Logarithmic asymptotics of the densities of SPDEs driven by spatially correlated noise

We consider the family of stochastic partial differential equations indexed by a parameter \eps\in(0,1], \begin{equation*} Lu^{\eps}(t,x) = \eps\sigma(u^\eps(t,x))\dot{F}(t,x)+b(u^\eps(t,x)), \end{equation*} (t,x)\in(0,T]\times\Rd with suitable initial conditions. In this equation, $L$ is a second-order partial differential operator with constant coefficients, $\sigma$ and $b$ are smooth functions and $\dot{F}$ is a Gaussian noise, white in time and with a stationary correlation in space. Let p^\eps_{t,x} denote the density of the law of u^\eps(t,x) at a fixed point (t,x)\in(0,T]\times\Rd. We study the existence of \lim_{\eps\downarrow 0} \eps^2\log p^\eps_{t,x}(y) for a fixed $y\in\R$. The results apply to a class of stochastic wave equations with $d\in\{1,2,3\}$ and to a class of stochastic heat equations with $d\ge1$.Comment: 39 pages. Will be published in the book " Stochastic Analysis and Applications 2014. A volume in honour of Terry Lyons". Springer Verla

Convergence to SPDEs in Stratonovich form

We consider the perturbation of parabolic operators of the form $\partial_t+P(x,D)$ by large-amplitude highly oscillatory spatially dependent potentials modeled as Gaussian random fields. The amplitude of the potential is chosen so that the solution to the random equation is affected by the randomness at the leading order. We show that, when the dimension is smaller than the order of the elliptic pseudo-differential operator $P(x,D)$, the perturbed parabolic equation admits a solution given by a Duhamel expansion. Moreover, as the correlation length of the potential vanishes, we show that the latter solution converges in distribution to the solution of a stochastic parabolic equation with a multiplicative term that should be interpreted in the Stratonovich sense. The theory of mild solutions for such stochastic partial differential equations is developed. The behavior described above should be contrasted to the case of dimensions that are larger than or equal to the order of the elliptic pseudo-differential operator $P(x,D)$. In the latter case, the solution to the random equation converges strongly to the solution of a homogenized (deterministic) parabolic equation as is shown in the companion paper [2]. The stochastic model is therefore valid only for sufficiently small space dimensions in this class of parabolic problems.Comment: 21 page

On the exchange of intersection and supremum of sigma-fields in filtering theory

We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page

Elliptic flow in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV: hybrid model assessment of the first data

We analyze the elliptic flow parameter v_2 in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV and in Au+Au collisions at sqrt{s_{NN}} =200 GeV using a hybrid model in which the evolution of the quark gluon plasma is described by ideal hydrodynamics with a state-of-the-art lattice QCD equation of state, and the subsequent hadronic stage by a hadron cascade model. For initial conditions, we employ Monte-Carlo versions of the Glauber and the Kharzeev-Levin-Nardi models and compare results with each other. We demonstrate that the differential elliptic flow v_2(p_T) hardly changes when the collision energy increases, whereas the integrated v_2 increases due to the enhancement of mean transverse momentum. The amount of increase of both v_2 and mean p_T depends significantly on the model of initialization.Comment: 5 pages, 5 figure

Distinct roles for Arabidopsis SUMO protease ESD4 and its closest homolog ELS1

SUMO conjugation affects a broad range of processes in Arabidopsis thaliana, including flower initiation, pathogen defense, and responses to cold, drought and salt stress. We investigated two sequence-related SUMO-specific proteases that are both widely expressed and show that they differ significantly in their properties. The closest homolog of SUMO protease ESD4, ESD4-LIKE SUMO PROTEASE 1 (ELS1, alternatively called AtULP1a) has SUMO-specific proteolytic activity, but is functionally distinct from ESD4, as shown by intracellular localization, mutant phenotype and heterologous expression in yeast mutants. Furthermore, we show that the growth defects caused by loss of ESD4 function are not due to increased synthesis of the stress signal salicylic acid, as was previously shown for a SUMO ligase, indicating that impairment of the SUMO system affects plant growth in different ways. Our results demonstrate that two A. thaliana SUMO proteases showing close sequence similarity have distinct in vivo functions

Large Deviations for the Stochastic Shell Model of Turbulence

In this work we first prove the existence and uniqueness of a strong solution to stochastic GOY model of turbulence with a small multiplicative noise. Then using the weak convergence approach, Laplace principle for so- lutions of the stochastic GOY model is established in certain Polish space. Thus a Wentzell-Freidlin type large deviation principle is established utilizing certain results by Varadhan and Bryc.Comment: 21 pages, submitted for publicatio

Cytotoxic Withanolide Constituents of Physalis longifolia

Fourteen new withanolides, 1–14, named withalongolides A–N, respectively, were isolated from the aerial parts of Physalis longifolia together with eight known compounds (15–22). The structures of compounds 1–14 were elucidated through spectroscopic techniques and chemical methods. In addition, the structures of withanolides 1, 2, 3, and 6 were confirmed by X-ray crystallographic analysis. Using a MTS viability assay, eight withanolides (1, 2, 3, 7, 8, 15, 16, and 19) and four acetylated derivatives (1a, 1b, 2a, and 2b) showed potent cytotoxicity against human head and neck squamous cell carcinoma (JMAR and MDA-1986), melanoma (B16F10 and SKMEL-28), and normal fetal fibroblast (MRC-5) cells with IC50 values in the range between 0.067 and 9.3 μM

