By Jeffrey Johnson
ISBN-10: 186094972X
ISBN-13: 9781860949722
The fashionable international is advanced past human realizing and regulate. The technological know-how of complicated platforms goals to discover new methods of puzzling over the various interconnected networks of interplay that defy conventional techniques. to date, study into networks has principally been constrained to pairwise relationships represented by way of hyperlinks among nodes. This quantity marks a massive extension of networks to multidimensional hypernetworks for modeling multi-element relationships, comparable to businesses making up the inventory industry, the neighborhoods forming a urban, humans making up committees, divisions making up businesses, pcs making up the net, males and machines making up armies, or robots operating as groups.
This quantity makes a tremendous contribution to the technology of advanced platforms by means of:
(i) extending community concept to incorporate dynamic relationships among many components;
(ii) delivering a mathematical concept capable of combine multilevel dynamics in a coherent approach; (iii)
delivering a brand new methodological method of research complicated platforms; and
(iv) illustrating the idea with sensible examples within the layout, administration and keep watch over of complicated structures taken from many parts of program.
Readership: lecturers: researchers, scientists, social scientists, complicated platforms scientists, economists, biologists; undefined: managers, planners, experts, wisdom execs, structures engineers, automation experts, provide chain managers; Public companies: Council officials, urban planners, shipping planners, wellbeing and fitness execs, welfare execs.
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Additional info for Hypernetworks in the Science of Complex Systems
Sample text
In our terms, Vanilla Ice Cream is a polyhedron with five vertices bound together by an indivisible 5-ary relation. This can be written as Vanilla Ice Cream = ⟨Cold, Sweet, Vanilla, Softness, Yellow ⟩ ̸= ⟨ Cold ⟩ + ⟨Sweet⟩ + ⟨Vanilla⟩ + ⟨ Softness⟩ + ⟨Yellow⟩ with the “Gestalt” construct of Vanilla Ice Cream represented by a polyhedron with five vertices. 7 illustrates the distinction between an unrelated set of vertices and the “Gestalt” polyhedron. It also illustrates the difference between a polyhedron with five vertices embedded in a 4-dimensional space and a networktheoretic clique embedded in 2-dimensional space in which every vertex is connected to every other by a 1-dimensional link.
Ketchup fried bread sausage waistcoat s ✪❡ ✪ ❡ ✪ ❡ s✪ ❡s jacket trousers (a) The Full Monty (b) English breakfast Fig. 6 Examples of simplices The phrase “The Full Monty” has come to mean “complete” or everything that could be expected. It is said to come from the Montague Burton tailoring chain which hired three-piece suits to men getting married ⟨jacket, trousers, waistcoat⟩ (Fig. 6(a)). Another, less likely, explanation is that it comes from the full English breakfasts General Montgomery recommended for his troops ⟨egg, bacon, sausage, fried bread, baked beans, mushrooms, tomatoes, ketchup⟩ ((Fig.
2 The Dual Berge hypergraphs Let R be a relation between A and B. Let the notation a R b mean that a is R-related to b. Let R(a) = {b | for all b in B with a R b} and R(b) = {a | for all a in A with a R b}. In general a relation R between sets A and B has two associated hypergraphs, HA (B; R) and HB (A; R), defined as follows: def HA (B; R) = {R(a) | a in A), def HB (A; R) = {R(b) | b in B). As an example let A = {London Bus, London Taxi, Postbox} and B = {red, black, big, small, wheels, slot, metal}.
Hypernetworks in the Science of Complex Systems by Jeffrey Johnson
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