A new STAR framework models integer-valued data with flexible distributions.
problem Modeling integer-valued data with flexibility and accuracy.
method Simultaneously Transforming and Rounding (STAR) a continuous-valued process.
result STAR framework designs a new BART model for integer-valued data with impressive predictive accuracy.
STAR framework reduces OPE variance by distilling complex problems into discrete ARPs.
problem High variance and bias in off-policy evaluation methods.
method STAR framework that includes various OPE estimators and leverages state abstraction.
result Predictions from ARPs estimated from off-policy data are asymptotically correct.
New set-valued star-shaped risk measures introduced for better risk assessment.
problem Improving risk assessment in financial contexts.
method Developed new set-valued star-shaped risk measures and proved their representation theorems.
result Set-valued star-shaped risk measures can be represented as unions of set-valued convex risk measures.
The paper studies dynamic star-shaped risk measures and their representation.
problem Representing dynamic star-shaped risk measures and their properties.
method Representation theorems for dynamic monetary and star-shaped risk measures.
result Dynamic star-shaped risk measures can be represented as the lower envelope of a family of dynamic convex risk measures.
Semiparametric STAR model improves mental health data analysis.
problem Overdispersed, zero-inflated, bounded count data in self-reported mental health surveys.
method STAR transformation and rounding of latent Gaussian model, nonparametric transformation estimation, EM algorithm for maximum likelihood.
result Substantial improvements in goodness-of-fit compared to existing models.
Neural networks can achieve optimal sample complexity for learning single-index models.
problem Achieving optimal computational-statistical tradeoff in learning Gaussian single-index models.
method Unified gradient-based algorithm for training a two-layer neural network, adaptable to various loss and activation functions.
result Sample complexity of d s ⋆ / 2 ∨ d d^{s^\star/2} \lor d d s ⋆ /2 ∨ d matches the SQ lower bound up to a polylogarithmic factor. Paper develops a new method for solving IBVPs on star-shaped domains.
problem Solving Inverse Boundary Value Problems (IBVP) for parallel transport equations.
method Covariant tomography, integrating geometric decomposition with specific interior extensions.
result Formal solvability criterion for higher-order IBVPs, validated through examples.
Introduces Star-Shaped deviation measures for risk analysis.
problem Risk measurement and analysis in finance.
method Characterizes Star-Shaped deviation measures through acceptance sets and convex deviation measures.
result Exposes the relationship between Star-Shaped risk measures and deviation measures.
Efficiently approximates Sparse PCA with significant speedups and minor error.
problem Sparse Principal Component Analysis (Sparse PCA) is NP-hard and computationally expensive.
method Approximates the covariance matrix with block-diagonal form, solves sub-problems in each block, and reconstructs the solution.
result Significant computational speedups with minor additive error.
Develops STC for sequential data with missing labels.
problem Learning from partially labeled and unsegmented sequential data.
method Introduces Star Temporal Classification (STC) using a star token and GTN framework.
result Recover most of supervised baseline performance with up to 70% missing labels.
Enhances GNNs to better capture local graph structures.
problem Limited expressiveness of GNNs due to star-shaped message passing.
method Extends local aggregation to subgraph patterns using GNN encoders.
result Significantly improved performance on graph ML tasks.
Algorithm achieves optimal regret for unknown Lipschitz convex losses.
problem Online learning with unknown Lipschitz constant and target vector norm.
method Develops an online learning algorithm without knowledge of G G G or ∥ w ⋆ ∥ \|w_\star\| ∥ w ⋆ ∥ . result Matches optimal regret bound G ∥ w ⋆ ∥ T G\|w_\star\|\sqrt{T} G ∥ w ⋆ ∥ T up to logarithmic factors. New star-shaped acceptability indexes generalize existing methods.
problem Generalizing existing acceptability measures.
method Characterizing acceptability indexes through star-shaped risk measures and sets.
result Introducing concrete examples linked to various financial measures.
The study optimizes machine learning classifiers for variable stars using CRTS data.
problem Classifying variable stars from CRTS data efficiently and accurately.
method Used multi-class, binary, and hierarchical ML schemes; optimized via cross-validation; applied Information Theory for feature selection.
result Random Forest classifier performs best in CRTS dataset, achieving balanced-accuracy of ~99% for δ δ δ -Scuti and ACEP. Paper proves conjecture about star-shaped curves evolving under GAPF, but not always preserves star shape.
problem What conditions guarantee global existence of Gage's area-preserving flow for nonconvex initial curves?
method Using Dittberner's singularity analysis theory, constructed a ``flying wing'' curve to show limitations.
result Gage's area-preserving flow does not always preserve star-shapedness of evolving curves.
