arXiv subjects

Jiawen Zhang

Publications and source records attributed to Jiawen Zhang.

120 records · Page 7Linked to original sources

arXiv2020

Quasi-local Algebras and Asymptotic Expanders

In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic expanders. We show that being a sequence of asymptotic expanders is a coarse property under certain connectedness condition, and it implies non-uniformly local amenability. Moreover, we also analyse some $C^*$-algebraic properties of uniform quasi-local algebras. In particular, we show that a uniform quasi-local algebra is nuclear if and only if the underlying metric space has Property A.

math.OA↗

arXiv2019

Limit operator theory for groupoids

We extend the symbol calculus and study the limit operator theory for $σ$-compact, étale and amenable groupoids, in the Hilbert space case. This approach not only unifies various existing results which include the cases of exact groups and discrete metric spaces with Property A, but also establish new limit operator theories for group/groupoid actions and uniform Roe algebras of groupoids. In the process, we extend a monumental result by Exel, Nistor and Prudhon, showing that the invertibility of an element in the groupoid $C^*$-algebra of a $σ$-compact amenable groupoid with a Haar system is equivalent to the invertibility of its images under regular representations.

math.OA↗

arXiv2019

A quasi-local characterisation of $L^p$-Roe algebras

Very recently, Špakula and Tikuisis provide a new characterisation of (uniform) Roe algebras via quasi-locality when the underlying metric spaces have straight finite decomposition complexity. In this paper, we improve their method to deal with the $L^p$-version of (uniform) Roe algebras for any $p\in [1,\infty)$. Due to the lack of reflexivity on $L^1$-spaces, some extra work is required for the case of $p=1$.

math.FA↗

arXiv2018

Quasi-Locality and Property A

Let $X$ be a metric space with bounded geometry, $p\in\{0\} \cup [1,\infty]$, and let $E$ be a Banach space. The main result of this paper is that either if $X$ has Yu's Property A and $p\in(1,\infty)$, or without any condition on $X$ when $p\in\{0,1,\infty\}$, then quasi-local operators on $\ell^p(X,E)$ belong to (the appropriate variant of) Roe algebra of $X$. This generalises the existing results of this type by Lange and Rabinovich, Engel, Tikuisis and the first author, and Li, Wang and the second author. As consequences, we obtain that uniform $\ell^p$-Roe algebras (of spaces with Property A) are closed under taking inverses, and another condition characterising Property A, akin to operator norm localisation for quasi-local operators.

math.FA↗

arXiv2018

Extreme cases of limit operator theory on metric spaces

The theory of limit operators was developed by Rabinovich, Roch and Silbermann to study the Fredholmness of band-dominated operators on $\ell^p(\mathbb{Z}^N)$ for $p \in \{0\} \cup [1,\infty]$, and recently generalised to discrete metric spaces with property A by Špakula and Willett for $p \in (1,\infty)$. In this paper, we study the remained extreme cases of $p \in\{0,1,\infty\}$ (in the metric setting) to fill the gaps.

math.FA↗

arXiv2018

Big enterprise registration data imputation: Supporting spatiotemporal analysis of industries in China

Big, fine-grained enterprise registration data that includes time and location information enables us to quantitatively analyze, visualize, and understand the patterns of industries at multiple scales across time and space. However, data quality issues like incompleteness and ambiguity, hinder such analysis and application. These issues become more challenging when the volume of data is immense and constantly growing. High Performance Computing (HPC) frameworks can tackle big data computational issues, but few studies have systematically investigated imputation methods for enterprise registration data in this type of computing environment. In this paper, we propose a big data imputation workflow based on Apache Spark as well as a bare-metal computing cluster, to impute enterprise registration data. We integrated external data sources, employed Natural Language Processing (NLP), and compared several machine-learning methods to address incompleteness and ambiguity problems found in enterprise registration data. Experimental results illustrate the feasibility, efficiency, and scalability of the proposed HPC-based imputation framework, which also provides a reference for other big georeferenced text data processing. Using these imputation results, we visualize and briefly discuss the spatiotemporal distribution of industries in China, demonstrating the potential applications of such data when quality issues are resolved.

cs.CY↗

arXiv2018

A four point characterisation for coarse median spaces

Coarse median spaces simultaneously generalise the classes of hyperbolic spaces and median algebras, and arise naturally in the study of the mapping class groups and many other contexts. One issue with their definition as originally conceived by Bowditch is the need to establish median approximations for all finite subsets of the space, an approach which allowed the definition of rank (a proxy for dimension) in terms of the dimensions of the approximating spaces. Here we provide a simplification of the definition in terms of a $4$-point condition analogous to the $4$-point condition defining hyperbolicity. We show how to define rank in this context, and use this to give a direct proof that rank $1$ geodesic coarse median spaces are $δ$-hyperbolic, bypassing Bowditch's use of asymptotic cones. A key ingredient of the proof is a new definition of intervals in coarse median spaces and an analysis of their interaction with geodesics.

math.MG↗

arXiv2017

A characterization for asymptotic dimension growth

We give a characterization for asymptotic dimension growth. We apply it to CAT(0) cube complexes of finite dimension, giving an alternative proof of N. Wright's result on their finite asymptotic dimension. We also apply our new characterization to geodesic coarse median spaces of finite rank and establish that they have subexponential asymptotic dimension growth. This strengthens a recent result of J. Spakula and N. Wright.

math.MG↗

arXiv2015

Equi-variant and Stable Finite Decomposition Complexity

In this paper, we introduce and study various kinds of decomposition complexity. First, we give a characterization of residually finite groups having finite decomposition complexity (FDC). Secondly, we introduce equi-variant straight FDC (sFDC), and prove that a group having equi-variant sFDC if and only if its box space having sFDC. Finally, we show that elementary amenable groups have equi-variant sFDC by introducing something called stable FDC.

math.GT↗

arXiv2015

Large scale properties for bounded automata groups

In this paper, we study some large scale properties of the mother groups of bounded automata groups. First we give two methods to prove every mother group has infinite asymptotic dimension. Then we study the decomposition complexity of certain subgroup in the mother group. We prove the subgroup belongs to $\mathcal{D}_ω$.

math.GR↗

arXiv2013

Manual Calibration System for Daya Bay Reactor Neutrino Experiment

The Daya Bay Reactor Neutrino Experiment has measured the last unknown neutrino mixing angle, θ13, to be non-zero at the 7.7σ level. This is the most precise measurement to θ13 to date. To further enhance the understanding of the response of the antineutrino detectors (ADs), a detailed calibration of an AD with the Manual Calibration System (MCS) was undertaken during the summer 2012 shutdown. The MCS is capable of placing a radioactive source with a positional accuracy of 25 mm in R direction, 20 mm in Z axis and 0.5° in Φ direction. A detailed description of the MCS is presented followed by a summary of its performance in the AD calibration run.

physics.ins-det↗

arXiv2010

Aging Study of RPC's for the SiD Hcal and Muon System

Preliminary test results on microscope investigation and BESIII-type RPC aging performance have revealed interesting aging phenomena that had not been seen before in Linseed oil coated Italian-type RPC. We report here on the aging performance of BESIII-type and its variant RPC, and on microscopic surface characterization of BESIII-type Bakelite electrodes.

physics.ins-det↗