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

Alteration of Retinal Rod Outer Segment Membrane Fluidity in a Rat Model of Smith-Lemli-Opitz Syndrome

Smith-Lemli-Opitz syndrome (SLOS) is caused by an inherited defect in the last step in cholesterol (Chol) biosynthesis, leading to abnormal accumulation of 7-dehydrocholesterol and decreased Chol levels. Progressive retinal degeneration occurs in an animal model of SLOS, induced by treating rats with AY9944, a selective inhibitor of the enzyme affected in SLOS. Here we evaluated alterations in the biochemical and physical properties of retinal rod outer segment (ROS) membranes in this animal model. At 1 month of AY9944 treatment, there were modest alterations in fatty acid composition, but no significant differences in cis-parinaric acid (cPA) spectroscopic parameters in ROS membranes from treated versus control rats. However, at 3 months, ROS docosahexaenoic acid (DHA) content was dramatically reduced, and cPA fluorescence anisotropy values were decreased, relative to controls. Also, 1, 6-diphenyl-1, 3, 5-hexatriene exhibited decreased rotational motion and increased orientational order in ROS membranes from 3 month-old AY9944-treated rats, relative to controls. No significant changes in protein:lipid ratios were observed; however, rhodopsin regenerability was compromised by 3 months of treatment. These findings are consistent with reduced ROS membrane fluidity in the SLOS rat model, relative to controls, primarily due to the dramatic reduction inmembraneDHA levels, rather than altered sterol composition

Spherical Spectral Synthesis and Two-Radius Theorems on Damek-Ricci Spaces

We prove that spherical spectral analysis and synthesis hold in Damek-Ricci spaces and derive two-radius theorems

Inhibition of pluripotency networks by the Rb tumor suppressor restricts reprogramming and tumorigenesis

Mutations in the retinoblastoma tumor suppressor gene Rb are involved in many forms of human cancer. In this study, we investigated the early consequences of inactivating Rb in the context of cellular reprogramming. We found that Rb inactivation promotes the reprogramming of differentiated cells to a pluripotent state. Unexpectedly, this effect is cell cycle independent, and instead reflects direct binding of Rb to pluripotency genes, including Sox2 and Oct4, which leads to a repressed chromatin state. More broadly, this regulation of pluripotency networks and Sox2 in particular is critical for the initiation of tumors upon loss of Rb in mice. These studies therefore identify Rb as a global transcriptional repressor of pluripotency networks, providing a molecular basis for previous reports about its involvement in cell fate pliability, and implicate misregulation of pluripotency factors such as Sox2 in tumorigenesis related to loss of Rb function

Inhibition of pluripotency networks by the Rb tumor suppressor restricts reprogramming and tumorigenesis

Mutations in the retinoblastoma tumor suppressor gene Rb are involved in many forms of human cancer. In this study, we investigated the early consequences of inactivating Rb in the context of cellular reprogramming. We found that Rb inactivation promotes the reprogramming of differentiated cells to a pluripotent state. Unexpectedly, this effect is cell cycle independent, and instead reflects direct binding of Rb to pluripotency genes, including Sox2 and Oct4, which leads to a repressed chromatin state. More broadly, this regulation of pluripotency networks and Sox2 in particular is critical for the initiation of tumors upon loss of Rb in mice. These studies therefore identify Rb as a global transcriptional repressor of pluripotency networks, providing a molecular basis for previous reports about its involvement in cell fate pliability, and implicate misregulation of pluripotency factors such as Sox2 in tumorigenesis related to loss of Rb function

Combined Effect of Dietary Cadmium and Benzo(a)pyrene on Metallothionein Induction and Apoptosis in the Liver and Kidneys of Bank Voles

Bank voles free living in a contaminated environment have been shown to be more sensitive to cadmium (Cd) toxicity than the rodents exposed to Cd under laboratory conditions. The objective of this study was to find out whether benzo(a)pyrene (BaP), a common environmental co-contaminant, increases Cd toxicity through inhibition of metallothionein (MT) synthesis—a low molecular weight protein that is considered to be primary intracellular component of the protective mechanism. For 6 weeks, the female bank voles were provided with diet containing Cd [less than 0.1 μg/g (control) and 60 μg/g dry wt.] and BaP (0, 5, and 10 μg/g dry wt.) alone or in combination. At the end of exposure period, apoptosis and analyses of MT, Cd, and zinc (Zn) in the liver and kidneys were carried out. Dietary BaP 5 μg/g did not affect but BaP 10 μg/g potentiated rather than inhibited induction of hepatic and renal MT by Cd, and diminished Cd-induced apoptosis in both organs. The hepatic and renal Zn followed a pattern similar to that of MT, attaining the highest level in the Cd + BaP 10-μg/g group. These data indicate that dietary BaP attenuates rather than exacerbates Cd toxicity in bank voles, probably by potentiating MT synthesis and increasing Zn concentration in the liver and kidneys