Sonoluminescence as a QED vacuum effect: Probing Schwinger's proposal

Several years ago Schwinger proposed a physical mechanism for sonoluminescence in terms of photon production due to changes in the properties of the quantum-electrodynamic (QED) vacuum arising from a collapsing dielectric bubble. This mechanism can be re-phrased in terms of the Casimir effect and has recently been the subject of considerable controversy. The present paper probes Schwinger's suggestion in detail: Using the sudden approximation we calculate Bogolubov coefficients relating the QED vacuum in the presence of the expanded bubble to that in the presence of the collapsed bubble. In this way we derive an estimate for the spectrum and total energy emitted. We verify that in the sudden approximation there is an efficient production of photons, and further that the main contribution to this dynamic Casimir effect comes from a volume term, as per Schwinger's original calculation. However, we also demonstrate that the timescales required to implement Schwinger's original suggestion are not physically relevant to sonoluminescence. Although Schwinger was correct in his assertion that changes in the zero-point energy lead to photon production, nevertheless his original model is not appropriate for sonoluminescence. In other works (see quant-ph/9805023, quant-ph/9904013, quant-ph/9904018, quant-ph/9905034) we have developed a variant of Schwinger's model that is compatible with the physically required timescales.Comment: 18 pages, ReV_TeX 3.2, 9 figures. Major revisions: This document is now limited to providing a probe of Schwinger's original suggestion for sonoluminescence. For details on our own variant of Schwinger's ideas see quant-ph/9805023, quant-ph/9904013, quant-ph/9904018, quant-ph/990503

Stochastic dynamics of Francisella tularensis infection and replication

We study the pathogenesis of Francisella tularensis infection with an experimental mouse model, agent-based computation and mathematical analysis. Following inhalational exposure to Francisella tularensis SCHU S4, a small initial number of bacteria enter lung host cells and proliferate inside them, eventually destroying the host cell and releasing numerous copies that infect other cells. Our analysis of disease progression is based on a stochastic model of a population of infectious agents inside one host cell, extending the birth-and-death process by the occurrence of catastrophes: cell rupture events that affect all bacteria in a cell simultaneously. Closed expressions are obtained for the survival function of an infected cell, the number of bacteria released as a function of time after infection, and the total bacterial load. We compare our mathematical analysis with the results of agent-based computation and, making use of approximate Bayesian statistical inference, with experimental measurements carried out after murine aerosol infection with the virulent SCHU S4 strain of the bacterium Francisella tularensis, that infects alveolar macrophages. The posterior distribution of the rate of replication of intracellular bacteria is consistent with the estimate that the time between rounds of bacterial division is less than 6 hours in vivo

Fusion and fission events regulate endosome maturation and viral escape

Endosomes are intracellular vesicles that mediate the communication of the cell with its extracellular environment. They are an essential part of the cell’s machinery regulating intracellular trafficking via the endocytic pathway. Many viruses, which in order to replicate require a host cell, attach themselves to the cellular membrane; an event which usually initiates uptake of a viral particle through the endocytic pathway. In this way viruses hijack endosomes for their journey towards intracellular sites of replication and avoid degradation without host detection by escaping the endosomal compartment. Recent experimental techniques have defined the role of endosomal maturation in the ability of enveloped viruses to release their genetic material into the cytoplasm. Endosome maturation depends on a family of small hydrolase enzymes (or GTPases) called Rab proteins, arranged on the cytoplasmic surface of its membrane. Here, we model endosomes as intracellular compartments described by two variables (its levels of active Rab5 and Rab7 proteins) and which can undergo coagulation (or fusion) and fragmentation (or fission). The key element in our approach is the “per-cell endosomal distribution” and its dynamical (Boltzmann) equation. The Boltzmann equation allows us to derive the dynamics of the total number of endosomes in a cell, as well as the mean and the standard deviation of its active Rab5 and Rab7 levels. We compare our mathematical results with experiments of Dengue viral escape from endosomes. The relationship between endosomal active Rab levels and pH suggests a mechanism that can account for the observed variability in viral escape times, which in turn regulate the viability of a viral intracellular infection

Phenotypic prediction based on metabolomic data : lasso vs Bolasso, primary data vs wavelet transformation

International audienceUnderstanding the relations between various 'omics data (such as metabolomics or genomics data) and phenotypes of interest is one of the current major challenges in biology. This question can be addressed by trying to learn a way to predict the phenotype value from the omic from joint observations of the omic and of the phenotype. In this paper, we focus on the prediction of a phenotype related to the quality of the meat from metabolomic data. As metabolomic data are high dimensional data and as, conjointly, the number of observations is often restricted, model selection methods are a way both to obtain a relevant solution to the prediction problem but also to select the most important metabolomes related to the phenotype under study. During the past years, model selection has know a growing interest in the statistical community: the first - and also probably the most known - selection method has been introducted by \citep{Tibshirani:1996} under the name of LASSO. Several variants of this original approach has then been proposed such as, recently, a bootstraped LASSO, named BOLASSO, introduced in (Bach, 2009). The proposal of this paper is to combine a wavelet representation of the metabolome spectra (see (Mallat, 1999) and (Antonini, 1992) for a complete introduction to wavelets) with the BOLASSO approach. We compare this methodology to more classical methods using either the original spectra as predictors (instead of the wavelet representation) or the original LASSO to select the model. The following section deals with the methodological description of the approach whereas the next one details the experiments and results

