The baker's map with a convex hole

We consider the baker's map $B$ on the unit square $X$ and an open convex set $H\subset X$ which we regard as a hole. The survivor set $\mathcal J(H)$ is defined as the set of all points in $X$ whose $B$-trajectories are disjoint from $H$. The main purpose of this paper is to study holes $H$ for which $\dim_H \mathcal J(H)=0$ (dimension traps) as well as those for which any periodic trajectory of $B$ intersects $\overline H$ (cycle traps). We show that any $H$ which lies in the interior of $X$ is not a dimension trap. This means that, unlike the doubling map and other one-dimensional examples, we can have $\dim_H \mathcal J(H)>0$ for $H$ whose Lebesgue measure is arbitrarily close to one. Also, we describe holes which are dimension or cycle traps, critical in the sense that if we consider a strictly convex subset, then the corresponding property in question no longer holds. We also determine $\delta>0$ such that $\dim_H \mathcal J(H)>0$ for all convex $H$ whose Lebesgue measure is less than $\delta$. This paper may be seen as a first extension of our work begun in [3, 4, 6, 7, 13] to higher dimensions.Comment: 31 pages, 10 figure

Made in America? The New World, the Old, and the Industrial Revolution

For two decades, the consensus explanation of the British Industrial Revolution has placed technological change and the supply side at center stage, affording little or no role for demand or overseas trade. Recently, alternative explanations have placed an emphasis on the importance of trade with New World colonies, and the expanded supply of raw cotton it provided. We test both hypotheses using calibrated general equilibrium models of the British economy and the rest of the world for 1760 and 1850. Neither claim is supported. Trade was vital for the progress of the industrial revolution; but it was trade with the rest of the world, not the American colonies, that allowed Britain to export its rapidly expanding textile output and achieve growth through extreme specialization in response to shifting comparative advantage.

Fixing the functoriality of Khovanov homology

We describe a modification of Khovanov homology (math.QA/9908171), in the spirit of Bar-Natan (math.GT/0410495), which makes the theory properly functorial with respect to link cobordisms. This requires introducing `disorientations' in the category of smoothings and abstract cobordisms between them used in Bar-Natan's definition. Disorientations have `seams' separating oppositely oriented regions, coming with a preferred normal direction. The seams satisfy certain relations (just as the underlying cobordisms satisfy relations such as the neck cutting relation). We construct explicit chain maps for the various Reidemeister moves, then prove that the compositions of chain maps associated to each side of each of Carter and Saito's movie moves (MR1238875, MR1445361) always agree. These calculations are greatly simplified by following arguments due to Bar-Natan and Khovanov, which ensure that the two compositions must agree, up to a sign. We set up this argument in our context by proving a result about duality in Khovanov homology, generalising previous results about mirror images of knots to a `local' result about tangles. Along the way, we reproduce Jacobsson's sign table (math.GT/0206303) for the original `unoriented theory', with a few disagreements.Comment: 91 pages. Added David Clark as co-author. Further detail on variations of third Reidemeister moves, to allow treatment of previously missing cases of movie move six. See changelog section for more detai

Mapping archaeological landscapes through aerial thermographic imaging

This project aims to develop techniques for efficient, high-resolution aerial thermal infrared imaging of archaeological sites and surrounding landscapes. Archaeologists have been aware since the 1970s that images which record thermal wavelengths of light can reveal surface and buried archaeological features that are otherwise invisible, but the costs and difficulty of the technology has made its application beyond the reach of most scholars. This project will develop methods for collecting high-resolution thermal infrared images using a specialized camera mounted on a remote-controlled unmanned aerial vehicle. Conducting surveys at archaeological sites in three environmentally and culturally distinct regions--Cyprus, Dubai and South Dakota--our results will demonstrate the potential and limitations of the technology in a variety of archaeological contexts, offer guidelines for executing surveys and processing results, and serve as a blueprint for other investigators in the future

The Compositional Structure of the Asteroid Belt

The past decade has brought major improvements in large-scale asteroid discovery and characterization with over half a million known asteroids and over 100,000 with some measurement of physical characterization. This explosion of data has allowed us to create a new global picture of the Main Asteroid Belt. Put in context with meteorite measurements and dynamical models, a new and more complete picture of Solar System evolution has emerged. The question has changed from "What was the original compositional gradient of the Asteroid Belt?" to "What was the original compositional gradient of small bodies across the entire Solar System?" No longer is the leading theory that two belts of planetesimals are primordial, but instead those belts were formed and sculpted through evolutionary processes after Solar System formation. This article reviews the advancements on the fronts of asteroid compositional characterization, meteorite measurements, and dynamical theories in the context of the heliocentric distribution of asteroid compositions seen in the Main Belt today. This chapter also reviews the major outstanding questions relating to asteroid compositions and distributions and summarizes the progress and current state of understanding of these questions to form the big picture of the formation and evolution of asteroids in the Main Belt. Finally, we briefly review the relevance of asteroids and their compositions in their greater context within our Solar System and beyond.Comment: Accepted chapter in Asteroids IV in the Space Science Series to be published Fall 201

Detection of the phosphorylation of the estrogen receptor alpha as an outcome of GPR30 activation

Phosphorylation of the serine residues in estrogen receptor (ER) α is important in transcriptional activation. Hence, methods to detect such posttranslational modifi cation events are valuable. We describe, in detail, the analysis of the phosphorylated ERα by electrophoretic separation of proteins and subsequent immuno-blotting techniques. In particular, phosphorylation of the ERα is one possible outcome of activation of the putative membrane estrogen receptor (mER), GPR30. Hence, phosphorylation represents a cross talk event between GPR30 and ERα and may be important in estrogen-regulated physiology

GPR30 activation decreases anxiety in the open field test but not in the elevated plus maze test in female mice

The GPR30 is a novel estrogen receptor (ER) that is a candidate membrane ER based on its binding to 17beta estradiol and its rapid signaling properties such as activation of the extracellular-regulated kinase (ERK) pathway. Its distribution in the mouse limbic system predicts a role for this receptor in the estrogenic modulation of anxiety behaviors in the mouse. A previous study showed that chronic administration of a selective agonist to the GPR30 receptor, G-1, in the female rat can improve spatial memory, suggesting that GPR30 plays a role in hippocampal-dependent cognition. In this study, we investigated the effect of a similar chronic administration of G-1 on behaviors that denote anxiety in adult ovariectomized female mice, using the elevated plus maze (EPM) and the open field test as well as the activation of the ERK pathway in the hippocampus. Although estradiol benzoate had no effect on behaviors in the EPM or the open field, G-1 had an anxiolytic effect solely in the open field that was independent of ERK signaling in either the ventral or dorsal hippocampus. Such an anxiolytic effect may underlie the ability of G-1 to increase spatial memory, by acting on the hippocampus