REVSTAT 

Abstract: • Network motifs are at the core of modern studies on biological networks, trying to encompass global features such as small-world or scale-free properties Detection of significant motifs may be based on two different approaches: either a comparison with randomized networks (requiring the simulation of a large number of networks), or the comparison with expected quantities in some well-chosen probabilistic model This second approach has been investigated here We first provide a simple and efficient probabilistic model for the distribution of the edges in undirected networks Then,we give exact formulas for the expectation and the variance of the number of occurrences of a motif Generalization to directed networks is discussed in the conclusion

Abstract: • The estimation of the extreme-value index γ based on a sample of independent and identically distributed random variables has received considerable attention in the extreme-value literature. However, the problem of combiningdata from several groups is hardly studied. In this paper we discuss the simultaneous estimation of tail indices when data on several independent data groups are available. The proposed methods are based on regression models linking tail related statistics to the extreme-value index and parameters describingthe second order tail behaviour. For heavy-tailed distributions ( γ> 0), estimators are derived from an exponential regression model for rescaled log-spacings of successive order statistics as described in Beirlant et al. (1999) and Feuerverger and Hall (1999). Estimators for γ ∈ R are obtained usingthe linear model for UH -statistics given in Beirlant et al. (2000). In both cases, the optimal number of extremes to be used in the estimation is derived from the asymptotic mean squared error matrix.

Abstract: • In this paper the properties of the modified EWMA control chart for detecting changes in the mean of an ARFIMA process are discussed. The central question is related to the false alarm probability and its behavior for different autocorrelation structures and parameters of the underlying process. It is shown under which conditions the false alarm probability of an ARFIMA(p,d,q) process is larger than that of the pure ARFIMA(0,d,0) process. Furthermore, it is shown that the false alarm probability for ARFIMA(0,d,0) and ARFIMA(1,d,1) is monotonic in d for common parameter values of the processes. Key-Words: • Statistical process control, EWMA control chart, long-memory process, ARFIMA process. AMS Subject Classification: • 62L10, 62M10. 2 Yarema Okhrin and Wolfgang Schmid EWMA Chart for Long-Memory Processes 3

Abstract: The authors acknowledge Foundation FCT (Fundacao para a Ciencia e Tecnologia) for funding through Individual Scholarship PhD PD/BD/105743/2014, Centre of Mathematics of Minho University and Center for Research & Development in Mathematics and Applications of Aveiro University within project UID/MAT/04106/2019.