In this paper, in the first step, we will introduce concept of occasionally weakly biased mappings type (A) which is a convenient generalization (A). second show that new definition coincides with our given [8]. third and last step give an example verifies validity result.

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).

Molecular spiders are synthetic bio-molecular systems which have "legs" made of short single-stranded segments of DNA. Spiders move on a surface covered with single-stranded DNA segments complementary to legs. Different mappings are established between various models of spiders and simple exclusion processes. For spiders with simple gait and varying number of legs we compute the diffusion coeff...

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...