This paper studies properties of weak reducing pairs in critical Heegaard splittings.
problem Characterize weak reducing pairs in critical Heegaard splittings.
method Analyze the properties of weak reducing pairs in critical Heegaard splittings.
result Provide a necessary condition for a Heegaard surface to be critical.
Contractibility of unknot's weak reducing disks shown.
problem Contractibility of unknot's weak reducing disks in 3-bridge position.
method Analysis of weak reducing disks in 3-bridge position.
result Complex of weak reducing disks for the unknot in 3-bridge position is contractible.
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.
Example shows disk surgeries can alter weak reducibility property.
problem Weak reducibility of compressing disks after surgery.
method Example of weak reducing disks and their surgeries.
result Weak reducibility property is not preserved by disk surgery.
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.
In this article, we prove that a tunnel number two knot induces a critical Heegaard splitting in its exterior if there are two weak reducing pairs such that each weak reducing pair contains the cocore disk of each tunnel. Moreover, we prove that a connected sum of two 2-bridge knots or more generally that of two $(1,1)…
Let (W,S) be a finite rank Coxeter system with W infinite. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex X of W. We consider many special cases, including W word hyperbolic, and X with isolated flats. We establish tha…
Let M be an orientable, irreducible 3-manifold and (V,W;F) a weakly reducible, unstabilized Heegaard splitting of M of genus at least three. In this article, we define an equivalent relation ∼ on the set of the generalized Heegaard splittings obtained by weak reductions and find special…
Mitigates bias in weakly supervised datasets.
problem Bias in weakly supervised datasets.
method Proposes a counterfactual fairness-based technique to mitigate bias.
result Improves accuracy by up to 32% while reducing demographic parity gap by 82.5%.
Control data constructed for smooth weak deformation retraction of stratified spaces.
problem Construct control data for smooth weak deformation retraction of stratified spaces.
method Show smooth local triviality with conical fibers, construct control data, use fiber-wise scalar multiplications.
result Obtain neighbourhood smooth weak deformation retraction of stratified spaces.
Study the geometry of weak para-f-structures and subclasses.
problem Understand the geometry of weak para-f-structures and their subclasses.
method Express covariant derivative of f, prove Killing characteristic vector fields, show foliations, and demonstrate rigidity.
result Prove that characteristic vector fields are Killing and ker f defines a totally geodesic foliation.
Paper studies how to cluster data with a weak oracle, reducing the number of queries needed.
problem Cluster data with limited oracle answers.
method Proposes algorithms for semi-supervised active clustering with weak oracles.
result Shows that a small number of queries is sufficient for effective clustering.
Removes singularity order for Willmore immersions, reducing bubbling scenarios.
problem Understanding the singularity order of weak limits of Willmore immersions.
method Obtains removability result on singularity order, reducing bubbling scenarios.
result Only three out of twelve non-planar minimal surfaces may occur as bubbles of Willmore immersions.
Study uses weak transport for non-convex costs in fixed-income markets.
problem Characterizing optimal caplet pricing in fixed-income markets.
method Introduced weak optimal transport for non-convex costs, reduced general costs to convex problems.
result Established robust super-replication results for fixed-income markets.
We study weakened f-structures on manifolds, generalizing classical results.
problem Classical f-structures and their properties on manifolds. method Introduced and studied weakened f-structures, subclasses, and their properties. result Generalized known results on globally framed f-manifolds. Novel SCUSUM detects weak spatial signals more efficiently.
problem Detecting weak clustered signals in spatial data.
method Spatial CUSUM (SCUSUM) using CUSUM procedure and false discovery rate control.
result SCUSUM achieves high classification accuracy for weak spatial signals.
W2S FT often outperforms weak teachers due to low intrinsic dimensionality.
problem Understanding why weak-to-strong finetuning outperforms weak models.
method Analyzing W2S in ridgeless regression setting, focusing on variance reduction.
result Weak teacher's variance is inherited by strong student in shared feature subspace, reduced in discrepancy subspace.
Improves label propagation for weakly supervised learning.
problem Reducing the need for labeled data in machine learning.
method Label Propagation with Weak Supervision (LPA) analysis.
result Demonstrated improvements over existing methods on weakly supervised classification tasks.
