Study of hypersurfaces with specific expansion properties.
problem Existence and properties of hypersurfaces with prescribed null expansion.
method Adapted Eichmair's Perron approach for existence.
result Topology theorem for hypersurfaces with prescribed null expansion.
We derive asymptotic expansions for option data to detect infinite variation volatility.
problem Detecting infinite variation volatility in high-frequency option data.
method Nonparametric higher-order asymptotic expansions for small-time changes of characteristic functions of Itô semimartingales.
result Evidence of infinite variation volatility in high-frequency option data.
A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.
problem Information loss in hypergraph expansions on either vertex or hyperedge level.
method Proposes a new hypergraph formulation named line expansion (LE) that treats vertices and hyperedges symmetrically.
result The proposed line expansion method outperforms state-of-the-art baselines on five hypergraph datasets.
The paper studies geometric properties of group equivariant operators and their Riemannian structure.
problem Understanding the geometric structure of group equivariant operators.
method Endowing the space of group equivariant non-expansive operators with a Riemannian manifold structure and using gradient descent methods.
result Gradient descent methods can be applied to minimize cost functions on the space of group equivariant non-expansive operators.
New method models portfolios with leptokurtic risk factors using Gram-Charlier expansions.
problem Modeling portfolios with excess kurtosis.
method GC-like expansions of the hyperbolic-secant law to account for leptokurtosis.
result Portfolio distribution with risk factors modeled as GC-like expansions of the HS law.
BERET improves binary expansion test for multivariate independence.
problem Testing independence of random vectors in arbitrary dimensions.
method Ensemble approach using sum of squared symmetry statistics and distance correlation.
result Improves power while preserving interpretability.
Estimates bandwidth for CMC initial data sets.
problem Estimating bandwidth for constant mean curvature (CMC) initial data sets.
method Three independent proofs: stability of null expansion, spacetime harmonic function perturbation, Dirac operator.
result Generalized Gromov's band width estimate to CMC initial data sets.
Study transverse metric expansion on null hypersurfaces, proving uniqueness for Killing horizons.
problem Analyzing transverse expansion of metric on null hypersurfaces.
method Covariant approach, general geometric identities, generalized symmetry generators.
result Transverse expansion of spacetime metric uniquely determined at non-degenerate Killing horizons.
New test for point processes without strong model assumptions.
problem Testing local independence in point processes without strong model assumptions.
method Expansion similar to Volterra expansions to represent marginalized intensities.
result Approximation of true marginalized intensity arbitrarily well.
We analyze the semi-hard triplet loss using Edgeworth expansion for better understanding of its behavior.
problem Understanding the behavior of the semi-hard triplet loss function.
method Developed a higher-order asymptotic analysis using the Edgeworth expansion.
result Derived explicit Edgeworth expansions revealing first-order corrections in terms of the third cumulant.
Rescaling expansiveness proven for k*-expansive vector fields.
problem Proving rescaling expansiveness for k*-expansive vector fields.
method Introducing and exploring singular-expansive flows.
result Rescaling expansiveness established for k*-expansive vector fields.
New theory explains how strong models can learn from weak ones.
problem Learning from weak, incomplete, or incorrect labels.
method New bounds based on data distribution and student hypothesis class.
result Existing weak supervision theory fails to account for pseudolabel correction and coverage expansion.
A new method builds sparse polynomial chaos expansions for models with dependent inputs.
problem Quantifying uncertainty in models with dependent inputs.
method Data-driven approach to construct orthonormal polynomials recursively based on input correlations.
result Reduces the number of observations and improves numerical stability and computational efficiency.
Sparse random features improve accuracy in data-scarce settings.
problem Limited accuracy of random feature methods in data-scarce applications.
method Sparse random feature expansion using compressive sensing.
result Improved generalization bounds for sparse random features.
The paper derives expansions for Green's operators and resolvents using Hadamard methods.
problem Analyzing normally hyperbolic operators and their Green's functions.
method Hadamard expansions for powers of Green's operators and resolvents.
result Derives expansions involving Hadamard coefficients for advanced/retarded Green's operators.
