New method defines GCM spheres in Kerr perturbations, proving their stability.
problem Stability of GCM spheres in Kerr perturbations.
method Effective uniformization theorem, canonical definition of ℓ=1 modes, intrinsic existence theorem. result Stability of GCM spheres in Kerr perturbations proven.
This paper constructs GCM hypersurfaces in Kerr spacetimes.
problem Extending the Kerr family stability proof to full stability.
method Concatenating a 1-parameter family of GCM spheres by solving an ODE system.
result Removes symmetry restrictions in GCM procedure.
This the first in a series of papers whose ultimate goal is to establish the full nonlinear stability of the Kerr family for ∣a∣≪m. The paper builds on the strategy laid out in \cite{KS} in the context of the nonlinear stability of Schwarzschild for axially symmetric polarized perturbations. In fact the central id…
DoWhy-GCM extends causal inference in graphical models for diverse queries.
problem Addressing diverse causal queries in graphical causal models.
method Specify cause-effect relations via a causal graph, fit causal mechanisms, pose causal queries.
result Identification of root causes, attribution of causal influences, diagnosis of causal structures.
New method preserves GCM spatial dependencies for better climate projections.
problem Systemic biases in GCM output and loss of spatial/temporal dependencies.
method SPECD approach using Vecchia approximation and semi-parametric quantile regression.
result SPECD preserves key marginal and joint distribution properties of precipitation and temperature.
EnScale learns to downscale climate models efficiently, capturing both spatial and temporal consistency.
problem Downscaling climate models from coarse to high-resolution data is computationally expensive and challenging.
method EnScale uses generative models and proper scoring rules to map GCM data to RCM data, reducing computational cost.
result EnScale achieves competitive performance and computational efficiency in downscaling multiple climate variables.
Paper compares feature selection methods using GCM and LOCO, showing GCM methods generally outperform LOCO.
problem Feature selection and importance estimation in model-agnostic settings.
method Comparison of feature selection methods related to GCM and LOCO under three model settings.
result GCM-related methods generally outperform LOCO under suitable regularity conditions, as shown by theoretical and empirical results.
We consider the pricing of European-style structured credit payoff in a static framework, where the underlying default times are independent given a common factor. A practical application would consist of the pricing of nth-to-default baskets under the Gaussian copula model (GCM). We provide necessary and sufficient co…
This paper corrects climate model biases using a factor model approach.
problem Systematic biases in GCM outputs due to unobserved confounders.
method Factor model approach to learn latent confounders from historical data and apply them to enhance bias correction.
result Significant improvements in the accuracy of precipitation outputs.
CE improves climate uncertainty quantification using GCM ensembles and observational data.
problem Uncertainty in climate projections due to model inadequacies and variability.
method Conformal ensembles integrating GCM ensembles and observational data.
result CE generates statistically rigorous, easy-to-interpret uncertainty estimates.
The methodology of community detection can be divided into two principles: imposing a network model on a given graph, or optimizing a designed objective function. The former provides guarantees on theoretical detectability but falls short when the graph is inconsistent with the underlying model. The latter is model-fre…
AnomalyCD discovers anomaly causes in large systems with binary flags, reducing computational burden.
problem Learning graphical causal models from large-scale binary anomaly data is computationally expensive.
method AnomalyCD uses anomaly data-aware causality testing, sparse data compression, and edge pruning.
result AnomalyCD reduces computation overhead and improves accuracy on binary anomaly datasets.
Statistical downscaling of global climate models (GCMs) allows researchers to study local climate change effects decades into the future. A wide range of statistical models have been applied to downscaling GCMs but recent advances in machine learning have not been explored. In this paper, we compare four fundamental st…
Develops geometric causal models for causal inference from dependent data.
problem Causal inference from structured, dependent data (e.g., spatial, network, molecular).
method Geometric causal models (GCMs) exploiting symmetries of data generating process, combining group theory, ergodic theory, and Bayesian inference.
result Establishes identification and estimation of causal effects from dependent data.
Turaev's shadow formula calculates the SU(2)-Reshetikhin-Turaev-Witten invariants using shadows, and its expression is somehow similar to a Euler characteristic. We give a short proof of this formula using skein theory. The formula applies to pairs (M,G) where M is a closed oriented 3-manifold and GcM is a (possibly em…
This paper proves a canonical foliation on null infinity for Kerr-like black holes.
problem Establishing well-defined physical quantities on null infinity for Kerr-like black holes.
method Existence and uniqueness results for GCM spheres by Klainerman-Szeftel.
result Existence of a canonical foliation on future null infinity with well-defined physical quantities.
