Singularity of Nearcritical Percolation Exploration Paths

We show that the laws of scaling limits of nearcritical percolation exploration paths with different parameters are singular with respect to each other. This generalises a result of Nolin and Werner, using a similar technique. As a corollary, the singularity can even be detected from an infinitesimal initial segment. Moreover, nearcritical scaling limits of exploration paths are mutually singular under scaling maps.Comment: 23 pages, 7 figures; an expository section added and minor change

Spontaneous Breaking of Rotational Symmetry with Arbitrary Defects and a Rigidity Estimate

The goal of this paper is twofold. First we prove a rigidity estimate, which generalises the theorem on geometric rigidity of Friesecke, James and M\"uller to 1-forms with non-vanishing exterior derivative. Second we use this estimate to prove a kind of spontaneous breaking of rotational symmetry for some models of crystals, which allow almost all kinds of defects, including unbounded defects as well as edge, screw and mixed dislocations, i.e. defects with Burgers vectors.Comment: 40 pages, 6 figures, minor change

Large Area Crop Inventory Experiment (LACIE). Bibliographic addenda, technical reports, papers, and memorandums published under supporting research and technology and other research, test, and evaluation contracts for the Earth observations division

There are no author-identified significant results in this report

Consciousness

Consciousness is the last great frontier of science. Here we discuss what it is, how it differs fundamentally from other scientific phenomena, what adaptive function it serves, and the difficulties in trying to explain how it works. The emphasis is on the adaptive function.

Computing Socially-Efficient Cake Divisions

We consider a setting in which a single divisible good ("cake") needs to be divided between n players, each with a possibly different valuation function over pieces of the cake. For this setting, we address the problem of finding divisions that maximize the social welfare, focusing on divisions where each player needs to get one contiguous piece of the cake. We show that for both the utilitarian and the egalitarian social welfare functions it is NP-hard to find the optimal division. For the utilitarian welfare, we provide a constant factor approximation algorithm, and prove that no FPTAS is possible unless P=NP. For egalitarian welfare, we prove that it is NP-hard to approximate the optimum to any factor smaller than 2. For the case where the number of players is small, we provide an FPT (fixed parameter tractable) FPTAS for both the utilitarian and the egalitarian welfare objectives

The New Male Mystique

Examines the rise in men reporting work-family conflict, factors that put men at risk for conflict, and those that help reduce it, including supervisor support and workplace flexibility. Makes recommendations for workplace policies and public dialogue

Is East Germany Catching Up? A Time Series Perspective

This paper assesses whether the economy of East Germany is catching up with the West German region in terms of welfare. While the primary measure for convergence and catching up is per capita output, we also look at other macroeconomic indicators such as unemployment rates, wage rates, and production levels in the manufacturingsector. In contrast to existing studies of convergence between regions of reunified Germany, our approach is purely based upon the time series dimension and is thus directly focused on the catching up process in East Germany as a region. Our testing setup includes standard ADF unit root tests as well as unit root tests that endogenously allow for a break in the deterministic component of the process. In our analysis, we find evidence of catching up for East Germany for most of the indicators. However, convergence speed is slow, and thus it can be expected that the catching up process will take further decades until the regional gap is closed.east germany, catching up, convergence, unit root tests