Proposes new conformal parametrizations for modified Einstein gravity.
problem Initial data in modified Einstein gravity theories.
method Proposes conformal parametrizations that lead to conformally covariant systems.
result Some conformal parametrizations give rise to conformally covariant systems.
Variationality of conformal geodesics fails in higher dimensions.
problem The variationality of conformal geodesics in higher dimensions.
method Analysis of conformal geodesics in three and higher dimensions.
result Variationality fails in both parametrized and un-parametrized conformal geodesics in higher dimensions.
Article explains and implements mean curvature flow for surface parametrization.
problem Surface parametrization challenges.
method Conformalized mean curvature flow implementation.
result Demonstrates effectiveness of mean curvature flow for surface parametrization.
The paper improves prediction intervals for non-parametric regression using histograms.
problem Computing accurate prediction intervals for non-parametric regression models.
method Uses conditional histograms to estimate conditional distributions and compute shortest prediction intervals.
result The method provides prediction intervals with provable marginal coverage and asymptotic conditional coverage.
The study proves a strong parametric h-principle for minimal surfaces.
problem Proving a parametric h-principle for minimal surfaces.
method Using a parametric h-principle due to Forstneric and Larusson.
result The space of complete nonflat conformal minimal immersions has the same homotopy type as the space of continuous maps.
Study geodesics in conformally compact manifolds, showing smoothness and asymptotic behavior.
problem Analyzing geodesics in conformally compact manifolds with varying curvature.
method Examining asymptotic behavior and regularity of geodesics near boundary.
result Non-trapped geodesics extend to conformal infinity with C1,α regularity, endpoints smooth on initial conditions. Unified review of Conformal Prediction theory and applications.
problem Distribution-free, non-parametric forecasting method for valid prediction sets.
method Minimal assumptions, straightforward predictions sets valid in finite sample cases.
result Unified review of Conformal Prediction theory and applications.
Proves bijection between smooth conformal immersions and immersions.
problem Finding conformal immersions of closed Riemannian surfaces.
method Reformulated using h-principle and proved bijection on path connected components. result Induces a bijection between smooth conformal immersions and immersions.
An eight-parametric family of complex connections on a class complex manifolds with Norden metric is introduced. The form of the curvature tensor with respect to each of these connections is obtained. The conformal group of the considered connections is studied and some conformal invariants are obtained.
The paper classifies and studies conformal variations of submanifolds.
problem Classifying and understanding conformal variations of submanifolds.
method Develops a Fundamental theorem and a rigidity theorem for Euclidean submanifolds.
result Fundamental theorem and rigidity theorem for Euclidean submanifolds.
A method for non-parametric conditional distribution estimation using CRPS-optimal binning.
problem Non-parametric conditional distribution estimation.
method Partitioning covariate-sorted observations into bins to minimize LOO-CRPS, selecting K by K-fold cross-validation of test CRPS.
result Produces narrower prediction intervals with near-nominal coverage compared to split-conformal competitors.
Let X be an infinite hyperbolic surface endowed with an upper bounded geodesic pants decomposition. Alessandrini, Liu, Papadopoulos, Su and Sun \cite{ALPSS}, \cite{ALPS} parametrized the quasiconformal Teichmüller space Tqc(X) and the length spectrum Teichmüller space Tls(X) using the Fenchel-Nielsen coordi…
New framework quantifies uncertainty in reduced-order models for PDEs.
problem Quantifying reliability of reduced-order model predictions for PDEs.
method Combining stochastic representation of reduced bases with conformal-type methods.
result Provides prediction sets with coordinate miscoverage guarantees.
The paper revisits Markowitz's pseudodistance on pseudo-Riemannian manifolds.
problem Characterizing and classifying pseudo-Riemannian manifolds using Markowitz's pseudodistance.
method Review and extension of Markowitz's construction of pseudodistance on pseudo-Riemannian manifolds, with examples and classifications.
result Classification of quasi-homogeneous domains in the Einstein-de Sitter space.
Two-dimensional conformally parametrized surfaces immersed in the su(N) algebra are investigated. The focus is on surfaces parametrized by solutions of the equations for the CP^(N-1) sigma model. The Lie-point symmetries of the CP^(N-1) model are computed for arbitrary N. The Weierstrass formula for immersion is determ…
Tractor calculus theory for curves in conformal geometry.
problem Understanding curves in conformal geometry.
method Tractor calculus for generic and null curves.
result Definition and expression of absolute conformal invariants.
