Breaking of Ensemble

Such functional modularity is mainly achieved by joint regulation of the genes within a module by a common set of TFs (also called the transcriptional

We follow up on the work published by Freund and Schapire [1] who first introduced the Hedge setting. This was improved by Gr¨ unwald et al.[3] with the development of the AdaHedge

There are results on the asymptotic number of labeled graphs with given degree sequence such that the degrees are o( √ n) [16] [17]. A constant homogeneous degree sequence has

2 Ensemble Nonequivalence in Random Graphs with Modular Struc- ture 25 §2.1 Introduction and main results.. 3 Covariance structure behind breaking of ensemble

Recently, the study of certain classes of uni-partite and bi-partite random graphs [92], [47] has shown that ensemble nonequivalence can manifest itself via an additional,

The framework is based on the separation of packing and force scales, together with an a priori flat measure in the force phase space under the constraints that the contact forces

Section 2 defines the two ensem- bles, gives the definition of equivalence of ensembles in the dense regime, recalls some basic facts about graphons, and states the large

We consider the case of a random graph with a given degree sequence (configuration model) and show that this formula correctly predicts that the specific relative entropy is