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…
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48 results for “spatial irregularity”
The understanding of geographical reality is a process of data representation and pattern discovery. Former studies mainly adopted continuous-field models to represent spatial variables and to investigate the underlying spatial continuity/heterogeneity in the regular spatial domain. In this article, we introduce a more…
Graph neural networks extend neural Bayes estimators to irregular spatial data.
problem Estimating parameters from irregular spatial data with computational efficiency.
method Employing graph neural networks to approximate Bayes estimators for irregular spatial data.
result Extending neural Bayes estimation to irregular spatial data with computational benefits.
TK-GCN forecasts spatiotemporal dynamics using Koopman-enhanced graph convolutional networks.
problem Forecasting complex spatiotemporal dynamics over irregular domains.
method Two-stage framework: Koopman-enhanced Graph Convolutional Network (K-GCN) for spatial encoding and Transformer for temporal modeling.
result TK-GCN outperforms state-of-the-art methods in spatiotemporal cardiac dynamics forecasting.
Nonlocal Bayesian modeling for continuous spatio-temporal dynamics
problem Handling irregular time points, sparse observations, and nonlocal interactions in spatio-temporal forecasting
method Hierarchical Bayesian framework with coordinate-based spatial basis expansion and continuous-time ODE
result Strong forecasting and uncertainty calibration
Neural networks improve geospatial data analysis by relaxing linearity assumptions.
problem Traditional geospatial analysis assumes linear models, limiting flexibility.
method Embedding neural networks within traditional geostatistical models for non-linear mean functions.
result NN-GLS algorithm provides consistent and scalable predictions for irregular spatial data.
On spatially irregular ordinary differential equations and a pathwise volatility modelling frameworkq-fin.MF
Develops a new framework for financial price processes without stochastic calculus.
problem Modeling non-stationary and irregularly varying volatility processes in finance.
method Introduces a pathwise approach to solving spatially irregular ODEs, using geometric Brownian motion.
result Establishes the uniqueness of solutions for strictly increasing, spatially irregular ODEs.
A framework uses deep learning for spatio-temporal data prediction.
problem Interpolation of continuous spatio-temporal fields on irregular points.
method Decomposes spatio-temporal processes into products of basis functions and spatial coefficients.
result Effectiveness in reconstructing coherent spatio-temporal fields.
Novel SCUSUM detects weak spatial signals more efficiently.
problem Detecting weak clustered signals in spatial data.
method Spatial CUSUM (SCUSUM) using CUSUM procedure and false discovery rate control.
result SCUSUM achieves high classification accuracy for weak spatial signals.
Domain Elastic Transform: Bayesian Function Registration for High-Dimensional Scientific Datastat.ML
DET unifies geometric and functional alignment for high-dimensional scientific data.
problem Challenges in nonrigid registration for high-dimensional, irregular data.
method Domain Elastic Transform (DET) treats data as functions on irregular domains, using a Bayesian framework for elastic motion registration.
result DET achieves 92% topological preservation on MERFISH data and successfully registers whole-embryo Stereo-seq atlases.
Inverse Models for Estimating the Initial Condition of Spatio-Temporal Advection-Diffusion Processesstat.ME
Paper tackles estimating initial conditions of spatio-temporal processes from sparse data.
problem Estimating initial conditions of spatio-temporal advection-diffusion processes from sparse data.
method Regularized convex optimization problem with Alternating Direction Method of Multipliers.
result Efficient solutions for non-uniform and shifted uniform sampling schemes.
Introduces a novel spatial attention module for convolutional networks.
problem Irregular boundaries in position-wise spatial attention maps hamper model generalization.
method Introduces a convolutional rectangular attention module with 5 parameters.
result Systematically outperforms position-wise counterparts in experiments.
DINo forecasts PDEs with flexible extrapolation and adaptability.
problem Fixed discretizations limit real-world PDE forecasting.
method DINo uses implicit neural representations for continuous-time dynamics.
result DINo outperforms other neural PDE forecasters.
Adaptive algorithm minimizes online prediction errors for irregular data.
problem Online adversarial regression with highly irregular prediction rules.
method Adaptive wavelet-based algorithm for Besov space regression.
result Minimax-optimal regret bounds in adversarial settings.
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.
Efficiently estimates spatial covariance models with corrections for bias.
problem Bias in spatial covariance model estimation due to boundary effects and aliasing.
method Debiased Spatial Whittle Likelihood method, addressing missing data and non-Gaussian processes.
result Consistent and asymptotically normal estimation under weak assumptions.
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.
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 , 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…
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 .
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.
A new method classifies hyperspectral images using dynamic graph convolutional networks.
problem Complex spatial context in HSI classification leads to inaccurate results.
method Develops a GCN-based method that captures long-range contextual relations and refines graph edges.
result Significant improvement in HSI classification performance compared to state-of-the-art methods.
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 (this class of sets was introduced by author). In the previous variant of the book we restrict ourself only to the case when is an -dimensional vector space under the field . 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.
The study bounds growth of Hodge numbers and computes -Betti numbers for irregular varieties.
problem Bounding growth of normalized Hodge numbers and computing -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 -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.
We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregular shaped spaces arising as subsets or submanifolds of R, R2, R3 and beyond. For example, in-GPs can accommodate spatial domains arising…
Diffusion Autoencoders with Perceivers for Long, Irregular and Multimodal Astronomical Sequencesstat.ML
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 , which produces a weighted count of dessins d'enfant. This analysis is then applied to topological recursion on the spectral curve , which takes the place of the Airy curve 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.
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.
We study triangulations defined on a closed disc satisfying the following condition: In the interior of , the valence of all vertices of except one of them (the irregular vertex) is . By using a flat singular Riemannian metric adapted to , we prove a uniqueness theorem when the valen…
LOT framework embeds high-dimensional cell data into interpretable Euclidean space.
problem Lack of interpretable methods for high-dimensional cell data.
method Adapts Linear Optimal Transport (LOT) to irregular point clouds.
result Accurate and interpretable classification and synthetic data generation.
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.
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.
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.
Given a closed oriented PL four-manifold and a closed surface embedded in with isolated cone singularities, we give a formula for the signature of an irregular dihedral cover of branched along . For 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.