Characterizes Kerr spacetimes using conformal methods.
problem Understanding Kerr spacetimes through conformal transformations.
method Conformally covariant characterization approach.
result Ideal characterization of Kerr spacetimes.
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48 results for “conformal covariant”
Researchers create a family of conformally covariant operators.
problem Developing a comprehensive set of conformally covariant operators.
method Constructing a family of conformally covariant tridifferential operators as tangential operators in the Fefferman--Graham ambient space.
result Symmetrization of ambient operators is formally self-adjoint.
The conformally covariant split system generates non-constant mean curvature vacuum initial data.
problem Creating non-constant mean curvature vacuum initial data for the Einstein equations.
method Proved existence of solutions to the conformally covariant split system on compact 3-manifolds using the implicit function theorem.
result The conformally covariant split system provides non-constant mean curvature vacuum initial data for the Einstein equations.
The article defines conditions for a manifold to be conformal to an Einstein space.
problem Determining when a manifold is conformal to an Einstein space.
method Algorithmic conditions based on the metric tensor and the Weyl endomorphism.
result General necessary and sufficient conditions for a pseudo-Riemannian manifold to be conformal to an Einstein space.
Let G be a finite connected simple graph. We define the moduli space of conformal structures on G. We propose a definition of conformally covariant operators on graphs, motivated by [25]. We provide examples of conformally covariant operators, which include the edge Laplacian and the adjacency matrix on graphs. In the …
Conformally covariant parametrizations for initial data in some modified Einstein gravity theoriesmath.DG
We propose further conformal parametrizations for initial data in some modified Einstein gravity theories. Some of them give rise to conformally covariant systems.
Researchers create new operators from Riemannian invariants.
problem Developing new mathematical tools for Riemannian geometry.
method Introducing formally self-adjoint conformally covariant polydifferential operators.
result Found a fourth-order, conformally covariant tridifferential operator.
The well known conformal covariance of the Dirac operator acting on spinor fields over a semi Riemannian spin manifold does not extend to powers thereof in general. For odd powers one has to add lower order curvature correction terms in order to obtain conformal covariance. We derive an algorithmic construction in term…
Network-assisted regression uses conformal prediction for valid inference.
problem Predicting node attributes using network and conventional covariates with valid statistical inference.
method Network analog of conformal prediction under mild joint exchangeability assumption.
result Achieves finite sample validity and asymptotic conditional validity for various network covariates.
WCPS extends CPS to handle covariate shifts, providing probabilistically calibrated predictions.
problem Applying CPS to scenarios with covariate shifts.
method WCPS uses likelihood ratios between training and testing covariate distributions.
result WCPS are probabilistically calibrated under covariate shift.
Kandinsky conformal prediction expands conditional coverage guarantees.
problem Disparities in coverage guarantees across different subpopulations.
method Flexible handling of overlapping and fractional group memberships.
result Minimax-optimal high-probability conditional coverage bound.
We revisit the Lichnerowicz-York method, and an alternative method of York, in order to obtain some conformally covariant systems. This type of parameterization is certainly more natural for non constant mean curvature initial data.
Researchers solve Yamabe problems for specific operators, finding both uniqueness and nonuniqueness.
problem Prescribing scalar, Q-, or σ₂-curvatures in conformal classes.
method Formally self-adjoint, conformally covariant, polydifferential operators.
result Uniqueness results on the sphere, nonuniqueness in general.
We describe a set of conformally covariant boundary operators associated to the Paneitz operator, in the sense that they give rise to a conformally covariant energy functional for the Paneitz operator on a compact Riemannian manifold with boundary. These operators naturally give rise to a first- and third-order conform…
In the study of conformal geometry, the method of elliptic partial differential equations is playing an increasingly significant role. Since the solution of the Yamabe problem, a family of conformally covariant operators (for definition, see section 2) generalizing the conformal Laplacian, and their associated conforma…
The paper addresses the reliability of conformal prediction under covariate shift.
problem Ensuring reliable prediction sets under covariate shift.
method Derives upper bounds on training-conditional coverage.
result Offers PAC guarantees for conformal prediction methods.
