Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

Three-dimensional space-borne synthetic aperture radar (SAR) imaging with multiple pass processing

Three-dimensional (3D) synthetic aperture radar (SAR) imaging via multiple-pass processing is an extension of interferometric SAR imaging. It exploits more than two flight passes to achieve a desired resolution in elevation. In this paper, a novel approach is developed to reconstruct a 3D space-borne SAR image with multiple-pass processing. It involves image registration, phase correction and elevational imaging. An image model matching is developed for multiple image registration, an eigenvector method is proposed for the phase correction and the elevational imaging is conducted using a Fourier transform or a super-resolution method for enhancement of elevational resolution. 3D SAR images are obtained by processing simulated data and real data from the first European Remote Sensing satellite (ERS-1) with the proposed approaches.

Cationic drug pharmacokinetics in diseased livers determined by fibrosis index, hepatic protein content, microsomal activity, and nature of drug

The disposition kinetics of six cationic drugs in perfused diseased and normal rat livers were determined by multiple indicator dilution and related to the drug physicochemical properties and liver histopathology. A carbon tetrachloride (CCl4)induced acute hepatocellular injury model had a higher fibrosis index (FI), determined by computer-assisted image analysis, than did an alcohol-induced chronic hepatocellular injury model. The alcohol-treated group had the highest hepatic alpha(1)- acid glycoprotein, microsomal protein (MP), and cytochrome P450 (P450) concentrations. Various pharmacokinetic parameters could be related to the octanol-water partition coefficient (log P-app) of the drug as a surrogate for plasma membrane partition coefficient and affinity for MP or P450, the dependence being lower in the CCl4-treated group and higher in the alcohol-treated group relative to controls. Stepwise regression analysis showed that hepatic extraction ratio, permeability-surface area product, tissue-binding constant, intrinsic clearance, partition ratio of influx (k(in)) and efflux rate constant (k(out)), and k(in)/k(out) were related to physicochemical properties of drug (log P-app or pK(a)) and liver histopathology (FI, MP, or P450). In addition, hepatocyte organelle ion trapping of cationic drugs was evident in all groups. It is concluded that fibrosis-inducing hepatic disease effects on cationic drug disposition in the liver may be predicted from drug properties and liver histopathology.

Empirical evidence for ultrametric structure in multi-layer perceptron error surfaces

Combinatorial optimization problems share an interesting property with spin glass systems in that their state spaces can exhibit ultrametric structure. We use sampling methods to analyse the error surfaces of feedforward multi-layer perceptron neural networks learning encoder problems. The third order statistics of these points of attraction are examined and found to be arranged in a highly ultrametric way. This is a unique result for a finite, continuous parameter space. The implications of this result are discussed.

MR image-based measurement of rates of change in volumes of brain structures. Part 1: Method and validation

A detailed analysis procedure is described for evaluating rates of volumetric change in brain structures based on structural magnetic resonance (MR) images. In this procedure, a series of image processing tools have been employed to address the problems encountered in measuring rates of change based on structural MR images. These tools include an algorithm for intensity non-uniforniity correction, a robust algorithm for three-dimensional image registration with sub-voxel precision and an algorithm for brain tissue segmentation. However, a unique feature in the procedure is the use of a fractional volume model that has been developed to provide a quantitative measure for the partial volume effect. With this model, the fractional constituent tissue volumes are evaluated for voxels at the tissue boundary that manifest partial volume effect, thus allowing tissue boundaries be defined at a sub-voxel level and in an automated fashion. Validation studies are presented on key algorithms including segmentation and registration. An overall assessment of the method is provided through the evaluation of the rates of brain atrophy in a group of normal elderly subjects for which the rate of brain atrophy due to normal aging is predictably small. An application of the method is given in Part 11 where the rates of brain atrophy in various brain regions are studied in relation to normal aging and Alzheimer's disease. (C) 2002 Elsevier Science Inc. All rights reserved.