Atmospheric gamma rays in the energy region 40–1000 GeV

A large stack of lead-emulsion sandwich detector assembly was flown over Hyderabad, India. High energy gamma rays at the float altitude were unambiguously identified from the cascades they induced, and their energies reliably determined by improved methods. From an analysis of 163 gamma rays of energy ≳ 30 GeV, it is found that the differential energy spectrum is represented by the power lawJ _r (E)= 129·4E ^{−2·62±0·12} photons m⁻² sr⁻¹sec⁻¹ GeV⁻¹ at an effective atmospheric depth of 14·3 g cm⁻²; this is the first reliable balloon measurement of atmospheric gamma rays in the energy range 40–1000 GeV. After correcting for the gamma rays radiated by the primary cosmic ray electrons, the production spectrum of gamma rays, resulting from the collisions of cosmic ray nuclei with air nuclei, at the top of the atmosphere isP _r (E, 0)=8·2 × 10⁻⁴ E^2.60±0.09 photons g⁻¹sr⁻¹sec⁻¹ GeV⁻¹. The atmospheric propagation of the electromagnetic component due to the cascade process is also derived from the gamma ray production spectrum.     

Probability theory and polymer physics

This study applies the theory of stochastic processes to the equilibrium statistical physics of polymers in solution. The topics treated include random copolymers and randomly branching polymers, with self-consistent mean field effects. A new and more natural way of dealing with Boltzmann weighting is discussed, which makes it possible from the beginning of a calculation to consider only the physical polymer conformations. We also show that in general the random copolymer problem can be reduced to the ordinary polymer problem, and treat the self-consistent field problem for a general branching polymer.     

Kernel regression estimation for continuous spatial processes

We investigate here a kernel estimate of the spatial regression function r(x) = E(Y _u | X _u = x), x ∈ ℝ^d, of a stationary multidimensional spatial process { Z _u = (X _u, Y _u), u ∈ ℝ ^N }. The weak and strong consistency of the estimate is shown under sufficient conditions on the mixing coefficients and the bandwidth, when the process is observed over a rectangular domain of ℝ^N. Special attention is paid to achieve optimal and suroptimal strong rates of convergence. It is also shown that this suroptimal rate is preserved by using a suitable spatial sampling scheme.      

复合广义齐次Poisson过程的多险种破产概率

本文推广了经典的复合泊松风险模型，建立了两类复合广义齐次poisson过程的多险种破产模型．对于新模型，我们得到了初始资本为u的破产概率φ(u)的精确表达式以及特殊情况下φ(0)的表达式，并且导出了调节系数方程和调节系数R的上下界．     

基于组合权重的系统评价模型

提出了基于组合权重的系统评价新模型 ( CWSE) ,即 :直接根据评价指标样本数据集 ,用基于加速遗传算法的投影寻踪方法确定各评价指标的分类权重 ,用基于加速遗传算法的层次分析法确定各评价指标的排序权重 ,用加速遗传算法对各评价指标的分类权重和排序权重进行综合得到组合权重 ,然后以这些组合权重与各评价对象相应评价指标的标准化值进行加权平均 ,得到系统评价的综合指标值 ,据此可对各评价对象进行分类排序 .用 CW SE模型评价中国 30个区域 1995年开发度的结果表明 ,根据开发度的强弱可把这些区域分成 3个强开发区域、6个较强开发区域、10个中等开发区域和 11个弱开发区域 ;CWSE模型简便、通用 ,计算结果较为客观和稳定 ,为系统工程理论和实践提供了新的研究方法 .     

Bounds on absorption times of directionally biased random sequences

A sequence of random variables X₀,X₁, … with values in {0, 1, …, n} representing a general finite-state stochastic process with absorbing state 0 is said to be directionally biased towards 0, if, for all j > 0, ϵ_j: = inf_k>0 {j − E[X_k | X_k−1 = j]} > 0. For such sequences, let t be the expected value of the time to absorption at 0. For a fixed set of biases, the least upper bound for this time can be computed with an algorithm requiring O(n²) steps. Simple upper bounds are described. In particular, t ≤ E[b_x0], where b_i = Σ_j≤i 1/¯ϵ_j and ¯ϵ_j = min_l≥j {ϵ_l}. If all ϵ_j ≤ ϵ_{j + 1} (so ¯ϵ_j = ϵ_j) and ϵ_n < 1, this bound for t is the best possible. For certain finite stochastic processes which we term conditionally independent of X₀ = i, b(i) bounds the expected time given X₀ = i. Similar results are given for lower bounds. The results of this paper were designed to be a useful tool for determining rates of convergence of stochastic optimization algorithms. © 1996 John Wiley & Sons, Inc.     

The structure of alternative tableaux

In this paper we study alternative tableaux introduced by Viennot [X. Viennot, Alternative tableaux, permutations and partially asymmetric exclusion process, talk in Cambridge, 2008]. These tableaux are in simple bijection with permutation tableaux, defined previously by Postnikov [A. Postnikov, Total positivity, Grassmannians, and networks, arXiv:math/0609764v1 [math.CO], 2006].We exhibit a simple recursive structure for alternative tableaux, from which we can easily deduce a number of enumerative results. We also give bijections between these tableaux and certain classes of labeled trees. Finally, we exhibit a bijection with permutations, and relate it to some other bijections that already appeared in the literature.     

Bayesian modeling of financial returns: A relationship between volatility and trading volume

The modified mixture model with Markov switching volatility specification is introduced to analyze the relationship between stock return volatility and trading volume. We propose to construct an algorithm based on Markov chain Monte Carlo simulation methods to estimate all the parameters in the model using a Bayesian approach. The series of returns and trading volume of the British Petroleum stock will be analyzed. Copyright © 2009 John Wiley & Sons, Ltd.