The Search for Intergalactic Hydrogen Clouds in Voids

I present the results of a search for intergalactic hydrogen clouds in voids. Clouds are detected by their HI LyA absorption lines in the HST spectra of low-redshift AGN. The parameter with which the environments of clouds are characterized is the tidal field, which places a lower limit on the cloud mass-density which is dynamically stable against disruption. Galaxy redshift catalogs are used to sum the tidal fields along the lines of sight, sorting clouds according to tidal field upper, or lower limits. The analytical methodology employed is designed to detect gas clouds whose expansion following reionization is restrained by dark matter perturbations. End-products are the cloud equivalent width distribution functions (EWDF) of catalogs formed by sorting clouds according to various tidal field upper, or lower limits. Cumulative EWDFs are steep in voids (S ~ -1.5 \pm 0.2), but flatter in high tidal field zones (S ~ -0.5 \pm 0.1). Most probable cloud Doppler parameters are ~30 km/s in voids and ~60 km/s in proximity to galaxies. In voids, the cumulative line density at low EW (~ 15 mA) is ~ 500 per unit redshift. The void filling factor is found to be 0.87 <= f_v <= 0.94. The void EWDF is remarkably uniform over this volume, with a possible tendency for more massive clouds to be in void centers. The size and nature of the void cloud population suggested by this study is completely unanticipated by the results of published 3-D simulations, which predict that most clouds are in filamentary structures around galaxy concentrations, and that very few observable absorbers would lie in voids. Strategies for modeling this population are briefly discussed.Comment: 21 pages, 19 figures, apjemulate style, to appear in ApJ vol. 57

Non-uniqueness of ergodic measures with full Hausdorff dimension on a Gatzouras-Lalley carpet

In this note, we show that on certain Gatzouras-Lalley carpet, there exist more than one ergodic measures with full Hausdorff dimension. This gives a negative answer to a conjecture of Gatzouras and Peres

A Titan exploration study: Science, technology and mission planning options, volume 1

Mission concepts and technology advancements that can be used in the exploration of the outer planet satellites were examined. Titan, the seventh satellite of Saturn was selected as the target of interest. Science objectives for Titan exploration were identified, and recommended science payloads for four basic mission modes were developed (orbiter, atmospheric probe, surface penetrator and lander). Trial spacecraft and mission designs were produced for the various mission modes. Using these trial designs as a base, technology excursions were then made to find solutions to the problems resulting from these conventional approaches and to uncover new science, technology and mission planning options. Several mission modes were developed that take advantage of the unique conditions expected at Titan. They include a combined orbiter, atmosphere probe and lander vehicle, a combined probe and surface penetrator configuration and concepts for advanced remote sensing orbiters

Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functions, then it holds uniformly in the function spaces. In the last appendix we prove that for the subclass of one-dimensional systems studied in \cite{young} the density of the absolutely continuous invariant measure belongs to a Besov space.Comment: 33 pages; companion of the paper math.DS/0412166; corrected version; to appear in Nonlinearit

Characterization of uncertainties in atmospheric trace gas inversions using hierarchical Bayesian methods

We present a hierarchical Bayesian method for atmospheric trace gas inversions. This method is used to estimate emissions of trace gases as well as "hyper-parameters" that characterize the probability density functions (PDFs) of the a priori emissions and model-measurement covariances. By exploring the space of "uncertainties in uncertainties", we show that the hierarchical method results in a more complete estimation of emissions and their uncertainties than traditional Bayesian inversions, which rely heavily on expert judgment. We present an analysis that shows the effect of including hyper-parameters, which are themselves informed by the data, and show that this method can serve to reduce the effect of errors in assumptions made about the a priori emissions and model-measurement uncertainties. We then apply this method to the estimation of sulfur hexafluoride (SF6) emissions over 2012 for the regions surrounding four Advanced Global Atmospheric Gases Experiment (AGAGE) stations. We find that improper accounting of model representation uncertainties, in particular, can lead to the derivation of emissions and associated uncertainties that are unrealistic and show that those derived using the hierarchical method are likely to be more representative of the true uncertainties in the system. We demonstrate through this SF6 case study that this method is less sensitive to outliers in the data and to subjective assumptions about a priori emissions and model-measurement uncertainties than traditional methods

In situ measurement of atmospheric krypton and xenon on Mars with Mars Science Laboratory

Mars Science Laboratory's Sample Analysis at Mars (SAM) investigation has measured all of the stable isotopes of the heavy noble gases krypton and xenon in the martian atmosphere, in situ, from the Curiosity Rover at Gale Crater, Mars. Previous knowledge of martian atmospheric krypton and xenon isotope ratios has been based upon a combination of the Viking mission's krypton and xenon detections and measurements of noble gas isotope ratios in martian meteorites. However, the meteorite measurements reveal an impure mixture of atmospheric, mantle, and spallation contributions. The xenon and krypton isotopic measurements reported here include the complete set of stable isotopes, unmeasured by Viking. The new results generally agree with Mars meteorite measurements but also provide a unique opportunity to identify various non-atmospheric heavy noble gas components in the meteorites. Kr isotopic measurements define a solar-like atmospheric composition, but deviating from the solar wind pattern at 80Kr and 82Kr in a manner consistent with contributions originating from neutron capture in Br. The Xe measurements suggest an intriguing possibility that isotopes lighter than 132Xe have been enriched to varying degrees by spallation and neutron capture products degassed to the atmosphere from the regolith, and a model is constructed to explore this possibility. Such a spallation component, however, is not apparent in atmospheric Xe trapped in the glassy phases of martian meteorites

On Hilberg's Law and Its Links with Guiraud's Law

Hilberg (1990) supposed that finite-order excess entropy of a random human text is proportional to the square root of the text length. Assuming that Hilberg's hypothesis is true, we derive Guiraud's law, which states that the number of word types in a text is greater than proportional to the square root of the text length. Our derivation is based on some mathematical conjecture in coding theory and on several experiments suggesting that words can be defined approximately as the nonterminals of the shortest context-free grammar for the text. Such operational definition of words can be applied even to texts deprived of spaces, which do not allow for Mandelbrot's ``intermittent silence'' explanation of Zipf's and Guiraud's laws. In contrast to Mandelbrot's, our model assumes some probabilistic long-memory effects in human narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic

Highly optimized tolerance and power laws in dense and sparse resource regimes

Power law cumulative frequency $(P)$ vs. event size $(l)$ distributions $P(\geq l)\sim l^{-\alpha}$ are frequently cited as evidence for complexity and serve as a starting point for linking theoretical models and mechanisms with observed data. Systems exhibiting this behavior present fundamental mathematical challenges in probability and statistics. The broad span of length and time scales associated with heavy tailed processes often require special sensitivity to distinctions between discrete and continuous phenomena. A discrete Highly Optimized Tolerance (HOT) model, referred to as the Probability, Loss, Resource (PLR) model, gives the exponent $\alpha=1/d$ as a function of the dimension $d$ of the underlying substrate in the sparse resource regime. This agrees well with data for wildfires, web file sizes, and electric power outages. However, another HOT model, based on a continuous (dense) distribution of resources, predicts $\alpha= 1+ 1/d$. In this paper we describe and analyze a third model, the cuts model, which exhibits both behaviors but in different regimes. We use the cuts model to show all three models agree in the dense resource limit. In the sparse resource regime, the continuum model breaks down, but in this case, the cuts and PLR models are described by the same exponent.Comment: 19 pages, 13 figure