Precise tail asymptotics of fixed points of the smoothing transform with general weights

We consider solutions of the stochastic equation $R=_d\sum_{i=1}^NA_iR_i+B$, where $N>1$ is a fixed constant, $A_i$ are independent, identically distributed random variables and $R_i$ are independent copies of $R$, which are independent both from $A_i$'s and $B$. The hypotheses ensuring existence of solutions are well known. Moreover under a number of assumptions the main being $\mathbb{E}|A_1|^{\alpha}=1/N$ and $\mathbb{E}|A_1|^{\alpha}\log|A_1|>0$, the limit $\lim_{t\to\infty}t^{\alpha}\mathbb{P}[|R|>t]=K$ exists. In the present paper, we prove positivity of $K$.Comment: Published at http://dx.doi.org/10.3150/13-BEJ576 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Large deviations for solutions to stochastic recurrence equations under Kesten's condition

In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten's condition [Acta Math. 131 (1973) 207-248] under which the solution of the stochastic recurrence equation has a marginal distribution with power law tails, while the noise sequence of the equations can have light tails. The results of the paper are analogs to those obtained by A. V. Nagaev [Theory Probab. Appl. 14 (1969) 51-64; 193-208] and S. V. Nagaev [Ann. Probab. 7 (1979) 745-789] in the case of partial sums of i.i.d. random variables. In the latter case, the large deviation probabilities of the partial sums are essentially determined by the largest step size of the partial sum. For the solution to a stochastic recurrence equation, the magnitude of the large deviation probabilities is again given by the tail of the maximum summand, but the exact asymptotic tail behavior is also influenced by clusters of extreme values, due to dependencies in the sequence. We apply the large deviation results to study the asymptotic behavior of the ruin probabilities in the model.Comment: Published in at http://dx.doi.org/10.1214/12-AOP782 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Characterization of a caleosin expressed during olive (Olea europaea L.) pollen ontogeny

<p>Abstract</p> <p>Background</p> <p>The olive tree is an oil-storing species, with pollen being the second most active site in storage lipid biosynthesis. Caleosins are proteins involved in storage lipid mobilization during seed germination. Despite the existence of different lipidic structures in the anther, there are no data regarding the presence of caleosins in this organ to date. The purpose of the present work was to characterize a caleosin expressed in the olive anther over different key stages of pollen ontogeny, as a first approach to unravel its biological function in reproduction.</p> <p>Results</p> <p>A 30 kDa caleosin was identified in the anther tissues by Western blot analysis. Using fluorescence and transmission electron microscopic immunolocalization methods, the protein was first localized in the tapetal cells at the free microspore stage. Caleosins were released to the anther locule and further deposited onto the sculptures of the pollen exine. As anthers developed, tapetal cells showed the presence of structures constituted by caleosin-containing lipid droplets closely packed and enclosed by ER-derived cisternae and vesicles. After tapetal cells lost their integrity, the caleosin-containing remnants of the tapetum filled the cavities of the mature pollen exine, forming the pollen coat. In developing microspores, this caleosin was initially detected on the exine sculptures. During pollen maturation, caleosin levels progressively increased in the vegetative cell, concurrently with the number of oil bodies. The olive pollen caleosin was able to bind calcium <it>in vitro</it>. Moreover, PEGylation experiments supported the structural conformation model suggested for caleosins from seed oil bodies.</p> <p>Conclusions</p> <p>In the olive anther, a caleosin is expressed in both the tapetal and germ line cells, with its synthesis independently regulated. The pollen oil body-associated caleosin is synthesized by the vegetative cell, whereas the protein located on the pollen exine and its coating has a sporophytic origin. The biological significance of the caleosin in the reproductive process in species possessing lipid-storing pollen might depend on its subcellular emplacement. The pollen inner caleosin may be involved in OB biogenesis during pollen maturation. The protein located on the outside might rather play a function in pollen-stigma interaction during pollen hydration and germination.</p

Maximizing the hyperpolarizability of one-dimensional systems

Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of conjugation, that could potentially be adjusted to improve the nonlinear-optical response. However, there were no conditions set on the optimized potential energy function to ensure that the resulting energies were consistent with what is observed in real molecules. Furthermore, the system was placed into a one-dimensional box with infinite walls, forcing the wavefunctions to vanish at the ends of the molecule. In the present work, the walls are separated by a distance much larger than the molecule's length; and, the variations of the potential energy function are restricted to levels that are more typical of a real molecule. In addition to being a more physically-reasonable model, our present approach better approximates the bound states and approximates the continuum states - which are usually ignored. We find that the same universal properties continue to be important for optimizing the nonlinear-optical response, though the details of the wavefunctions differ from previous result.Comment: 10 pages, 5 figure

Generalized Berreman's model of the elastic surface free energy of a nematic liquid crystal on a sawtoothed substrate

In this paper we present a generalization of Berreman's model for the elastic contribution to the surface free-energy density of a nematic liquid crystal in presence of a sawtooth substrate which favours homeotropic anchoring, as a function of the wavenumber of the surface structure $q$, the tilt angle $\alpha$ and the surface anchoring strength $w$. In addition to the previously reported non-analytic contribution proportional to $q\ln q$, due to the nucleation of disclination lines at the wedge bottoms and apexes of the substrate, the next-to-leading contribution is proportional to $q$ for a given substrate roughness, in agreement with Berreman's predictions. We characterise this term, finding that it has two contributions: the deviations of the nematic director field with respect to the corresponding to the isolated disclination lines, and their associated core free energies. Comparison with the results obtained from the Landau-de Gennes model shows that our model is quite accurate in the limit $wL>1$, when strong anchoring conditions are effectively achieved.Comment: 13 pages, 9 figures; revised version submitted to Phys. Rev.

Monocular, Real-Time Surface Reconstruction using Dynamic Level of Detail

We present a scalable, real-time capable method for robust surface reconstruction that explicitly handles multiple scales. As a monocular camera browses a scene, our algorithm processes images as they arrive and incrementally builds a detailed surface model. While most of the existing reconstruction approaches rely on volumetric or point-cloud representations of the environment, we perform depth-map and colour fusion directly into a multi-resolution triangular mesh that can be adaptively tessellated using the concept of Dynamic Level of Detail. Our method relies on least-squares optimisation, which enables a probabilistically sound and principled formulation of the fusion algorithm. We demonstrate that our method is capable of obtaining high quality, close-up reconstruction, as well as capturing overall scene geometry, while being memory and computationally efficient

Modelling Heat Transfer of Carbon Nanotubes

Modelling heat transfer of carbon nanotubes is important for the thermal management of nanotube-based composites and nanoelectronic device. By using a finite element method for three-dimensional anisotropic heat transfer, we have simulated the heat conduction and temperature variations of a single nanotube, a nanotube array and a part of nanotube-based composite surface with heat generation. The thermal conductivity used is obtained from the upscaled value from the molecular simulations or experiments. Simulations show that nanotube arrays have unique cooling characteristics due to its anisotropic thermal conductivity.Comment: 10 pages, 4 figure