We consider a general QBD process as defining a FIFO queue and obtain the stationary distribution of the sojourn time of a customer in that queue as a matrix exponential distribution, which is identical to a phase-type distribution under a certain condition. Since QBD processes include many queueing models where the arrival and service process are dependent, these results form a substantial gen...

Using spin hyperpolarized xenon ((129)Xe) we investigate the impact of the local molecular environment on reversible host-guest interactions. We label Xe guest atoms that are temporarily bound to cryptophane-A hosts using the Hyper-CEST technique. By varying the length of the saturation pulse and utilizing an inverse Laplace transform we can determine depolarization times for the noble gas in d...

In this note, two characterizations of the exponential distribution are established. Theorem 1: Let a > -1, a ~ O. A positive random variable X has an exponential distribution if and only if E[CX-y)aI X > y] is a finite constant for all y ~ O. Theorem 2: Let Xl ,X2, ..• ,Xn be i.i.d. random variables having a continuous distribution FCx), and XCl)'XC2)' ... 'XCn) their order statistics. Let a >...

Goodness of fit of the distribution function governing the time to occurrence of a recurrent event is considered. We develop a chi-squared type of test (henceforward called R test) based on a nonparametric maximum likelihood estimator (NPMLE) of the inter-event time distribution for recurrent events. The test compares a parametric null to the NPMLE over k partitions of a calendar time over the ...

We study the geodesic exponential maps corresponding to Sobolev type right-invariant (weak) Riemannian metrics μ (k ≥ 0) on the Virasoro group and show that for k ≥ 2, but not for k = 0, 1, each of them defines a smooth Fréchet chart of the identity. For k = 0 and k = 1 the corresponding geodesic flows are related to the Korteweg de Vries and Camassa Holm equations. In particular, the geodesic ...

Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed λ-calculus and the modal μ-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of programs that are not expressible in the modal μ-calculus. This paper provides complexity results for its model checking problem. In particular, we consider those fragme...

The minimum k-assignment of an m×n matrix X is the minimum sum of k entries of X, no two of which belong to the same row or column. If X is generated by choosing each entry independently from the exponential distribution with mean 1, then Coppersmith and Sorkin conjectured that the expected value of its minimum k-assignment is