Survey article on Kahler-Einstein metrics and algebraic geometry.
problem Understanding Kahler-Einstein metrics in algebraic geometry.
method Not specified in the abstract, likely involves mathematical analysis and algebraic geometry techniques.
result Discussion of recent developments and challenges in the field.
Proves rigidity for maps between manifolds using degree theory and current developments.
problem Lipschitz-volume rigidity for maps between metric manifolds and Riemannian manifolds.
method Degree theory and recent developments of Lipschitz-volume rigidity for integral currents.
result Proves a Lipschitz-volume rigidity result for 1-Lipschitz maps.
The paper develops residue currents for cohesive modules and proves a generalized Poincaré-Lelong formula.
problem Analyzing coherent sheaves on complex manifolds using global analytic methods.
method Developing residue currents for cohesive modules and proving their properties.
result Proves a generalized Poincaré-Lelong formula for cohesive modules.
We define generalized currents associated with immersions of abstract solenoids with a transversal measure. We realize geometrically the full real homology of a compact manifold with these generalized currents, and more precisely with immersions of minimal uniquely ergodic solenoids. This makes precise and geometric De…
A 3D area-minimizing current in R^5 has a 2-fold essential singularity.
problem Understanding singularities in area-minimizing currents.
method Construction of a specific current with prescribed boundary properties.
result The boundary regularity theory is dimensionally sharp.
We present an alternate proof of the Bismut-Zhang localization formula for η-invariants without using the analytic techniques developed by Bismut-Lebeau. A Riemann-Roch property for Chern-Simons currents, which is of independent interest, is established in due course.
Compact currents and charges in Carnot groups proved.
problem Compactness of normal currents in Carnot groups.
method Dual compactness argument for Rumin forms using pseudo-differential calculus.
result Compactness of normal currents in Carnot groups in flat topology.
In this note we give an overview of some applications of the Calabi-Yau theorem to the construction of singular positive (1,1) currents on compact complex manifolds. We show how recent developments allow us to give streamlined proofs of existing results, as well as new ones.
Develops local population-risk certificates for model updates
problem Model updates in machine learning
method Certify population-risk increments around a model
result Certified upper endpoint yields a risk-controlled update rule
A quick overview is provided on the current development of the WP metric geometry.
Develops framework to analyze pruning of neural networks.
problem Understanding pruning of neural networks in non-imaging data.
method Develops framework to plant and hide winning tickets in neural networks.
result Similar trends in ticket sparsity observed across different tasks.
This paper defines and studies currents and slices in the Heisenberg group, with new challenges and insights.
problem Defining and studying currents and slices in the Heisenberg group Hn. method Definition and classification of currents, slicing of currents, and analysis of properties.
result New challenges and insights in the study of currents on the Heisenberg group, including a unique slice dimension.
Extends curve functions to geodesic currents with a simple criterion.
problem Continuous extension of curve functions to geodesic currents.
method Simple criterion based on smoothing property.
result Extends known curve functions and introduces new examples.
Theory of space-time currents for geometric evolutions.
problem Analysis of geometric evolutions driven by dislocations.
method Development of space-time integral currents with bounded variation, introduction of Lipschitz deformation distance.
result Agreement of Lipschitz deformation distance with integral Whitney flat metric for boundaryless currents.
Develops a multi-class classifier using quantum detection theory.
problem Improving multi-class classification models in machine learning.
method Inspired by quantum detection theory, develops a multi-class classifier.
result Demonstrates improved effectiveness of multi-class classification models.
We generalize subset currents on hyperbolic groups to surfaces.
problem Generalizing subset currents to surfaces.
method Developed the theory of subset currents on π_1(Σ), proving they are a measure-theoretic completion of conjugacy classes of subgroups.
result The space of subset currents on Σ is a measure-theoretic completion of conjugacy classes of non-trivial subgroups, each geometrically corresponding to a convex core.
Deep learning generates addresses for under-addressed cities.
problem Lack of street addresses in developing countries.
method Deep learning applied to satellite images to generate addresses.
result Algorithm generates addresses for neighborhoods and regions.
