Equivalence of the perturbation theories of Hori and Deprit

Equivalence of perturbation theories of Hori and Deprit, based on Poisson brackets, and computer calculations through sixth orde

Type Ia Supernovae, Evolution, and the Cosmological Constant

We explore the possible role of evolution in the analysis of data on SNe Ia at cosmological distances. First, using a variety of simple sleuthing techniques, we find evidence that the properties of the high and low redshift SNe Ia observed so far differ from one another. Next, we examine the effects of including simple phenomenological models for evolution in the analysis. The result is that cosmological models and evolution are highly degenerate with one another, so that the incorporation of even very simple models for evolution makes it virtually impossible to pin down the values of $\Omega_M$ and $\Omega_\Lambda$, the density parameters for nonrelativistic matter and for the cosmological constant, respectively. Moreover, we show that if SNe Ia evolve with time, but evolution is neglected in analyzing data, then, given enough SNe Ia, the analysis hones in on values of $\Omega_M$ and $\Omega_\Lambda$ which are incorrect. Using Bayesian methods, we show that the probability that the cosmological constant is nonzero (rather than zero) is unchanged by the SNe Ia data when one accounts for the possibility of evolution, provided that we do not discriminate among open, closed and flat cosmologies a priori. The case for nonzero cosmological constant is stronger if the Universe is presumed to be flat, but still depends sensitively on the degree to which the peak luminosities of SNe Ia evolve as a function of redshift. The estimated value of $H_0$, however, is only negligibly affected by accounting for possible evolution.Comment: 45 pages, 15 figures; accepted for publication in The Astrophysical Journal. Minor revisions and clarifications made including addition of recent reference

High-Frequency network activity, global increase in Neuronal Activity, and Synchrony Expansion Precede Epileptic Seizures In Vitro

How seizures start is a major question in epilepsy research. Preictal EEG changes occur in both human patients and animal models, but their underlying mechanisms and relationship with seizure initiation remain unknown. Here we demonstrate the existence, in the hippocampal CA1 region, of a preictal state characterized by the progressive and global increase in neuronal activity associated with a widespread buildup of low-amplitude high-frequency activity (HFA) (100 Hz) and reduction in system complexity.HFAis generated by the firing of neurons, mainly pyramidal cells, at much lower frequencies. Individual cycles ofHFAare generated by the near-synchronous (within 5 ms) firing of small numbers of pyramidal cells. The presence of HFA in the low-calcium model implicates nonsynaptic synchronization; the presence of very similar HFA in the high-potassium model shows that it does not depend on an absence of synaptic transmission. Immediately before seizure onset, CA1 is in a state of high sensitivity in which weak depolarizing or synchronizing perturbations can trigger seizures. Transition to seizure is haracterized by a rapid expansion and fusion of the neuronal populations responsible for HFA, associated with a progressive slowing of HFA, leading to a single, massive, hypersynchronous cluster generating the high-amplitude low-frequency activity of the seizure

Deep Photometry of the Globular Cluster M5: Distance Estimates from White Dwarf and Main Sequence Stars

We present deep VI photometry of stars in the globular cluster M5 (NGC 5904) based on images taken with the Hubble Space Telescope. The resulting color-magnitude diagram reaches below V ~ 27 mag, revealing the upper 2-3 magnitudes of the white dwarf cooling sequence, and main sequence stars eight magnitudes and more below the turn-off. We fit the main sequence to subdwarfs of known parallax to obtain a true distance modulus of (m-M)_0 = 14.45 +/- 0.11 mag. A second distance estimate based on fitting the cluster white dwarf sequence to field white dwarfs with known parallax yielded (m-M)_0 = 14.67 +/- 0.18 mag. We couple our distance estimates with extensive photometry of the cluster's RR Lyrae variables to provide a calibration of the RR Lyrae absolute magnitude yielding M_V(RR) = 0.42 +/- 0.10 mag at [Fe/H] = -1.11 dex. We provide another luminosity calibration in the form of reddening-free Wasenheit functions. Comparison of our calibrations with predictions based on recent models combining stellar evolution and pulsation theories shows encouraging agreement. (Abridged)Comment: AASTeX, 29 pages including 5 figures. Complete photometry data and FITS-format images are available at http://physics.bgsu.edu/~layden/ASTRO/PUBL/published.html . Accepted for publication in the Astrophysical Journal, 2005 October 20. Replaced errant wording in last sentence of paragraph 4 of conclusion

Bayesian model comparison applied to the Explorer-Nautilus 2001 coincidence data

Bayesian reasoning is applied to the data by the ROG Collaboration, in which gravitational wave (g.w.) signals are searched for in a coincidence experiment between Explorer and Nautilus. The use of Bayesian reasoning allows, under well defined hypotheses, even tiny pieces of evidence in favor of each model to be extracted from the data. The combination of the data of several experiments can therefore be performed in an optimal and efficient way. Some models for Galactic sources are considered and, within each model, the experimental result is summarized with the likelihood rescaled to the insensitivity limit value (``${\cal R}$ function''). The model comparison result is given in in terms of Bayes factors, which quantify how the ratio of beliefs about two alternative models are modified by the experimental observationComment: 16 pages, 4 figures. Presented at the GWDAW2002 conference, held in Kyoto on Dec.,2002. This version includes comments by the referees of CQG, which has accepted the paper for pubblication in the special issue of the conference. In particular, note that in Eq. 12 there was a typeset error. As suggested by one of the referees, a uniform prior in Log(alpha) has also been considere