Conformalized KRR offers computationally efficient predictive confidence regions.
problem Lack of confidence measures in non-Bayesian predictive models.
method Developed a conformal procedure for Kernel Ridge Regression.
result Conformalized KRR can yield valid predictive confidence regions.
Study of how small changes in triangulated surfaces affect their geometry.
problem Understanding how small changes in triangulated surfaces affect their geometry.
method Investigates infinitesimal conformal deformations of triangulated surfaces in Euclidean space.
result There is a one-to-one correspondence between infinitesimal conformal deformations and infinitesimal isometric deformations of the stereographic image on the sphere.
It is shown that a superconformal surface with arbitrary codimension in flat Euclidean space has a (necessarily unique) dual superconformal surface if and only if the surface is S-Willmore, the latter a well-known necessary condition to allow a dual as shown by Ma \cite{ma}. Duality means that both surfaces envelope th…
A new method for predicting insurance claims with statistical guarantees.
problem Creating accurate prediction intervals for insurance claims.
method Model-agnostic framework using split conformal prediction for frequency-severity modeling.
result Shows effectiveness on simulated and real datasets using various models.
A four-parametric family of linear connections preserving the almost complex structure is defined on an almost complex manifold with Norden metric. Necessary and sufficient conditions for these connections to be natural are obtained. A two-parametric family of complex connections is studied on a conformal Kähler manifo…
Researchers classify homomorphisms for a specific algebra using singular vectors and symmetric polynomials.
problem Classifying homomorphisms for conformal Galilei algebras.
method Identifying homomorphisms with singular vectors and coefficients of symmetric polynomial expansions.
result Explicit description and classification of homomorphisms for conformal Galilei algebras.
The Clifford torus minimizes Willmore energy closely for small perturbations.
problem Finding the closest shape to the Clifford torus under small perturbations of Willmore energy.
method Analyzing integral 2-varifolds with specific properties and showing quantitative closeness to the Clifford torus.
result The support of the varifold is quantitatively close to the Clifford torus after a conformal transformation.
Study robustness of split conformal prediction in data contamination setting.
problem Robustness of split conformal prediction under data contamination.
method Analyze split conformal prediction's performance in a contaminated data setting and propose a new method.
result Demonstrated the impact of corrupted data on prediction intervals' coverage and efficiency.
SCIENCE improves prediction intervals for individual causal effects.
problem Wide prediction intervals limit practical utility of causal inference.
method Surrogate-assisted conformal inference for efficient individual causal effects.
result SCIENCE produces more efficient prediction intervals for individual causal effects.
Study projective and almost conformally symplectic structures on manifolds.
problem Relations between projective and almost conformally symplectic structures.
method Single almost conformally symplectic connection with totally trace-free torsion.
result Generalizes Fedosov structures and encodes variability of connections in projective class.
Conformal prediction offers distribution-free inference for complex models.
problem Traditional predictive inference methods are limited by assumptions about data distributions and model details.
method Conformal prediction uses symmetry assumptions and treats learning algorithms as black boxes.
result Conformal prediction provides exact finite-sample guarantees, even under limited assumptions.
We consider the Einstein-Maxwell-fluid constraint equations, and make use of the conformal method to construct and parametrize constant-mean-curvature hyperboloidal initial data sets that satisfy the shear-free condition. This condition is known to be necessary in order that a spacetime development admit a regular conf…
Unified approach to conformal and modular invariants on surfaces.
problem Constructing a general family of conformal invariants on surfaces.
method Using an identification of Teichmüller space and rigged moduli space, and analytic work on harmonic functions.
result Unified conformal and modular invariants can be viewed as generalized modular invariants and functions on the rigged moduli space.
Split conformal prediction provides finite-sample guarantees for black-box models without distributional assumptions.
problem Weak performance guarantees for modern predictive models under minimal assumptions.
method Develops finite-sample guarantees for split conformal prediction, a method that uses nested prediction sets and order statistics.
result The coverage of prediction sets based on order statistics stochastically dominates the Beta distribution.
Neural optimal transport improves multivariate conformal prediction.
problem Multivariate quantile regression challenges and existing methods ignore joint distribution geometry.
method Combines neural optimal transport with amortized optimization for efficient training and faster inference.
result Constructs tighter and more informative predictive regions for multivariate conformal prediction.
SAGA predicts multi-year earnings with adaptive intervals, improving forecast accuracy.
problem Forecasting long-range nonlinear structure in lifetime earnings.
method Decoder-only transformer for irregular tabular sequences, split conformal calibration.
result Significant improvement in forecast accuracy compared to existing methods.
