8,162 research outputs found
Stationary probability of the identity for the TASEP on a ring
Consider the following Markov chain on permutations of length . At each
time step we choose a random position. If the letter at that position is
smaller than the letter immediately to the left (cyclically) then these letters
swap positions. Otherwise nothing happens, corresponding to a loop in the
Markov chain. This is the circular TASEP. We compute the average proportion of
time the chain spends at the identity permutation (and, in greater generality,
at sorted words). This answers a conjecture by Thomas Lam.Comment: 6 page
The effect of screening on treatment cost: The case of colorectal cancer
This paper presents a medical cost function developed for a screening programme. The medical cost function is a function of advancement both directly and indirectly through survival. We discuss how the medical cost function is affected by screening through a shift in the distribution of cancers according to advancement. We show that screening reduces the treatment cost for cancers diagnosed at the screening, even though the medical cost function not unambiguously increases with stage of advancement. This is the first step in a cost-effectiveness analysis, and even though the results are favourable to the introduction of screening for colorectal cancer as a preventive health measure, total screening costs and health benefits must be evaluated to arrive at a recommendation.treatment cost; stage of advancement; screening; probabilistic sensitivity analysis; bootstrap method
Pecuniary compensation increases the participation rate in screening for colorectal cancer
Typically, the participation rate is below 100 per cent. In this paper pecuniary compensation is used to increase the participation rate. In a postal questionnaire to 5,000 people invited to screening for colorectal cancer, those not participating were asked "would you participate if you were given NOK X in compensation?" The results show that compensation increases participation and that the participation probability systematically varies with travel expenses, income, age, county, native country, marital status, use of health care services, genetic predisposition, expected benefit from the screening, subjective health status, and education. The estimated costs per additional screening are increasingparticipation; willingness-to pay; compensation; costs; binary probit
A product formula for the TASEP on a ring
For a random permutation sampled from the stationary distribution of the
TASEP on a ring, we show that, conditioned on the event that the first entries
are strictly larger than the last entries, the order of the first entries is
independent of the order of the last entries. The proof uses multi-line queues
as defined by Ferrari and Martin, and the theorem has an enumerative
combinatorial interpretation in that setting.
Finally, we present a conjecture for the case where the small and large
entries are not separated.Comment: 13 page
Optical bistability in one dimensional doped photonic crystals with spontaneously generated coherence
We investigate optical bistability in a multilayer one-dimensional photonic
crystal where the central layer is doped with -type three level atoms.
We take into account the influence of spontaneously generated coherence when
the lower atomic levels are sufficiently close to each other, in which case
Kerr-type nonlinear response of the atoms is enhanced. We calculate the
propagation of a probe beam in the defect mode window using numerical nonlinear
transfer matrix method. We find that Rabi frequency of a control field acting
on the defect layer and the detuning of the probe field from the atomic
resonance can be used to control the size and contrast of the hysteresis loop
and the threshold of the optical bistability. In particular we find that, at
the optimal spontaneously generated coherence, three orders of magnitude lower
threshold can be achieved relative to the case without the coherence.Comment: 9 pages, 7 figure
Multivariate Estimation of Poisson Parameters
This paper is devoted to the multivariate estimation of a vector of Poisson
means. A novel loss function that penalises bad estimates of each of the
parameters and the sum (or equivalently the mean) of the parameters is
introduced. Under this loss function, a class of minimax estimators that
uniformly dominate the maximum likelihood estimator is derived. Crucially,
these methods have the property that for estimating a given component
parameter, the full data vector is utilised. Estimators in this class can be
fine-tuned to limit shrinkage away from the maximum likelihood estimator,
thereby avoiding implausible estimates of the sum of the parameters. Further
light is shed on this new class of estimators by showing that it can be derived
by Bayesian and empirical Bayesian methods. In particular, we exhibit a
generalisation of the Clevenson-Zidek estimator, and prove its admissibility.
Moreover, a class of prior distributions for which the Bayes estimators
uniformly dominate the maximum likelihood estimator under the new loss function
is derived. A section is included involving weighted loss functions, notably
also leading to a procedure improving uniformly on the maximum likelihood
method in an infinite-dimensional setup. Importantly, some of our methods lead
to constructions of new multivariate models for both rate parameters and count
observations. Finally, estimators that shrink the usual estimators towards a
data based point in the parameter space are derived and compared
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