Article
Materials Science, Multidisciplinary
P. R. N. Falcao, M. L. Lyra
Summary: In this study, we investigate a one-dimensional tight-binding model with power-law decaying hopping amplitudes to explore the wave-function maximum distributions related to Anderson localization phenomenon. We find that in the regime of extended states, the wave-function intensities follow the Porter-Thomas distribution while their maxima assume the Gumbel distribution. At the critical point, scaling laws govern the regimes of small and large wave-function intensities with a multifractal singularity spectrum. The distribution of maxima deviates from the usual Gumbel form, and characteristic finite-size scaling exponents are reported. Within the localization regime, the wave-function intensity distribution exhibits a sequence of pre-power-law, power-law, exponential, and anomalous localized regimes. These regimes are strongly correlated and significantly affect the emerging extreme values distribution.
Article
Engineering, Industrial
Baorui Dai, Ye Xia, Qi Li
Summary: This study proposes a novel clustering algorithm based on the generalized extreme value mixture model (GEVMM) to accurately predict extreme values. By selecting the optimal number of clusters and considering the overlap among the original mixture components, this method demonstrates strong applicability in extreme value prediction.
RELIABILITY ENGINEERING & SYSTEM SAFETY
(2022)
Review
Mathematics
Natalia Markovich, Marijus Vaiciulis
Summary: This paper summarizes recent research results on the evolution of random networks and related extreme value statistics, which are of great interest due to their numerous applications. The focus is on the statistical methodology rather than the structure of random networks. The problems arising in evolving networks, particularly due to the heavy-tailed nature of node indices, are discussed. Topics such as tail and extremal indices, preferential and clustering attachments, community detection, stationarity and dependence of graphs, information spreading, and finding influential leading nodes and communities are surveyed. The paper aims to propose possible solutions to unsolved problems and provides a comprehensive review of estimators for tail and extremal indices on random graphs.
Article
Statistics & Probability
John H. J. Einmahl, Yi He
Summary: We extend extreme value statistics to independent data with possibly very different distributions. In particular, we present novel asymptotic normality results for the Hill estimator, which estimates the extreme value index of the average distribution. Due to heterogeneity, the asymptotic variance can be substantially smaller than that in the i.i.d. case. We also present applications to assess the tail heaviness of earthquake energies and of cross-sectional stock market losses.
ANNALS OF STATISTICS
(2023)
Article
Computer Science, Artificial Intelligence
Amanda O. C. Ayres, Fernando J. Von Zuben
Summary: This article introduces a new evolving fuzzy-rule-based algorithm named extreme value evolving predictor (EVeP), which offers a statistically well-founded approach to improve the prediction performance of rules by using evolving fuzzy granules and fuzzy structural relationships. It outperforms the state-of-the-art evolving algorithms in terms of prediction performance.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2022)
Article
Acoustics
Zhao Zhao, Ying Min Low
Summary: This study presents an analytical method for extreme analysis of multivariate stationary Gaussian processes, which efficiently solves high-dimensional problems and has diverse applications. By defining a maximum process and utilizing the Poisson approximation method to estimate extreme value distribution, the method ensures fast computation.
JOURNAL OF SOUND AND VIBRATION
(2023)
Article
Astronomy & Astrophysics
S. J. Naus, J. Qiu, C. R. DeVore, S. K. Antiochos, J. T. Dahlias, J. F. Drake, M. Swisdak
Summary: We analyzed the structure and evolution of ribbons from the M7.3 flare and found that the ribbon width is highly intermittent and closely related to nonthermal hard X-ray emissions. Our results suggest a strong connection between the production of nonthermal electrons and the locally enhanced perpendicular extent of flare ribbon fronts.
ASTROPHYSICAL JOURNAL
(2022)
Article
Engineering, Marine
Xiaoyu Zhou, Hongxia Li, Yi Huang, Yihua Liu
Summary: This study proposes a new extreme statistics strategy to predict the extreme parametric rolling angle with minimal model test observations. The strategy utilizes a synthetic moment method based on the Hermite transformation and Markov chain to predict extreme values for stationary processes. A specific simplification technique is also introduced to address the non-stationarity issue of parametric roll. By applying the new strategy, the CDF and PDF of the extreme parametric rolling angle for the C11 container ship are obtained from only one observed model test time history. The validity of these predictions is verified through data statistics of other model tests and numerous numerical simulations.
Article
Engineering, Mechanical
Oleg Gaidai, Fang Wang, Yu Wu, Yihan Xing, Ausberto Rivera Medina, Junlei Wang
Summary: This paper presents a practical approach to studying extreme wind speeds and wave heights in offshore engineering, as well as a new technique to improve correlated extreme value predictions.
