G. Moran. Parametrization for stationary patterns of the r-majority operators on 0-1 sequences. Discrete Mathematics, 132:175--195, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... has been concentrated on determining the asymptotic behaviors of di erent majority rules on di erent graph structures, focusing on the study of con gurations leading to periodic dynamics on nite graphs [10, 21] on the number of xed points on nite rings [1, 11] and ( nite and in nite) lines [14, 15], and on the behaviors of in nite graphs [16] However, very little is known about patterns leading to monochromatic xed points, i.e. dynamos. This is quite surprising considering that dynamos describe occurrences of faults which lead the entire system to a faulty behaviour. Most of the ....

G. Moran. Parametrization for stationary patterns of the r-majority operators on 0-1 sequences. Discrete Mathematics, 132:175-195, 1994. 18

....the symmetric neural network model. For example, dynamical systems with more general threshold functions and allowing for more than two possible colors are studied in [PS83, PT86a, PT86b] while sufficient conditions for the property in the case of LMP on infinite graphs were studied in [M94a, M94b, M95] 3 Structural properties Let s start by presenting a class of graphs that are m.c.c. and a class of graphs that are not m.c.c. Proposition 3. a) A graph G with more than n=2 masters is a majority consensus computer. b) A graph G with exactly (n Gamma 1) 2 masters is not a majority ....

G. Moran, Parametrization for stationary patterns of the r-majority operators on 0-1 sequences, Discr. Math., vol 132, 175-195, 1994.

....and by N.S.E.R.C under grant #A2415. on the study of the period two behavior of symmetric weighted majorities on finite f0; 1g Gamma and f0; pg colored graphs [8, 18] on the number of fixed points on finite f0; 1g colored rings [1, 2, 9] on finite and infinite f0; 1g colored lines [11, 12], on the behaviors of infinite, connected f0; 1g colored graphs [13] Furthermore, dynamic majority has been applied to the immune system and to image processing [1, 7] Although the majority rule has been extensively investigated, not much is known regarding dynamos. Some results are known in ....

G. Moran. Parametrization for stationary patterns of the r-majority operators on 0--1 sequences. Discrete Mathematics, 132:175--195, 1994.

....here (after a vertex becomes black, it stands black forever) is called irreversible majority, as opposed to reversible majority where a vertex always assumes the color of the majority of its neighbourds. The latter rule may lead to non stabilizing situations, in several network topologies [2, 9, 10, 14, 15, 16, 21]. Related results have been This work has been supported in part by the Government of Italy, under a cooperation project with Jordan 1 Lower Bound Upper Bound Butterfly 2 b n Gamma1 2 c 2 n Gamma2 Toroidal 2 b n 2 c 2 n Gamma2 2 n Gamma3 2 n Gamma4 Butterfly CCC maxfb n 1 ....

G. Moran. Parametrization for stationary patterns of the r-majority operators on 0--1 sequences. Discrete Mathematics 132 (1994) 175-195.

.... as a vector x t = x t 1 ; x t n ) where x t i represents the value at node v i after time step t) For instance, the fact that the period of such sequences is either one or two is proved (in various contexts) in [GoOl80, PoSu83, PoTu86] The problem was studied further in [Mor94c, Mor94b, Mor94a]. Also, the applicability of majority voting as a tool for fault local mending was investigated in [KP95a, KP95b] 3 2 Upper Bounds Given a graph G = V; E) a vertex x 2 V , and a set S ae V , we denote by deg G (x; S) the number of neighbors of x in G belonging to S, namely, j Gamma 1 (x) ....

G. Moran. Parametrization for stationary patterns of the r-majority operators on 0-1 sequences. Discrete Mathematics, 132:175--195, 1994.

.... (represented as a vector x t = x t 1 ; x t n ) where x t i represents the value at node v i after time step t) For instance, the fact that the period of such sequences is either one or two is proved (in various contexts) in [GO80, PS83, PT86] The problem was studied further in [Mor94c, Mor94b, Mor94a]. Also, the applicability of majority voting as a tool for fault local mending was investigated in [KP95a, KP95b] 2 [1; r] controlling coalitions Definition9. Given an n vertex graph G, a packing is a collection P = fP 1 ; P t g of disjoint neighborhoods in G. For each neighborhood P i ....

G. Moran. Parametrization for stationary patterns of the r-majority operators on 0-1 sequences. Discrete Mathematics, 132:175--195, 1994.

.... research has focused, for example, on the study of the period two behavior of symmetric weighted majorities on finite f0; 1g Gamma and f0; pg colored graphs [8, 18] on the number of fixed points on finite f0; 1g colored rings [1, 2, 9] on finite and infinite f0; 1g colored lines [11, 12], on the behaviors of infinite, connected f0; 1g colored graphs [13] Furthermore, dynamic majority has been applied to the immune system and to image processing [1, 7] Although the majority rule has been extensively investigated, not much is known regarding dynamos. Some results are known in ....

G. Moran. Parametrization for stationary patterns of the r-majority operators on 0--1 sequences. Discrete Mathematics, 132:175--195, 1994.

....r = 1 [A 88, Gr91] and r 1 [A91] The behavior of infinite sequences, and infinite graphs in general, was also studied under the r majority operator. For infinite structures the period 2 property is not guaranteed to hold, and conditions sufficient to ensure it were established in [M94a, M94b, M94c] 8.1.3 Size bounds Bounds on the size of monopolies in the dynamic case have also been considered. Here the focus is on cases in which the system reaches a monochromatic fixpoint. A set of vertices M is said to be a dynamic monopoly, abbreviated dynamo, if starting the game with the ....

G. Moran. Parametrization for stationary patterns of the r-majority operators on 0-1 sequences. Discrete Mathematics, 132:175--195, 1994.

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G. Moran. Parametrization for stationary patterns of the r-majority operators on 0-1 sequences. Discrete Mathematics, 132:175--195, 1994.

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