Efficient simulation scheme for rough Heston model reduces computational cost.
problem Accurate and efficient simulation of the rough Heston model for option pricing.
method Weak simulation scheme based on Markovian approximations of the rough Heston process.
result The new scheme exhibits second order weak convergence with linear computational cost.
Improved multi-class AdaBoost algorithm with stronger weak learnability condition.
problem Multi-class classification problem with at least two labels.
method Recursive ensemble algorithm inspired by SAMME, strengthening weak learnability condition.
result Final hypothesis converges to correct label with probability 1 and generalization error bounds exponentially.
An active learner is given a hypothesis class, a large set of unlabeled examples and the ability to interactively query labels to an oracle of a subset of these examples; the goal of the learner is to learn a hypothesis in the class that fits the data well by making as few label queries as possible. This work addresses…
Deep learning reduces noise in weak lensing mass maps using GANs.
problem Noise reduction in weak lensing mass maps.
method Generative adversarial networks (GANs) applied to Subaru Hyper Suprime-Cam data.
result GANs successfully reproduce non-Gaussian information in denoised maps, showing stronger cosmological dependence.
We give a new proof of Brakke's partial regularity theorem up to C^{1,ς} for weak varifold solutions of mean curvature flow by utilizing parabolic monotonicity formula, parabolic Lipschitz approximation and blow-up technique. The new proof extends to a general flow whose velocity is the sum of the mean curvature and an…
Study shows equivalence of two methods for solving scalar curvature problem.
problem Prescribing scalar curvature of closed Riemannian manifolds.
method Subcritical approximations or negative pseudo gradient flows.
result Equivalence of both approaches with respect to zero weak limits.
Improves SGD for convex functions with mini-batches, proving linear convergence.
problem Minimizing convex functions with constraints.
method Projected semi-stochastic gradient descent with mini-batches.
result Linear convergence under weak strong convexity assumption.
Tensor completion requires fewer samples with weak side information.
problem Tensor completion with limited samples and side information.
method Algorithm utilizing weak side information to reduce sample complexity.
result Consistent estimator with O(n1+κ) samples for any small constant κ>0. We introduce the notion of weak reduciblity for Dupin submanifolds with arbitrary codimension. We give a complete characterization of all weakly reducible Dupin submanifolds, as a consequence of a general result on a broader class of Euclidean submanifolds. As a main application, we derive an explicit recursive procedu…
Study Anosov representations of reducible suspensions of hyperbolic groups.
problem Characterize dynamical properties of reducible suspensions of Anosov representations.
method Analyzing linear representations of non-elementary hyperbolic groups, focusing on weak unipotent actions on subspaces.
result Characterize when reducible suspensions are discrete and faithful, quasi-isometrically embedded, and Anosov.
We consider the prediction of weak effects in a multiple-output regression setup, when covariates are expected to explain a small amount, less than ≈1, of the variance of the target variables. To facilitate the prediction of the weak effects, we constrain our model structure by introducing a novel Bayesian ap…
We present an invariant of connected and oriented closed 3-manifolds based on a coribbon Weak Hopf Algebra H with a suitable left-integral. Our invariant can be understood as the generalization to Weak Hopf Algebras of the Hennings-Kauffman-Radford evaluation of an unoriented framed link using a dual quantum-trace. Thi…
Estimates CATEs for structured treatments using a new decomposition method.
problem Estimating conditional average treatment effects for complex data types.
method Generalized Robinson decomposition, isolating causal estimand, arbitrary model plugging, quasi-oracle convergence guarantee.
result Demonstrates superior performance in CATE estimation compared to prior work.
Boosting for off-policy learning reduces empirical risk.
problem Learning from logged bandit feedback without labeled data.
method A boosting algorithm optimizing policy's expected reward.
result Excess empirical risk decreases with each round of boosting.
