Intrinsic expansions for averaged diffusion processes

We show that the rate of convergence of asymptotic expansions for solutions of SDEs is generally higher in the case of degenerate (or partial) diffusion compared to the elliptic case, i.e. it is higher when the Brownian motion directly acts only on some components of the diffusion. In the scalar case, this phenomenon was already observed in (Gobet and Miri 2014) using Malliavin calculus techniques. In this paper, we provide a general and detailed analysis by employing the recent study of intrinsic functional spaces related to hypoelliptic Kolmogorov operators in (Pagliarani et al. 2016). Relevant applications to finance are discussed, in particular in the study of path-dependent derivatives (e.g. Asian options) and in models incorporating dependence on past information

A Yosida's parametrix approach to Varadhan's estimates for a degenerate diffusion under the weak Hörmander condition

We adapt and extend Yosida's parametrix method, originally introduced for the construction of the fundamental solution to a parabolic operator on a Riemannian manifold, to derive Varadhan-type asymptotic estimates for the transition density of a degenerate diffusion under the weak Hörmander condition. This diffusion process, widely studied by Yor in a series of papers, finds direct application in the study of a class of path-dependent financial derivatives known as Asian options. We obtain a Varadhan-type formula which relates the transition density p of the stochastic process with the optimal cost Ψ of a deterministic control problem associated to the diffusion. We provide a partial proof of this formula, and present numerical evidence to support the validity of an intermediate inequality that is required to complete the proof. We also derive an asymptotic expansion of the cost function Ψ, expressed in terms of elementary functions, which is useful in order to design efficient approximation formulas for the transition density

Numerical solution of kinetic SPDEs via stochastic Magnus expansion

In this paper, we show how the Itô-stochastic Magnus expansion can be used to efficiently solve stochastic partial differential equations (SPDE) with two space variables numerically. To this end, we will first discretize the SPDE in space only by utilizing finite difference methods and vectorize the resulting equation exploiting its sparsity. As a benchmark, we will apply it to the case of the stochastic Langevin equation with constant coefficients, where an explicit solution is available, and compare the Magnus scheme with the Euler–Maruyama scheme. We will see that the Magnus expansion is superior in terms of both accuracy and especially computational time by using a single GPU and verify it in a variable coefficient case. Notably, we will see speed-ups of order ranging form 20 to 200 compared to the Euler–Maruyama scheme, depending on the accuracy target and the spatial resolution

Clinical, biochemical and genetic features of glycogen debranching enzyme deficiency

Deficiency of debrancher enzyme causes Glycogen Storage Disease (GSD) type III, an autosomal recessive disorder, characterized by tissue accumulation of abnormally structured glycogen. This report reviews current clinical and molecular knowledge about this disorder and describes the variability at phenotype and genotype levels of a large group of Italian GSDIII patient

Effect of a Klamath algae product ("AFA-B12") on blood levels of vitamin B12 and homocysteine in vegan subjects: a pilot study

none8Vitamin B12 is a critical nutrient that is often inadequate in a plant-based (vegan) diet, thus the inclusion of a reliable vitamin B12 source in a vegan diet is recommended as essential. Unfortunately, many natural sources of vitamin B12 have been proven to contain biologically inactive vitamin B12 analogues, inadequate for human supplementation. The aim of this non-randomized open trial was to determine whether supplementation with a natural Klamath algae-based product ("AFA-B12", Aphanizomenon flos-aquae algae plus a proprietary mix of enzymes) could favorably affect the vitamin B12 status of a group of 15 vegan subjects. By assessing blood concentration of vitamin B12, folate, and more importantly homocysteine (Hcy, a reliable marker in vegans of their B12 absorption), the vitamin B12 status of the participants at the end of the 3-month intervention period, while receiving the Klamath-algae supplement (T2), was compared with their vitamin B12 status at the end of the 3-month control period (T1), when they were not receiving any supplement, having stopped taking their usual vitamin B12 supplement at the beginning of the study (T0). Compared to the control period, in the intervention period participants improved their vitamin B12 status, significantly reducing Hcy blood concentration (p=0.003). In conclusion, the Klamath algae product AFA-B12 appears to be, in a preliminary study, an adequate and reliable source of vitamin B12 in humans.openL.Baroni; S.Scoglio; S.Benedetti; C.Bonetto; S.Pagliarani; Y.Benedetti; M.Rocchi; F.CanestrariL., Baroni; S., Scoglio; Benedetti, Serena; C., Bonetto; S., Pagliarani; Y., Benedetti; Rocchi, MARCO BRUNO LUIGI; Canestrari, Franc

Characterization of metabolic profiles and lipopolysaccharide effects on porcine vascular wall mesenchymal stem cells

The link between metabolic remodeling and stem cell fate is still unclear. To explore this topic, the metabolic profile of porcine vascular wall mesenchymal stem cells (pVW-MSCs) was investigated. At the first and second cell passages, pVW-MSCs exploit both glycolysis and cellular respiration to synthesize adenosine triphosphate (ATP), but in the subsequent (third to eighth) passages they do not show any mitochondrial ATP turnover. Interestingly, when the first passage pVW-MSCs are exposed to 0.1 or 10 μg/ml lipopolysaccharides (LPSs) for 4 hr, even if ATP synthesis is prevented, the spare respiratory capacity is retained and the glycolytic capacity is unaffected. In contrast, the exposure of pVW-MSCs at the fifth passage to 10 μg/ml LPS stimulates mitochondrial ATP synthesis. Flow cytometry rules out any reactive oxygen species (ROS) involvement in the LPS effects, thus suggesting that the pVW-MSC metabolic pattern is modulated by culture conditions via ROS-independent mechanisms

Grapevine phyllosphere community analysis in response to elicitor application against powdery mildew

The reduction of antimicrobial treatments and mainly the application of environmentally friendly compounds, such as resistance elicitors, is an impelling challenge to undertake more sustainable agriculture. We performed this research to study the effectiveness of non-conventional compounds in reducing leaf fungal attack and to investigate whether they influence the grape phyllosphere. Pathogenicity tests were conducted on potted Vitis vinifera “Nebbiolo” and “Moscato” cultivars infected with the powdery mildew agent (Erysiphe necator) and treated with three elicitors. Differences in the foliar microbial community were then evaluated by community-level physiological profiling by using BiologTM EcoPlates, high throughput sequencing of the Internal Transcribed Spacer (ITS) region, and RNA sequencing for the viral community. In both cultivars, all products were effective as they significantly reduced pathogen development. EcoPlate analysis and ITS sequencing showed that the microbial communities were not influenced by the alternative compound application, confirming their specific activity as plant defense elicitors. Nevertheless, “Moscato” plants were less susceptible to the disease and presented different phyllosphere composition, resulting in a richer viral community, when compared with the “Nebbiolo” plants. The observed effect on microbial communities pointed to the existence of distinct genotype-specific defense mechanisms independently of the elicitor application