Geometrically realizes Khovanov homology for semiadequate links.
problem Computing Khovanov homology for semiadequate links.
method Introducing partial presimplicial sets and their geometric realization.
result Concrete formula for homotopy type of geometric realization.
Differential structure on partial isometries over Grassmannian constructed.
problem No specific problem stated; abstract focuses on method and result.
method Construction of differential structure on partial isometries over restricted Grassmannian.
result Set of partial isometries over restricted Grassmannian becomes a Banach Lie groupoid.
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.
In this paper, we study CAT(0) groups and Coxeter groups whose boundaries are scrambled sets. Suppose that a group G acts geometrically (i.e. properly and cocompactly by isometries) on a CAT(0) space X. (Such group G is called a {\it CAT(0) group}.) Then the group G acts by homeomorphisms on the boundary $\part…
We characterize value functions in partially observable MDPs as semi-algebraic sets.
problem Understanding feasible value functions in partially observable Markov decision processes.
method Characterization of feasible value functions as semi-algebraic sets defined by polynomial inequalities.
result The feasible set of value functions in POMDPs is a semi-algebraic set, not a polytope as in MDPs.
Ribbon cobordisms form a partial order on 3-manifolds.
problem Understanding the partial order structure of 3-manifolds.
method Building on Agol's proof for knots, we extend the partial order to 3-manifolds.
result Ribbon rational homology cobordism forms a partial order.
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.
New protocol for online learning with partial feedback, extending classical methods.
problem Learning with partial feedback where only one acceptable label is observed per round.
method Introducing a collection version space to address the lack of direct extension of classical methods.
result Characterization of learnability in set-realizable regime using Partial-Feedback Littlestone dimension and Partial-Feedback Measure Shattering dimension.
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.
In this paper, we investigate the fixed-point set of an element of a CAT(0) group in its boundary. Suppose that a group G acts geometrically on a CAT(0) space X. Let g∈G and let Fg be the fixed-point set of g in the boundary ∂X. Then we show that Fg=L(Zg), where Zg is …
Introduces three types of partial bihamiltonian structures.
problem None explicitly stated; focuses on definitions and geometrical objects.
method Definition and study of geometrical objects linked with partial bihamiltonian structures.
result Examples of partial bihamiltonian structures in finite and infinite dimensions.
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.
We fully describe the horofunction boundary ∂hL2 with the word metric associated with the generating set {t,at} (i.e the metric arising in the Diestel-Leader graph DL(2,2)). The visual boundary ∂∞L2 with this metric is a subset of ∂hL2. Although $\partial_\infty L_2…
New algorithm minimizes expert selection regret in partial bandit feedback.
problem Minimizing expert selection regret in partial bandit feedback.
method Develops a sequential minimax optimal algorithm for a generalized partial monitoring setting.
result Second order regret bounds against a general expert selection sequence.
Proposes a method to create predictive sets from partially labeled data.
problem Efficiently using weakly supervised data for structured prediction tasks.
method Introduces probe functions and a false discovery proportion-type loss.
result Validates the effectiveness of the proposed predictive set construction.
We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting of the analysis to stochastic partial differential equations. Considering mainly …
Study on Hausdorff dimension of lamination endpoints for fully irreducible automorphisms.
problem Hausdorff dimension of lamination endpoints for fully irreducible automorphisms of free groups.
method Analysis of attracting laminations and ending laminations, using properties of hyperbolic surfaces and free-by-cyclic groups.
result For fully irreducible automorphisms, the set of endpoints of the ending lamination has Hausdorff dimension 0.
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.
Study expands multiclass classification models with new rates and partial concept classes.
problem Multiclass classification with a bounded number of labels under various conditions.
method Extends traditional PAC model to distribution-dependent and data-dependent learning rates, characterizes optimal rates for universal and partial concept classes.
result Characterizes three types of learning rates (exponential, linear, arbitrarily slow) for fixed distributions and complexity measures for partial concept classes.
For a Riemannian manifold (M,g) with strictly convex boundary ∂M, the lens data consists in the set of lengths of geodesics γ with endpoints on ∂M, together with their endpoints (x−,x+)∈∂M×∂M and tangent exit vectors (v−,v+)∈Tx−M×Tx+M. We show …
Paper approximates backward heat equation using wave equations and Ricci flow.
problem Solving backward heat equation on manifolds using wave equations.
method Approximates solutions of a wave equation on a larger manifold with Ricci flow to solve the backward heat equation.
result The approximation provides solutions to the backward heat equation on manifolds.
New method for analyzing elliptic and parabolic equations.
problem Analyzing elliptic and parabolic equations.
method Level set version of partial uniform ellipticity.
result Effective approach to investigate equations.
Given a hyperbolic subgroup H of a hyperbolic group G for which a Cannon-Thurston map $\hat i:\partial H \ra \partial G$ exists, we study the limit set ΛH of H with respect to its action on ∂G. We prove that the set of conical limit points is exactly the subset of ΛH consisting of the points to wh…
Let Q be a smooth compact orientable 3--manifold with smooth boundary ∂Q. Let B be the set of exact 2--forms B∈Ω2(Q) such that j∂Q∗B=0, where j∂Q:∂Q→Q is the inclusion map. The group D=Diff0(Q) of self-diffeomorphisms of Q isot…
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.
Study proves a sharp upper bound for the zero set area of a static manifold's potential.
problem Proving a sharp upper bound for the zero set area of a static manifold's potential.
method Proved a rigidity theorem for the Euclidean closed unit ball in R^3.
result Sharp upper bound for the area of the zero set of the potential.
We give a survey of some recent papers by the authors and Masaaki Wada relating the twisted Alexander polynomial with a partial order on the set of prime knots. We also give examples and pose open problems.
