Abstract: Review of Index theorem and its applications.
problem Index theorem applications in differential geometry.
method Review of Atiyah-Singer Index theorem.
result Basic knowledge required for understanding.
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Main theorem of this paper states that Floer cohomology groups in a Hilbert space are isomorphic to the cohomological Conley Index. It is also shown that calculating cohomological Conley Index does not require finite dimensional approximations of the vector field. Further directions are discussed.
New method learns SIMs with arbitrary monotone activations without strong distributional assumptions.
problem Learning Single-Index Models with arbitrary monotone activations.
method Based on omniprediction with calibrated multiaccuracy and Bregman divergences.
result First agnostic learning result for SIMs with arbitrary monotone activations.
A Note on the Morse Index Theorem for Geodesics between Submanifolds in semi-Riemannian Geometrymath.DG
The computation of the index of the Hessian of the action functional in semi-Riemannian geometry at geodesics with two variable endpoints is reduced to the case of a fixed final endpoint. Using this observation, we give an elementary proof of the Morse Index Theorem for Riemannian geodesics with two variable endpoints,…
We discuss the relation between arc index, maximal Thurston--Bennequin number, and Khovanov homology for knots. As a consequence, we calculate the arc index and maximal Thurston--Bennequin number for all knots with at most 11 crossings. For some of these knots, the calculation requires a consideration of cables which a…
New process capability index for non-normal data.
problem Measuring process capability when data does not follow normal distributions.
method Developed a new multivariate non-parametric PCI using Support Vector Data Description (SVDD).
result Demonstrated improved accuracy in process capability measurement for non-normal data.
New algorithm learns from sparse data without knowing sparsity index.
problem Sparse bandit problem where only a subset of features affects reward.
method Sparsity-agnostic Lasso Bandit algorithm that doesn't require prior sparsity index knowledge.
result Established tight regret bounds and outperforms existing methods.
Local index formula for Lorentzian Dirac operators on spacetimes.
problem Index theory for Lorentzian Dirac operators with nontrivial dynamics.
method Local index formula based on microlocal analysis.
result Established a local index formula for Lorentzian Dirac-type operators.
Method improves volatility targeting for index construction.
problem High turnover, leverage spikes, and sensitivity to estimation error in existing volatility-targeting strategies.
method Proportional-control approach for setting index weights that corrects tracking error through feedback.
result The proportional-control approach achieves the target volatility more effectively than open-loop alternatives.
New algorithm reduces sample complexity for omnipredictors of SIMs.
problem Learning optimal predictors for various loss functions.
method Sharp analysis of Isotron algorithm for agnostic learning.
result Improved sample complexity to for bi-Lipschitz link functions.
New pruning technique reduces index size for DNNs.
problem Irregular index form in fine-grained pruning limits parallelism and memory usage.
method Proposes a low-rank binary index matrix for efficient compression and decompression.
result Fine-grained pruning with binary matrices achieves lower memory footprint and higher parallelism.
This review analyzes recent advances in solving index tracking problems.
problem Creating a portfolio that closely follows a specific index with lower costs.
method Systematic review of mathematical approaches and metaheuristics.
result Metaheuristics have been extensively applied and improved in solving index tracking problems.
Paper presents models for stock price prediction using SPX index.
problem Predicting stock prices using time series data.
method Four models: martingale, ordinary linear, generalized linear, and RNN.
result RNN model performs best among the four models.
The study finds multiple closed Reeb orbits on specific contact forms.
problem Finding geometrically distinct closed Reeb orbits on prequantization bundles.
method Analyzes contact forms on prequantization bundles with specific index requirements.
result Establishes multiplicity results for closed Reeb orbits under certain conditions.
Massive fermions help understand index theorems without chiral symmetry.
problem Understanding index theorems in massive fermion systems.
method Reformulate chiral anomaly and index theorems with massive Dirac operators.
result Nontrivial mathematical relations between massless and massive fermions.
The stick index of a knot is the least number of line segments required to build the knot in space. We define two analogous 2-dimensional invariants, the planar stick index, which is the least number of line segments in the plane to build a projection, and the spherical stick index, which is the least number of great c…
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.
Paper presents an efficient exploration method for reinforcement learning.
problem Efficient exploration in reinforcement learning with uncertainty quantification.
method Parameterized Indexed Value Function (PIV) using index sampling.
result Proves the regret bound for learning PIV in a tabular setting and proposes PINs for computational learning.
