The paper studies maps from pseudo-Hermitian to Kähler manifolds, proving harmonic map properties.
problem Analyzing maps between pseudo-Hermitian and Kähler manifolds.
method Investigates partial energy functionals and critical maps, proving foliated results for ∂b- and ∂b-harmonic maps. result Generalizes Siu's holomorphicity result to ∂b- and ∂b-harmonic maps. Paper tackles distribution matching by partially matching distributions, achieving robust results.
problem Robustly aligning two probability distributions.
method Developed a partial Wasserstein adversarial network (PWAN) to efficiently approximate the partial Wasserstein-1 (PW) discrepancy.
result The PWAN effectively produces highly robust matching results, outperforming state-of-the-art methods.
Study partially hyperbolic diffeomorphisms on 3-manifolds, proving some classification results.
problem Classifying partially hyperbolic diffeomorphisms on 3-manifolds.
method Detailed proofs of results on partially hyperbolic diffeomorphisms on 3-manifolds, focusing on dynamically coherent cases.
result Some results towards the classification of partially hyperbolic diffeomorphisms on 3-manifolds.
The paper proves a property of complex geometry under transformations.
problem The ∂∂-lemma property in complex geometry. method Simple proof using a blow-up formula and morphism.
result Heredity and bimeromorphic invariance of the ∂∂-lemma property. Unique continuation for X-ray transforms of one-forms with partial data.
problem Proving unique continuation for X-ray transforms of one-forms with limited data.
method Proved unique continuation for the normal operator of X-ray transforms of one-forms, leading to partial data results.
result Unique continuation for X-ray transforms of one-forms with partial data.
The paper studies deformations of Calabi-Yau manifolds using Gauduchon metrics.
problem Deformations of Calabi-Yau manifolds under co-polarised conditions.
method Analyzes local deformations of Calabi-Yau ∂∂ˉ-manifolds using Gauduchon metrics and constructs a new hp-HS form. result Proves the p-SKT h-∂∂ˉ-property is deformation open. New method stabilizes quantum ergodicity for mixed quantization and partial hyperbolicity.
problem Stabilizing quantum ergodicity for complex systems.
method Combines mixed quantization techniques with stable ergodicity results for partially hyperbolic systems.
result Establishes stable quantum ergodicity for spin Hamiltonians.
Prove strong ribbon concordance induces a partial order on links, certify minimality for a handful of knots, and find minimal ribbon minimal knots.
problem Prove strong ribbon concordance induces a partial order on links.
method Use results from knot Floer homology to certify minimality under the ribbon partial order.
result Certify minimality for a handful of knots and find minimal ribbon minimal knots.
We consider a financial market model with a single risky asset whose price process evolves according to a general jump-diffusion with locally bounded coefficients and where market participants have only access to a partial information flow. For any utility function, we prove that the partial information financial marke…
Partial coverings of hyperbolic surfaces equidistribute with geodesics.
problem Equidistribution of partial coverings defined from geodesics.
method Sequence of geodesics equidistributing in unit tangent bundle implies equidistribution of associated partial coverings.
result Partial coverings equidistribute with a sequence of geodesics.
Partial covariance factorizes in path diagrams, simplifying analysis.
problem Understanding partial covariance in complex diagrams.
method Factorization of partial covariance over nodes and edges.
result Simpson's paradox cannot occur in singly-connected diagrams.
In this paper we prove that, in the category of chain complexes, partial algebras can be functorially replaced by quasi-isomorphic algebras. In particular, partial algebras contain all of the important homological and homotopical information that genuine algebras do. Applying this result to McClure's partial algebra in…
The Hodge-de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study some related results concerning a class of partial differential equation in a nove…
IDS algorithm optimizes sequential decisions in various monitoring settings.
problem Optimizing sequential decisions in complex monitoring scenarios.
method Information-directed sampling (IDS) algorithm for linear partial monitoring.
result IDS achieves nearly worst-case rate optimality in finite-action games.
Extends Brouwer fixed point theorem with new conditions for continuous maps.
problem Existence of fixed points for continuous maps from an n-ball to itself.
method Using absolute retracts and blockading sets, and degree theory.
result Existence of fixed points under specific conditions.
Ergodicity proven for certain hyperbolic 3-manifold diffeomorphisms.
problem Proving ergodicity for conservative partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds.
method Analyzing accessibility and deducing ergodicity from conservative C1+ partially hyperbolic diffeomorphisms. result Ergodicity of conservative C1+ partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds. 3-manifold curvature comparison with rotationally symmetric bodies.
problem Comparing scalar curvature of 3-manifolds with rotationally symmetric boundaries.
method Inspired by Gromov, comparing mean curvatures and induced metrics.
result Flatness of 3-manifolds under certain curvature conditions.
