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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)
— In this paper we introduce the problem of reachability analysis of hybrid automata to decide safety properties. Then we describe ARIADNE, an in-progress open environment to design algorithms for computing with hybrid automata. We show that ARIADNE relies on a rigorous computable analysis theory to represent geometric objects, in order to achieve provable(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)
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)
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 an important step in such constructions is a product operation, which constructs a new product hybrid automaton by combining two simpler(More)
— A new approach is presented for computing approximations of the reached sets of linear hybrid automata. First, we present some new theoretical results on termination of a class of reachability algorithms, which includes Botchkarev's, based on ellipsoidal calculus. The main contribution of the paper is a revised reachability computation that avoids the(More)
Motivated by the need for scalable symbolic reasoning methodologies aimed at systems biology, as well as the novel opportunities made possible by powerful hybrid automata models of biochemical networks, we have embarked upon the Algorithmic Algebraic Model Checking (AAMC) project that combines symbolic computation with model checking to analyze biochemical(More)