Leibniz algebroid associated with a Nambu-Poisson structure

The notion of Leibniz algebroid is introduced, and it is shown that each Nambu-Poisson manifold has associated a canonical Leibniz algebroid. This fact permits to define the modular class of a Nambu-Poisson manifold as an appropiate cohomology class, extending the well-known modular class of Poisson manifolds

Computational approach to the Schottky problem

We present a computational approach to the classical Schottky problem based on Fay's trisecant identity for genus $g\geq 4$. For a given Riemann matrix $\mathbb{B}\in\mathbb{H}^{g}$, the Fay identity establishes linear dependence of secants in the Kummer variety if and only if the Riemann matrix corresponds to a Jacobian variety as shown by Krichever. The theta functions in terms of which these secants are expressed depend on the Abel maps of four arbitrary points on a Riemann surface. However, there is no concept of an Abel map for general $\mathbb{B} \in \mathbb{H}^{g}$. To establish linear dependence of the secants, four components of the vectors entering the theta functions can be chosen freely. The remaining components are determined by a Newton iteration to minimize the residual of the Fay identity. Krichever's theorem assures that if this residual vanishes within the finite numerical precision for a generic choice of input data, then the Riemann matrix is with this numerical precision the period matrix of a Riemann surface. The algorithm is compared in genus 4 for some examples to the Schottky-Igusa modular form, known to give the Jacobi locus in this case. It is shown that the same residuals are achieved by the Schottky-Igusa form and the approach based on the Fay identity in this case. In genera 5, 6 and 7, we discuss known examples of Riemann matrices and perturbations thereof for which the Fay identity is not satisfied

Late time cosmic acceleration from vacuum Brans-Dicke theory in 5D

We show that the scalar-vacuum Brans-Dicke equations in 5D are equivalent to Brans-Dicke theory in 4D with a self interacting potential and an effective matter field. The cosmological implication, in the context of FRW models, is that the observed accelerated expansion of the universe comes naturally from the condition that the scalar field is not a ghost, i.e., $\omega > - 3/2$. We find an effective matter-dominated 4D universe which shows accelerated expansion if $- 3/2 < \omega < - 1$. We study the question of whether accelerated expansion can be made compatible with large values of $\omega$, within the framework of a 5D scalar-vacuum Brans-Dicke theory with variable, instead of constant, parameter $\omega$. In this framework, and based on a general class of solutions of the field equations, we demonstrate that accelerated expansion is incompatible with large values of $\omega$.Comment: In V2 the summary section is expanded. To be published in Classical and Quantum Gravity

Is dark matter an extra-dimensional effect?

We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the presence of dark matter, is the result of the dynamical evolution of particles in higher dimensional space-times. Hence, dark matter may be a direct consequence of the presence of an extra force, generated by the presence of extra-dimensions, which modifies the dynamic law of motion, but does not change the intrinsic properties of the particles, like, for example, the mass (inertia). We discuss in some detail several possible particular forms for the extra force, and the acceleration law of the particles is derived. Therefore, the constancy of the galactic rotation curves may be considered as an empirical evidence for the existence of the extra dimensions.Comment: 11 pages, no figures, accepted for publication in MPLA; references adde

Effective spacetime from multi-dimensional gravity

We study the effective spacetimes in lower dimensions that can be extracted from a multidimensional generalization of the Schwarzschild-Tangherlini spacetimes derived by Fadeev, Ivashchuk and Melnikov ({\it Phys. Lett,} {\bf A 161} (1991) 98). The higher-dimensional spacetime has $D = (4 + n + m)$ dimensions, where $n$ and $m$ are the number of "internal" and "external" extra dimensions, respectively. We analyze the effective $(4 + n)$ spacetime obtained after dimensional reduction of the $m$ external dimensions. We find that when the $m$ extra dimensions are compact (i) the physics in lower dimensions is independent of $m$ and the character of the singularities in higher dimensions, and (ii) the total gravitational mass $M$ of the effective matter distribution is less than the Schwarzshild mass. In contrast, when the $m$ extra dimensions are large this is not so; the physics in $(4 + n)$ does explicitly depend on $m$, as well as on the nature of the singularities in high dimensions, and the mass of the effective matter distribution (with the exception of wormhole-like distributions) is bigger than the Schwarzshild mass. These results may be relevant to observations for an experimental/observational test of the theory.Comment: A typo in Eq. (24) is fixe

Distribution of Manganese in a Bio-Topo Sequence of Southeastern Iowa Soils

Manganese extractable by sodium hydrosulfite was determined for 9 soil profiles of a bio-topo (vegetation and drainage) sequence in southeastern Iowa. The distribution of manganese in the soils studied is influenced by vegetation, drainage, and pH. Under prairie vegetation the manganese is evenly distributed with depth in the well-drained soil, but with increasing wetness of the soil profile, manganese is apparently lost from the A1 horizon and accumulates in the lower part of the B horizon. Manganese accumulates in the A1 and A2 horizons of the well-drained soils developed under forest vegetation, but in profiles of increasing wetness the amount of manganese in the A1 and A2 horizons decreases and the amount of manganese in the lower B horizon increases. The distribution of manganese in the transition prairie forest soils was intermediate between soils developed under prairie vegetation and those developed under forest vegetation

Active gravitational mass and the invariant characterization of Reissner-Nordstrom spacetime

We analyse the concept of active gravitational mass for Reissner-Nordstrom spacetime in terms of scalar polynomial invariants and the Karlhede classification. We show that while the Kretschmann scalar does not produce the expected expression for the active gravitational mass, both scalar polynomial invariants formed from the Weyl tensor, and the Cartan scalars, do.Comment: 6 pages Latex, to appear in General Relativity and Gravitatio

Functional characterization of the iPSC generated hepatocytes using genome-wide transcriptomic analysis

Advances in iPSC technologies now allow us to consider non-invasive large-scale in-vitro disease modeling experiments on disease appropriate cell types in human subjects to better understand human disease pathophysiology, disease genetics and to develop better diagnostic and therapeutic technologies. We performed differential gene expression and functional annotation analysis using genome wide mRNA sequencing data to evaluate the functional and disease modeling potential of iPSC generated hepatocytes. Following the criteria moderated t statistics FDR corrected p-value ≤ 0.05 and fold change-absolute ≥ 2.0, 7,246 genes/transcripts were significantly differentially expressed iPSCs and hepatocytes. The 3,791 of these DE genes/transcripts were significantly upregulated in the hepatocytes and accounted for about 55% of the hepatocytes total expressed transcriptome. The heatmap and principal component analysis suggests a discrete and uniform resetting of cellular transcriptome during iPSC to hepatocyte differentiation. The functional annotation analysis of the 3,791 significantly upregulated hepatocytes genes/transcripts showed significant enrichment hepatocytes associated cellular functions and canonical pathways. The gene known to be associated with various common human liver disorders and toxicities were also significantly enriched in hepatocytes upregulated 3,791 genes/transcripts. These results suggest that iPSC generated hepatocytes have a functional profile very similar to human primary hepatocytes and are suitable for in-vitro modeling of human liver disorders and toxicities