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...

Abstract In this article, the length-biased power hazard rate distribution has introduced and investigated several statistical properties. This reports an extension of probability distributions, namely: exponential, Rayleigh, Weibull, linear rate. The procedure maximum likelihood estimation is taken for parameters. Finally, applicability model explored by three real data sets. To examine, perfo...