RSF improves risk prediction accuracy using Harrell's C index instead of log-rank split criterion.
problem Improving risk prediction accuracy in clinical studies using random survival forests.
method Comparing log-rank and C index split criteria in RSF models, and evaluating their impact on prediction accuracy.
result Harrell's C index improves RSF prediction accuracy, especially in high censoring or informative predictor scenarios.
Proposes a new log-rank test using RKHSs for robust two-sample analysis.
problem Two-sample problem in right-censored data.
method Test statistic based on supremum of RKHS-weighted log-rank tests.
result Proposed test is omnibus for a specific family of RKHSs.
Survival trees exhibit end-cut preference, leading to biased splits.
problem End-cut preference in survival trees causes biased splits and poor interpretability.
method Proposed a smooth sigmoid surrogate (SSS) approach to replace hard-threshold indicator function.
result Smooth sigmoid surrogate (SSS) effectively mitigates end-cut preference in survival trees.
Study examines survival models for ALS, focusing on proportional hazards assumption.
problem Impact of proportional hazards assumption on survival models for ALS.
method Theoretical and empirical investigation of survival forests and their variants.
result Alternative split procedures can improve model performance in non-proportional hazards situations.
Paper proposes a novel SVM method for creating survival trees.
problem Creating non-linear survival trees for right-censored data.
method L2-regularized dipole splitting criteria with kernel methods.
result Non-linear splits using polynomial and Gaussian kernels show similar predictive power but often smaller tree sizes.
A new method selects variables for random survival forests using maximally selected rank statistics.
problem Random survival forests can be biased in selecting variables, especially for non-linear effects.
method Use maximally selected rank statistics for variable selection in random survival forests, comparing on p-value scale.
result The new method outperforms other approaches in prediction performance and computational speed.
Efficiently clusters survival curves without computationally intensive resampling.
problem Identifying clusters of survival curves efficiently and scalably.
method Log-rank test combined with k-means clustering.
result Achieves comparable results to bootstrap-based methods but with improved efficiency.
SurvMixClust clusters survival data and predicts individual survival curves.
problem Integrating clustering into survival analysis for precision medicine.
method SurvMixClust learns latent representations for clustering and predicts survival functions using a mixture of non-parametric experts.
result SurvMixClust creates balanced clusters with distinct survival curves, outperforming clustering baselines and competing with non-clustering models in predictive accuracy.
DPFE extracts approved features privately, preserving sensitive information.
problem Protecting sensitive information while allowing feature extraction.
method Selective exchange of information, log-rank privacy measure, and smartphone implementation.
result DPFE achieves high accuracy for primary tasks while preserving sensitive feature privacy.
A new test detects non-linear independence in censored survival data.
problem Detecting non-linear independence between survival times and covariates.
method A kernel log-rank test using reproducing kernel Hilbert spaces.
result The test correctly rejects the null hypothesis under any alternative.
Study compares Cox model and RSF for predicting patient survival, finding RSF superior in certain scenarios.
problem Comparing predictive accuracy of Cox proportional hazards model and Random Survival Forest for patient-specific survival probabilities.
method Conducted a comprehensive comparison study using simulation scenarios and real-world datasets.
result RSF outperforms Cox model in nonproportional hazards settings and with treatment-covariate interactions.
We present a nonparametric Bayesian method for disease subtype discovery in multi-dimensional cancer data. Our method can simultaneously analyse a wide range of data types, allowing for both agreement and disagreement between their underlying clustering structure. It includes feature selection and infers the most likel…
Risk-stratify improves risk stratification for cardiovascular disease.
problem Accurately stratify patients for cardiovascular disease prognosis.
method Two-phase algorithm: tree partitioning followed by graph decomposition.
result Significant reduction in false discovery rate (33%) compared to state-of-the-art methods.
Develops methods to estimate high rank tensors from noisy data.
problem Estimating high rank tensors from noisy observations.
method Generative latent variable tensor model, polynomial-time spectral algorithm.
result Achieves computationally optimal rate for signal tensor estimation.
SPlit optimizes dataset splitting for better model performance.
problem Improving model performance through optimal dataset splitting.
method Adapting Support Points (SP) algorithm for subsampling and categorical variables in a sequential nearest neighbor approach.
result SPlit significantly improves worst-case testing performance compared to random splitting.
