BASIC MATHEMATICAL FORM OF MICHELL STRUCTURE

John Michell Clarke

Mathematical Morphology: Basic Principles

This paper is intended as a rst introduction into mathematical morphology, and does not require any preliminary knowledge in this eld. The paper discusses the basic morphological operators, such as dilations, erosions, openings, closings, rank operators, skeletons, and reconstruction operators. Furthermore, it introduces the complete lattice framework for morphology. The paper concludes with an...

Michell Trusses and Lines of Principal Action

We study the problem of Michell trusses when the system of applied equilibrated forces is a vector measure with compact support. We introduce a class of stress tensors which can be written as a superposition of rank-one tensors carried by curves (lines of principal strains). Optimality conditions are given for such families showing in particular that optimal stress tensors are carried by mutual...

Basic Properties of Mathematical Population Models

Mathematical population models are constructed based on plausible explicit and implicit biological assumptions. While it is easy to incorporate explicit assumptions correctly in the models, those implicit ones are often ill treated or forgotten. Indeed, this happens to some well known models in the literature and examples of such will be mentioned and discussed. For a model to be logically cred...

Klinotaxis as a basic form of navigation

In their article, Gomez-Marin and Louis (2014) found that runs in Drosophila larval chemotaxis bend toward the direction of higher concentration. This steering process called weathervaning or klinotaxis was previously discovered in the worm C. elegans (Ward, 1973; Iino and Yoshida, 2009) and raises the question: how is it performed? Although Gomez-Marin and Louis (2014) found that run orientati...