Double martingale structure and existence of φ-moments for weighted branching processes

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PageRank in scale-free random graphs

We analyze the distribution of PageRank on a directed configuration model and show that as the size of the graph grows to infinity it can be closely approximated by the PageRank of the root node of an appropriately constructed tree. This tree approximation is in turn related to the solution of a linear stochastic fixed point equation that has been thoroughly studied in the recent literature

Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices

Given a sequence $(M_{n},Q_{n})_{n\ge 1}$ of i.i.d.\ random variables with generic copy $(M,Q) \in GL(d, \R) \times \R^d$, we consider the random difference equation (RDE) $$R_{n}=M_{n}R_{n-1}+Q_{n},$$ $n\ge 1$, and assume the existence of $\kappa >0$ such that \lim_{n \to \infty}(\E{\norm{M_1 ... M_n}^\kappa})^{\frac{1}{n}} = 1 . We prove, under suitable assumptions, that the sequence $S_n = R_1 + ... + R_n$, appropriately normalized, converges in law to a multidimensional stable distribution with index $\kappa$. As a by-product, we show that the unique stationary solution $R$ of the RDE is regularly varying with index $\kappa$, and give a precise description of its tail measure. This extends the prior work http://arxiv.org/abs/1009.1728v3 .Comment: 15 page

The COMET-L3 experiment on long-term melt - concrete interaction and cooling by surface flooding

民族生态审美叙事的关键是科技隐喻与民族生态隐喻交合互动 ,它在正义性原则指导下可保证民族生存与文化具有可持续生存指标 ,一种吸收变革而不丧失认同性活力的能指 ,从而使人与自然及民族间的交往灵活地进行。进而 ,在科技隐喻与民族生态隐喻等“多重隐喻”的功能交合辐射的过程中 ,人类超越自身而形成把握实在意义的方式与前景 ,最终形成对科技导致的生态危机与民族冲突的超越

Computer tomographic investigation of subcutaneous adipose tissue as an indicator of body composition

<p>Abstract</p> <p>Background</p> <p>Modern computer tomography (CT) equipment can be used to acquire whole-body data from large animals such as pigs in minutes or less. In some circumstances, computer assisted analysis of the resulting image data can identify and measure anatomical features. The thickness of subcutaneous adipose tissue at a specific site measured by ultrasound, is used in the pig industry to assess adiposity and inform management decisions that have an impact on reproduction, food conversion performance and sow longevity. The measurement site, called "P2", is used throughout the industry. We propose that CT can be used to measure subcutaneous adipose tissue thickness and identify novel measurement sites that can be used as predictors of general adiposity.</p> <p>Methods</p> <p>Growing pigs (<it>N </it>= 12), were each CT scanned on three occasions. From these data the total volume of adipose tissue was determined and expressed as a proportion of total volume (fat-index). A computer algorithm was used to determined 10,201 subcutaneous adipose thickness measurements in each pig for each scan. From these data, sites were selected where correlation with fat-index was optimal.</p> <p>Results</p> <p>Image analysis correctly identified the limits of the relevant tissues and automated measurements were successfully generated. Two sites on the animal were identified where there was optimal correlation with fat-index. The first of these was located 4 intercostal spaces cranial to the caudal extremity of the last rib, the other, a further 5 intercostal spaces cranially.</p> <p>Conclusion</p> <p>The approach to image analysis reported permits the creation of various maps showing adipose thickness or correlation of thickness with other variables by location on the surface of the pig. The method identified novel adipose thickness measurement positions that are superior (as predictors of adiposity) to the site which is in current use. A similar approach could be used in other situations to quantify potential links between subcutaneous adiposity and disease or production traits.</p

A new view of electrochemistry at highly oriented pyrolytic graphite

Major new insights on electrochemical processes at graphite electrodes are reported, following extensive investigations of two of the most studied redox couples, Fe(CN)64–/3– and Ru(NH3)63+/2+. Experiments have been carried out on five different grades of highly oriented pyrolytic graphite (HOPG) that vary in step-edge height and surface coverage. Significantly, the same electrochemical characteristic is observed on all surfaces, independent of surface quality: initial cyclic voltammetry (CV) is close to reversible on freshly cleaved surfaces (>400 measurements for Fe(CN)64–/3– and >100 for Ru(NH3)63+/2+), in marked contrast to previous studies that have found very slow electron transfer (ET) kinetics, with an interpretation that ET only occurs at step edges. Significantly, high spatial resolution electrochemical imaging with scanning electrochemical cell microscopy, on the highest quality mechanically cleaved HOPG, demonstrates definitively that the pristine basal surface supports fast ET, and that ET is not confined to step edges. However, the history of the HOPG surface strongly influences the electrochemical behavior. Thus, Fe(CN)64–/3– shows markedly diminished ET kinetics with either extended exposure of the HOPG surface to the ambient environment or repeated CV measurements. In situ atomic force microscopy (AFM) reveals that the deterioration in apparent ET kinetics is coupled with the deposition of material on the HOPG electrode, while conducting-AFM highlights that, after cleaving, the local surface conductivity of HOPG deteriorates significantly with time. These observations and new insights are not only important for graphite, but have significant implications for electrochemistry at related carbon materials such as graphene and carbon nanotubes