Dynamical urn models, such as the Ehrenfest model, have played an important role in the early days of statistical mechanics. Dynamical many-urn models generalize the former models in two respects: the number of urns is macroscopic, and thermal effects are included. These many-urn models are exactly solvable in the mean-field geometry. They allow analytical investigations of the characteristic f...

In this work we discuss two urn models with general weight sequences (A,B) associated to them, A = (αn)n∈N andB = (βm)m∈N, generalizing two well known Pólya-Eggenberger urn models, namely the so-called sampling without replacement urn model and the OK Corral urn model. We derive simple explicit expressions for the distribution of the number of white balls, when all black have been drawn, and ob...

IV. Automata and generalized urn logic 11 A. Partition logic 13 B. Generalized urn models 13 C. Automaton models 13 D. Proof of logical equivalence 14 1. Direct construction of automaton models from generalized urn models 14 2. Direct construction of generalized urn models from automaton models 14 3. Schemes using dispersion-free states 14 4. Example 1: The generalized urn logic L12 16 5. Examp...

In this work we are concerned with so-called Pólya-Eggenberger urn models, which in the simplest case of two colors can be described as follows. At the beginning, the urn contains n white and m black balls. At every step, we choose a ball at random from the urn, examine its color and put it back into the urn and then add/remove balls according to its color by the following rules: if the ball is...

Urn models have been widely studied and applied in both scientific and social disciplines. In clinical studies, the adoption of urn models in treatment allocation schemes has been proved to be beneficial to both researchers, by providing more efficient clinical trials, and patients, by increasing the probability of receiving the better treatment. In this paper, we endeavor to derive a very gene...

Urn models have been studied a lot because they are analytically tractable and contain rich physical phenomena, e.g., slow relaxation or condensation phenomena.1–5 It has been revealed that the urn models are related to zero range processes and asymmetric simple exclusion processes6 which are stochastic processes for studying nonequilibrium statistical physics. Furthermore, the urn models have ...

Cholesterol content can vary distinctly between normal and cancer cells, with elevated levels in cancer cells. Here, we investigated cholesterol sequestration with methyl-β-cyclodextrin (MCD), and pore-formation with the ostreolysin A/pleurotolysin B (OlyA/PlyB) protein complex that binds to cholesterol/sphingomyelin-rich membrane domains. We evaluated the effects on viability of T24 invasive a...