Analysing degeneracies in networks spectra

Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network's adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks spectra. We find that the eigenvectors associated with the degenerate eigenvalues shed light on the structures contributing to the degeneracy. Since these degeneracies are rarely observed in model graphs, we present results for various cancer networks. This approach gives an opportunity to search for structures contributing to degeneracy which might have an important role in a network.Comment: 5 pages, 3 figures and Supplementary Materia

Antibody-mediated cross-linking of gut bacteria hinders the spread of antibiotic resistance

The body is home to a diverse microbiota, mainly in the gut. Resistant bacteria are selected for by antibiotic treatments, and once resistance becomes widespread in a population of hosts, antibiotics become useless. Here, we develop a multiscale model of the interaction between antibiotic use and resistance spread in a host population, focusing on an important aspect of within-host immunity. Antibodies secreted in the gut enchain bacteria upon division, yielding clonal clusters of bacteria. We demonstrate that immunity-driven bacteria clustering can hinder the spread of a novel resistant bacterial strain in a host population. We quantify this effect both in the case where resistance pre-exists and in the case where acquiring a new resistance mutation is necessary for the bacteria to spread. We further show that the reduction of spread by clustering can be countered when immune hosts are silent carriers, and are less likely to get treated, and/or have more contacts. We demonstrate the robustness of our findings to including stochastic within-host bacterial growth, a fitness cost of resistance, and its compensation. Our results highlight the importance of interactions between immunity and the spread of antibiotic resistance, and argue in the favor of vaccine-based strategies to combat antibiotic resistance.Comment: 49 pages, 11 figure

Discussion on various model of multiple scattering in acoustics and elastic heterogeneous media

International audienceThe propagation of acoustic or elastic wave through an heterogeneous domain is investigated in 2D. For heterogeneous medium composed of discrete scattered embedded in a homogeneous matrix, effective medium theories consists in modeling the coherent part of the wave obtained form equivalent propagation along various distribution of scatterer. The main objective is to determine attenuation and dispersion of the wave. In the case of half-space or slab, transmission and reflection coefficient can be obtained. Here various model are presented and compared in the classical case: half-space heterogeneous domain probed by incident plane wave. A synthetic formalism is the occasion to generalized this problem to any bounded domain. It is the occasion to highlight some particular features of this full 2D-problem (where translational invariance along one direction is broken). In particular a new synthetic formulation of the QCA is proposed. Asymptotic calculation will be presented for low-frequency regime or dilute media

Solving the stochastic dynamics of population growth

Population growth is a fundamental process in ecology and evolution. The population size dynamics during growth are often described by deterministic equations derived from kinetic models. Here, we simulate several population growth models and compare the size averaged over many stochastic realizations with the deterministic predictions. We show that these deterministic equations are generically bad predictors of the average stochastic population dynamics. Specifically, deterministic predictions overestimate the simulated population sizes, especially those of populations starting with a small number of individuals. Describing population growth as a stochastic birth process, we prove that the discrepancy between deterministic predictions and simulated data is due to unclosed-moment dynamics. In other words, the deterministic approach does not consider the variability of birth times, which is particularly important with small population sizes. We show that some moment-closure approximations describe the growth dynamics better than the deterministic prediction. However, they do not reduce the error satisfactorily and only apply to some population growth models. We explicitly solve the stochastic growth dynamics, and our solution applies to any population growth model. We show that our solution exactly quantifies the dynamics of a community composed of different strains and correctly predicts the fixation probability of a strain in a serial dilution experiment. Our work sets the foundations for a more faithful modeling of community and population dynamics. It will allow the development of new tools for a more accurate analysis of experimental and empirical results, including the inference of important growth parameters

Efficient shape reconstruction of non-circular tubes using broadband acoustic measurements

