3-manifolds can be made parallelisable via surgery.
problem Making 3-manifolds parallelisable.
method Surgery presentation, refined by Kaplan, contact geometry.
result All closed, orientable 3-manifolds are parallelisable.
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48 results for “Kaplan refinement”
KAPLAN-HR models survival data without manual interactions, outperforming existing methods.
problem Survival analysis challenges with complex covariates and time-varying effects.
method Kolmogorov-Arnold Networks (KAN) for nonparametric hazard estimation.
result KAPLAN-HR matches or exceeds existing methods in clinical survival data.
We begin a systematic study of these spaces, initially following along the lines of Eberlein's comprehensive study of the Riemannian case. In particular, we integrate the geodesic equation, discuss the structure of the isometry group, and make a study of lattices and periodic geodesics. Some major differences from the …
Proves algebraicity of Hodge loci in arithmetic quotients.
problem Proving algebraicity of Hodge loci in arithmetic quotients.
method Real semi-algebraic structure and o-minimal theory.
result Hodge locus is a countable union of algebraic subvarieties.
Reservoir computer dimensions estimated using three methods.
problem Estimating the dimension of reservoir computer signals.
method Used three dimension estimation methods: false nearest neighbor, covariance, and Kaplan-Yorke.
result Signals in reservoir system exist on a low dimensional surface.
Nonasymptotic error bounds and strong consistency rates for survival analysis methods.
problem Establishing reliable error bounds and consistency rates for survival analysis methods.
method Nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators in metric spaces.
result Rates of strong consistency match existing lower bounds for conditional CDF estimation.
Let be a connected non-compact -dimensional manifold possibly with boundary and be a foliation on such that each leaf is homeomorphic to and has a trivially foliated neighborhood. Such foliations on the plane were studied by W. Kaplan who also gave their topological classification. H…
KM-GPT: An Automated Pipeline for Reconstructing Individual Patient Data from Kaplan-Meier Plotscs.LG
KM-GPT automates IPD reconstruction from KM plots with high accuracy and scalability.
problem Manual digitization of IPD from KM plots is error-prone and lacks scalability.
method KM-GPT integrates advanced image preprocessing, multi-modal reasoning, and iterative reconstruction algorithms.
result KM-GPT generates high-quality IPD without manual input or intervention, achieving superior accuracy.
Proposes a privacy-preserving method for survival function estimation.
problem Privacy leakage in survival function estimation using sensitive data.
method Differential privacy framework applied to Kaplan-Meier estimator and related metrics.
result The method provides utility and strong privacy guarantees with real-world data.
Method detects and predicts iceberg orders on CME.
problem Detect and predict iceberg orders on CME.
method Detect native and synthetic iceberg orders using discrepancies and order modifications. Train model with Kaplan--Meier estimator. Predict iceberg sizes.
result Model predicts iceberg sizes with out-of-sample validation.
New Lie groups generalize H-type groups with nondegenerate centers.
problem Generalizing H-type groups with nondegenerate centers.
method Defined and investigated 2-step nilpotent Lie groups.
result Geometric properties of new Lie groups investigated.
The paper addresses supervised learning with censored data, proposing a method to estimate risk.
problem Learning from censored data in regression problems.
method Proposes a plug-in estimate of the true risk based on a Kaplan-Meier estimator of the censorship distribution.
result The learning rate of minimizers of the proposed risk functional is of order \(O_{\mathbb{P}}(\sqrt{\log(n)/n})\).
This paper addresses issues with the Brier score in administrative censoring scenarios.
problem Problems with the Brier score in administrative censoring scenarios.
method Proposes an alternative Brier score for administratively censored data.
result The administrative Brier score is valid even when censoring times can be identified from covariates.
Study predicts colorectal polyp recurrence using medical records and statistical models.
problem Identifying patient characteristics influencing colorectal polyp recurrence.
method Natural language processing for extracting polyp characteristics, Kaplan-Meier curves, Cox proportional hazards modeling, random survival forest models.
result Polyp size, number, location, and patient smoking status significantly influence recurrence risk.
The paper tackles survival analysis with censored data, proposing methods to incorporate incomplete information into models.
problem Survival analysis with censored data, where the target output is often incomplete.
method The paper explores three categories of loss functions: partial likelihood methods, rank methods, and a classification method based on a Wasserstein metric and Kaplan Meier estimate.
result The proposed method optimizes the expected C-index, a common evaluation metric for ranking survival models.
