Data Geometry and Extreme Value Distribution

In extreme values theory, there exist two approaches about data treatment: block maxima and peaks-over-threshold (POT) methods, which take in account data over a fixed value. But, those approaches are limited. We show that if a certain geometry is modeled with stochastic graphs, probabilities computed with Generalized Extreme Value (GEV) Distribution can be deflated. In other words, taking data geometry in account change extremes distribution. Otherwise, it appears that if the density characterizing the states space of data system is uniform, and if the quantile studied is positive, then the Weibull distribution is insensitive to data geometry, when it is an area attraction, and the Fréchet distribution becomes the less inflationary.

Evolution of the Inclusion Population During the Processing of Al-killed Steel

The increasing demand for higher inclusion cleanliness levels motivates the control over the formation and evolution of inclusions in the steel production process. In this work, the evolution of the chemical composition and size distribution of inclusions throughout a slab production process of Al-killed steel, including ladle furnace (LF) treatment and continuous casting (CC), was followed. The initial solid Al2O3 and Al2O3-MgO inclusions were modified to liquid Al2O3-CaO-MgO inclusions during LF treatment. The evolution of the size distributions during LF treatment was associated with the growth and removal of inclusions, as new inclusions were not created after the deoxidation process, according to a population density function (PDF) analysis. Additionally, the size distributions tended to be similar as the LF treatment progressed regardless of their initial features, whereas they differed during CC. Analysis of the upper tails of the distributions through generalized extreme values theory showed that inclusion distributions shifted from larger to smaller sizes as the process progressed. There were great changes in the distributions of large inclusions throughout the LF treatment and between the end of the LF treatment and the start of the CC process. Additionally, distributions of large inclusions differed at the end of the LF treatment, whereas such differences decreased as CC progressed.

Accelerated Climate Changes in Weddell Sea Region of Antarctica Detected by Extreme Values Theory

On 13 February 2020, The Guardian, followed by many other newspapers and websites, published the news that on 9 February 2020, Antarctic air temperatures rose to about 20.75 ∘C in a base logged at Seymour Island. This value has not yet been validated by the WMO (World Meteorological Organization), but it is not the first time that an extreme temperature was registered in these locations. The recorded temperatures have often been described as “abnormal and anomalous”, according to a statement made by scientists working at the Antarctic bases. Since polar regions have shown the most rapid rates of climate change in recent years, this abnormality is of primary interest in the context of vulnerability of the Antarctic to climate changes. Using data detected at different Antarctic bases, we investigate yearly maxima and minima of recorded temperatures, in order to establish whether they can be considered as usual extreme events or abnormal. We found evidence for disagreement with the extreme values theory, indicating accelerated climate changes in the Antarctic, that is, a local warming rate that is much faster than global averages.

Maximum Values of Frozen Soil’s Depth and Hoar Frost’s Thickness Estimated on the Basis of Extreme Values Theory

Extreme climatic phenomena present risk factors for agriculture, health, constructions, etc. and are studied profoundly these past years using extreme value theory. Several relation that describe positive extreme values’ probability Generalized Extreme Value and Gumbel distribution are presented in the article. As a example, we show the maps of characteristic and reference values of the maximum depth of the frozen soil and thickness of hoar-frost with a probability of exceeding per year equal to 0,02, which is equivalent to the mean return interval of 50 years. The obtained results could serve as a base for elaboration of national annexes in constructions.

Computing absorbing times via fluid approximations

In this paper we compute the absorbing timeTnof ann-dimensional discrete-time Markov chain comprisingncomponents, each with an absorbing state and evolving in mutual exclusion. We show that the random absorbing timeTnis well approximated by a deterministic timetnthat is the first time when a fluid approximation of the chain approaches the absorbing state at a distance 1 /n. We provide an asymptotic expansion oftnthat uses the spectral decomposition of the kernel of the chain as well as the asymptotic distribution ofTn, relying on extreme values theory. We show the applicability of this approach with three different problems: the coupon collector, the erasure channel lifetime, and the coupling times of random walks in high-dimensional spaces.