Estrogenic activity of phenolic additives determined by an in vitro yeast bioassay

Copyright @ 2001 Environmental Health PerspectivesWe used a recombinant yeast estrogen assay to assess the activity of 73 phenolic additives that are used as sunscreens, preservatives, disinfectants, antioxidants, flavorings, or for perfumery. Thirty-two of these compounds displayed activity: 22 with potencies relative to 17 beta -estradiol, ranging from 1/3,000 to -estradiol. Forty-one compounds were inactive. The major criteria for activity appear to be the presence of an unhindered phenolic OH group in a para position and a molecular weight of 140-250 Da.This work was supported in part under contract with the U.K. Department of Trade and Industry as part of the Government Chemist Programme

Liouville quantum gravity spheres as matings of finite-diameter trees

We show that the unit area Liouville quantum gravity sphere can be constructed in two equivalent ways. The first, which was introduced by the authors and Duplantier, uses a Bessel excursion measure to produce a Gaussian free field variant on the cylinder. The second uses a correlated Brownian loop and a "mating of trees" to produce a Liouville quantum gravity sphere decorated by a space-filling path. In the special case that $γ=\sqrt{8/3}$, we present a third equivalent construction, which uses the excursion measure of a $3/2$-stable Lévy process (with only upward jumps) to produce a pair of trees of quantum disks that can be mated to produce a sphere decorated by SLE$_6$. This construction is relevant to a program for showing that the $γ=\sqrt{8/3}$ Liouville quantum gravity sphere is equivalent to the Brownian map

Connection probabilities for conformal loop ensembles

The goal of the present paper is to explain, based on properties of the conformal loop ensembles \CLE_\kappa (both with simple and non-simple loops, i.e., for the whole range $\kappa \in (8/3, 8)$) how to derive the connection probabilities in domains with four marked boundary points for a conditioned version of \CLE_\kappa which can be interpreted as a \CLE_{{\kappa}} with wired/free/wired/free {boundary conditions} on four boundary arcs (the wired parts being viewed as portions of to-be-completed loops). In particular, in the case of a square, we prove that the probability that the two wired sides of the square hook up so that they create one single loop is equal to $1/(1 - 2 \cos (4 \pi / \kappa ))$. Comparing this with the corresponding connection probabilities for discrete O($N$) models for instance indicates that if a dilute O($N$) model (respectively a critical FK($q$)-percolation model on the square lattice) has a non-trivial conformally invariant scaling limit, then necessarily this scaling limit is \CLE_\kappa where $\kappa$ is the value in $(8/3, 4]$ such that $-2 \cos (4 \pi / \kappa )$ is equal to $N$ (resp.\ the value in $[4,8)$ such that $-2 \cos (4\pi / \kappa)$ is equal to $\sqrt {q}$). Our arguments and computations build on the one hand on Dub\'edat's SLE commutation relations (as developed and used by Dub\'edat, Zhan or Bauer-Bernard-Kyt\"ol\"a) and on the other hand, on the construction and properties of the conformal loop ensembles and their relation to Brownian loop-soups, restriction measures, and the Gaussian free field (as recently derived in works with Sheffield and with Qian)

Scaling limit of the uniform infinite half-plane quadrangulation in the Gromov-Hausdorff-Prokhorov-uniform topology

We prove that the uniform infinite half-plane quadrangulation (UIHPQ), with either general or simple boundary, equipped with its graph distance, its natural area measure, and the curve which traces its boundary, converges in the scaling limit to the Brownian half-plane. The topology of convergence is given by the so-called Gromov-Hausdorff-Prokhorov-uniform (GHPU) metric on curve-decorated metric measure spaces, which is a generalization of the Gromov-Hausdorff metric whereby two such spaces $(X_1, d_1 , \mu_1,\eta_1)$ and $(X_2, d_2 , \mu_2,\eta_2)$ are close if they can be isometrically embedded into a common metric space in such a way that the spaces $X_1$ and $X_2$ are close in the Hausdorff distance, the measures $\mu_1$ and $\mu_2$ are close in the Prokhorov distance, and the curves $\eta_1$ and $\eta_2$ are close in the uniform distance.E.G. was supported by the U.S. Department of Defense via an NDSEG fellowship

Non-simple \SLE curves are not determined by their range

We show that when observing the range of a chordal \SLE_\kappa curve for $\kappa \in (4,8)$, it is not possible to recover the order in which the points have been visited. We also derive related results about conformal loop ensembles (CLE): (i) The loops in a \CLE_\kappa for $\kappa \in (4,8)$ are not determined by the \CLE_\kappa gasket. (ii) The continuum percolation interfaces defined in the fractal carpets of conformal loop ensembles \CLE_{\kappa} for $\kappa \in (8/3, 4)$ (we defined these percolation interfaces in earlier work, where we also showed there that they are \SLE_{16/\kappa} curves) are not determined by the \CLE_{\kappa} carpet that they are defined in

