We shall first consider the classical neutral Moran model with two alleles whose fate is either to become extinct or to reach fixation. We will study an ergodic version of the Moran model obtained by conditioning it to never hit the boundaries, making use of a Doob transform. We shall call it the recurrent Moran model. We will show that the Siegmund dual of the recurrent Moran process exists an...

The relationship between the Moran model and stochastic Lotka-Volterra competition (SLVC) model is explored via time scale separation arguments. For neutral systems the two are found to be equivalent at long times. For systems with selective pressure, their behavior differs. It is argued that the SLVC is preferable to the Moran model since in the SLVC population size is regulated by competition...

The management of urban sprawl is fundamental to achieving sustainable urban development. Monitoring urban sprawl is, however, challenging. This study proposes the use of two spatial statistics, namely global Moran and local Moran to indentify statistically significant urban sprawl hot and cold spots. The findings reveal that the Moran indexes are sensitive to the distance band spatial weight m...

We say that a set system F ⊆ 2 shatters a given set S ⊆ [n] if 2 = {F ∩ S : F ∈ F}. The Sauer-Shelah lemma states that in general, a set system F shatters at least |F| sets. Here we concentrate on the case of equality. A set system is called shattering-extremal if it shatters exactly |F| sets. A conjecture of Rónyai and the second author and of Litman and Moran states that if a family is shatte...

Jia Shao, Sergey V. Buldyrev, Reuven Cohen, Maksim Kitsak, Shlomo Havlin, and H. Eugene Stanley Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA Department of Physics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel Minerva Center and Departme...