Triviality of the 2D stochastic Allen-Cahn equation

We consider the stochastic Allen-Cahn equation driven by mollified space-time white noise. We show that, as the mollifier is removed, the solutions converge weakly to 0, independently of the initial condition. If the intensity of the noise simultaneously converges to 0 at a sufficiently fast rate, then the solutions converge to those of the deterministic equation. At the critical rate, the limiting solution is still deterministic, but it exhibits an additional damping term

Impact of coverage-dependent marginal costs on optimal HPV vaccination strategies

AbstractThe effectiveness of vaccinating males against the human papillomavirus (HPV) remains a controversial subject. Many existing studies conclude that increasing female coverage is more effective than diverting resources into male vaccination. Recently, several empirical studies on HPV immunization have been published, providing evidence of the fact that marginal vaccination costs increase with coverage. In this study, we use a stochastic agent-based modeling framework to revisit the male vaccination debate in light of these new findings. Within this framework, we assess the impact of coverage-dependent marginal costs of vaccine distribution on optimal immunization strategies against HPV. Focusing on the two scenarios of ongoing and new vaccination programs, we analyze different resource allocation policies and their effects on overall disease burden. Our results suggest that if the costs associated with vaccinating males are relatively close to those associated with vaccinating females, then coverage-dependent, increasing marginal costs may favor vaccination strategies that entail immunization of both genders. In particular, this study emphasizes the necessity for further empirical research on the nature of coverage-dependent vaccination costs

Thermal quantum electrodynamics of nonrelativistic charged fluids

The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for non relativistic fluids, based on a joint functional integral representation of matter and field variables. In this formalism cluster expansion techniques of classical statistical mechanics become operative. They provide an alternative to the usual Feynman diagrammatics in many-body problems which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interaction between quantum charges is partially screened by thermalized photons at large distances. More precisely one observes an exact cancellation of the dipolar electric part of the interaction, so that the asymptotic particle density correlation is now determined by relativistic effects. It has still the $r^{-6}$ decay typical for quantum charges, but with an amplitude strongly reduced by a relativistic factor.Comment: 32 pages, 0 figures. 2nd versio

On the well-posedness of the stochastic Allen-Cahn equation in two dimensions

White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical and biological systems in space dimensions d = 1,2,3. Whereas existence and uniqueness of weak solutions to these equations are well established in one dimension, the situation is different for d \geq 2. Despite their popularity in the applied sciences, higher dimensional versions of these SPDE models are generally assumed to be ill-posed by the mathematics community. We study this discrepancy on the specific example of the two dimensional Allen-Cahn equation driven by additive white noise. Since it is unclear how to define the notion of a weak solution to this equation, we regularize the noise and introduce a family of approximations. Based on heuristic arguments and numerical experiments, we conjecture that these approximations exhibit divergent behavior in the continuum limit. The results strongly suggest that a series of published numerical studies are problematic: shrinking the mesh size in these simulations does not lead to the recovery of a physically meaningful limit.Comment: 21 pages, 4 figures; accepted by Journal of Computational Physics (Dec 2011

Modeling the natural history of ductal carcinoma in situ based on population data

Background: The incidence of ductal carcinoma in situ (DCIS) has increased substantially since the introduction of mammography screening. Nevertheless, little is known about the natural history of preclinical DCIS in the absence of biopsy or complete excision. Methods: Two well-established population models evaluated six possible DCIS natural history submodels. The submodels assumed 30%, 50%, or 80% of breast lesions progress from undetectable DCIS to preclinical screen-detectable DCIS; each model additionally allowed or prohibited DCIS regression. Preclinical screen-detectable DCIS could also progress to clinical DCIS or invasive breast cancer (IBC). Applying US population screening dissemination patterns, the models projected age-specific DCIS and IBC incidence that were compared to Surveillance, Epidemiology, and End Results data. Models estimated mean sojourn time (MST) in the preclinical screen-detectable DCIS state, overdiagnosis, and the risk of progression from preclinical screen-detectable DCIS. Results: Without biopsy and surgical excision, the majority of DCIS (64-100%) in the preclinical screen-detectable state progressed to IBC in submodels assuming no DCIS regression (36-100% in submodels allowing for DCIS regression). DCIS overdiagnosis differed substantially between models and submodels, 3.1-65.8%. IBC overdiagnosis ranged 1.3-2.4%. Submodels assuming DCIS regression resulted in a higher DCIS overdiagnosis than submodels without DCIS regression. MST for progressive DCIS varied between 0.2 and 2.5 years. Conclusions: Our findings suggest that the majority of screen-detectable but unbiopsied preclinical DCIS lesions progress to IBC and that the MST is relatively short. Nevertheless, due to the heterogeneity of DCIS, more research is needed to understand the progression of DCIS by grades and molecular subtypes

Phylogenetic Patterns of Colonization and Extinction in Experimentally Assembled Plant Communities

Evolutionary history has provided insights into the assembly and functioning of plant communities, yet patterns of phylogenetic community structure have largely been based on non-dynamic observations of natural communities. We examined phylogenetic patterns of natural colonization, extinction and biomass production in experimentally assembled communities.We used plant community phylogenetic patterns two years after experimental diversity treatments (1, 2, 4, 8 or 32 species) were discontinued. We constructed a 5-gene molecular phylogeny and statistically compared relatedness of species that colonized or went extinct to remaining community members and patterns of aboveground productivity. Phylogenetic relatedness converged as species-poor plots were colonized and speciose plots experienced extinctions, but plots maintained more differences in composition than in phylogenetic diversity. Successful colonists tended to either be closely or distantly related to community residents. Extinctions did not exhibit any strong relatedness patterns. Finally, plots that increased in phylogenetic diversity also increased in community productivity, though this effect was inseparable from legume colonization, since these colonists tended to be phylogenetically distantly related.We found that successful non-legume colonists were typically found where close relatives already existed in the sown community; in contrast, successful legume colonists (on their own long branch in the phylogeny) resulted in plots that were colonized by distant relatives. While extinctions exhibited no pattern with respect to relatedness to sown plotmates, extinction plus colonization resulted in communities that converged to similar phylogenetic diversity values, while maintaining differences in species composition

The Fukushima Daiichi Accident

The Fukushima Daiichi Accident consists of a Report by the IAEA Director General and five technical volumes. It is the result of an extensive international collaborative effort involving five working groups with about 180 experts from 42 Member States with and without nuclear power programmes and several international bodies. It provides a description of the accident and its causes, evolution and consequences, based on the evaluation of data and information from a large number of sources available at the time of writing. The set contains six printed parts and five supplementary CD-ROMs. Contents: Report by the Director General; Technical Volume 1/5, Description and Context of the Accident; Technical Volume 2/5, Safety Assessment; Technical Volume 3/5, Emergency Preparedness and Response; Technical Volume 4/5, Radiological Consequences; Technical Volume 5/5, Post-accident Recovery; Annexes. The JRC contributed to volumes 1,2 and 3, which are attached.JRC.F.5-Nuclear Reactor Safety Assessmen