[PDF] Top 20 From kernels in directed graphs to fixed points and negative cycles in Boolean networks

... of and-nets, which are Boolean networks such that each component is a conjunction of its (positive or negative) ...where kernels, a graph-theoretical notion introduced by von Neumann ... Voir le document complet

... statement, and the resulting upper bound is one (hence, Theorem ...positive cycles which is important to obtain several fixed points (or asynchronous at- tractors), but much more the ... Voir le document complet

... comes from the versatility of negative cycles: depending on the way they are connected to positive cycles, that can either be favorable or unfavorable to the presence of many ... Voir le document complet

... the directed graph whose the adjacency matrix is the discrete Jacobian matrix of f evaluated at point x, and they proved that if Gf (x) has no directed cycle for all x in {0, 1} n , then f has ... Voir le document complet

... interested in the number of fixed points in AND-OR- NOT networks (AND-OR-NOT-nets for ...are Boolean networks in which the update function associated ... Voir le document complet

... f from G(f ) only. There are many results in this direction (see [1] for a ...review). In most cases, the studied dynamical properties are invariant by isomorphism: number of fixed or periodic ... Voir le document complet

... of fixed points for the negative clique and the positive clique, we then show that positive cycles are not necessarily useful in order to create many fixed ... Voir le document complet

... states and the topology of Boolean ...a Boolean network with n components is usually described by the successive iterations of a map F from {0, 1} n to ...correspond to the ... Voir le document complet

... a Boolean network f is usually represented via its interaction graph, which is the digraph G with vertex set {1, ...arcs from a vertex to itself). In many contexts, as in molecular ... Voir le document complet

... interested in fixed points in Boolean networks, ...f from {0, 1} n to itself. We define the sub- networks of f as the restrictions of f to the ... Voir le document complet

... Introduction In the course of his analysis of discrete iterations, Robert introduced a discrete Jacobian matrix for Boolean maps and the notion of Boolean eigenvalue [2, 3, 4, ...Shih ... Voir le document complet

... provided in [19]. In this paper, we propose discrete counterparts of Thomas’ rules in the general Boolean case and demonstrate ...them. In the differential framework, C. Soulé ... Voir le document complet

... results in Section 2, we start in Section 3 by studying how the number of vertex-disjoint cycles of different lengths in an undirected graph behaves in relation to the minimum ... Voir le document complet

... vertices in the faces x 2 = ±1. Now if we set x 3 = −x 1 in (39) with x 2 = ±1, we see that the first and third equations are ...−1) to (−1, ±1, 1) is ...as in the previous sections, ... Voir le document complet

... Indeed, in this case T is a regular tournament of degree ...strongly-connected, and then, by Theorem 10, we get that T is ...a directed cycle of order 2δ + 1, and we are ...up to the ... Voir le document complet

... measures and transitional properties Given a strictly positive similarity measure s(x, y), the function κ(x, y) = ln s(x, y) is the corresponding logarithmic similarity ...j, and k, while sij sjk = sik sjj ... Voir le document complet

... also that, as stated, it might be a little bit optimistic: maybe one should replace X by its normalization (as it is not clear whether X is normal or not). A special case of an element σ normalizing W is when σ is a root ... Voir le document complet

... deposit and dissemination of sci- entific research documents, whether they are pub- lished or ...come from teaching and research institutions in France or abroad, or from public or ... Voir le document complet

... follows: In Sections 2 and 3 we recall the most important results in the traditional scenario and we add some ...devoted to the anticipative ...pessimistic and conservative ... Voir le document complet

... Directed Virtual Path Layouts in ATM Networks Jean-Claude Bermond, Nausica Marlin, David Peleg, Stéphane Pérennes.. To cite this version: Jean-Claude Bermond, Nausica Marlin, David Peleg[r] ... Voir le document complet