Gabriel graph of geomagnetic Sq variations

Sridharan, M.; Ramasamy, A. M. S.

doi:10.2478/s11600-010-0004-y

Cited by 6 publications

(6 citation statements)

References 10 publications

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“…Proximity graphs found their applications in many fields of science and engineering. The application domains related to topics of the paper include routing in ad hoc wireless networks [18,32,29,25,38], road network analysis [39,40], study percolation [11] and analysis of magnetic field [33]. Structure of proximity graphs represents so wide range of natural and engineering system that it would be productive to compare Physarum graph P and highway graph H to relative neighborhood graph RNG, β-skeleton BS(1.5) (β-skeleton B was calculated for β = 1.5 to make an 'intermediate' graph between RNG and GG), Gabriel graph GG and minimum spanning tree MST (Fig.…”

Section: Physarum Proximity Graphs and Highwaysmentioning

confidence: 99%

Approximating Mexican highways with slime mould

et al. 2011

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Plasmodium of Physarum polycephalum is a single cell visible by unaided eye. During its foraging behavior the cell spans spatially distributed sources of nutrients with a protoplasmic network. Geometrical structure of the protoplasmic networks allows the plasmodium to optimize transport of nutrients between remote parts of its body. Assuming major Mexican cities are sources of nutrients how much structure of Physarum protoplasmic network correspond to structure of Mexican Federal highway network? To find an answer undertook a series of laboratory experiments with living Physarum polycephalum. We represent geographical locations of major cities by oat flakes, place a piece of plasmodium in Mexico city area, record the plasmodium's foraging behavior and extract topology of nutrient transport networks. Results of our experiments show that the protoplasmic network formed by Physarum is isomorphic, subject to limitations imposed, to a network of principle highways. Ideas and results of the paper may contribute towards future developments in bio-inspired road planning

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Section: Physarum Proximity Graphs and Highwaysmentioning

confidence: 99%

Approximating Mexican highways with slime mould

et al. 2011

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“…Proximity graphs found their applications in fields of science and engineerings: geographical variational analysis [9,16,20], evolutionary biology [15], spatial analysis in biology [13,6,7,11], simulation of epidemics [23]. Proximity graphs are used in physics to study percolation [5] and analysis of magnetic field [22].…”

Section: Introductionmentioning

confidence: 99%

Excitable β-Skeletons

Adamatzky

2013

Reaction-Diffusion Automata: Phenomenology, Localisations, Computation

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A β-skeleton, β ≥ 1, is a planar proximity undirected graph of an Euclidean point set where nodes are connected by an edge if their lune-based neighborhood contains no other points of the given set. Parameter β determines size and shape of the nodes' neighborhoods. In an excitable β-skeleton every node takes three statesresting, excited and refractory, and updates its state in discrete time depending on states of its neighbors. We design families of β-skeletons with absolute and relative thresholds of excitability and demonstrate that several distinct classes of space-time excitation dynamics can be selected using β. The classes include spiral and target waves of excitation, branching domains of excitation and oscillating localizations.

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“…Proximity graphs are applied in many fields of science and engineerings: from image processing (eps. reconstructing the shape of a two-dimensional object, given a set of sample points on the boundary of the object), visualisation and physical modelling to analysis and design of communication and transport networks [1,3,5,7,8,9,13,17,21,22,24,25,26,29,31,32,33,34,35,36,37,38] A β-skeleton is the Gabriel graph [25] for β = 1 and it is the relative neighbourhood graph for β = 2 [16,20]. A β-skeleton, in general case, becomes disconnected for β > 2 and continues losing its edges with further increase of β.…”

Section: Introductionmentioning

confidence: 99%

On growing connected β -skeletons

Adamatzky

2013

Computational Geometry

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A β-skeleton, β ≥ 1, is a planar proximity undirected graph of an Euclidean points set, where nodes are connected by an edge if their lune-based neighbourhood contains no other points of the given set. Parameter β determines the size and shape of the lune-based neighbourhood. A β-skeleton of a random planar set is usually a disconnected graph for β > 2. With the increase of β, the number of edges in the β-skeleton of a random graph decreases. We show how to grow stable β-skeletons, which are connected for any given value of β and characterise morphological transformations of the skeletons governed by β and a degree of approximation. We speculate how the results obtained can be applied in biology and chemistry.

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Gabriel graph of geomagnetic Sq variations

Cited by 6 publications

References 10 publications

Approximating Mexican highways with slime mould

Approximating Mexican highways with slime mould

Excitable β-Skeletons

On growing connected β -skeletons

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