Study shows stability of locally conformally balanced condition under modifications but not under small deformations.
problem Stability of locally conformally balanced condition under small deformations and modifications.
method Proved stability under proper modifications and instability under small deformations using examples and Hilbert-Chow map.
result Stability of locally conformally balanced condition under proper modifications and instability under small deformations.
Study locally conformally balanced metrics on specific Lie algebras.
problem Characterize and classify locally conformally balanced metrics on almost abelian Lie algebras.
method Characterizations and classifications based on specific properties of Lie algebras.
result Classification of six-dimensional almost abelian Lie algebras with locally conformally balanced metrics.
Study non-Kähler metrics on complex nilmanifolds, proving torus structure under certain conditions.
problem Understanding special non-Kähler metrics on complex nilmanifolds.
method Analyzing locally conformally Kähler, k-Gauduchon, balanced, and locally conformally balanced metrics on compact complex manifolds. result Compact complex nilmanifolds with balanced or k-Gauduchon metrics are tori, extending previous results. Flow of conformally balanced metrics converges on Kahler manifolds.
problem Non-Kahler geometry and its relation to string theory.
method Anomaly flow, convergence proof on Kahler manifolds.
result Flow converges on Kahler manifolds for suitable initial data.
Flow stabilizes on non-Kähler metrics near Calabi-Yau.
problem Stability of conformally balanced metrics flow near Calabi-Yau manifolds.
method Proving stability of the anomaly flow around Calabi-Yau metrics.
result The flow can converge on non-Kähler metrics near Calabi-Yau.
Study on balanced Hermitian structures on Lie algebras twisted by representations.
problem Conditions for balanced and locally conformally balanced Hermitian structures on Lie algebras.
method Analysis of Hermitian structures on twisted cartesian products of Lie algebras.
result Classification of six-dimensional balanced Hermitian twisted cartesian products Lie algebras.
The paper solves a problem related to curvature in complex geometry.
problem Resolving the prescribed Chern scalar curvature problem.
method Divided into three cases based on the sign of the Gauduchon degree, analyzed separately.
result Proves that certain functions are Chern scalar curvatures of conformal metrics.
Proposes SCD-split for CP to balance interpretability and efficiency.
problem Difficult interpretation of disconnected subintervals in CP prediction sets.
method Incorporates smoothing operations into CP framework.
result SCD-split balances interval length and subinterval number, theoretically provable.
Characterizes complex Finsler metrics and their properties.
problem Characterize complex Finsler metrics and their geometric properties.
method Defined the canonical connection and investigated holomorphic sectional curvature tensors and Ricci curvatures.
result Characterizes balanced complex Finsler metrics and provides sufficient and necessary conditions.
The abstract discusses conjectures about metrics on complex manifolds.
problem The abstract tackles the conjectures about metrics on complex manifolds, specifically balanced, SKT, and LCK.
method The abstract uses complex Hermitian manifolds, closed 1-forms, and conjectures to explore these metrics.
result The abstract verifies a conjecture about the Bott--Chern homology for all known classes of LCK manifolds.
Procedure confirms covariate balance anytime from unlabeled data.
problem Ensuring covariate balance in sequential data.
method Time-uniform confidence sequences for continuous monitoring.
result Probability of false confirmation controlled.
Study balanced Hermitian structures on almost abelian Lie algebras, classifying six-dimensional cases.
problem Classify balanced Hermitian structures on almost abelian Lie algebras.
method Classify six-dimensional almost abelian Lie algebras with balanced structures, investigate flow of balanced metrics and anomaly flow.
result Prove conjecture for compact almost abelian solvmanifolds with left-invariant complex structures.
Classifies Kähler structures with special foliations using symplectic techniques.
problem Classifying Kähler structures with specific foliations.
method Weinstein's method of constructing symplectic bundles applied to Kähler data.
result New Kähler structures and metrics are obtained.
A novel clustering method uses torque balance to group objects.
problem Grouping similar objects in various scientific fields.
method Inspired by gravitational interactions, a parameter-free clustering algorithm based on mass and distance.
result The algorithm effectively clusters objects regardless of their shape, size, or density.
Survey of recent geometric flows in complex geometry.
problem Preserving conformally balanced property of Hermitian metrics.
method Anomaly flow, a flow of (2,2)-forms on a 3-fold. result Anomaly flow is a higher order extension of the Ricci flow.
New boundary and point constraints for controlling conformal surfaces.
problem Controlling the geometry of surfaces defined by minimizers of conformal variational problems.
method Introducing new boundary conditions, point constraints, and flux constraints to control the metric and conformal scale factor.
result Introduces intuitive controls for exploring a subspace of conformal immersions.