New method detects changes in data streams efficiently.
problem Quickest change-point detection in data streams.
method Inductive Conformal Martingales for quickest change-point detection.
result Inductive Conformal Martingales are efficient under general conditions.
By studying spaces of flow graphs in a closed oriented manifold, we construct operations on its cohomology, parametrized by the homology of the moduli spaces of compact Riemann surfaces with boundary marked points. We show that the operations satisfy the gluing axiom of an open homological conformal field theory. This …
We prove that conformally parametrized surfaces in Euclidean space $\Rcubec$ of curvature c admit a symmetry reduction of their Gauss-Codazzi equations whose general solution is expressed with the sixth Painlevé function. Moreover, it is shown that the two known solutions of this type (Bonnet 1867, Bobenko, Eitner an…
Enhances conformal prediction for better uncertainty estimates in armed conflict fatalities.
problem Lack of individual-level uncertainty estimates in existing forecasting models.
method Introduces bin-conditional conformal prediction (BCCP) to improve coverage rates across subsets of the outcome variable.
result Demonstrates improved local coverage and well-calibrated uncertainty estimates across various ranges of fatalities.
Combining the definition of Schwarzian derivative for conformal mappings between Riemannian manifolds given by Osgood and Stowe with that for parametrized curves in Euclidean space given by Ahlfors, we establish injectivity criteria for holomorphic curves φ:D→Cn. The result can be considered a ge…
Let M be an open Riemann surface. It was proved by Alarcón and Forstnerič (arXiv:1408.5315) that every conformal minimal immersion M→R3 is isotopic to the real part of a holomorphic null curve M→C3. In this paper, we prove the following much stronger result in this direction: for any $n\geq …
The paper proves a theorem for discretizing Gaussian curvature on surfaces.
problem Discretizing Gaussian curvature on surfaces with nonpositive Euler number.
method Discrete conformal theory and variational principles with constraints.
result Each decorated piecewise Euclidean metric on surfaces with nonpositive Euler number is discrete conformal to a metric with a specific discrete curvature constant.
New algorithm improves Gaussian process hyperparameter tuning for large datasets.
problem Scalable hyperparameter tuning for Gaussian processes on large datasets.
method Estimates smoothness and length-scale parameters in Matern kernel using novel loss functions.
result Improved uncertainty quantification over traditional methods.
All parabolic geometries, i.e. Cartan geometries with homogeneous model a real generalized flag manifold, admit highly interesting classes of distinguished curves. The geodesics of a projective class of connections on a manifold, conformal circles on conformal Riemannian manifolds, and Chern--Moser chains on CR--manifo…
Paper constructs Lawson surfaces using Fuchsian DPW potentials.
problem Constructing Lawson surfaces using Fuchsian DPW potentials.
method Combining existence and regularity of Plateau solutions with topological information.
result Existence of Fuchsian DPW potential for Lawson surfaces.
A very simple expression is conjectured for arbitrary colored Jones and HOMFLY polynomials of a rich (g+1)-parametric family of Pretzel knots and links. The answer for the Jones and HOMFLY polynomials is fully and explicitly expressed through the Racah matrix of U_q(SU_N), and looks related to a modular transformatio…
In this paper, the Weierstrass technique for harmonic maps S^2 -> CP^(N-1) is employed in order to obtain surfaces immersed in multidimensional Euclidean spaces. It is shown that if the CP^(N-1) model equations are defined on the sphere S^2 and the associated action functional of this model is finite, then the generali…
In this paper we study Clifford and harmonic analysis on some conformal flat spin manifolds. In particular we treat manifolds that can be parametrized by U/Γ where U is a simply connected subdomain of either Sn or Rn and Γ is a Kleinian group acting discontinuously on U. Examples of such manifolds t…
We study the renormalized volume of asymptotically hyperbolic Einstein (AHE in short) manifolds (M,g) when the conformal boundary $\pl M$ has dimension n even. Its definition depends on the choice of metric h0 on ∂M in the conformal class at infinity determined by g, we denote it by ${\rm Vol}_R(M,g;…
Proposes LSCP for spatial data uncertainty quantification.
problem Uncertainty quantification in spatial statistics, especially for complex and heterogeneous datasets.
method Localized quantile regression for spatial conformal prediction.
result LSCP provides more accurate and consistent prediction intervals.
In the search for appropriate discretizations of surface theory it is crucial to preserve such fundamental properties of surfaces as their invariance with respect to transformation groups. We discuss discretizations based on Möbius invariant building blocks such as circles and spheres. Concrete problems considered in t…