Given a group Γ and a biased graph (G,B), we define a what is meant by a Γ-realization of (G,B) and a notion of equivalence of Γ-realizations. We prove that for a finite group Γ and t ≥ 3, that there are numbers n(Γ) and n(Γ, t) such that the number of Γ-realizations of a vertically 3-connected biased graph is at most n(Γ) and that the number of Γ-realizations of a nonseparable biased graph wit...

The Full Strategy Minority Game (FSMG) is an instance of the Minority Game (MG) which includes a single copy of every potential agent. In this work, we explicitly solve the FSMG thanks to certain symmetries of this game. Furthermore, by considering the MG as a statistical sample of the FSMG, we compute approximated values of the key variable σ/N in the symmetric phase for different versions of ...

We discuss the relationship between the vertical connectivity of a biased graph Ω and the Tutte connectivity of the frame matroid of Ω (also known as the bias matroid of Ω).

Quasars at large redshifts provide a powerful probe of structure formation in the early universe. Several arguments suggest that the formation of ellipticals and massive bulges may have involved an early quasar phase. At very large redshifts, such structures are likely to be found at the highest peaks of the density field, and would thus be highly biased tracers: the earliest (massive) galaxy f...

A common objective in follow-up studies is to characterize the relationship between longitudinal measurements and time-to-event outcomes. For this aim, various methods were proposed in the statistical literature, such as an extended version of the Cox model with longitudinal covariates or a two-stage approach. However, these techniques have several limitations, including the possibility of bias...

T his paper investigates the gain of bilateral trade between China and U.S. in manufacturing sectors when both countries play a role in asymmetric (biased) growth of  international trade. Our model includes a special case of Biased Growth Theory in international trade. We collected labor productivity, export and import data by using classification of manufacturing industries, for U.S...

Given a 3-connected biased graph Ω with three node-disjoint unbalanced circles, at most one of which is a loop, we describe how the bias matroid of Ω is uniquely represented by Ω.

Traditional theories of child language acquisition center around the existence of a language acquisition device which is speciically tuned for learning a particular class of languages. More recent proposals suggest that language acquisition is assisted by the evolution of languages towards forms that are easily learnable. In this paper, we evolve combinatorial languages which can be learned by ...

t his paper investigates the gain of bilateral trade between china and u.s. in manufacturing sectors when both countries play a role in asymmetric (biased) growth of  international trade. our model includes a special case of biased growth theory in international trade. we collected labor productivity, export and import data by using classification of manufacturing industries, for u.s. and china...

A geometric lattice is a frame if its matroid, possibly after enlargement, has a basis such that every atom lies under a join of at most two basis elements. Examples include all subsets of a classical root system. Using the fact that nitary frame matroids are the bias matroids of biased graphs, we characterize modular coatoms in frames of nite rank and we describe explicitly the frames that are...