PROBABILISTIC ENGINEERING MECHANICS
(2022)
Article
Biochemical Research Methods
Weijia Kong, Bertrand Jern Han Wong, Harvard Wai Hann Hui, Kai Peng Lim, Yulan Wang, Limsoon Wong, Wilson Wen Bin Goh
Summary: Missing values can have negative effects on data analysis and machine learning model development. A new mixed-model method called ProJect (Protein inJection) is proposed for missing value imputation, which is an improvement over existing methods. ProJect consistently outperforms other methods in tests on various high-throughput data types. It handles different types of missing values and achieves more accurate and reliable imputation outcomes.
BRIEFINGS IN BIOINFORMATICS
(2023)
Article
Engineering, Marine
Connor J. McCluskey, Manton J. Guers, Stephen C. Conlon
Summary: Extreme value statistics is a method for determining maximum design loads in extreme conditions, with accurate predictions requiring large sample sizes and small sample sizes leading to greater variation. The proposed method estimates minimum sample sizes by obtaining an acceptable variance for extreme value processes and is designed for use with various distribution behaviors.
Article
Mathematics
Pavel Loskot
Summary: This paper introduces a computationally effective generative model for sampling from arbitrary but known marginal distributions with defined pairwise correlations, which is generally accurate for correlation coefficients with magnitudes up to about 0.3. The generative models of graph signals can also be used to sample multivariate distributions for which closed-form mathematical expressions are not known or are too complex.
Article
Mechanics
Alessandro Taloni, Stefano Zapperi
Summary: The fracture stress of materials typically depends on sample size and is traditionally explained using extreme value statistics. A recent study interpreted the carrying capacity of long polyamide and polyester wires in terms of a probabilistic argument called the St. Petersburg paradox, but the same results can be better explained using extreme value statistics. The relevance of rate dependent effects was also discussed.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Article
Meteorology & Atmospheric Sciences
Marc-Andre Falkensteiner, Harald Schellander, Gregor Ehrensperger, Tobias Hell
Summary: This paper proposes a modification of the MEVD method, called TMEV, for the analysis of non-stationary precipitation extremes. The TMEV method can explicitly account for seasonal differences and identify longterm trends and seasonal variations. Experimental results show that the TMEV method provides similar error characteristics to the simplified MEVD method for estimating quantiles.
WEATHER AND CLIMATE EXTREMES
(2023)
Article
Optics
Pei Wang, Rosario Fazio
Summary: In this paper, the driven-dissipative p-spin models for p >= 2 were studied using a semiclassical approach to derive the equation of motion in the thermodynamic limit. Long-time asymptotic states were analytically obtained, showing multistability in certain regions of the parameter space. Both first-order and continuous dissipative phase transitions were found, with transition properties depending on the symmetry and semiclassical multistability, exhibiting different behaviors for p = 2, odd p (p >= 3), and even p (p >= 4).
Article
Physics, Mathematical
Yan Fyodorov, Pierre Le Doussal
JOURNAL OF STATISTICAL PHYSICS
(2020)
Article
Statistics & Probability
Yan V. Fyodorov, Stephen Muirhead
Summary: The study examines a random permutation of a lattice box with a Boltzmann weight based on total Euclidean displacement. The main result establishes the band structure of the model as the box size and inverse temperature tend towards infinity and zero, respectively. The connection between random permutations and Gaussian fields via matrix permanents is utilized in the proofs, providing novel insights into the study of random permutations and yielding asymptotics for Kac-Murdock-Szego matrices.
PROBABILITY THEORY AND RELATED FIELDS
(2021)
Article
Multidisciplinary Sciences
Gerard Ben Arous, Yan V. Fyodorov, Boris A. Khoruzhenko
Summary: With increased interaction strength, a nonlinear autonomous system typically transitions from a single stable equilibrium to a topologically nontrivial regime of absolute instability, where stable equilibria are exponentially abundant but typically unstable.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2021)
Article
Physics, Multidisciplinary
Y. Fyodorov, M. Osman
Summary: This study presents explicit distributions of diagonal non-orthogonality overlaps, also known as Petermann factors, characterizing eigenmodes in a wave-chaotic cavity. It shows that these factors determine deep dips in wave reflection experiments and are valid for arbitrary coupling strengths within the framework of random matrix theory. Further simplifications are possible in the regime of weak coupling.
