The paper proves extremal black holes form at a critical point of gravitational collapse.
problem Formation of extremal black holes in gravitational collapse.
method Constructing smooth families of spherically symmetric solutions to the Einstein-Maxwell-Vlasov system.
result Extremal Reissner-Nordström black holes form at the critical collapse threshold.
Efficiently estimates GEV distribution parameters using neural networks.
problem Computational intensity of maximum likelihood estimation for GEV distribution.
method Neural network-based likelihood-free estimation method.
result Comparable accuracy to maximum likelihood method with significant speedup.
A new method selects algorithms and optimizes their hyper-parameters efficiently.
problem Redundant hyper-parameter search space in AutoML.
method Cascaded algorithm selection and hyper-parameter optimization with ER-UCB bandit.
result ER-UCB strategy achieves optimal regret bound for algorithm selection.
Study optimal dividends in dual risk model under extreme parameter conditions.
problem Optimal dividends in a dual risk model with extreme parameters.
method Asymptotic analysis of optimal control problem.
result Insights into optimal strategies and values under extreme parameter conditions.
A new method transfers parameters in ELM networks using projective model.
problem Parameter transfer in extreme learning machine networks.
method Projective model to bridge source and target model parameters, L2,1-norm penalty for joint feature selection and parameter transfer.
result Significantly outperforms non-transfer ELM networks and other methods.
Extremely accurate prediction of dynamical system bifurcations using control inputs.
problem Predicting complex bifurcation structures in dynamical systems.
method Extending extreme learning machines with control inputs to model system dynamics.
result The model can nearly reproduce the entire structure of bifurcations using only a few parameter values.
Develops a method to estimate extreme event statistics in high-dimensional systems with few samples.
problem Estimating extreme event statistics in high-dimensional nonlinear systems with limited data.
method Sequential sampling strategy using Gaussian process regression and Bayesian inference.
result Accurately estimates extreme event statistics in a high-dimensional system with limited samples.
Pricing extremely long-dated liabilities market consistently deals with the decline in liquidity of financial instruments on long maturities. The aim is to quantify the uncertainty of rates up to maturities of a century. We assume that the interest rates follow the affine mean-reverting Vasicek model. We model paramete…
We here present a model of the dynamics of extremism based on opinion dynamics in order to understand the circumstances which favour its emergence and development in large fractions of the general public. Our model is based on the bounded confidence hypothesis and on the evolution of initially anti-conformist agents to…
A compact manifold is called Bieberbach if it carries a flat Riemannian metric. Bieberbach manifolds satisfy an isosystolic inequality by a general and fundamental result of M. Gromov. In dimension 3, there exist four classes of non-orientable Bieberbach manifolds up to an affine diffeomorphism. In this paper, We prove…
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.
Researchers derive expressions for metric perturbations of extremal surfaces.
problem Understanding changes in extremal surfaces under metric perturbations.
method Derived explicit expressions for position and surface area changes.
result Found an expansion of surface area involving multiple integrals of geometric quantities.
Modeling spatial extremes with non-Gaussian fields using SAR models and CNNs.
problem Challenges in modeling spatial data with heavy-tailed distributions and missing cells.
method Spatial autoregressive models with Generalized Extreme Value innovations, combined with CNN for fast parameter estimation.
result Effective modeling of spatial extremes in non-Gaussian fields, demonstrated on precipitation data.
A new Randomized-Hyperopt method improves XGBoost hyperparameter tuning.
problem Improving the performance of XGBoost through hyperparameter optimization.
method Proposes Randomized-Hyperopt for XGBoost hyperparameter tuning.
result Randomized-Hyperopt outperforms other methods in terms of accuracy and execution time.
ML models predict extreme events in the Hénon map with accuracy scaling with system parameters.
problem Predicting extreme events in chaotic dynamical systems like the Hénon map.
method Used machine learning algorithms to analyze and forecast extreme events in the Hénon map.
result The success rate of ML models depends on prediction time, number of training samples, and network size, with scaling relations to the system's topological entropy.
Extends extreme value mixture models to identify changepoints in financial extreme regimes.
problem Inference over financial extreme regimes is affected by threshold choice.
method Extends extreme value mixture models to account for distributional extreme changepoints using MCMC algorithms.
result Inclusion of different extreme regimes improves financial applications compared to static and dynamic approaches.
