ExGAN generates realistic extreme samples using GANs and EVT.
problem Generating realistic extreme scenarios for risk management.
method ExGAN combines GANs with EVT to model extreme tails of distributions.
result ExGAN efficiently generates extreme samples with constant time complexity.
Study on extremals in sub-Lorentzian geometry defined by antinorm.
problem Characterizing extremals in sub-Lorentzian structures.
method Deriving Hamiltonian system and conditions for extremal trajectories.
result Conditions for normal extremal trajectories and properties of abnormal extremals.
Study models extreme skew surges along French Atlantic coast.
problem Appropriate modelling of extreme skew surges for coastal risk management.
method Peak-over-threshold framework, multivariate generalized Pareto distribution, extreme regression framework.
result Reconstructed historical skew surge time series at stations with limited data.
Blowups of Kähler manifolds can inherit extremal metrics.
problem Extending extremal metrics to blowups of Kähler manifolds.
method Analyzing the action of a torus on blowups and weighted extremal metrics.
result Blowups of Kähler manifolds can inherit weighted extremal metrics.
New approach to extremal hyperbolic surfaces using NEC groups.
problem Structural description of extremal hyperbolic surfaces.
method Uniformization by NEC groups for surfaces with cusps and/or geodesic boundary.
result Full description of automorphism groups of extremal surfaces.
Paper develops a novel approach to identify clusters of features in multivariate extremes.
problem Understanding the complex structure of multivariate extremes in various fields.
method Optimization-based approach to assess the dependence structure of extremes.
result Estimating clusters of features that best capture the support of extremes.
Deep learning models complex multivariate extremes using geometric shapes.
problem Modeling complex extremal dependencies in high-dimensional data.
method Geometric representation and deep learning for flexible semi-parametric models.
result First approach to modeling limit sets using deep learning for high-dimensional data.
Spectral clustering identifies clusters of multivariate extremes.
problem Analyzing the dependence structure of multivariate extremes.
method Spectral clustering based on a random k k k -nearest neighbor graph. result Spectral clustering can consistently identify clusters of multivariate extremes under certain conditions.
New framework estimates treatment effects in extreme data.
problem Hindered by unavailability of counterfactual outcomes and rarity of extreme data.
method Proposes a new framework based on extreme value theory.
result Quantifies treatment effects using tail decay rates of potential outcomes.
Let X X X be a compact Riemann surface of genus ≥ 2 \geq 2 ≥ 2 of constant negative curvature -1. An extremal disk is an embedded (resp. covering) disk of maximal (resp. minimal) radius. A surface containing an extremal disk is an {\em extremal surface}. This paper gives formulas enumerating extremal surfaces of genus ≥ 4 \geq 4 ≥ 4 …
Framework for Granger causality in extreme events.
problem Identifying causal links from extreme events in time series.
method Causal tail coefficient and novel inference method.
result Framework outperforms state-of-the-art methods in detecting Granger causality in extremes.
We define regular points of an extremal subset in an Alexandrov space and study their basic properties. We show that a neighborhood of a regular point in an extremal subset is almost isometric to an open subset in Euclidean space and that the set of regular points in an extremal subset has full measure and is dense in …
Study on extremal subsets in geodesically complete spaces with curvature constraints.
problem Characterizing extremal subsets in GCBA spaces.
method Introduced and analyzed extremal subsets in GCBA spaces, proving their properties.
result Set of topological singularities forms an extremal subset under additional assumptions.
Model predicts unseen climate extremes to inform risk planning.
problem Missing unseen climate extremes in historical records.
method DeepX-GAN model capturing spatial dependence.
result Unseen heat extremes disproportionately threaten vulnerable regions.
PCA simplifies multivariate extreme data analysis.
problem Analyzing multivariate extreme values with high-dimensional data.
method Principal Component Analysis (PCA) for dimensionality reduction.
result PCA helps preserve essential information for extreme value analysis.
Combines GANs and EVT for better modeling of spatial climate extremes.
problem Modeling dependencies between climate extremes, especially in high-dimensional spaces.
method Generative Adversarial Networks (GANs) combined with Extreme Value Theory (EVT).
result evtGAN outperforms classical GANs and statistical approaches in modeling spatial extremes.
