Study infinite-dimensional Toda manifold at irregular singularity, revealing non-uniqueness of formal solutions.
problem Non-uniqueness of formal solutions to the Dubrovin equation at irregular singularity.
method Revisited canonical coordinates, formal solutions analysis, Borel resummation, Stokes matrices computation.
result Infinite-dimensional Stokes matrices computed from resummed formal solutions.
Paper extends neural network method to irregular solutions in PDEs.
problem Solving irregular and data-enriched PDEs.
method Deep neural networks for numerical PDE solutions, extending to irregular and data-enhanced cases.
result Demonstrates ease and integration of large datasets in PDE modeling.
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.
Efficient surrogate modeling for complex PDEs with physical laws.
problem High computational cost of repeated PDE simulations.
method LC-prior Gaussian process with POD and RBF-FD.
result Significantly reduced computational cost and improved accuracy.
Paper connects Painlevé VI equation to irregular systems, solving monodromy data.
problem Solving monodromy data for irregular systems related to Painlevé VI.
method Expressed Frobenius integrability in terms of PVI, computed monodromy data for coalescing eigenvalues.
result Computed monodromy data for transcendentals holomorphic at critical points of PVI.
In many fields observations are performed irregularly along time, due to either measurement limitations or lack of a constant immanent rate. While discrete-time Markov models (as Dynamic Bayesian Networks) introduce either inefficient computation or an information loss to reasoning about such processes, continuous-time…
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.
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.
Paper proves short-time existence for network flow, providing detailed insights.
problem Short-time existence for the flow of a network of curves in the plane.
method Direct PDE approach, handling singularities at vertices using self-similar expanding solutions.
result Substantially more detailed information about network resolution into a regular one.
Neural controlled DEs model irregular time series by adjusting based on observations.
problem Modeling irregularly sampled multivariate time series with memory-efficient adjoint-based backpropagation.
method Neural controlled differential equations (CDEs) that adjust based on subsequent observations.
result Achieves state-of-the-art performance on various datasets.
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.
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…
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.
We show that there are no irregular Sasaki-Einstein structures on rational homology 5-spheres. On the other hand, using K-stability we prove the existence of continuous families of non-toric irregular Sasaki-Einstein structures on odd connected sums of S2×S3.
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 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.
LSTM improves cross-network recommendations by capturing user preference changes and irregular time intervals.
problem Offline cross-network recommender solutions fail to capture user preference changes and dynamic environments.
method Proposes a multi-layered LSTM network with attention mechanisms, higher order interactions, and time-aware gates.
result The model consistently outperforms state-of-the-art in accuracy, diversity, and novelty.
Neural Jump ODEs improve online filtering and classification with robust performance.
problem Online filtering and classification in settings with irregular and partial observations.
method Modeling conditional expectation using Neural Jump ODEs, with theoretical convergence guarantees.
result Demonstrated superior performance over classical methods, especially in complex scenarios.
We construct a new five parameter family of constant mean curvature trinoids with two asymptotically Delaunay ends and one irregular end.
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.
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.
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…
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.
We present a countably infinite number of new explicit co-homogeneity one Sasaki-Einstein metrics on S^2 x S^3, in both the quasi-regular and irregular classes. These give rise to new solutions of type IIB supergravity which are expected to be dual to N=1 superconformal field theories in four-dimensions with compact or…
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.
Machine learning methods such as convolutional neural networks (CNNs) are becoming an integral part of scientific research in many disciplines, spatial vector data often fail to be analyzed using these powerful learning methods because of its irregularities. With the aid of graph Fourier transform and convolution theor…
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.
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.
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.
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.
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.
We study triangulations T defined on a closed disc X satisfying the following condition: In the interior of X, the valence of all vertices of T except one of them (the irregular vertex) is 6. By using a flat singular Riemannian metric adapted to T, we prove a uniqueness theorem when the valen…
Transformer-based multi-scale model outperforms traditional methods in solving PDEs on irregular domains.
problem Solving partial differential equations on irregular domains using deep learning.
method Introduces Multi-Scale Attention Transformer (\msat{}) for solving PDEs.
result Achieves state-of-the-art generalization on complex geometry problems with significant speedup.
We explore the use of graph networks to deal with irregular-geometry detectors in the context of particle reconstruction. Thanks to their representation-learning capabilities, graph networks can exploit the full detector granularity, while natively managing the event sparsity and arbitrarily complex detector geometries…
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.
This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's squared volatility, or `cumulative variance'. In the new framework, corresponding p…
Given a closed oriented PL four-manifold X and a closed surface B embedded in X with isolated cone singularities, we give a formula for the signature of an irregular dihedral cover of X branched along B. For X simply-connected, we deduce a necessary condition on the intersection form of a simply-connected i…
We describe the moduli spaces of meromorphic connections on trivial holomorphic vector bundles over the Riemann sphere with at most one (unramified) irregular singularity and arbitrary number of simple poles as Nakajima's quiver varieties. This result enables us to solve partially the additive irregular Deligne-Simpson…
New method forecasts values and timing in irregular time series.
problem Forecasting values and timing in sparse, irregularly sampled multivariate time series.
method Proposes a novel approach for forecasting values and timing in irregular time series.
result Successfully forecasts values and timing in irregular time series.
Short survey based on talk given at the Institut Henri Poincare January 17th 2012, during program on surface groups. The aim was to describe some background results before describing in detail (in subsequent talks) the results of [Boa11c] related to wild character varieties and irregular mapping class groups.
A new method uses sinusoidal functions to represent timestamps as dense vectors for improving irregularly sampled time series learning.
problem Challenges in supervised learning with irregularly sampled time series due to irregular time intervals.
method Proposes a novel method to represent timestamps as dense vectors using sinusoidal functions, called Time Embeddings.
result Improves LSTM-based and classical machine learning models, especially with very irregular data.
Method learns dynamics from sparse, irregular feature data.
problem Learn system dynamics from sparse, irregularly sampled feature time series.
method Formulates as high-dimensional linear regression using signatures.
result Oracle bound on prediction error with explicit sampling dependencies.
We consider the optimal stopping problem with non-linear f-expectation (induced by a BSDE) without making any regularity assumptions on the reward process ξ. and with general filtration. We show that the value family can be aggregated by an optional process Y. We characterize the process Y as the $\mathcal{E}^f…
Defines weak normals for irregular curves in high-dimensional spaces.
problem Dealing with irregular curves in high-dimensional Euclidean spaces.
method Using sequences of inscribed polygonals and Gram-Schmidt procedure, introduces a relaxed notion of weak normals.
result Weak normals for irregular curves are the strong limit of approximating polygonals and agree with relaxed energy.