Generative model improves wind field downscaling from coarse climate models.
problem Limited spatial resolution and biases in GCMs for wind energy studies.
method SerpentFlow for domain alignment and conditional fine-scale learning.
result Improved spatial coherence, inter-variable consistency, robustness under climate change.
Study combines variational inference and transformers for seasonal climate predictions.
problem Lack of robust seasonal predictions due to limited historical records and computational constraints.
method Combines variational inference with transformer models trained on climate model output.
result Method provides skilful predictions beyond climate change-induced trends in various regions.
A new measure of causal influence quantifies intrinsic contributions in DAGs.
problem Quantifying intrinsic causal contributions in Directed Acyclic Graphs (DAGs).
method Recursive decomposition of node contributions, structure-preserving interventions, Shapley symmetrization.
result A measure of intrinsic causal contribution that is invariant to node relabeling.
ECCIT improves conditional independence tests by calibrating for miscalibration.
problem Inaccurate frequentist guarantees in CITs, especially in small samples and misspecified models.
method Empirically Calibrated Conditional Independence Tests (ECCIT) that optimize and correct for miscalibration.
result ECCIT achieves valid FDR with higher power than existing calibration strategies.
New method selects causal features from diverse data types.
problem Discovering causal relationships from non-continuous data types.
method Transformation-Model (TRAM) based Invariant Causal Prediction (TRAM-ICP) with TRAM-GCM and TRAM-Wald tests.
result Improved power and type I error control for diverse response types.
MinShap improves feature selection accuracy and stability in complex models.
problem Challenging feature selection in unknown non-linear relationships.
method Combines Shapley values with a modified approach to feature selection.
result MinShap outperforms state-of-the-art algorithms in accuracy and stability.
New research finds 145 infinite families of CS spheres are standard.
problem Determining which Cappell-Shaneson spheres are diffeomorphic to the standard 4-sphere.
method Using Kirby calculus and new families of CS spheres.
result Proves 145 new infinite families of CS spheres are standard.
Kervaire's sphere-link is equivalent to a ribbon sphere-link, simplifying complex 2-complexes.
problem Understanding the structure of 2-complexes and their asphericity.
method Using Kervaire's sphere-link and ribbon sphere-link equivalence, analyzing the compact complement of ribbon disk-links.
result Every connected subcomplex of a contractible finite 2-complex is aspherical.
New theory proves infinite homology 3-spheres in homology 4-spheres.
problem Existence of homology 3-spheres in homology 4-spheres.
method Diagrammatics of surface cross sections, Taubes' work.
result Infinite number of homology 3-spheres in homology 4-spheres.
The 3-sphere has either 2 minimal 2-spheres or an optimal foliation by 2-spheres.
problem Proving existence of minimal 2-spheres or optimal foliations in arbitrary Riemannian 3-spheres.
method Analyzing the properties of arbitrary Riemannian metrics on 3-spheres.
result The existence of at least two minimal 2-spheres or an optimal foliation in 3-spheres with arbitrary metrics.
Infinitely many splitting spheres found for unlinked 2-spheres in 4-space.
problem Existence of pairwise non-isotopic splitting spheres for unlinked 2-spheres in 4-space.
method Analytical proof showing non-isotopic spheres.
result Infinitely many non-isotopic splitting spheres found.
Reduces weak reducing pairs to spheres in 3-sphere Heegaard surfaces.
problem Finding reducing spheres for weak reducing pairs in Heegaard surfaces.
method Proves existence of reducing spheres for weak reducing pairs in 3-sphere Heegaard surfaces.
result Reduction of weak reducing pairs to spheres if genus is at most 3.
The study shows how to construct d-spheres from (d−1)-spheres and d-balls without additional vertices.
problem Constructing d-spheres from (d−1)-spheres and d-balls without additional vertices. method Examining specific types of spheres (flag, stacked, join of spheres) and d-balls to determine if constructions can be made without extra vertices. result Affirmative answers to constructing d-spheres from (d−1)-spheres and d-balls without additional vertices for certain types of spheres and d-balls. New proof for sphere recognition algorithm.
problem Sphere recognition algorithm proof.
method New proof of a lemma in Abigail Thompson's algorithm.
result New proof of a lemma in Abigail Thompson's proof of the Recognition Algorithm for 3-spheres.
Proves stability of convex spheres with similar geodesic lengths.
problem Stability of convex spheres with specific geodesic properties.
method Proves C^0 Cheeger-Gromov closeness to the round sphere.
result Strictly convex 2-spheres are close to the round sphere.
