Exponential dichotomies of evolution operators in Banach spaces

This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces. Connections between these concepts are illustrated. Using the notion of Green function, we give necessary conditions and sufficient ones for strong exponential dichotomy. Some illustrative examples are presented to prove that the converse of some implication type theorems are not valid

A unified parameter identification method for nonlinear time-delay systems

This paper deals with the problem of identifying unknown time-delays and model parameters in a general nonlinear time-delay system. We propose a unified computational approach that involves solving a dynamic optimization problem, whose cost function measures the discrepancy between predicted and observed system output, to determine optimal values for the unknown quantities. Our main contribution is to show that the partial derivatives of this cost function can be computed by solving a set of auxiliary time-delay systems. On this basis, the parameter identification problem can be solved using existing gradient-based optimization techniques. We conclude the paper with two numerical simulations

Nitrogen acquisition by roots: physiological and developmental mechanisms ensuring plant adaptation to a fluctuating resource

International audienceNitrogen (N) is one of the key mineral nutrients for plants and its availability has a major impact on their growth and development. Most often N resources are limiting and plants have evolved various strategies to modulate their root uptake capacity to compensate for both spatial and temporal changes in N availability in soil. The main N sources for terrestrial plants in soils of temperate regions are in decreasing order of abundance, nitrate, ammonium and amino acids. N uptake systems combine, for these different N forms, high- and low-affinity transporters belonging to multige families. Expression and activity of most uptake systems are regulated locally by the concentration of their substrate, and by a systemic feedback control exerted by whole-plant signals of N status, giving rise to a complex combinatory network. Besides modulation of the capacity of transport systems, plants are also able to modulate their growth and development to maintain N homeostasis. In particular, root system architecture is highly plastic and its changes can greatly impact N acquisition from soil. In this review, we aim at detailing recent advances in the identification of molecular mechanisms responsible for physiological and developmental responses of root N acquisition to changes in N availability. These mechanisms are now unravelled at an increasing rate, especially in the model plant Arabidopsis thaliana L.. Within the past decade, most root membrane transport proteins that determine N acquisition have been identified. More recently, molecular regulators in nitrate or ammonium sensing and signalling have been isolated, revealing common regulatory genes for transport system and root development, as well as a strong connection between N and hormone signalling pathways. Deciphering the complexity of the regulatory networks that control N uptake, metabolism and plant development will help understanding adaptation of plants to sub-optimal N availability and fluctuating environments. It will also provide solutions for addressing the major issues of pollution and economical costs related to N fertilizer use that threaten agricultural and ecological sustainability