We show that Cohen’s Kappa and Matthews Correlation Coefficient (MCC), both extended and contrasted measures of performance in multi-class classification, are correlated in most situations, albeit can differ in others. Indeed, although in the symmetric case both match, we consider different unbalanced situations in which Kappa exhibits an undesired behaviour, i.e. a worse classifier gets higher Kappa score, differing qualitatively from that of MCC. The debate about the incoherence in the behaviour of Kappa revolves around the convenience, or not, of using a relative metric, which makes the interpretation of its values difficult. We extend these concerns by showing that its pitfalls can go even further. Through experimentation, we present a novel approach to this topic. We carry on a comprehensive study that identifies an scenario in which the contradictory behaviour among MCC and Kappa emerges. Specifically, we find out that when there is a decrease to zero of the entropy of the elements out of the diagonal of the confusion matrix associated to a classifier, the discrepancy between Kappa and MCC rise, pointing to an anomalous performance of the former. We believe that this finding disables Kappa to be used in general as a performance measure to compare classifiers.

We consider a family of non-deterministic fluid models that can be approximated under heavy traffic conditions by a multidimensional reflected fractional Brownian motion (rfBm). Specifically, we prove a heavy traffic limit theorem for multi-station fluid models with feedback and non-deterministic arrival process generated by a large enough number of heavy tailed ON/OFF sources, say N . Scaling in time by a factor r and in state space conveniently, and letting N and r approach infinity (in this order) we prove that the scaled immediate workload process converges in some sense to a rfBm.

We prove that, under rather general conditions, the law of a continuous Gaussian process represented by a stochastic integral of a deterministic kernel, with respect to a standard Wiener process, can be weakly approximated by the law of some processes constructed from a standard Poisson process. An example of a Gaussian process to which this result applies is the fractional Brownian motion with any Hurst parameter.

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Airborne pollen records are a suitable indicator for the study of climate change. The present work focuses on the role of annual pollen indices for the detection of bioclimatic trends through the analysis of the aerobiological spectra of 11 taxa of great biogeographical relevance in Catalonia over an 18-year period (1994-2011), by means of different parametric and non-parametric statistical methods. Among others, two non-parametric rank-based statistical tests were performed for detecting monotonic trends in time series data of the selected airborne pollen types and we have observed that they have similar power in detecting trends. Except for those cases in which the pollen data can be well-modeled by a normal distribution, it is better to apply non-parametric statistical methods to aerobiological studies. Our results provide a reliable representation of the pollen trends in the region and suggest that greater pollen quantities are being liberated to the atmosphere in the last years, specially by Mediterranean taxa such as Pinus, Total Quercus and Evergreen Quercus, although the trends may differ geographically. Longer aerobiological monitoring periods are required to corroborate these results and survey the increasing levels of certain pollen types that could exert an impact in terms of public health.

We consider a class of fluid queueing networks with multiple fluid classes and feedback allowed, which are fed by N heavy tailed ON/OFF sources. We study the asymptotic behavior when N → ∞ of these queueing systems in a heavy traffic regime (that is, when they are asymptotically critical). As performance processes we consider the workload W N (the amount of time needed for each server to complete processing of all the fluid in queue), and the fluid queue Z N (the quantity of each fluid class in the system). We show the convergence of √ NW N and √ NZ N (toŴ andẐ) in heavy traffic if state space collapse (SSC) holds. (SSC) is a condition that establishes a relationship between those components ofẐ that correspond to fluid classes processed by the same server, which implies thatẐ = Ŵ for a deterministic lifting matrix . Our main contribution is to prove that assuming that the other hypotheses are true, (SSC) is not only sufficient for this convergence, but necessary. Furthermore, we prove that processesŴ andẐ, conveniently scaled in time, converge to W (a reflected fractional Brownian motion) and Z (= W ). We illustrate the application of our results with some examples including a tandem queue.