Labyrinthine pathways towards supercycle attractors in unimodal maps

We uncover previously unknown properties of the family of periodic superstable cycles in unimodal maps characterized each by a Lyapunov exponent that diverges to minus infinity. Amongst the main novel properties are the following: i) The basins of attraction for the phases of the cycles develop fractal boundaries of increasing complexity as the period-doubling structure advances towards the transition to chaos. ii) The fractal boundaries, formed by the preimages of the repellor, display hierarchical structures organized according to exponential clusterings that manifest in the dynamics as sensitivity to the final state and transient chaos. iii) There is a functional composition renormalization group (RG) fixed-point map associated to the family of supercycles. iv) This map is given in closed form by the same kind of $q$-exponential function found for both the pitchfork and tangent bifurcation attractors. v) There is a final stage ultra-fast dynamics towards the attractor with a sensitivity to initial conditions that decreases as an exponential of an exponential of time.Comment: 8 pages, 13 figure

On the diffusive anomalies in a long-range Hamiltonian system

We scrutinize the anomalies in diffusion observed in an extended long-range system of classical rotors, the HMF model. Under suitable preparation, the system falls into long-lived quasi-stationary states presenting super-diffusion of rotor phases. We investigate the diffusive motion of phases by monitoring the evolution of their probability density function for large system sizes. These densities are shown to be of the $q$-Gaussian form, $P(x)\propto (1+(q-1)[x/\beta]^2)^{1/(1-q)}$, with parameter $q$ increasing with time before reaching a steady value $q\simeq 3/2$. From this perspective, we also discuss the relaxation to equilibrium and show that diffusive motion in quasi-stationary trajectories strongly depends on system size.Comment: 5 pages, 5 figures. References added and correcte

Dynamics towards the Feigenbaum attractor

We expose at a previously unknown level of detail the features of the dynamics of trajectories that either evolve towards the Feigenbaum attractor or are captured by its matching repellor. Amongst these features are the following: i) The set of preimages of the attractor and of the repellor are embedded (dense) into each other. ii) The preimage layout is obtained as the limiting form of the rank structure of the fractal boundaries between attractor and repellor positions for the family of supercycle attractors. iii) The joint set of preimages for each case form an infinite number of families of well-defined phase-space gaps in the attractor or in the repellor. iv) The gaps in each of these families can be ordered with decreasing width in accord to power laws and are seen to appear sequentially in the dynamics generated by uniform distributions of initial conditions. v) The power law with log-periodic modulation associated to the rate of approach of trajectories towards the attractor (and to the repellor) is explained in terms of the progression of gap formation. vi) The relationship between the law of rate of convergence to the attractor and the inexhaustible hierarchy feature of the preimage structure is elucidated.Comment: 8 pages, 12 figure

Proper motions of Local Group dwarf spheroidal galaxies I: First ground-based results for Fornax

In this paper we present in detail the methodology and the first results of a ground-based program to determine the absolute proper motion of the Fornax dwarf spheroidal galaxy. The proper motion was determined using bona-fide Fornax star members measured with respect to a fiducial at-rest background spectroscopically confirmed Quasar, \qso. Our homogeneous measurements, based on this one Quasar gives a value of (\mua,\mud)$= (0.64 \pm 0.08, -0.01 \pm 0.11)$ \masy. There are only two other (astrometric) determinations for the transverse motion of Fornax: one based on a combination of plates and HST data, and another (of higher internal precision) based on HST data. We show that our proper motion errors are similar to those derived from HST measurements on individual QSOs. We provide evidence that, as far as we can determine it, our motion is not affected by magnitude, color, or other potential systematic effects. Last epoch measurements and reductions are underway for other four Quasar fields of this galaxy, which, when combined, should yield proper motions with a weighted mean error of $\sim50\,\mu$as y$^{-1}$, allowing us to place important constraints on the orbit of Fornax.Comment: Accepted for publication in Publications of the Astronomical Society of the Pacific, PASP. To appear in July issue. 64 pages, 18 figure

Comparative transcriptomics reveals key differences in the response to milk oligosaccharides of infant gut-associated bifidobacteria.

Breast milk enhances the predominance of Bifidobacterium species in the infant gut, probably due to its large concentration of human milk oligosaccharides (HMO). Here we screened infant-gut isolates of Bifidobacterium longum subsp. infantis and Bifidobacterium bifidum using individual HMO, and compared the global transcriptomes of representative isolates on major HMO by RNA-seq. While B. infantis displayed homogeneous HMO-utilization patterns, B. bifidum were more diverse and some strains did not use fucosyllactose (FL) or sialyllactose (SL). Transcriptomes of B. bifidum SC555 and B. infantis ATCC 15697 showed that utilization of pooled HMO is similar to neutral HMO, while transcriptomes for growth on FL were more similar to lactose than HMO in B. bifidum. Genes linked to HMO-utilization were upregulated by neutral HMO and SL, but not by FL in both species. In contrast, FL induced the expression of alternative gene clusters in B. infantis. Results also suggest that B. bifidum SC555 does not utilize fucose or sialic acid from HMO. Surprisingly, expression of orthologous genes differed between both bifidobacteria even when grown on identical substrates. This study highlights two major strategies found in Bifidobacterium species to process HMO, and presents detailed information on the close relationship between HMO and infant-gut bifidobacteria

On Weierstra{\ss} semigroups at one and two points and their corresponding Poincar\'e series

The aim of this paper is to introduce and investigate the Poincar\'e series associated with the Weierstra{\ss} semigroup of one and two rational points at a (not necessarily irreducible) non-singular projective algebraic curve defined over a finite field, as well as to describe their functional equations in the case of an affine complete intersection.Comment: Beginning of Section 3 and Subsection 3.1 were modifie

Interpolated potential energy surface and classical dynamics for H₃⁺+HD and H₃⁺+D₂

A potential energy surface for H₅⁺ has been constructed by a modified Shepard interpolation on a sparse set of data points, using second order Möller–Plesset perturbation theory. An improved version of the surface was also obtained by substituting the energy values at the data points with values evaluated using a coupled cluster treatment (with single and double excitations, and perturbative treatment of triple excitations). Classical simulations for the collisions between H₃⁺+HD and H₃⁺+D2 were carried out in order to calculate the total integral cross sections and rate coefficients for these systems. There is good agreement with earlier experimental data for rate coefficients at temperatures between 80 and 300 K, but the predicted rate coefficient for the reaction of H₃⁺+HD at 10 K deviates from the most recent experimental measurement, suggesting that quantum rather than classical reactiondynamics are necessary