Weak Convergence of CD Kernels: A New Approach on the Circle and Real Line

Let m be a probability measure supported on some infinite and compact set K in the complex plane and let p_n(z) be the corresponding degree n orthonormal polynomial with positive leading coefficient. Let v_n be the normalized zero counting measure for the polynomial p_n and let u_n be the probability measure given by (n+1)u_n=K_n(z,z)m, where K_n(z,w) is the reproducing kernel for polynomials of degree at most n. If m is supported on a compact subset of the real line or the unit circle, we provide a new proof of a 2009 theorem due to Simon, that for any fixed natural number k, the k^{th} moment of u_n and v_{n+1} differ by at most O(1/n) as n tends to infinity.Comment: 6 pages; Version 2 includes minor changes to the exposition and corrects minor typo

Intracellular free sodium and potassium, post-carbachol hyperpolarization, and extracellular potassium-undershoot in rat sympathetic neurones

Double-barrelled ion-sensitive microelectrodes were used to record the free intracellular Na+- and K+-concentrations ([Na+]i, [K+]i) and to determine their relation to changes in membrane potential and extracellular K+ ([K+]e) in rat sympathetic ganglia. The application of 50 μmol/l carbachol resulted in an elevation of [K+]e followed by a post-carbachol [K+]e-undershoot. The membrane depolarization of the sympathetic neurones was associated with an increase in [Na+]i and a decrease in [K+]i. A membrane hyperpolarization and a recovery of [K+]i and [Na+]i to their baseline levels were observed during the [K+]e-undershoot. The time course of the [K+]e-undershoot correlated exactly with the duration of the rise in [Na+]i and decrease of [K+]i. No K+-reuptake occurred in the presence of ouabain. These data confirm, by direct measurements of intracellular ion concentration changes, the contribution of the Na+, K+-pump to the post-carbachol membrane hyperpolarization and [K+]e-undershoot

Review of \u3cem\u3eThe End of Normal: The Great Crisis and the Future of Growth\u3c/em\u3e. James K. Galbraith. Reviewed by Charles Levenstein

James K. Galbraith, The End of Normal: The Great Crisis and the Future of Growth. Simon and Schuster (2014), 304 pages, $26.00 (hardcover),$16.00 (paperback)

A version of Herbert A. Simon's model with slowly fading memory and its connections to branching processes

Construct recursively a long string of words w1. .. wn, such that at each step k, w k+1 is a new word with a fixed probability p $\in$ (0, 1), and repeats some preceding word with complementary probability 1 -- p. More precisely, given a repetition occurs, w k+1 repeats the j-th word with probability proportional to j $\alpha$ for j = 1,. .. , k. We show that the proportion of distinct words occurring exactly times converges as the length n of the string goes to infinity to some probability mass function in the variable $\ge$ 1, whose tail decays as a power function when 1 -- p > $\alpha$/(1 + $\alpha$), and exponentially fast when 1 -- p < $\alpha$/(1 + $\alpha$)

Search for high-mass dilepton resonances with the ATLAS experiment at sqrt(s) = 7 TeV

We present a search for high-mass l+l- resonances in pp collisions at a centre-of-mass energy of 7 TeV recorded by the ATLAS experiment in 2011. No statistically significant excess above the Standard Model expectation is observed in a dataset corresponding to an integrated luminosity of approximately 1/fb. Consequently, upper limits are set on the cross-section times branching ratio of resonances decaying to muon pairs as a function of the resonance mass. In particular, a Sequential Standard Model Z' is excluded for masses below 1.83 TeV, and a Randall-Sundrum Kaluza-Klein graviton with coupling k/M_Pl = 0.1 is excluded for masses below 1.63 TeV, both at the 95% C.L.Comment: 3 pages, 3 figures, 2 tables, XXXI Physics In Collision Proceeding

The role of assumptions in causal discovery

The paper looks at the conditional independence search approach to causal discovery, proposed by Spirtes et al. and Pearl and Verma, from the point of view of the mechanism-based view of causality in econometrics, explicated by Simon. As demonstrated by Simon, the problem of determining the causal structure from data is severely underconstrained and the perceived causal structure depends on the a priori assumptions that one is willing to make. I discuss the assumptions made in the independence search-based causal discovery and their identifying strength