New concept of partial comonotonicity connects riskmetrics and dependence.
problem Understanding and quantifying risk metrics under partial comonotonicity.
method Developed a new notion of partial comonotonicity and established its connection to distortion riskmetrics.
result Partial comonotonicity uniquely characterizes a class of distortion riskmetrics through additivity.
Defines tangent spaces on causal sets using partial derivatives and metrics.
problem Defining geometric structures on causal sets.
method Using partial derivatives and metrics to define tangent spaces, connection, curvature, parallel transport, and geodesics.
result Approaches expected values for a flat spacetime as density increases.
Proves well-posedness of mixed Robin boundary value problem on manifolds with bounded geometry.
problem Well-posedness of mixed Robin boundary value problem on manifolds with boundary and bounded geometry.
method Analyzes operators on sections of a vector bundle with bounded geometry, proving regularity and well-posedness in Sobolev spaces.
result Main result is well-posedness in Sobolev spaces Hs(M;E) for s≥0 on non-compact manifolds. New methods compute partial dependence curves directly from data.
problem Limited accessibility and interpretability of partial dependence curves.
method Developed methods for numerical and categorical variables, directly from training data.
result Our methods provide a direct estimate of partial dependence without fitting models.
Classifies 3D partially hyperbolic systems, proving ergodicity.
problem Ergodicity of partially hyperbolic diffeomorphisms in 3-manifolds.
method Topological classification, Anosov flows, foliations, Gromov hyperbolicity.
result Complete answer to Hertz-Hertz-Ures conjecture for 3D systems.
Study off-policy evaluation in partially observable environments, reducing bias and errors.
problem Bias and large errors in off-policy evaluation for partially observable environments.
method Defined and solved off-policy evaluation for POMDPs, introduced Decoupled POMDP model.
result Demonstrated and compared off-policy evaluation methods, showing benefits of new approach.
New theorems on Hodge numbers and Kähler structures derived from complex differential forms.
problem Deformation invariance and local stability of Hodge numbers and Kähler structures.
method Using the exponential operator and power series method, the approach focuses on d-closed extensions and foliated cases. result Local stabilities of transversely p-Kähler structures and new theorems on Hodge numbers. The paper explores partial identifiability in nonnegative matrix factorization under specific conditions.
problem Identifying specific columns of the matrices in nonnegative matrix factorization.
method Mathematical rigor and geometric interpretation to analyze partial identifiability of columns in nonnegative matrix factorization.
result The partial uniqueness of a single column of C or S can be guaranteed under certain sparsity and algebraic conditions. Compute Dolbeault and Bott-Chern cohomologies of complex solvmanifolds.
problem Compute cohomologies of complex solvmanifolds.
method Build finite-dimensional double subcomplexes and decompose them into indecomposable ones.
result Characterize the ∂∂ˉ-Lemma property and compute triple ABC-Massey products. The paper studies the invertibility of the Laplacian on manifolds with boundary and bounded geometry.
problem When is the Laplace-Beltrami operator invertible on manifolds with boundary and bounded geometry?
method The study considers manifolds with boundary and bounded geometry, proving a Poincaré inequality and using it to show the invertibility of the Laplacian under certain conditions.
result The Laplace-Beltrami operator is invertible for manifolds with finite width and mixed boundary conditions.
An differential field (F;∂1,...,∂m) of characteristic zero, a subgroup H of affine group GL(n,C)∝Cn with respect to its identical representation in Fn and the following two fields of differential rational functions in x=(x1,x2,...,xn)-column vector, $$C< x, \partial >^H=\{f^{\part…
The paper introduces a new class of manifolds based on the Hodge decomposition and spectral sequences.
problem Characterizing and understanding new classes of compact complex manifolds.
method Introducing a new class of page-r-∂∂ˉ-manifolds and using spectral sequences. result Characterized and provided examples of the new class of manifolds.
Study area-minimizing currents with specific boundary properties.
problem Understanding the structure of area-minimizing currents with tangentially immersed boundaries.
method Analyzes n-dimensional area-minimizing currents with boundary constraints. result Near the boundary of the current, the structure is either uncontrolled or a union of controlled hypersurfaces.
The Kazdan-Warner problem is solved for Riemann surfaces with smooth boundaries.
problem Realizing smooth functions as Gaussian and geodesic curvatures on compact Riemann surfaces.
method Existence results of Brezis-Merle type equations and uniformization theorem extension.
result Any smooth function on compact Riemann surface with smooth boundary can be realized as a Gaussian curvature function and any on the boundary as a geodesic curvature function.
Partial boundary regularity for area-minimizing currents at tangential boundary points.
problem Boundary regularity of co-dimension one area-minimizing currents.
method Proof closely follows Hardt and Simon's boundary regularity result.
result Partial regularity of tangent cones, uniqueness of tangent cone.