New model improves cancer screening prediction accuracy.
problem Modeling disease progression with heterogeneous populations and irregular data.
method Hierarchical Hidden Markov Jump Processes with piece-wise stationary transitions and scalable EM algorithm.
result Model outperforms state-of-the-art models in prediction accuracy and generating Kaplan-Meier estimators.
Securely analyzes survival data across multiple institutions without revealing individual patient records.
problem Privacy concerns in federated survival analysis of health data.
method Multiparty homomorphic encryption for approximate floating-point computation and encrypted aggregation.
result Privacy-preserving federated Kaplan--Meier survival analysis with high fidelity and predictable overhead.
New methods estimate survival functions with time-varying covariates.
problem Estimating survival functions with time-varying covariates.
method Generalized conditional inference and relative risk forests, adapted transformation forest.
result Proposed methods outperform traditional models in estimating survival functions.
We prove that the uniformizing map of any arithmetic quotient, as well as the period map associated to any pure polarized -variation of Hodge structure on a smooth complex quasi-projective variety , are topologically tame. As an easy corollary of these results and of Peterzil-Starchenko's o-…
We introduce a special class of nilpotent Lie groups of step 2, that generalizes the so called (eisenberg)-type groups, defined by A. Kaplan in 1980. We change the presence of inner product to an arbitrary scalar product and relate the construction to the composition of quadratic forms. We present the geodesic equat…
SDPM models survival analysis without parametric assumptions, achieving competitive performance.
problem Estimating survival distributions from censored data with flexibility and accuracy.
method Generative model using denoising diffusion, avoiding parametric assumptions and discretization.
result SDPM achieves competitive predictive performance across various metrics.
We study a generalization of Hodge structures which first appeared in the work of Cecotti and Vafa. It consists of twistors, that is, holomorphic vector bundles on P^1, with additional structure, a flat connection on C^*, a real subbundle and a pairing. We call these objects TERP-structures. We generalize to TERP-struc…
This monograph introduces deep learning models for predicting time-to-event outcomes.
problem Predicting critical events and their timing from time series data.
method Neural networks and deep learning models for survival analysis.
result Improved accuracy in predicting time-to-event outcomes using deep learning.
H-type Lie algebras were introduced by Kaplan as a class of real Lie algebras generalizing the familiar Heisenberg Lie algebra . The H-type property depends on a choice of inner product on the Lie algebra . Among the H-type Lie algebras are the complex Heisenberg Lie algebras $\mathfrak{h}…
Unified treatment of two extension problems using heat equation in Heisenberg group.
problem Two extension problems for pseudo-differential operators in Heisenberg group.
method Heat equation, fractional powers, semigroup methods.
result Explicit computation of fundamental solutions for pseudo-differential operators.
New inequality for refined knot invariants in a specific space.
problem General adjunction inequality for refined -invariants does not hold.
method Introduced an adjunction inequality for a specific spatial refinement in .
result An adjunction inequality holds for the -version of the -refinement in .
We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which co…
Refines neural network predictions using background knowledge for improved accuracy.
problem Compensate for lack of labeled data in neural networks.
method Introduces differentiable refinement functions and Iterative Local Refinement (ILR) algorithm to refine predictions efficiently and accurately.
result ILR finds competitive results in MNIST addition task and refines predictions on complex SAT formulas.
New research shows label refinement and weak training have limitations for aligning LLMs.
problem Limitations of refinement methods for aligning large language models.
method Analyzed probabilistic assumptions and alternative approaches to label refinement and weak training.
result Label refinement and weak training suffer from irreducible error, leaving a performance gap.
Refines Khovanov homology for knots with involution.
problem Detecting mutations in knots with an involution.
method Introduces a triply-graded theory with two filtrations.
result Shows the refinement can detect mutation.
In a previous paper we constructed a spectrum-level refinement of Khovanov homology. This refinement induces stable cohomology operations on Khovanov homology. In this paper we show that these cohomology operations commute with cobordism maps on Khovanov homology. As a consequence we obtain a refinement of Rasmussen's …
New homotopy refinements for tangle invariants.
problem Stable homotopy refinements for tangle invariants.
method Refined Khovanov and Chen-Khovanov spectra.
result Induces refinements of platform algebras and invariants.
