A1A_1 theory of weights for rough homogeneous singular integrals and commutators

Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: % $$\|T_\Omega \|_{L^p(w)}\le c_{n,p}\|\Omega\|_{L^\infty} [w]_{A_1}^{\frac{1}{p}}\,[w]_{A_{\infty}}^{1+\frac{1}{p'}}\|f\|_{L^p(w)}$$ % and % $$\| [b,T_{\Omega}]f\|_{L^{p}(w)}\leq c_{n,p}\|b\|_{BMO}\|\Omega\|_{L^{\infty}} [w]_{A_1}^{\frac{1}{p}}[w]_{A_{\infty}}^{2+\frac{1}{p'}}\|f\|_{L^{p}\left(w\right)},$$ % for $1<p<\infty$ and $1/p+1/p'=1$.Comment: 19 page

N_c and m_pi dependence of rho and sigma mesons from unitarized Chiral Perturbation Theory

We review our work on the rho and sigma resonances derived from the Inverse Amplitude Method. In particular, we study the leading 1/N_c behavior of the resonances masses and widths and their evolution with changing m_pi. The 1/N_c expansion gives a clear definition of quark-antiquark states, which is neatly satisfied by the rho but not by the sigma, showing that its dominant component is not quark-antiquark. The m_pi dependence of the resonance properties is relevant to connect with lattice studies. We show that our predictions compare well with some lattice results and we find that the rho-pi-pi coupling constant is m_pi independent, in contrast with the sigma-pi-pi coupling, that shows a strong m_pi dependence.Comment: To appear in the Proceedings of the Chiral10 Workshop, June 21-24 2010. Valencia, Spai

On the equilibrium concept for overlapping generations organizations

A necessary feature for equilibrium is that beliefs about the behavior of other agents are rational. We argue that in stationary OLG environments this implies that any future generation in the same situation as the initial generation must do as well as the initial generation did in that situation. We conclude that the existing equilibrium concepts in the literature do not satisfy this condition. We then propose an alternative equilibrium concept, organizational equilibrium, that satisfies this condition. We show that equilibrium exists, it is unique, and it improves over autarky without achieving optimality. Moreover, the equilibrium can be readily found by solving a maximization program.Economics ; Equilibrium (Economics) - Mathematical models

Higher-order symmetry energy and neutron star core-crust transition with Gogny forces

We study the symmetry energy and the core-crust transition in neutron stars using the finite-range Gogny nuclear interaction and examine the deduced crustal thickness and crustal moment of inertia. We start by analyzing the second-, fourth- and sixth-order coefficients of the Taylor expansion of the energy per particle in powers of the isospin asymmetry for Gogny forces. These coefficients provide information about the departure of the symmetry energy from the widely used parabolic law. The neutron star core-crust transition is evaluated by looking at the onset of thermodynamical instability of the liquid core. The calculation is performed with the exact (i.e., without Taylor expansion) Gogny EoS for the core, and also with its Taylor expansion in order to assess the influence of isospin expansions on locating the inner edge of neutron star crusts. It is found that the properties of the core-crust transition derived from the exact EoS differ from the predictions of the Taylor expansion even when the expansion is carried through sixth order in the isospin asymmetry. Gogny forces, using the exact EoS, predict the ranges $0.094 \text{ fm}^{-3} \lesssim \rho_t \lesssim 0.118\text{ fm}^{-3}$ for the transition density and $0.339 \text{ MeV fm}^{-3} \lesssim P_t \lesssim 0.665 \text{ MeV fm}^{-3}$ for the transition pressure. The transition densities show an anticorrelation with the slope parameter $L$ of the symmetry energy. The transition pressures are not found to correlate with $L$. Neutron stars obtained with Gogny forces have maximum masses below $1.74M_\odot$ and relatively small moments of inertia. The crustal mass and moment of inertia are evaluated and comparisons are made with the constraints from observed glitches in pulsars.Comment: 24 pages, 15 figures, discussions and bibliography updated, to appear in Physical Review

Vascular fibrosis in aging and hypertension: molecular mechanisms and clinical implications

Aging is the primary risk factor underlying hypertension and incident cardiovascular disease. With aging, the vasculature undergoes structural and functional changes characterized by endothelial dysfunction, wall thickening, reduced distensibility, and arterial stiffening. Vascular stiffness results from fibrosis and extracellular matrix (ECM) remodelling, processes that are associated with aging and are amplified by hypertension. Some recently characterized molecular mechanisms underlying these processes include increased expression and activation of matrix metalloproteinases, activation of transforming growth factor-β1/SMAD signalling, upregulation of galectin-3, and activation of proinflammatory and profibrotic signalling pathways. These events can be induced by vasoactive agents, such as angiotensin II, endothelin-1, and aldosterone, which are increased in the vasculature during aging and hypertension. Complex interplay between the “aging process” and prohypertensive factors results in accelerated vascular remodelling and fibrosis and increased arterial stiffness, which is typically observed in hypertension. Because the vascular phenotype in a young hypertensive individual resembles that of an elderly otherwise healthy individual, the notion of “early” or “premature” vascular aging is now often used to describe hypertension-associated vascular disease. We review the vascular phenotype in aging and hypertension, focusing on arterial stiffness and vascular remodelling. We also highlight the clinical implications of these processes and discuss some novel molecular mechanisms of fibrosis and ECM reorganization

Gel Electrophoresis of DNA Knots in Weak and Strong Electric Fields

Gel electrophoresis allows to separate knotted DNA (nicked circular) of equal length according to the knot type. At low electric fields, complex knots being more compact, drift faster than simpler knots. Recent experiments have shown that the drift velocity dependence on the knot type is inverted when changing from low to high electric fields. We present a computer simulation on a lattice of a closed, knotted, charged DNA chain drifting in an external electric field in a topologically restricted medium. Using a simple Monte Carlo algorithm, the dependence of the electrophoretic migration of the DNA molecules on the type of knot and on the electric field intensity was investigated. The results are in qualitative agreement with electrophoretic experiments done under conditions of low and high electric fields: especially the inversion of the behavior from low to high electric field could be reproduced. The knot topology imposes on the problem the constrain of self-avoidance, which is the final cause of the observed behavior in strong electric field.Comment: 17 pages, 5 figure

Invariant manifolds and equilibrium states for non-uniformly hyperbolic horseshoes

In this paper we consider horseshoes containing an orbit of homoclinic tangency accumulated by periodic points. We prove a version of the Invariant Manifolds Theorem, construct finite Markov partitions and use them to prove the existence and uniqueness of equilibrium states associated to H\"older continuous potentials.Comment: 33 pages, 6 figure

Redox stress defines the small artery vasculopathy of hypertension: how do we bridge the bench-to-bedside gap?

Although convincing experimental evidence demonstrates the importance of vascular reactive oxygen and nitrogen species (RONS), oxidative stress, and perturbed redox signaling as causative processes in the vasculopathy of hypertension, this has not translated to the clinic. We discuss this bench-to-bedside disparity and the urgency to progress vascular redox pathobiology from experimental models to patients by studying disease-relevant human tissues. It is only through such approaches that the unambiguous role of vascular redox stress will be defined so that mechanism-based therapies in a personalized and precise manner can be developed to prevent, slow, or reverse progression of small-vessel disorders and consequent hypertension