CLE PERCOLATIONS

Conformal loop ensembles (CLEs) are random collections of loops in a simply connected domain, whose laws are characterized by a natural conformal invariance property. The set of points not surrounded by any loop is a canonical random connected fractal set — a random and conformally invariant analog of the Sierpinski carpet or gasket. In the present paper, we derive a direct relationship between the CLEs with simple loops (CLEκ for κ ∈ (8/3, 4), whose loops are Schramm’s SLEκ -type curves) and the corresponding CLEs with nonsimple loops (CLEκ 0 with κ 0 := 16/κ ∈ (4, 6), whose loops are SLEκ 0-type curves). This correspondence is the continuum analog of the Edwards–Sokal coupling between the q-state Potts model and the associated FK random cluster model, and its generalization to noninteger q. Like its discrete analog, our continuum correspondence has two directions. First, we show that for each κ ∈ (8/3, 4), one can construct a variant of CLEκ as follows: start with an instance of CLEκ 0 , then use a biased coin to independently color each CLEκ 0 loop in one of two colors, and then consider the outer boundaries of the clusters of loops of a given color. Second, we show how to interpret CLEκ 0 loops as interfaces of a continuum analog of critical Bernoulli percolation within CLEκ carpets — this is the first construction of continuum percolation on a fractal planar domain. It extends and generalizes the continuum percolation on open domains defined by SLE6 and CLE6. These constructions allow us to prove several conjectures made by the second author and provide new and perhaps surprising interpretations of the relationship between CLEs and the Gaussian free field. Along the way, we obtain new results about generalized SLEκ (ρ) curves for ρ < −2, such as their decomposition into collections of SLEκ -type ‘loops’ hanging off of SLEκ 0-type ‘trunks’, and vice versa (exchanging κ and κ 0 ). We also define a continuous family of natural CLE variants called boundary conformal loop ensembles (BCLEs) that share some (but not all) of the conformal symmetries that characterize CLEs, and that should be scaling limits of critical models with special boundary conditions. We extend the CLEκ /CLEκ 0 correspondence to a BCLEκ /BCLEκ 0 correspondence that makes sense for the wider range κ ∈ (2, 4] and κ 0 ∈ [4, 8).J.M.’s work was partially supported by DMS-1204894. S.S.’s work was also partially supported by a grant from the Simons Foundation and NSF grant DMS-1209044. W.W. acknowledges the support of SNF grant 155922, and the support of the Clay Foundation. W.W. is part of the NCCR Swissmap

Star Formation in Violent and Normal Evolutionary Phases

Mergers of massive gas-rich galaxies trigger violent starbursts that - over timescales of $> 100$ Myr and regions $> 10$ kpc - form massive and compact star clusters comparable in mass and radii to Galactic globular clusters. The star formation efficiency is higher by 1 - 2 orders of magnitude in these bursts than in undisturbed spirals, irregulars or even BCDs. We ask the question if star formation in these extreme regimes is just a scaled-up version of the normal star formation mode of if the formation of globular clusters reveals fundamentally different conditions.Comment: 4 pages To appear in The Evolution of Galaxies. II. Basic building blocks, eds. M. Sauvage, G. Stasinska, L. Vigroux, D. Schaerer, S. Madde

Cut-off for lamplighter chains on tori: dimension interpolation and phase transition

Given a finite, connected graph \SG, the lamplighter chain on \SG is the lazy random walk $X^\diamond$ on the associated lamplighter graph \SG^\diamond=\Z_2 \wr \SG. The mixing time of the lamplighter chain on the torus $\Z_n^d$ is known to have a cutoff at a time asymptotic to the cover time of $\Z_n^d$ if $d=2$, and to half the cover time if $d \ge 3$. We show that the mixing time of the lamplighter chain on \ttorus=\Z_n^2 \times \Z_{a \log n} has a cutoff at $\psi(a)$ times the cover time of \ttorus as $n \to \infty$, where $\psi$ is an explicit weakly decreasing map from $(0,\infty)$ onto $[1/2,1)$. In particular, as $a > 0$ varies, the threshold continuously interpolates between the known thresholds for $\Z_n^2$ and $\Z_n^3$. Perhaps surprisingly, we find a phase transition (non-smoothness of $\psi$) at the point $a_*=\pi r_3 (1+\sqrt{2})$, where high dimensional behavior ($\psi(a)=1/2$ for all $a \ge a_*$) commences. Here $r_3$ is the effective resistance from $0$ to $\infty$ in $\Z^3$

Liouville quantum gravity as a metric space and a scaling limit

Over the past few decades, two natural random surface models have emerged within physics and mathematics. The first is Liouville quantum gravity, which has its roots in string theory and conformal field theory from the 1980s and 1990s. The second is the Brownian map, which has its roots in planar map combinatorics from the 1960s together with recent scaling limit results. This article surveys a series of works with Sheffield in which it is shown that Liouville quantum gravity (LQG) with parameter $\gamma=\sqrt{8/3}$ is equivalent to the Brownian map. We also briefly describe a series of works with Gwynne which use the $\sqrt{8/3}$-LQG metric to prove the convergence of self-avoiding walks and percolation on random planar maps towards SLE$_{8/3}$ and SLE$_6$, respectively, on a Brownian surface

A filament of dark matter between two clusters of galaxies

It is a firm prediction of the concordance Cold Dark Matter (CDM) cosmological model that galaxy clusters live at the intersection of large-scale structure filaments. The thread-like structure of this "cosmic web" has been traced by galaxy redshift surveys for decades. More recently the Warm-Hot Intergalactic Medium (WHIM) residing in low redshift filaments has been observed in emission and absorption. However, a reliable direct detection of the underlying Dark Matter skeleton, which should contain more than half of all matter, remained elusive, as earlier candidates for such detections were either falsified or suffered from low signal-to-noise ratios and unphysical misalignements of dark and luminous matter. Here we report the detection of a dark matter filament connecting the two main components of the Abell 222/223 supercluster system from its weak gravitational lensing signal, both in a non-parametric mass reconstruction and in parametric model fits. This filament is coincident with an overdensity of galaxies and diffuse, soft X-ray emission and contributes mass comparable to that of an additional galaxy cluster to the total mass of the supercluster. Combined with X-ray observations, we place an upper limit of 0.09 on the hot gas fraction, the mass of X-ray emitting gas divided by the total mass, in the filament.Comment: Nature, in pres