Paper integrates multiple data types for better cancer prediction.
problem How to effectively use diverse medical data for accurate cancer prediction.
method Multi-Kernel LS-SVM pipeline for integrative analysis of molecular and clinical data.
result Integration of various data types improves log-rank statistics and clinical status prediction.
The paper extends keenness concept to bridge splittings and finds conditions for existence.
problem Extending keenness concept to bridge splittings and finding conditions for existence.
method Extending the concept of keenness to bridge splittings and proving existence conditions.
result Existence of strongly keen (g,b)-splitting of a link with distance n for certain integers g, b, and n. Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split structures appear in the first case as deformations of a split reduction and in the …
Study flippable Heegaard splittings in Seifert fibered spaces.
problem Identifying flippable Heegaard splittings in Seifert fibered spaces.
method Examining isotopies that interchange Heegaard splitting sides in Seifert fibered spaces.
result Characterized which Heegaard splittings are flippable in Seifert fibered spaces.
The paper proves infinitely many non-isotopic splitting 3-spheres for split sphere links in 4D.
problem Proving the existence of infinitely many non-isotopic splitting 3-spheres for split sphere links in 4D.
method Establishing a general sufficient condition for infinitely many topologically non-isotopic splitting 3-spheres in connected sums of 4-manifolds.
result Proves infinitely many non-isotopic splitting 3-spheres for split sphere links in 4D.
Bound on splitting number in terms of four-genus of knots.
problem Understanding the relationship between splitting number and four-genus of knots.
method Provided a bound on the splitting number in terms of the four-genus of related knots.
result Bound on splitting number in terms of four-genus.
We study the self-dual Yang-Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described.
New methods improve prediction regions for high-dimensional data.
problem Creating effective prediction regions for high-dimensional data.
method CD-split and HPD-split methods that combine split method and data-driven partition.
result CD-split and HPD-split converge to oracle highest predictive density set and satisfy local and asymptotic conditional validity.
This paper constructs keen weakly reducible Heegaard splittings of arbitrary genus.
problem Creating Heegaard splittings with specific properties.
method Construction of keen weakly reducible splittings.
result Arbitrary genus Heegaard splittings can be constructed.
New spheres can split a 4D link in ways not possible in 3D.
problem Exploring how splitting spheres behave in 4D space.
method Constructing specific 2-component surface-links in S4. result Found non-isotopic splitting spheres in S4∖Lm,n. 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.
The paper extends Lorentzian splitting theorems under curvature-dimension bounds.
problem Analyzing Lorentzian spacetimes with curvature-dimension bounds.
method Using Bakry-Émery-Ricci tensor, extending singularity and splitting theorems.
result Theorems hold for all synthetic dimensions, including negative and positive.
We show that if a split link is obtained from a split link L in S3 by 1/n-Dehn surgery along a trivial knot C, then the link L∪C is splittable. That is to say, it is impossible to obtain a split link from a split link via a non-trivial twisting. As its corollary, we completely determine when a trivial li…
New concept of strongly keen Heegaard splittings found.
problem Finding Heegaard splittings with specific properties.
method Introducing and proving existence of strongly keen Heegaard splittings.
result Existence of Heegaard splittings with specified genus and Hempel distance.
Study evaluates when splitting classifiers can improve performance despite disparate treatment.
problem Impact of disparate treatment in classification models.
method Comparison of split classifiers and group-blind classifiers, quantifying performance improvement.
result Proves an equivalent expression for the benefit-of-splitting which can be efficiently computed.
New methods convert complex link presentations to simpler, recognizable forms.
problem Representing split and composite links in a clear, recognizable way.
method Pocket and flip moves to transform link presentations.
result Pocket moves are the only obstruction to representing split links by split plat presentations.
Study shows arc and curve graphs are retracts of free group splitting complexes.
problem Understanding free group splittings through arc and curve graphs.
method Proved arc and curve graphs are coarse Lipschitz retracts of free splitting complexes and other related graphs.
result Arc and curve graphs are retracts of free group splitting complexes.