ACTA PHYSICA POLONICA A
(2021)
Article
Physics, Multidisciplinary
Bertrand Lacroix-A-Chez-Toine, Yan Fyodorov
Summary: We study a nonlinear autonomous random dynamical system with Gaussian random interactions. By computing the average modulus of the determinant of the random Jacobian matrix, we obtain the annealed complexities of stable equilibria and all types of equilibria. For short-range correlated coupling fields, we derive exact analytical results for the complexities in the large system limit, extending previous results for homogeneous relaxation spectrum. We find a "topology trivialisation" transition from a complex phase with exponentially many equilibria to a simple phase with a single equilibrium as the magnitude of the random field decreases. Within the complex phase, the complexity of stable equilibria undergoes an additional transition from a phase with exponentially small probability of finding a single stable equilibrium to a phase with exponentially many stable equilibria as the fraction of gradient component of the field increases. The behavior of the complexity at the transition is conjectured to be universal, depending only on the small lambda behavior of the relaxation rate spectrum. We also provide insights into a counting problem related to wave scattering in a disordered nonlinear medium.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Multidisciplinary
Lei Chen, Steven M. Anlage, Yan V. Fyodorov
Summary: Through experimental and theoretical analysis, we studied the statistical properties of complex Wigner time delay in subunitary wave-chaotic scattering systems. Experimental results showed good agreement with the developed theory.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Yan Fyodorov, Mohammed Osman
Summary: Motivated by coherent perfect absorption, this study investigates the shape of the deepest dips in the frequency-dependent single-channel reflection of waves from a cavity with spatially uniform losses. Non-orthogonality factors O(nn) of eigenmodes associated with the non-selfadjoint effective Hamiltonian play a major role in determining the shape. For cavities supporting chaotic ray dynamics, random matrix theory is used to derive the explicit distribution of non-orthogonality factors, revealing that they follow a heavy-tail distribution. Additionally, an explicit non-perturbative expression for the resonance density in single-channel chaotic systems is derived.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Multidisciplinary
Yan Fyodorov, Rashel Tublin
Summary: In this study, we analyze the statistical features of the 'optimization landscape' in a basic constrained optimization problem and derive the exact expressions for key metrics of the problem. These findings provide important insights for solving the problem numerically.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Correction
Physics, Multidisciplinary
Bertrand Lacroix-A-Chez-Toine, Yan Fyodorov
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Mathematical
Bertrand Lacroix-A-Chez-Toine, Yan V. Fyodorov, Sirio Belga Fedeli
Summary: This paper investigates a high-dimensional random landscape model obtained by superimposing random plane waves and subject to a uniform parabolic confinement. By studying the spectral properties of the characteristic matrix, the annealed complexity of the landscape is computed.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Physics, Multidisciplinary
Yan V. V. Fyodorov, Boris A. A. Khoruzhenko, Mihail Poplavskyi
Summary: Complex eigenvalues of random matrices J = GUE + i(gamma)diag(1,0, ... ,0) provide a simple model for studying resonances in wave scattering from a quantum chaotic system. The eigenvalue density of J undergoes a restructuring at gamma = 1, beyond which a single eigenvalue outlier appears. We describe the scaling with N of the critical region width, resonance positions, resonance widths, and density of extreme eigenvalues in the critical regime.
Article
Physics, Fluids & Plasmas
Yan V. Fyodorov, Elizaveta Safonova
Summary: Using the method of random matrix theory with supersymmetry within the framework of the Heidelberg approach, this study provides a statistical description of stationary intensity inside an open wave-chaotic cavity. It is shown that the probability density of single-point intensity decays as a power law for large intensities when incoming waves are fed via a finite number of open channels, with a marked difference from the Rayleigh law. The joint probability density of intensities in multiple observation points and the statistics for the maximal intensity in the observation pattern are also analyzed.
Article
Physics, Fluids & Plasmas
Lei Chen, Steven M. Anlage, Yan Fyodorov
Summary: This paper introduces a complex generalization of the Wigner time delay for subunitary scattering systems, providing theoretical expressions and experimental validation. It is found that certain features of time delay and the scattering matrix can serve as reliable indicators of coherent perfect absorption conditions. This work offers a method to identify poles and zeros of the scattering matrix from experimental data in lossy systems, and enables achieving coherent perfect absorption at arbitrary frequencies in complex scattering systems.
Article
Physics, Fluids & Plasmas
S. Belga Fedeli, Y. Fyodorov, J. R. Ipsen
Summary: The study found that as long as the origin remains stable, the system will be surrounded by a resilience gap with no other fixed points within a radius r(*) > 0. When the origin loses local stability, the radius r(*) disappears, leading to the system becoming less resilient.
Article
Physics, Multidisciplinary
Yan V. Fyodorov, Wojciech Tarnowski
Summary: The research focuses on the distribution of eigenvalue condition numbers associated with real eigenvalues of partially asymmetric N x N random matrices. It reveals that the asymmetry of the matrices affects the orthogonality of eigenvectors and the sensitivity of eigenvalues against perturbations. The study also shows different scaling regimes and characteristics of the joint density functions in the case of weak and strong asymmetry.
ANNALES HENRI POINCARE
(2021)
