[PDF] Top 20 Local negative circuits and fixed points in Boolean networks

... one fixed point? As main result, we settle this problem under the additional condition that, for all x ∈ {0, 1} n , the out-degree of each vertex of G F (x) is at most ...words: Boolean network, Interaction ... Voir le document complet

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

... results and a question Since the seminal works of Kauffman [5, 6] and Thomas [17, 19], Boolean net- works are extensively used to model gene regulatory ...networks. In this context, the ... Voir le document complet

... no negative cycle, then f has at least one fixed ...4 and 5 give a nice proof “by dichotomy” of Robert’s theorem: the absence of posi- tive cycle gives the uniqueness, and absence of ... Voir le document complet

... of fixed points in a conjunctive boolean network with G as interaction ...sets in G and the maximum number of maximal independent sets among all the graphs obtained from G by ... Voir le document complet

... x, and they proved that if Gf (x) has no directed cycle for all x in {0, 1} n , then f has a unique fixed point .... In this paper, we generalize Shih-Dong’s theorem using, as main tool, the ... Voir le document complet

... 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 points, number and size of ... Voir le document complet

... of Boolean networks ...processes and thereby predict perturbations for their control [1,5,6,7,18,24]. In Boolean networks, each gene or protein is modelled as a binary variable, ... Voir le document complet

... a fixed point y such that the distance between x and y is at most ...embed, in a similar way, a n-component network with negative loops into a m-component monotone network? Maybe this would ... Voir le document complet

... described in Figure 6. It has been proved in [9] that H n is the unique connected graph with n vertices and µ(n) maximal independent ...symmetric negative AND-NOT-net with H n as ... Voir le document complet

... interested in networks f which can be fixed in polynomial time, ...interested in families F which can be fixed in polynomial ...families, and for each, we will ... Voir le document complet

... generalise and adapt the techniques developed from network coding and coding theory to tackle the problem of maximising fixed points for signed ...digraphs in Theorem 1. This approach ... Voir le document complet

... predecessor and at most one unsigned predecessor, and if G has no undirected negative cycle, then G has exactly 2 topological fixed ...1 and i ( ˜ G is ...positive, and α i = 1 ... Voir le document complet

... as Boolean networks if A = {0, 1}) with a given interaction graph, that describes which local functions depend on which ...variables. In this paper, we generalise the so-called reduction of ... Voir le document complet

... rate and c > 0 is a logistic term which represents competition between ...processes and is also a special case of logistic branching ...role in population dynamics, where it is probably the ... Voir le document complet

... sequential circuits are very rigid in their timing specifications because the behavior of the system at every clock cycle is ...flexibility in physical implementation because the latency of ... Voir le document complet

... comparison in terms of energy consumption 5 Computational Results We have used CPLEX to execute the discrete and the continuous program models related to the MCMCF with step increasing and piecewise ... Voir le document complet

... the fixed points of general transcendental meromorphic functions for almost four decades (see ...the fixed points of solutions of differential equations. It was in year 2000 that ... Voir le document complet

... proper fixed points of the power operator and the commutative pseudovarieties of ...a fixed point of P and all proper fixed points are of this ...proper fixed ... Voir le document complet

... the Boolean configurations (states), and edges represent the possible iterations ...described in ( 2 ) constitutes a more promising structure to visualize the attractor basins and undergoing ... Voir le document complet