Sleep Disorders and Demand for Medical Services: Evidence from a Population-Based Longitudinal Study

Background: The aim of this study was to investigate whether insomnia and obstructive sleep apnea (OSA) were predictors of hospitalizations or emergency department visits during two years following the Sao Paulo Epidemiologic Sleep Study (EPISONO) sample. Methods and Findings: All participants (n = 1,101) who underwent a baseline evaluation between July and December 2007 were contacted in December 2009 and asked to fill out a questionnaire about body weight changes, number of hospitalizations and visits to the emergency department. Participants lost during the follow-up period represented 3.2 % (n = 35) and 7 subjects had died. Hospitalizations were reported by 116 volunteers (10.5%) and emergency department visits were reported by 136 participants (12.4%). The average body mass index (BMI) did not vary significantly between the first and the second assessment [26.7(95%CI:26.3–27.1) vs. 26.9(26.5–27.4) kg/m2]. After adjusting for confounders, a multiple logistic regression model revealed that female gender [1.4(1.0–1.9)], age $40 years, insomnia diagnosed according to the DSM-IV criteria [1.6(1.0–2.6)], and apneahypopnea index$15 [1.5(1.0–2.2)] were predictors of hospitalizations and/or demand for emergency services. Conclusion: Our study of a probabilistic sample of the Sao Paulo inhabitants shows that over a period of two years, insomnia and OSA were both associated with health impairment. Considering the high prevalence and public health burden of slee

Early Treatment with Fumagillin, an Inhibitor of Methionine Aminopeptidase-2, Prevents Pulmonary Hypertension in Monocrotaline-Injured Rats

Pulmonary Hypertension (PH) is a pathophysiologic condition characterized by hypoxemia and right ventricular strain. Proliferation of fibroblasts, smooth muscle cells, and endothelial cells is central to the pathology of PH in animal models and in humans. Methionine aminopeptidase-2 (MetAP2) regulates proliferation in a variety of cell types including endothelial cells, smooth muscle cells, and fibroblasts. MetAP2 is inhibited irreversibly by the angiogenesis inhibitor fumagillin. We have previously found that inhibition of MetAP2 with fumagillin in bleomycin-injured mice decreased pulmonary fibrosis by selectively decreasing the proliferation of lung myofibroblasts. In this study, we investigated the role of fumagillin as a potential therapy in experimental PH. In vivo, treatment of rats with fumagillin early after monocrotaline injury prevented PH and right ventricular remodeling by decreasing the thickness of the medial layer of the pulmonary arteries. Treatment with fumagillin beginning two weeks after monocrotaline injury did not prevent PH but was associated with decreased right ventricular mass and decreased cardiomyocyte hypertrophy, suggesting a direct effect of fumagillin on right ventricular remodeling. Incubation of rat pulmonary artery smooth muscle cells (RPASMC) with fumagillin and MetAP2-targeting siRNA inhibited proliferation of RPASMC in vitro. Platelet-derived growth factor, a growth factor that is important in the pathogenesis of PH and stimulates proliferation of fibroblasts and smooth muscle cells, strongly increased expression of MetP2. By immunohistochemistry, we found that MetAP2 was expressed in the lesions of human pulmonary arterial hypertension. We propose that fumagillin may be an effective adjunctive therapy for treating PH in patients

Therapeutic efficacy of TBC3711 in monocrotaline-induced pulmonary hypertension

Background: Endothelin-1 signalling plays an important role in pathogenesis of pulmonary hypertension. Although different endothelin-A receptor antagonists are developed, a novel therapeutic option to cure the disease is still needed. This study aims to investigate the therapeutic efficacy of the selective endothelin-A receptor antagonist TBC3711 in monocrotaline-induced pulmonary hypertension in rats. Methods: Monocrotaline-injected male Sprague-Dawley rats were randomized and treated orally from day 21 to 35 either with TBC3711 (Dose: 30 mg/kg body weight/day) or placebo. Echocardiographic measurements of different hemodynamic and right-heart hypertrophy parameters were performed. After day 35, rats were sacrificed for invasive hemodynamic and right-heart hypertrophy measurements. Additionally, histologic assessment of pulmonary vascular and right-heart remodelling was performed. Results: The novel endothelin-A receptor antagonist TBC3711 significantly attenuated monocrotaline-induced pulmonary hypertension, as evident from improved hemodynamics and right-heart hypertrophy in comparison with placebo group. In addition, muscularization and medial wall thickness of distal pulmonary vessels were ameliorated. The histologic evaluation of the right ventricle showed a significant reduction in fibrosis and cardiomyocyte size, suggesting an improvement in right-heart remodelling. Conclusion: The results of this study suggest that the selective endothelin-A receptor antagonist TBC3711 demonstrates therapeutic benefit in rats with established pulmonary hypertension, thus representing a useful therapeutic approach for treatment of pulmonary hypertension