On large deviation regimes for random media models

The focus of this article is on the different behavior of large deviations of random subadditive functionals above the mean versus large deviations below the mean in two random media models. We consider the point-to-point first passage percolation time $a_n$ on $\mathbb{Z}^d$ and a last passage percolation time $Z_n$. For these functionals, we have $\lim_{n\to\infty}\frac{a_n}{n}=\nu$ and $\lim_{n\to\infty}\frac{Z_n}{n}=\mu$. Typically, the large deviations for such functionals exhibits a strong asymmetry, large deviations above the limiting value are radically different from large deviations below this quantity. We develop robust techniques to quantify and explain the differences.Comment: Published in at http://dx.doi.org/10.1214/08-AAP535 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

IL-10 production in macrophages is regulated by a TLR-driven CREB-mediated mechanism that is linked to genes involved in cell metabolism

IL-10 is produced by macrophages in diverse immune settings and is critical in limiting immune-mediated pathology. In helminth infections, macrophages are an important source of IL-10; however, the molecular mechanism underpinning production of IL-10 by these cells is poorly characterized. In this study, bone marrow–derived macrophages exposed to excretory/secretory products released by Schistosoma mansoni cercariae rapidly produce IL-10 as a result of MyD88-mediated activation of MEK/ERK/RSK and p38. The phosphorylation of these kinases was triggered by TLR2 and TLR4 and converged on activation of the transcription factor CREB. Following phosphorylation, CREB is recruited to a novel regulatory element in the Il10 promoter and is also responsible for regulating a network of genes involved in metabolic processes, such as glycolysis, the tricarboxylic acid cycle, and oxidative phosphorylation. Moreover, skin-resident tissue macrophages, which encounter S. mansoni excretory/secretory products during infection, are the first monocytes to produce IL-10 in vivo early postinfection with S. mansoni cercariae. The early and rapid release of IL-10 by these cells has the potential to condition the dermal microenvironment encountered by immune cells recruited to this infection site, and we propose a mechanism by which CREB regulates the production of IL-10 by macrophages in the skin, but also has a major effect on their metabolic state

The Exact Hausdorff Measure of the Zero Set ofFractional Brownian Motion

Let {X(t), t∈ℝN} be a fractional Brownian motion in ℝd of index H. If L(0,I) is the local time of X at 0 on the interval I⊂ℝN, then there exists a positive finite constant c(=c(N,d,H)) such that $$m_\phi\bigl(X^{-1}(0)\cap I\bigr)=cL(0,I),$$ where $\phi(t)=t^{N-dH}(\log\log\frac{1}{t})^{dH/N}$ , and m φ(E) is the Hausdorff φ-measure ofE. This refines a previous result of Xiao (Probab. Theory Relat. Fields 109: 126-197, 1997) on the relationship between the local time and the Hausdorff measure of zero set for d-dimensional fractional Brownian motion on ℝ

CD4+ T cell hyporesponsiveness after repeated exposure to Schistosoma mansoni larvae is dependent upon interleukin-10

The effect that multiple percutaneous exposures to Schistosoma larvae has on the development of early CD4+ lymphocyte reactivity is unclear, yet it is important in the context of humans living in areas where schistosomiasis is endemic. In a murine model of multiple infections, we show that exposure of mice to repeated doses (4×) of Schistosoma mansoni cercariae, compared to a single dose (1×), results in CD4+ T cell hyporesponsiveness within the skin-draining lymph nodes (sdLN), manifested as reduced CD4+ cell proliferation and cytokine production. FoxP3+ CD4+ regulatory T cells were present in similar numbers in the sdLN of 4× and 1× mice and thus are unlikely to have a role in effecting hyporesponsiveness. Moreover, anergy of the CD4+ cell population from 4× mice was slight, as proliferation was only partly circumvented through the in vitro addition of exogenous interleukin-2 (IL-2), and the in vivo blockade of the regulatory molecule PD1 had a minimal effect on restoring responsiveness. In contrast, IL-10 was observed to be critical in mediating hyporesponsiveness, as CD4+ cells from the sdLN of 4× mice deficient for IL-10 were readily able to proliferate, unlike those from 4× wild-type cohorts. CD4+ cells from the sdLN of 4× mice exhibited higher levels of apoptosis and cell death, but in the absence of IL-10, there was significantly less cell death. Combined, our data show that IL-10 is a key factor in the development of CD4+ T cell hyporesponsiveness after repeated parasite exposure involving CD4+ cell apoptosis

Hölder properties of local times for fractional Brownian motions

We study the local times of fractional Brownian motions for all temporal dimensions, N, spatial dimensions d and Hurst parameters H for which local times exist. We establish a Hölder continuity result that is a refinement of Xiao (Probab Th Rel Fields 109:129-157, 1997). Our approach is an adaptation of the more general attack of Xiao (Probab Th Rel Fields 109:129-157, 1997) using ideas of Baraka and Mountford (1997, to appear), the principal result of this latter paper is contained in this articl

On large deviations for the parabolic Anderson model

The focus of this article is on the different behavior of large deviations of random functionals associated with the parabolic Anderson model above the mean versus large deviations below the mean. The functionals we treat are the solution u(x, t) to the spatially discrete parabolic Anderson model and a functional A n which is used in analyzing the a.s. Lyapunov exponent for u(x, t). Both satisfy a “law of large numbers”, with $${\lim_{t\to \infty} \frac{1}{t} \log u(x,t)=\lambda (\kappa)}$$ and $${\lim_{n\to \infty} \frac{A_n}{n}=\alpha}$$ . We then think of αn and λ(κ)t as being the mean of the respective quantities A n and log u(t, x). Typically, the large deviations for such functionals exhibits a strong asymmetry; large deviations above the mean take on a different order of magnitude from large deviations below the mean. We develop robust techniques to quantify and explain the differences