The intrinsic geometry of the Kerr ergosurface on constant Boyer-Lindquist (BL), Kerr, and Doran time slices is characterized. Unlike the BL slice, which had been previously studied, the other slices (i) do not have conical singularities at the poles (except the Doran slice in the extremal limit), (ii) have finite pola…
Neural Bayes methods simplify fitting complex bivariate extremal models.
problem Inference on complex multivariate extremal dependence models with computationally expensive likelihood functions.
method Use neural networks to approximate Bayes estimators and classifiers for model selection.
result Proposed neural Bayes methods enable routine implementation of complex extreme-value dependence models.
A new method for choosing thresholds in data sequences without assuming distribution.
problem Choosing thresholds for random sequences without distributional assumptions.
method Data-driven threshold machine (DTM) that estimates three parameters of extreme value distributions and extremal index.
result DTM provides a reliable estimate of thresholds with robustness and computational efficiency.
New method uses extreme value theory to estimate neural network errors.
problem Quantifying the error of neural networks, especially for large values.
method Applying extreme value theory to approximate the distribution of error.
result Developed a new estimator for the shape parameter of the Pareto distribution.
Study proves curvature estimates for Kerr spacetime's linearized perturbations.
problem Proving elliptic L2(S2)-estimates for linearised curvature quantities in Kerr spacetime. method Applies linearised system from doctoral thesis, covers full sub-extremal range of Kerr parameters.
result Elliptic L2(S2)-estimates for linearised curvature quantities in the full sub-extremal range of Kerr parameters. New method models precipitation extremes and spatial dependence.
problem Estimating dependencies of precipitation maxima in space and time.
method Generative neural networks for max-stable processes.
result Explicit nonparametric estimate of spatial dependence.
Paper proposes a statistical model for detecting mu-suppression in EEG signals.
problem Detecting mu-suppression in motor imagery EEG signals.
method Proposes a statistical model based on the generalized extreme value distribution (GEV) and a linear classifier.
result Preliminary results show good classification accuracy in detecting mu-suppression and distinguishing EEG events.
Left invariant metrics induced by the p-norms of the trace in the matrix algebra are studied on the general lineal group. By means of the Euler-Lagrange equations, existence and uniqueness of extremal paths for the length functional are established, and regularity properties of these extremal paths are obtained. Minimi…
A study on preventing catastrophic forgetting in neural networks using conditional computation.
problem Catastrophic forgetting in connectionist neural networks.
method Conditional computation framework where parameters are conditioned on each input example.
result Proposed conditional rehearsal to prevent forgetting of previously learned examples.
Although much research has been devoted to extremal problems on non-overlapping domains little is known about all solutions of this problems. We generalized some of this problems on the case of more general systems of points. It was solved using separating transformations and learning functions in detail. Methods used …
New model explains volatility after extreme stock market events.
problem Understanding volatility dynamics after extreme stock market events.
method Proposed a new dynamical model using high frequency minute data.
result Volatility after extreme events follows a stretched exponential decay initially and a power law decay later.
Study of harmonic maps with extreme Kerr-like singularities.
problem Analyzing harmonic maps with specific singularities.
method Asymptotic analysis of harmonic maps from 3D Euclidean space to hyperbolic plane.
result Existence and classification of tangent harmonic maps at extreme black hole horizons.
The standard intensity-based approach for modeling defaults is generalized by making the deterministic term structure of the survival probability stochastic via a common jump process. The survival copula of the vector of default times is derived and it is shown to be explicit and of the functional form as dealt with in…
ELMs benefit from using equal number of hidden nodes to training samples.
problem Overfitting and underfitting in ELMs with hidden nodes.
method ELMs with hidden nodes equal to training samples achieve perfect training.
result ELMs with larger hidden nodes outperform traditional ELMs.
Improves forecast calibration for extreme events using modified loss functions.
problem Improperly specified models do not issue calibrated forecasts for extreme events.
method Adapting loss functions based on weighted scoring rules and tail miscalibration regularization.
result Calibrated forecasts for extreme wind speeds can be improved by suitable adaptations to the loss function during model training.