New -connection characterizes 4D spaces conformal to Einstein spaces.
problem Characterizing 4D spaces conformal to Einstein spaces.
method Introducing -connection, a Weyl connection that preserves conformal invariance.
result Characterizes non-degenerate spaces conformal to Einstein spaces.
Proposes a new method for conformal prediction under covariate shift with posterior drift.
problem Improving classification performance in target domains with limited training data.
method Weighted conformal classifier that leverages source and target samples.
result Demonstrates favorable asymptotic properties and practical utility.
New operators generalize Rankin-Cohen brackets for differential forms.
problem Extending classical operators to differential forms.
method Constructing conformally covariant bi-differential operators for differential forms.
result Generalized operators for differential forms are constructed.
In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli-Silvestre and a class of conformally covariant operators in conformal geometry.
This paper improves STL inference reliability under covariate shift.
problem Ensuring correct STL formulas in real-world settings with distribution shift.
method Proposes a conformalized STL inference framework that addresses covariate shift.
result Significantly improves symbolic learning reliability at deployment time.
Proposes a method for generating prediction intervals in dose-response models using conformal prediction.
problem Uncertainty quantification in continuous treatments for personalized healthcare decisions.
method Causal dose-response problem framed as covariate shift, using weighted conformal prediction with propensity estimation and kernel functions.
result Demonstrates the significance of covariate shift assumptions for robust prediction intervals.
Filtered conformal ellipsoids for graph-native time series
problem Joint prediction sets for multivariate time series
method Filtered conformal ellipsoids
result Sharper at-target ellipsoids than static-covariance and non-filter baselines
We show that the Teukolsky connection, which defines generalized wave operators governing the behavior of massless fields on Einstein spacetimes of Petrov type D, has its origin in a distinguished conformally and GHP covariant connection on the conformal structure of the spacetime. The conformal class has a (metric com…
Bayesian optimization enhanced with conformal prediction for better outcome reliability.
problem Uncertainty and model misspecification in Bayesian optimization.
method Conformal prediction to provide coverage guarantees and Bayesian optimization to select queries.
result Significant improvement in query coverage without sacrificing sample-efficiency.
In this paper we study the extent to which conformally compact asymptotically hyperbolic metrics may be characterized intrinsically. Building on the work of the first author, we prove that decay of sectional curvature to -1 and decay of covariant derivatives of curvature outside an appropriate compact set yield Hölder …
We study conformal -subgeometry of submanifolds in a semi-Riemannian -manifold, focusing on conformal -manifolds and their Poincaré-Einstein metrics . Our approach is based on the spectral theory of Dirac operator in the ambient -manifold, and associated spinor valued meromorp…
The paper tackles uncertainty quantification in multi-source settings.
problem Uncertainty quantification under covariate shift is challenging in multi-source settings.
method The paper addresses this by proposing two extensions of weighted conformal prediction: merge-based aggregation and data-pooling.
result Theoretical guarantees are provided for the proposed approaches, and experiments validate their effectiveness.
This is the first of two papers where we address and partially confirm a conjecture of Deser and Schwimmer, originally postulated in high energy physics. The objects of study are scalar Riemannian quantities constructed out of the curvature and its covariant derivatives, whose integrals over compact manifolds are invar…
The paper introduces new boundary operators and proves higher order CR Sobolev trace inequalities for Siegel domain and complex ball.
problem Establishing higher order CR Sobolev trace inequalities for Siegel domain and complex ball.
method Introducing conformally covariant boundary operators, proving extension theorems, and establishing trace inequalities.
result Generalized CR Sobolev trace inequalities for all γ ∈ (0, n+1) \mathbb{N}.
A classification scheme of the conformal almost contact metric manifolds with respect to the covariant derivative of the Lee form is given. The subclasses of one basic class and their exact characterizations by the maximal subgroups of the contact conformal group preserving itself are found.
CoDrug uses KDE to create valid prediction sets for drug molecules under covariate shift.
problem Creating reliable uncertainty estimates for drug properties from computational models.
method CoDrug employs an energy-based model and KDE to assess and rectify distribution shift.
result CoDrug reduces the coverage gap by over 35% compared to non-adjusted conformal prediction sets.
New boundary operators for sixth-order GJMS operator on manifolds.
problem Developing boundary operators for sixth-order GJMS operator.
method Conformally covariant boundary operators and fractional GJMS operators.
result New realization of fractional GJMS operators and Sobolev trace inequalities.
