New Sasaki-Einstein structures found on odd connected sums of spheres.
problem Existence of irregular Sasaki-Einstein metrics on specific manifolds.
method K-stability used to prove existence of continuous families of non-toric irregular Sasaki-Einstein structures.
result Continuous families of non-toric irregular Sasaki-Einstein structures on odd connected sums of S2imesS3. The paper studies complex affine structures near irregular singularities.
problem Understanding complex affine structures near irregular singularities.
method Introducing local invariants and a Delaunay decomposition.
result Upper bounds on the complexity of the Delaunay decomposition.
Study local wild mapping class groups for irregular connections on complex curves.
problem Understanding the moduli spaces of irregular connections on complex curves.
method Using isomonodromic deformations, focusing on reflections cosets, and introducing fission trees.
result Complete classification of local wild mapping class groups for various structure groups.
A new method classifies signals on irregular domains using convolutional cluster pooling.
problem Classifying signals on irregular domains with shared properties.
method Convolutional Cluster Pooling layer exploiting multi-scale clustering.
result Generalizes CNNs for graph data, capturing both local and global patterns.
TGNN4I model forecasts irregularly observed graph data using ODEs.
problem Forecasting graph-structured data with irregular time steps and partial observations.
method Introduces a time-continuous latent state in each node using ODEs and GRUs, integrating graph neural network layers.
result Validated usefulness of graph structure and time-continuous dynamics in irregular observation settings.
LLapDiff models irregular multivariate time series without step-by-step integration.
problem Trade-off between discrete and continuous methods for long-horizon forecasting.
method Generative framework that models target as a low-dimensional latent trajectory, guided by modal parameterization and Laplace domain poles.
result Improves long-horizon forecasting over baselines and supports missing-value imputation.
The paper discusses new Lagrangian constructions and examples.
problem Exploring new Lagrangian constructions in complex projective spaces.
method Generalized Delaunay construction among minimal Lagrangians.
result Uncountably many new special Lagrangian cones found.
Moon phases added to stock market analysis for better pattern recognition.
problem Finding meaningful patterns in stock market data using irregular time sampling.
method Incorporating Moon phases into the Gregorian calendar time sampling methods for stock market analysis.
result Moon phases provide unique, irregular sampling features for stock market pattern recognition.
SCOTCH learns system structure from irregular time series using neural SDEs.
problem Learning system structure from irregular time series data.
method SCOTCH uses neural stochastic differential equations (SDE) with variational inference.
result SCOTCH improves structure learning performance on synthetic and real-world datasets.
daep learns from irregular, multimodal astronomical data.
problem Learning from irregular, multimodal astronomical sequences.
method Diffusion Autoencoder with Perceivers (daep) tokenizes, compresses, and reconstructs data.
result daep outperforms VAE and maep baselines in reconstruction and fine-scale structure preservation.
Paper reviews multi-way graph signal processing for tensor data.
problem Maximizing use of multi-way structure in irregular tensor data.
method Generalizes GSP to multi-way data, focusing on graph signals across tensor modes.
result Synthesizes common themes in combining GSP with tensor analysis.
The paper calculates graph Ricci curvature and finds properties of specific graph types.
problem Understanding Ricci curvature on irregular graphs.
method Developed a formula for graph Ricci curvature based on optimal bijections.
result Derived structural and theorem results for specific graph types.
Paper develops a method for causal representation learning from irregular tensors.
problem Complex patterns in high-dimensional, irregular tensor data.
method Novel causal formulation and CaRTeD framework integrating temporal causal representation learning with irregular tensor decomposition.
result Framework provides theoretical guarantees and outperforms state-of-the-art techniques.
New family of trinoids with irregular end found.
problem Finding constant mean curvature trinoids with irregular ends.
method Constructing a five-parameter family of trinoids.
result New family of trinoids with one irregular end.
Study on flat connections with controlled irregularity.
problem Boundedness of algebraic flat connections with limited irregularity.
method Analysis of families of algebraic flat connections and holonomic D-modules.
result Established boundedness of families of algebraic flat connections with controlled irregularity.
The paper introduces surface signatures for irregular surfaces and rough surfaces.
problem Characterizing and integrating highly irregular paths and surfaces.
method Introducing surface signatures and proving extension theorems.
result Surface signatures are universal for surface holonomy and rough surfaces.
Detects illegal stock market trading behaviors using graph ranking methods.
problem Detecting irregular trade behaviors in the stock market.
method Three graph Laplacian based semi-supervised ranking methods.
result Un-normalized and symmetric normalized graph Laplacian based methods outperform the random walk Laplacian method.
