On the Algebra of Ghost Fields

We study in detail the algebra of free ghost fields which we realize in a Hilbert-Fock space with positive metric. The investigation of causality clarifies the exact reason for the failure of the spin-statistics theorem and leads to the introduction of the Krein Operator. We study the charge algebra of the ghost fields which gives a representation of ${\rm gl}(2,{\cal C})$. The symmetries of the $S$-matrix in ghost space are pointed out.Comment: Plain TeX, 16 page

Non-Uniqueness of Quantized Yang-Mills Theories

We consider quantized Yang-Mills theories in the framework of causal perturbation theory which goes back to Epstein and Glaser. In this approach gauge invariance is expressed by a simple commutator relation for the S-matrix. The most general coupling which is gauge invariant in first order contains a two-parametric ambiguity in the ghost sector - a divergence- and a coboundary-coupling may be added. We prove (not completely) that the higher orders with these two additional couplings are gauge invariant, too. Moreover we show that the ambiguities of the n-point distributions restricted to the physical subspace are only a sum of divergences (in the sense of vector analysis). It turns out that the theory without divergence- and coboundary-coupling is the most simple one in a quite technical sense. The proofs for the n-point distributions containing coboundary-couplings are given up to third or fourth order only, whereas the statements about the divergence-coupling are proven in all orders.Comment: 22 pages. The paper is written in TEX. The necessary macros are include

The Epstein-Glaser approach to pQFT: graphs and Hopf algebras

The paper aims at investigating perturbative quantum field theory (pQFT) in the approach of Epstein and Glaser (EG) and, in particular, its formulation in the language of graphs and Hopf algebras (HAs). Various HAs are encountered, each one associated with a special combination of physical concepts such as normalization, localization, pseudo-unitarity, causality and an associated regularization, and renormalization. The algebraic structures, representing the perturbative expansion of the S-matrix, are imposed on the operator-valued distributions which are equipped with appropriate graph indices. Translation invariance ensures the algebras to be analytically well-defined and graded total symmetry allows to formulate bialgebras. The algebraic results are given embedded in the physical framework, which covers the two recent EG versions by Fredenhagen and Scharf that differ with respect to the concrete recursive implementation of causality. Besides, the ultraviolet divergences occuring in Feynman's representation are mathematically reasoned. As a final result, the change of the renormalization scheme in the EG framework is modeled via a HA which can be seen as the EG-analog of Kreimer's HA.Comment: 52 pages, 5 figure

On Gauge Invariance and Spontaneous Symmetry Breaking

We show how the widely used concept of spontaneous symmetry breaking can be explained in causal perturbation theory by introducing a perturbative version of quantum gauge invariance. Perturbative gauge invariance, formulated exclusively by means of asymptotic fields, is discussed for the simple example of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant for the electroweak theory, as pointed out elsewhere.Comment: 13 pages, latex, no figure

Mitogenomics of Central American weakly-electric fishes

Electric fishes are a diverse group of freshwater organisms with the ability to generate electric organ discharges (EODs) that are used for communication and electrolocation. This group (ca. 200 species) has originated in South America, and six species colonized the Central American Isthmus. Here, we assembled the complete mitochondrial genomes (mitogenomes) for three Central American electric fishes (i.e. Sternopygus dariensis, Brachyhypopomus occidentalis, and Apteronotus rostratus), and, based on these data, explored their phylogenetic position among Gymnotiformes. The three mitogenomes show the same gene order, as reported for other fishes, with a size ranging from 16,631 to 17,093 bp. We uncovered a novel 60 bp intergenic spacer (IGS) located between the COII and tRNALys genes, which appears to be unique to the Apteronotidae. Furthermore, phylogenetic relationships supported the traditional monophyly of Gymnotiformes, with the three species positioned within their respective family. In addition, the genus Apteronotus belongs to the early diverging lineage of the order. Finally, we found high sequence divergence (13%) between our B. occidentalis specimen and a sequence previously reported in GenBank, suggesting that the prior mitogenome of B. occidentalis represents a different South American species. Indeed, phylogenetic analyses using Cytochrome b gene across the genus placed the previously reported individual within B. bennetti. Our study provides novel mitogenome resources that will advance our understanding of the diversity and phylogenetic history of Neotropical fishesElectric fishes are a diverse group of freshwater organisms with the ability to generate electric organ discharges (EODs) that are used for communication and electrolocation. This group (ca. 200 species) has originated in South America, and six species colonized the Central American Isthmus. Here, we assembled the complete mitochondrial genomes (mitogenomes) for three Central American electric fishes (i.e. Sternopygus dariensis, Brachyhypopomus occidentalis, and Apteronotus rostratus), and, based on these data, explored their phylogenetic position among Gymnotiformes. The three mitogenomes show the same gene order, as reported for other fishes, with a size ranging from 16,631 to 17,093 bp. We uncovered a novel 60 bp intergenic spacer (IGS) located between the COII and tRNALys genes, which appears to be unique to the Apteronotidae. Furthermore, phylogenetic relationships supported the traditional monophyly of Gymnotiformes, with the three species positioned within their respective family. In addition, the genus Apteronotus belongs to the early diverging lineage of the order. Finally, we found high sequence divergence (13%) between our B. occidentalis specimen and a sequence previously reported in GenBank, suggesting that the prior mitogenome of B. occidentalis represents a different South American species. Indeed, phylogenetic analyses using Cytochrome b gene across the genus placed the previously reported individual within B. bennetti. Our study provides novel mitogenome resources that will advance our understanding of the diversity and phylogenetic history of Neotropical fishe