New method approximates M-estimator and predictions without solving fixed-point equations.
problem Characterize behavior of M-estimator and predictions in single index models.
method Develops data-driven observable adjustments to proximal operators.
result Empirical distributions of M-estimator and predictions are approximated without solving fixed-point equations.
The paper proves continuity of Morse index for Ricci shrinkers.
problem Lower and upper semi-continuity of the Morse index for gradient Ricci shrinkers.
method Adapting and refining recent arguments on CMC hypersurfaces and polynomially weighted Sobolev spaces, with techniques for non-compact shrinkers.
result Identifies a condition ensuring the Morse index of asymptotically conical shrinkers is bounded below by the f-index of their asymptotic cone.
Extensions to given-data Sobol' index estimators for large models.
problem Efficiently compute Sobol' indices for models with many inputs.
method General definition, streaming algorithm, heuristic filtering.
result Comparable accuracy and lower memory usage for large models.
Proposes a transfer learning framework for sparse SIMs without raw source data.
problem Lack of direct access to raw source data and known link functions in transfer learning.
method Source-data-free framework based on SIM, using summary statistics and a multilayer perceptron.
result Consistent improvements over existing approaches in synthetic and real-world data.
A new method optimizes diversity and sparsity for index tracking.
problem Accurately replicating a benchmark index with a small number of diverse assets.
method Jointly optimizes diversity and sparsity using a regularizer based on asset similarity.
result The proposed algorithm outperforms existing methods in out-of-sample backtesting.
StackNet learns new tasks without forgetting old ones.
problem Catastrophic forgetting in continual learning.
method StackNet combines an index module with a StackNet to retain old task performance.
result StackNet prevents performance degradation of previously learned tasks.
The Surprise index assesses autonomous systems' competency in uncertain environments.
problem Evaluating competency of autonomous systems in dynamic, uncertain environments.
method Surprise index, a measure that quantifies system performance based on available data.
result The Surprise index can be computed for dynamic systems with Gaussian marginal distributions.
Global Morse index theorem applied to Jacobi fields on CMC surfaces.
problem Existence and structural theorem of Jacobi fields on CMC surfaces.
method Global Morse index theorem proof via set-continuity of domain shapes and eigenvalue continuity.
result Global Morse index theorem provides structural existence of Jacobi fields.
Paper proves existence of Dirac-harmonic maps with trivial index.
problem Finding Dirac-harmonic maps with trivial index.
method Defining a new quantity and proving its homotopy invariance.
result Existence of Dirac-harmonic maps from closed Riemann surfaces to Kähler manifolds.
Tensor methods tackle high-dimensional additive index models with discordance and heterogeneity.
problem High-dimensional datasets with sampling problems and heterogeneity.
method Method of moments based procedures for estimating indices of discordant additive index models.
result Rates of convergence of estimators in both high and low-dimensional settings.
Paper proves non-vanishing of index map for low-degree cohomology classes.
problem Non-vanishing of index map for low-degree cohomology classes.
method Analysis of -equivariant -homology and -algebra of group .
result Non-vanishing of the image of low-degree cohomology classes under the index map.
New condition extends Diederich-Fornæss index for pseudoconvex domains.
problem Determine sufficient conditions for Diederich-Fornæss index to be close to 1.
method Derive sufficient condition on Levi-flat sets of the boundary.
result Diederich-Fornæss index is 1 if Levi-flat sets are transversal to holomorphic tangent vector fields.
A new method tracks index using topological data analysis for sparse portfolios.
problem Sparse index tracking with robust risk management.
method Topological learning via Vietoris-Rips filtration for sparse regularization.
result The method outperforms state-of-the-art techniques in various market conditions.
New validity index for fuzzy-possibilistic c-means clustering.
problem Conflicting results in determining the optimal number of clusters due to noisy data points and outliers.
method Introducing a new validity index (FP index) for fuzzy-possibilistic c-means clustering.
result FP index works well in datasets with varying cluster shapes and densities.
Bayesian optimization with cost-awareness using Gittins index.
problem Optimizing unknown functions with limited data evaluations and costs.
method Developed a connection between cost-aware Bayesian optimization and the Pandora's Box problem, using the Gittins index as an acquisition function.
result The Gittins index-based acquisition function performs well in cost-aware Bayesian optimization, especially in high dimensions.
Hybrid quantum-classical method optimizes financial index tracking.
problem Optimizing asset weights for financial index replication.
method Hybrid quantum-classical optimization with pruning algorithm.
result Improved performance through quantum and classical optimization.
Prediction of Compression Index of Fine-Grained Soils Using a Gene Expression Programming Modelstat.AP
Gene expression programming predicts compression index of fine-grained soils efficiently.
problem Estimating the compression index of fine-grained soils is costly and time-consuming.
method Developed a gene expression programming model using soil parameters.
result The GEP model predicts the compression index more accurately than conventional methods.
Develops methods for estimating volatility models in high dimensions.
problem Estimating volatility in high-dimensional settings with heavy-tailed data.
method Uses Stein's identities for variance index estimation in high-dimensional settings.
result Matches minimax optimal rate for mean index estimation in high-dimensional settings.
The paper uses machine learning to predict volatility from option data.
problem Improving predictability and liquidity of VIX-styled volatility indices.
method Regularized regression and Feedforward Neural Networks (FNN) were tested on S&P 500 Index and its option data.
result Ridge regression and FNN improve volatility indexing with higher prediction performance and fewer options required.
The Generative Leap: Sharp Sample Complexity for Efficiently Learning Gaussian Multi-Index Modelscs.LG
Study efficient estimation of hidden subspaces in Gaussian Multi-index models.
problem Estimating hidden subspaces in Gaussian Multi-index models with low-dimensional projections.
method Introduced the generative leap exponent and developed an agnostic sequential estimation procedure using spectral U-statistics.
result Achieved optimal sample complexity of $n=Θ(d^{1 \vee \k/2})$ for efficient estimation.
A new OOD detector using an overlap index improves accuracy without high computational costs.
problem Effective OOD detection for machine learning models in open-world scenarios.
method Proposes an overlap index-based confidence score function for OOD detection.
result The proposed method achieves competitive accuracy with lower computational costs compared to state-of-the-art detectors.
The paper demonstrates that a pure-diffusion 3/2 model is able to capture the observed upward-sloping implied volatility skew in VIX options. This observation contradicts a common perception in the literature that jumps are required for the consistent modelling of equity and VIX derivatives. The pure-diffusion model, h…
Proves a strengthening of Chang, Weinberger, and Yu's theorem on positive scalar curvature.
problem Existence of positive scalar curvature metrics on compact manifolds with boundary.
method Constructs relative and absolute indices of Dirac operators and relates them via K-theory.
result Positive scalar curvature on the whole manifold implies vanishing of the relative index.
The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections. Roughly speaking, a normally non-singular map is a map together with such a …
A new index measures confounding effects in medical data.
problem Misleading predictive performance due to unaccounted confounders.
method Introduces a novel index to quantify confounding effects.
result Validated on simulated and real-world data.
Study introduces new methods to estimate stock return rates.
problem Estimating the required rate of return for stocks and private companies.
method Maximum likelihood, Bayesian, and Kalman filtering methods applied to historical data.
result Suggested methods can accurately estimate the required rate of return.
A new method for choosing thresholds in data sequences without assuming distribution.
problem Choosing thresholds for random sequences without distributional assumptions.
method Data-driven threshold machine (DTM) that estimates three parameters of extreme value distributions and extremal index.
result DTM provides a reliable estimate of thresholds with robustness and computational efficiency.
New RL algorithms learn Gittins indices for unknown Markovian states.
problem Learning Gittins indices for unknown Markovian state transitions.
method Tabular (QGI) and Deep RL (DGN) algorithms based on retirement formulation.
result Lower run time, less storage space, better convergence to Gittins index.
Study introduces new methods to estimate equity and liability required rates of return.
problem Estimating the required rates of return for equity and liabilities of companies.
method Used maximum likelihood, Bayesian, Kalman filtering, and market value evaluation methods.
result The new methods can accurately estimate the required rates of return.
We introduce a monoid corresponding to knotted surfaces in four space, from its hyperbolic splitting represented by marked diagram in braid like form. It has four types of generators: two standard braid generators and two of singular type. Then we state relations on words that follows from topological Yoshikawa moves. …