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

Turbulence and galactic structure

Interstellar turbulence is driven over a wide range of scales by processes including spiral arm instabilities and supernovae, and it affects the rate and morphology of star formation, energy dissipation, and angular momentum transfer in galaxy disks. Star formation is initiated on large scales by gravitational instabilities which control the overall rate through the long dynamical time corresponding to the average ISM density. Stars form at much higher densities than average, however, and at much faster rates locally, so the slow average rate arises because the fraction of the gas mass that forms stars at any one time is low, ~10^{-4}. This low fraction is determined by turbulence compression, and is apparently independent of specific cloud formation processes which all operate at lower densities. Turbulence compression also accounts for the formation of most stars in clusters, along with the cluster mass spectrum, and it gives a hierarchical distribution to the positions of these clusters and to star-forming regions in general. Turbulent motions appear to be very fast in irregular galaxies at high redshift, possibly having speeds equal to several tenths of the rotation speed in view of the morphology of chain galaxies and their face-on counterparts. The origin of this turbulence is not evident, but some of it could come from accretion onto the disk. Such high turbulence could help drive an early epoch of gas inflow through viscous torques in galaxies where spiral arms and bars are weak. Such evolution may lead to bulge or bar formation, or to bar re-formation if a previous bar dissolved. We show evidence that the bar fraction is about constant with redshift out to z~1, and model the formation and destruction rates of bars required to achieve this constancy.Comment: in: Penetrating Bars through Masks of Cosmic Dust: The Hubble Tuning Fork strikes a New Note, Eds., K. Freeman, D. Block, I. Puerari, R. Groess, Dordrecht: Kluwer, in press (presented at a conference in South Africa, June 7-12, 2004). 19 pgs, 5 figure

CMB Telescopes and Optical Systems

The cosmic microwave background radiation (CMB) is now firmly established as a fundamental and essential probe of the geometry, constituents, and birth of the Universe. The CMB is a potent observable because it can be measured with precision and accuracy. Just as importantly, theoretical models of the Universe can predict the characteristics of the CMB to high accuracy, and those predictions can be directly compared to observations. There are multiple aspects associated with making a precise measurement. In this review, we focus on optical components for the instrumentation used to measure the CMB polarization and temperature anisotropy. We begin with an overview of general considerations for CMB observations and discuss common concepts used in the community. We next consider a variety of alternatives available for a designer of a CMB telescope. Our discussion is guided by the ground and balloon-based instruments that have been implemented over the years. In the same vein, we compare the arc-minute resolution Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT). CMB interferometers are presented briefly. We conclude with a comparison of the four CMB satellites, Relikt, COBE, WMAP, and Planck, to demonstrate a remarkable evolution in design, sensitivity, resolution, and complexity over the past thirty years.Comment: To appear in: Planets, Stars and Stellar Systems (PSSS), Volume 1: Telescopes and Instrumentatio

A facile chemical conversion synthesis of Sb2S3 nanotubes and the visible light-driven photocatalytic activities

We report a simple chemical conversion and cation exchange technique to realize the synthesis of Sb2S3 nanotubes at a low temperature of 90°C. The successful chemical conversion from ZnS nanotubes to Sb2S3 ones benefits from the large difference in solubility between ZnS and Sb2S3. The as-grown Sb2S3 nanotubes have been transformed from a weak crystallization to a polycrystalline structure via successive annealing. In addition to the detailed structural, morphological, and optical investigation of the yielded Sb2S3 nanotubes before and after annealing, we have shown high photocatalytic activities of Sb2S3 nanotubes for methyl orange degradation under visible light irradiation. This approach offers an effective control of the composition and structure of Sb2S3 nanomaterials, facilitates the production at a relatively low reaction temperature without the need of organics, templates, or crystal seeds, and can be extended to the synthesis of hollow structures with various compositions and shapes for unique properties

Finite Intersection Property and Dynamical Compactness

[EN] Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in Huang et al. (J Differ Equ 260(9):6800-6827, 2016). In this paper we continue to investigate this notion. In particular, we prove that all dynamical systems are dynamically compact with respect to a Furstenberg family if and only if this family has the finite intersection property. We investigate weak mixing and weak disjointness by using the concept of dynamical compactness. We also explore further difference between transitive compactness and weak mixing. As a byproduct, we show that the -limit and the -limit sets of a point may have quite different topological structure. Moreover, the equivalence between multi-sensitivity, sensitive compactness and transitive sensitivity is established for a minimal system. Finally, these notions are also explored in the context of linear dynamics.Wen Huang and Sergii Kolyada acknowledge the hospitality of the School of Mathematical Sciences of the Fudan University, Shanghai. Sergii Kolyada also acknowledges the hospitality of the Max-Planck-Institute fur Mathematik (MPIM) in Bonn, the Departament de Matematica Aplicada of the Universitat Politecnica de Valencia, the partial support of Project MTM2013-47093-P, and the Department of Mathematics of the Chinese University of Hong Kong. We thank the referees for careful reading and constructive comments that have resulted in substantial improvements to this paper. Wen Huang was supported by NNSF of China (11225105, 11431012); Alfred Peris was supported by MINECO, Projects MTM2013-47093-P and MTM2016-75963-P, and by GVA, Project PROMETEOII/2013/013; and Guohua Zhang was supported by NNSF of China (11671094).Huang, W.; Khilko, D.; Kolyada, S.; Peris Manguillot, A.; Zhang, G. (2018). 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The Cosmological Constant

This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its magnitude, and the physics of a small (and potentially nonzero) vacuum energy.Comment: 50 pages. Submitted to Living Reviews in Relativity (http://www.livingreviews.org/), December 199

Antimetastatic Effects of Norcantharidin on Hepatocellular Carcinoma by Transcriptional Inhibition of MMP-9 through Modulation of NF-kB Activity

The rate of morbidity and mortality of hepatocellular carcinoma (HCC) in Taiwan has not lessened because of difficulty in treating tumor metastasis. Norcantharidin (NCTD) is currently used as an anticancer drug for hepatoma, breast cancer, and colorectal adenocarcinoma. NCTD possesses various biological anticancer activities, including apoptosis. However, detailed effects and molecular mechanisms of NCTD on metastasis are unclear. Thus, HCC cells were subjected to treatment with NCTD and then analyzed to determine the effects of NCTD on cell metastasis.Modified Boyden chamber assays revealed that NCTD treatment inhibited cell migration and invasion capacities of HCC cells substantially. Results of zymography and western blotting showed that activities and protein levels of matrix metalloproteinase-9 (MMP-9) and urokinase plasminogen activator (u-PA) were inhibited by NCTD. Western blot analysis showed that NCTD inhibits phosphorylation of ERK1/2. Testing of mRNA level, quantitative real-time PCR, and promoter assays evaluated the inhibitory effects of NCTD on MMP-9 and u-PA expression in HCC cells. The chromatin immunoprecipitation (ChIP) assay for analyzing the genomic DNA sequences bound to these proteins was reactive to the transcription protein nuclear factor (NF)-kappaB, which was inhibited by NCTD. The expression of NF-kappa B was measured by western blot analysis, which revealed decreased nuclear-factor DNA-binding activity after NCTD treatment.NCTD inhibited MMP-9 and u-PA expression through the phosphorylation of ERK1/2 and NF-kappaB signaling pathway which serves as a powerful chemopreventive agent in HCC cell metastasis

Effective Inhibition of Xenografts of Hepatocellular Carcinoma (HepG2) by Rapamycin and Bevacizumab in an Intrahepatic Model

10.1007/s11307-009-0213-4Molecular Imaging and Biology115334-342CPIM