In this article, we introduce the notion of star-Ricci tensors in the real hypersurfaces of complex quadric Q m Q^m Q m . It is proved that there exist no Hopf hypersurfaces in Q m , m ≥ 3 Q^m,m\geq3 Q m , m ≥ 3 , with commuting star-Ricci tensor or parallel star-Ricci tensor. As a generalization of star-Einstein metric, star-Ricci solitons on M M M …
Classifies star products on Lie algebroid duals and extends to projectable quantizations.
problem Classifying and extending quantizations on Lie algebroid duals.
method Classification through second Lie algebroid cohomology, extension to projectable quantizations.
result Quantization commutes with reduction in the considered setting.
This paper connects geometric diagrams to spherical T-duality.
problem Establishing equivalence between geometric and string-theory frameworks.
method Introducing ⋆ \star ⋆ -diagrams and proving their equivalence to spherical T-dual pairs. result Concrete geometric realization of spherical T-duality.
Flow turns star-shaped curves into circles.
problem Transforming star-shaped curves into circles.
method Gage's area-preserving flow.
result Curves evolve into circles over time.
Paper disproves symmetry of stars at infinity in a specific graph.
problem Symmetry of stars at infinity in a specific graph.
method Defined incidence geometry of stars at infinity; provided an example.
result Relation of one boundary point being included in a star of another is not symmetric.
Study star products on Poisson manifolds compatible with reduction.
problem Finding star products compatible with coisotropic reduction.
method Compute second constraint Hochschild cohomology of constraint algebra.
result Determine infinitesimal star products on Poisson manifolds.
Study shows computational and statistical gaps in Gaussian Single-Index Models.
problem Statistical and computational trade-offs in high-dimensional regression problems.
method Analysis of SQ and LDP frameworks, partial-trace algorithm.
result Computational algorithms require significantly more samples than information-theoretic limits.
The paper characterizes dynamic return and star-shaped risk measures via BSDEs.
problem Characterizing dynamic return and star-shaped risk measures.
method Characterization of star-shaped functionals and BSDEs.
result Existence of convex BSDEs with non-empty set of supersolutions.
This work improves Q-learning for average-reward MDPs, reducing sample and communication complexities in federated settings.
problem Improving sample complexity of Q-learning for average-reward MDPs.
method Simple Q-learning algorithm with carefully chosen parameters for both single-agent and federated scenarios.
result Established first federated Q-learning algorithm for average-reward MDPs with provable efficiency in sample and communication complexities.
Deform moment map on symplectic connections using star product algebras.
problem Understanding symplectic connections and their deformations.
method Study vector bundle of Fedosov star product algebras, formal connection, curvature, and star product trace.
result Showed star product trace as a formal symplectic form and moment map.
CasVAE outperforms supervised methods for star-galaxy classification.
problem Challenges in machine learning for astronomy data.
method Cascade Variational Auto-Encoder (CasVAE) for unsupervised star-galaxy classification.
result CasVAE outperforms baseline models in accuracy and stability.
Paper analyzes Birkhoff relaxation for graph alignment, providing theoretical guarantees.
problem Finding vertex correspondence between two graphs to maximize edge overlap.
method Birkhoff relaxation as a convex relaxation of the quadratic assignment problem (QAP).
result Theoretical guarantees on the performance of Birkhoff relaxation under specific conditions.
New partition designs reduce star discrepancy in high-dimensional sampling.
problem Improving the expected star discrepancy in high-dimensional sampling.
method Developed non-equal volume partitions to achieve lower expected star discrepancy.
result Explicit upper bounds for expected star discrepancy under non-equal volume partitions.
Develops a Riemannian archetypal analysis for interpretable non-linear data.
problem Limited performance of classical archetypal analysis on non-linear data.
method Riemannian geometry for data-driven pullback, geodesic convex combinations, convex relaxation followed by non-convex refinement.
result Combines interpretability of classical archetypal analysis with expressive power of modern non-linear models.
Novel Hodge theory developed for Carrollian bundles, addressing black hole event horizons.
problem Developing Hodge theory on Carrollian bundles with degenerate metrics.
method Constructing Hodge star and Laplacian operators on Carrollian R i m e s \mathbb{R}^ imes R i m es -bundles. result Hodge--de Rham Laplacian defined on event horizons of Schwarzschild black holes.
We compare the star surgery operations introduced in [KS] to the generalized rational blow-down. We show that star surgery shares the properties that make rational blow-down useful for constructions of small exotic symplectic 4-manifolds. Then we show that star surgery operations provide a strictly more general class o…
We derive a closed formula for a star-product on complex projective space and on the domain S U ( n + 1 ) / S ( U ( 1 ) × U ( n ) ) SU(n+1)/S(U(1)\times U(n)) S U ( n + 1 ) / S ( U ( 1 ) × U ( n )) using a completely elementary construction: Starting from the standard star-product of Wick type on C n + 1 ∖ { 0 } C^{n+1} \setminus \{ 0 \} C n + 1 ∖ { 0 } and performing a quantum analogue of Marsden-Weinstein reduction, we ca…
Estimates how many times a star appears due to gravitational lensing.
problem Estimating the number of times an observer sees a star due to gravitational lensing.
method Use affine linking numbers to estimate the number of times an observer sees a star.
result Estimates the number of times an observer sees a star due to gravitational lensing.
