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Abstract: We consider a hybrid version of the basic predator–prey differential equation model: a pure jump stochastic model for the prey variable x coupled with a differential equation model for the predator variable y. This hybrid model is derived from the classical birth and death process. The model contains a parameter ω which represents the number of individuals for one unit of prey: x =1 corresponds to ω individual prey. It is shown by the mean of simulations and explained by a mathematical analysis based on a result from the singular perturbation theory – the so-called theory of Canards – that qualitative properties of the model like persistence or extinction are dramatically sensitive to ω. For instance, in our example, if ω =107 we have extinction and if ω =108 we have persistence. This means that we must be very cautious when we use continuous variables in place of discrete ones in dynamic population modeling even when we use stochastic differential equations in place of deterministic ones. [Copyright &y& Elsevier]

Abstract: This paper deals with the existence and stability of multiple equilibrium profiles in tubular bioreactors. We prove here that a tubular biological reactor can posses one or several equilibrium profiles according to the dispersion and convection terms as long as the kinetic function belongs to a general class of non-monotonic functions. Such systems allow the characterization of the hydrodynamic behavior of most real systems in classifying them between completely mixed systems and perfect Plug Flow systems. The stability analysis of equilibrium profiles is also carried out and it is shown that they are alternatively stable, unstable, stable, etc. [Copyright &y& Elsevier]

The aim of this paper is to show that the representation with the help of non-standard analysis of a real phenomenon, presenting different observation scales, allows an important simplification of language. Indeed, it is convenient to have available the concept of infinitely small and infinitely large quantities in dealing with the macroscopic effects of microscopic phenomena. This is illustrated on two examples: the representation of two time scales systems and the representation of noise. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we study a model of the chemostat where the species are present in two forms, isolated and aggregated individuals, such as attached bacteria or bacteria in flocks. We show that our general model contains a lot of models that were previously considered in the literature. Assuming that flocculation and deflocculation dynamics is fast compared to the growth of the species, we construct a reduced chemostat-like model in which both the growth functions and the apparent dilution rate depend on the density of the species. We also show that such a model involving monotonic growth rates may exhibit bi-stability, while it may occur in the classical chemostat model, but when the growth rate is non-monotonic. [Copyright &y& Elsevier]

Although mathematical modelling has reached a degree of maturity in the last decades, microbial ecology is still developing, albeit at a rapid pace thanks to new insights provided by modern molecular tools. However, whilst microbiologists have long enjoyed the perspectives that particular mathematical frameworks can provide, there remains a reluctance to fully embrace the potential of models, which appear too complex, esoteric or distant from the “real-world”. Nevertheless there is a strong case for pursuing the development of mathematical models to describe microbial behaviour and interactions, dynamically, spatially and across scales. Here we put forward perspectives on the current state of mathematical modelling in microbial ecology, looking back at the developments that have defined the synergies between the disciplines, and outline some of the existing challenges that motivate us to provide practical models in the hope that greater engagement with empiricists and practitioners in the microbiological domain may be achieved. We also indicate recent advances in modelling that have had impact in both the fundamental understanding of microbial ecology and its practical application in engineered biological systems. In this way, it is anticipated that interest can be garnered from across the microbiological spectrum resulting in a broader uptake of mathematical concepts in lecture theatres, laboratories and industrial systems. [ABSTRACT FROM AUTHOR]

Loss of function mutations and deletions encompassing the plant homeodomain finger 6 (PHF6) gene are present in about 20% of T-cell acute lymphoblastic leukemias (ALLs). Here, we report the identification of recurrent mutations in PHF6 in 10/353 adult acute myeloid leukemias (AMLs). Genetic lesions in PHF6 found in AMLs are frameshift and nonsense mutations distributed through the gene or point mutations involving the second plant homeodomain (PHD)-like domain of the protein. As in the case of T-ALL, where PHF6 alterations are found almost exclusively in males, mutations in PHF6 were seven times more prevalent in males than in females with AML. Overall, these results identify PHF6 as a tumor suppressor gene mutated in AML and extend the role of this X-linked tumor suppressor gene in the pathogenesis of hematologic tumors. [ABSTRACT FROM AUTHOR]

This paper deals with a generic approach for the analysis of interconnected biological systems. The equilibrium points as well as the asymptotic behaviour of these systems are investigated from a qualitative point of view. In particular, a new generic approach is used to show that a series of Continuously Stirred Tank Reactors (CSTRs) can exhibit multiple steady state profiles, for any non-monotonic kinetics. This multiplicity property disappears when the number of reactors becomes sufficiently large (for a given total volume). These results are to be taken in account when CSTRs in series are used to approximate a Piston Flow Reactor (PFR). [ABSTRACT FROM AUTHOR]