Consistent partial identification of causal effects proved for neural models.
problem Consistency of neural causal partial identification methods.
method Proving consistency for neural models with continuous and categorical variables, considering architecture design and Lipschitz regularization.
result Proven consistency of partial identification via neural causal models in a general setting.
Research on mixed polynomials, extending non-degeneracy concepts to complex variables.
problem Extending non-degeneracy concepts to mixed polynomials in complex variables.
method Generalization of Mondal's partial non-degeneracy to mixed polynomials, introducing new concepts and proving properties.
result Strong partial non-degeneracy implies isolated singularities, and mixed polynomials that are strongly inner non-degenerate satisfy the strong Milnor condition.
Paper explores VRM for PSMLC with partially labeled medical images.
problem Improving PSMLC with limited labeled data.
method Applies VRM to PSMLC for better model performance.
result VRM improves PSMLC performance with partial labels.
Paper introduces a new test for conditional independence using weighted partial copulas.
problem Testing conditional independence between variables.
method The approach uses a weighted partial copula function and a bootstrap procedure to compute regions of rejection.
result The proposed test has competitive power compared to existing methods.
Clarifies when certain stochastic PDEs have affine solutions.
problem Existence of affine realizations for semilinear SPDEs driven by Lévy processes.
method Analyzes conditions for affine solutions to SPDEs driven by Lévy processes.
result Conditions for the existence of affine realizations are established.
Improved 3D scene understanding from partial point sets using multiview fusion.
problem Challenging task of 3D scene semantic understanding from partial point clouds.
method Multiview representation of 360° point clouds and fusion with original data.
result Overall increase of 31.9% and 4.3% in segmentation accuracy for partial and complete scenes.
We study smooth {\sf traversing} vector fields v on compact manifolds X with boundary. A traversing v admits a Lyapunov function f:X→R such that df(v)>0. We show that the trajectory spaces T(v) of {\sf traversally generic} v-flows are {\sf Whitney stratified spaces}, and thus admit tr…
Proposes a new Armijo's condition for general functions and provides an algorithm for its application.
problem Finding suitable step sizes for general functions in optimization.
method Introduces a coordinate-wise Armijo's condition and provides an algorithm to find suitable step sizes.
result Proves convergent results for various functions using the proposed algorithm.
In this paper we first consider the Hamiltonian action of a compact connected Lie group on an H-twisted generalized complex manifold M. Given such an action, we define generalized equivariant cohomology and generalized equivariant Dolbeault cohomology. If the generalized complex manifold M satisfies the $\bar{\pa…
The paper examines partial regularity of Lipschitz solutions to minimal surface system.
problem Understanding the regularity of solutions to the minimal surface system.
method Investigation of stationary, integral weak, and viscosity solutions; interior gradient estimate using maximum principle.
result Partial regularity results for Lipschitz solutions, including interior gradient estimate.
Improved algorithm for partial recovery of tree-structured graphs with noisy data.
problem Learning Ising tree models with noisy observations.
method Symmetrized Geometric Averaging (SGA) algorithm with improved sample complexity.
result Significantly better sample complexity for partial tree recovery.
This study uses partially annotated data to improve TempRel extraction.
problem Lack of fully annotated data for TempRel extraction makes the task labor-intensive and limited in coverage.
method Utilizes partially annotated data (P) for TempRel extraction, even when annotations are missing.
result Partially annotated data (P) can still be a useful supervision signal for TempRel extraction within a constrained learning framework.
Maps from the hyperbolic plane to CAT(-1) spaces are induced by isometries if they respect cross ratios asymptotically.
problem Understanding when maps from the hyperbolic plane to CAT(-1) spaces are induced by isometries.
method Generalizing Bourdon's result to the hyperbolic plane, considering asymptotically Moebius maps and their limits.
result There exists a sequence of isometries and a limit map that induces an isometric embedding of the hyperbolic plane into the CAT(-1) space.
In this paper we consider the lens rigidity problem with partial data for conformal metrics in the presence of a magnetic field on a compact manifold of dimension ≥3 with boundary. We show that one can uniquely determine the conformal factor and the magnetic field near a strictly convex (with respect to the magne…
This work characterizes reward function partial identifiability and its impact on policy optimization.
problem Reward function partial identifiability in complex tasks.
method Formal characterisation of partial identifiability using various reward learning data sources.
result Unified framework for comparing data sources and downstream tasks by their invariances.
Paper proposes methods for estimating partially ranked data with graph regularization.
problem Estimating parameters for partially ranked data with missing data.
method Graph regularization in conjunction with Expectation-Maximization algorithm.
result The proposed estimators work well under non-ignorable missing mechanisms.