Powell's conjecture about Goeritz groups for genus 3 splittings is confirmed.
problem Determining the minimum set of elements needed to generate the Goeritz group of Heegaard splittings.
method Proof for splittings of genus 3 and a framework for higher genus splittings.
result Powell's conjecture is correct for splittings of genus 3.
The splitting number of a link is the minimal number of crossing changes between different components required, on any diagram, to convert it to a split link. We introduce new techniques to compute the splitting number, involving covering links and Alexander invariants. As an application, we completely determine the sp…
Lower bounds on splitting number derived from signature and nullity.
problem Determining the minimal number of crossing changes to split a link.
method Using multivariable signature and nullity to derive lower bounds.
result Efficiently computed splitting numbers for many links.
Little is known on the classification of Heegaard splittings for hyperbolic 3-manifolds. Although Kobayashi gave a complete classification of Heegaard splittings for the exteriors of 2-bridge knots, our knowledge of other classes is extremely limited. In particular, there are very few hyperbolic manifolds that are know…
New proof of Lorentzian splitting theorems using elliptic operators.
problem Proving splitting theorems in Lorentzian geometry.
method Using a negative homogeneity elliptic p-d'Alembert operator to prove theorems.
result Lorentzian splitting theorems are proven in a framework similar to Riemannian geometry.
New proof of Giroux Correspondence for tight contact 3-manifolds.
problem Proving the Giroux Correspondence for tight contact 3-manifolds.
method Introducing tight Heegaard splittings, using refinement process, and translating moves between splittings to moves between open books.
result Proves the tight Giroux Correspondence for contact 3-manifolds.
Paper generalizes splitting number to classify plane curve arrangements.
problem Distinguishing embedded topology of plane curves.
method Introduces splitting graph to generalize splitting number.
result Classifies embedded topology of specific plane curve arrangements.
Let M_1 and M_2 be compact, orientable 3-manifolds, and M the manifold obtained by gluing some component F of \bdy M_1 to some component of \bdy M_2 by a homeomorphism φ. We show that when φis "sufficiently complicated" then (1) the amalgamation of low genus, unstabilized, boundary-unstabilized Heegaard splittings of M…
Minimal splitting factors help study scalar curvature constraints.
problem Scalar curvature constraints in geometry.
method Introducing minimal splitting factors with positive scalar curvature.
result Minimal splitting factors have properties similar to area minimizing hypersurfaces.
Non-isotopic Heegaard splittings of non-minimal genus were known previously only for very special 3-manifolds. We show in this paper that they are in fact a wide spread phenomenon in 3-manifold theory: We exhibit a large class of knots and manifolds obtained by Dehn surgery on these knots which admit such splittings. M…
Introduces nonlinear splittings on fibre bundles for generalizing connections.
problem Generalizing connections on fibre bundles.
method Definition and properties of nonlinear splittings, including affine, homogeneous, and principal splittings.
result Curvature map defined for nonlinear splittings, linking to nonholonomic systems and magnetic Lagrangian systems.
Paper strengthens splitting theorem using weak KAM theory.
problem Splitting theorem in warped product spaces.
method Weak KAM theory approach.
result Strengthened splitting theorem.
New method escapes local optima in neural architecture optimization.
problem Escaping local optima in neural architecture optimization.
method Signed neural splitting in steepest descent framework.
result Escapes local optima, leading to better performance.
We define a notion of Hempel distance for one-sided Heegaard splittings and show that the existence of alternate surfaces restricts distance for one-sided splittings in a manner similar to Hartshorn's and Scharlemann-Tomova's results for two-sided splittings. We also show that every geometrically compressible one-sided…
We explicitly compute the lower algebraic K-theory of the split three-dimensional crystallographic groups; i.e., the groups G that act properly and cocompactly on three-dimensional Euclidean space by isometries, such that the natural map from G to O(3) is a split injection onto its image. There are 73 split three-dimen…
Splits a spectrum related to Madsen-Tillmann spectra at prime 2.
problem Homotopy equivalence and splitting of Madsen-Tillmann spectra.
method Uses Steinberg idempotents and Whitehead conjecture.
result Splits MTO(n) off BO(n)+ at prime 2.