arXiv subjects
Publications and source records attributed to Meng Wu.
In this paper, we study the multiple ergodic averages of a locally constant real-valued function in linear Cookie-Cutter dynamical systems. The multifractal spectrum of these multiple ergodic averages is completely determined.
Model-based iterative reconstruction (MBIR) techniques have demonstrated many advantages in X-ray CT image reconstruction. The MBIR approach is often modeled as a convex optimization problem including a data fitting function and a penalty function. The tuning parameter value that regulates the strength of the penalty function is critical for achieving good reconstruction results but difficult to choose. In this work, we describe two path seeking algorithms that are capable of efficiently generating a series of MBIR images with different strengths of the penalty function. The root-mean-squared-differences of the proposed path seeking algorithms are below 4 HU throughout the entire reconstruction path. With the efficient path seeking algorithm, we suggest a path-based iterative reconstruction (PBIR) to obtain complete information from the scanned data and reconstruction model.
We prove that for random affine code tree fractals the affinity dimension is almost surely equal to the unique zero of the pressure function. As a consequence, we show that the Hausdorff, packing and box counting dimensions of such systems are equal to the zero of the pressure. In particular, we do not presume the validity of the Falconer-Sloan condition or any other additional assumptions which have been essential in all the previously known results.
Finite element method (FEM) is one of the most important numerical methods in modern engineering design and analysis. Since traditional serial FEM is difficult to solve large FE problems efficiently and accurately, high-performance parallel FEM has become one of the essential way to solve practical engineering problems. Based on MiniFE program, which is released by National Energy Research Scientific Computing Center(NERSC), this work analyzes concrete steps, key computing pattern and parallel mechanism of parallel FEM. According to experimental results, this work analyzes the proportion of calculation amount of each module and concludes the main performance bottleneck of the program. Based on that, we optimize the MiniFE program on a server platform. The optimization focuses on the bottleneck of the program - SpMV kernel, and uses an efficient storage format named BCRS. Moreover, an improving plan of hybrid MPI+OpenMP programming is provided. Experimental results show that the optimized program performs better in both SpMV kernel and synchronization. It can increase the performance of the program, on average, by 8.31%. Keywords : finite element, parallel, MiniFE, SpMV, performance optimization
The characterization and applications of topological insulators depend critically on their protected surface states, which, however, can be obscured by the presence of trivial dangling bond states. Our first principle calculations show that this is the case for the pristine $(111)$ surface of SnTe. Yet, the predicted surface states unfold when the dangling bond states are passivated in proper chemisorption. We further extract the anisotropic Fermi velocities, penetration lengths and anisotropic spin textures of the unfolded $\barΓ$- and $\bar M$-surface states, which are consistent with the theory in http://dx.doi.org/10.1103/PhysRevB.86.081303 Phys. Rev. B 86, 081303 (R). More importantly, this chemisorption scheme provides an external control of the relative energies of different Dirac nodes, which is particularly desirable in multi-valley transport.
Quantum transport measurements including the Altshuler-Aronov-Spivak (AAS) and Aharonov-Bohm (AB) effects, universal conductance fluctuations (UCF), and weak anti-localization (WAL) have been carried out on epitaxial Bi thin films ($10-70$ bilayers) on Si(111). The results show that while the film interior is insulating all six surfaces of the Bi thin films are robustly metallic. We propose that these properties are the manifestation of a novel phenomenon, namely, a topologically trivial bulk system can become topologically non-trivial when it is made into a thin film. We stress that what's observed here is entirely different from the predicted 2D topological insulating state in a single bilayer Bi where only the four side surfaces should possess topologically protected gapless states.
In this paper we study the multiple ergodic averages $$ \frac{1}{n}\sum_{k=1}^n φ(x_k, x_{kq}, ..., x_{k q^{\ell-1}}), \qquad (x_n) \in Σ_m $$ on the symbolic space $Σ_m ={0, 1, ..., m-1}^{\mathbb{N}^*}$ where $m\ge 2, \ell\ge 2, q\ge 2$ are integers. We give a complete solution to the problem of multifractal analysis of the limit of the above multiple ergodic averages. Actually we develop a non-invariant and non-linear version of thermodynamic formalism that is of its own interest. We study a large class of measures (called telescopic measures) and the special case of telescopic measures defined by the fixed points of some non-linear transfer operators plays a crucial role in studying our multiplicatively invariant sets. These measures share many properties with Gibbs measures in the classical thermodynamic formalism. Our work also concerns with variational principle, pressure function and Legendre transform in this new setting.
Let $(X, T)$ be a topological dynamical system and let $Φ: X^r \to \mathbb{R}$ be a continuous function on the product space $X^r= X\times ... \times X$ ($r\ge 1$). We are interested in the limit of V-statistics taking $Φ$ as kernel: [\lim_{n\to \infty} n^{-r}\sum_{1\le i_1, ..., i_r\le n} Φ(T^{i_1}x, ..., T^{i_r} x).] The multifractal spectrum of topological entropy of the above limit is expressed by a variational principle when the system satisfies the specification property. Unlike the classical case ($r=1$) where the spectrum is an analytic function when $Φ$ is Hölder continuous, the spectrum of the limit of higher order V-statistics ($r\ge 2$) may be discontinuous even for very nice kernel $Φ$.
This paper discusses the dimension of spline spaces with highest order smoothness over hierarchical T-meshes over certain type of hierarchical T-meshes. The major step is to set up a bijection between the spline space with highest order smoothness over a hierarchical T-mesh and a univariate spline space whose definition depends on the l-edges of the extended T-mesh. We decompose the univariate spline space into direct sums in the sense of isomorphism using the theory of the short exact sequence in homological algebra. According to the decomposition of the univariate spline space, the dimension formula of the spline space with highest order smoothness over certain type of hierarchical T-mesh is presented. A set of basis functions of the spline space is also constructed.
In this paper we present a complete solution to the problem of multifractal analysis of multiple ergodic averages in the case of symbolic dynamics for functions of two variables depending on the first coordinate.