Quantitative Structure-Toxicity Relationships Using Tops-Mode. 2. Neurotoxicity of a Non-Congeneric Series of Solvents

Abstract

Neurotoxicities of a series of solvents in rats and mice have been modeled by means of the TOPS-MODE approach. Two quantitative structure-toxicity relationship (QSTR) models were obtained explaining more than 80% of the variance in the experimental values of neurotoxicity of 45 solvents. Only one compound was detected as statistical outlier for these models. In contrast, previous models explained less than 60% of the variance in this property for 44 solvents. Finally, the contributions to neurotoxicity in rats and mice for a series of structural fragments were found. Structural characteristics of chlorinated fragments responsible for their different neurotoxicities were analyzed. The differences in neurotoxic behavior of some fragments in rats and mice were also analyzed, which could give insights on the toxicological mechanism of action of solvents studied.     

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.     

Boundary problems for fractional differential equations

In this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.     

Entire large solutions of semilinear equations involving the fractional Laplacian

We investigate the existence and nonexistence of positive entire large solutions of a class of semilinear equations involving the fractional Laplacian. Sharp lower and upper bounds of the minimal solution, if it exists, are also given.     

Fractional Bilinear Stochastic Equations with the Drift in the First Fractional Chaos

Abstract

In the paper we compute the explicit form of the fractional chaos decomposition of the solution of a fractional stochastic bilinear equation with the drift in the fractional chaos of order one and initial condition in a finite fractional chaos. The large deviations principle is also obtained for the one-dimensional distributions of the solution of the equation perturbed by a small noise.     

On Weak Solutions of Stochastic Differential Equations II

In the first part of this article a new method of proving existence of weak solutions to stochastic differential equations with continuous coefficients having at most linear growth was developed. In this second part, we show that the same method may be used even if the linear growth hypothesis is replaced with a suitable Lyapunov condition.     

New application of human eye model in the verification of spot diagram with refractive diopter

In response to the rapid advancement of auto-refractor technology, most optometry shops provide refraction services. Despite their speed and convenience, the measurement values provided by auto-refractors include a significant degree of error due to psychological and physical factors. Therefore, there is a need for repetitive testing to obtain a smaller mean error value. However, even repetitive testing itself might not be sufficient to ensure accurate measurements. Therefore, research on a method of measurement that can complement auto-refractor measurements and provide confirmation of refraction results needs to be conducted. The customized optometry model described herein can satisfy the above requirements. From the existing optical technologies, using human eye measurement devices to obtain individual relevant optical feature parameters is no longer difficult. These parameters allow us to construct an optometry model for individual eyeballs. They also allow us to compute spot diagrams produced from the optometry model using the CODE V macro programming language before recognizing the geometrical spot diagram with the back-propagation neural network algorithm to obtain the accurate refractive diopter. Results show that the accuracy achieved was above 98% and that this application could significantly enhance the service quality of refraction.     

Statistical inference for Vasicek-type model driven by Hermite processes

Let $Z$ denote a Hermite process of order $q\ge 1$ and self-similarity parameter $H\in (\frac{1}{2},1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $q?2$. In this paper, we deal with a Vasicek-type model driven by $Z$, of the form $d{X}_t=a(b?X_t)dt+d{Z}_t$. Here, $a>0$ and $b\in \mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations.