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.
Kernel Induced Random Survival Forests (KIRSF) is a statistical learning algorithm which aims to improve prediction accuracy for survival data. As in Random Survival Forests (RSF), Cumulative Hazard Function is predicted for each individual in the test set. Prediction error is estimated using Harrell's concordance inde…
We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the Cauchy-Schwarz inequality--is used to produce ``parameter-free'', ``projection-free'' vers…
Improves random survival forest model by weighted averaging.
problem Improving the performance of random survival forest.
method Modifies random forest by weighted averaging of trees, optimizing weights via quadratic optimization to maximize Harrell's C-index.
result The weighted random survival forest outperforms the original model in numerical examples.
C-index varies among software, complicating model comparison.
problem Variation in C-index calculations across software.
method Comparison of C-index estimators in R and Python.
result Different implementations yield varying results.
Ensemble model predicts AD progression from CN status with high accuracy.
problem Early prediction of clinical progression from cognitively normal to mild cognitive impairment or Alzheimer's disease.
method Ensemble survival analysis combining penalized Cox regression, advanced survival models, and aggregation techniques.
result Ensemble model achieved peak C-index of 0.907 and integrated time-dependent AUC of 0.904, outperforming baseline models.
Deep learning predicts human survival from cardiac MRI motion data.
problem Predicting human survival from cardiac MRI motion data.
method Fully convolutional network for dense motion modeling, autoencoder for latent code learning, Cox partial likelihood loss for right-censored data.
result Predictive accuracy (C-index) significantly higher (p < .0001) for deep learning model (C=0.73) than human benchmark (C=0.59).
In this paper, we obtain a new abstract formula relating eigenvalues of a self-adjoint operator to two families of symmetric and skew-symmetric operators and their commutators. This formula generalizes earlier ones obtained by Harrell, Stubbe, Hook, Ashbaugh, Hermi, Levitin and Parnovski. We also show how one can use t…
Study benchmarks 19 survival models on 34 datasets, finding Cox model still best.
problem Quantitative comparison of survival models on low-dimensional data.
method Comprehensive benchmarking of 19 models on 34 datasets, tuning and evaluating using 6 metrics.
result Cox Proportional Hazards model remains best overall for low-dimensional, right-censored data.
The study examines Cox models for lifetime loan default risk, addressing biased estimates by incorporating recurrent events.
problem Ignoring recurrent default events in Cox models leads to biased and inaccurate PD estimates.
method Investigates and compares different Cox models (Andersen-Gill and Prentice-Williams-Peterson) for lifetime loan default risk.
result The Andersen-Gill model underperforms compared to the Prentice-Williams-Person model and the time to first default model.
A new clustering evaluation index based on density estimation.
problem Improving internal clustering evaluation indices.
method The index is a mixture of Ambiguous and Similarity sub-indices, calculated using density estimation.
result The new index significantly outperforms other internal clustering evaluation indices.
Study on symmetric operators on non-compact manifolds, focusing on their index modulo 2.
problem Investigating elliptic operators with a specific symmetry and their index modulo 2.
method Analysis of Callias-type operators on non-compact manifolds, establishing mod 2 versions of index theorems.
result Established mod 2 versions of the Gromov-Lawson relative index theorem, Callias index theorem, and Boutet de Monvel's index theorem for Toeplitz operators.
The paper studies knot densities under various constraints and degenerations.
problem Understanding knot densities under different constraints and their degenerations.
method Introduces and analyzes unconstrained and ropelength-windowed p-densities of knot types. result The degenerations in the unconstrained theory and the introduction of ropelength-windowed densities.
New index formula connects numerical and K-theoretic indices.
problem Equivariant index for proper group actions on manifolds.
method Developed a trace on group conjugacy classes to relate numerical and K-theoretic indices. result Shows that numerical index equals K-theoretic index under certain conditions. New index connects Diederich-Fornæss index to boundary conditions.
problem Understanding the Diederich-Fornæss index for complex domains.
method Defined and proved new index equivalence; used complex geometric analytic techniques.
result First precise non-trivial Diederich-Fornæss index in Euclidean spaces.
