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no code implementations • 3 Nov 2021 • Yingying Wu, Shusheng Xu, Shing-Tung Yau, Yi Wu

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused an ongoing pandemic infecting 219 million people as of 10/19/21, with a 3. 6% mortality rate.

no code implementations • 22 Feb 2021 • Tristan C. Collins, Sebastien Picard, Shing-Tung Yau

Let $X$ be a compact, K\"ahler, Calabi-Yau threefold and suppose $X\mapsto \underline{X}\leadsto X_t$ , for $t\in \Delta$, is a conifold transition obtained by contracting finitely many disjoint $(-1,-1)$ curves in $X$ and then smoothing the resulting ordinary double point singularities.

Differential Geometry High Energy Physics - Theory Algebraic Geometry

no code implementations • 30 Jun 2020 • Yang-Hui He, Shing-Tung Yau

Graph Laplacians as well as related spectral inequalities and (co-)homology provide a foray into discrete analogues of Riemannian manifolds, providing a rich interplay between combinatorics, geometry and theoretical physics.

no code implementations • ICLR 2020 • Dongsheng An, Yang Guo, Na lei, Zhongxuan Luo, Shing-Tung Yau, Xianfeng GU

In order to tackle the both problems, we explicitly separate the manifold embedding and the optimal transportation; the first part is carried out using an autoencoder to map the images onto the latent space; the second part is accomplished using a GPU-based convex optimization to find the discontinuous transportation maps.

no code implementations • ECCV 2020 • Dongsheng An, Yang Guo, Min Zhang, Xin Qi, Na lei, Shing-Tung Yau, Xianfeng GU

Though generative adversarial networks (GANs) areprominent models to generate realistic and crisp images, they often encounter the mode collapse problems and arehard to train, which comes from approximating the intrinsicdiscontinuous distribution transform map with continuousDNNs.

no code implementations • 13 Nov 2019 • Enno Keßler, Artan Sheshmani, Shing-Tung Yau

We call a map $\Phi\colon M\to N$ a super $J$-holomorphic curve if its differential maps the almost complex structure on $\mathcal{D}$ to $J$.

Differential Geometry Mathematical Physics Algebraic Geometry Mathematical Physics

no code implementations • 16 Oct 2019 • Jin Cao, Hossein Movasati, Shing-Tung Yau

We describe an algebra of meromorphic functions on the Siegel domain of genus two which contains Siegel modular forms for an arithmetic index six subgroup of the symplectic group and it is closed under three canonical derivations of the Siegel domain.

Algebraic Geometry Mathematical Physics Complex Variables Mathematical Physics

no code implementations • 8 Feb 2019 • Na lei, Yang Guo, Dongsheng An, Xin Qi, Zhongxuan Luo, Shing-Tung Yau, Xianfeng GU

This work builds the connection between the regularity theory of optimal transportation map, Monge-Amp\`{e}re equation and GANs, which gives a theoretic understanding of the major drawbacks of GANs: convergence difficulty and mode collapse.

no code implementations • 16 Sep 2018 • Huidong Liu, Yang Guo, Na lei, Zhixin Shu, Shing-Tung Yau, Dimitris Samaras, Xianfeng GU

Experimental results on an eight-Gaussian dataset show that the proposed OT can handle multi-cluster distributions.

no code implementations • 26 May 2018 • Na Lei, Zhongxuan Luo, Shing-Tung Yau, David Xianfeng Gu

In this work, we give a geometric view to understand deep learning: we show that the fundamental principle attributing to the success is the manifold structure in data, namely natural high dimensional data concentrates close to a low-dimensional manifold, deep learning learns the manifold and the probability distribution on it.

no code implementations • 16 Oct 2017 • Na Lei, Kehua Su, Li Cui, Shing-Tung Yau, David Xianfeng Gu

In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes.

no code implementations • CVPR 2013 • Yun Zeng, Chaohui Wang, Stefano Soatto, Shing-Tung Yau

This paper introduces an efficient approach to integrating non-local statistics into the higher-order Markov Random Fields (MRFs) framework.

no code implementations • CVPR 2013 • Rui Shi, Wei Zeng, Zhengyu Su, Hanna Damasio, Zhonglin Lu, Yalin Wang, Shing-Tung Yau, Xianfeng GU

This work conquer this problem by changing the Riemannian metric on the target surface to a hyperbolic metric, so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints.

2 code implementations • 12 Jul 2012 • Alexander Grigor'yan, Yong Lin, Yuri Muranov, Shing-Tung Yau

In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex.

Combinatorics Algebraic Topology

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