Retrieving descriptor information (x information) from a value of an objective variable (y) is a fundamental problem in inverse quantitative structure-property relationship (inverse-QSPR) analysis but challenging because of the complexity of the preimage function. Herewith, we propose using a cluster-wise multiple linear regression (cMLR) model as a QSPR model for inverse-QSPR analysis. x information is acquired as a probability density function by combining cMLR and the prior distribution modeled with a mixture of Gaussians (GMMs). Three case studies were conducted to demonstrate various aspects of the potential of cMLR. It was found that the predictive power of cMLR was superior to that of MLR, especially for data with nonlinearity. Moreover, it turned out that the applicability domain could be considered since the posterior distribution inherits the prior distribution's feature (i.e., training data feature) and represents the possibility of having the desired property. Finally, a series of inverse analyses with the GMMs/cMLR was demonstrated with the aim to generate de novo structures having specific aqueous solubility.

The notion of compatibility for point-to-point mappings recently defined by Jungck is generalized to include multi-valued mappings. This idea is used to establish a fixed point theorem for a generalized contractive multi-valued mapping and a single-valued napping.

No abstract

in Wiley InterScience (www.interscience.wiley.com).Soft sensors are used widely to estimate a process variable which is difficult to measure online. One of the crucial difficulties of soft sensors is that predictive accuracy drops due to changes of state of chemical plants. To cope with this problem, a regression model can be updated. However, if the model is updated with an abnormal sample, the predictive ability can deteriorate. We have applied the independent component analysis (ICA) method to the soft sensor to increase fault detection ability. Then, we have tried to increase the predictive accuracy. By using the ICA-based fault detection and classification model, the objective variable can be predicted, updating the PLS model appropriately. We analyzed real industrial data as the application of the proposed method. The proposed method achieved higher predictive accuracy than the traditional one. Furthermore, the nonsteady state could be detected as abnormal correctly by the ICA model.

Abstract. In this paper we establish Gauss-type quadrature formulas for weakly singular integrals. An application of the quadrature scheme is given to obtain numerical solutions of the weakly singular Fredholm integral equation of the second kind. We call this method a discrete product-integration method since the weights involved in the standard product-integration method are computed numerically.