Let X be a compact Kähler manifold and {θ} be a big cohomology class. We prove several results about the singularity type of full mass currents, answering a number of open questions in the field. First, we show that the Lelong numbers and multiplier ideal sheaves of θ-plurisubharmonic functions with full mass a…
The paper uses SVAR modeling to analyze how demographic changes affect the current account and economic growth.
problem The impacts of demographic changes on the current account and economic growth.
method SVAR modeling to track dynamic impacts between population growth, current account, and economic growth.
result The long-run net impact on economic growth of the domestic working population growth and demand labor for emigrants is positive.
This study assesses risk concentration in MDB portfolios using Monte Carlo simulations.
problem Risk concentration in MDB portfolios of a few borrowers.
method Realistic MDB portfolio simulations and Monte Carlo analysis.
result Current risk adjustments may be overly conservative.
Currents represent generalized surfaces studied in geometric measure theory. They range from relatively tame integral currents representing oriented compact manifolds with boundary and integer multiplicities, to arbitrary elements of the dual space of differential forms. The flat norm provides a natural distance in the…
New method improves smoothness of minimizing currents near singular points.
problem Improving smoothness of minimizing currents near singular points.
method New method to estimate the full singular set of the foliation by minimizers and proof of superlinear decay of closeness.
result Generic smoothness of minimizers improved to n−9−εn for n≥11. We adapt the theory of currents in metric spaces, as developed by the first-mentioned author in collaboration with B. Kirchheim, to currents with coefficients in Z_p. Building on S. Wenger's work in the orientable case, we obtain isoperimetric inequalities mod(p) in Banach spaces and we apply these inequalities to prov…
The Basel II Accords have sparked increased interest in the development of approaches based on internal ratings systems and have initiated the elaboration of models for remote ratings forecasts based on external ones as part of Risk Management and Early Warning Systems. This article evaluates the peculiarities of curre…
Modern geometric measure theory, developed largely to solve the Plateau problem, has generated a great deal of technical machinery which is unfortunately regarded as inaccessible by outsiders. Some of its tools (e.g., flat norm distance and decomposition in generalized surface space) hold interest from a theoretical pe…
Survey of EEG market and machine learning applications.
problem Improving neurology through data-driven research.
method Comprehensive survey of EEG applications and market.
result Machine learning enhances EEG applications and market growth.
Curious hierarchical reinforcement learning improves learning performance.
problem Combining hierarchical abstraction and curiosity-driven exploration in reinforcement learning.
method Developed a method that combines hierarchical reinforcement learning with curiosity.
result Curiosity can more than double learning performance and success rates.
Survey on AI math foundations, focusing on neural networks.
problem Lack of rigorous mathematical foundation for AI.
method Survey and discussion of theoretical directions in AI.
result Discussion of open problems in AI math.
New method predicts VIV in 3D currents for marine risers.
problem Uncertainty in predicting VIV due to 3D current effects.
method Data-driven modeling using random forest regression.
result Data-driven method outperforms traditional models in 3D current conditions.
Develops higher-order Euler-Poincaré field equations for principal G-bundles.
problem Formulating field equations for higher-order jet bundles of principal G-bundles.
method Reduction theory applied to G-invariant Lagrangian field theories on jet bundles, transferring Hamilton's principle to reduced configuration bundles. result Higher-order Euler-Poincaré field equations are equivalent to conservation of Noether current.
Paper develops methods for evaluating mHealth interventions using historical data.
problem Evaluating the long-term effectiveness of mHealth interventions designed for near-term outcomes.
method Develops off-policy estimation techniques to infer long-term average outcomes from historical data.
result Provides estimators and confidence intervals for evaluating mHealth policies.
Study shows unique tangent cones for area-minimizing currents at boundary points.
problem Uniqueness of tangent cones for area-minimizing currents with arbitrary multiplicity.
method Analysis of area minimizing currents in C2 submanifolds with arbitrary boundary multiplicity. result Tangent cones are unique at density Q/2 boundary points. GAMA is a user-friendly AutoML system for machine learning pipeline optimization.
problem Empowering users to control and optimize machine learning pipelines.
method Modular AutoML system with three search algorithms and two post-processing steps.
result GAMA allows users to track and control the search process for optimal machine learning pipelines.
