General Convolution Identities for Bernoulli and Euler Polynomials

Using general identities for difference operators, as well as a technique of symbolic computation and tools from probability theory, we derive very general kth order (k \ge 2) convolution identities for Bernoulli and Euler polynomials. This is achieved by use of an elementary result on uniformly distributed random variables. These identities depend on k positive real parameters, and as special cases we obtain numerous known and new identities for these polynomials. In particular we show that the well-known identities of Miki and Matiyasevich for Bernoulli numbers are special cases of the same general formula.Comment: 20 page

Perturbative Hamiltonian constraints for higher order theories

We present a method for constructing a consistent low energy canonical formalism for higher order time-derivative theories, extending the Dirac method to include perturbative Hamiltonian constraints. We apply it to two paradigmatic examples: the Pais-Uhlenbeck oscillator and the Bernard-Duncan scalar field. We also compare the results, both at the classical and quantum level, with the ones corresponding to a direct perturbative construction applied to the exact higher order theory. This comparison highligths the soundness of the present formalism.Comment: 26 pages, 4 figures; review section shortened and appendices change

Genetic characterization of Erve virus, a European Nairovirus distantly related to Crimean-Congo hemorrhagic fever virus

Erve virus (ERVEV) is a European Nairovirus that is suspected to cause severe headache (thunderclap headache) and intracerebral hemorrhage. The mode of transmission to humans (ticks or mosquitoes) is still unknown. Currently, no standardized testing method for ERVEV exists and only a small partial sequence of the polymerase gene is available. Here, we present the first complete genome sequence of ERVEV S, M, and L segments. Phylogenetic comparison of the amino acid sequence of the L-protein (RNA-dependent RNA polymerase) revealed only 48 % homology to available L-protein sequences of other Nairoviruses like Crimean-Congo hemorrhagic fever virus, Nairobi sheep disease virus, Hazara virus, Kupe virus, and Dugbe virus. Among themselves, these Nairoviruses show 62-89 % homology in the L-protein sequences. Therefore, ERVEV seems to be only distantly related to other Nairoviruses. The new sequence data can be used for the development of diagnostic methods and the identification of the natural vector

Phenotypic Plasticity of Leaf Shape along a Temperature Gradient in Acer rubrum

Both phenotypic plasticity and genetic determination can be important for understanding how plants respond to environmental change. However, little is known about the plastic response of leaf teeth and leaf dissection to temperature. This gap is critical because these leaf traits are commonly used to reconstruct paleoclimate from fossils, and such studies tacitly assume that traits measured from fossils reflect the environment at the time of their deposition, even during periods of rapid climate change. We measured leaf size and shape in Acer rubrum derived from four seed sources with a broad temperature range and grown for two years in two gardens with contrasting climates (Rhode Island and Florida). Leaves in the Rhode Island garden have more teeth and are more highly dissected than leaves in Florida from the same seed source. Plasticity in these variables accounts for at least 6–19 % of the total variance, while genetic differences among ecotypes probably account for at most 69–87 %. This study highlights the role of phenotypic plasticity in leaf-climate relationships. We suggest that variables related to tooth count and leaf dissection in A. rubrum can respond quickly to climate change, which increases confidence in paleoclimate methods that use these variables