A distributional study of the path edge-covering numbers for random trees

We study for various tree families the distribution of the number of edge-disjoint paths required to cover the edges of a random tree of size n. For all tree families considered we can show a central limit theorem with expectation ∼μn and variance ∼νn with constants μ, ν depending on the specific tree family.     

Degenerate Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic Oscillators

A stochastic variational inequality is proposed to model a white noise excited elasto-plastic oscillator. The solution of this inequality is essentially a continuous diffusion process for which a governing diffusion equation is obtained to study the evolution in time of its probability distribution. The diffusion equation is degenerate, but using the fact that the degeneracy occurs on a bounded region we are able to show the existence of a unique solution satisfying the desired properties. We prove the ergodic properties of the process and characterize the invariant measure. Our approach relies on extending Khasminskii’s method (Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, 1980), which in the present context leads to the study of degenerate Dirichlet problems with nonlocal boundary conditions. This research was partially supported by a grant from CEA, Commissariat à l’énergie atomique and by the National Science Foundation under grant DMS-0705247.     

随机算子的拓扑横截性

本文给出了横截的随机算子的定义并介绍了它的性质及其应用.     

Analysis of numerical limits in 2-D simulations of a ferromagnetic/antiferromagnetic interface using the random field Ising model

This paper explains the Random Field Ising Model simulations of a two-dimensional ferromagnetic/antiferromagnetic interface, influenced by the exchange-bias interaction. Exchange-biased shifts, coercivity fields, the number of unreversed spins as well as the numerical errors are provided. These were tested for different structure dimensions and boundary conditions in order to find limitations of the method. The algorithm developed is simple, very effective, and provides deeper insight into the nature of the exchange-bias phenomenon.     

基于二维真实隐马氏模型的手写体文字识别算法

近几年来，人们采用各种方法试图将1D隐马氏模型(HMM)^[2]推广到2D隐马氏模型。令人失望的是由于在建立合适的2D模型及其计算上的复杂度问题上存在困难，前面的尝试都没有得到一个真实的2DHMM．本文对于应用真实2D隐马氏模型(隐马氏网格随机场HMMRF)^[1,4]进行手写字符识别问题提出新的框架，针对文献[1]中的单点最优算法给出局部最优的译码算法。HMMRF模型是1D隐马氏模型到2D的扩展，能更好的描述字符的2D特性。HMMRF在字符识别中的应用具有两个相——学习相和译码相。在学习相和译码相中我们的最优标准是基于极大边缘后验概率的。不过，在涉及到2D模型中的计算问题时，对模型做出某些简单化的假设是必要的。本文用到的方法对于在合理的模型假设下解决手写字符识别问题呈现了很大的潜力。     

一类随机算子方程随机解的存在性

研究了一类随机算子方程的随机解，推广了几个重要的定理. 同时，得到了若干新的结果.      

CdTe and PbTe nanostructures on the oxidized pentagonal surface of an icosahedral AlPdMn quasicrystal

By means of congruent evaporation, we have deposited CdTe and PbTe onto the oxidized fivefold-symmetry surface of an icosahedral AlPdMn quasicrystal. This procedure results in the formation of nanocrystals in both cases. While the azimuthal orientations of the crystallites are random, the polar orientations are well defined. The crystalline CdTe and PbTe domains expose their (1 1 1) and (0 0 1) faces, respectively, which are aligned parallel to the pentagonal surface of the quasicrystal. The nanometric size of the domains is not a result of the lattice mismatch between the growing film and the substrate as usually observed in molecular-beam epitaxy, but of the limited size of the oxide domains of the substrate surface.     

Groupoids,von Neumann Algebras and the Integrated Density of States

We study spectral properties of random operators in the general setting of groupoids and von Neumann algebras. In particular, we establish an explicit formula for the canonical trace of the von Neumann algebra of random operators and define an abstract density of states. While the treatment applies to a general framework we lay special emphasis on three particular examples: random Schrödinger operators on manifolds, quantum percolation and quasi–crystal Hamiltonians. For these examples we show that the distribution function of the abstract density of states coincides with the integrated density of states defined via an exhaustion procedure.     

Kinetic-growth self-avoiding walks on small-world networks

Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz small-world networks, rewired from a two-dimensional square lattice. The maximum length L of this kind of walks is limited in regular lattices by an attrition effect, which gives finite values for its mean value 〈L 〉. For random networks, this mean attrition length 〈L 〉 scales as a power of the network size, and diverges in the thermodynamic limit (system size N ↦∞). For small-world networks, we find a behavior that interpolates between those corresponding to regular lattices and randon networks, for rewiring probability p ranging from 0 to 1. For p < 1, the mean self-intersection and attrition length of kinetically-grown walks are finite. For p = 1, 〈L 〉 grows with system size as N^1/2, diverging in the thermodynamic limit. In this limit and close to p = 1, the mean attrition length diverges as (1-p)^-4. Results of approximate probabilistic calculations agree well with those derived from numerical simulations.     

Blocking effects in irreversible adsorption of linear macromolecules

A new variant of random sequential adsorption (RSA), namely random sequential ballistic adsorption (RSBA), is proposed to explore the possible role of blocking effects in the adsorption dynamics of ballistically arriving objects. These objects upon adsorption can protrude outside the substrate and in turn can obstruct and hence reject the adsorption of newly arriving objects. Adsorption of linear macromolecules (modeled as infinitesimally thin needles), on a two-dimensional continuum substrate is studied using RSBA model. It is shown analytically that in late time regime, the number n(t) of adsorbed objects at time t follows a power law n(t) ∼ t^α, as in RSA, but with a different exponent, α = 2/3. Computer simulations are also carried out. The simulation results are found to be in close agreement with the analytical results. The exponent behavior for real experimental conditions is also analyzed.