Identifiability problem for recovering the mortality rate in an age-structured population dynamics model

In this article is studied the identifiability of the age-dependent mortality rate of the Von Foerster-Mc Kendrick model, from the observation of a given age group of the population. In the case where there is no renewal for the population, translated by an additional homogeneous boundary condition to the Von Foerster equation, we give a necessary and sufficient condition on the initial density that ensures the mortality rate identifiability. In the inhomogeneous case, modeled by a non local boundary condition, we make explicit a sufficicent condition for the identifiability property, and give a condition for which the identifiability problem is ill-posed. We illustrate this latter case with numercial simulation

Infection load structured SI model with exponential velocity and external source of contamination

International audienceA mathematical SI model is developed for the dynamics of a contagious disease in a closed population with an external source of contamination. We prove existence and uniqueness of a non-negative mild solution of the problem using semigroup theory. We finally illustrate the model with numerical simulations

Asymptotic behavior and numerical simulations for an infection load-structured epidemiological model; Application to the transmission of prion pathologies

In this article is studied an infection load-structured SI model with exponential growth of the infection, that incorporates a potential external source of contamination. We perform the analysis of the time asymptotic behavior of the solution by exhibiting epidemiological thresholds, such as the basic reproduction number, that ensure extinction or persistence of the disease in the contagion process. Moreover, a numerical scheme adapted to the model is developped and analyzed. This scheme is then used to illustrate the model with simulations, applying this last to the transmission of prion pathologies

Asymptotic behavior of age-structured and delayed Lotka-Volterra models

In this work we investigate some asymptotic properties of an age-structured Lotka-Volterra model, where a specific choice of the functional parameters allows us to formulate it as a delayed problem, for which we prove the existence of a unique coexistence equilibrium and characterize the existence of a periodic solution. We also exhibit a Lyapunov functional that enables us to reduce the attractive set to either the nontrivial equilibrium or to a periodic solution. We then prove the asymptotic stability of the nontrivial equilibrium where, depending on the existence of the periodic trajectory, we make explicit the basin of attraction of the equilibrium. Finally, we prove that these results can be extended to the initial PDE problem.Comment: 29 page

A new anti-neutrino detection technique based on positronium tagging with plastic scintillators

The main signature for anti-neutrino detection in reactor and geo-neutrino experiments based on scintillators is provided by the space-time coincidence of positron and neutron produced in the Inverse Beta Decay reaction. Such a signature strongly suppresses backgrounds and allows for measurements performed underground with a relatively high signal-to-background ratio. In an aboveground environment, however, the twofold coincidence technique is not sufficient to efficiently reject the high background rate induced by cosmogenic events. Enhancing the positron-neutron twofold coincidence efficiency has the potential to pave the way future aboveground detectors for reactor monitoring. We propose a new detection scheme based on a threefold coincidence, between the positron ionization, the ortho-positronium (o-Ps) decay, and the neutron capture, in a sandwich detector with alternated layers of plastic scintillator and aerogel powder. We present the results of a set of dedicated measurements on the achievable light yield and on the o-Ps formation and lifetime. The efficiencies for signal detection and background rejection of a preliminary detector design are also discussed.Comment: 18 pages, 10 figure

Relaxing the Hypotheses of Symmetry and Time-Reversibility in Genome Evolutionary Models

International audienceVarious genome evolutionary models have been proposed these last decades to predict the evolution of a DNA sequence over time, essentially described using a mutation matrix. By essence, all of these models relate the evolution of DNA sequences to the computation of the successive powers of the mutation matrix. To make this computation possible, hypotheses are assumed for the matrix, such as symmetry and time-reversibility, which are not compatible with mutation rates that have been recently obtained experimentally on genes ura3 and can1 of the Yeast Saccharomyces cerevisiae. In this work, authors investigate systematically the possibility to relax either the symmetry or the time-reversibility hypothesis of the mutation matrix, by investigating all the possible matrices of size 2 and 3. As an application example, the experimental study on the Yeast Saccharomyces cerevisiae has been used in order to deduce a simple mutation matrix, and to compute the future evolution of the rate purine/pyrimidine for ura3 on the one hand, and of the particular behavior of cytosines and thymines compared to purines on the other hand

Criterion of positivity for semilinear problems with applications in biology

International audienceThe goal of this article is to provide an useful criterion of positivity and well-posedness for a wide range of infinite dimensional semilinear abstract Cauchy problems. This criterion is based on some weak assumptions on the non-linear part of the semilinear problem and on the existence of a strongly continuous semigroup generated by the differential operator. To illustrate a large variety of applications, we exhibit the feasibility of this criterion through three examples in mathematical biology: epidemiology, predator-prey interactions and oncology

Measurement of ortho-Positronium Properties in Liquid Scintillators

Pulse shape discrimination in liquid scintillator detectors is a well-established technique for the discrimination of heavy particles from light particles. Nonetheless, it is not efficient in the separation of electrons and positrons, as they give rise to indistinguishable scintillator responses. This inefficiency can be overtaken through the exploitation of the formation of ortho-Positronium (o-Ps), which alters the time profile of light pulses induced by positrons. We characterized the o-Ps properties in the most commonly used liquid scintillators, i.e. PC, PXE, LAB, OIL and PC + PPO. In addition, we studied the effects of scintillator doping on the o-Ps properties for dopants currently used in neutrino experiments, Gd and Nd. Further measurements for Li-loaded and Tl-loaded liquid scintillators are foreseen. We found that the o-Ps properties are suitable for enhancing the electron-positron discrimination.Comment: 4 pages, 1 figure. Contribution to proceedings of the Low Radioactivity Techniques 2013 Workshop at LNGS, Assergi (AQ), Italy, April 10-12 201

The Waveform Digitiser of the Double Chooz Experiment: Performance and Quantisation Effects on PhotoMultiplier Tube Signals

We present the waveform digitiser used in the Double Chooz experiment. We describe the hardware and the custom-built firmware specifically developed for the experiment. The performance of the device is tested with regards to digitising low light level signals from photomultiplier tubes and measuring pulse charge. This highlights the role of quantisation effects and leads to some general recommendations on the design and use of waveform digitisers.Comment: 14 pages, 8 figures, accepted for publication in JINS

New limits on heavy sterile neutrino mixing in 8B{^{8}\rm{B}}-decay obtained with the Borexino detector

If heavy neutrinos with mass $m_{\nu_{H}}\geq$2$m_e$ are produced in the Sun via the decay ${^8\rm{B}} \rightarrow {^8\rm{Be}} + e^+ + \nu_H$ in a side branch of pp-chain, they would undergo the observable decay into an electron, a positron and a light neutrino $\nu_{H}\rightarrow\nu_{L}+e^++e^-$. In the present work Borexino data are used to set a bound on the existence of such decays. We constrain the mixing of a heavy neutrino with mass 1.5 MeV $\leq m_{\nu_{H}} \le$ 14 MeV to be $|U_{eH}|^2\leq (10^{-3}-4\times10^{-6})$ respectively. These are tighter limits on the mixing parameters than obtained in previous experiments at nuclear reactors and accelerators.Comment: 7 pages, 6 figure