Steady State Analysis and Heavy Traffic Limits for Regulated Markov Chains.

Consider a continuous time finite state irreducible Markov chain whose jump transitions are partitioned into one group that is regulated and the other group that is not. The regulated transitions are only allowed to occur if there is a token available. We collect the tokens in a buer and allow a regulated transition to occur simultaneously with the removal of a token from the buffer. New tokens are added to the buer at a constant Poisson rate but the regulated transitions will be blocked if they occur too quickly. We will apply matrix analysis to the joint distribution for the state of the Markov chain and the number of tokens in the buffer. We will give a simple stability condition for the joint process and show that its steady state distribution will have a matrix geometric distribution. Moreover, we obtain from our analysis a heavy traffic limit for this joint steady state distribution which has a product form structure. This Markov chain model and steady state analysis generalizes the work of many earlier papers on specific queueing systems such as Konheim and Reiser or Latouche and Neuts, but most significantly the work of Kogan and Puhalskii.Markov Chains, Matrix-Geometric Solution, Heavy-Traffic Limits, Product Form Solution, Tensor and Kronecker Products.

Determining the exit time distribution for a closed cyclic network

AbstractConsider a closed, N-node, cyclic network, where each node has an independent, exponential single server. Using lattice-Bessel functions, we can explicitly solve for the transition probabilities of events that occur prior to one of the nodes becoming empty. This calculation entails associating with this absorbing process a symmetry group that is the semidirect product of simpler groups. As a byproduct, we are able to compute explicitly the entire spectrum for the finite-dimensional matrix generator of this process. When the number of nodes exceeds 1, such a spectrum is no longer purely real. Moreover, we are also able to obtain the quasistationary distribution or the limiting behavior of the network conditioned on no node ever being idle

Determination of left ventricular volumes with use of a new nongeometric echocardiographic method: Clinical validation and potential application

AbstractA new nongeometric echocardiographic technique for measurement of right and left ventricular volumes was recently validated in vitro. With this method, all images are taken from one point on the chest wall as the transducer is tilted through the ventricle. This approach offers several advantages. No geometric assumptions about ventricular shape are made. All images are acquired from the best echocardiographic window. Furthermore, the digitized points can be used to make a three-dimensional reconstruction of the ventricle.The present study addresses the clinical feasibility of imaging the heart from a single pivoting point in short axis and compares the accuracy of the method in determining left ventricular volumes with that of biplane cineangiography. Twenty-four patients underwent echocardiographic studies within 2 h before angiography. At catheterization, volumes determined by the biplane area-length method ranged between 95 and 368 ml at end-diastole and between 15 and 303 ml at end-systole. A good correlation was observed between ventricular volumes by angiography and echocardiography at end-diastole and end-systole (r = 0.92 and 0.96, respectively). Correlations between volumes by the two techniques were equally good in patients with wall motion abnormalities (n = 13; r = 0.97). Ventricular ejection fraction ranged between 18% and 84% at angiography and correlated well with echocardiographic measurements (r = 0.82).Thus, the echocardiographic tilt method provides accurate determination of left ventricular volume and ejection fraction. This nongeometric method offers the potential for the determination of right ventricular volume and three-dimensional display of the heart

Economic Feasibility of Impermeable Lagoon Covers

Environmental Economics and Policy,

A transient analysis of the two-node series Jackson network

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Inbreeding : its meaning, uses and effects on farm animals (1993)

Technically, inbreeding is defined as the mating of animals more closely related than the average relationship within the breed or population concerned. Matings between animals less closely related than this, then, would constitute outbreeding. These two systems of mating are described in this publication

Determining the exit time distribution for a closed cyclic network

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Controlling Chaos through Compactification in Cosmological Models with a Collapsing Phase

We consider the effect of compactification of extra dimensions on the onset of classical chaotic "Mixmaster" behavior during cosmic contraction. Assuming a universe that is well-approximated as a four-dimensional Friedmann-Robertson--Walker model (with negligible Kaluza-Klein excitations) when the contraction phase begins, we identify compactifications that allow a smooth contraction and delay the onset of chaos until arbitrarily close the big crunch. These compactifications are defined by the de Rham cohomology (Betti numbers) and Killing vectors of the compactification manifold. We find compactifications that control chaos in vacuum Einstein gravity, as well as in string theories with N = 1 supersymmetry and M-theory. In models where chaos is controlled in this way, the universe can remain homogeneous and flat until it enters the quantum gravity regime. At this point, the classical equations leading to chaotic behavior can no longer be trusted, and quantum effects may allow a smooth approach to the big crunch and transition into a subsequent expanding phase. Our results may be useful for constructing cosmological models with contracting phases, such as the ekpyrotic/cyclic and pre-big bang models.Comment: 1 figure. v2/v3: minor typos correcte