We present a new test for studying asphericity and diagrammatic reducibility of group presentations. Our test can be applied to prove diagrammatic reducibility in cases where the classical weight test fails. We use this criterion to generalize results of J. Howie and S.M. Gersten on asphericity of LOTs and of Adian pre…
A geometric interpretation is given for certain elliptic-hyperbolic systems in the plane. Among several examples, one which reduces in the elliptic region to the equations for harmonic 1-forms on the projective disc is studied in detail. A boundary-value problem for this example is formulated and is shown to possess we…
This paper studies the interplay between the N=2 gauge theories in three and four dimensions that have a geometric description in terms of twisted compactification of the six-dimensional (2,0) SCFT. Our main goal is to construct the three-dimensional domain walls associated to any three-dimensional cobordism. We find t…
Bayesian approach confirms no return predictability for 1926-2004 data, weak evidence for 1953-2021.
problem Investigating return predictability using Bayesian methods.
method Developed a new shrinkage type prior for a model parameter in a VAR system, compared to other estimation methods.
result Bayesian approach outperforms reduced-bias estimator in terms of size and power.
Analyzes projections of test configurations to vector fields, proving moment convergence.
problem Analyzing moment convergence in projections of test configurations.
method Analytic approach involving moment convergence and weak geodesic ray.
result Proves moment convergence of weight distributions in projections.
Study on tradeoffs between mistakes and ERM oracle calls in online and transductive learning.
problem Analyzing online and transductive learning with limited ERM and weak consistency oracle access.
method Proves lower bounds and upper bounds on mistakes and oracle calls, considering realizable and agnostic cases.
result Achieves optimal mistake bounds with weak consistency queries for certain concept classes.
Model explains how stablecoin runs are influenced by large sales and reserve quality.
problem Understanding and predicting stablecoin runs due to large sales and poor reserve quality.
method Global game model addressing both large sales and poor reserve quality, analyzing risk components.
result The probability of a run increases with large sales and decreases with precise public knowledge, but increases with precise private signals when fundamentals are weak.
Proposes a new estimator for weak instrumental variables in panel data models.
problem Weak instrumental variables due to ignored nonlinearities in panel data.
method Triangular simultaneous equation model with a nonlinear reduced form equation and a control function approach using Super Learner.
result The proposed SLCF estimator is consistent and asymptotically normal, achieving a parametric rate of convergence.
Model user preferences for conversational LLMs using weak rewards.
problem Lack of persistent user models in conversational LLMs leading to repeated user restatements.
method Vector-Adapted Retrieval Scoring (VARS) framework that updates user vectors online from weak scalar rewards.
result Full VARS agent achieves strongest overall performance, matches strong Reflection baseline in task success, and reduces user effort.
We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for developing a conditionally Gaussian approximation to the loss distribution. Nume…
Algorithm reduces bias in generative models using unlabeled reference data.
problem Detect and mitigate bias in generative models trained on biased datasets.
method Weakly supervised algorithm using density ratio technique and data from both biased and reference datasets.
result Generative models achieve up to 34.6% reduction in bias over baselines.
New methods validate a hypothesis explaining how neural nets generalize well.
problem Why over-parameterized nets generalize well despite memorizing training data.
method Developed new algorithms to suppress weak gradient directions without per-example gradients.
result Validated a hypothesis about gradient directions and their role in generalization.
Socratic learning improves generative models by identifying and adapting to latent subsets in training data.
problem Lack of sufficient labeled training data for discriminative models.
method Uses feedback from a discriminative model to identify and adapt latent subsets in a generative model.
result Reduces error by up to 56.06% for relation extraction tasks compared to state-of-the-art techniques.
Boosting classifiers improve accuracy with noisy inputs.
problem Noisy communication or computation degrades boosting classifier accuracy.
method Optimize resource allocation for base classifiers based on importance metrics.
result Optimized noisy boosting classifiers are more robust than bagging.
We show that certain submanifolds of generalized complex manifolds ("weak branes") admit a natural quotient which inherits a generalized complex structure. This is analog to quotienting coisotropic submanifolds of symplectic manifolds. In particular Gualtieri's generalized complex submanifolds ("branes") quotient to sp…
Improved approximations for rough Heston model reduce errors.
problem Lack of Markov and semimartingale properties in rough Heston model.
method Markovian approximations with weak error analysis.
result Super-polynomial convergence of new approximations.