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This paper presents an innovative extension of spatial autoregressive (SAR) models, introducing spatial coefficients specific to each spatial region that evolve over time. The proposed estimation methodology covers both homoscedastic and…
We introduce the modified planar rotator method (MPRS), a physically inspired machine learning method for spatial/temporal regression. MPRS is a non-parametric model which incorporates spatial or temporal correlations via short-range,…
This article presents a new mathematical framework to perform statistical analysis on time-indexed sequences of 2D or 3D shapes. At the core of this statistical analysis is the task of time interpolation of such data. Current models in use…
It is shown that under essentially all conditions, the non-linear classical equations governing gravitation and matter in cosmology have a solution in which far outside the horizon in a suitable gauge the reduced spatial metric (the spatial…
We derive a Voronoi-type series approximation for the local weighted mean of an arithmetical function that is associated to Dirichlet series satisfying a functional equation with gamma factors. The series is exploited to study the…
Mobility data science offers insights into the complex interconnections of spatial data of moving objects and their surroundings, often based on a combination of vector and raster data. For example, mobility traces are usually in vector…
This study presents a comprehensive spatial eigenanalysis of fully-discrete discontinuous spectral element methods, now generalizing previous spatial eigenanalysis that did not include time integration errors. The influence of discrete time…
We propose a quantum-Hamiltonian-learning-based sequential reconstruction framework for dynamic two-dimensional magnetic-field maps using a local likelihood model derived from a nitrogen-vacancy-center spin-1 Hamiltonian. Local measurements…
The estimation of modal parameters from a set of noisy measured data is a highly judgmental task, with user expertise playing a significant role in distinguishing between estimated physical and noise modes of a test-piece. Various methods…
Diagnostics such as Moran's index and approximate profile likelihood-based estimators (APLE) for Gaussian spatial autoregressive models are widely used in exploratory data analysis to assess the strength of spatial dependence. Yet, although…
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…
Focusing on the well motivated aperture mass statistics $\Map$, we study the possibility of constraining cosmological parameters using future space based SNAP class weak lensing missions. Using completely analytical results we construct the…
We report on the measurement of the two-point correlation function, and the pairwise peculiar velocity of galaxies in the IRAS PSCz survey. We compute these statistics first in redshift space, and then obtain the projected functions which…
Interval-valued data receives much attention due to its wide applications in the fields of finance, econometrics, meteorology and medicine. However, most regression models developed for interval-valued data assume observations are mutually…
Decision trees remain central for tabular prediction but struggle with (i) capturing spatial dependence and (ii) producing locally stable (robust) explanations. We present SX-GeoTree, a self-explaining geospatial regression tree that…
This paper proposes schemes for automated and weighted Self-Organizing Time Maps (SOTMs). The SOTM provides means for a visual approach to evolutionary clustering, which aims at producing a sequence of clustering solutions. This task we…
We propose a pseudo-structural framework for analyzing contemporaneous co-movements in reduced-rank matrix autoregressive (RRMAR) models. Unlike conventional vector-autoregressive (VAR) models that would discard the matrix structure, our…
We study the problem of traffic forecasting, aiming to predict the inflow and outflow of a region in the subsequent time slot. The problem is complex due to the intricate spatial and temporal interdependence among regions. Prior works study…
We show examples which reveal influences of spatial topologies to dynamics, using a class of spatially {\it closed} inhomogeneous cosmological models. The models, called the {\it locally U(1)$\times$U(1) symmetric models} (or the {\it…
Image based diagnostics are interpreted in the context of spatial resolution. The same is true for tomographic image reconstruction. Current empirically driven approaches to quantify spatial resolution rely on a deterministic formulation…