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

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

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

Table of contents and editorial information for Vol. 32, no. 2, Spring 2005

Table of contents and editorial information for Vol. 32, no. 2, Spring 2005 - a special issue on Preparing Educational Leaders

Preparing Educational Leaders: A Roadmap to Success

Many have argued that educational leadership preparation programs are under siege. Although the mounting national attention can be traced back to the 1980s and perhaps earlier, the past few years have been witness to highly objectionable media commentaries and politicized disputes about leadership preparation

Educational Considerations, vol. 32(2) Full Issue

Educational Considerations, vol. 32(2)-Spring 2005-Full issu

Signaling via interleukin-4, receptor alpha chain is required for successful vaccination against schistosomiasis in BALB/c mice

Radiation-attenuated (RA) schistosome larvae are potent stimulators of innate immune responses at the skin site of exposure (pinna) that are likely to be important factors in the development of Th1-mediated protective immunity. In addition to causing an influx of neutrophils, macrophages, and dendritic cells (DCs) into the dermis, RA larvae induced a cascade of chemokine and cytokine secretion following in vitro culture of pinna biopsy samples. While macrophage inflammatory protein 1 and interleukin-1 (IL-1) were produced transiently within the first few days, the Th1-promoting cytokines IL-12 and IL-18 were secreted at high levels until at least day 14. Assay of C3H/HeJ mice confirmed that IL-12 secretion was not due to lipopolysaccharide contaminants binding Toll-like receptor 4. Significantly, IL-12 p40 secretion was sustained in pinnae from vaccinated mice but not in those from nonprotected infected mice. In contrast, IL-10 was produced from both vaccinated and infected mice. This cytokine regulates IL-12-associated dermal inflammation, since in vaccinated IL-10/ mice, pinna thickness was greatly increased concurrent with elevated levels of IL-12 p40. A significant number of IL-12 p40 cells were detected as emigrants from in vitro-cultured pinnae, and most were within a population of rare large granular cells that were Ia, consistent with their being antigen-presenting cells. Labeling of IL-12 cells for CD11c, CD205, CD8, CD11b, and F4/80 indicated that the majority were myeloid DCs, although a proportion were CD11c F4/80, suggesting that macrophages were an additional source of IL-12 in the skin

Flexible C : N ratio enhances metabolism of large phytoplankton when resource supply is intermittent

Abstract. Phytoplankton cell size influences particle sinking rate, food web interactions and biogeographical distributions. We present a model in which the uptake, storage and assimilation of nitrogen and carbon are explicitly resolved in different-sized phytoplankton cells. In the model, metabolism and cellular C : N ratio are influenced by the accumulation of carbon polymers such as carbohydrate and lipid, which is greatest when cells are nutrient starved, or exposed to high light. Allometric relations and empirical data sets are used to constrain the range of possible C : N, and indicate that larger cells can accumulate significantly more carbon storage compounds than smaller cells. When forced with extended periods of darkness combined with brief exposure to saturating irradiance, the model predicts organisms large enough to accumulate significant carbon reserves may on average synthesize protein and other functional apparatus up to five times faster than smaller organisms. The advantage of storage in terms of average daily protein synthesis rate is greatest when modeled organisms were previously nutrient starved, and carbon storage reservoirs saturated. Small organisms may therefore be at a disadvantage in terms of average daily growth rate in environments that involve prolonged periods of darkness and intermittent nutrient limitation. We suggest this mechanism is a significant constraint on phytoplankton C : N variability and cell size distribution in different oceanic regimes. </jats:p

The Exact Hausdorff Measure of the Zero Set of Fractional Brownian Motion

Let {X(t), t is an element of R-N} be a fractional Brownian motion in R-d of index H. If L(0,I) is the local time of X at 0 on the interval I subset of R-N, then there exists a positive finite constant c(=c(N,d,H)) such tha