Approximating schedules for dynamic process graphs efficiently

A model for parallel and distributed programs, the dynamic process graph (DPG), is investigated under graph-theoretic and complexity aspects. Such graphs embed constructors for parallel programs, synchronization mechanisms as well as conditional branches. They are capable of representing all possible executions of a parallel or distributed program in a very compact way. The size of this representation can be as small as logarithmic with respect to the size of any execution of the program.

In a preceding paper [A. Jakoby, et al., Scheduling dynamic graphs, in: Proc. 16th Symposium on Theoretical Aspects in Computer Science STACS'99, LNCS, vol. 1563, Springer, 1999, pp. 383–392] we have analysed the expressive power of the general model and various variants of it. We have considered the scheduling problem for DPGs given enough parallelism taking into account communication delays between processors when exchanging data. Given a DPG the question arises whether it can be executed (that means whether the corresponding parallel program has been specified correctly), and what is its minimum schedule length.

In this paper we study a subclass of dynamic process graphs called -output DPGs, which are appropriate in many situations, and investigate their expressive power. In a previous paper we have shown that the problem to determine the minimum schedule length is still intractable for this subclass, namely this problem is -complete as is the general case. Here we will investigate structural properties of the executions of such graphs. A natural graph-theoretic conjecture that executions must always split into components that are isomorphic to subgraphs turns out to be wrong. We are able to prove a weaker property. This implies a quadratic upper bound on the schedule length that may be necessary in the worst case, in contrast to the general case, where the optimal schedule length may be exponential with respect to the size of the representing DPG. Making this bound constructive, we obtain an approximation to a -complete problem. Computing such a schedule and then executing the program can be done on a parallel machine in polynomial time in a highly distributive fashion.     

Multi-point Taylor expansions of analytic functions

Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obtaining Laurent expansions in several points as well as Taylor-Laurent expansions.

     

Gd2O3:Eu纳米晶的制备及其光谱性质研究

以EDTA为络合剂，聚乙二醇为有机分散剂，用络合溶胶—凝胶法制备出Gd2O3:Eu纳米晶。用XRD，SEM，X—射线能量色散谱仪(EDS)，荧光分光光度计等分析手段对Gd2O3:Eu的纳米晶结构、形貌、组分的均匀性以及发光特性进行了研究。结果表明：EDTA—M凝胶仅在800℃焙烧即可得到颗粒细小、组分均匀、纯立方相的Gd2O3:Eu纳米晶，颗粒基本呈球形，粒径为30nm左右。对样品的激发光谱、发射光谱测定表明：Gd2O3:Eu纳米晶在269nm光激发下发红光，发射光谱谱峰在611nm，与体材料基本相同；激发光谱中电荷迁移带(CTB)明显红移，从体材料的255nm移至269nm，移动了约14nm；猝灭浓度从体材料的6％提高到8％。     

The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process

In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф（r） = r^N-d/α （log log l/r）d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general （N, d, α） strictly stable processes.     

Unique continuation along curves and hypersurfaces for second order anisotropic hyperbolic systems with real analytic coefficients

In this paper we prove the following kind of unique continuation property. That is, the zero on each geodesic of the solution in a real analytic hypersurface for second order anisotropic hyperbolic systems with real analytic coefficients can be continued along this curve.

     

A risk model driven by Lévy processes

We present a general risk model where the aggregate claims, as well as the premium function, evolve by jumps. This is achieved by incorporating a Lévy process into the model. This seeks to account for the discrete nature of claims and asset prices. We give several explicit examples of Lévy processes that can be used to drive a risk model. This allows us to incorporate aggregate claims and premium fluctuations in the same process. We discuss important features of such processes and their relevance to risk modeling. We also extend classical results on ruin probabilities to this model. Copyright © 2003 John Wiley & Sons, Ltd.     

The Asymmetric Avalanche Process

An asymmetric stochastic process describing the avalanche dynamics on a ring is proposed. A general kinetic equation which incorporates the exclusion and avalanche processes is considered. The Bethe ansatz method is used to calculate the generating function for the total distance covered by all particles. It gives the average velocity of particles which exhibits a phase transition from an intermittent to continuous flow. We calculated also higher cumulants and the large deviation function for the particle flow. The latter has the universal form obtained earlier for the asymmetric exclusion process and conjectured to be common for all models of the Kardar–Parisi–Zhang universality class.     

酵母蛋白质网络的动力学性质

蛋白质-蛋白质、蛋白质-DNA相互作用网络决定了细胞中各种关键功能的执行．基于芽殖酵母(budding yeast saccharomyces cerevisiae)的蛋白质-蛋白质相互作用网络数据和相关的实验文献，我们建立了调控细胞周期和生命周期(cell cycle and life cycle)的蛋白质网络，并利用离散模型研究了该网络的动力学性质，研究表明：细胞周期网络的动力学性质具有很强的稳定性，约94％的蛋白质初态将演化到对应于生物学G1基态的稳定态，使其成为惟一的全局吸引点；同时，绝大多数的初态的演化路径都通过由G1激发态到G1基态的细胞周期演化路径，使细胞周期路径成为全局性的“吸引”路径。     

Liminf results on the increments of an (N,d)-Gaussian process

We establish some liminf theorems on the increments of a (N,d)-Gaussian process with the usual Euclidean norm, via estimating upper bounds of large deviation probabilities on the suprema of the (N,d)-Gaussian process. This revised version was published online in June 2006 with corrections to the Cover Date.     

A theoretical analysis of the TiO2/Sn doped (1 1 0) surface properties

We have used the periodic quantum-mechanical method with density functional theory at the B3LYP level in order to study TiO₂/Sn doped (1 1 0) surfaces and have investigated the structural, electronic and energy band properties of these oxides. Our calculated relaxation directions for TiO₂ is the experimental one and is also in agreement with other theoretical results. We also observe for the doped systems relaxation of lattice positions of the atoms. Modification of Sn, O and Ti charges depend on the planes and positions of the substituted atoms. Doping can modify the Fermi levels, energy gaps as well as the localization and composition of both valence and conduction band main components. Doping can also modify the chemical, electronic and optical properties of these oxides surfaces increasing their suitability for use as gas sensors and optoelectronic devices.