arXiv research

Future stability of FLRW solutions in expanding 3D space is shown for compact perturbations.

MSFA clusters high-dimensional spatial data using spline-based covariance structures.

The 2008 financial crisis revealed banking consolidation paradoxically increased systemic fragility and global financial contagion with negligible spatial decay.

New method finds precise late-time behavior of wave equations.

The paper studies harmonic map heat flow stability and decay rates.

We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay rates.

Study on infinitely-wide CNNs and their adaptability to function spatial scales.

In this note, we compute the limit of the Wang-Yau quasi-local mass on unit spheres at spatial infinity of an asymptotically flat initial data set. Similar to the small sphere limit of the Wang-Yau quasi-local mass, we prove that the leading order term of the quasi-local mass recovers the stress-energy tensor. For a va…

Diffusion Transformer captures spatial-temporal dependencies in sequential data.

Stability proved for open Milne spacetime, showing gravity's long-term behavior.

Stability of catenoid in 4D Minkowski space proven without symmetry assumptions.

A cubing strategy identifies stable hyperparameter regions for uncertainty quantification in spatial deep learning.

Kulldorff's (1997) seminal paper on spatial scan statistics (SSS) has led to many methods considering different regions of interest, different statistical models, and different approximations while also having numerous applications in epidemiology, environmental monitoring, and homeland security. SSS provides a way to …

New proof shows perturbed non-compact Einstein spaces attract to unique global solution.

Proposes a new model for complex multivariate event data.

The paper proves stability of certain cosmological models with negative spatial curvature.

Proposes a transformer model with geostatistical inductive bias for spatio-temporal forecasting.

In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of $n+1$-dimensional, $n \geq 3$, spatially compact spacetimes which generalizes the $k=-1$ Friedmann--Robertson--Walker vacuum spacetime. Our results demonstrate causal geodes…

WBCP improves conformal prediction for distribution shifts using weighted Dirichlet posteriors.

The paper analyzes multivariate Hawkes processes and their induced population processes.

Novel heat flow estimates on ALE manifolds for Schrödinger operators.

We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a finite temperature on hypercubic lattices in dimensions up to 5. The model includes a ` social\rq local field which contains the magnetization at time $t$. The nearest neighbour quenched interactions are drawn from a bin…

Global well-posedness and asymptotic convergence for vacuum Einstein's equations proved.

Study shows global oscillatory solutions for Yang-Mills heat flow in 4D space.

Self-similar solutions to geometric flows are stable under small perturbations.

We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a finite temperature on hypercubic lattices in dimensions up to 5. The model includes a ` social\rq local field which contains the magnetization at time $t$. The nearest neighbour quenched interactions are drawn from a bin…

Study on Wasserstein gradient flow for MMD between Coulomb measures.

Extends Minkowski stability proof to minimal decay assumptions.

New method creates vacuum data at minimal and borderline decay thresholds.

The Matérn covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Matérn class is that it is possible to get precise control over the degree of mean-square differentiability of the random process. However, the Matérn class possesses e…

Unique solutions found for wave-like decaying null infinity equations.

A new EnKF method for elliptic PDEs reduces dimensionality for accurate state estimation.

New findings on flatness of certain metrics with fast decay.

Study on curvature decay in steady Ricci solitons, proving dichotomy.

Cautious Weight Decay modifies weight decay for better optimization.

Study on scalar curvature decay on non-compact manifolds linked at infinity.

Study on massless Vlasov equation on Reissner-Nordström spacetimes, showing decay rates and non-decay phenomena.

In 1996, Huisken-Yau proved that every three-dimensional Riemannian manifold can be uniquely foliated near infinity by stable closed surfaces of constant mean curvature (CMC) if it is asymptotically equal to the (spatial) Schwarzschild solution. Later, their decay assumptions were weakened by Metzger, Huang, Eichmair-M…

New non-separable covariance kernels for spatiotemporal data derived from harmonic oscillator physics.

Introduces gradient decay in Softmax for better generalization.

Study examines wave equation decay and Strichartz estimates on conic manifolds.

Spatial blind source separation simplifies multivariate spatial prediction.

Study shows uniform decay rate for singular mean curvature flows.

Weight decay stabilizes training dynamics by slowing progressive sharpening.

Polynomial decay of correlations shown for curved surfaces.

The paper introduces groupoid racks for spatial surfaces.

Machine learning algorithms find frequent application in spatial prediction of biotic and abiotic environmental variables. However, the characteristics of spatial data, especially spatial autocorrelation, are widely ignored. We hypothesize that this is problematic and results in models that can reproduce training data …

Extends Onsager's conjecture to Besov spaces on manifolds with boundary.