The Space within Fisherman's Folly: Playing with a Puzzle in Mereotopology

Abstract

In this paper we propose a spatial ontology for reasoning about holes, rigid objects and a string, taking a classical puzzle as a motivating example. In this ontology the domain is composed of spatial regions whereby a theory about holes is defined over a mereotopological basis. Within this theory we define a data structure, named chain, that facilitates a clear and efficient representation of the puzzle states and its solution.     

A stationary bow shock model for plasmas: The spherical blunt obstacle problem

We present an analytic model of a stationary bow shock which describes the interaction between a supermagnetosonic ambient wind and an obstacle with spherical-like frontal shape. We develop expressions for the bow shock’s geometry and the physical properties of the plasma sheath as functions of the upstream conditions. The solution is limited to magnetic fields parallel to the upstream velocity. The model allows to use any value of the upstream alfvenic and sonic Mach numbers and the polytropic index (γ$\gamma$), pointing out the influence of γ$\gamma$ for the magnetosheath compression and the bow shock shape. When both Mach numbers are small, the upstream magnetic field intensity affects also the bow shock shape. We compare our results with other models finding important consistencies. We also compare our results with in-situ data, we fund a reasonable qualitative agreement; however, it seems that our model underestimates the magnetosheath size.     

Framing holes within a loop hierarchy

We investigate the relation between nontrivial spatial concepts such as holes and string loops from a qualitative spatial reasoning perspective. In particular, we concentrate on a family of puzzles dealing with this kind of objects and explain how a loop formed in a string shows a similar behavior to a hole in an object, at least regarding the qualitative constraints it imposes on the solution of the puzzle. Unlike regular holes, however, we describe how string loops can be dynamically created and destroyed depending on the actions on the string. Furthermore, under a Knowledge Representation point of view, we provide a formalization that allows the different puzzle states to be described in terms of string crossings and loops, together with the actions that can be executed for a state transition and the complex effects they cause on the state representation. This implies the consideration of a formal representation of the side effects of actions that create or destroy string loops and the soundness of this representation with respect to the more general representation of string states in knot theory.     

SOLID3: a multiplex antibody microarray-based optical sensor instrument for in situ life detection in planetary exploration

The search for unequivocal signs of life on other planetary bodies is one of the major challenges for astrobiology. The failure to detect organic molecules on the surface of Mars by measuring volatile compounds after sample heating, together with the new knowledge of martian soil chemistry, has prompted the astrobiological community to develop new methods and technologies. Based on protein microarray technology, we have designed and built a series of instruments called SOLID (for "Signs Of LIfe Detector") for automatic in situ detection and identification of substances or analytes from liquid and solid samples (soil, sediments, or powder). Here, we present the SOLID3 instrument, which is able to perform both sandwich and competitive immunoassays and consists of two separate functional units: a Sample Preparation Unit (SPU) for 10 different extractions by ultrasonication and a Sample Analysis Unit (SAU) for fluorescent immunoassays. The SAU consists of five different flow cells, with an antibody microarray in each one (2000 spots). It is also equipped with an exclusive optical package and a charge-coupled device (CCD) for fluorescent detection. We demonstrated the performance of SOLID3 in the detection of a broad range of molecular-sized compounds, which range from peptides and proteins to whole cells and spores, with sensitivities at 1-2?ppb (ng?mL?1) for biomolecules and 10? to 103 spores per milliliter. We report its application in the detection of acidophilic microorganisms in the Río Tinto Mars analogue and report the absence of substantial negative effects on the immunoassay in the presence of 50?mM perchlorate (20 times higher than that found at the Phoenix landing site). Our SOLID instrument concept is an excellent option with which to detect biomolecules because it avoids the high-temperature treatments that may destroy organic matter in the presence of martian oxidants.     

Integrated method for crater detection from topography and optical images and the new PH9224GT catalogue of Phobos impact craters

In a large majority of lunar and planetary surface images, impact craters are the most abundant geological features. Therefore, it is not surprising that crater detection algorithms (CDAs) are one of the most studied subjects of image processing and analysis in lunar and planetary science. In this work we are proposing an Integrated CDA, consisting of: (1) utilization of DEM (digital elevation map)-based CDA; (2) utilization of an optical-based CDA; (3) re-projection of used datasets and crater coordinates from normal to rotated view and back; (4) correction of the brightness and contrast of a used optical image; and (5) tile generation for the optical-based CDA and an assembling of results with an elimination of multiple detections, in combination with a pyramid approach down to the resolution of the available DEM image; and (6) a final integration of the results of DEM-based and optical-based CDAs, including a removal of duplicates. The proposed CDA is applied to one specific asteroid-like body, the small Martian moon Phobos. The experimental evaluation of the proposed CDA is done by a manual verification of crater-candidates and a search for uncatalogued craters. The evaluation has shown that the proposed CDA was used successfully for cataloging Phobos craters. The major result of this paper is the PH9224GT – currently the most complete global catalogue of the 9224 Phobos craters. The possible applications of the new catalogue are: (1) age estimations for any selected location; and (2) comparison/evaluation of the different chronology and production functions for Phobos. This confirms the practical applicability of the new Integrated CDA – an additional result of this paper, which can be used in order to considerably extend the current crater catalogues.     