Study axisymmetric waves on extremal Kerr spacetime using physical-space estimates.
problem Obtain integrated local energy decay estimates for axisymmetric waves on extremal Kerr backgrounds.
method Use physical-space analysis and a method introduced by Stogin, simplifying Aretakis' derivation.
result Extend Morawetz estimates to extremal Kerr spacetime using purely classical currents.
Extremal metrics exist if uniformly K K K -stable over models.
problem Existence of extremal metrics on complex projective varieties.
method Uniform K K K -stability over models of extremal tori. result Extremal metrics exist if uniformly K K K -stable. Kernel PCA helps analyze multivariate extremes and clusters them effectively.
problem Analyzing the dependence structure of multivariate extremes.
method Kernel PCA as a method for clustering and dimension reduction.
result Kernel PCA preimages effectively identify clusters in multivariate extremes.
Study examines dependence of extreme electricity prices in Australian markets.
problem Understanding and managing risks of extreme price outcomes in Australian electricity markets.
method Examined extremal dependence using extremograms for 5-minute and 30-minute price data.
result Persistence and dependence of extreme prices are influenced by market structure and renewable energy share.
New extremal metrics found on Kähler manifolds.
problem Constructing extremal metrics on Kähler manifolds.
method Test configurations for strictly semistable Kähler manifolds.
result Infinitely many new examples of manifolds with extremal Kähler metrics.
Verifying probabilistic forecasts for extreme events is a highly active research area because popular media and public opinions are naturally focused on extreme events, and biased conclusions are readily made. In this context, classical verification methods tailored for extreme events, such as thresholded and weighted …
Uniqueness of weighted extremal metrics on Kähler manifolds proven.
problem Uniqueness of weighted extremal Kähler metrics on compact Kähler manifolds.
method Proof of uniqueness using modified Mabuchi energy and weighted K-semistability.
result Uniqueness of weighted extremal Kähler metrics up to automorphisms.
Paper improves risk estimation for extreme events.
problem Estimating extreme risks accurately.
method Modified Bayes risk for expectiles, asymptotic expansions, efficient estimators.
result Asymptotic normality of estimators proved.
Extremal dependence between international stock markets is of particular interest in today's global financial landscape. However, previous studies have shown this dependence is not necessarily stationary over time. We concern ourselves with modeling extreme value dependence when that dependence is changing over time, o…
A new method reduces uncertainty in predicting rare extreme events without assuming their presence in training data.
problem Predicting rare and extreme events in complex systems with high uncertainty.
method Extreme Event Aware (e2a or η) learning, which enforces extreme event statistics during training.
result Models generate unprecedented extreme events even when training data lacks extremes.
Stability of weighted extremal manifolds proven through blowups.
problem Stability of weighted extremal manifolds.
method Blowup technique to analyze weighted extremal Kähler manifolds.
result Proves weighted extremal manifolds are relatively weighted K-polystable.
New method estimates root-directed tree from extreme data.
problem Discovering causality in river networks from extreme flow data.
method Qualitative max-linear Bayesian network approach to estimate bivariate scores and root-directed spanning tree.
result The new estimator is consistent under max-linear Bayesian network model with noise.
The study finds no extremal metrics for eigenvalues on compact manifolds but constructs examples for annuli.
problem Finding extremal metrics for eigenvalues on compact manifolds.
method Construction of conformally extremal metrics in annuli and analysis of non-existence.
result Construction of conformally extremal metrics in annuli and characterization of these metrics.
Extremal Kähler submanifolds of complex projective spaces have natural extensions.
problem Understanding the structure and properties of extremal Kähler submanifolds.
method Analyzing the natural extensions and holomorphic isometric immersions of extremal Kähler submanifolds.
result Every connected extremal Kähler submanifold has a natural extension which is a complete Kähler manifold.
Extremal length is an important conformal invariant on Riemann surface. It is closely related to the geometry of Teichmuller metric on Teichmuller space. By identifying extremal length functions with energy of harmonic maps from Riemann surfaces to R \mathbb{R} R -trees, we study the second variation of extremal length fu…
Extremal length systole is maximized at the Bolza surface.
problem Finding the surface with the maximum extremal length systole.
method Analyzing the Bolza surface and comparing its extremal length systole to others.
result The extremal length systole of the Bolza surface is 2 \sqrt{2} 2 and is a strict local maximum. Proves minimization for Kähler manifolds with automorphisms.
problem Minimizing CM degree for Kähler manifolds with automorphisms.
method Equivariant CM minimization conjecture, asymptotic filtration Chow stability.
result Strict minimization by extremal filling.