T. Mochizuki constructs a theory of variations of wild Hodge structure for which the underlying flat connection can have irregular singularities at infinity. He extends in this way the correspondence of Corlette and Simpson between irreducible flat bundles and stables Higgs bundles, taking into account objects with irr…
Study irregular behavior of ball averages for non-amenable group actions on foliations.
problem Exploring irregular behavior of ball averages for non-amenable group actions.
method Introducing a new mechanism based on group structure to analyze irregular behavior.
result First examples of codimension one foliations with non-existent length averages.
GCNs model complex spatial patterns of POI check-ins.
problem Capturing complex spatial patterns in irregular data.
method Graph Convolutional Neural Networks (GCNs) for semi-supervised prediction.
result Demonstrates feasibility of GCNs for complex geographic data.
EDICT learns evidential distributions for irregular time series, improving predictions and uncertainty quantification.
problem Challenges in predicting and characterizing uncertainty for irregular time series data.
method EDICT (Evidential Distributions for Irregular Time Series) learns a continuous-time evidential distribution.
result EDICT achieves competitive performance on time series classification tasks and provides better uncertainty quantification.
With the developments of the last decade on complete constant mean curvature 1 (CMC 1) surfaces in the hyperbolic 3-space H3, many examples of such surfaces are now known. However, most of the known examples have regular ends. (An end is irregular, resp. regular, if the hyperbolic Gauss map of the surface has an ess…
Derives a recursion formula for irregular spectral curves.
problem Calculating the mean of irregular spectral curves.
method Variant of replica method by Brezín and Hikami, generalized to generalized Laguerre polynomial case.
result Derives a recursion formula for special times where terms are polynomials.
Paper simplifies CNNs for irregular data using MIMO graph filters.
problem Challenges in applying CNNs to irregularly structured data.
method Introduces MIMO graph filters to CNNs, simplifying architectures.
result Proposed architectures reduce model complexity and computational cost.
Study deformation spaces of irregular isomonodromy systems on Riemann surfaces.
problem Understanding the topology of irregular isomonodromy systems.
method Define and study moduli spaces of deformations of irregular classes on Riemann surfaces.
result Generalize G-braid groups to study fundamental groups of deformation spaces.
UT module refines VAE latent space, improving disentanglement and interpretability.
problem Irregular latent distributions cause posterior collapse and misalignment in VAEs.
method UT module uses G-KDE clustering, GM modeling, and PIT to transform latent space into uniform distribution.
result UT module enhances disentanglement and interpretability of latent representations.
Modeling disease progression using irregular time intervals in EHRs.
problem Challenges in analyzing temporal data from EHRs.
method Developed a Markovian generative model using EHR data.
result Model accurately recovers underlying disease progression patterns from irregular time intervals.
In this paper we study K-cosymplectic manifolds, i.e., smooth cosymplectic manifolds for which the Reeb field is Killing with respect to some Riemannian metric. These structures generalize coKähler structures, in the same way as K-contact structures generalize Sasakian structures. In analogy to the contact case, we dis…
CRUs model irregular time series with continuous hidden states.
problem Handling irregular time intervals in sequential data.
method Continuous Recurrent Units (CRUs) that integrate hidden states via a linear stochastic differential equation.
result CRUs outperform methods based on neural ordinary differential equations in irregular time series interpolation.
Develops a RNN model to predict obesity status improvement using irregular activity data.
problem Predicting obesity status improvement using irregular activity data.
method Develops a RNN-based time-aware architecture to handle irregular observation times and extract relevant features from longitudinal patient records.
result Achieves an accuracy of 77-86% in predicting obesity status improvement.
Study triangulations with a unique irregular vertex of valence 6k.
problem Characterize triangulations with a specific valence for vertices.
method Use a flat singular Riemannian metric adapted to triangulations.
result Uniqueness theorem for triangulations with irregular vertex valence not a multiple of 6.
For a complex polynomial in two variables we study the morphism induced in homology by the embedding of an irregular fiber in a regular neighborhood of it. We give necessary and sufficient conditions for this morphism to be injective, surjective. Particularly this morphism is an isomorphism if and only if the correspon…
Proposes MVGPR for spatiotemporal data modal analysis.
problem Sparse and irregularly sampled data in complex flows.
method Multivariate Gaussian process regression (MVGPR) with kernel design.
result MVGPR outperforms DMD and SPOD in modal analysis of sparse and irregular data.
