Stan Zachary

Bio: Stan Zachary is an academic researcher from Heriot-Watt University. The author has contributed to research in topics: Random walk & Extreme value theory. The author has an hindex of 22, co-authored 83 publications receiving 1891 citations. Previous affiliations of Stan Zachary include University of Edinburgh.

Stochastic networks : theory and applications

Abstract: 1. Convergence to equilibria for fluid models of FIFO and processor sharing queueing networks 2. Optimal draining of fluid re-entrant lines: some solved examples 3. On the approximation of queueing networks in heavy traffic 4. The BIGSTEP approach to flow management in stochastic processing networks 5. Queue lengths and departures at single-server resources 6. Large deviations of stationary reflected Brownian motions 7. Limit theorems for workload input models 8. Notes on effective bandwidths 9. Traffic characterisation and effective bandwidths for broadband network traces 10. Nonparametric estimation for quantities of interest in queues 11. The asymptotic behaviour of large loss networks 12. Admission controls for loss networks with diverse routing 13. On load balancing in Erlang networks 14. Analysing system behaviour on different timescales 15. Optimal returns and suboptimality bounds for systems satisfying generalised conservation laws 16. Approximate solutions for open networks with breakdowns and repairs 17. Stationary ergodic Jackson networks: results and counter-examples 18. The Cesaro limit of departures from certain ./GI/1 queueing tandems 19. The Poisson-independence hypothesis for infintely-growing fully-connected packet-switching networks 20. A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks

Distributed admission control

Abstract: This paper describes a framework for admission control for a packet-based network where the decisions are taken by edge devices or end-systems, rather than resources within the network. The decisions are based on the results of probe packets that the end-systems send through the network, and require only that resources apply a mark to packets in a way that is load dependent. One application example is the Internet, where marking information is fed back via an ECN bit, and we show how this approach allows a rich QoS framework for flows or streams. Our approach allows networks to be explicitly analyzed, and consequently engineered.

Countable State Space Markov Random Fields and Markov Chains on Trees

Abstract: Let $S$ and $A$ be countable sets and let $\mathscr{G}(\Pi)$ be the set of Markov random fields on $S^A$ (with the $\sigma$-field generated by the finite cylinder sets) corresponding to a specification $\Pi$, Markov with respect to a tree-like neighbour relation in $A$. We define the class $\mathscr{M}(\Pi)$ of Markov chains in $\mathscr{G}(\Pi)$, and generalise results of Spitzer to show that every extreme point of $\mathscr{G}(\Pi)$ belongs to $\mathscr{M}(\Pi)$. We establish a one-to-one correspondence between $\mathscr{M}(\Pi)$ and a set of "entrance laws" associated with $\Pi$. These results are applied to homogeneous Markov specifications on regular infinite trees. In particular for the case $|S| = 2$ we obtain a quick derivation of Spitzer's necessary and sufficient condition for $|\mathscr{G}(\Pi)| = 1$, and further show that if $|\mathscr{M}(\Pi)| > 1$ then $|\mathscr{M}(\Pi)| = \infty$.

The maximum on a random time interval of a random walk with long-tailed increments and negative drift

Abstract: We study the asymptotics for the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift. We extend to a general stopping time a result by Asmussen, simplify its proof and give some converses.

Point process limits of lattice processes

Abstract: Starting from a suitable sequence of auto-Poisson lattice schemes, it is shown that (almost) any purely inhibitory pairwise-interaction point process can be obtained in the limit. Further pairwise-interaction processes are obtained as limits of sequences of auto-logistic lattice schemes. SPATIAL POINT PROCESS; AUTO-POISSON SCHEME; AUTO-LOGISTIC SCHEME; STRAUSS PROCESS; PAIRWISE-INTERACTION PROCESS: INHIBITORY POINT PROCESS; HARDCORE POINT PROCESS

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Applied Probability and Queues

Abstract: (1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.

Determinantal point processes for machine learning

Abstract: Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and hard to approximate in the presence of negative correlations, DPPs offer efficient and exact algorithms for sampling, marginalization, conditioning, and other inference tasks. We provide a gentle introduction to DPPs, focusing on the intuitions, algorithms, and extensions that are most relevant to the machine learning community, and show how DPPs can be applied to real-world applications like finding diverse sets of high-quality search results, building informative summaries by selecting diverse sentences from documents, modeling non-overlapping human poses in images or video, and automatically building timelines of important news stories.