Improved SGD learning for single index models reduces sample complexity.
problem Learning a single index model with optimal sample complexity.
method Using smoothed loss in online SGD to reduce sample complexity.
result Online SGD with smoothed loss achieves optimal sample complexity of d k ⋆ / 2 d^{k^\star/2} d k ⋆ /2 . The paper finds at least four prime closed characteristics on star-shaped hypersurfaces in 8D space.
problem Finding prime closed characteristics on compact star-shaped hypersurfaces in 8D space.
method Proved existence of at least four prime closed characteristics for non-degenerate C 3 C^3 C 3 compact star-shaped hypersurfaces in R 8 \mathbb{R}^{8} R 8 without prime closed characteristics of Maslov-type index -1. result Existence of at least four prime closed characteristics on compact star-shaped hypersurfaces in R 8 \mathbb{R}^{8} R 8 . This paper connects monetary and star-shaped risk measures by showing their equivalence under certain conditions.
problem Understanding the relationship between monetary and star-shaped risk measures.
method Analyzing the acceptability of 0 and the normalization property.
result Monetary risk measures are only a translation away from star-shapedness under mild conditions.
The paper proves inequalities for star-shaped and F F F -mean convex hypersurfaces in R n + 1 \mathbb{R}^{n+1} R n + 1 .
problem Proving geometric inequalities for specific types of hypersurfaces.
method Using anisotropic p p p -momentum, perimeter, and volume, the paper derives inequalities for star-shaped and F F F -mean convex hypersurfaces. result The Wulff shape of F F F is the unique minimizer of the corresponding functionals among all star-shaped and F F F -mean convex sets. HyperAgent improves RL exploration in large-scale problems.
problem Efficient exploration in large-scale reinforcement learning problems.
method Hypermodel framework for incremental posterior approximation without conjugacy.
result HyperAgent achieves logarithmic per-step computational complexity and sublinear regret.
We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points in the family. This generalizes the formal Hitchin connection introduced by the first author. We establish a necess…
Constructs non-unital monoidal category of contact manifolds and Legendrian correspondence calculus
problem Constructing a non-unital monoidal category of contact manifolds without contact forms
method Developing contact topology without contact forms and defining the star product
result Proving the associativity of the star product and the pentagon axiom
Parallelizes DEC on curved meshes using group actions.
problem Efficiently solving DEC operators on curved and 3D meshes.
method Universal block-diagonalization framework for d d d and ⋆ \star ⋆ operators, exploiting group actions. result Block-diagonal structure inherited by operators, enabling parallel solvers.
The paper characterizes law-invariant star-shaped risk measures.
problem Understanding and characterizing law-invariant star-shaped risk measures.
method Developed characterizations for positively homogeneous and star-shaped functionals, derived Kusuoka-type representations, and offered representations of general law-invariant star-shaped functionals.
result Characterizations of law-invariant star-shaped functionals, including their connections to Value-at-Risk and Expected Shortfall.
Sharp inequalities for star bodies in 2D space.
problem Understanding star bodies in 2D space.
method Sharp inequalities for star bodies in R 2 \mathbb{R}^2 R 2 . result New inequalities and proofs for star bodies.
The study counts geodesics on curved surfaces with specific intersections.
problem Counting geodesics with exact intersection numbers on curved surfaces.
method Introduced a dynamical scattering operator and used Pollicott-Ruelle resonances.
result Asymptotic growth of geodesics with prescribed intersections.
Introduces Star-Shaped DDPMs for non-Gaussian distributions.
problem Difficulties in defining DDPMs for non-Gaussian distributions.
method Star-shaped diffusion process, duality with specific Markovian diffusions, efficient algorithms.
result SS-DDPMs can model distributions like Beta, von Mises-Fisher, Dirichlet, Wishart.
Study tunnel numbers of cable knots and their companions, proving new bounds and constructing examples.
problem Understanding the relationship between the tunnel numbers of a knot and its cable.
method Combinatorial techniques and analysis of Heegaard splittings.
result Proves that for many cases, the tunnel number of a cable knot equals the original knot's tunnel number plus one.
The paper generalizes convex and star-shaped concepts to symplectic spaces and studies variational problems.
problem Generalizing convex and star-shaped concepts to symplectic vector spaces.
method Study of variational problems for symplectically convex and star-shaped curves.
result Extremal points of the variational problem are rigid multiply traversed conics for a range of parameters.
Proposes a probabilistic framework for smart contract risk quantification.
problem Quantifying financial risk of smart contract cyber attacks and failures.
method Probabilistic graph-theoretical framework using bond percolation models.
result Analytical results and numerical examples for aggregate loss distribution.