13,233 research outputs found
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
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