Approximated maximum likelihood estimation in multifractal random walks

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package in the R computer language. Its performance is tested on synthetic data and compared to an inference approach based on the generalized method of moments. The method is applied to estimate parameters for various financial stock indices.Comment: 8 pages, 3 figures, 2 table

Thermodynamic large fluctuations from uniformized dynamics

Large fluctuations have received considerable attention as they encode information on the fine-scale dynamics. Large deviation relations known as fluctuation theorems also capture crucial nonequilibrium thermodynamical properties. Here we report that, using the technique of uniformization, the thermodynamic large deviation functions of continuous-time Markov processes can be obtained from Markov chains evolving in discrete time. This formulation offers new theoretical and numerical approaches to explore large deviation properties. In particular, the time evolution of autonomous and non-autonomous processes can be expressed in terms of a single Poisson rate. In this way the uniformization procedure leads to a simple and efficient way to simulate stochastic trajectories that reproduce the exact fluxes statistics. We illustrate the formalism for the current fluctuations in a stochastic pump model

Elevated Serum Carboxymethyl-Lysine, an Advanced Glycation End Product, Predicts Severe Walking Disability in Older Women: The Women's Health and Aging Study I

Advanced glycation end products (AGEs) have been implicated in the pathogenesis of sarcopenia. Our aim was to characterize the relationship between serum carboxymethyl-lysine (CML), a major circulating AGE, and incident severe walking disability (inability to walk or walking speed $<0.4$ m/sec) over 30 months of followup in 394 moderately to severely disabled women, $\ge 65$ years, living in the community in Baltimore, Maryland (the Women's Health and Aging Study I). During followup, 154 (26.4%) women developed severe walking disability, and 23 women died. Women in the highest quartile of serum CML had increased risk of developing of severe walking disability in a multivariate Cox proportional hazards model, adjusting for age and other potential confounders. Women with elevated serum CML are at an increased risk of developing severe walking disability. AGEs are a potentially modifiable risk factor. Further work is needed to establish a causal relationship between AGEs and walking disability

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

Predictors of anemia in preschool children: Biomarkers Reflecting Inflammation and Nutritional Determinants of Anemia (BRINDA) project.

Background: A lack of information on the etiology of anemia has hampered the design and monitoring of anemia-control efforts.Objective: We aimed to evaluate predictors of anemia in preschool children (PSC) (age range: 6-59 mo) by country and infection-burden category.Design: Cross-sectional data from 16 surveys (n = 29,293) from the Biomarkers Reflecting Inflammation and Nutritional Determinants of Anemia (BRINDA) project were analyzed separately and pooled by category of infection burden. We assessed relations between anemia (hemoglobin concentration &lt;110 g/L) and severe anemia (hemoglobin concentration &lt;70 g/L) and individual-level (age, anthropometric measures, micronutrient deficiencies, malaria, and inflammation) and household-level predictors; we also examined the proportion of anemia with concomitant iron deficiency (defined as an inflammation-adjusted ferritin concentration &lt;12 μg/L). Countries were grouped into 4 categories on the basis of risk and burden of infectious disease, and a pooled multivariable logistic regression analysis was conducted for each group.Results: Iron deficiency, malaria, breastfeeding, stunting, underweight, inflammation, low socioeconomic status, and poor sanitation were each associated with anemia in &gt;50% of surveys. Associations between breastfeeding and anemia were attenuated by controlling for child age, which was negatively associated with anemia. The most consistent predictors of severe anemia were malaria, poor sanitation, and underweight. In multivariable pooled models, child age, iron deficiency, and stunting independently predicted anemia and severe anemia. Inflammation was generally associated with anemia in the high- and very high-infection groups but not in the low- and medium-infection groups. In PSC with anemia, 50%, 30%, 55%, and 58% of children had concomitant iron deficiency in low-, medium-, high-, and very high-infection categories, respectively.Conclusions: Although causal inference is limited by cross-sectional survey data, results suggest anemia-control programs should address both iron deficiency and infections. The relative importance of factors that are associated with anemia varies by setting, and thus, country-specific data are needed to guide programs

Occupation times of exclusion processes

In this paper we consider exclusion processes $\{\eta_t: t\geq{0}\}$ evolving on the one-dimensional lattice $\mathbb{Z}$, under the diffusive time scale $tn^2$ and starting from the invariant state $\nu_\rho$ - the Bernoulli product measure of parameter $\rho\in{[0,1]}$. Our goal consists in establishing the scaling limits of the additive functional $\Gamma_t:=\int_{0}^{tn^2} \eta_s(0)\, ds$ - {\em{ the occupation time of the origin}}. We present a method, recently introduced in \cite{G.J.}, from which a {\em{local Boltzmann-Gibbs Principle}} can be derived for a general class of exclusion processes. In this case, this principle says that $\Gamma_t$ is very well approximated to the additive functional of the density of particles. As a consequence, the scaling limits of $\Gamma_t$ follow from the scaling limits of the density of particles. As examples we present the mean-zero exclusion, the symmetric simple exclusion and the weakly asymmetric simple exclusion. For the latter under a strong asymmetry regime, the limit of $\Gamma_t$ is given in terms of the solution of the KPZ equation.FC

Rational Design of Photoelectrodes for the Fully Integrated Polymer Electrode Membrane–Photoelectrochemical Water-Splitting System: A Case Study of Bismuth Vanadate

Photoelectrochemical (PEC) reactors based on polymer electrolyte membrane (PEM) electrolyzers are an attractive alternative to improve scalability compared to conventional monolithic devices. To introduce narrow band gap photoabsorbers such as BiVO4 in PEM-PEC system requires cost-effective and scalable deposition techniques beyond those previously demonstrated on monolithic FTO-coated glass substrates, followed by the preparation of membrane electrode assemblies. Herein, we address the significant challenges in coating narrow band gap metal-oxides on porous substrates as suitable photoelectrodes for the PEM-PEC configuration. In particular, we demonstrate the deposition and integration of W-doped BiVO4 on porous conductive substrates by a simple, cost-effective, and scalable deposition based on the SILAR (successive ionic layer adsorption and reaction) technique. The resultant W-doped BiVO4 photoanode exhibits a photocurrent density of 2.1 mA·cm–2, @1.23V vs RHE, the highest reported so far for the BiVO4 on any porous substrates. Furthermore, we integrated the BiVO4 on the PEM-PEC reactor to demonstrate the solar hydrogen production from ambient air with humidity as the only water source, retaining 1.55 mA·cm–2, @1.23V vs RHE. The concept provides insights into the features necessary for the successful development of materials suitable for the PEM-PEC tandem configuration reactors and the gas-phase operation of the reactor, which is a promising approach for low-cost, large-scale solar hydrogen production.</p

Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon

Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise

The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large deviation principle for different types of SPDE such as stochastic reaction-diffusion equations, stochastic porous media equations and fast diffusion equations, and the stochastic p-Laplace equation in Hilbert space. The weak convergence approach is employed in the proof to establish the Laplace principle, which is equivalent to the large deviation principle in our framework.Comment: 31 pages, published in Appl. Math. Opti