Comparison of a black-box model to a traditional numerical model for hydraulic head prediction

Two different methodologies for hydraulic head simulation were compared in this study. The first methodology is a classic numerical groundwater flow simulation model, Princeton Transport Code (PTC), while the second one is a black-box approach that uses Artificial Neural Networks (ANNs). Both methodologies were implemented in the Bavaria region in Germany at thirty observation wells. When using PTC, meteorological and geological data are used in order to compute the simulated hydraulic head following the calibration of the appropriate model parameters. The ANNs use meteorological and hydrological data as input parameters. Different input parameters and ANN architectures were tested and the ANN with the best performance was compared with the PTC model simulation results. One ANN was trained for every observation well and the hydraulic head change was simulated on a daily time step. The performance of the two models was then compared based on the real field data from the study area. The cases in which one model outperforms the other were summarized, while the use of one instead of the other depends on the application and further use of the model

Bioactive natural products: facts, applications, and challenges

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Today, there are a strong debate and interest regarding the safety aspects of chemical preservatives addedwidely inmany food products to prevent mainly growth of spoilage and pathogenic microbes. Synthetic compounds are considered responsible for carcinogenic and teratogenic attributes and residual toxicity. To avoid the aforementioned problems, consumers and authorities have increased pressure on food manufacturers to substitute the harmful artificial additives with alternative, more effective, nontoxic, and natural sub-stances. In this context, the use of natural compounds with antimicrobial action presents an intriguing case. Natural antioxidants also demonstrate a wide range of biological and pharmacological activities and are considered to have bene

Maximum likelihood drift estimation for a threshold diffusion

We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold diffusion is called drifted Oscillating Brownian motion.For this continuously observed diffusion, the maximum likelihood estimator coincide with a quasi-likelihood estimator with constant diffusion term. We show that this estimator is the limit, as observations become dense in time, of the (quasi)-maximum likelihood estimator based on discrete observations. In long time, the asymptotic behaviors of the positive and negative occupation times rule the ones of the estimators. Differently from most known results in the literature, we do not restrict ourselves to the ergodic framework: indeed, depending on the signs of the drift, the process may be ergodic, transient or null recurrent. For each regime, we establish whether or not the estimators are consistent; if they are, we prove the convergence in long time of the properly rescaled difference of the estimators towards a normal or mixed normal distribution. These theoretical results are backed by numerical simulations

Off-Critical SLE(2) and SLE(4): a Field Theory Approach

Using their relationship with the free boson and the free symplectic fermion, we study the off-critical perturbation of SLE(4) and SLE(2) obtained by adding a mass term to the action. We compute the off-critical statistics of the source in the Loewner equation describing the two dimensional interfaces. In these two cases we show that ratios of massive by massless partition functions, expressible as ratios of regularised determinants of massive and massless Laplacians, are (local) martingales for the massless interfaces. The off-critical drifts in the stochastic source of the Loewner equation are proportional to the logarithmic derivative of these ratios. We also show that massive correlation functions are (local) martingales for the massive interfaces. In the case of massive SLE(4), we use this property to prove a factorisation of the free boson measure.Comment: 30 pages, 1 figures, Published versio

Noncolliding Brownian Motion with Drift and Time-Dependent Stieltjes-Wigert Determinantal Point Process

Using the determinantal formula of Biane, Bougerol, and O'Connell, we give multitime joint probability densities to the noncolliding Brownian motion with drift, where the number of particles is finite. We study a special case such that the initial positions of particles are equidistant with a period $a$ and the values of drift coefficients are well-ordered with a scale $\sigma$. We show that, at each time $t >0$, the single-time probability density of particle system is exactly transformed to the biorthogonal Stieltjes-Wigert matrix model in the Chern-Simons theory introduced by Dolivet and Tierz. Here one-parameter extensions ($\theta$-extensions) of the Stieltjes-Wigert polynomials, which are themselves $q$-extensions of the Hermite polynomials, play an essential role. The two parameters $a$ and $\sigma$ of the process combined with time $t$ are mapped to the parameters $q$ and $\theta$ of the biorthogonal polynomials. By the transformation of normalization factor of our probability density, the partition function of the Chern-Simons matrix model is readily obtained. We study the determinantal structure of the matrix model and prove that, at each time $t >0$, the present noncolliding Brownian motion with drift is a determinantal point process, in the sense that any correlation function is given by a determinant governed by a single integral kernel called the correlation kernel. Using the obtained correlation kernel, we study time evolution of the noncolliding Brownian motion with drift.Comment: v2: REVTeX4, 34 pages, 4 figures, minor corrections made for publication in J. Math. Phy

