This paper summarizes recent work on the theory of epsilon entropy for probability distributions on complete separable metric spaces. The theory was conceived [3] in order to have a framework for discussing the quality of data storage and transmission systems. The concept of data source was defined in [4] as a probabilistic metric space: a complete separable metric space together with a probabi...

We propose two generalizations of the Banzhaf value for partition function form games. In both cases our approach is based on probability distributions over the set of coalition structures that may arise for any given set of players. First, we introduce a family of values, one for each collection of these latter probability distributions, defined as the Banzhaf value of a coalitional game obtai...

OF THE DISSERTATION Service Outage Based Adaptive Transmission in Fading Channels by Jianghong Luo Dissertation Director: Prof. Roy Yates, Prof. Predrag Spasojević The service outage based allocation problem explores variable rate transmission schemes and combines the concepts of ergodic capacity and outage capacity for fading channels. The ergodic capacity determines the maximum achievable rat...

We propose a random partition distribution indexed by pairwise similarity information such that partitions compatible with the similarities are given more probability. The use of pairwise similarities, in the form of distances, is common in some clustering algorithms (e.g., hierarchical clustering), but we show how to use this type of information to define a prior partition distribution for fle...

We present exact calculations of the Potts model partition function Z(G, q, v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of transverse widths equal to L vertices and for arbitrarily great length equal to m vertices, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These parti...

A partition {Ci}i∈I of a Boolean algebra S in a probability measure space (S, p) is called a Reichenbachian common cause system for the correlated pair A, B of events in S if any two elements in the partition behave like a Reichenbachian common cause and its complement, the cardinality of the index set I is called the size of the common cause system. It is shown that given any correlation in (S...

The notion of noncrossing linked partition arose from the study of certain transforms in free probability theory. It is known that the number of noncrossing linked partitions of [n+1] is equal to the n-th large Schröder number rn, which counts the number of Schröder paths. In this paper we give a bijective proof of this result. Then we introduce the structures of linked partitions and linked cy...

In the planted partition problem, the n vertices of a random graph are partitioned into k “clusters,” and edges between vertices in the same cluster and different clusters are included with constant probability p and q, respectively (where 0 ≤ q < p ≤ 1). We give an efficient spectral algorithm that recovers the clusters with high probability, provided that the sizes of any two clusters are eit...

In the Crawford–Sobel (uniform, quadratic utility) cheap-talk model, we consider a simple mediation scheme (a communication device) in which informed agent reports one of N possible elements partition to mediator and then suggests actions uninformed decision-maker according probability distribution device. We show that no such mediated equilibrium can improve upon unmediated N-partition when pr...