Exact solutions to the four Goldstone modes around a dark soliton of the nonlinear Schroedinger equation

This article is concerned with the linearisation around a dark soliton solution of the nonlinear Schr\"odinger equation. Crucially, we present analytic expressions for the four linearly-independent zero eigenvalue solutions (also known as Goldstone modes) to the linearised problem. These solutions are then used to construct a Greens matrix which gives the first-order spatial response due to some perturbation. Finally we apply this Greens matrix to find the correction to the dark-soliton wavefunction of a Bose-Einstein condensate in the presence of fluctuations.Comment: 14 pages, 3 figures, submitted to Journal of Physics

Money in monetary policy design: monetary cross-checking in the New-Keynesian model

In the New-Keynesian model, optimal interest rate policy under uncertainty is formulated without reference to monetary aggregates as long as certain standard assumptions on the distributions of unobservables are satisfied. The model has been criticized for failing to explain common trends in money growth and inflation, and that therefore money should be used as a cross-check in policy formulation (see Lucas (2007)). We show that the New-Keynesian model can explain such trends if one allows for the possibility of persistent central bank misperceptions. Such misperceptions motivate the search for policies that include additional robustness checks. In earlier work, we proposed an interest rate rule that is near-optimal in normal times but includes a cross-check with monetary information. In case of unusual monetary trends, interest rates are adjusted. In this paper, we show in detail how to derive the appropriate magnitude of the interest rate adjustment following a significant cross-check with monetary information, when the New-Keynesian model is the central bank’s preferred model. The cross-check is shown to be effective in offsetting persistent deviations of inflation due to central bank misperceptions. Keywords: Monetary Policy, New-Keynesian Model, Money, Quantity Theory, European Central Bank, Policy Under Uncertaint

Excretion of Vancomycin-Resistant Enterococci by Wild Mammals

A survey of fecal samples found enterococcal excretion in 82% of 388 bank voles (Clethrionomys glareolus), 92% of 131 woodmice (Apodemus sylvaticus), and 75% of 165 badgers (Meles meles). Vancomycin-resistant enterococci, all Enterococcus faecium of vanA genotype, were excreted by 4.6% of the woodmice and 1.2% of the badgers, but by none of the bank voles

The Quantity Theory of Money is Valid. The New Keynesians are Wrong!

We test the quantity theory of money (QTM) using a novel approach and a large new sample. We do not follow the usual approach of first differentiating the logarithm of the Cambridge equation to obtain an equation relating the growth rate of real GDP, the growth rate of money and inflation. These variables must then again be ‘integrated’ by averaging in order to obtain stable relationships. Instead we suggest a much simpler procedure for testing directly the stability of the coefficient of the Cambridge equation. For 125 countries and post-war data we find the coefficient to be surprisingly stable. We do not select for high inflation episodes as was done in most empirical studies; inflation rates do not even appear in our data set. Much work supporting the QTM has been done by economic historians and at the University of Chicago by Milton Friedman and his associates. The QTM was a foundation stone of the monetarist revolution. Subsequently belief in it waned. The currently dominant New Keynesian School, implicitly or explicitly denies the validity of the QTM. We survey this history and argue that the QTM is valid and New Keynesians are wrong

The SXS Collaboration catalog of binary black hole simulations

Accurate models of gravitational waves from merging black holes are necessary for detectors to observe as many events as possible while extracting the maximum science. Near the time of merger, the gravitational waves from merging black holes can be computed only using numerical relativity. In this paper, we present a major update of the Simulating eXtreme Spacetimes (SXS) Collaboration catalog of numerical simulations for merging black holes. The catalog contains 2018 distinct configurations (a factor of 11 increase compared to the 2013 SXS catalog), including 1426 spin-precessing configurations, with mass ratios between 1 and 10, and spin magnitudes up to 0.998. The median length of a waveform in the catalog is 39 cycles of the dominant $\ell=m=2$ gravitational-wave mode, with the shortest waveform containing 7.0 cycles and the longest 351.3 cycles. We discuss improvements such as correcting for moving centers of mass and extended coverage of the parameter space. We also present a thorough analysis of numerical errors, finding typical truncation errors corresponding to a waveform mismatch of $\sim 10^{-4}$. The simulations provide remnant masses and spins with uncertainties of 0.03% and 0.1% ($90^{\text{th}}$ percentile), about an order of magnitude better than analytical models for remnant properties. The full catalog is publicly available at https://www.black-holes.org/waveforms .Comment: 33+18 pages, 13 figures, 4 tables, 2,018 binaries. Catalog metadata in ancillary JSON file. v2: Matches version accepted by CQG. Catalog available at https://www.black-holes.org/waveform