Researchers prove index invariance under cobordism for Callias-type operators.
problem Index calculation for elliptic operators on compact manifolds.
method Introduce cobordism of Callias-type operators and prove index invariance.
result Index is preserved by cobordism of Callias-type operators.
The paper explores global index formulas for one-dimensional holomorphic foliations.
problem Global index formulas for one-dimensional holomorphic foliations.
method Microlocal point of view and short proofs for existing index formulas.
result Generalizations of existing index formulas.
Explain Arnold's proof of the Morse index theorem using Maslov index.
problem Proving the Morse index theorem in Riemannian geometry.
method Using symplectic arguments and the Maslov index.
result Self-contained exposition of Arnold's proof.
CCI30 is a new cryptocurrency index.
problem None explicitly stated in the abstract.
method Not specified in the abstract.
result Not specified in the abstract.
The p-index improves investment performance for NYSE stocks but not for SSE stocks.
problem Improving investment performance for stocks using the p-index.
method Comparing different p-ratio strategies and empirical efficient frontiers for SSE and NYSE stocks.
result The p-index enhances investment performance for NYSE stocks but not for SSE stocks.
Study Whittle index learning algorithms for restless bandits with constant stepsizes.
problem Optimizing decisions in restless multi-armed bandits with constant stepsizes.
method Developed Q-learning algorithms with constant stepsizes for index learning in restless bandits, extending to DQN and function approximations.
result The algorithms learn the Whittle index effectively.
Paper introduces danceability index as a new bridge index definition.
problem Defining the bridge index in various mathematical contexts.
method Proves danceability index as equivalent to bridge index, extends to virtual knots.
result Danceability index is a new equivalent definition of the bridge index.
Constructs index class for manifolds with group action.
problem Index class construction for manifolds with group action.
method Constructs coarse index class with support condition using equivariant Dirac operator.
result Shows coarse relative index theorem and compatibility with suspension isomorphism.
Mod 2 index theorem for non-orientable pin^- manifolds.
problem Analyzing real vector bundles over non-orientable pin^- manifolds.
method Using twisted Dirac operators and KO-theory.
result Extends Atiyah-Singer index theorem to non-orientable manifolds.
New techniques simplify computing geometric index of links in solid tori.
problem Computing the geometric index of links in solid tori.
method Introducing geometric index for solid chambers and proving its computation under specific conditions.
result Simplified computation of geometric index for new examples.
A new index rebalancing strategy reduces large constituent weights without undesirable effects.
problem Undesirable effects of current Nasdaq-100 index rebalancing.
method A simple rebalancing strategy that avoids undesirable effects.
result Preserves the order of index weights and prevents maximum weight increase.
Study on symmetric braid index of ribbon knots, deriving bounds and characterizations.
problem Understanding the symmetric braid index of ribbon knots.
method Defining symmetric braid index, using Khovanov homology, and calculating bounds.
result Existence of knots with symmetric braid index greater than braid index.
Study proves bridge and braid indices match for twist positive knots.
problem Determining when bridge and braid indices are equal for knots.
method Used knot Floer torsion order to prove for all twist positive knots.
result Bridge and braid indices coincide for all twist positive knots.
Minimal grid diagrams for 15,735 knots with 14 crossings and arc index 14.
problem Representing prime knots with 14 crossings and specific arc indices using grid diagrams.
method Enumerated all prime knots with 14 crossings, categorized by arc index, and found minimal grid diagrams for those with arc index 14.
result 8,027 knots with arc index 13 and 15,735 knots with arc index 14 were represented by minimal grid diagrams.
The chord index extends knot invariants and has applications in virtual knot theory.
problem Defining and applying finite type invariants to virtual knots.
method Introducing chord index, indexed Jones polynomial, and indexed quandle.
result The chord index generalizes classical knot invariants and has applications in twisted knot theory.
Given a proper, cocompact action of a Lie groupoid, we define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this pairing by applying the van Est map and algebraic index theory. Finally we discuss in examples th…
Proves the index of a Möbius band in 4D ball equals 5.
problem Determining the Morse index of critical non-orientable surfaces.
method Comparison theorem between Steklov spectral index and energy index.
result Proves the index of critical Möbius band in B4 equals 5. Enhanced indexation uses equity and index options for better performance.
problem Improving portfolio performance through enhanced indexation.
method Integrating index options into an enhanced indexation strategy based on second-order stochastic dominance.
result Introducing option strategies in enhanced indexation leads to improved out-of-sample performance.
