In science:

We then consider two methods of sequential updating that differ from each other only in the selection rule of the links to be updated.

Synchronous and Asynchronous Recursive Random Scale-Free Nets

To obtain time-scales comparable to the parallel update, we therefore have to rescale time as t = T /(2M ), identifying a single random update with the asymptotically inﬁnitesimal time step dt = 1/(2M ).

Message passing for vertex covers

This reﬂects the persistence time that a message is not updated at all: The fraction of variables which are not selected in N single-spin updates is e−1 .

Message passing for vertex covers

In this section using the updated version of the norm equations, we update some deﬁnability and decidability results for totally real inﬁnite extensions of Q.

Diophantine Definability and Decidability in the Extensions of Degree 2 of Totally Real Fields

We ﬁnd that the mean ﬁeld predictions are conﬁrmed (i) for random sequential updating of multi-networks and (ii) for both parallel and random sequential updating of simple-networks with γ = 2.25 and γ = 2.6.

This method uses Eq. (2) as the basis for an iteration scheme, in which the voltage Vi at node i at the nth update step is computed from (2) using the values of Vj at the (n − 1)st update in the right-hand side of this equation.

When we update just one choice at each time step, X = 1, sequential updating reaches equilibrium faster than random update but the equilibrium values are the same, F2 = 1/2 in Fig. 16.

Randomness and Complexity in Networks

E updates random updating has not updated all elements while sequential has.

Randomness and Complexity in Networks

DILOC in (10) is distributed since (i) the update is implemented at each sensor independently; (ii) at sensor l ∈ Ω, the update of the state, cl (t + 1), is obtained from the states of its m + 1 neighboring nodes in Θl ; and (iii) there is no central location and only local information is available.

Distributed Sensor Localization in Random Environments using Minimal Number of Anchor Nodes

More formally, let X ℓ be the set of all updating random walks of length ℓ, and let X ℓ good be the set of updating random walks such that all variables have been updated (at least once) after ℓ steps.

Agnostically Learning Juntas from Random Walks

Note that unlike in the original updating random walk model, we determine the sequence F of updating outcomes before we determine the positions to be updated.

We recall that correlations in other types of update such as parallel updating has been discussed in [16, 17].

Asymmetric Exclusion Processes with Disorder: Effect of Correlations

We consider RBNs of N nodes with a ﬁxed number K of randomly assigned inputs per node and with the update function at each node chosen at random among all possible update functions.

Perturbation propagation in random and evolved Boolean networks

Some complications arise as recomputation of the Jacobian is triggered by the time integrator: on the one hand, rather than just updating the Jacobian J , the sparse matrix 1 − γ J (with γ ∈ [0, 1) given) has to be created and updated (in parallel) as well.