Median-Unbiased Estimation in DF-GLS Regressions and the PPP Puzzle

Using median-unbiased estimation based on Augmented-Dickey-Fuller (ADF) regressions, recent research has questioned the validity of Rogoff's "remarkable consensus" of 3-5 year half-lives of deviations from PPP. The confidence intervals of these half-life estimates, however, are extremely wide, with lower bounds of about one year and upper bounds of infinity. We extend median-unbiased estimation to the DF-GLS regression of Elliott, Rothenberg, and Stock (1996). We find that combining median-unbiased estimation with this regression has the potential to tighten confidence intervals for the half-lives. Using long horizon real exchange rate data, we find that the typical lower bound of the confidence intervals for median-unbiased half-lives is just under 3 years. Thus, while previous confidence intervals for median-unbiased half-lives are consistent with virtually anything, our tighter confidence intervals are inconsistent with economic models with nominal rigidities as candidates for explaining the observed behavior of real exchange rates and move us away from solving the PPP puzzle.PPP puzzle, median-unbiased, persistence.

Relativistic Effects in Extrasolar Planetary Systems

This paper considers general relativistic (GR) effects in currently observed extrasolar planetary systems. Although GR corrections are small, they can compete with secular interactions in these systems and thereby play an important role. Specifically, some of the observed multiple planet systems are close to secular resonance, where the dynamics is extremely sensitive to GR corrections, and these systems can be used as laboratories to test general relativity. For the three-planet solar system Upsilon Andromedae, secular interaction theory implies an 80% probability of finding the system with its observed orbital elements if GR is correct, compared with only a 2% probability in the absence of GR. In the future, tighter constraints can be obtained with increased temporal coverage.Comment: Accepted for publication in International Journal of Modern Physics D; this paper received ``Honorable Mention'' in the 2006 Essay Competition of the Gravity Research Foundation; 9 pages including 1 figur

Binaries and core-ring structures in self-gravitating systems

Low energy states of self-gravitating systems with finite angular momentum are considered. A constraint is introduced to confine cores and other condensed objects within the system boundaries by gravity alone. This excludes previously observed astrophysically irrelevant asymmetric configurations with a single core. We show that for an intermediate range of a short-distance cutoff and small angular momentum, the equilibrium configuration is an asymmetric binary. For larger angular momentum or for a smaller range of the short distance cutoff, the equilibrium configuration consists of a central core and an equatorial ring. The mass of the ring varies between zero for vanishing rotation and the full system mass for the maximum angular momentum $L_{max}$ a localized gravitationally bound system can have. The value of $L_{max}$ scales as $\sqrt{\ln(1/x_0)}$, where $x_0$ is a ratio of a short-distance cutoff range to the system size. An example of the soft gravitational potential is considered; the conclusions are shown to be valid for other forms of short-distance regularization.Comment: 6 pages, 3 figure

Network formation of tissue cells via preferential attraction to elongated structures

Vascular and non-vascular cells often form an interconnected network in vitro, similar to the early vascular bed of warm blooded embryos. Our time-lapse recordings show that the network forms by extending sprouts, i.e., multicellular linear segments. To explain the emergence of such structures, we propose a simple model of preferential attraction to stretched cells. Numerical simulations reveal that the model evolves into a quasi-stationary pattern containing linear segments, which interconnect above the critical volume fraction of 0.2. In the quasi-stationary state the generation of new branches offset the coarsening driven by surface tension. In agreement with empirical data, the characteristic size of the resulting polygonal pattern is density-independent within a wide range of volume fractions

Relativistic Resonant Relations between Massive Black Hole Binary and Extreme Mass Ratio Inspiral

One component of a massive black hole binary (MBHB) might capture a small third body, and then a hierarchical, inclined triple system would be formed. With the post-Newtonian approximation including radiation reaction, we analyzed the evolution of the triple initially with small eccentricities. We found that an essentially new resonant relation could arise in the triple system. Here relativistic effects are crucial. Relativistic resonances, including the new one, stably work even for an outer MBHB of comparable masses, and significantly change the orbit of the inner small body.Comment: 9 pages, 5 figures, to appear in PR

Thermal instabilities in protogalactic clouds

The means by which a protogalaxy can fragment to form the first generation of stars and globular clusters remains an important problem in astrophysics. Gravitational instabilities grow on timescales too long to drive fragmentation before the background density grows by many orders of magnitude (see Murray and Lin 1989a, and references therein). Thermal instability provides a much more likely mechanism. After its initial collapse, a protogalactic cloud is expected to be shock heated to its virial temperature approx. 10(exp 6) K. Cooling by H and He+ below 10(exp 6) K has a negative slope, so that the cloud is subject to strong thermal instabilities. Density enhancements may then grow rapidly, fragmenting the protogalaxy as it cools to lower temperatures. The role of dynamical effects upon the growth of perturbations is considered here. The method used is similar to that used in Murray and Lin (1989a; see also the Erratum to appear September 15), which examined the growth of thermal instabilities with a one-dimensional Lagrangian hydrodynamics code, written for spherical symmetry. Perturbed regions therefore take the form of shells. The dynamical variables are integrated explicitly, while the temperature, ionization fraction, and molecular fraction are integrated implicitly, and account is taken for non-equilibrium values of these quantities