Entropy of the Schwarzschild-de Sitter Black Hole due to arbitrary spin fields in different Coordinates

By using the Newman-Penrose formalism and the improved thin-layer ``brick wall'' approach, the statistical-mechanical entropies of the Schwarzschild-de Sitter black hole arising from quantum massless arbitrary spin fields are studied in the Painlev\'e and Lemaitre coordinates. Although the metrics in both the Painlev\'e and the Lemaitre coordinates do not obviously possess the singularities as that in the Schwarzschild-like coordinate, we find that, for arbitrary spin fields, the entropies in the Painlev\'e and Lemaitre coordinates are exactly equivalent to that in the Schwarzschild-like coordinate.Comment: 14 pages, no figure, to be published in JHE

Weak convergence of Vervaat and Vervaat Error processes of long-range dependent sequences

Following Cs\"{o}rg\H{o}, Szyszkowicz and Wang (Ann. Statist. {\bf 34}, (2006), 1013--1044) we consider a long range dependent linear sequence. We prove weak convergence of the uniform Vervaat and the uniform Vervaat error processes, extending their results to distributions with unbounded support and removing normality assumption

An Empirical Process Central Limit Theorem for Multidimensional Dependent Data

Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$, under which weak convergence of $(U_n(t))_{t\in\R^d}$ can be proved. This is particularly useful when dealing with data arising from dynamical systems or functional of Markov chains. This result improves those of [DDV09] and [DD11], where the technique was first introduced, and provides new applications.Comment: to appear in Journal of Theoretical Probabilit

Modelling the Linkage Between Landscape Metrics and Water Quality Indices of Hydrological Units in Sihu Basin, Hubei Province, China: An Allometric Model

AbstractStudying quantitative relationships between landscape pattern and water quality is a fundamental step to assess the impacts of non-point source pollution. Many hydrological models with multi-functionality have been developed as useful tools to study several key mechanisms in non-point source pollution. In landscape ecological studies, however, the empirical modelling approaches have been dominated with emphasis on the relationships between the landscape metrics and water quality indices. The main techniques for developing those models of landscape-water quality are statistical regression analysis based on linear models. In this article, Allometric models and the traditional multiple linear regression models for estimating the linkage between landscape metrics and water quality were tested in Sihu Basin, Hubei Province, China. The models at patch class level were established in 24 hydrological units of the basin, which took nine water quality indices (EC, pH, SS, DO, COD, TN, TP, NO3--N, NH4+-N) as the dependent variables and eighteen landscape metrics calculated in FRAGSTATS 3.3 as independent variables. The results suggested that, compared with the traditional multiple linear regression models, Allometric models were more suitable for SS, DO, TP, TN, NH4+-N, in which landscape pattern metrics could explain the 80.5%, 77.7%, 58.2%, 43.9%, 67.6% of total variation, respectively. There had little difference between multiple linear regression models and Allometric models for EC and NO3--N. The coefficients of determination in Allometric models were not as strong as that obtained in the multiple linear regression models for pH and COD. The above results indicated that using Allometric model may potentially provide a new way to study the linkage between landscape metrics and water quality indices, which will help protect our regional water resources

Reduction principles for quantile and Bahadur-Kiefer processes of long-range dependent linear sequences

In this paper we consider quantile and Bahadur-Kiefer processes for long range dependent linear sequences. These processes, unlike in previous studies, are considered on the whole interval $(0,1)$. As it is well-known, quantile processes can have very erratic behavior on the tails. We overcome this problem by considering these processes with appropriate weight functions. In this way we conclude strong approximations that yield some remarkable phenomena that are not shared with i.i.d. sequences, including weak convergence of the Bahadur-Kiefer processes, a different pointwise behavior of the general and uniform Bahadur-Kiefer processes, and a somewhat "strange" behavior of the general quantile process.Comment: Preprint. The final version will appear in Probability Theory and Related Field

Morphology and Orientation Selection of Non-Metallic Inclusions in Electrified Molten Metal

The effect of electric current on morphology and orientation selection of non-metallic inclusions in molten metal has been investigated using theoretical modelling and numerical calculation. Two geometric factors, namely the circularity (fc) and alignment ratio (fe) were introduced to describe the inclusions shape and configuration. Electric current free energy was calculated and the values were used to determine the thermodynamic preference between different microstructures. Electric current promotes the development of inclusion along the current direction by either expatiating directional growth or enhancing directional agglomeration. Reconfiguration of the inclusions to reduce the system electric resistance drives the phenomena. The morphology and orientation selection follows the routine to reduce electric free energy. The numerical results are in agreement with our experimental observations

Retromer binds the FANSHY sorting motif in SorLA to regulate amyloid precursor protein sorting and processing

sorLA is a sorting receptor for amyloid precursor protein (APP) genetically linked to Alzheimer's disease (AD). Retromer, an adaptor complex in the endosome-to-Golgi retrieval pathway, has been implicated in APP transport because retromer deficiency leads to aberrant APP sorting and processing and levels of retromer proteins are altered in AD. Here we report that sorLA and retromer functionally interact in neurons to control trafficking and amyloidogenic processing of APP. We have identified a sequence (FANSHY) in the cytoplasmic domain of sorLA that is recognized by the VPS26 subunit of the retromer complex. Accordingly, we characterized the interaction between the retromer complex and sorLA and determined the role of retromer on sorLA-dependent sorting and processing of APP. Mutations in the VPS26 binding site resulted in receptor redistribution to the endosomal network, similar to the situation seen in cells with VPS26 knockdown. The sorLA mutant retained APP-binding activity but, as opposed to the wild-type receptor, misdirected APP into a distinct non-Golgi compartment, resulting in increased amyloid processing. In conclusion, our data provide a molecular link between reduced retromer expression and increased amyloidogenesis as seen in patients with sporadic AD

Possible origins of macroscopic left-right asymmetry in organisms

I consider the microscopic mechanisms by which a particular left-right (L/R) asymmetry is generated at the organism level from the microscopic handedness of cytoskeletal molecules. In light of a fundamental symmetry principle, the typical pattern-formation mechanisms of diffusion plus regulation cannot implement the "right-hand rule"; at the microscopic level, the cell's cytoskeleton of chiral filaments seems always to be involved, usually in collective states driven by polymerization forces or molecular motors. It seems particularly easy for handedness to emerge in a shear or rotation in the background of an effectively two-dimensional system, such as the cell membrane or a layer of cells, as this requires no pre-existing axis apart from the layer normal. I detail a scenario involving actin/myosin layers in snails and in C. elegans, and also one about the microtubule layer in plant cells. I also survey the other examples that I am aware of, such as the emergence of handedness such as the emergence of handedness in neurons, in eukaryote cell motility, and in non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue. Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec

AR and MA representation of partial autocorrelation functions, with applications

We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.Comment: Published in Probability Theory and Related Field

Equation of state and phonon frequency calculations of diamond at high pressures

The pressure-volume relationship and the zone-center optical phonon frequency of cubic diamond at pressures up to 600 GPa have been calculated based on Density Functional Theory within the Local Density Approximation and the Generalized Gradient Approximation. Three different approaches, viz. a pseudopotential method applied in the basis of plane waves, an all-electron method relying on Augmented Plane Waves plus Local Orbitals, and an intermediate approach implemented in the basis of Projector Augmented Waves have been used. All these methods and approximations yield consistent results for the pressure derivative of the bulk modulus and the volume dependence of the mode Grueneisen parameter of diamond. The results are at variance with recent precise measurements up to 140 GPa. Possible implications for the experimental pressure determination based on the ruby luminescence method are discussed.Comment: 10 pages, 6 figure