Megavariate Analysis of Environmental QSAR Data. Part II – Investigating Very Complex Problem Formulations Using Hierarchical, Non-Linear and Batch-Wise Extensions of PCA and PLS

Summary Three extensions of the basic PCA and PLS methodologies are described. These extensions are hierarchical, non-linear and batch-based in nature. The objectives of these methods are to assist in problem understanding and problem solving in very complex (QSAR) problem formulations. The method extensions are illustrated using two example QSAR data sets containing many X- and Y-variables.     

Lazy structure-activity relationships (lazar) for the prediction of rodent carcinogenicity and Salmonella mutagenicity

lazar is a new tool for the prediction of toxic properties of chemical structures. It derives predictions for query structures from a database with experimentally determined toxicity data. lazar generates predictions by searching the database for compounds that are similar with respect to a given toxic activity and calculating the prediction from their activities. Apart form the prediction, lazar provides the rationales (structural features and similar compounds) for the prediction and a reliable condence index that indicates, if a query structure falls within the applicability domain of the training database. Leave-one-out (LOO) crossvalidation experiments were carried out for 10 carcinogenicity endpoints ({female|male} {hamster|mouse|rat} carcinogenicity and aggregate endpoints {hamster|mouse|rat} carcinogenicity and rodent carcinogenicity) and Salmonella mutagenicity from the Carcinogenic Potency Database (CPDB). An external validation of Salmonella mutagenicity predictions was performed with a dataset of 3895 structures. Leave-one-out and external validation experiments indicate that Salmonella mutagenicity can be predicted with 85% accuracy for compounds within the applicability domain of the CPDB. The LOO accuracy of lazar predictions of rodent carcinogenicity is 86%, the accuracies for other carcinogenicity endpoints vary between 78 and 95% for structures within the applicability domain.     

Robust regression techniques A useful alternative for the detection of outlier data in chemical analysis

The validation of an analytical procedure means the evaluation of some performance criteria such as accuracy, sensitivity, linear range, capability of detection, selectivity, calibration curve, etc. This implies the use of different statistical methodologies, some of them related with statistical regression techniques, which may be robust or not. The presence of outlier data has a significant effect on the determination of sensitivity, linear range or capability of detection amongst others, when these figures of merit are evaluated with non-robust methodologies.In this paper some of the robust methods used for calibration in analytical chemistry are reviewed: the Huber M-estimator; the Andrews, Tukey and Welsh GM-estimators; the fuzzy estimators; the constrained M-estimators, CM; the least trimmed squares, LTS. The paper also shows that the mathematical properties of the least median squares (LMS) regression can be of great interest in the detection of outlier data in chemical analysis. A comparative analysis is made of the results obtained by applying these regression methods to synthetic and real data. There is also a review of some applications where this robust regression works in a suitable and simple way that proves very useful to secure an objective detection of outliers. The use of a robust regression is recommended in ISO 5725-5.     

The heat equation with singular nonlinearity and singular initial data

We study the existence, uniqueness and regularity of positive solutions of the parabolic equation ut−Δu=a(x)uq+b(x)up in a bounded domain and with Dirichlet's condition on the boundary. We consider here a∈Lα(Ω), b∈Lβ(Ω) and 0<q?1<p. The initial data u(0)=u₀ is considered in the space Lr(Ω), r?1. In the main result (0<q<1), we assume a,b?0 a.e. in Ω and we assume that u₀?γdΩ for some γ>0. We find a unique solution in the space .     

Quasilinear elliptic equations with subquadratic growth

In this paper we consider nonlinear boundary value problems whose simplest model is the following:

(0.1)     

Regularity results for the gradient of solutions linear elliptic equations with L 1, λ data

We prove that if f belongs to the Morrey space , with λ ∊ [0, n−2], and u is the solution of the problem

The Sigmoidal Transfer Function and the Gain-Threshold Exponential Dependence for Neurons from Statistical Mechanics Treatment

Analogy is used to treat the system of non-interacting integrate-and-fire neurons as an ideal Fermi gas. It allows to obtain the nonlinear gain curve in the form of sigmoid in agreement with biological findings. As the by-product the gain-threshold mechanism in neurons is presented. Surprisingly enough, this is in agreement with new biological findings, too. Besides, the application of this mechanism to the dynamics of neurons leads to the non-monotone transfer function.     

An explanation for deviations from the quark number scaling of elliptic flows in low pT region

We carry out a systematic study of the different contributions to the deviations of the elliptic flows from the quark number scaling in high energy heavy ion collision in a quark combination model.The effects that we considered are:the resonance decay,the flavor dependence of the quark elliptic flow and the combination of quarks/antiquarks with slightly different transverse momenta.Our results show that the deviations observed in experiments can be well reproduced within the combination framework if all the three effects are considered. We make a detailed analysis of the different contributions using a Monte-Carlo program and suggest measuring the quark number scaling in intermediate pT range more precisely.     

Systematics on fission fragment mass distribution of neutron induced 235U fission

Based on the neutron induced fission fragment mass distribution data up to neutron energy 20 MeV measured with the double kinetic energy method (KEM) and the radio active method (RAM), the systematics of fission fragment mass distribution was investigated by using 5 Gaussian model and the systematics parameters were obtained by fitting the experimental data. With the systematics, the yields of any mass A and at any energy in the region from 0 to 20 MeV of neutron energy can be calculated. The calculated results could well reproduce the experimental data measured with KEM, but show some systematical deviation from the data measured by RAM, which reflects some systematical deviations between the two kinds of measured data.The error of systematics yield was calculated in an exact error transformation way, including from the error of the experimental yield data to the error of the discrete parameters, then to the systematics parameters,and at last to the yield calculated with systematics.     

大气激光通信链路的性能仿真

大气衰减和大气湍流严重影响着大气激光通信的链路质量。建立了大气信道的激光通信链路模型，研究了衰减信道和湍流信道中光链路的传输影响，对最大通信速率、链路功率余量和误码率进行了分析和计算。结果表明，大气湍流严重影响系统误码率，当大气闪烁指数斫是0．07时，可达到的最小误码率为10^-9。分析结果可为系统设计提供参考依据。