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Zheng Kuang

Publications and source records attributed to Zheng Kuang.

5 recordsLinked to original sources
arXiv2026

Near full groups of bounded type, \rom{2}

We give sufficient conditions for a group of bounded type to contain the AF alternating group. We axiomatize the containment process through alternating data, diagonal inheritance, propagation by selectors, and bounded absorption. We also isolate a class of fragmentations that produce selectors. As an application, we show that a fragmentation group of the modified Fabrykowski--Gupta group contains the AF alternating group, has absorption delay at most $2$, and has parity completion equal to its topological full group.

math.GR↗
arXiv2026

Near full groups of bounded type: full group completion

We study finitely generated groups of bounded type arising from tile inflation processes over Bratteli diagrams and containing the alternating group of the associated tail groupoid. Under a localization condition on finitely many singular germs, we show that the topological full group is obtained by adjoining finitely many finitary transformations. The number of adjoined transformations can be taken to be the dimension of a quotient of the mod-$2$ dimension group, and equality with the topological full group is characterized by surjectivity of the parity map restricted to the finitary elements of the original group. Under an additional parity condition on the AF truncations arising in the localization, the original group is near full, and its index is the order of the same parity quotient. We give a criterion for localization in terms of finitely many representatives of singular germs preserving arbitrarily deep cylinders, and an odd-order criterion which implies the parity condition. As an application, we study a fragmentation group of the modified LMS-group associated with the Penrose tiling and prove that it coincides with its topological full group.

math.GR↗
arXiv2025

Bizard: A Community-Driven Platform for Accelerating and Enhancing Biomedical Data Visualization

Biomedical research increasingly relies on heterogeneous, high-dimensional datasets, yet effective visualization remains hindered by fragmented code resources, steep programming barriers, and limited domain-specific guidance. Bizard is an open-source visualization code repository engineered to streamline data analysis in biomedical research. It aggregates a diverse array of executable visualization scripts, empowering researchers to select and tailor optimal graphical methods for their specific investigative demands. The platform features an intuitive interface equipped with sophisticated browsing and filtering capabilities, exhaustive tutorials, and interactive discussion forums that foster knowledge dissemination. Through its community-driven paradigm, Bizard promotes continual refinement and functional expansion, establishing itself as an essential resource for elevating biomedical data visualization and analytical standards. By harnessing Bizard's infrastructure, researchers can augment their visualization proficiency, propel methodological progress, and enhance interpretive rigor, ultimately accelerating precision medicine and personalized therapeutics. Bizard is freely accessible at https://openbiox.github.io/Bizard/.

q-bio.GN↗
arXiv2024

Growth of groups with incompressible elements, I

We define the class of groups of bounded type from tile inflations. These tile inflations also determine some automata describing the groups. In the case when the automata are stationary, we show that if the set of incompressible elements of a group in this class is finite, then this group has subexponential growth with a bounded power in the exponent. Then we describe some examples with certain special structures of orbital graphs and give explicit ways to find the upper bounds for the growth functions of these groups.

math.GR↗