Inverse problems of symbolic dynamics

This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval exchange transformation. Rauzy graphs language can express many important combinatorial and some dynamical properties. In this case combinatorial properties are considered as being generated by substitutional system, and dynamical properties are considered as criteria of superword being generated by interval exchange transformation. As a consequence, one can get a morphic word appearing in interval exchange transformation such that frequencies of letters are algebraic numbers of an arbitrary degree. Concerning multydimensional systems, our main result is the following. Let P(n) be a polynomial, having an irrational coefficient of the highest degree. A word $w$ (w=(w_n), n\in \nit) consists of a sequence of first binary numbers of $\{P(n)\}$ i.e. $w_n=[2\{P(n)\}]$. Denote the number of different subwords of $w$ of length $k$ by $T(k)$ . \medskip {\bf Theorem.} {\it There exists a polynomial $Q(k)$, depending only on the power of the polynomial $P$, such that $T(k)=Q(k)$ for sufficiently great $k$.

Fast Ray Tracing of Lunar Digital Elevation Models

Ray-tracing (RT) of Lunar Digital Elevation Models (DEM)'s is performed to virtually derive the degree of radiation incident to terrain as a function of time, orbital and ephemeris constraints [I- 4]. This process is an integral modeling process in lunar polar research and exploration due to the present paucity of terrain information at the poles and mission planning activities for the anticipated spring 2009 launch of the Lunar Reconnaissance Orbiter (LRO). As part of the Lunar Exploration Neutron Detector (LEND) and Lunar Crater Observation and Sensing Satellite (LCROSS) preparations RI methods are used to estimate the critical conditions presented by the combined effects of high latitude, terrain and the moons low obliquity [5-7]. These factors yield low incident solar illumination and subsequently extreme thermal, and radiation conditions. The presented research uses RT methods both for radiation transport modeling in space and regolith related research as well as to derive permanently shadowed regions (PSR)'s in high latitude topographic minima, e.g craters. These regions are of scientific and human exploration interest due to the near constant low temperatures in PSRs, inferred to be < 100 K. Hydrogen is thought to have accumulated in PSR's through the combined effects of periodic cometary bombardment and/or solar wind processes, and the extreme cold which minimizes hydrogen sublimation [8-9]. RT methods are also of use in surface position optimization for future illumination dependent on surface resources e.g. power and communications equipment

Comparison of Image Restoration Methods for Lunar Epithermal Neutron Emission Mapping

Orbital measurements of neutrons by the Lunar Exploring Neutron Detector (LEND) onboard the Lunar Reconnaissance Orbiter are being used to quantify the spatial distribution of near surface hydrogen (H). Inferred H concentration maps have low signal-to-noise (SN) and image restoration (IR) techniques are being studied to enhance results. A single-blind. two-phase study is described in which four teams of researchers independently developed image restoration techniques optimized for LEND data. Synthetic lunar epithermal neutron emission maps were derived from LEND simulations. These data were used as ground truth to determine the relative quantitative performance of the IR methods vs. a default denoising (smoothing) technique. We review and used factors influencing orbital remote sensing of neutrons emitted from the lunar surface to develop a database of synthetic "true" maps for performance evaluation. A prior independent training phase was implemented for each technique to assure methods were optimized before the blind trial. Method performance was determined using several regional root-mean-square error metrics specific to epithermal signals of interest. Results indicate unbiased IR methods realize only small signal gains in most of the tested metrics. This suggests other physically based modeling assumptions are required to produce appreciable signal gains in similar low SN IR applications

Are Slope Streaks Indicative of Global-Scale Aqueous Processes on Contemporary Mars?

Acknowledgments We acknowledge the editorial board of Reviews of Geophysics for inviting the submission of this review article. We extend our gratitude to the efforts of the handling editor and the reviewers. We thank NASA, JPL‐Caltech, JPL/Goddard, University of Arizona, Malin Space Science systems, Arizona State University, USGS, ESA/DLR/FU Berlin, and Google Earth for providing various satellite images, maps, and JMARS software free of charge. The paper is theoretical, and no new data have been generated during the work. All the used satellite images of Mars can be rendered on JMARS software using the image ID provided in the respective figure captions, and the image sources have also been duly acknowledged in the respective figure captions. The maps in various figures have been created using ArcGIS version 10.4 (http://desktop.arcgis.com/en/arcmap/latest/get‐started/setup/arcgis‐desktop‐quick‐start‐guide.htm). Although we have cited all the previous research results used in the paper, we here acknowledge the efforts of all those researchers in providing the essential inputs for our study. A. B. acknowledges the Swedish Research Council for supporting his research in cold arid environments. L. S. acknowledges the German Academic Exchange Service (DAAD) for her PhD scholarship.Peer reviewedPublisher PD

Isolation Effects on the Moon: High Topographic Slope Observations from the LRO and LOLA Instruments

The extremely low temperatures in the Moon's polar permanent shadow regions (PSR) has long been considered a unique factor necessary for entrapping volatile Hydrogen (H). However, recent discoveries indicate some H concentrations lie outside PSR, suggesting other geophysical factors may also influence H distributions. In this study we consider insolation and its resulting thermal effects as a loss/redistribution process influencing the Moon's near-surface < 1m volatile H budget. To isolate regional (5deg latitude band) insolation effects we correlate two data sets collected from the ongoing, 1.5 year long mapping mission of the Lunar Reconnaissance Orbiter (LRO). Epithermal neutron mapping data from the Lunar Exploration Neutron Detector (LEND) is registered and analyzed in the context of slope derivations from Lunar topography maps produced by the Lunar Observing Laser Altimeter (LOLA). Lunar epithermal neutrons are inferred to be direct geochemical evidence for near-surface H due to the correlated suppression of surface leakage fluxes of epithermal neutrons with increased H concentration. Regional suppressions of neutrons seen in LEND maps are considered localized evidence of H concentration increase in the upper 1 m of the Lunar surface. To quantify spatially localized insolation effects, LEND data are averaged from sparsely distributed pixels, classed as a function of the LOLA slope derivations

Estimation of Orbital Neutron Detector Spatial Resolution by Systematic Shifting of Differential Topographic Masks

We present a method and preliminary results related to determining the spatial resolution of orbital neutron detectors using epithermal maps and differential topographic masks. Our technique is similar to coded aperture imaging methods for optimizing photonic signals in telescopes [I]. In that approach photon masks with known spatial patterns in a telescope aperature are used to systematically restrict incoming photons which minimizes interference and enhances photon signal to noise. Three orbital neutron detector systems with different stated spatial resolutions are evaluated. The differing spatial resolutions arise due different orbital altitudes and the use of neutron collimation techniques. 1) The uncollimated Lunar Prospector Neutron Spectrometer (LPNS) system has spatial resolution of 45km FWHM from approx. 30km altitude mission phase [2]. The Lunar Rennaissance Orbiter (LRO) Lunar Exploration Neutron Detector (LEND) with two detectors at 50km altitude evaluated here: 2) the collimated 10km FWHM spatial resolution detector CSETN and 3) LEND's collimated Sensor for Epithermal Neutrons (SETN). Thus providing two orbital altitudes to study factors of: uncollimated vs collimated and two average altitudes for their effect on fields-of-view