On a functional equation appearing in characterization of distributions by the optimality of an estimate

Let $X$ be a second countable locally compact Abelian group containing no subgroup topologically isomorphic to the circle group $\mathbb{T}$. Let $\mu$ be a probability distribution on $X$ such that its characteristic function $\hat\mu(y)$ does not vanish and $\hat\mu(y)$ for some $n \geq 3$ satisfies the equation $$\prod_{j=1}^{n} \hat\mu(y_j + y) = \prod_{j=1}^{n}\hat\mu(y_j - y), \quad \sum_{j=1}^{n} y_j = 0, \quad y_1,\dots,y_n,y \in Y.$$ Then $\mu$ is a convolution of a Gaussian distribution and a distribution supported in the subgroup of $X$ generated by elements of order 2

Synchronizing to the Environment: Information Theoretic Constraints on Agent Learning

We show that the way in which the Shannon entropy of sequences produced by an information source converges to the source's entropy rate can be used to monitor how an intelligent agent builds and effectively uses a predictive model of its environment. We introduce natural measures of the environment's apparent memory and the amounts of information that must be (i) extracted from observations for an agent to synchronize to the environment and (ii) stored by an agent for optimal prediction. If structural properties are ignored, the missed regularities are converted to apparent randomness. Conversely, using representations that assume too much memory results in false predictability.Comment: 6 pages, 5 figures, Santa Fe Institute Working Paper 01-03-020, http://www.santafe.edu/projects/CompMech/papers/stte.htm

New insight into the physical state of solar system objects

The application of IUE to observations of solar system objects is summarized and a brief survey of discoveries made during the first two years of IUE operation is given

A study of the feasibility of ultraviolet spectrometry for cometary missions

Ultraviolet spectra fo the comet West obtained by sounding rocket experiments in 1976 are reproduced and interpreted in order to estimate the expected brightness of the emission features and determine the spatial extent of these features for the proposed Halley Flyby/Tempel 2 rendezvous and the possible Halley or Encke flybys close to perihelion. A coma model was constructed and evaluated for the physical condition of candidate targets such as heliocentric distance, gas production, and composition. In addition to brightness profiles, the neutral and ion densities of the principal species are also dervied. The brightness profiles can be used to determine the feasibility of utilizing the space telescope to provide supporting observations during the mission. Basic parameters identified are spectral range, wavelength resolution, spatial resolution, sensitivity and dynamic range, rejection of scattered light, and integration or accumulation time

Rocket and laboratory studies in aeronomy and astrophysics

Progress from March 1, 1986 to August 31, 1986 is covered and includes the work performed in response to a proposal entitled A Spartan Payload for Spatially Resolved Spectroscopy of Extended Faint Sources in the Extreme Ultraviolet (EUV). During this period, one rocket was launched, the reflight of the payload to observe Halley's comet on March 13, 1986. Most of the effort during this period was concentrated on detailed mechanical and electronic design of a Spartan payload and on the reduction and analysis of the data from the two Halley rocket flights and from the UVX experiment which flew on STS-61C in January 1986

Rocket and laboratory studies in aeronomy and astronomy

Data extracted from semi-annual status reports presented include: a list of all sounding rocket launches performed under NASA sponsorship; a list of Ph.D. and M.A. degrees awarded to students who worked in these programs; a summary bibliography of all publications through 1983; the most recent list of the publications from the IUE program; a summary of instrument development supported by the Johns Hopkins sounding rocket program; and a list of faculty and post-doctoral research associates whose work was supported by this grant

A Rigorous Proof of Fermi Liquid Behavior for Jellium Two-Dimensional Interacting Fermions

Using the method of continuous constructive renormalization group around the Fermi surface, it is proved that a jellium two-dimensional interacting system of Fermions at low temperature $T$ remains analytic in the coupling constant $\lambda$ for $|\lambda| |\log T| \le K$ where $K$ is some numerical constant and $T$ is the temperature. Furthermore in that range of parameters, the first and second derivatives of the self-energy remain bounded, a behavior which is that of Fermi liquids and in particular excludes Luttinger liquid behavior. Our results prove also that in dimension two any transition temperature must be non-perturbative in the coupling constant, a result expected on physical grounds. The proof exploits the specific momentum conservation rules in two dimensions.Comment: 4 pages, no figure

The Temperature and Density Structure of the Solar Corona. I. Observations of the Quiet Sun with the EUV Imaging Spectrometer (EIS) on Hinode

Measurements of the temperature and density structure of the solar corona provide critical constraints on theories of coronal heating. Unfortunately, the complexity of the solar atmosphere, observational uncertainties, and the limitations of current atomic calculations, particularly those for Fe, all conspire to make this task very difficult. A critical assessment of plasma diagnostics in the corona is essential to making progress on the coronal heating problem. In this paper we present an analysis of temperature and density measurements above the limb in the quiet corona using new observations from the EUV Imaging Spectrometer (EIS) on \textit{Hinode}. By comparing the Si and Fe emission observed with EIS we are able to identify emission lines that yield consistent emission measure distributions. With these data we find that the distribution of temperatures in the quiet corona above the limb is strongly peaked near 1 MK, consistent with previous studies. We also find, however, that there is a tail in the emission measure distribution that extends to higher temperatures. EIS density measurements from several density sensitive line ratios are found to be generally consistent with each other and with previous measurements in the quiet corona. Our analysis, however, also indicates that a significant fraction of the weaker emission lines observed in the EIS wavelength ranges cannot be understood with current atomic data.Comment: Submitted to Ap