We derive formulas for the Reshetikhin-Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra g in terms of the Seifert invariants and standard data for g. A main corollary is a determination of the full asymptotic expansions …
The paper examines how kernel approximations affect Gaussian process regression in large data applications.
problem Effect of kernel approximations on Gaussian process regression in large data applications.
method Unified framework to analyze Gaussian process regression under computational and epistemic misspecification.
result Theoretical analysis of Gaussian process regression under various misspecifications.
We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian processes we also develop priors on the coefficients, for tuning the model flexibi…
Paper proves existence of ambient manifolds for null hypersurfaces solving Einstein equations.
problem Analyzing transverse expansion of metrics at null hypersurfaces.
method Covariant approach proving existence of ambient manifolds given asymptotic expansion and constraint equations.
result Existence of ambient manifolds solving Einstein equations to infinite order at null hypersurfaces.
Develops a martingale expansion for stochastic volatility models.
problem Approximating marginal distributions of stochastic volatility models.
method Martingale expansion framework for continuous stochastic volatility models.
result First-order perturbation expansions for small volatility-of-volatility and fast mean-reversion models.
RPN unifies various models with a reconciled polynomial network.
problem Unifying diverse models for deep function learning.
method RPN disentangles functions into inner products of expansion and reconciliation functions.
result RPN accurately approximates underlying functions for data distributions.
Taylor expansions improve reinforcement learning policies.
problem Improving reinforcement learning policy optimization.
method Taylor expansion policy optimization.
result Taylor expansions enhance performance of distributed algorithms.
Analytic torsion expansions for symmetric and complex homogeneous spaces.
problem Calculating the full asymptotic expansion of analytic torsion for various spaces.
method Explicit calculation and comparison with existing results.
result Explicit full asymptotic expansions for symmetric and complex homogeneous spaces.
Proved cyclotomic expansion for double twist knots' HOMFLY-PT invariants.
problem Proving cyclotomic expansion for colored HOMFLY-PT invariants of double twist knots.
method Cyclotomic expansion formula for double twist knots.
result Confirmed cyclotomic expansion conjecture for SU(N)-invariants.
We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis type. An option pricing formula is derived from the same superposition of Black…
Sparse Polynomial Chaos expansions improve accuracy and efficiency in simulations.
problem Challenges in computational efficiency and accuracy for Polynomial Chaos modeling.
method Sparse Bayesian learning using Variational Relevance Vector Machines.
result Sparse Polynomial Chaos expansions achieve comparable performance to compressive sensing with fewer data points.
Study on future stability of FLRW spacetime solutions with decelerated expansion.
problem Stability of solutions to Einstein equations coupled with a nonlinear scalar field.
method Decomposition of metric and scalar field perturbations into spatial averages and oscillatory remainders.
result Future-stability of FLRW spacetime solutions for 1/3<p<1. Gradient-enhanced GSA uses Poincaré chaos expansions for accurate sensitivity analysis.
problem Accurately estimating Sobol' indices with limited data.
method Integrates sparse, gradient-enhanced regression with Poincaré chaos expansions for derivative-based sensitivity analysis.
result Accurately estimated Sobol' indices using limited data.
Study examines USD exchange rate dynamics using Kramers-Moyal expansion.
problem Understanding and predicting exchange rate instability.
method Kramers-Moyal expansion and Fokker-Planck formalism applied to log-return data.
result Identifies a stabilizing linear drift and nonlinear diffusion term in exchange rate fluctuations.
We study the problem of nonparametric dependence detection. Many existing methods may suffer severe power loss due to non-uniform consistency, which we illustrate with a paradox. To avoid such power loss, we approach the nonparametric test of independence through the new framework of binary expansion statistics (BEStat…
Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the Decomposed Convolutional Filters network (DCFNet), where the expansion coefficient…
Asymmetric expansion preserves convexity in hyperbolic geometry.
problem Maintaining convexity in hyperbolic geometry under asymmetric expansions.
method Generalizing earlier results on radial expansion to asymmetric expansion.
result Asymmetric expansion of hyperbolic convex sets remains convex.