We investigate the singular sets of solutions of conformally covariant elliptic operators of fractional order with the goal of developing generalizations of some well-known properties of solutions of the singular Yamabe problem.
Classification of ground state solutions to critical Dirac equation on spheres.
problem Classifying ground state solutions of the critical Dirac equation.
method Exploiting conformal covariance and relating to the Yamabe equation.
result Ground state solutions are given by Killing spinors up to conformal diffeomorphisms.
Let (M,g) be a compact Riemannian manifold of dimension >2. We show that there is a metric h conformal to g and of volume 1 such that the first positive eigenvalue the conformal Laplacian with repect to h is arbitrarily large. A similar statement is proven for the first positive eigenvalue of the Dirac operator on a sp…
Robust Conformalized Selection controls FDR under noisy responses.
problem Existing conformal selection methods fail to control FDR under contaminated calibration data.
method RCS framework for selective classification with valid FDR control under label contamination.
result RCS framework controls FDR and maintains power under contaminated calibration data.
Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularizationstat.ML
New method for valid prediction sets in high-dimensional covariate shifts.
problem Valid prediction sets in high-dimensional covariate shifts.
method Likelihood-ratio regularized quantile regression (LR-QR) algorithm.
result LR-QR constructs valid prediction sets with desired coverage in target domain.
Improved multivariate conformal prediction by standardizing residuals.
problem Weak conditional coverage in heteroskedastic multivariate settings.
method Natural extension of univariate normalization to multivariate setting, whitening residuals and standardizing local variance.
result Standardized residuals yield asymptotic conditional coverage under certain distributions.
Study improves conformal prediction for missing covariate data.
problem Uncertainty quantification with missing covariate values.
method Generalized conformalized quantile regression framework, missing data augmentation.
result Improved prediction intervals valid conditionally to missing data patterns.
Study conformal invariants from nodal sets on manifolds with boundary.
problem Understanding conformal invariants from nodal sets and eigenvalues on manifolds with boundary.
method Analysis of conformal covariant operators and eigenvalues on manifolds with boundary.
result Relate Dirichlet and Neumann eigenvalues and apply results to curvature prescription problems.
This research develops prediction sets for regression on manifolds using conformal inference.
problem Prediction sets for regression on manifolds, especially in non-Euclidean spaces.
method Conformal inference principles extended to manifolds, proving asymptotic almost sure convergence.
result Empirical prediction sets on manifolds converge to population counterparts.
We prove an explicit residue formula for a meromorphic continuation of conformally covariant integral operators between differential forms on and on its hyperplane. The results provide a simple and new construction of the conformally covariant differential symmetry breaking operators between differential fo…
We give a complete classification of conformally covariant differential operators between the spaces of -forms on the sphere and -forms on the totally geodesic hypersphere . Moreover, we find explicit formulæ for these new matrix-valued operators in the flat coordinates in terms of basic operators …
We study conformal invariants that arise from functions in the nullspace of conformally covariant differential operators. The invariants include nodal sets and the topology of nodal domains of eigenfunctions in the kernel of GJMS operators. We establish that on any manifold of dimension , there exist many metr…
The paper introduces boundary operators for Poincaré-Einstein manifolds and proves higher order trace inequalities.
problem Proving higher order trace inequalities on Poincaré-Einstein manifolds.
method Introducing conformally covariant boundary operators and using them to set up higher order Dirichlet problems.
result Sharp higher order Sobolev trace inequalities on the ball are obtained.
New method for valid prediction intervals with coarsened data.
problem Handling missing data and censored outcomes in training samples.
method Multiply robust conformal risk control with semiparametric theory.
result Stronger coverage properties under covariate shift.
Weyl-Ambient Geometrieshep-th
Extends Weyl geometry from conformal to Weyl manifolds using ambient metrics.
problem Generalizing ambient constructions to Weyl manifolds.
method Introduces Weyl-ambient metric and Weyl-Fefferman-Graham gauge; shows Weyl-ambient space induces Weyl geometry; defines Weyl-connection and Weyl structure.
result Weyl-ambient construction for Weyl manifolds provides a well-defined initial value problem.