The size of the giant high‐order component in random hypergraphs

The phase transition in the size of the giant component in random graphs is one of the most well‐studied phenomena in random graph theory. For hypergraphs, there are many possible generalizations of the notion of a connected component. We consider the following: two j‐sets (sets of j vertices) are j‐connected if there is a walk of edges between them such that two consecutive edges intersect in at least j vertices. A hypergraph is j‐connected if all j‐sets are pairwise j‐connected. In this paper, we determine the asymptotic size of the unique giant j‐connected component in random k‐uniform hypergraphs for any and .     

Noncommutative Dynamics of Random Operators

We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra А on a transformation groupoid Γ = E × G where E is the total space of a principal fibre bundle over spacetime, and G a suitable group acting on Γ . We show that every a ∊ А defines a random operator, and we study the dynamics of such operators. In the noncommutative regime, there is no usual time but, on the strength of the Tomita–Takesaki theorem, there exists a one-parameter group of automorphisms of the algebra А which can be used to define a state dependent dynamics; i.e., the pair (А, ϕ), where ϕ is a state on А, is a “dynamic object.” Only if certain additional conditions are satisfied, the Connes–Nikodym–Radon theorem can be applied and the dependence on ϕ disappears. In these cases, the usual unitary quantum mechanical evolution is recovered. We also notice that the same pair (А, ϕ) defines the so-called free probability calculus, as developed by Voiculescu and others, with the state ϕ playing the role of the noncommutative probability measure. This shows that in the noncommutative regime dynamics and probability are unified. This also explains probabilistic properties of the usual quantum mechanics.     

静态随机访问存储器型现场可编程门阵列辐照效应测试系统研制

在调研静态随机访问存储器型现场可编程门阵列(FPGA)器件空间辐照效应失效机理的基础上,详细论述FPGA辐照效应测试系统内部存储器测试、功能测试及功耗测试的实现原理,给出了系统的软硬件实现方法。所建立的系统可以测试FPGA器件的配置存储器翻转截面、块存储器翻转截面、功能失效截面、闭锁截面等多个参数,其长线传输距离达到50 m以上,最大可测门数达到了100万门,为FPGA辐照效应研究提供了测试平台。     

The ground state energy of the Edwards-Anderson spin glass model with a parallel tempering Monte Carlo algorithm

We study the efficiency of parallel tempering Monte Carlo technique for calculating true ground states of the Edwards-Anderson spin glass model. Bimodal and Gaussian bond distributions were considered in two- and three-dimensional lattices. By a systematic analysis we find a simple formula to estimate the values of the parameters needed in the algorithm to find the GS with a fixed average probability. We also study the performance of the algorithm for single samples, quantifying the difference between samples where the GS is hard, or easy, to find. The GS energies we obtain are in good agreement with the values found in the literature. Our results show that the performance of the parallel tempering technique is comparable to more powerful heuristics developed to find the ground state of Ising spin glass systems.     

Centrality of the collision and random matrix theory

I discuss the results from a study of the central 12CC collisions at 4.2 A GeV/c.The data have been analyzed using a new method based on the Random Matrix Theory.The simulation data coming from the Ultra Relativistic Quantum Molecular Dynamics code were used in the analyses.I found that the behavior of the nearest neighbor spacing distribution for the protons,neutrons and neutral pions depends critically on the multiplicity of secondary particles for simulated data.I conclude that the obtained results offer the possibility of fixing the centrality using the critical values of the multiplicity.     

Existence and uniqueness of path wise solutions for stochastic integral equations driven by Lévy noise on separable Banach spaces

The stochastic integrals of M- type 2 Banach valued random functions w.r.t. compensated Poisson random measures introduced in (Rüdiger, B., 2004, In: Stoch. Stoch. Rep., 76, 213–242.) are discussed for general random functions. These are used to solve stochastic integral equations driven by non Gaussian Lévy noise on such spaces. Existence and uniqueness of the path wise solutions are proven under local Lipshitz conditions for the drift and noise coefficients on M-type 2 as well as general separable Banach spaces. The continuous dependence of the solution on the initial data as well as on the drift and noise coefficients are shown. The Markov properties for the solutions are analyzed.     

Initial classification of joint data in EM estimation of latent class joint model

The latent class mixture-of-experts joint model is one of the important methods for jointly modelling longitudinal and recurrent events data when the underlying population is heterogeneous and there are nonnormally distributed outcomes. The maximum likelihood estimates of parameters in latent class joint model are generally obtained by the EM algorithm. The joint distances between subjects and initial classification of subjects under study are essential to finding good starting values of the EM algorithm through formulas. In this article, separate distances and joint distances of longitudinal markers and recurrent events are proposed for classification purposes, and performance of the initial classifications based on the proposed distances and random classification are compared in a simulation study and demonstrated in an example.     

制备软X光多层膜的转速控厚法

本文提出了一种新的监控软X光多层膜膜厚的方法——转速控厚法,利用这种方法镀制的设计周期厚度分别为8.4和10nm,周期数达50对和30对的W/C多层膜,经小角X光衍射测试,结果表明周期厚度随机误差在0.1nm左右。     

B值随机元阵列加权和的收敛性与大数定律

令｛Ｘｎｉ，１≤ｉ≤ｋｎ↑∞，ｎ≥１｝为Ｂ值随机元阵列，｛ａｎｉ，１≤ｉ≤ｋｎ，ｎ≥１｝为实数阵列．讨论加权和Ｓｎ＝ｋｎｉ＝１ａｎｉＸｎｉ，ｎ≥１的收敛性．在条件ｓｕｐｎ，ｉＰ（Ｘｎｉ＞ｘ）＝０（ｘ－ｒ）下给出了一些收敛性结果（１≤ｒ＜ｐ≤２），同时用这种收敛性刻划了Ｂａｎａｃｈ空间的ｐ型性质     

Ring-Opening Copolymerization of 2,2-Dimethyltrimethylene Carbonate and ε-Caprolactone Using Rare Earth Aryloxides Substituted by Various Alkyl Groups

A variety of single component rare earth aryloxides substituted by various alkyl groups [Ln(OAr)₃] such as methyl, isopropyl, tert‐butyl have been surveyed in the ring‐opening copolymerization of 2,2‐dimethyltrimethylene carbonate (DTC) and ε‐caprolactone (ε‐CL). It was worthwhile to note that activity of the catalyst varied with both the ligands' structure and the number of alkyl groups on phenyl ring. The stronger ability of electron‐donation of alkyl groups on phenyl ring, and the more numbers of alkyl groups on phenyl ring, the higher catalytic activity. The experimental results show that lanthanum tris(2,4,6‐tri‐tert‐butylphenolate) [La(OTTBP)₃] exhibits highest activity in all lanthanum aryloxides. ¹H NMR spectral data of copolymer obtained showed that the polymerization mechanism is in agreement with the coordination insertion mechanism.