Degrees and distances in random and evolving Apollonian networks

This paper studies Random and Evolving Apollonian networks (RANs and EANs), in d dimension for any d>=2, i.e. dynamically evolving random d dimensional simplices looked as graphs inside an initial d-dimensional simplex. We determine the limiting degree distribution in RANs and show that it follows a power law tail with exponent tau=(2d-1)/(d-1). We further show that the degree distribution in EANs converges to the same degree distribution if the simplex-occupation parameter in the n-th step of the dynamics is q_n->0 and sum_{n=0}^infty q_n =infty. This result gives a rigorous proof for the conjecture of Zhang et al. that EANs tend to show similar behavior as RANs once the occupation parameter q->0. We also determine the asymptotic behavior of shortest paths in RANs and EANs for arbitrary d dimensions. For RANs we show that the shortest path between two uniformly chosen vertices (typical distance), the flooding time of a uniformly picked vertex and the diameter of the graph after n steps all scale as constant times log n. We determine the constants for all three cases and prove a central limit theorem for the typical distances. We prove a similar CLT for typical distances in EANs

Miscommunication in the institutional context of the broadcast news interview : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Psychology at Massey University, Palmerston North, New Zealand

This study examined the pattern and relative success of linguistic interaction in the Broadcast News Interview (BNI). BNI is modelled as a genre of institutional communication. The psychological and functional characteristics of the BNI were examined from the viewpoint of how communicative conventions that normally regulate interview performance may, at times, impede effective communication. The BNI is intended to transfer information from an expert witness to an interested, though relatively uninformed audience. The interviewer is supposed to act as both conduit and catalyst. Pragmatic properties of the interlocutors' speech as they orient themselves towards the context of the conversation was analysed in order to reveal the manner in which prior assumptions or beliefs may lead to faulty inferences. The notion of miscommunication is used to describe and explain the faults associated with processes of representing the illocutionary force of an utterance, rather than deficiencies in pronunciation or auditory sensation and perception. Opting for a qualitative analysis, an attempt was made to ground explanations in relevant theoretical models of interpersonal communication and communication failure. Results indicate that the conventions that distinguish the BNI from more mundane types of interaction impede successful communication. The study highlights that participants who wish to attain their communicative goal must be more aware of the functional procedures of the BNI and anticipate impediments to successful communication

Markov chains, R\mathscr R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via M\"obius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.Comment: Dedicated to Stuart Margolis on the occasion of his sixtieth birthday; 71 pages; final version to appear in IJA

Reliable miniature spaceborne memory Interim engineering report, 19 Nov. 1964 - 26 Jul. 1965

Reliable miniature spaceborne memory system design, and testing of breadboard version of circuits and memory plan