Effects of Different Extraction Methods on Vanilla Aroma

To establish the analytic conditions for examining the aroma quality of vanilla pods, we compared different extraction methods and identified a suitable option. We utilized headspace solid-phase microextraction (HS-SPME), steam distillation (SD), simultaneous steam distillation (SDE) and alcoholic extraction combined with gas chromatography (GC) and gas chromatography–mass spectrometry (GC-MS) to identify volatile components of vanilla pods. A total of 84 volatile compounds were identified in this experiment, of which SDE could identify the most volatile compounds, with a total of 51 species, followed by HS-SPME, with a total of 28 species. Ten volatile compounds were identified by extraction with a minimum of 35% alcohol. HS-SPME extraction provided the highest total aroma peak areas, and the peak areas of aldehydes, furans, alcohols, monoterpenes and phenols compounds were several times higher than those of the other extraction methods. The results showed that the two technologies, SDE and HS-SPME, could be used together to facilitate analysis of vanilla pod aroma.     

Monte Carlo Simulation of Stochastic Differential Equation to Study Information Geometry

Information Geometry is a useful tool to study and compare the solutions of a Stochastic Differential Equations (SDEs) for non-equilibrium systems. As an alternative method to solving the Fokker–Planck equation, we propose a new method to calculate time-dependent probability density functions (PDFs) and to study Information Geometry using Monte Carlo (MC) simulation of SDEs. Specifically, we develop a new MC SDE method to overcome the challenges in calculating a time-dependent PDF and information geometric diagnostics and to speed up simulations by utilizing GPU computing. Using MC SDE simulations, we reproduce Information Geometric scaling relations found from the Fokker–Planck method for the case of a stochastic process with linear and cubic damping terms. We showcase the advantage of MC SDE simulation over FPE solvers by calculating unequal time joint PDFs. For the linear process with a linear damping force, joint PDF is found to be a Gaussian. In contrast, for the cubic process with a cubic damping force, joint PDF exhibits a bimodal structure, even in a stationary state. This suggests a finite memory time induced by a nonlinear force. Furthermore, several power-law scalings in the characteristics of bimodal PDFs are identified and investigated.     

Unbiased truncated quadratic variation for volatility estimation in jump diffusion processes

The problem of integrated volatility estimation for an Ito semimartingale is considered under discrete high-frequency observations in short time horizon. We provide an asymptotic expansion for the integrated volatility that gives us, in detail, the contribution deriving from the jump part. The knowledge of such a contribution allows us to build an unbiased version of the truncated quadratic variation, in which the bias is visibly reduced. In earlier results to have the original truncated realized volatility well-performed the condition $\beta >\frac{1}{2(2-\alpha )}$ on $\beta$ (that is such that ${\left(\frac{1}{n}\right)}^{\beta }$ is the threshold of the truncated quadratic variation) and on the degree of jump activity $\alpha$ was needed (see Mancini, 2011; Jacod, 2008). In this paper we theoretically relax this condition and we show that our unbiased estimator achieves excellent numerical results for any couple ($\alpha$, $\beta$).     

Stratonovich Anticipative Stochastic Differential Equations In The Plane

We apply the techniques of the quasi-sure analysis to prove that the stochastic differential equation in the plane with smooth and nondegenerate initial condition can be solved     

Stochastic PDEs Driven by Nonlinear Noise and Backward Doubly SDEs

We study a new kind of backward doubly stochastic differential equations, where the nonlinear noise term is given by Itô–Kunita's stochastic integral. This allows us to give a probabilistic interpretation of classical and Sobolev's solutions of semilinear parabolic stochastic partial differential equations driven by a nonlinear space-time noise.     

Comparative study of extraction techniques for determination of garlic flavor components by gas chromatography–mass spectrometry

Several sampling techniques based on steam distillation (SD), simultaneous distillation and solvent extraction (SDE), solid-phase trapping solvent extraction (SPTE), and headspace solid-phase microextraction (HS-SPME) have been compared for the determination of Korean garlic flavor components by gas chromatography–mass spectrometry (GC–MS). Diallyl disulfide (57.88%), allyl sulfide (23.59%), and diallyl trisulfide (11.40%) were found to be the predominant flavor components of garlic samples extracted by SDE whereas these components were at levels of 89.77%, 2.43%, and 3.89% when the same sample was extracted by SD, 97.77%, 0.17%, and 0.10% by SPTE, and 97.85%, 0.01%, and 0.01% by HS-SPME using the 50/30-m divinyl benzene/carboxen/polydimethylsiloxane (DVB/CAR/PDMS) fiber. Thermal degradation of components such as allyl methyl sulfide, dimethyl disulfide, and thiirane were observed for SDE and SD but not for SPTE or HS-SPME. HS-SPME had several advantages compared with SD, SDE, and SPTE—rapid solvent-free extraction, no apparent thermal degradation, less laborious manipulation, and less sample requirement. Five different fiber coatings were evaluated to select a suitable fiber for HS-SPME of garlic flavor components. DVB/CAR/PDMS was most efficient among the five types of fiber investigated.