Clastic Polygonal Networks Around Lyot Crater, Mars: Possible Formation Mechanisms From Morphometric Analysis

Polygonal networks of patterned ground are a common feature in cold-climate environments. They can form through the thermal contraction of ice-cemented sediment (i.e. formed from fractures), or the freezing and thawing of ground ice (i.e. formed by patterns of clasts, or ground deformation). The characteristics of these landforms provide information about environmental conditions. Analogous polygonal forms have been observed on Mars leading to inferences about environmental conditions. We have identified clastic polygonal features located around Lyot crater, Mars (50°N, 30°E). These polygons are unusually large (> 100 m diameter) compared to terrestrial clastic polygons, and contain very large clasts, some of which are up to 15 metres in diameter. The polygons are distributed in a wide arc around the eastern side of Lyot crater, at a consistent distance from the crater rim. Using high-resolution imaging data, we digitised these features to extract morphological information. These data are compared to existing terrestrial and Martian polygon data to look for similarities and differences and to inform hypotheses concerning possible formation mechanisms. Our results show the clastic polygons do not have any morphometric features that indicate they are similar to terrestrial sorted, clastic polygons formed by freeze-thaw processes. They are too large, do not show the expected variation in form with slope, and have clasts that do not scale in size with polygon diameter. However, the clastic networks are similar in network morphology to thermal contraction cracks, and there is a potential direct Martian analogue in a sub-type of thermal contraction polygons located in Utopia Planitia. Based upon our observations, we reject the hypothesis that polygons located around Lyot formed as freeze-thaw polygons and instead an alternative mechanism is put forward: they result from the infilling of earlier thermal contraction cracks by wind-blown material, which then became compressed and/or cemented resulting in a resistant fill. Erosion then leads to preservation of these polygons in positive relief, while later weathering results in the fracturing of the fill material to form angular clasts. These results suggest that there was an extensive area of ice-rich terrain, the extent of which is linked to ejecta from Lyot crater

Answer Set Programming Modulo `Space-Time'

We present ASP Modulo `Space-Time', a declarative representational and computational framework to perform commonsense reasoning about regions with both spatial and temporal components. Supported are capabilities for mixed qualitative-quantitative reasoning, consistency checking, and inferring compositions of space-time relations; these capabilities combine and synergise for applications in a range of AI application areas where the processing and interpretation of spatio-temporal data is crucial. The framework and resulting system is the only general KR-based method for declaratively reasoning about the dynamics of `space-time' regions as first-class objects. We present an empirical evaluation (with scalability and robustness results), and include diverse application examples involving interpretation and control tasks

Flow rate of polygonal grains through a bottleneck: Interplay between shape and size

We report two-dimensional simulations of circular and polygonal grains passing through an aperture at the bottom of a silo. The mass flow rate for regular polygons is lower than for disks as observed by other authors. We show that both the exit velocity of the grains and the packing fraction are lower for polygons, which leads to the reduced flow rate. We point out the importance of the criteria used to define when two objects of different shape are considered to be of the same size. Depending on this criteria, the mass flow rate may vary significantly for some polygons. Moreover, the particle flow rate is non-trivially related to a combination of mass flow rate, particle shape and particle size. For some polygons, the particle flow rate may be lower or higher than that of the corresponding disks depending on the size comparison criteria.Comment: 9 pages, 8 figure

An object-based classification approach for mapping "migrant housing" in the mega-urban area of the Pearl River Delta (China)

Urban areas develop on formal and informal levels. Informal development is often highly dynamic, leading to a lag of spatial information about urban structure types. In this work, an object-based remote sensing approach will be presented to map the migrant housing urban structure type in the Pearl River Delta, China. SPOT5 data were utilized for the classification (auxiliary data, particularly up-to-date cadastral data, were not available). A hierarchically structured classification process was used to create (spectral) independence from single satellite scenes and to arrive at a transferrable classification process. Using the presented classification approach, an overall classification accuracy of migrant housing of 68.0% is attained

Shape matching and clustering in design

Generalising knowledge and matching patterns is a basic human trait in re-using past experiences. We often cluster (group) knowledge of similar attributes as a process of learning and or aid to manage the complexity and re-use of experiential knowledge [1, 2]. In conceptual design, an ill-defined shape may be recognised as more than one type. Resulting in shapes possibly being classified differently when different criteria are applied. This paper outlines the work being carried out to develop a new technique for shape clustering. It highlights the current methods for analysing shapes found in computer aided sketching systems, before a method is proposed that addresses shape clustering and pattern matching. Clustering for vague geometric models and multiple viewpoint support are explored

Convex lattice polygons of fixed area with perimeter dependent weights

We study fully convex polygons with a given area, and variable perimeter length on square and hexagonal lattices. We attach a weight t^m to a convex polygon of perimeter m and show that the sum of weights of all polygons with a fixed area s varies as s^{-theta_{conv}} exp[K s^(1/2)] for large s and t less than a critical threshold t_c, where K is a t-dependent constant, and theta_{conv} is a critical exponent which does not change with t. We find theta_{conv} is 1/4 for the square lattice, but -1/4 for the hexagonal lattice. The reason for this unexpected non-universality of theta_{conv} is traced to existence of sharp corners in the asymptotic shape of these polygons.Comment: 8 pages, 5 figures, revtex

On k-Convex Polygons

We introduce a notion of $k$-convexity and explore polygons in the plane that have this property. Polygons which are \mbox{$k$-convex} can be triangulated with fast yet simple algorithms. However, recognizing them in general is a 3SUM-hard problem. We give a characterization of \mbox{$2$-convex} polygons, a particularly interesting class, and show how to recognize them in \mbox{$O(n \log n)$} time. A description of their shape is given as well, which leads to Erd\H{o}s-Szekeres type results regarding subconfigurations of their vertex sets. Finally, we introduce the concept of generalized geometric permutations, and show that their number can be exponential in the number of \mbox{$2$-convex} objects considered.Comment: 23 pages, 19 figure