[Tip: Study the MC, QT, and Little's law lectures together: CTMC (MC lecture), M/M/1 queue (QT lecture), Little's law lecture (when deriving the mean response time from mean number of customers), DTMC (MC lecture), M/M/1 queue derivation using DTMC analysis, derive distribution of response time in M/M/1 queue (QT lecture), relation between Markov property and mem-oryless property (MC lecture), ...

Adaptive chains are chains that are able to learn from all previous elements in the chain. It is an extension of Markov chains. It is proved convergence of adaptive chains that satisses a strong Doeblin condition (i.e., the transition density r from x i to y satisses r(y; x 1 ; x 2 ; : : : ; x i) a i (y) for all x 1 ; : : : ; x i ; y in the state space.) By using the previous iterations of the ...

NANNY WERMUTH , D.R . COX and GIOVANNI M. MARCHETTI 3 Mathematical Statistics, Chalmers/Gothenburg University, Chalmers tvärgata 3, 41296 Göteborg, Sweden. E-mail: [email protected] Nuffield College, Oxford OX1 1NF, UK. E-mail: [email protected] Dipartimento di Statistica, Università degli Studi di Firenze ‘Giuseppe Parenti’, Viale Morgagni 59, Italy. E-mail: Giovanni.marchetti@u...

purification of drinking and industrial water required usage of high molecular weight polymer to cause flocculation process of dispersed suspension of contaminants. polyelectrolytes, including ionic polyacrylamide are especially appropriate for these purposes, because in this case the suspension stability can be controlled by both steric and electrostatic forces. thus the influence of solution ...

We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...

Granular chains are made of hollow steel balls connected by thin metal rods. They can be purchased at your neighborhood hardware store. Add a shaker and a little bit of imagination and you have a rich laboratory for polymer physics [1], nonequilibrium statistical mechanics [2], nonlinear dynamics [3, 4], and biological physics [5]. The attached video and the brief summaries below highlight a se...

We address the problem of very efficient reasoning and update in ≤, <-chains, where a ≤, <-chain is a directed acyclic graph such that there is a directed path between every pair of vertices, and edges are consistently labelled by ≤ or <. It is easy to show that, subsequent to an O(n) labelling scheme, queries concerning implied ≤ and < relations can be answered in O(1) time. However this schem...

Even since pioneering work of Levine and Athans and Melzer and Kuo, control of vehicular formations has been a topic of active research. In spite of its apparent simplicity, this problem poses significant engineering challenges, and it has often inspired theoretical developments. In this article, we view vehicular formations as a particular instance of dynamical systems over networks and summar...

More advanced technologies demand higher degrees of specialization – and longer chains of production connecting raw inputs to final outputs. Longer production chains are subject to a “weakest link” effect: they are more fragile and more prone to failure. Optimal chain length is determined by the trade-off between the gains to specialization and the higher failure rate associated with longer cha...

This paper describes the challenges of maritime supply chain compared to land transport and discusses new digital initiatives simplify processes enable a better plan for entire chain. First, background is outlined with an example extensive admin in road transport, followed by case presenting booking. The study concludes that lack integration costly terms both resources, as well lost capacity on...