Estimates treatment effects in rare extreme events using EVT.
problem Estimating treatment effects in rare, impactful events like extreme climate events.
method Introduces a novel framework using EVT and multivariate regular variation for consistent treatment effect estimation.
result Developed a consistent estimator for extreme treatment effects with rigorous non-asymptotic analysis.
Flexible XVAE model for efficient spatial extremes simulation.
problem Complex tail dependence structures in spatial extremes processes.
method Variational autoencoder (XVAE) for modeling flexible and non-stationary dependence.
result XVAE provides fast inference and outperforms traditional models in high dimensions.
Criterion found for Teichmüller extremal maps on infinite Riemann surfaces.
problem Finding necessary and sufficient conditions for Teichmüller extremal maps.
method Established a criterion for Teichmüller-type extremal maps.
result Criterion for Teichmüller extremal maps on infinite Riemann surfaces.
Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals---the waiting time between consecutive extremes---we show that these extreme returns are predictable on the short term. Examining a range of different types of returns and th…
The paper classifies rotationally symmetric extremal Kähler metrics on complex manifolds.
problem Classifying extremal Kähler metrics on complex manifolds.
method Analyzing polynomial zeros in Calabi's extremal equation.
result No U ( n ) U(n) U ( n ) invariant complete extremal Kähler metrics on C n \mathbb C^n C n with positive bisectional curvature. In this paper, we study extremal subsets in Alexandrov spaces with dimension n n n , curvature ≥ κ \geκ ≥ κ , and diameter ≤ D \le D ≤ D . We show that the following three quantities are uniformly bounded above in terms of n n n , κ κ κ , and D D D : (1) the number of extremal subsets in an Alexandrov space; (2) the Betti numbers of an extremal…
Study confirms conjecture on extremal length of hyperbolic metrics.
problem Determining the extremal length of hyperbolic metrics on Riemann surfaces.
method Analyzes the topology of closed hyperbolic Riemann surfaces to find extremal lengths.
result Extremal length is topology-dependent and has a specific upper bound.
This paper uses VAE to generate extreme events from multivariate data.
problem Generating accurate extremes from observational data for risk assessment.
method Variational Autoencoder (VAE) approach for multivariate heavy-tailed distributions.
result Improves learning of dependency structure between extremes.
xVAE models extreme turbulence events in turbulent flows.
problem Capturing extreme events in turbulent flows.
method Max-infinitely divisible process with heavy-tailed distributions embedded into a standard VAE framework.
result xVAE more robust in capturing extreme values compared to POD modes.
Method tracks change-points in crypto-assets extremes.
problem Tracking change-points in multivariate extremes.
method Statistical method for modeling change-points on crypto-assets extremes.
result Developed a method to track crypto-assets extremes.
The thesis evaluates and compares extreme mixture models in finance and insurance.
problem Estimating tail risk measures in finance and insurance.
method Extreme mixture models and methods, including kernel density estimation and GARCH preprocessing.
result Kernel density estimation-based models do not outperform others in tail risk estimation.
Paper explores new Kähler metrics from old, aiming to solve YTD conjecture.
problem Extending classical extremal Kähler metrics to include new objects.
method Surveying recent works on weighted extremal Kähler metrics and the YTD conjecture.
result Survey of recent research on weighted extremal Kähler metrics.
New model predicts financial tail events using RIA-EVT-Copula.
problem Predicting financial tail events for risk management.
method RIA-EVT-Copula framework combining POT, RIA, and copulas.
result Improved accuracy in predicting financial extremes.
Paper develops a neural model to assess cascading extreme events.
problem Risk assessment of domino effects like earthquakes and tsunamis.
method Develops a Kolmogorov-Arnold neural network (KANE) framework.
result Estimates the probability of one extreme event triggering another.
We provide a new proof of a result of X.X.Chen and G.Tian : for a polarized extremal Kähler manifold, an extremal metric attains the minimum of the modified K-energy. The proof uses an idea of C.Li adapted to the extremal metrics using some weighted balanced metrics.