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The distribution of arrival directions of ultra-high energy cosmic rays may yield clues to their mysterious origin. We introduce a method of {\it invariant statistics} to analyze cosmic ray data which eliminates coordinate-dependent…
A stationary spatial model is an idealization and we expect that the true dependence structures of physical phenomena are spatially varying, but how should we handle this non-stationarity in practice? We study the challenges involved in…
The recent advancements in 3D Gaussian splatting (3D-GS) have not only facilitated real-time rendering through modern GPU rasterization pipelines but have also attained state-of-the-art rendering quality. Nevertheless, despite its…
In this paper, we analyze stability regions of a non-static restricted class of axially symmetric spacetime with anisotropic matter distribution. We consider $f(R)=R+{\epsilon}R^2$ model and assume hydrostatic equilibrium of the axial…
Recent observations on the quasar absorption spectra supply evidence for the variation of the fine structure constant $\alpha$. In this paper, we propose another interpretation of the observational data on the quasar absorption spectra: a…
Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…
Reconstructing realistic underwater scenes from underwater video remains a meaningful yet challenging task in the multimedia domain. The inherent spatiotemporal degradations in underwater imaging, including caustics, flickering,…
In this paper, we propose a Bayesian matrix-variate spatiotemporal modeling framework for jointly analyzing multiple response variables observed at spatial locations over time. The approach relaxes the standard assumption of spatial…
We study the dynamics and morphology of grain growth with anisotropic energy and mobility of grain boundaries using a generalized phase field model. In contrast to previous studies, both inclination and misorientation of the boundaries are…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…
Discrete time spatial time series data arise routinely in meteorological and environmental studies. Inference and prediction associated with them are mostly carried out using any of the several variants of the linear state space model that…
Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance…
When magnetohydrodynamic turbulence evolves in the presence of a large-scale mean magnetic field, an anisotropy develops relative to that preferred direction. The well-known tendency is to develop stronger gradients perpendicular to the…
Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be…
Precipitation is a large-scale, spatio-temporally heterogeneous phenomenon, with frequent anomalies exhibiting unusually high or low values. We use Markov Random Fields (MRFs) to detect spatio-temporally coherent anomalies in gridded annual…
We introduce SeaSplat, a method to enable real-time rendering of underwater scenes leveraging recent advances in 3D radiance fields. Underwater scenes are challenging visual environments, as rendering through a medium such as water…
Stationary Random Functions have been successfully applied in geostatistical applications for decades. In some instances, the assumption of a homogeneous spatial dependence structure across the entire domain of interest is unrealistic. A…
A stochastic gravitational-wave (GW) background consists of a large number of weak, independent and uncorrelated events of astrophysical or cosmological origin. The GW power on the sky is assumed to contain anisotropies on top of an…
We present the geodesics on homogeneous and isotropic negatively curved spaces in a simple form suitable for application to cosmological problems. We discuss how the patterns in the microwave sky of anisotropic homogeneous universes can be…
Technological developments and open data policies have made large, global environmental datasets accessible to everyone. For analysing such datasets, including spatiotemporal correlations using traditional models based on Gaussian processes…