7 papers
A three-dimensional corner configuration involving the Omega function
Zhuowen Guo, Rongzhong Xiao, Shuhao Zhang
Let denote the number of prime factors of , counted with multiplicity. We prove that if has positive upper Banach density, then there are $(x,y,z)\…
An affirmative answer to Owings's sumset question
Wen Huang, Zhengxing Lian, Song Shao +3
We give an affirmative answer to Owings's sumset question: for any -coloring of natural numbers, there is an infinite such that is monochromatic. Mo…
Positive Rokhlin Entropy Implies Infinite -Orbit Multiplicity: A Negative Answer to Thouvenot's Question
Zongrui Hu, Leiye Xu, Shuhao Zhang
We prove that every free ergodic measure-preserving action of a countably infinite amenable group with positive Rokhlin entropy has infinite complex -orbit multiplicity, both…
All-Atom GPCR-Ligand Simulation via Residual Isometric Latent Flow
Jiying Zhang, Shuhao Zhang, Pierre Vandergheynst +1
G-protein-coupled receptors (GPCRs), primary targets for over one-third of approved therapeutics, rely on intricate conformational transitions to transduce signals. While Molecular…
Fractal transference principles for subsets of of positive density
Zhuowen Guo, Kangbo Ouyang, Jiahao Qiu +1
We establish a multidimensional fractal transference principle for digit-restricted sets associated with subsets of , extending the one-dimensional framework of Nakaj…
Independence and mean sensitivity in minimal systems under group actions
Chunlin Liu, Leiye Xu, Shuhao Zhang
In this paper, we mainly study the relation between regularity, independence and mean sensitivity for minimal systems. In the first part, we show that if a minimal system is incont…