The book is devoted to study so-called irregular subsets of the Grassmannian manifold Gkn(V) (this class of sets was introduced by author). In the previous variant of the book we restrict ourself only to the case when V is an n-dimensional vector space under the field R. Now we consider irregular subsets …
ACSSM models irregular time series with continuous dynamics.
problem Modeling irregular time series data.
method ACSSM uses a multi-marginal Doob's h-transform and variational inference with stochastic optimal control.
result ACSSM outperforms in tasks like classification, regression, interpolation, and extrapolation.
Graph CNN method improves classification of irregular spatial data like building patterns.
problem Challenges in analyzing irregular spatial data with machine learning.
method Graph Fourier transform and convolution theorem to convert irregular spatial data into a learnable format.
result Significantly improved classification of building patterns compared to other methods.
The study bounds growth of Hodge numbers and computes L2-Betti numbers for irregular varieties.
problem Bounding growth of normalized Hodge numbers and computing L2-Betti numbers for irregular varieties. method Analysis of abelian covers, weak generic Nakano vanishing theorem, and convergence of plurigenera.
result Optimal bounds on the growth of normalized Hodge numbers and computation of L2-Betti numbers. Neural Laplace Control tackles offline RL for continuous-time delayed systems with irregular observations.
problem Offline reinforcement learning problems involving continuous-time environments with delays and irregular observations.
method Combines a Neural Laplace dynamics model with a model predictive control (MPC) planner.
result Achieves near expert policy performance on continuous-time delayed environments.
Optimal stopping problem solved for irregular reward processes without regularity assumptions.
problem Optimal stopping with non-linear f-expectation for irregular reward processes. method Characterization of value process Y as Ef-Snell envelope of ξ; infinitesimal characterization via Reflected BSDE. result Value process Y can be aggregated by an optional process Y. A new wavelet method for analyzing lead-lag effects between financial assets.
problem Analyzing lead-lag relationships between financial assets.
method Wavelet-based framework bridging continuous-time and discrete-time models.
result Developed an asymptotic theory for multi-scale analysis of lead-lag effects.
This paper deals with moduli spaces of framed principal bundles with connections with irregular singularities over a compact Riemann surface. These spaces have been constructed by Boalch by means of an infinite-dimensional symplectic reduction. It is proved that the symplectic structure induced from the Atiyah--Bott fo…
Improved MCMC sampling for expensive, irregular likelihoods.
problem Bayesian inference challenges with irregular, expensive likelihoods.
method Adapt subset samplers, introduce data-driven proxies, adaptive controller.
result Improved HINTS algorithm achieves best sampling error in fixed budget.
We study topological recursion on the irregular spectral curve xy2−xy+1=0, which produces a weighted count of dessins d'enfant. This analysis is then applied to topological recursion on the spectral curve xy2=1, which takes the place of the Airy curve x=y2 to describe asymptotic behaviour of enumerative proble…
The paper extends metrics and solitons on toric Fano manifolds with irregular Sasaki-Einstein metrics.
problem Extension of metrics and solitons on toric Fano manifolds with irregular Sasaki-Einstein metrics.
method Verification of the extension of momentum construction of Kaehler-Einstein metrics and Kaehler-Ricci solitons on the total space of positive rational powers of the canonical line bundle.
result The extended metric along the zero section has an expression that can be extended to the total space, and restricts to a transversely Kaehler-Einstein (Sasakian eta-Einstein) metric.
Study of symplectic groupoids from tt*-Toda equations.
problem Geometry of meromorphic connections with irregular singularities.
method Holomorphic symplectic groupoid structure over Steinberg cross section.
result Proves the space of tt*-Toda connections is a symplectic Lie groupoid.
New BdryMatérn GP model for reliable boundary integration on irregular domains.
problem Incorporating boundary information in Gaussian process models for complex phenomena.
method Proposes a novel BdryMatérn GP framework with a new covariance kernel derived via path integral and stochastic PDE.
result Sample paths from the BdryMatérn GP satisfy desired boundaries with smoothness control on derivatives.
DR-FRL learns functional states from irregular histories for causal inference.
problem Causal inference with irregularly sampled longitudinal data.
method DR-FRL workflow combining functional and temporal encoders, nuisance heads, and EIF-targeted validation.
result DR-FRL can improve causal inference when pseudo-outcomes are heavy-tailed or measurement is informative.
Study finds volume minimization principle for conical Calabi-Yau structures on horospherical cones.
problem Existence and classification of conical Calabi-Yau structures on horospherical cones.
method Variational approach to establish equivalence between volume minimization and existence of conical Calabi-Yau structures.
result Existence of many irregular horospherical cones with mild singularities.