We improve current instability-based methods for the selection of the number of clusters k in cluster analysis by developing a normalized cluster instability measure that corrects for the distribution of cluster sizes, a previously unaccounted driver of cluster instability. We show that our normalized instability mea…
This paper develops a theoretical model for SPPC prices and improves accounting standards.
problem Lack of theoretical price for SPPC and issues in current accounting standards.
method Developed a theoretical SPPC price model with a marginal utility-based approach, explicitly indicated stochastic processes, and proposed a convenient model.
result Improved theoretical price model and addressed problems in current accounting standards.
The paper develops a bootstrap method to measure algorithmic convergence in regression.
problem Ensuring a randomized ensemble performs nearly as well as an ideal infinite ensemble.
method Bootstrap method for regression setting, complementing classification setting.
result Theoretical guarantees for the bootstrap method can be established under weaker assumptions.
PASE method protects machine learning models from membership inference attacks without significant accuracy loss.
problem Membership inference attacks on machine learning models.
method Switching ensembles approach to mitigate privacy leakage.
result PASE method provides effective privacy protection with minimal accuracy penalty.
Machine learning enhances fuzzing for better software testing.
problem Challenges in traditional fuzzing.
method Applications of machine learning to improve fuzzing.
result Machine learning tools have successfully addressed fuzzing bottlenecks.
This survey was written for the Current Developments in Mathematics conference, 2012, and is an updating of my article "The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations," in the Seattle 2005 proceedings. We trace progress and thinking about the SYZ conjecture since its introduction in 1996. …
Neural networks predict ODT formulations, reducing development time.
problem Efficiently predicting ODT formulations for quality control.
method Artificial Neural Network (ANN) and Deep Neural Network (DNN) techniques.
result DNN model outperformed ANN in predicting ODT disintegrating time.
Study area minimizing currents in Riemannian manifolds, proving unique structure and decay.
problem Area minimizing currents in Riemannian manifolds with moduli.
method Structural results and uniqueness theorem, inspired by Simon's techniques.
result Uniqueness and decay towards tangent cones for area minimizing currents.
Develops a Causal Transformer for estimating counterfactual outcomes from longitudinal data.
problem Estimating counterfactual outcomes over time from observational data is challenging due to complex, long-range dependencies.
method Combines three transformer subnetworks with separate inputs for time-varying covariates, previous treatments, and previous outcomes into a joint network with in-between cross-attentions. Uses a custom, end-to-end training procedure with a counterfactual domain confusion loss to address confounding bias.
result Achieves superior performance over current baselines in synthetic and real-world datasets.
Novel model selection method outperforms current state-of-the-art in high-dimensional graphical models.
problem Accurate model selection in high-dimensional graphical models.
method Graphical Neighbour Information (GNI) criterion.
result Demonstrates oracle performance in high-dimensional model selection, outperforming current methods.
This note announces a general construction of characteristic currents for singular connections on a vector bundle. It develops, in particular, a Chern-Weil-Simons theory for smooth bundle maps α:E→F which, for smooth connections on E and F, establishes formulas of the type $$ φ\ = \ \text{\rm Res}_φΣ…
FedVision uses federated learning to improve object detection without transmitting data.
problem Challenges in building object detection models on large training datasets due to privacy and cost issues.
method Federated learning (FL) platform for easy integration by non-experts.
result Significant efficiency improvement and cost reduction in smart city applications.
Starting from the candidate Bloch-Beilinson filtration on Chow groups of 0-cycles constructed by J. Lewis, we develop and describe geometrically a series of Hodge-theoretic invariants defined on the graded pieces. Explicit formulas (in terms of currents and membrane integrals) are given for certain quotients of the inv…
Belief networks are a new, potentially important, class of knowledge-based models. ARCO1, currently under development at the Atlantic Richfield Company (ARCO) and the University of Southern California (USC), is the most advanced reported implementation of these models in a financial forecasting setting. ARCO1's underly…
Survey of software developers' experience with Github Copilot tool.
problem Investigate developers' acceptance of AI-generated code.
method Survey with 18 questions distributed to 42 programmers.
result Mixed developer opinions, mostly positive but reluctance to use.