Counting Dyck paths by area and rank

The set of Dyck paths of length $2n$ inherits a lattice structure from a bijection with the set of noncrossing partitions with the usual partial order. In this paper, we study the joint distribution of two statistics for Dyck paths: \emph{area} (the area under the path) and \emph{rank} (the rank in the lattice). While area for Dyck paths has been studied, pairing it with this rank function seems new, and we get an interesting $(q,t)$-refinement of the Catalan numbers. We present two decompositions of the corresponding generating function: one refines an identity of Carlitz and Riordan; the other refines the notion of $\gamma$-nonnegativity, and is based on a decomposition of the lattice of noncrossing partitions due to Simion and Ullman. Further, Biane's correspondence and a result of Stump allow us to conclude that the joint distribution of area and rank for Dyck paths equals the joint distribution of length and reflection length for the permutations lying below the $n$-cycle $(12...n)$ in the absolute order on the symmetric group.Comment: 24 pages, 7 figures. Connections with work of C. Stump (arXiv:0808.2822v2) eliminated the need for 5 pages of proof in the first draf

Multiplicative versus additive noise in multi-state neural networks

The effects of a variable amount of random dilution of the synaptic couplings in Q-Ising multi-state neural networks with Hebbian learning are examined. A fraction of the couplings is explicitly allowed to be anti-Hebbian. Random dilution represents the dying or pruning of synapses and, hence, a static disruption of the learning process which can be considered as a form of multiplicative noise in the learning rule. Both parallel and sequential updating of the neurons can be treated. Symmetric dilution in the statics of the network is studied using the mean-field theory approach of statistical mechanics. General dilution, including asymmetric pruning of the couplings, is examined using the generating functional (path integral) approach of disordered systems. It is shown that random dilution acts as additive gaussian noise in the Hebbian learning rule with a mean zero and a variance depending on the connectivity of the network and on the symmetry. Furthermore, a scaling factor appears that essentially measures the average amount of anti-Hebbian couplings.Comment: 15 pages, 5 figures, to appear in the proceedings of the Conference on Noise in Complex Systems and Stochastic Dynamics II (SPIE International

Controlling the ellipticity of attosecond pulses produced by laser irradiation of overdense plasmas

The interaction of high-intensity laser pulses and solid targets provides a promising way to create compact, tunable and bright XUV attosecond sources that can become a unique tool for a variety of applications. However, it is important to control the polarization state of this XUV radiation, and to do so in the most efficient regime of generation. Using the relativistic electronic spring (RES) model and particle-in-cell (PIC) simulations, we show that the polarization state of the generated attosecond pulses can be tuned in a wide range of parameters by adjusting the polarization and angle of incidence of the laser radiation. In particular, we demonstrate the possibility of producing circularly polarized attosecond pulses in a wide variety of setups.Comment: 6 pages, 3 figure

Personalidad jurídico-canónica y derecho español. Comentario a una sentencia del Tribunal Supremo.

Material incluido en el volumen especial de la revista del Instituto Martín de Azpilcueta, Universidad de Navarra : Ius Canonicum (1999), en honor de Javier Hervada

The Near-Infrared Photometric Properties of Bright Giants in the Central Regions of the Galactic Bulge

Images recorded through broad (J, H, K), and narrow (CO, and 2.2micron continuum) band filters are used to investigate the photometric properties of bright (K < 13.5) stars in a 6 x 6 arcmin field centered on the SgrA complex. The giant branch ridgelines in the (K, J-K) and (K, H-K) color-magnitude diagrams are well matched by the Baade's Window (BW) M giant sequence if the mean extinction is A_K ~ 2.8 mag. Extinction measurements for individual stars are estimated using the M_K versus infrared color relations defined by M giants in BW, and the majority of stars have A_K between 2.0 and 3.5 mag. The extinction is locally high in the SgrA complex, where A_K ~ 3.1 mag. Reddening-corrected CO indices, CO_o, are derived for over 1300 stars with J, H, and K brightnesses, and over 5300 stars with H and K brightnesses. The distribution of CO_o values for stars with K_o between 11.25 and 7.25 can be reproduced using the M_K versus CO_o relation defined by M giants in BW. The data thus suggest that the most metal-rich giants in the central regions of the bulge and in BW have similar photometric properties and 2.3micron CO strengths. Hence, it appears that the central region of the bulge does not contain a population of stars that are significantly more metal-rich than what is seen in BW.Comment: 29 pages, including 14 figure

HDL and LDL: Potential New Players in Breast Cancer Development.

Breast cancer is the most prevalent cancer and primary cause of cancer-related mortality in women. The identification of risk factors can improve prevention of cancer, and obesity and hypercholesterolemia represent potentially modifiable breast cancer risk factors. In the present work, we review the progress to date in research on the potential role of the main cholesterol transporters, low-density and high-density lipoproteins (LDL and HDL), on breast cancer development. Although some studies have failed to find associations between lipoproteins and breast cancer, some large clinical studies have demonstrated a direct association between LDL cholesterol levels and breast cancer risk and an inverse association between HDL cholesterol and breast cancer risk. Research in breast cancer cells and experimental mouse models of breast cancer have demonstrated an important role for cholesterol and its transporters in breast cancer development. Instead of cholesterol, the cholesterol metabolite 27-hydroxycholesterol induces the proliferation of estrogen receptor-positive breast cancer cells and facilitates metastasis. Oxidative modification of the lipoproteins and HDL glycation activate different inflammation-related pathways, thereby enhancing cell proliferation and migration and inhibiting apoptosis. Cholesterol-lowering drugs and apolipoprotein A-I mimetics have emerged as potential therapeutic agents to prevent the deleterious effects of high cholesterol in breast cancer

Absolute elastic differential cross sections for electron scattering by C6H5CH3 and C6H5CF3 at 1.5–200 eV: a comparative experimental and theoretical study with C6H6

We present absolute differential cross sections DCS for elastic scattering from two benzene derivatives C6H5CH3 and C6H5CF3. The crossed-beam method was used in conjunction with the relative flow technique using helium as the reference gas to obtain absolute values. Measurements were carried out for scattering angles 15° –130° and impact energies 1.5–200 eV. DCS results for these two molecules were compared to those of C6H6 from our previous study. We found that 1 these three molecules have DCS with very similar magnitudes and shapes over the energy range 1.5–200 eV, although DCS for C6H5CF3 increase steeply toward lower scattering angles due to the dipole moment induced long-range interaction at 1.5 and 4.5 eV, and 2 that the molecular structure of the benzene ring significantly determines the collision dynamics. From the measured DCS, elastic integral cross sections have been calculated. Furthermore, by employing a corrected form of the independent-atom method known as the screen corrected additive rule, DCS calculations have been carried out without any empirical parameter fittings, i.e., in an ab initio nature. Results show that the calculated DCS are in excellent agreement with the experimental values at 50, 100, and 200 eV