Soliton spheres are immersed 2-spheres in the conformal 4-sphere S^4=HP^1 that allow rational, conformal parametrizations f:CP^1->HP^1 obtained via twistor projection and dualization from rational curves in CP^{2n+1}. Soliton spheres can be characterized as the case of equality in the quaternionic Pluecker estimate. A …
Study on sphere immersions and their stability indices.
problem Analyzing the stability of sphere immersions.
method Calculation of Morse indices and stability indices for specific sphere immersions.
result Bounds on stability index of associative cone in R7. The paper constructs biharmonic maps between spheres using polynomial maps.
problem Creating biharmonic maps between spheres.
method Using harmonic homogeneous polynomial maps of different degrees to generate proper biharmonic maps.
result Established a method for constructing proper biharmonic product maps.
Characterizes a specific type of convex curves on a 3-sphere.
problem Understanding convex curves on a 3-sphere.
method Decomposes curves on 3-sphere into 2-sphere curves, characterizes locally convex ones.
result Completely characterized a class of convex curves on the 3-sphere.
Reduces connectivity problem for genus-4 Heegaard surface in 3-sphere.
problem Connectivity problem in reducing sphere complex for genus-4 Heegaard surface.
method Presented a sufficient condition for a non-separating weak reducing pair to be separated by a reducing sphere.
result Reduced connectivity problem to showing disjointness of representative reducing spheres from a fixed disk.
Author provides an alternate proof of the free ribbon lemma.
problem Proving that every free sphere-link in the 4-sphere is a ribbon sphere-link.
method An alternate proof of the free ribbon lemma.
result Provides an alternate proof of the free ribbon lemma.
Paper studies inscribed sphere and lines through centers of Apollonius spheres in n dimensions.
problem Tangency of spheres and lines through their centers.
method Lie sphere geometry and two-step construction of Apollonius spheres.
result Center of inscribed sphere coincides with point PX. Sharp convergence theorem for sphere submanifolds proved.
problem Sphere submanifolds in spheres.
method Proved a sharp convergence theorem.
result New differentiable sphere theorem for submanifolds in spheres.
In the 1-parameter family of Berger spheres S^3(a), a > 0 (S^3(1) is the round 3-sphere of radius 1) we classify the stable constant mean curvature spheres, showing that in some Berger spheres (a close to 0) there are unstable constant mean curvature spheres. Also, we classify the orientable compact stable constant mea…
We introduce and study a new class of homotopy spheres called Farrell-Jones spheres. Using Farrell-Jones sphere we construct examples of closed negatively curved manifolds M2n, where n=7 or 8, which are homeomorphic but not diffeomorphic to complex hyperbolic manifolds, thereby giving a partial answer to a que…
In this paper we show that for m>n the set of cobordism classes of maps from m-sphere to n-sphere is trivial. The determination of the cobordism homotopy groups of spheres admits applications to the covers for spheres.
Study finds infinite families of Sasaki-Einstein metrics on spheres.
problem Finding Sasaki-Einstein metrics on spheres and exotic spheres.
method Analyzing odd-dimensional spheres and exotic spheres that bound parallelizable manifolds.
result Infinitely many families of Sasaki-Einstein metrics on spheres and exotic spheres.
We show that among Seifert fibered integer homology spheres, Poincare sphere (with either orientation) is the only non-trivial example which has trivial Heegaard Floer homology. Together with an earlier result, this shows that if an integer homology sphere has trivial Heegaard Floer homology, then it is a connected sum…
We prove a Reeb sphere theorem for finite simple graphs. The result bridges two different definitions of spheres in graph theory. We also reformulate Morse conditions in terms of the center manifolds, the level surface graphs {f=f(x)} in the unit sphere S(x). In the Morse case these graphs are either spheres, the empty…
Study biharmonic hypersurfaces in spheres, proving unique continuation theorem.
problem Characterize biharmonic hypersurfaces in spheres.
method Prove CMC Unique Continuation Theorem for biharmonic hypersurfaces of spheres.
result Supports the conjecture that biharmonic submanifolds of Euclidean spheres must be of constant mean curvature.
Standard S4 proved to be diffeomorphic to a curious homotopy sphere.
problem Determining the diffeomorphism of a curious homotopy sphere to the standard S4. method Proof based on properties of homotopy spheres and loose corks.
result The curious homotopy sphere is diffeomorphic to the standard S4. Formula derived for discrete improper affine spheres.
problem Constructing discrete improper affine spheres.
method Loop group factorizations and Birkhoff decomposition.
result Representation formula for discrete indefinite affine spheres.