Tangent bundle geometry from dynamics: application to the Kepler problem

In this paper we consider a manifold with a dynamical vector field and inquire about the possible tangent bundle structures which would turn the starting vector field into a second order one. The analysis is restricted to manifolds which are diffeomorphic with affine spaces. In particular, we consider the problem in connection with conformal vector fields of second order and apply the procedure to vector fields conformally related with the harmonic oscillator (f-oscillators) . We select one which covers the vector field describing the Kepler problem.Comment: 17 pages, 2 figure

Floras from red beds of the Permian Basin of Lodève (Southern France)

Las plantas fósiles de las capas rojas de la cuenca de Lodève son generalmente escasas y su estado de conservación es relativamente pobre comparada a la flora del “Autuniense gris”. De acuerdo con los trabajos previos de Doubinger y tras una reevaluación de las colecciones disponibles gracias a nuevos datos, son propuestas unas listas de las floras de las “capas rojas” de la “zona de transición” de la Formación de Rabejac y, por primera vez, de la Formación de Salagou. Callipteris cf. uralensis y Supaia representan dos taxones significativos; el primero aparece en las capas rojas mientras que Supaia solamente es conocido en la Formación de Rabejac. Este género, previamente considerado endémico de Arizona, ha sido citado como presente en Rusia, España y China, además de la cuenca de Lodève, en la que su presencia podría indicar una edad Artinskiana tardía a Kunguriana para esta sección basal de lo que se conocía como “grupo Saxoniano”. También es interesante el hecho de que algunas coníferas de Rabejac y de la Formación de Salagou, más reciente, muestran conos y/o hojas suculentas, similares a los de algunas coníferas Triásicas, lo que con toda certeza representa un cambio importante en la flora como respuesta a un clima progresivamente más seco. Debido a las condiciones desfavorables de fosilización y teniendo en cuenta la importancia de la actividad animal en los ecosistemas de playa de la Formación de Salagou, estas plantas poco frecuentes son interpretadas como los restos de una vegetación originalmente mucho más diversificada, posiblemente dominada por coníferas arborescentes

Tensorial dynamics on the space of quantum states

A geometric description of the space of states of a finite-dimensional quantum system and of the Markovian evolution associated with the Kossakowski-Lindblad operator is presented. This geometric setting is based on two composition laws on the space of observables defined by a pair of contravariant tensor fields. The first one is a Poisson tensor field that encodes the commutator product and allows us to develop a Hamiltonian mechanics. The other tensor field is symmetric, encodes the Jordan product and provides the variances and covariances of measures associated with the observables. This tensorial formulation of quantum systems is able to describe, in a natural way, the Markovian dynamical evolution as a vector field on the space of states. Therefore, it is possible to consider dynamical effects on non-linear physical quantities, such as entropies, purity and concurrence. In particular, in this work the tensorial formulation is used to consider the dynamical evolution of the symmetric and skew-symmetric tensors and to read off the corresponding limits as giving rise to a contraction of the initial Jordan and Lie products.Comment: 31 pages, 2 figures. Minor correction

Comment on "Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction" [J. Chem. Phys. 137, 22A530 (2012)]

In spite of the relevance of the proposal introduced in the recent work A. Abedi, N. T. Maitra and E. K. U. Gross, J. Chem. Phys. 137, 22A530, 2012, there is an important ingredient which is missing. Namely, the proof that the norms of the electronic and nuclear wavefunctions which are the solutions to the nonlinear equations of motion are preserved by the evolution. To prove the conservation of these norms is precisely the objective of this Comment.Comment: 2 pages, published versio

Biased gene conversion and GC-content evolution in the coding sequences of reptiles and vertebrates.

Mammalian and avian genomes are characterized by a substantial spatial heterogeneity of GC-content, which is often interpreted as reflecting the effect of local GC-biased gene conversion (gBGC), a meiotic repair bias that favors G and C over A and T alleles in high-recombining genomic regions. Surprisingly, the first fully sequenced nonavian sauropsid (i.e., reptile), the green anole Anolis carolinensis, revealed a highly homogeneous genomic GC-content landscape, suggesting the possibility that gBGC might not be at work in this lineage. Here, we analyze GC-content evolution at third-codon positions (GC3) in 44 vertebrates species, including eight newly sequenced transcriptomes, with a specific focus on nonavian sauropsids. We report that reptiles, including the green anole, have a genome-wide distribution of GC3 similar to that of mammals and birds, and we infer a strong GC3-heterogeneity to be already present in the tetrapod ancestor. We further show that the dynamic of coding sequence GC-content is largely governed by karyotypic features in vertebrates, notably in the green anole, in agreement with the gBGC hypothesis. The discrepancy between third-codon positions and noncoding DNA regarding GC-content dynamics in the green anole could not be explained by the activity of transposable elements or selection on codon usage. This analysis highlights the unique value of third-codon positions as an insertion/deletion-free marker of nucleotide substitution biases that ultimately affect the evolution of proteins