International audienceWe propose an algorithm for reconstructing the boundaries of a non-circular cylindrical tube from broadband acoustic measurements. This algorithm is based on the minimization of a cost function, which is the average over frequency of the absolute difference between the estimated and the measured scattered field. The estimated field is computed efficiently (very fast) using ICBA, an analytic method that provides an approximate solution of the forward problem. Numerical results show that our algorithm is robust and provides an accurate reconstruction without any explicit regularization

Challenges and pitfalls of inferring microbial growth rates from lab cultures

IntroductionAfter more than 100 years of generating monoculture batch culture growth curves, microbial ecologists and evolutionary biologists still lack a reference method for inferring growth rates. Our work highlights the challenges of estimating the growth rate from growth curve data. It shows that inaccurate estimates of growth rates significantly impact the estimated relative fitness, a principal quantity in evolution and ecology. Methods and resultsFirst, we conducted a literature review and found which methods are currently used to estimate growth rates. These methods differ in the meaning of the estimated growth rate parameter. Mechanistic models estimate the intrinsic growth rate µ, whereas phenomenological methods – both model-based and model-free – estimate the maximum per capita growth rate µmax. Using math and simulations, we show the conditions in which µmax is not a good estimator of µ. Then, we demonstrate that inaccurate absolute estimates of µ are not overcome by calculating relative values. Importantly, we find that poor approximations for µ sometimes lead to wrongly classifying a beneficial mutant as deleterious. Finally, we re-analyzed four published data sets, using most of the methods found in our literature review. We detected no single best-fitting model across all experiments within a data set and found that the Gompertz models, which were among the most commonly used, were often among the worst-fitting. DiscussionOur study suggests how experimenters can improve their growth rate and associated relative fitness estimates and highlights a neglected but fundamental problem for nearly everyone who studies microbial populations in the lab

Time-domain numerical simulations of multiple scattering to extract elastic effective wavenumbers

Elastic wave propagation is studied in a heterogeneous 2-D medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident wavelength is similar to the radius of the inclusions. A purely numerical methodology is presented, with which the limitations usually associated with low scatterer concentrations can be avoided. The elastodynamic equations are integrated by a fourth-order time-domain numerical scheme. An immersed interface method is used to accurately discretize the interfaces on a Cartesian grid. The effective field is extracted from the simulated data, and signal-processing tools are used to obtain the complex effective wavenumbers. The numerical reference solution thus-obtained can be used to check the validity of multiple scattering analytical models. The method is applied to the case of concrete. A parametric study is performed on longitudinal and transverse incident plane waves at various scatterers concentrations. The phase velocities and attenuations determined numerically are compared with predictions obtained with multiple scattering models, such as the Independent Scattering Approximation model, the Waterman-Truell model, and the more recent Conoir-Norris model.Comment: Waves in Random and Complex Media (2012) XX

Evolutionary rescue in a fluctuating environment: periodic versus quasi-periodic environmental changes

No environment is constant over time, and environmental fluctuations impact the outcome of evolutionary dynamics. Survival of a population not adapted to some environmental conditions is threatened unless, for example, a mutation rescues it, an eco-evolutionary process termed evolutionary rescue. We here investigate evolutionary rescue in an environment that fluctuates between a favourable state, in which the population grows, and a harsh state, in which the population declines. We develop a stochastic model that includes both population dynamics and genetics.We derive analytical predictions for the mean extinction time of a non-adapted population given that it is not rescued, the probability of rescue by amutation, and the mean appearance time of a rescue mutant, which we validate using numerical simulations. We find that stochastic environmental fluctuations, resulting in quasi-periodic environmental changes, accelerate extinction and hinder evolutionary rescue compared with deterministic environmental fluctuations, resulting in periodic environmental changes. We demonstrate that high equilibrium population sizes and per capita growth rates maximize the chances of evolutionary rescue. We show that an imperfectly harsh environment, which does not fully prevent births but makes the death rate to birth rate ratio much greater than unity, has almost the same rescue probability as a perfectly harsh environment, which fully prevents births. Finally, we put our results in the context of antimicrobial resistance and conservation biology