IL7 receptor signalling in T cells: a mathematical modelling perspective

Interleukin‐7 (IL7) plays a nonredundant role in T cell survival and homeostasis, which is illustrated in the severe T cell lymphopenia of IL7‐deficient mice, or demonstrated in animals or humans that lack expression of either the IL7Rα or γ c chain, the two subunits that constitute the functional IL7 receptor. Remarkably, IL7 is not expressed by T cells themselves, but produced in limited amounts by radio‐resistant stromal cells. Thus, T cells need to constantly compete for IL7 to survive. How T cells maintain homeostasis and further maximize the size of the peripheral T cell pool in face of such competition are important questions that have fascinated both immunologists and mathematicians for a long time. Exceptionally, IL7 downregulates expression of its own receptor, so that IL7‐signaled T cells do not consume extracellular IL7, and thus, the remaining extracellular IL7 can be shared among unsignaled T cells. Such an altruistic behavior of the IL7Rα chain is quite unique among members of the γ c cytokine receptor family. However, the consequences of this altruistic signaling behavior at the molecular, single cell and population levels are less well understood and require further investigation. In this regard, mathematical modeling of how a limited resource can be shared, while maintaining the clonal diversity of the T cell pool, can help decipher the molecular or cellular mechanisms that regulate T cell homeostasis. Thus, the current review aims to provide a mathematical modeling perspective of IL7‐dependent T cell homeostasis at the molecular, cellular and population levels, in the context of recent advances in our understanding of the IL7 biology

Not all adiabatic vacua are physical states

Adiabatic vacua are known to be Hadamard states. We show, however that the energy-momentum tensor of a linear Klein-Gordon field on Robertson-Walker spaces developes a generic singularity on the initial hypersurface if the adiabatic vacuum is of order less than four. Therefore, adiabatic vacua are physically reasonable only if their order is at least four. A certain non-local large momentum expansion of the mode functions has recently been suggested to yield the subtraction terms needed to remove the ultraviolet divergences in the energy-momentum tensor. We find that this scheme fails to reproduce the trace anomaly and therefore is not equivalent to adiabatic regularisation.Comment: 13 pages, LaTex2

Renormalization of the nonequilibrium dynamics of fermions in a flat FRW universe

We derive the renormalized equations of motion and the renormalized energy-momentum tensor for fermions coupled to a spatially homogeneous scalar field (inflaton) in a flat FRW geometry. The fermion back reaction to the metric and to the inflaton field is formulated in one-loop approximation. Having determined the infinite counter terms in an $\bar{MS}$ scheme we formulate the finite terms in a form suitable for numerical computation. We comment on the trace anomaly which is inferred from the standard analysis. We also address the problem of initial singularities and determine the Bogoliubov transformation by which they are removed.Comment: 26 pages, LaTe

Has the Universe always expanded ?

We consider a cosmological setting for which the currently expanding era is preceded by a contracting phase, that is, we assume the Universe experienced at least one bounce. We show that scalar hydrodynamic perturbations lead to a singular behavior of the Bardeen potential and/or its derivatives (i.e. the curvature) for whatever Universe model for which the last bounce epoch can be smoothly and causally joined to the radiation dominated era. Such a Universe would be filled with non-linear perturbations long before nucleosynthesis, and would thus be incompatible with observations. We therefore conclude that no observable bounce could possibly have taken place in the early universe if Einstein gravity together with hydrodynamical fluids is to describe its evolution, and hence, under these conditions, that the Universe has always expanded.Comment: 11 pages, LaTeX-ReVTeX, no figures, submitted to PR

Spinodal Decomposition and Inflation: Dynamics and Metric Perturbations

We analyse the dynamics of spinodal decomposition in inflationary cosmology using the closed time path formalism of out of equilibrium quantum field theory combined with the non-perturbative Hartree approximation. In addition to a general analysis, we compute the detailed evolution of two inflationary models of particular importance: lambda Phi^4 new inflation and natural inflation. We compute the metric fluctuations resulting from inflationary phase transitions in the slow roll approximation, showing that there exists a regime for which quantum fluctuations of the inflaton field result in a significant deviation in the predictions of the spectrum of primordial density perturbations from standard results. We provide case examples for which a blue tilt to the power spectrum (i.e. n_s > 1) results from the evolution of a single inflaton field, and demonstrate that field fluctuations may result in a scalar amplitude of fluctuations significantly below standard predictions, resulting in a slight alleviation of the inflationary fine tuning problem. We show explicitly that the metric perturbation spectrum resulting from inflation depends upon the state at the outset of the inflationary phase.Comment: 26 pages, 19 figure