Lipschitz regularity for elliptic equations with random coefficients

We develop a higher regularity theory for general quasilinear elliptic equations and systems in divergence form with random coefficients. The main result is a large-scale $L^\infty$-type estimate for the gradient of a solution. The estimate is proved with optimal stochastic integrability under a one-parameter family of mixing assumptions, allowing for very weak mixing with non-integrable correlations to very strong mixing (e.g., finite range of dependence). We also prove a quenched $L^2$ estimate for the error in homogenization of Dirichlet problems. The approach is based on subadditive arguments which rely on a variational formulation of general quasilinear divergence-form equations.Comment: 85 pages, minor revisio

Fixing the Pole in the Pyramid

We revisit the problem of the hidden sector Landau pole in the Pyramid Scheme. There is a fixed line in the plane of hidden sector gauge coupling and a Yukawa coupling between the trianon fields. We postulate that the couplings flow to this line, at a point where the hidden sector gauge coupling is close to the strong coupling edge of its perturbative regime. Below the masses of the heavier trianons, the model quickly flows to a confining N_F=N_C=3 supersymmetric gauge theory, as required by phenomenological considerations. We study possible discrete R-symmetries, which guarantee, among other things, that the basin of attraction of the fixed line has full co-dimension in the space of R-allowed couplings. The Yukawa couplings required to get the fixed line violate the pyrma-baryon symmetries we invoked in previous work to find a dark matter candidate. Omitting one of them, we have a dark matter candidate, and an acceptable RG flow down from the unification scale, if the confinement scale of the hidden sector group is lowered from 5 to 2 TeV.Comment: 14 pages, 3 table

Evolution of Scholarly Communication: How Small and Medium-Sized Libraries are Adapting

For the transformation of scholarly publishing to succeed, it is imperative that small and medium-sized institutions are actively engaged in scholarly communication initiatives. This paper presents the results of a survey of scholarly communication initiatives at selected U.S institutions and discusses the influence of institutional variables on the approaches that are employed. The survey was designed to gather information comparable to a 2007 ARL (Association of Research Libraries) survey

The additive structure of elliptic homogenization

One of the principal difficulties in stochastic homogenization is transferring quantitative ergodic information from the coefficients to the solutions, since the latter are nonlocal functions of the former. In this paper, we address this problem in a new way, in the context of linear elliptic equations in divergence form, by showing that certain quantities associated to the energy density of solutions are essentially additive. As a result, we are able to prove quantitative estimates on the weak convergence of the gradients, fluxes and energy densities of the first-order correctors (under blow-down) which are optimal in both scaling and stochastic integrability. The proof of the additivity is a bootstrap argument, completing the program initiated in \cite{AKM}: using the regularity theory recently developed for stochastic homogenization, we reduce the error in additivity as we pass to larger and larger length scales. In the second part of the paper, we use the additivity to derive central limit theorems for these quantities by a reduction to sums of independent random variables. In particular, we prove that the first-order correctors converge, in the large-scale limit, to a variant of the Gaussian free field.Comment: 118 pages, to appear in Invent. Math. This version is a merger of v2 and arXiv:1603.03388 and supersedes the latter. Other changes in v3 are mino

Mesoscopic higher regularity and subadditivity in elliptic homogenization

We introduce a new method for obtaining quantitative results in stochastic homogenization for linear elliptic equations in divergence form. Unlike previous works on the topic, our method does not use concentration inequalities (such as Poincar\'e or logarithmic Sobolev inequalities in the probability space) and relies instead on a higher ($C^{k}$, $k \geq 1$) regularity theory for solutions of the heterogeneous equation, which is valid on length scales larger than a certain specified mesoscopic scale. This regularity theory, which is of independent interest, allows us to, in effect, localize the dependence of the solutions on the coefficients and thereby accelerate the rate of convergence of the expected energy of the cell problem by a bootstrap argument. The fluctuations of the energy are then tightly controlled using subadditivity. The convergence of the energy gives control of the scaling of the spatial averages of gradients and fluxes (that is, it quantifies the weak convergence of these quantities) which yields, by a new "multiscale" Poincar\'e inequality, quantitative estimates on the sublinearity of the corrector.Comment: 44 pages, revised version, to appear in Comm. Math. Phy

The dynamics of trade and competition

We present, extend and estimate a model of international trade with firm heterogeneity in the tradition of Melitz (2003) and Melitz and Ottaviano (2005). The model is constructed to yield testable implications for the dynamics of international prices, productivity levels and markups as functions of openness to trade at a sectoral level. The theory lends itself naturally to a difference in differences estimation, with international differences in trade openness at the sector level reflecting international differences in the competitive structure of markets. Predictions are derived for the effects of both domestic and foreign openness on each economy. Using disaggregated data for EU manufacturing over the period 1989-1999 we find evidence that trade openness exerts a competitive effect, with prices and markups falling and productivity rising. Consistent with theory however, these effects diminish and may even revert in the longer term as less competitive economies become attractive havens from which to export from. We provide evidence that this entry into less open economies induces pro-competitive effects overseas in response to domestic trade liberalization.Competition, Globalization, Markups, Openness, Prices, Productivity, Trade

Molecular cloning and characterization of a new member of the gap junction gene family, connexin-31

A new member of the connexin gene family has been identified and designated rat connexin-31 (Cx31) based on its predicted molecular mass of 30,960 daltons. Cx31 is 270 amino acids long and is coded for by a single copy gene. It is expressed as a 1.7-kilobase mRNA that is detected in placenta, Harderian gland, skin, and eye. Cx31 is highly conserved and can be detected in species as distantly related to rat as Xenopus laevis. It exhibits extensive sequence similarity to the previously identified connexins, 58, 50, and 40% amino acid identity to Cx26, Cx32, and Cx43, respectively. When conservation of predicted phosphorylation sites is used to adjust the alignment of Cx31 to other connexins, a unique alignment of three predicted protein kinase C phosphorylation sites near the carboxyl terminus of Cx31 with three sites at the carboxyl terminus of Cx43 is revealed