On extremal index of max-stable processes

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Gaussian approximation of perturbed chi-square risks

In this paper we show that the conditional distribution of perturbed chi-square risks can be approximated by certain distributions including the Gaussian distributions. Our results are of interest for conditional extreme value models and multivariate extremes as shown in three applications

Generalized Pickands constants and stationary max-stable processes

Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of expectations involving fractional Brownian motions and, as such, their exact value is often unknown. Recently, Dieker and Yakir (Bernoulli, 20(3), 1600–1619, 2014) derived a novel representation of Pickands constant as a simple expected value that does not involve a limit operation. In this paper we show that the notion of Pickands constants and their corresponding Dieker–Yakir representations can be extended to a large class of stochastic processes, including general Gaussian and Lévy processes. We furthermore develop a link to extreme value theory and show that Pickands-type constants coincide with certain constants arising in the study of max-stable processes with mixed moving maxima representations

Extremes of homogeneous Gaussian random fields

Let {X (s, t): s, t >= 0} be a centred homogeneous Gaussian field with almost surely continuous sample paths and correlation function r (s, t) = cov(X(s, t), X(0, 0)) such that r(s, t) = 1 - vertical bar s vertical bar(alpha 1) - vertical bar t vertical bar(alpha 2) + o(vertical bar s vertical bar(alpha 1) + vertical bar t vertical bar(alpha 2)), s,t -> 0, with alpha 1, alpha 2 is an element of(0,2], and r (s, t) < 1 for (s, t) not equal (0, 0). In this contribution we derive an asymptotic expansion (as u -> infinity) of P(sup((sn1(u),tn2(u))is an element of[0,x]x[0,y]) X(s,t) <= u), where n(1)(u)n(2)(u) = u(2/alpha 1+2/alpha 2) Psi(u), which holds uniformly for (x, y) is an element of [A, B](2) with A, B two positive constants and Psi the survival function of an N(0, 1) random variable. We apply our findings to the analysis of extremes of homogeneous Gaussian fields over more complex parameter sets and a ball of random radius. Additionally, we determine the extremal index of the discretised random field determined by X (s, t)

Finite-time ruin probability of aggregate Gaussian processes

Let (Sigma(n)(i)=1 lambda X-i(i)(t) - g(t), t is an element of [0, T]} be an aggregate Gaussian risk process with a trend g(t). We derive exact asymptotics of the finite-time ruin probability given by P((sup)(t is an element of[0,T]) (Sigma(i=1) lambda X-i(i)(t) - g(t)) > u) as u -> infinity for {X-i(t), t is an element of [0,T]}, i <= n, satisfying some asymptotic conditions. Further, we derive asymptotic results for the finite-time ruin probabilities of risk processes perturbed by an aggregate Gaussian process

Comparison inequalities for order statistics of Gaussian arrays

Normal comparison lemma and Slepian’s inequality are essential tools for the analysis of extremes of Gaussian processes. In this paper we show that the Normal comparison lemma for Gaussian vectors can be extended to order statistics of Gaussian arrays. Our applications include the derivation of mixed Gumbel limit laws for the order statistics of stationary Gaussian processes and the investigation of lower tail behavior of order statistics of self-similar Gaussian processes

Re-identification of individuals from images using spot constellations : a case study in Arctic charr (Salvelinus alpinus)

The long-term monitoring of Arctic charr in lava caves is funded by the Icelandic Research Fund, RANNÍS (research grant nos. 120227 and 162893). E.A.M. was supported by the Icelandic Research Fund, RANNÍS (grant no. 162893) and NERC research grant awarded to M.B.M. (grant no. NE/R011109/1). M.B.M. was supported by a University Research Fellowship from the Royal Society (London). C.A.L. and B.K.K. were supported by Hólar University, Iceland. The Titan Xp GPU used for this research was donated to K.T. by the NVIDIA Corporation.The ability to re-identify individuals is fundamental to the individual-based studies that are required to estimate many important ecological and evolutionary parameters in wild populations. Traditional methods of marking individuals and tracking them through time can be invasive and imperfect, which can affect these estimates and create uncertainties for population management. Here we present a photographic re-identification method that uses spot constellations in images to match specimens through time. Photographs of Arctic charr (Salvelinus alpinus) were used as a case study. Classical computer vision techniques were compared with new deep-learning techniques for masks and spot extraction. We found that a U-Net approach trained on a small set of human-annotated photographs performed substantially better than a baseline feature engineering approach. For matching the spot constellations, two algorithms were adapted, and, depending on whether a fully or semi-automated set-up is preferred, we show how either one or a combination of these algorithms can be implemented. Within our case study, our pipeline both successfully identified unmarked individuals from photographs alone and re-identified individuals that had lost tags, resulting in an approximately 4 our multi-step pipeline involves little human supervision and could be applied to many organisms.Publisher PDFPeer reviewe

The BSUIN project

Baltic Sea Underground Innovation Network (BSUIN) is an European Union funded project that extends capabilities of underground laboratories. The aim of the project is to join efforts in making the underground laboratories in the Baltic Sea Region’s more accessible for innovation, business development and science by improving the availability of information about the underground facilities, service offerings, user experience, safety and marketing.The development of standards for the characterization of underground laboratories will allow to compared them with each other. This will help you choose the best places for physical measurements such as neutrino physics or searching for dark matter. The project concerns laboratories where so far no measurements have been made, and even undergrounds where there are no organized laboratories yet.The description of the BSUIN project and the first results of characterization of natural radioactive background in underground laboratories will be presented ˙ The BSUIN Project is funded by Interreg Baltic Sea funding cooperation [2]