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The analysis of the first plant genomes provided unexpected evidence for genome duplication events in species that had previously been considered as true diploids on the basis of their genetics. These polyploidization events may have had important consequences in plant evolution, in particular for species radiation and adaptation and for the modulation of(More)
Hybrid systems are dynamical systems with the ability to describe mixed discrete-continuous evolution of a wide range of systems. Consequently, at first glance, hybrid systems appear powerful but recalcitrant, neither yielding to analysis and reasoning through a purely continuous-time modeling as with systems of differential equations , nor open to(More)
This paper addresses questions regarding the decidability of hybrid automata that may be constructed hierarchically and in a modular way, as is the case in many exemplar systems, be it natural or engineered. Since the basic fundamental step in such constructions is a product operation , an essential property that would be desired is that the reachability(More)
Biotechnological innovations that allow one to sample gene expression (e.g. gene-expression arrays or real-time Polymerase Chain Reaction (PCR)), have made it possible to measure the gene expression levels of a biological system with varying degree of accuracy, cost and speed. By repeating the measurement steps at different sampling rates during the system(More)
In this paper we propose a hybrid model of a neural oscillator, obtained by partially discretizing a well-known continuous model. Our construction points out that in this case the standard techniques, based on replacing sigmoids with step functions, is not satisfactory. Then, we study the hybrid model through both symbolic methods and approximation(More)