Finite index subgroups of relatively hyperbolic groups have equal index.
problem Finite index subgroups of relatively hyperbolic groups have equal index.
method Demonstrating that the number of simplices in a simplicial classifying space grows linearly with index.
result Finite index subgroups of relatively hyperbolic groups have equal index.
Study of differential operators on von Neumann algebras with applications to index theory.
problem Index theory for differential operators on non-compact manifolds.
method Relative index and Callias-type index theorems for von Neumann indexes.
result Cobordism invariance of the index of Callias-type operators.
The abstract discusses connecting quantum mechanics and algebraic index theories.
problem Exploring the connection between quantum mechanics and algebraic index theories.
method Explains how the classical algebraic index theorem can be proved in terms of BV quantization of topological quantum mechanics and 2d chiral CFT.
result Shows how the generating function of all genus Gromov-Witten invariants on elliptic curves is mirror equivalent to an elliptic chiral index.
Researchers construct an index map for contact manifolds using K-theory.
problem Constructing an index for maximally hypoelliptic operators on contact manifolds.
method Using Higson's construction for symbol class in K-theory, they derive a series of maps whose induced map in K-theory is the Heisenberg Atiyah-Singer index map.
result Explicit construction of a series of maps leading to the Heisenberg Atiyah-Singer index map.
Analyzes necessary and sufficient conditions for domains to have trivial Diederich-Fornæss index.
problem Understanding domains with trivial Diederich-Fornæss index in complex spaces.
method New geometric analysis method based on Riemannian geometry and de Rham cohomology.
result Analytical and geometric conditions for domains to have trivial index.
Deep learning predicts market sensitivities for cost-effective index tracking.
problem Costly and impractical replication of index funds.
method Learning to predict market sensitivities using deep learning models.
result Significant reduction in prediction errors compared to historical methods.
New index formula for hypoelliptic operators on manifolds.
problem Index computation for hypoelliptic differential operators.
method Generalized index formula for *-maximally hypoelliptic operators.
result Explicit index computations for Hormander's sum of squares operators.
Study on minimal surfaces with free boundary in a half-space, improving index estimates.
problem Non-existence of index two embedded minimal surfaces with free boundary in a half-space.
method Improved estimates of Neumann and Dirichlet indices, simplified proof of lower bounds.
result Answered Ambrozio et al.'s question and provided new lower bounds.
New theorem for manifolds with boundaries calculates operator index.
problem Calculating index of Callias-type operators on manifolds with boundaries.
method Combines indexes of induced operators on a compact hypersurface.
result Generalizes Callias-type index theorem to manifolds with compact boundaries.
Note proves index theorem for non-elliptic Heisenberg operators.
problem Proving index theorem for non-elliptic Heisenberg operators.
method Galois covering, Heisenberg elliptic differential operators, Γ-index theorem. result Example of Heisenberg operators with non-trivial Γ-index. An upper bound of the superbridge index of the connected sum of two knots is given in terms of the braid index of the summands. Using this upper bound and minimal polygonal presentations, we give an upper bound in terms of the superbridge index and the bridge index of the summands when they are torus knots. In contrast…
A new stock index model simplifies high-dimensional stock data.
problem Reflecting the overall stock market activity in high-dimensional data.
method Manifold learning and feature detection on discrete Laplace-Beltrami operator.
result The MF index series approximates the stock market better and has lower risk.
Listed 19,513 prime knots with arc index 12-16.
problem Tabulating prime knots with specific arc indices.
method Provided list of prime knots with minimal grid diagrams.
result 19,513 prime knots with arc index 12-16.
New method accurately reconstructs Russell 3000 index, revealing crowded portfolios.
problem Crowding in index portfolios during reconstitution events.
method Developed a Python package for accurate index reconstruction using CRSP US Stock data.
result Annual Russell 3000 portfolios are more crowded than quarterly ones, suggesting lower transaction costs.
Paper introduces unknotting index for virtual knots.
problem Computing and understanding virtual knots.
method Using writhe invariants and relationships with virtual knot module.
result Existence of virtual knots with specific unknotting indices.