Multicyclic Norias: A First-Transition Approach to Extreme Values of the Currents

For continuous-time Markov chains we prove that, depending on the notion of effective affinity F, the probability of an edge current to ever become negative is either 1 if F < 0 else ∼ exp - F . The result generalizes a "noria" formula to multicyclic networks. We give operational insights on the effective affinity and compare several estimators, arguing that stopping problems may be more accurate in assessing the nonequilibrium nature of a system according to a local observer. Finally we elaborate on the similarity with the Boltzmann formula. The results are based on a constructive first-transition approach.

Causal modelling of heavy-tailed variables and confounders with application to river flow

Confounding variables are a recurrent challenge for causal discovery and inference. In many situations, complex causal mechanisms only manifest themselves in extreme events, or take simpler forms in the extremes. Stimulated by data on extreme river flows and precipitation, we introduce a new causal discovery methodology for heavy-tailed variables that allows the effect of a known potential confounder to be almost entirely removed when the variables have comparable tails, and also decreases it sufficiently to enable correct causal inference when the confounder has a heavier tail. We also introduce a new parametric estimator for the existing causal tail coefficient and a permutation test. Simulations show that the methods work well and the ideas are applied to the motivating dataset.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10687-022-00456-4.

Enhanced ultrasonic detection of near-surface flaws using transverse-wave backscatter

Diffuse ultrasonic backscatter measurements have been shown to enhance the detection capability of sub-wavelength flaws when combined with extreme value statistics. However, for a normal-incidence immersion measurement, a "dead zone" created by the ring-down of the front-wall echo will hide near-surface flaws. In this article, a pulse-echo transverse wave backscatter measurement is used to detect near-surface flaws under high gain. The approach is validated using a magnesium specimen with side-drilled holes. The confidence bounds of the grain noise from this specimen are given by a transverse-to-transverse scattering model, which takes the grain size distribution and the hexagonal crystal symmetry into account. The upper bound is then treated as a time-dependent threshold for the C-scan. Experiments show that the developed method has good performance for detecting sub-wavelength, near-surface flaws, and can suppress both missed detections and false positives.

Third-Order Phase Transition: Random Matrices and Screened Coulomb Gas with Hard Walls

Consider the free energy of a d-dimensional gas in canonical equilibrium under pairwise repulsive interaction and global confinement, in presence of a volume constraint. When the volume of the gas is forced away from its typical value, the system undergoes a phase transition of the third order separating two phases (pulled and pushed). We prove this result (i) for the eigenvalues of one-cut, off-critical random matrices (log-gas in dimension d = 1 ) with hard walls; (ii) in arbitrary dimension d ≥ 1 for a gas with Yukawa interaction (aka screened Coulomb gas) in a generic confining potential. The latter class includes systems with Coulomb (long range) and delta (zero range) repulsion as limiting cases. In both cases, we obtain an exact formula for the free energy of the constrained gas which explicitly exhibits a jump in the third derivative, and we identify the 'electrostatic pressure' as the order parameter of the transition. Part of these results were announced in Cunden et al. (J Phys A 51:35LT01, 2018).

Statistics associated with the scattering of ultrasound from microstructure

The spatial statistics of an ensemble of waveforms containing ultrasonic scattering from microstructure are investigated. The standard deviation of the waveforms is of primary interest, because it is related to the maximum scattering amplitudes in the extreme value statistics theory. Further statistical measures are employed to define theoretical confidence bounds, which bound the experimentally calculated maximum amplitude when a finite number of waveforms are included in the ensemble. These statistical measures are applied in conjunction with a previously developed ultrasonic backscatter model. It is validated through ultrasonic scattering measurements performed on a stainless-steel pipe sample. These considerations are important for forward models related to the probability of detection (POD) of defects and inverse models used for characterization of polycrystalline microstructures.

Internal validation of near-crashes in naturalistic driving studies: a continuous and multivariate approach

Large naturalistic driving studies give extremely detailed insight into how traffic accidents happen and what causes them. However, even in very large studies there are only relatively few crashes. Hence one additionally selects and studies crash surrogates, so called "near-crashes", i.e. situations when a crash almost happened. The selection procedures invariably entail severe risks of causing bias. In this paper we use extreme value statistics to develop two methods to study the extent and form of this bias. The methods are applied to a large naturalistic driving study, the 100-car study. Both methods identified a severe discrepancy between the rear-striking near-crashes and the rear-striking crashes. Perhaps surprisingly, one conclusion is that, for rear-striking and in this study, the crashes have little relevance for increasing traffic safety. We believe substantial efforts should be made to develop statistical methods for using near-crashes and crashes in future large naturalistic driving studies (such as the SHRP2 study).