tempo and mode of allopatric divergence in the weakly electric fish Sternopygus dariensis in the Isthmus of Panama

Spatial isolation is one of the main drivers of allopatric speciation, but the extent to which spatiallysegregated populations accumulate genetic differences relevant to speciation is not always clear. We used data from ultraconserved elements (UCEs) and whole mitochondrial genomes (i.e., mitogenomes) to explore genetic variation among allopatric populations of the weakly electric fish Sternopygus dariensis across the Isthmus of Panama. We found strong genetic divergence between eastern and western populations of S. dariensis. Over 77% of the UCE loci examined were differentially fixed between populations, and these loci appear to be distributed across the species’ genome. Population divergence occurred within the last 1.1 million years, perhaps due to global glaciation oscillations during the Pleistocene. Our results are consistent with a pattern of genetic differentiation under strict geographic isolation, and suggest the presence of incipient allopatric species within S. dariensis. Genetic divergence in S. dariensis likely occurred in situ, long after the closure of the Isthmus of Panama. Our study highlights the contribution of spatial isolation and vicariance to promoting rapid diversification in Neotropical freshwater fishes. The study of spatially-segregated populations within the Isthmus of Panama could reveal how genetic differences accumulate as allopatric speciation proceeds.Spatial isolation is one of the main drivers of allopatric speciation, but the extent to which spatiallysegregated populations accumulate genetic differences relevant to speciation is not always clear. We used data from ultraconserved elements (UCEs) and whole mitochondrial genomes (i.e., mitogenomes) to explore genetic variation among allopatric populations of the weakly electric fish Sternopygus dariensis across the Isthmus of Panama. We found strong genetic divergence between eastern and western populations of S. dariensis. Over 77% of the UCE loci examined were differentially fixed between populations, and these loci appear to be distributed across the species’ genome. Population divergence occurred within the last 1.1 million years, perhaps due to global glaciation oscillations during the Pleistocene. Our results are consistent with a pattern of genetic differentiation under strict geographic isolation, and suggest the presence of incipient allopatric species within S. dariensis. Genetic divergence in S. dariensis likely occurred in situ, long after the closure of the Isthmus of Panama. Our study highlights the contribution of spatial isolation and vicariance to promoting rapid diversification in Neotropical freshwater fishes. The study of spatially-segregated populations within the Isthmus of Panama could reveal how genetic differences accumulate as allopatric speciation proceeds

Fluctuations and differential contraction during regeneration of Hydra vulgaris tissue toroids

We studied regenerating bilayered tissue toroids dissected from Hydra vulgaris polyps and relate our macroscopic observations to the dynamics of force-generating mesoscopic cytoskeletal structures. Tissue fragments undergo a specific toroid-spheroid folding process leading to complete regeneration towards a new organism. The time scale of folding is too fast for biochemical signalling or morphogenetic gradients which forced us to assume purely mechanical self-organization. The initial pattern selection dynamics was studied by embedding toroids into hydro-gels allowing us to observe the deformation modes over longer periods of time. We found increasing mechanical fluctuations which break the toroidal symmetry and discuss the evolution of their power spectra for various gel stiffnesses. Our observations are related to single cell studies which explain the mechanical feasibility of the folding process. In addition, we observed switching of cells from a tissue bound to a migrating state after folding failure as well as in tissue injury. We found a supra-cellular actin ring assembled along the toroid's inner edge. Its contraction can lead to the observed folding dynamics as we could confirm by finite element simulations. This actin ring in the inner cell layer is assembled by myosin- driven length fluctuations of supra-cellular {\alpha}-actin structures (myonemes) in the outer cell-layer.Comment: 19 pages and 8 figures, submitted to New Journal of Physic