Method transfers knowledge between partially labeled domains to classify all samples.
problem Weakly supervised open-set domain adaptation between partially labeled domains.
method Collaborative Distribution Alignment (CDA) method for bilaterally knowledge transfer and outlier identification.
result Achieves state-of-the-art performance on Office benchmark and person reidentification.
A novel transformer model improves classification of partially ordered sequences.
problem Classification of partially ordered sequences with uncertainty in timestamps.
method Developed a transformer-based model for partially ordered sequences, benchmarked against set models.
result Transformer-based model outperforms set models on three datasets.
New depth function for partial orders helps compare machine learning algorithms.
problem Comparing machine learning algorithms using non-standard data types.
method Adapted simplicial depth to partial orders, using ufg depth for comparison.
result Demonstrates promising variety of analysis approaches based on ufg methods.
Rational homology ribbon cobordism defines a partial order on 3-manifolds.
problem Classifying 3-manifolds based on their homology
method Proving a partial order on homeomorphism classes of 3-manifolds
result Closed, connected, oriented 3-manifolds are partially ordered by rational homology ribbon cobordism.
Survey on Nambu-Poisson structures in infinite dimensions.
problem Generalization of Poisson and Nambu-Poisson structures in infinite dimensions.
method Study properties of associated characteristic distribution and projective/direct limits.
result Properties and limits of Nambu-Poisson structures in convenient setting.
Neural nets replicate hedging payoffs for realistic discrete-time settings.
problem Hedging in realistic, discrete-time financial markets with transaction costs.
method Deep learning techniques to train neural networks to replicate modified payoff functions.
result Neural networks can better accommodate realistic hedging scenarios and transaction costs.
New algorithms for best arm identification in delayed feedback MABs.
problem Best arm identification in multi-armed bandits with delayed feedback.
method Generalized framework for modeling partial and delayed feedback, efficient algorithms for biased and unbiased estimators, and parallel MAB extensions.
result Exploiting partial feedback can lead to significant improvements over baselines in sequential and parallel MAB settings.
Paper improves conformal prediction for imprecise training data.
problem Applying conformal prediction to partially labeled data.
method Generalizes conformal prediction for set-valued training and calibration data.
result Validates the proposed method and shows it outperforms baselines.
CAT(0) spaces can split into products if their boundary has certain properties.
problem Detecting product splittings in CAT(0) spaces.
method Analyzing the boundary properties of CAT(0) spaces and their group actions.
result Conditions for a CAT(0) space to contain a quasi-dense, closed convex subspace that splits as a product.
Study jets of flat partial connections in foliations.
problem Characterize and understand flat partial connections in foliations.
method Define and apply jets to flat partial connections in smooth foliations and locally free sheaves, focusing on codimension one and arbitrary codimension foliations.
result Define and apply jets to characterize transversely affine and projective structures in foliations.
This paper extends policy gradient methods to partially observable environments.
problem Learning optimal policies in partially observable environments.
method Developed new tools including advantage function to generalize policy gradient algorithms and study their convergence in partially observable Markovian policies.
result Generalized theoretical guarantees of policy gradient algorithms to partially observable domains.
Study shows offline RL under Q⋆-approximation and partial coverage is harder than previously thought.
problem Theoretical limits of offline reinforcement learning under Q⋆-approximation and partial coverage. method Introduced a decision-estimation framework to decompose offline RL complexity into decision and value estimation errors.
result Answered the open question by proving sample inefficiency under partial coverage is not guaranteed by Q⋆-realizability and Bellman completeness. Study shows partially-typed NER datasets can match fully-typed ones in model performance.
problem Leveraging multiple partially-typed NER datasets for training models without fully-typed annotations.
method Systematic analysis and controlled experiments comparing partially-typed and fully-typed datasets.
result Models trained with partially-typed annotations can achieve similar performance to those trained with fully-typed annotations.
In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound with respect to the partial order. Moreover, given any 2-bridge knot K…
Efficient RL in partially observable risk-sensitive environments with hindsight observations.
problem Risk-sensitive reinforcement learning in partially observable environments.
method Integrates hindsight observations into POMDP framework, develops novel RL algorithm.
result Achieves polynomial regret with provable efficiency, outperforming existing methods.
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.
New attacks fool black-box classifiers under limited query and partial information settings.
problem Adversarial attacks on black-box neural networks with limited query access and partial information.
method Developed new attacks for query-limited, partial-information, and label-only threat models.
result Effective attacks against real-world classifiers under realistic threat models.
New method identifies causal variables from partially observed data.
problem Learning from unpaired observations with instance-dependent partial observability.
method Proposes two methods enforcing sparsity in the inferred representation.
result Establishes two identifiability results for linear and piecewise linear mixing functions.
The paper offers methods to estimate and infer the boundary of a set-identified linear model.
problem Estimating and inferring the boundary of a set-identified linear model with many covariates.
method The paper uses semiparametric moment equations and Neyman-orthogonality combined with sample splitting to construct a root-N consistent, uniformly asymptotically Gaussian estimator and a multiplier bootstrap procedure for inference.
result The paper provides a method to estimate and infer the boundary of a set-identified linear model.
Artemis framework improves distributed learning with bidirectional compression and partial participation.
problem Learning in distributed or federated settings with communication constraints and device partial participation.
method Artemis framework using bidirectional compression, memory mechanism, and Polyak-Ruppert averaging.
result Fast rates of convergence (linear up to a threshold) under weak assumptions on stochastic gradients.
The paper classifies 3D contact partially hyperbolic diffeomorphisms.
problem Classifying contact partially hyperbolic diffeomorphisms in 3D.
method Smooth classification, conjugation to known flows or automorphisms, use of invariant distributions.
result Classification up to finite quotient or power, conjugation to known structures.