Disjointness of M\"{o}bius from asymptotically periodic functions

In this paper, we investigate asymptotically periodic functions from the point of view of operator algebra and dynamical systems. To study the M\"{o}bius disjointness of these functions, we prove a general result on the averages of multiplicative functions in short arithmetic progressions. As an application, we show that Sarnak's M\"{o}bius Disjointness Conjecture holds for certain topological dynamical systems.Comment: 46 page

Directed Transmission Method, A Fully Asynchronous approach to Solve Sparse Linear Systems in Parallel

In this paper, we propose a new distributed algorithm, called Directed Transmission Method (DTM). DTM is a fully asynchronous and continuous-time iterative algorithm to solve SPD sparse linear system. As an architecture-aware algorithm, DTM could be freely running on all kinds of heterogeneous parallel computer. We proved that DTM is convergent by making use of the final-value theorem of Laplacian Transformation. Numerical experiments show that DTM is stable and efficient.Comment: v1: poster presented in SPAA'08; v2: full paper; v3: rename EVS to GNBT; v4: reuse EVS. More info, see my web page at http://weifei00.googlepages.co

Integral Points for Groups of Multiplicative Type

We construct a finite subgroup of Brauer-Manin obstruction for detecting the existence of integral points on integral models of homogeneous spaces of linear algebraic groups of multiplicative type. As application, the strong approximation theorem for linear algebraic groups of multiplicative type is established. Moreover, the sum of two integral squares over some quadratic fields is discussed.Comment: 18 pages,Advances in Mathematics (to appear

Integral Points for Multi-norm Tori

We construct a finite subgroup of Brauer-Manin obstruction for detecting the existence of integral points on integral models of principle homogeneous spaces of multi-norm tori. Several explicit examples are provided.Comment: 25 pages. This version is organized much different from the last on

Dynamic evolution of cross-correlations in the Chinese stock market

We study the dynamic evolution of cross-correlations in the Chinese stock market mainly based on the random matrix theory (RMT). The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving window with a size of 400 days. The evolutions of the statistical properties of the correlation coefficients, eigenvalues, and eigenvectors of the correlation matrices are carefully analyzed. We find that the stock correlations are significantly increased in the periods of two market crashes in 2001 and 2008, during which only five eigenvalues significantly deviate from the random correlation matrix, and the systemic risk is higher in these volatile periods than calm periods. By investigating the significant contributors of the deviating eigenvectors in different moving windows, we observe a dynamic evolution behavior in business sectors such as IT, electronics, and real estate, which lead the rise (drop) before (after) the crashes