8,413 research outputs found
Repotting the Geraniums: On Nested Graph Transformation Rules
We propose a scheme for rule amalgamation based on nested graph predicates. Essentially, we extend all the graphs in such a predicate with right hand sides. Whenever such an enriched nested predicate matches (i.e., is satisfied by) a given host graph, this results in many individual match morphisms, and thus many “small” rule applications. The total effect is described by the amalgamated rule. This makes for a smooth, uniform and very powerful amalgamation scheme, which we demonstrate on a number of examples. Among the examples is the following, which we believe to be inexpressible in very few other parallel rule formalism proposed in the literature: repot all flowering geraniums whose pots have cracked.\u
Majority rules with random tie-breaking in Boolean gene regulatory networks
We consider threshold boolean gene regulatory networks, where the update function of each gene is described as a majority rule evaluated among the regulators of that gene: it is turned ON when the sum of its regulator contributions is positive (activators contribute positively whereas repressors contribute negatively) and turned OFF when this sum is negative. In case of a tie (when contributions cancel each other out), it is often assumed that the gene keeps it current state. This framework has been successfully used to model cell cycle control in yeast. Moreover, several studies consider stochastic extensions to assess the robustness of such a model. Here, we introduce a novel, natural stochastic extension of the majority rule. It consists in randomly choosing the next value of a gene only in case of a tie. Hence, the resulting model includes deterministic and probabilistic updates. We present variants of the majority rule, including alternate treatments of the tie situation. Impact of these variants on the corresponding dynamical behaviours is discussed. After a thorough study of a class of two-node networks, we illustrate the interest of our stochastic extension using a published cell cycle model. In particular, we demonstrate that steady state analysis can be rigorously performed and can lead to effective predictions; these relate for example to the identification of interactions whose addition would ensure that a specific state is absorbing
The Number of Different Binary Functions Generated by NK-Kauffman Networks and the Emergence of Genetic Robustness
We determine the average number , of \textit{NK}-Kauffman
networks that give rise to the same binary function. We show that, for , there exists a connectivity critical value such that () for and
for . We find that is not a
constant, but scales very slowly with , as . The problem of genetic robustness emerges as a statistical property
of the ensemble of \textit{NK}-Kauffman networks and impose tight constraints
in the average number of epistatic interactions that the genotype-phenotype map
can have.Comment: 4 figures 18 page
The Number of Different Binary Functions Generated by NK-Kauffman Networks and the Emergence of Genetic Robustness
We determine the average number , of \textit{NK}-Kauffman
networks that give rise to the same binary function. We show that, for , there exists a connectivity critical value such that () for and
for . We find that is not a
constant, but scales very slowly with , as . The problem of genetic robustness emerges as a statistical property
of the ensemble of \textit{NK}-Kauffman networks and impose tight constraints
in the average number of epistatic interactions that the genotype-phenotype map
can have.Comment: 4 figures 18 page
Thermodynamic graph-rewriting
We develop a new thermodynamic approach to stochastic graph-rewriting. The
ingredients are a finite set of reversible graph-rewriting rules called
generating rules, a finite set of connected graphs P called energy patterns and
an energy cost function. The idea is that the generators define the qualitative
dynamics, by showing which transformations are possible, while the energy
patterns and cost function specify the long-term probability of any
reachable graph. Given the generators and energy patterns, we construct a
finite set of rules which (i) has the same qualitative transition system as the
generators; and (ii) when equipped with suitable rates, defines a
continuous-time Markov chain of which is the unique fixed point. The
construction relies on the use of site graphs and a technique of `growth
policy' for quantitative rule refinement which is of independent interest. This
division of labour between the qualitative and long-term quantitative aspects
of the dynamics leads to intuitive and concise descriptions for realistic
models (see the examples in S4 and S5). It also guarantees thermodynamical
consistency (AKA detailed balance), otherwise known to be undecidable, which is
important for some applications. Finally, it leads to parsimonious
parameterizations of models, again an important point in some applications
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