Normed-convergence theory for supercritical branching processes

AbstractA proof is given of the basic normed-convergence theorem for the ordinary supercritical Bienaymé-Galton-Watson process with finite mean. Part of it is adapted to obtain an analogous result for inhomogeneous supercritical processes (i.e. branching processes in varying environment). This is used in part to give a detailed discussion on the normed- convergence behaviour of the ordinary process in the ‘explosive’ case (i.e with infinite mean); and rather pathological limit behaviour is found to obtain

Approaching the Ground State of a Quantum Spin Glass using a Zero-Temperature Quantum Monte Carlo

Here we discuss the annealing behavior of an infinite-range $\pm J$ Ising spin glass in presence of a transverse field using a zero-temperature quantum Monte Carlo. Within the simulation scheme, we demonstrate that quantum annealing not only helps finding the ground state of a classical spin glass, but can also help simulating the ground state of a quantum spin glass, in particularly, when the transverse field is low, much more efficiently.Comment: 8 pages, 6 fig

Transient behaviour in finite absorbing Markov chains

Thesis (M.Sc.) -- University of Adelaide, Dept. of Mathematics, 196

A note on models using the branching process with immigration stopped at zero

Abstract The Galton-Watson process with immigration which is time-homogeneous but not permitted when the process is in state 0 (so that this state is absorbing) is briefly studied in the subcritical and supercritical cases. Results analogous to those for the ordinary Galton-Watson process are found to hold. Partly-new techniques are required, although known end-results on the standard process with and without immigration are used also. In the subcritical case a new parameter is found to be relevant, replacing to some extent the criticality parameter

Random Surfing Without Teleportation

In the standard Random Surfer Model, the teleportation matrix is necessary to ensure that the final PageRank vector is well-defined. The introduction of this matrix, however, results in serious problems and imposes fundamental limitations to the quality of the ranking vectors. In this work, building on the recently proposed NCDawareRank framework, we exploit the decomposition of the underlying space into blocks, and we derive easy to check necessary and sufficient conditions for random surfing without teleportation.Comment: 13 pages. Published in the Volume: "Algorithms, Probability, Networks and Games, Springer-Verlag, 2015". (The updated version corrects small typos/errors

Annotation of genomics data using bidirectional hidden Markov models unveils variations in Pol II transcription cycle

DNA replication, transcription and repair involve the recruitment of protein complexes that change their composition as they progress along the genome in a directed or strand-specific manner. Chromatin immunoprecipitation in conjunction with hidden Markov models (HMMs) has been instrumental in understanding these processes, as they segment the genome into discrete states that can be related to DNA-associated protein complexes. However, current HMM-based approaches are not able to assign forward or reverse direction to states or properly integrate strand-specific (e.g.,RNA expression) with non-strand-specific (e.g.,ChIP) data, which is indispensable to accurately characterize directed processes. To overcome these limitations, we introduce bidirectional HMMs which infer directed genomic states from occupancy profiles de novo. Application to RNA polymerase II-associated factors in yeast and chromatin modifications in human T cells recovers the majority of transcribed loci, reveals gene-specific variations in the yeast transcription cycle and indicates the existence of directed chromatin state patterns at transcribed, but not at repressed, regions in the human genome. In yeast, we identify 32 new transcribed loci, a regulated initiation-elongation transition, the absence of elongation factors Ctk1 and Paf1 from a class of genes, a distinct transcription mechanism for highly expressed genes and novel DNA sequence motifs associated with transcription termination. We anticipate bidirectional HMMs to significantly improve the analyses of genome-associated directed processes