An Investigation into Mechanisms of Loss of Safe Basins in a 2 D.O.F. Nonlinear Oscillator

In this work we consider the transient stability of coupled motions of a 2 D.O.F. nonlinear oscillator that can represent, for example, the motions of a sea vessel under the action of trains of regular lateral waves. Instability is studied as the escape of the system from a safe potential well. The set of initial conditions in phase space that lead to acceptable motions constitutes its safe basin. We investigate the evolution of these safe basins under variation of parameters such as frequency and amplitude of waves, and an internal tuning parameter. Complex nonlinear phenomena are known to play an important role in determining the loss of safe basins as, say, wave amplitude is increased. We therefore investigate those processes, and attempt to classify them in terms of their speed relative to changes in parameter values. "Mechanism basins" are produced depicting regions of parameter space in which rapid or slow losses of safe basin are observed. We propose that a comprehensive understanding of mechanisms of loss of safe basins can be a valuable tool in assessing stability properties of these systems, and we give a conceptual view of how such information could be used.

Membrane proteins: functional and structural studies using reconstituted proteoliposomes and 2-D crystals

Reconstitution of membrane proteins into lipid bilayers is a powerful tool to analyze functional as well as structural areas of membrane protein research. First, the proper incorporation of a purified membrane protein into closed lipid vesicles, to produce proteoliposomes, allows the investigation of transport and/or catalytic properties of any membrane protein without interference by other membrane components. Second, the incorporation of a large amount of membrane proteins into lipid bilayers to grow crystals confined to two dimensions has recently opened a new way to solve their structure at high resolution using electron crystallography. However, reconstitution of membrane proteins into functional proteoliposomes or 2-D crystallization has been an empirical domain, which has been viewed for a long time more like "black magic" than science. Nevertheless, in the last ten years, important progress has been made in acquiring knowledge of lipid-protein-detergent interactions and has permitted to build upon a set of basic principles that has limited the empirical approach of reconstitution experiments. Reconstitution strategies have been improved and new strategies have been developed, facilitating the success rate of proteoliposome formation and 2-D crystallization. This review deals with the various strategies available to obtain proteoliposomes and 2-D crystals from detergent-solubilized proteins. It gives an overview of the methods that have been applied, which may be of help for reconstituting more proteins into lipid bilayers in a form suitable for functional studies at the molecular level and for high-resolution structural analysis.

Choix d'un associateur 2-D pour le balayage multiple et optimisation de l'estimation des pistes

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

d-Koszul algebras, 2-d-determined algebras and 2-d-Koszul algebras

The relationship between an algebra and its associated monomial algebra is investigated when at least one of the algebras is d-Koszul It is shown that an algebra which has a reduced Grobnerbasis that is composed of homogeneous elements of degree d is d-Koszul if and only if its associated monomial algebra is d-Koszul The class of 2-d-determined algebras and the class 2-d-Koszul algebras are introduced In particular it is shown that 2-d-determined monomial algebras are 2-d-Koszul algebras and the structure of the ideal of relations of such an algebra is completely determined (C) 2010 Elsevier B V All rights reserved