This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calcula…
New algorithm tackles stochastic bandits with unknown scale using kurtosis bounds.
problem Existing strategies for stochastic bandits require known scale parameters.
method Develops a scale-free algorithm for stochastic bandits with a bound on kurtosis.
result Generalizes results for Gaussian and uniform distributions to non-parametric setup.
Paper develops deep learning for metocean variable extremes.
problem Estimating multivariate joint extremes of metocean variables.
method SPAR model with GP distribution for radial tail, kernel density for angular variable, deep neural networks for GP parameters.
result The method provides good description of metocean variables joint extremes.
Recently Guillemin gave an explicit combinatorial way of constructing "toric" Kahler metrics on (symplectic) toric varieties, using only data on the moment polytope. In this paper, differential geometric properties of these metrics are investigated using Guillemin's construction. In particular, a nice combinatorial for…
Study proves existence of special surface shapes in capillarity problems.
problem Existence of volume-constrained minimal surfaces in capillarity problems.
method Variational techniques to find saddle-type critical points.
result Existence of extremals characterized as saddle-type critical points.
A new method reduces memory usage for large models by three orders of magnitude.
problem Memory limitations in training large models.
method Extreme tensoring for adaptive preconditioning.
result Significant reduction in memory usage without performance degradation.
We assess cluster stability by trimming extreme points and tracking data range reduction.
problem Assessing stability of one-dimensional clusters.
method Probabilistic method using diameter-shrinkage ratio to track data range reduction.
result Our method achieves higher accuracy than classical tests in small or noisy samples.
The hemisphere rigidity theorem connects to the Gelfand problem, providing a precise value for the extremal parameter.
problem Finding the extremal parameter for a specific nonlinear equation on a hemisphere.
method Interpreting the hemisphere rigidity theorem within the context of the Gelfand problem and applying it to a fourth-order Gelfand problem.
result A precise value for the extremal parameter is derived for the Gelfand problem under certain conditions.
WEINCE improves contrastive learning by correcting softmax biases.
problem Softmax in InfoNCE can lead to misaligned statistical assumptions in contrastive learning.
method WEINCE uses anchor-wise online batch statistics to blend softmax logits with an endpoint shortfall correction.
result WEINCE yields consistent improvements in frozen-feature evaluation across five vision benchmarks.
Develops a model for analyzing cryptocurrency returns focusing on extreme values.
problem Analyzing extreme returns in cryptocurrency time series.
method Linear expectile hidden Markov model with time-dependent coefficients.
result The method effectively captures the temporal evolution of extreme returns.
Two tests identify heterogeneous components in distributed learning.
problem Identifying parameter heterogeneity in distributed learning with minimal data transmission.
method Two tests: Wald and Extreme Contrast (ECT).
result ECT avoids bias accumulation and is robust to varying levels of sparsity.
AGBoost uses attention weights to improve GBM for regression problems.
problem Improving gradient boosting machine for regression tasks.
method Attention-based modification of GBM with trainable attention weights.
result AGBoost achieves better performance on regression datasets.
Paper introduces a new indicator to predict financial extremes using stock price network degree.
problem Predicting financial market extremes during bull and bear markets.
method Constructs an indicator based on the degree of stock price network generated from time series.
result The new indicator shows strong predictive power for financial extremes, both peaks and troughs.
Capillarity functionals are parameter invariant functionals defined on classes of two-dimensionals parametric surfaces in R3 as the sum of the area integral with an anisotropic term of suitable form. In the class of parametric surfaces with the topological type of S2 and with fixed volume, extremals of capillarity func…
Paper proposes efficient GCN learning method for limited data.
problem Learning GCNs from data with extremely limited annotations.
method Adaptive sampling strategy and model compression.
result Cut down annotation requirement by 90% and compress parameters 6x.
MACH reduces memory usage for extreme classification by hashing.
problem Expensive training of deep models with large softmax layers.
method Merged-Average Classifiers via Hashing (MACH) using count-min sketch.
result Significant memory reduction and training speedup.
In our physically inspired in-tree (IT) based clustering algorithm and the series after it, there is only one free parameter involved in computing the potential value of each point. In this work, based on the Delaunay Triangulation or its dual Voronoi tessellation, we propose a nonparametric process to compute potentia…