Digital LQR control scheme to maintain the separation distance of the NASA benchmark tetrahedron constellation

In previous papers, the authors developed an active control scheme based on the linear quadratic regulator (LQR) to maintain the separation distance constraints of the NASA benchmark tetrahedron constellation. Two different active control schemes were used to maintain the separation distance constraints, but one control scheme applied to every eccentricity of the NASA benchmark problem. Through this paper, the digital LQR strategy will be developed with this active control scheme to maintain the separation distance conditions of the tetrahedron constellation. The motion of a pair of satellites in an elliptical orbit about the Earth is defined by the linearized Tschauner–Hempel (TH) equations. These equations will be defined discretely in the true anomaly angle for the development of the digital control scheme. In summary, the digital LQR approach will be implemented and studied to determine how this active control scheme maintains the separation distance constraints for different specific sizes of the NASA benchmark tetrahedron constellation.     

Sounding rocket developments in Spain

This paper contemplates the efforts and developments in the field of sounding rockets carried out in Spain from the decade of the 1960s to the early 1990s when the use of such vehicles was abandoned worldwide.The initial sounding rocket planning within the National Space Research Programs around 1964 (when Spain joined ESRO) is presented.The status of the rocket technology in Spain in 1964 is analysed, reviewing the main technology gaps and the way they were filled to make the planned developments possible.Three Spanish sounding rockets are presented: the INTA-255 (150 km apogee with formative objectives, first launched in 1969), the INTA-300 (300 km apogee with high characteristics and commercial capabilities, first launched in 1974) and the INTA-100 (115 km apogee being finally a totally national product, first launched in 1980).Some guided rocket vehicle projects which were based, on some way, on the previous sounding rockets activities are also mentioned in this paper.     

Automated determination of the orientation of dust devil tracks in mars orbiter images

The paper presents and evaluates three methods for automatically estimating the main orientation of Martian dust devil tracks in MOC and HiRISE images. Inferring such information about dust devils from their tracks is important to better understand the near surface wind. The methods considered were based on gradient direction, directional openings and morphological granulometry. The accuracy of the methods was asserted by comparing the results to a set of directions estimated visually and assumed to be the ground truth. The higher accuracy was reached using directional openings. Besides, the directions inferred by this method were compared to those predicted by the GCM and the results agreed.     

A Portrait of the Nucleus of Comet 67P/Churyumov-Gerasimenko

In 2003, comet 67P/Churyumov–Gerasimenko was selected as the new target of the Rosetta mission as the most suitable alternative to the original target, comet 46P/Wirtanen, on the basis of orbital considerations even though very little was known about the physical properties of its nucleus. In a matter of a few years and based on highly focused observational campaigns as well as thorough theoretical investigations, a detailed portrait of this nucleus has been established that will serve as a baseline for planning the Rosetta operations and observations. In this review article, we present a novel method to determine the size and shape of a cometary nucleus: several visible light curves were inverted to produce a size–scale free three–dimensional shape, the size scaling being imposed by a thermal light curve. The procedure converges to two solutions which are only marginally different. The nucleus of comet 67P/Churyumov–Gerasimenko emerges as an irregular body with an effective radius (that of the sphere having the same volume) = 1.72 km and moderate axial ratios a/b = 1.26 and a/c = 1.5 to 1.6. The overall dimensions measured along the principal axis for the two solutions are 4.49–4.75 km, 3.54–3.77 km and 2.94–2.92 km. The nucleus is found to be in principal axis rotation with a period = 12.4–12.7 h. Merging all observational constraints allow us to specify two regions for the direction of the rotational axis of the nucleus: RA = 220°^+50° _−30° and Dec = −70^° ± 10^° (retrograde rotation) or RA = 40°^+50° _-30° and Dec = +70^°± 10^° (prograde), the better convergence of the various determinations presently favoring the first solution. The phase function, although constrained by only two data points, exhibits a strong opposition effect rather similar to that of comet 9P/Tempel 1. The definition of the disk–integrated albedo of an irregular body having a strong opposition effect raises problems, and the various alternatives led to a R-band geometric albedo in the range 0.045–0.060, consistent with our present knowledge of cometary nuclei. The active fraction is low, not exceeding ~ 7% at perihelion, and is probably limited to one or two active regions subjected to a strong seasonal effect, a picture coherent with the asymmetric behaviour of the coma. Our slightly downward revision of the size of the nucleus of comet 67P/Churyumov-Gerasimenko resulting from the present analysis (with the correlative increase of the albedo compared to the originally assumed value of 0.04), and our best estimate of the bulk density of 370 kg m⁻³, lead to a mass of ~ 8 × 10¹² kg which should ease the landing of Philae and insure the overall success of the Rosetta mission.     

The knowledge of knots: an interdisciplinary literature review

ABSTRACT

Knots can be found and used in a variety of situations in the 3D world, such as in vines, in the DNA, polymer chains, electrical wires, in mountaineering, seamanship and when ropes or other flexible objects are involved for exerting forces and holding objects in place. Research on knots as topological entities has contributed with a number of findings, not only of interest to pure mathematics, but also to statistical mechanics, quantum physics, genetics, and chemistry. Yet, the cognitive (or algorithmic) aspects involved in the act of tying a knot are a largely uncharted territory. This paper presents a review of the literature related to the investigation of knots from the topological, physical, cognitive and computational (including robotics) standpoints, aiming at bridging the gap between pure mathematical work on knot theory and macroscopic physical knots, with an eye to applications and modeling.