A Hermitian metric on a complex manifold of complex dimension n is called {\em astheno-Kähler} if its fundamental 2-form F satisfies the condition ∂∂Fn−2=0. If n=3, then the metric is {\em strong KT}, i.e. F is ∂∂-closed. By using blow-ups and the …
We show that holographic renormalization of relativistic gravity in asymptotically Lifshitz spacetimes naturally reproduces the structure of gravity with anisotropic scaling: The holographic counterterms induced near anisotropic infinity take the form of the action for gravity at a Lifshitz point, with the appropriate …
Proposes BCOPS for balanced and outlier detection in multi-class classification.
problem Classification problems with different training and test distributions.
method BCOPS combines supervised learning with conformal prediction to optimize out-of-sample performance and detect outliers.
result BCOPS constructs prediction sets with finite-sample coverage guarantees and outlier detection rate estimation.
Paper constructs solutions to a system using Aeppli class without auxiliary gauge connection.
problem Constructing solutions to the Hull-Strominger system without auxiliary gauge connection.
method Deforming conformally balanced metric and tuning by Aeppli class to satisfy anomaly cancellation condition.
result Existence of family of solutions obtained via implicit function theorem.
Locally conformal SKT structures are introduced and studied on Lie groups and their compact quotients.
problem Existence and classification of LCSKT structures on Lie groups and their quotients.
method Introducing LCSKT structures and studying their properties on Lie groups and their quotients.
result Existence of non-trivial LCSKT structures on 6-dimensional nilpotent Lie algebras and almost abelian Lie algebras.
Study shows compact Vaisman manifolds cannot have certain special Hermitian metrics.
problem Compact Vaisman manifolds and their compatibility with special Hermitian structures.
method Proof of non-existence of specific Hermitian metrics on compact Vaisman manifolds.
result Compact Vaisman manifolds cannot admit special Hermitian metrics like special k-Gauduchon metrics or pluriclosed metrics. Using Traizet's regeneration method, we prove the existence of many new 3-dimensional families of embedded, doubly periodic minimal surfaces. All these families have a foliation of 3-dimensional Euclidean space by vertical planes as a limit. In the quotient, these limits can be realized conformally as noded Riemann sur…
CIR method constructs efficient prediction intervals with guaranteed coverage.
problem Efficiently constructing near-minimal prediction intervals with guaranteed coverage.
method Conditional Interquantile Regression (CIR) and CIR+ (enhanced version).
result Optimal balance between predictive accuracy and computational efficiency.
CPATTA uses conformal prediction for efficient test-time adaptation.
problem Low data selection efficiency in existing ATTA methods.
method Conformal Prediction, online weight-update algorithm, domain-shift detector, staged update scheme.
result CPATTA consistently outperforms state-of-the-art methods by 5% in accuracy.
Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant complex structure J and compatible metric g, which is not required to be invariant. We give classifications of 6-dimensional nilmanifolds M admitting strong Kähler with torsion, balanced or locally conformal Kähler structures (J,g).
Compact complex manifolds get special metrics that minimize a functional.
problem Finding special metrics on compact complex manifolds.
method Finite dimensional approximations and generalized balanced metrics.
result Special metrics minimize a modified Mabuchi functional.
The paper analyzes systoles of complex projective spaces under various metrics.
problem Behavior of systoles in complex projective spaces for different metrics.
method Integral geometric techniques and careful analysis of systole functional.
result Balanced metrics locally minimize the systole on volume-normalized metrics.
Unified flow approach to curvature problem on specific manifolds.
problem Prescribed Chern scalar curvature problem on compact Hermitian manifolds with negative Gauduchon degree.
method Unified flow approach with conditions on curvature function f. result Flow converges to a conformal Hermitian metric with specified curvature.
New research confirms conjecture for balanced BTP 4-folds.
problem Constant holomorphic sectional curvature in non-Kähler geometry.
method Classification and analysis of balanced BTP manifolds.
result Conjecture holds for all balanced BTP 4-folds.
LOO-StabCP speeds up CP for multiple predictions.
problem Balancing computational efficiency and prediction accuracy in CP.
method Leave-One-Out Stable Conformal Prediction (LOO-StabCP) using algorithmic stability.
result LOO-StabCP is faster and more accurate than RO-StabCP.
Two-step conformal prediction method for adaptive bounding box uncertainties in multi-object detection.
problem Quantifying predictive uncertainty for multi-object detection in safety-critical applications.
method Developed a two-step conformal prediction approach to propagate uncertainty in predicted class labels into bounding box uncertainties, ensuring coverage for incorrectly classified objects.
result Desired coverage levels are satisfied with practically tight predictive uncertainty intervals on real-world datasets.