Front- and Back-End Employee Satisfaction during Service Transition

Purpose Scholars studying servitization argue that manufacturers moving into services need to develop new job roles or modify existing ones, which must be enacted by employees with the right mentality, skill sets, attitudes and capabilities. However, there is a paucity of empirical research on how such changes affect employee-level outcomes. Design/methodology/approach The authors theorize that job enrichment and role stress act as countervailing forces during the manufacturer's service transition, with implications for employee satisfaction. The authors test the hypotheses using a sample of 21,869 employees from 201 American manufacturers that declared revenues from services over a 10-year period. Findings The authors find an inverted U-shaped relationship between the firm's level of service infusion and individual employee satisfaction, which is flatter for front-end staff. This relationship differs in shape and/or magnitude between firms, highlighting the role of unobserved firm-level idiosyncratic factors. Practical implications Servitized manufacturers, especially those in the later stage of their transition (i.e. when services start to account for more than 50% of annual revenues), should try to ameliorate their employees' role-induced stress to counter a drop in satisfaction. Originality/value This is one of the first studies to examine systematically the relationship between servitization and individual employee satisfaction. It shows that back-end employees in manufacturing firms are considerably affected by an increasing emphasis on services, while past literature has almost exclusively been concerned with front-end staff

On small-noise equations with degenerate limiting system arising from volatility models

The one-dimensional SDE with non Lipschitz diffusion coefficient $dX_{t} = b(X_{t})dt + \sigma X_{t}^{\gamma} dB_{t}, \ X_{0}=x, \ \gamma<1$ is widely studied in mathematical finance. Several works have proposed asymptotic analysis of densities and implied volatilities in models involving instances of this equation, based on a careful implementation of saddle-point methods and (essentially) the explicit knowledge of Fourier transforms. Recent research on tail asymptotics for heat kernels [J-D. Deuschel, P.~Friz, A.~Jacquier, and S.~Violante. Marginal density expansions for diffusions and stochastic volatility, part II: Applications. 2013, arxiv:1305.6765] suggests to work with the rescaled variable $X^{\varepsilon}:=\varepsilon^{1/(1-\gamma)} X$: while allowing to turn a space asymptotic problem into a small-$\varepsilon$ problem with fixed terminal point, the process $X^{\varepsilon}$ satisfies a SDE in Wentzell--Freidlin form (i.e. with driving noise $\varepsilon dB$). We prove a pathwise large deviation principle for the process $X^{\varepsilon}$ as $\varepsilon \to 0$. As it will become clear, the limiting ODE governing the large deviations admits infinitely many solutions, a non-standard situation in the Wentzell--Freidlin theory. As for applications, the $\varepsilon$-scaling allows to derive exact log-asymptotics for path functionals of the process: while on the one hand the resulting formulae are confirmed by the CIR-CEV benchmarks, on the other hand the large deviation approach (i) applies to equations with a more general drift term and (ii) potentially opens the way to heat kernel analysis for higher-dimensional diffusions involving such an SDE as a component.Comment: 21 pages, 1 figur

An overview of Viscosity Solutions of Path-Dependent PDEs

This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial di erential equations. We start by a quick review of the Crandall- Ishii notion of viscosity solutions, so as to motivate the relevance of our de nition in the path-dependent case. We focus on the wellposedness theory of such equations. In partic- ular, we provide a simple presentation of the current existence and uniqueness arguments in the semilinear case. We also review the stability property of this notion of solutions, in- cluding the adaptation of the Barles-Souganidis monotonic scheme approximation method. Our results rely crucially on the theory of optimal stopping under nonlinear expectation. In the dominated case, we provide a self-contained presentation of all required results. The fully nonlinear case is more involved and is addressed in [12]