The paper finds that bear markets cause recessions and bull markets cause expansions, with bull markets having a stronger causal effect.
problem Understanding the asymmetric causal relationships between market conditions and economic cycles.
method Asymmetric causality tests using partial sums of positive and negative market components, with bootstrap simulations and leverage adjustments.
result Bear markets cause recessions and bull markets cause expansions, with bull markets having a stronger causal effect.
Enhances polynomial chaos models with uncertainty intervals.
problem Uncertainty quantification in surrogate models.
method Jackknife-based conformal prediction integrated into polynomial chaos expansions.
result Produces accurate predictive intervals for low-accuracy models.
The UCR Time Series Archive - introduced in 2002, has become an important resource in the time series data mining community, with at least one thousand published papers making use of at least one data set from the archive. The original incarnation of the archive had sixteen data sets but since that time, it has gone th…
Extends results on marginally outer trapped surfaces to general null expansion.
problem Analyzing geometry and topology of expanding horizons.
method Introduces g-stability and proves conditions for positive Yamabe type and scalar curvature. result Initial data sets with compact boundary of positive null expansion have positive mass.
The paper calculates asymptotic expansions for specific types of oscillatory integrals.
problem Analyzing oscillatory integrals with complex phase functions.
method Using asymptotic expansions of simpler phase functions to derive results for more complex cases.
result Explicit computation of coefficients in asymptotic expansions for certain integrals.
Dropout increases the generalization of neural networks by expanding the weight space.
problem Understanding and improving the generalization of neural networks.
method Introducing weight expansion and showing that dropout leads to it.
result Dropout increases the generalization of neural networks by expanding the weight space.
New insights into contrastive learning reveal how projectors affect downstream performance.
problem Understanding how projectors in contrastive learning impact downstream linear classification accuracy.
method Identified and modeled two effects: expansion and shrinkage induced by contrastive loss.
result Linear projectors operating in the shrinkage regime hinder downstream classification accuracy.
Paper improves CDO calibration using Magnus Expansion and Deep Learning.
problem Calibrating CDO to iTraxx market data.
method Large basket approximation, SPDE, Magnus expansion, Deep Learning.
result Highly accurate calibration to market data.
New derivation of knot invariants from universal invariant.
problem Deriving knot invariants from universal invariant.
method Using Hopf algebra D and a Mathematica implementation to compute ZD(K). result Derivation of large-color expansion from universal invariant.
This work explores functional expansions to handle path dependence in various fields.
problem Path dependence and infinite-dimensional problems in non-Markovian systems.
method Generalizes Wiener series and functional Taylor expansion to handle static and dynamic functionals.
result Elegant separation of functionals from future trajectories in dynamic cases.
In the planar limit of the 't Hooft expansion, the Wilson-loop average in 3d Chern-Simons theory (i.e. the HOMFLY polynomial) depends in a very simple way on representation (the Young diagram), so that the (knot-dependent) Ooguri-Vafa partition function becomes a trivial KP tau-function. We study higher genus correctio…
We discuss a natural form of Ricci--flow conjugation between two distinct general relativistic data sets given on a compact n≥3-dimensional manifold Σ. We establish the existence of the relevant entropy functionals for the matter and geometrical variables, their monotonicity properties, and the associated conve…
DEPTS learns to forecast periodic time series with improved accuracy.
problem Forecasting periodic time series is challenging due to complex dependencies and diverse periods.
method DEPTS uses a decoupled formulation with an expansion module and a periodicity module to handle these challenges.
result DEPTS significantly improves forecasting accuracy, reducing errors by up to 20%.
Paper calculates third coefficient in Kaehler-Einstein metric expansion.
problem Understanding Kaehler-Einstein metrics and their epsilon functions.
method Computes the third coefficient in the TYCZ-expansion of the epsilon function.
result Discovers the vanishing of the third coefficient's significance.
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.
Sharp privacy bounds for sequential analysis of sensitive data.
problem Privacy degradation under sequential analysis of sensitive data.
method Edgeworth expansion in f-differential privacy framework.
result Improved privacy bounds under composition with refined approximation accuracy.