Massive Vector Mesons and Gauge Theory

We show that the requirements of renormalizability and physical consistency imposed on perturbative interactions of massive vector mesons fix the theory essentially uniquely. In particular physical consistency demands the presence of at least one additional physical degree of freedom which was not part of the originally required physical particle content. In its simplest realization (probably the only one) these are scalar fields as envisaged by Higgs but in the present formulation without the ``symmetry-breaking Higgs condensate''. The final result agrees precisely with the usual quantization of a classical gauge theory by means of the Higgs mechanism. Our method proves an old conjecture of Cornwall, Levin and Tiktopoulos stating that the renormalization and consistency requirements of spin=1 particles lead to the gauge theory structure (i.e. a kind of inverse of 't Hooft's famous renormalizability proof in quantized gauge theories) which was based on the on-shell unitarity of the $S$-matrix. We also speculate on a possible future ghostfree formulation which avoids ''field coordinates'' altogether and is expected to reconcile the on-shell S-matrix point of view with the off-shell field theory structure.Comment: 53 pages, version to appear in J. Phys.

The validation service of the hydrological SAF geostationary and polar satellite precipitation products

Abstract. The development phase (DP) of the EUMETSAT Satellite Application Facility for Support to Operational Hydrology and Water Management (H-SAF) led to the design and implementation of several precipitation products, after 5 yr (2005–2010) of activity. Presently, five precipitation estimation algorithms based on data from passive microwave and infrared sensors, on board geostationary and sun-synchronous platforms, function in operational mode at the H-SAF hosting institute to provide near real-time precipitation products at different spatial and temporal resolutions. In order to evaluate the precipitation product accuracy, a validation activity has been established since the beginning of the project. A Precipitation Product Validation Group (PPVG) works in parallel with the development of the estimation algorithms with two aims: to provide the algorithm developers with indications to refine algorithms and products, and to evaluate the error structure to be associated with the operational products. In this paper, the framework of the PPVG is presented: (a) the characteristics of the ground reference data available to H-SAF (i.e. radar and rain gauge networks), (b) the agreed upon validation strategy settled among the eight European countries participating in the PPVG, and (c) the steps of the validation procedures. The quality of the reference data is discussed, and the efforts for its improvement are outlined, with special emphasis on the definition of a ground radar quality map and on the implementation of a suitable rain gauge interpolation algorithm. The work done during the H-SAF development phase has led the PPVG to converge into a common validation procedure among the members, taking advantage of the experience acquired by each one of them in the validation of H-SAF products. The methodology is presented here, indicating the main steps of the validation procedure (ground data quality control, spatial interpolation, up-scaling of radar data vs. satellite grid, statistical score evaluation, case study analysis). Finally, an overview of the results is presented, focusing on the monthly statistical indicators, referred to the satellite product performances over different seasons and areas

CAG Repeats Determine Brain Atrophy in Spinocerebellar Ataxia 17: A VBM Study

Abnormal repeat length has been associated with an earlier age of onset and more severe disease progression in the rare neurodegenerative disorder spinocerebellar ataxia 17 (SCA17).To determine whether specific structural brain degeneration and rate of disease progression in SCA17 might be associated with the CAG repeat size, observer-independent voxel-based morphometry was applied to high-resolution magnetic resonance images of 16 patients with SCA17 and 16 age-matched healthy controls. The main finding contrasting SCA17 patients with healthy controls demonstrated atrophy in the cerebellum bilaterally. Multiple regression analyses with available genetic data and also post-hoc correlations revealed an inverse relationship again with cerebellar atrophy. Moreover, we found an inverse relationship between the CAG repeat length and rate of disease progression.Our results highlight the fundamental role of the cerebellum in this neurodegenerative disease and support the genotype-phenotype relationship in SCA17 patients. Genetic factors may determine individual susceptibility to neurodegeneration and rate of disease progression