My project was in part to investigate the variance of playing the Shepp urn under the strategy which maximizes expected value. To this end after much experimentation I was able to conjecture and subsequently prove that if we play the Shepp urn with p postive balls and β(p) negative balls then the variance of our results grows at a rate of roughly √ p. I didn’t see as obvious of a pattern for ot...

We introduce a simple model which shows non-trivial self organized critical properties. The model describes a system of interacting units, modelled by Polya urns, subject to perturbations and which occasionally break down. Three equivalent formulations stochastic, quenched and deterministic are shown to reproduce the same dynamics. Among the novel features of the model are a non-homogeneous sta...

Imagine an urn with colored balls but with an unknown composition i.e. you do not know what are the specific colors in the urn nor their relative proportions. The urn could be composed by infinitely many colors and to learn about its composition you have been sampling balls with replacement from it. In this extended abstract we will construct exact confidence intervals for the proportion in the...

We consider a stochastic process in a modified Ehrenfest urn model. The modification prescribes there to be a minimum number of balls in each urn, and the process records the differences between treatment assignments under a sampling scheme implemented with this modified Ehrenfest urn model. In contrast to the result that the difference process forms a Markov chain and converges to a stationary...

Underwater radiated noise (URN) was previously primarily of interest in connection with the signature of naval vessels. Recently it has become increasingly relevant for other vessel types, such as cruise and merchant ships, due to a growing concern that marine life is affected by rising anthropogenic noise levels in the oceans. Shipping is a main contributor to those noise levels, with the cavi...

Performance analysis of an Asynchronous Transfer Mode (ATM) switch involves modeling the input traffic source, the switching mechanism, and the cell departure process. A main issue which determines the overall accuracy in performance evaluation of ATM switch, is the use of an appropriate probabilistic model to describe the cell departure process. Until now, little work has been done in the lite...

Urn models are very popular and useful for adaptive designs in clinical studies. Among various urn models, the drop-the-loser rule is an efficient adaptive treatment allocation scheme, recently proposed for comparing different treatments in clinical trials. This rule is superior to other randomization schemes in terms of variability and power. In this paper, the drop-the-loser rule is generaliz...

The aim of these lecture notes is a description of the statics and dynamics of zero-range processes and related models. After revisiting some conceptual aspects of the subject, emphasis is then put on the study of the class of zero-range processes for which a condensation transition arises. From urn models to zero-range processes: statics and dynamics 2 Introduction

Urn automata are a new class of automata consisting of an input tape, a finite-state controller, and an urn containing tokens with a finite set of colors, where the finite-state controller can sample and replace tokens in the urn but cannot control which tokens it receives. We consider the computational power of urn automata, showing that an urn automaton with O(f(n)) tokens can, with high prob...