The distribution of age-of-information performance measures for message processing systems

Queueing Systems - The idea behind the recently introduced “age-of-information” performance measure of a network message processing system is that it indicates our knowledge regarding...     

Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments

We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks.     

Monitoring Phase II Comparative Clinical Trials with Two Endpoints and Penalty for Adverse Events

Adverse events in Phase II comparative clinical trials have received limited attention in the literature. Bersimis et al. (Stat Med 34:197–214, 2014) in proposed a class of comparative sequential designs with bivariate endpoints, where as a special case, the termination of the clinical trial due to the occurrence of a severe adverse event is treated. In this paper, using the Markov chain embedding technique, we extend this class of designs proposing two new designs, which treat cases where the development of an adverse event does not immediately stop the clinical trial, but penalizes appropriately the treatment that caused it. In both designs the penalty can be chosen either by assessing the severity of the adverse event or by optimizing the power. The numerical results show an excellent performance, achieving small expected sample sizes in conjunction with large values for power, satisfying in this way the ethical requirement for small sample sizes and fast decisions in clinical practice. The formulation of the procedure as a stochastic process is elegantly accomplished while it offers the necessary mathematical framework for further generalizing the designs covering more cases such as group sequential designs, etc.     

A multilinear algebra proof of the Cauchy–Binet formula and a multilinear version of Parsevalʼs identity

We prove the Cauchy–Binet determinantal formula using multilinear algebra by first generalizing it to an identity not involving determinants. By extending the formula to abstract Hilbert spaces we obtain, as a corollary, a generalization of the classical Parseval identity.     

High‐Throughput Metabolomics by 1D NMR

Metabolomics deals with the whole ensemble of metabolites (the metabolome). As one of the ‐omic sciences, it relates to biology, physiology, pathology and medicine; but metabolites are chemical entities, small organic molecules or inorganic ions. Therefore, their proper identification and quantitation in complex biological matrices requires a solid chemical ground. With respect to for example, DNA, metabolites are much more prone to oxidation or enzymatic degradation: we can reconstruct large parts of a mammoth's genome from a small specimen, but we are unable to do the same with its metabolome, which was probably largely degraded a few hours after the animal's death. Thus, we need standard operating procedures, good chemical skills in sample preparation for storage and subsequent analysis, accurate analytical procedures, a broad knowledge of chemometrics and advanced statistical tools, and a good knowledge of at least one of the two metabolomic techniques, MS or NMR. All these skills are traditionally cultivated by chemists. Here we focus on metabolomics from the chemical standpoint and restrict ourselves to NMR. From the analytical point of view, NMR has pros and cons but does provide a peculiar holistic perspective that may speak for its future adoption as a population‐wide health screening technique.     

Divergences without probability vectors and their applications

In general, divergences and measures of information are defined for probability vectors. However, in some cases, divergences are ‘informally’ used to measure the discrepancy between vectors, which are not necessarily probability vectors. In this paper we examine whether divergences with nonprobability vectors in their arguments share the properties of probabilistic or information theoretic divergences. The results indicate that divergences with nonprobability vectors share, under some conditions, some of the properties of probabilistic or information theoretic divergences and therefore can be considered and used as information measures. We then use these divergences in the problem of actuarial graduation of mortality rates. Copyright © 2009 John Wiley & Sons, Ltd.     

Limiting Properties of Random Graph Models with Vertex and Edge Weights

This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-order asymptotics of heaviest paths allowing weights both on edges and vertices and assuming that weights on edges are signed. We aim at an exposition that summarizes, simplifies, and extends proof ideas. We also study sparse graph asymptotics, showing convergence of the weighted random graphs to a certain weighted graph that can be constructed in terms of Poisson processes. We are motivated by numerous applications, ranging from ecology to parallel computing models. It is the latter set of applications that necessitates the introduction of vertex weights. Finally, we discuss some open problems and research directions.