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pro vyhledávání: '"Liu, Yucheng"'
Autor:
Liu, Yucheng
We consider the convolution equation $(\delta - J) * G = g$ on $\mathbb R^d$, $d>2$, where $\delta$ is the Dirac delta function and $J,g$ are given functions. We provide conditions on $J, g$ that ensure the deconvolution $G(x)$ to decay as $( x \cdot
Externí odkaz:
http://arxiv.org/abs/2411.16058
This paper presents a large-scale parallel solver, specifically designed to tackle the challenges of solving high-dimensional and high-contrast linear systems in heat transfer topology optimization. The solver incorporates an interpolation technique
Externí odkaz:
http://arxiv.org/abs/2410.06850
Multigrid preconditioners are one of the most powerful techniques for solving large sparse linear systems. In this research, we address Darcy flow problems with random permeability using the conjugate gradient method, enhanced by a two-grid precondit
Externí odkaz:
http://arxiv.org/abs/2410.06832
Spatial orientation is essential for people to effectively navigate and interact with the environment in everyday life. With age-related cognitive decline, providing VR locomotion techniques with better spatial orientation performance for older adult
Externí odkaz:
http://arxiv.org/abs/2407.06846
Autor:
Liu, Yucheng, Li, Xiaodong
We investigate how to select the number of communities for weighted networks without a full likelihood modeling. First, we propose a novel weighted degree-corrected stochastic block model (DCSBM), in which the mean adjacency matrix is modeled as the
Externí odkaz:
http://arxiv.org/abs/2406.05340
We consider the Ising model on a $d$-dimensional discrete torus of volume $r^d$, in dimensions $d>4$ and for large $r$, in the vicinity of the infinite-volume critical point $\beta_c$. We prove that for $\beta=\beta_c- {\rm const}\, r^{-d/2}$ (with a
Externí odkaz:
http://arxiv.org/abs/2405.17353
In this paper, we apply the theory of Bridgeland stability conditions, which was originated from string theory, to study the derived category of coherent sheaves on Fargues--Fontaine curves. This leads us to consider the quasi-coherent sheaves $\math
Externí odkaz:
http://arxiv.org/abs/2404.04551
Autor:
Liu, Yucheng
We prove a sufficient condition for the two-point function of a statistical mechanical model on $\mathbb{Z}^d$, $d > 2$, to be bounded uniformly near a critical point by $|x|^{-(d-2)} \exp [ -c|x| / \xi ]$, where $\xi$ is the correlation length. The
Externí odkaz:
http://arxiv.org/abs/2310.17321
Autor:
Liu, Yucheng, Slade, Gordon
We present a new proof of $|x|^{-(d-2)}$ decay of critical two-point functions for spread-out statistical mechanical models on $\mathbb{Z}^d$ above the upper critical dimension, based on the lace expansion and assuming appropriate diagrammatic estima
Externí odkaz:
http://arxiv.org/abs/2310.07640
Autor:
Liu, Yucheng, Slade, Gordon
We give conditions on a real-valued function $F$ on $\mathbb{Z}^d$, for $d>2$, which ensure that the solution $G$ to the convolution equation $(F*G)(x) = \delta_{0,x}$ has Gaussian decay $|x|^{-(d-2)}$ for large $|x|$. Precursors of our results were
Externí odkaz:
http://arxiv.org/abs/2310.07635