Brief note on the variation of constants formula for fuzzy differential equations

This note gives a theory of state transition matrices for linear systems of fuzzy differential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations are elementary solutions of eigenvalue-eigenvector problems. In particular, for nonnegative or nonpositive matrices, the problems at each level set, can easily be solved in MATLAB to give the level sets of the fuzzy solution. (C) 2002 Elsevier Science B.V. All rights reserved.

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.

Phenotypic divergence along lines of genetic variance

Natural populations inhabiting the same environment often independently evolve the same phenotype. Is this replicated evolution a result of genetic constraints imposed by patterns of genetic covariation? We looked for associations between directions of morphological divergence and the orientation of the genetic variance-covariance matrix (G) by using an experimental system of morphological evolution in two allopatric nonsister species of rainbow fish. Replicate populations of both Melanotaenia eachamensis and Melanotaenia duboulayi have independently adapted to lake versus stream hydrodynamic environments. The major axis of divergence (z) among all eight study populations was closely associated with the direction of greatest genetic variance (g(max)), suggesting directional genetic constraint on evolution. However, the direction of hydrodynamic adaptation was strongly associated with vectors of G describing relatively small proportions of the total genetic variance, and was only weakly associated with g(max). In contrast, divergence between replicate populations within each habitat was approximately proportional to the level of genetic variance, a result consistent with theoretical predictions for neutral phenotypic divergence. Divergence between the two species was also primarily along major eigenvectors of G. Our results therefore suggest that hydrodynamic adaptation in rainbow fish was not directionally constrained by the dominant eigenvector of G. Without partitioning divergence as a consequence of the adaptation of interest (here, hydrodynamic adaptation) from divergence due to other processes, empirical studies are likely to overestimate the potential for the major eigenvectors of G to directionally constrain adaptive evolution.

A class of self-stabilizing MCA learning algorithms

In this letter, we propose a class of self-stabilizing learning algorithms for minor component analysis (MCA), which includes a few well-known MCA learning algorithms. Self-stabilizing means that the sign of the weight vector length change is independent of the presented input vector. For these algorithms, rigorous global convergence proof is given and the convergence rate is also discussed. By combining the positive properties of these algorithms, a new learning algorithm is proposed which can improve the performance. Simulations are employed to confirm our theoretical results.