Refined 3D indexhep-th
Refined 3D index uses surgery and gradings to distinguish 3-manifolds.
problem Distinguishing 3-manifolds and gauge theories phases.
method Dehn surgery presentation, ideal triangulation, and enhanced flavor symmetries.
result Invariance of refined index under various transformations.
Refines deep generative models to improve data density precision.
problem Achieving precise representation of data probability density in deep models.
method Iterated generative modeling to refine latent space, addressing topological obstructions.
result Latent Space Refinement (LaSeR) protocol improves generative model precision.
Bauer-Furuta invariantsmath.DG
Established a stable cohomotopy refinement for Pin(2) monopole invariants.
problem Refining monopole invariants for Pin(2) structures.
method Adapted Bauer-Furuta's Seiberg-Witten refinement method to Pin(2) monopole invariants.
result Connected sum formula for the refined invariants.
Refined 1-cocycle for knots helps quantify isotopies.
problem Quantify knot isotopies using refined tangle equations.
method Refined combinatorial 1-cocycle for regular isotopies of knots.
result Refined tangle equations provide quantitative knot information.
New estimator for survival function with missing not at random censoring indicators.
problem Estimating survival function with missing not at random censoring indicators.
method Proposes a new estimator based on a conditional copula model for the missingness mechanism.
result Provides a new method for estimating conditional survival function with MNAR censoring indicators.
Braverman and Kappeler introduced a refinement of the Ray-Singer analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold. We study this notion and improve the Braverman-Kappeler theorem comparing the refined analytic torsion with Farber-Turaev refinement of the combinatorial torsion. …
EGR refines and assesses protein complex structures.
problem Improving the accuracy of protein complex 3D structures for drug discovery.
method E(3)-equivariant graph neural network (GNN) for multi-task refinement and assessment.
result EGR achieves state-of-the-art performance in refining and assessing protein complexes.
A novel framework refines diffusion models iteratively for better downstream reward optimization.
problem Optimizing reward functions during inference of diffusion models.
method Iterative refinement process with noising and reward-guided denoising steps.
result Superior empirical performance in protein and DNA design.
Machine learning improves kidney transplant outcomes prediction.
problem Improving prediction of kidney transplant success.
method Random forest machine learning model trained on kidney donor risk index data.
result Random forest predicted 2,148 more successful transplants than the risk index.
Formula conjectured for refined SU(3) Vafa-Witten invariants of surfaces.
problem Calculating refined SU(3) Vafa-Witten invariants for smooth surfaces.
method Proved modularity transformation and used Mochizuki's formula and Maulik-Thomas's definition.
result Conjectured formula satisfies refined S-duality and verified in examples.
We formulate large duality of refined Chern-Simons theory with a torus knot/link in . By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the -background. This form enables us to relate refined C…
Study uses AI to refine loan assessments, improving credit default predictions.
problem Improving credit default prediction accuracy using AI-refined text.
method Comparative analysis of human-written and AI-refined loan assessments using deep learning techniques.
result AI-refined texts significantly enhance credit default predictions, especially when combined with structured data.
Let be a flat complex vector bundle over a closed oriented odd dimensional manifold endowed with a flat connection . The refined analytic torsion for was defined and studied by Braverman and Kappeler. Recently Mathai and Wu defined and studied the analytic torsion for the twisted de Rham complex…
The refined analytic torsion, defined by M. Braverman and T. Kappeler on closed manifolds, can be viewed as a refinement of the Ray-Singer torsion, since it is a canonical choice of an element with Ray-Singer norm one, in case of unitary representations. The complex phase of the refinement is given by the rho-invariant…
Refined BN-S model improves crude oil hedging with machine learning.
problem Finding optimal hedging strategy for commodity markets.
method Implemented a refined Barndorff-Nielsen and Shephard model with machine learning algorithms.
result The refined model performs better than the classical BN-S model.
Private estimation of many quantiles using differential privacy.
problem Estimating quantiles of a distribution privately.
method Two approaches: 1) Private estimation of empirical quantiles, 2) Uniform density estimation.
result There is a tradeoff between estimating quantiles at specific points and uniformly estimating the quantile function.