Rare-event analysis of mixed Poisson random variables, and applications in staffing

A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this paper we consider a mixed Poisson arrival process with arrival rates that are resampled every $N^{a}$ time units, where $a> 0$ and $N$ a scaling parameter. In the first part of the paper we analyse the asymptotic tail distribution of this doubly stochastic arrival process. That is, for large $N$ and i.i.d. arrival rates $X_1, \dots, X_N$, we focus on the evaluation of $P_N(A)$, the probability that the scaled number of arrivals exceeds $NA$. Relying on elementary techniques, we derive the exact asymptotics of $P_N(A)$: For $a 3$ we identify (in closed-form) a function $\tilde{P}_N(A)$ such that $P_N(A) / P_N(A)$ tends to $1$ as $N \to \infty$. For $a \in [\frac{1}{3},\frac{1}{2})$ and $a\in [2, 3)$ we find a partial solution in terms of an asymptotic lower bound. For the special case that the $X_i$s are gamma distributed, we establish the exact asymptotics across all $a> 0$. In addition, we set up an asymptotically efficient importance sampling procedure that produces reliable estimates at low computational cost. The second part of the paper considers an infinite-server queue assumed to be fed by such a mixed Poisson arrival process. Applying a scaling similar to the one in the definition of $P_N(A)$, we focus on the asymptotics of the probability that the number of clients in the system exceeds $NA$. The resulting approximations can be useful in the context of staffing. Our numerical experiments show that, astoundingly, the required staffing level can actually decrease when service times are more variable

A method to deconvolve stellar rotational velocities

Rotational speed is an important physical parameter of stars and knowing the distribution of stellar rotational velocities is essential for the understanding stellar evolution. However, it cannot be measured directly but the convolution of the rotational speed and the sine of the inclination angle, $v \sin i$. We developed a method to deconvolve this inverse problem and obtain the cumulative distribution function (CDF) for stellar rotational velocities extending the work of Chandrasekhar & M\"unch (1950). This method is applied a) to theoretical synthetic data recovering the original velocity distribution with very small error; b) to a sample of about 12.000 field main--sequence stars, corroborating that the velocity distribution function is non--Maxwellian, but is better described by distributions based on the concept of maximum entropy, such as Tsallis or Kaniadakis distribution functions. This is a very robust and novel method that deconvolve the rotational velocity cumulative distribution function from a sample of $v \sin i$ data in just one single step without needing any convergence criteria.Comment: Accepted in A&

Recent Advances in Medicago truncatula Genomics

Legume rotation has allowed a consistent increase in crop yield and consequently in human population since the antiquity. Legumes will also be instrumental in our ability to maintain the sustainability of our agriculture while facing the challenges of increasing food and biofuel demand. Medicago truncatula and Lotus japonicus have emerged during the last decade as two major model systems for legume biology. Initially developed to dissect plant-microbe symbiotic interactions and especially legume nodulation, these two models are now widely used in a variety of biological fields from plant physiology and development to population genetics and structural genomics. This review highlights the genetic and genomic tools available to the M. truncatula community. Comparative genomic approaches to transfer biological information between model systems and legume crops are also discussed

Recent Advances in \u3cem\u3eMedicago truncatula\u3c/em\u3e Genomics

Legume rotation has allowed a consistent increase in crop yield and consequently in human population since the antiquity. Legumes will also be instrumental in our ability to maintain the sustainability of our agriculture while facing the challenges of increasing food and biofuel demand. Medicago truncatula and Lotus japonicus have emerged during the last decade as two major model systems for legume biology. Initially developed to dissect plant-microbe symbiotic interactions and especially legume nodulation, these two models are now widely used in a variety of biological fields from plant physiology and development to population genetics and structural genomics. This review highlights the genetic and genomic tools available to the M. truncatula community. Comparative genomic approaches to transfer biological information between model systems and legume crops are also discussed

Adult age differences in prospective memory in the laboratory : Are they related to higher stress levels in the elderly?

Peer reviewedPublisher PD

Junctional adhesion molecule (JAM)-C deficient C57BL/6 mice develop a severe hydrocephalus

The junctional adhesion molecule (JAM)-C is a widely expressed adhesion molecule regulating cell adhesion, cell polarity and inflammation. JAM-C expression and function in the central nervous system (CNS) has been poorly characterized to date. Here we show that JAM-C−/− mice backcrossed onto the C57BL/6 genetic background developed a severe hydrocephalus. An in depth immunohistochemical study revealed specific immunostaining for JAM-C in vascular endothelial cells in the CNS parenchyma, the meninges and in the choroid plexus of healthy C57BL/6 mice. Additional JAM-C immunostaining was detected on ependymal cells lining the ventricles and on choroid plexus epithelial cells. Despite the presence of hemorrhages in the brains of JAM-C−/− mice, our study demonstrates that development of the hydrocephalus was not due to a vascular function of JAM-C as endothelial re-expression of JAM-C failed to rescue the hydrocephalus phenotype of JAM-C−/− C57BL/6 mice. Evaluation of cerebrospinal fluid (CSF) circulation within the ventricular system of JAM-C−/− mice excluded occlusion of the cerebral aqueduct as the cause of hydrocephalus development but showed the acquisition of a block or reduction of CSF drainage from the lateral to the 3rd ventricle in JAM-C−/− C57BL/6 mice. Taken together, our study suggests that JAM-C−/− C57BL/6 mice model the important role for JAM-C in brain development and CSF homeostasis as recently observed in humans with a loss-of-function mutation in JAM-C