their rigidity under curvature constraints.
problem Rigidity of contracting maps between manifolds with positive curvature.
method Analysis of curvature pinching and contracting conditions involving singular values.
result Established the relation between curvature pinching and contracting conditions.
In this paper, we first prove the -mean curvature comparison in a smooth metric measure space when the Bakry-Emery Ricci tensor is bounded from below and is bounded. Based on this, we define a Myers-type compactness theorem by generalizing the results of Cheeger, Gromov, and Taylor and of Wan for the Bakry-Eme…
Machine learning has started to be deployed in fields such as healthcare and finance, which propelled the need for and growth of privacy-preserving machine learning (PPML). We propose an actively secure four-party protocol (4PC), and a framework for PPML, showcasing its applications on four of the most widely-known mac…
In this paper, we give the first detailed proof of the short-time existence of Deane Yang's local Ricci flow. Then using the local Ricci flow, we prove short-time existence of the Ricci flow on noncompact manifolds, whose Ricci curvature has global lower bound and sectional curvature has only local average integral bou…
For any closed complex manifold , we calculate the Poincaré and Hodge polynomials of the delocalized equivariant cohomology with a grading specified by physicists. As a consequence, we recover a special case of a formula for the elliptic genera of symmetric products in Dijkgraaf-Moore-Verlinde-Verlin…
Inspired by the work of Leung-Wan, we study the mean curvature flow in hyperkähler manifolds starting from hyper-Lagrangian submanifolds, a class of middle dimensional submanifolds, which contains the class of complex Lagrangian submanifolds. For each hyper-Lagrangian submanifold, we define a new energy concept called …
A Note on harmonic mapsmath.DG
Harmonic maps are described using Jacobi elliptic functions.
problem None explicitly stated; focuses on existing work.
method Use of Jacobi elliptic functions to describe harmonic maps.
result Harmonic maps can be described using Jacobi elliptic functions.
We show how neural models can be used to realize piece-wise constant functions such as decision trees. The proposed architecture, which we call locally constant networks, builds on ReLU networks that are piece-wise linear and hence their associated gradients with respect to the inputs are locally constant. We formally …
Generalizing a theorem of Huang, Cheng and Wan classified the complete hypersurfaces of with non-zero constant mean curvature and constant scalar curvature. In our work, we obtain results of this nature in higher dimensions. In particular, we prove that if a complete hypersurface of has cons…
The paper constructs hyperbolic elements in multiple spaces.
problem Constructing hyperbolic elements in multiple Gromov-hyperbolic spaces.
method Explicit construction under minimal conditions.
result Set of simultaneously hyperbolic elements has strictly positive density.
Numerical valuation of European options under two-asset infinite-activity exponential Lévy modelsmath.NA
Method extends option valuation for 2D Lévy models.
problem Valuation of European options under 2-asset infinite-activity Lévy models.
method Developed numerical method extending Wang et al. (2007) for 1D to 2D, using Fourier transform for integral term and semi-Lagrangian theta-method for temporal discretization.
result Favourable second-order convergence for Normal Tempered Stable dynamics.
This paper generalizes a result about bounded differentials to higher-order differentials and studies their geometric implications.
problem The study of bounded holomorphic differentials and their geometric properties.
method Generalization of Wan's result to r-differentials and analysis of induced curvature.
result Equivalences between the boundedness of holomorphic differentials and negative upper bounds of induced curvature on various geometric objects.
Extends results on marginally outer trapped surfaces to general null expansion.
problem Analyzing geometry and topology of expanding horizons.
method Introduces -stability and proves conditions for positive Yamabe type and scalar curvature.
result Initial data sets with compact boundary of positive null expansion have positive mass.
Logarithmic -lemma and several geometric applications (with an Appendix joint with Sheng Rao)math.AG
The paper proves a logarithmic partial derivative lemma and applies it to several geometric problems.
problem Proving a logarithmic partial derivative lemma for compact Kähler manifolds.
method Developed a new -type lemma for logarithmic differential forms.
result Confirmed a conjecture by X. Wan and derived several geometric applications.
Deep adaptive sampling improves surrogate modeling for complex systems.
problem Statistical errors in random sampling for high-dimensional problems.
method DAS^2 method, using deep generative models to refine training sets.
result Reduces statistical errors in approximating solutions for low-regularity problems.
New algorithm for decentralized online convex optimization with unknown delays.
problem Decentralized online convex optimization with unknown, time-varying feedback delays.
method Proposes a novel algorithm that incorporates adaptive learning rates and gossip-based delay estimation.
result Achieves improved regret bounds of O(N √d tot + N √T (1-σ^2)^(1/4)) and O(N δmax ln T α) for different settings.
The paper studies entropy and free energy for harmonic metrics on cyclic Higgs bundles.
problem Quantifying the degree of mutual misalignment of metrics on Higgs bundles.
method Introduced entropy and free energy to quantify mutual misalignment; provided conditions for entropy and free energy to change.
result Extended work on boundedness of functions related to entropy and free energy on the unit disc.