BackgroundThe dramatic mass mortalities amongst hibernating bats in Northeastern America caused by “white nose-syndrome” (WNS) continue to threaten populations of different bat species. The cold-loving fungus, Geomyces destructans, is the most likely causative agent leading to extensive destruction of the skin, particularly the wing membranes. Recent investigations in Europe confirmed the presence of the fungus G. destructans without associated mass mortality in hibernating bats in six countries but its distribution remains poorly known.Methodology/Principal FindingsWe collected data on the presence of bats with white fungal growth in 12 countries in Europe between 2003 and 2010 and conducted morphological and genetic analysis to confirm the identity of the fungus as Geomyces destructans. Our results demonstrate the presence of the fungus in eight countries spanning over 2000 km from West to East and provide compelling photographic evidence for its presence in another four countries including Romania, and Turkey. Furthermore, matching prevalence data of a hibernaculum monitored over two consecutive years with data from across Europe show that the temporal occurrence of the fungus, which first becomes visible around February, peaks in March but can still be seen in some torpid bats in May or June, is strikingly similar throughout Europe. Finally, we isolated and cultured G. destructans from a cave wall adjacent to a bat with fungal growth.Conclusions/Significance G. destructans is widely found over large areas of the European continent without associated mass mortalities in bats, suggesting that the fungus is native to Europe. The characterisation of the temporal variation in G. destructans growth on bats provides reference data for studying the spatio-temporal dynamic of the fungus. Finally, the presence of G. destructans spores on cave walls suggests that hibernacula could act as passive vectors and/or reservoirs for G. destructans and therefore, might play an important role in the transmission process.

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Abstract. For curved projective manifolds we introduce a notion of a normal tractor frame field, based around any point. This leads to canonical systems of (redundant) coordinates that generalise the usual homogeneous coordinates on projective space. These give preferred local maps to the model projective space that encode geometric contact with the model to a level that is optimal, in a suitable sense. In terms of the trivialisations arising from the special frames, normal solutions of classes of natural linear PDE (so-called first BGG equations) are shown to be necessarily polynomial in the generalised homogeneous coordinates; the polynomial system is the pull back of a polynomial system that solves the corresponding problem on the model. Thus questions concerning the zero locus of solutions, as well as related finer geometric and smooth data, are reduced to a study of the corresponding polynomial systems and algebraic sets. We show that a normal solution determines a canonical manifold stratification that reflects an orbit decomposition of the model. Applications include the construction of structures that are analogues of Poincaré-Einstein manifolds.

The properties of lead zirconate titanate (PZT) ceramics are determined by the microstructure and chemical homogeneity of Zr, Ti, and dopants within the grains as well as the presence of secondary grain boundary phases. Stoichiometric 53/47 PZT and compositions with 3 mol% PbO excess were prepared by the mixed-oxide process, and were densified by pressureless sintering in oxygen. The influence of PbO content and different La concentrations on the densification behavior was analyzed by dilatometric measurements. Quantitative image analysis showed a different relative density and grain size dependence for samples containing >0.5 mol% additives compared to samples with <0.5 mol% La. On the basis of a model experiment and by using different analytical methods (microprobe analysis, HRTEM, STEM, and Auger spectroscopy) three types of inhomogeneities could be detected in conventionally prepared PZT ceramics: the existence of Ti and La enrichment in the core of PZT grains, and PbO-rich secondary phases in triple junctions as well as in grain boundary films. The results of the microstructural characterization and the analysis of the densification behavior were finally combined to deduce a sintering model based on a Pb-vacancy concentration gradient within the PZT grains.

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The continuous-space symbiotic branching model describes the evolution of two interacting populations that can reproduce locally only in the simultaneous presence of each other. If started with complementary Heaviside initial conditions, the interface where both populations coexist remains compact. Together with a diffusive scaling property, this suggests the presence of an interesting scaling limit. Indeed, in the present paper, we show weak convergence of the diffusively rescaled populations as measure-valued processes in the Skorokhod, respectively the Meyer-Zheng, topology (for suitable parameter ranges). The limit can be characterized as the unique solution to a martingale problem and satisfies a "separation of types" property. This provides an important step toward an understanding of the scaling limit for the interface. As a corollary, we obtain an estimate on the moments of the width of an approximate interface. This is an electronic reprint of the original article published by the Institute of Mathematical Statistics in The Annals of Probability, 2016, Vol. 44, No. 2, 807-866. This reprint differs from the original in pagination and typographic detail. 1 4 J. BLATH, M. HAMMER AND M. ORTGIESE before Corollary 1.2. Recently, analogous results have been derived by Döring and Mytnik in the case ̺ ∈ (−1, 1) in [9, 10]. Returning to the continuous-space set-up, for ̺ = −1 (the stepping stone model) Tribe [27] proves a "functional limit theorem": For a pair of (continuous) functions (u, v), define R(u, v) := sup{x : u(x) > 0}, L(u, v) = inf{x : v(x) > 0}. (5)Note that for a solution (u t , v t ) t≥0 of the symbiotic branching model, the interface at time t is contained in the interval [L(u t , v t ), R(u t , v t )]. It is proved in [27] for ̺ = −1 and for continuous initial conditions u 0 = 1 − v 0 which satisfy −∞ < L(u 0 , v 0 ) ≤ R(u 0 , v 0 ) < ∞ that under Brownian rescaling, the motion of the position of the right endpoint of the interface t → 1 n R(u n 2 t , 1 − u n 2 t ), t ≥ 0, converges to a Brownian motion as n → ∞.The above results suggest the existence of an interesting diffusive scaling limit for the continuous-space symbiotic branching model (and its interface) for ̺ > −1. This is the starting point of our investigation. However, compared to the case ̺ = −1, the situation is more involved here: For example, the total mass of the solution is not necessarily bounded, and in particular, moments of the solution may diverge as t → ∞, depending on ̺. For instance, second moments diverge for ̺ ≥ 0. In order to state this result, which was obtained in [3]

We give recursions for the expected site-frequency spectrum associated with so-called Xi-coalescents, that is exchangeable coalescents which admit simultaneous multiple mergers of ancestral lineages. Xi-coalescents arise, for example, in association with population models of skewed offspring distributions with diploidy, recurrent advantageous mutations, or strong bottlenecks. In contrast, the simpler Lambda-coalescents admit multiple mergers of lineages, but at most one such merger each time. Xi-coalescents, as well as Lambda-coalescents, can predict an excess of singletons, compared to the Kingman coalescent. We compare estimates of coalescent parameters when Xi-coalescents are applied to data generated by Lambda-coalescents, and vice versa. In general, Xi-coalescents predict fewer singletons than corresponding Lambda-coalescents, but a higher count of mutations of size larger than singletons. We fit examples of Xi-coalescents to unfolded site-frequency spectra obtained for autosomal loci of the diploid Atlantic cod, and obtain different coalescent parameter estimates than obtained with corresponding Lambda-coalescents. Our results provide new inference tools, and suggest that for autosomal population genetic data from diploid or polyploid highly fecund populations who may have skewed offspring distributions, one should not apply Lambda-coalescents, but Xi-coalescents.