Study of complex structures on specific solvmanifolds, proving existence and non-existence results.
problem Classification and properties of complex structures on six-dimensional solvmanifolds.
method Classification of Lie algebras, analysis of complex structures, study of Hermitian metrics.
result Determination of new balanced solvmanifolds and confirmation of conjectures.
A new method for predicting uncertainties in stream networks.
problem Uncertainty quantification in spatiotemporal graphs with directional flow constraints.
method Spatio-Temporal Adaptive Conformal Inference (STACI) integrating network topology and temporal dynamics.
result STACI effectively balances prediction efficiency and coverage, outperforming existing methods.
Consider E a holomorphic vector bundle over a projective manifold X polarized by an ample line bundle L. Fix k large enough, the holomorphic sections H0(E⊗Lk) provide embeddings of X in a Grassmanian space. We define the \textit{balancing flow for bundles} as a flow on the space of projectively equ…
Develops a two-stage conformal prediction method for Parkinson's disease medication needs.
problem Heterogeneous disease progression and treatment response in Parkinson's Disease.
method Two-stage conformal prediction framework with statistical guarantees.
result Quantifies uncertainty in medication needs predictions, improving clinical trust and quality of life.
Conformal-DP improves differential privacy on manifold data by calibrating perturbations based on local densities.
problem Lack of density-awareness in existing differential privacy mechanisms for manifold data leads to biased and suboptimal privacy-utility trade-offs.
method Proposes Conformal-DP, a density-aware differential privacy mechanism using conformal transformations to calibrate perturbations based on local densities.
result Demonstrates improved privacy-utility trade-off in heterogeneous data distribution settings compared to state-of-the-art mechanisms.
New approach to fairness in machine learning models using conformal prediction.
problem Fairness in machine learning models' downstream decision-making.
method Theoretical derivation and empirical evaluation of label-clustered conformal prediction.
result Label-clustered conformal prediction often provides a favorable balance between utility and substantive fairness.
PH-CS selects test inputs with reliability guarantees, adapting FDR to data.
problem Fixed FDR limits adaptability to downstream needs.
method Post-hoc conformal selection with e-variables, e-BH procedure.
result PH-CS provides reliable FDP estimates and competitive FDR control.
CTI produces efficient prediction intervals with guaranteed coverage.
problem Efficient and reliable uncertainty quantification in regression.
method CTI estimates conditional density for interval length, then thresholds intervals based on this density.
result CTI achieves smaller prediction sets with guaranteed coverage compared to existing methods.
The study explores metrics with constant curvature on compact manifolds.
problem Finding Hermitian metrics with constant second scalar curvature on compact manifolds.
method Analyzes Yamabe-type and elliptic equations, derives geometric consequences, and proves existence under specific curvature conditions.
result Under certain curvature conditions, a pluriclosed Gauduchon Hermitian metric has constant second Chern scalar curvature, leading to the existence of Kähler-Einstein metrics.
CPPS selects portfolios using conformal prediction for better returns.
problem Optimizing portfolio returns with predictive models and uncertainty.
method Conformal prediction framework for portfolio selection.
result CPPS outperforms simpler strategies in delivering superior returns.
Develops a new representation for constant mean curvature surfaces in hyperbolic 3-space.
problem Finding conformal immersions of constant mean curvature in hyperbolic 3-space.
method Uses a Weierstrass-Kenmotsu type representation based on the Hermitian model, balanced spectral deformation, and Iwasawa splitting of $\SL$.
result Establishes an explicit correspondence with Aiyama and Akutagawa's representation and interprets the construction in terms of Kokubu's adjusted normal Gauss map.
Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh st…
The paper explores Hermitian structures on tangent bundles of affine manifolds with Riemannian metrics.
problem Understanding Hermitian structures on tangent bundles of affine manifolds.
method Analyzes the conditions for various generalized Kähler conditions on (TM,J1,g1) and (TkM,Jk,gk). result Develops a machinery to construct generalized Kähler manifolds.
This paper applies Thompson Sampling to asymmetric α-stable bandits for financial and wireless data.
problem Optimizing exploration-exploitation in multi-armed bandits with asymmetric α-stable distributions. method Thompson Sampling applied to unknown asymmetric α-stable reward distributions. result Demonstrates effectiveness of Thompson Sampling for asymmetric α-stable bandits. We give a procedure for constructing an 8n-dimensional HKT Lie algebra starting from a 4n-dimensional one by using a quaternionic representation of the latter. The strong (respectively, weak, hyper-Kähler, balanced) condition is preserved by our construction. As an application of our results we obtain a new compact…
New framework calibrates decision robustness using inverse conformal risk control.
problem Inadequate robustness levels in decision-making due to ad hoc choices.
method Constructs valid estimators to trace miscoverage-regret Pareto frontier.
result Provides distribution-free, finite-sample guarantees on robustness levels.