Results 221 to 230 of about 326,953 (255)
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2020
Buffon’s needle, Varignon’s theorem, Jung’s theorem, Sylvester's problem, are all hints that random allocations of spatial objects often obey to geometric restrictions. Further, it can be speculated that, so long as population distributions on surfaces might be represented by strings of symbols, there is no apparent reason why the arcsine law and ...
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Buffon’s needle, Varignon’s theorem, Jung’s theorem, Sylvester's problem, are all hints that random allocations of spatial objects often obey to geometric restrictions. Further, it can be speculated that, so long as population distributions on surfaces might be represented by strings of symbols, there is no apparent reason why the arcsine law and ...
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Chaotic spatial bifurcation by complex coupling
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2007A spatial bifurcation (a transition from stationary to oscillatory regime) in a chain of unidirectionally coupled phase systems is studied. It is shown that complication of coupling terms can make this bifurcation spatially chaotic in contrast to the previously observed “regular” and “predictable” type. It is demonstrated that the found type of spatial
Shalfeev, Vladimir D. +2 more
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THE GEOMETRY OF THE DEHN COMPLEX FOR A SPATIAL GRAPH
Journal of Knot Theory and Its Ramifications, 2009It is well-known that the "all right" metric structure on the Dehn complex of a knot is non-positively curved, or CAT(0), if and only if the knot projection is prime and alternating. We extend these ideas to spatial graphs and introduce the idea of ψ-alternating graphs as the appropriate analog of alternating knots.
Glasser, David +4 more
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Spatial Complexity and the Future
2020Three sets of determinants of spatial complexity have been identified: (i) probabilistic (entropy, randomness), (ii) geometrical (symmetries, intersections, orthogonality, curvature), (iii) topological (boundaries, genus, dimension, knottedness, braiding, knotting, linking, braiding, writhing).
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Complexity and Spatial Networks
2013The modern spatial economy has a global “networked” character that is generating important socio-economic and political changes. In this respect, new forms of connectivity play a significant role through their dynamic and complex interplay with the economic and political driving forces behind globalization.
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2020
From Thurston’s geometrization theorem to the Banach-Tarski paradox, spatial complexity can be enigmatic, due to singularities, immersions, infinities (e.g. Alexander’s wild knots, Antoine’s necklace, Ford circles, Hilbert curves). Measuring spatial complexity in already “complex” spatial settings constitutes a major challenge for future research, as ...
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From Thurston’s geometrization theorem to the Banach-Tarski paradox, spatial complexity can be enigmatic, due to singularities, immersions, infinities (e.g. Alexander’s wild knots, Antoine’s necklace, Ford circles, Hilbert curves). Measuring spatial complexity in already “complex” spatial settings constitutes a major challenge for future research, as ...
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Complex spatial patterns on planar continua
Physical Review Letters, 1993The Landau-Ginzburg equations used to describe periodic spatial patterns in two dimensions are extended to a set or spatiotemporal equations. The extension is determined by the requirement that the equations or motion commute with translations, reflections, and rotations in the plane.
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1990
Abstract : The work done with this grant was on the topic of complex spatial dynamics, and included progress in three areas: (1) analysis of the space of cellular automation rules, particularly with an eye toward the question of where complex cellular automata live in this space, and (2) analyzing data from complex spatial systems, and (3) nonlinear ...
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Abstract : The work done with this grant was on the topic of complex spatial dynamics, and included progress in three areas: (1) analysis of the space of cellular automation rules, particularly with an eye toward the question of where complex cellular automata live in this space, and (2) analyzing data from complex spatial systems, and (3) nonlinear ...
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Spatial and Temporal Complexity
1974In the first section we examined some of the mainly holistic studies of lake benthos that have been undertaken. Opponents of this approach would suggest that no two lakes are, in reality, alike and that the complexity of nature prevents the holistic view from achieving its goal of developing general statements about the nature of lakes. In this section
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