Related papers: Fractal and Smoothness Properties of Space-Time Ga…
We investigate the expanding and collapsing regions by taking two well-known spherically symmetric spacetimes. For this purpose, the general formalism is developed by using Israel junction conditions for arbitrary spacetimes. This has been…
Spatiotemporal data analysis with massive zeros is widely used in many areas such as epidemiology and public health. We use a Bayesian framework to fit zero-inflated negative binomial models and employ a set of latent variables from…
This paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely-drifting satellite-tracked instruments. The proposed time series models are used to summarise large multivariate datasets and infer…
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…
We construct a Gaussian random field (GRF) that combines fractional smoothness with spatially varying anisotropy. The GRF is defined through a stochastic partial differential equation (SPDE), where the range, marginal variance, and…
We consider a stationary spatio-temporal random process and assume that we have a sample. By defining a sequence of discrete Fourier transforms at canonical frequencies at each location, and using these complex valued random varables as…
Herein we shall argue for the utility of "spacetime geodesy", a point of view where one delays as long as possible worrying about dynamical equations, in favour of the maximal utilization of both symmetries and geometrical features. This…
Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…
This paper presents a new framework for oriented texture modeling. We introduce a new class of Gaussian fields, called Locally Anisotropic Fractional Brownian Fields, with prescribed local orientation at any point. These fields are a local…
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…
The spectral distribution $f(\omega)$ of a stationary time series $\{Y_t\}_{t\in\mathbb{Z}}$ can be used to investigate whether or not periodic structures are present in $\{Y_t\}_{t\in\mathbb{Z}}$, but $f(\omega)$ has some limitations due…
We present evidences of the diffusive motion of the ground and tunnels and show that if systematic movements are excluded then the remaining uncorrelated component of the motion obeys a characteristic fractal law with the displacement…
We present a useful method for the construction of cosmological models by solving the differential equations arising from calculating the kinematical invariants (shear, rotation, expansion and acceleration) of an observer field in proper…
Motivated by the need for analysing large spatio-temporal panel data, we introduce a novel dimensionality reduction methodology for $n$-dimensional random fields observed across a number $S$ spatial locations and $T$ time periods. We call…
Motivated by investigating spatio-temporal patterns of the distribution of continuous variables, we consider describing the conditional distribution function of the response variable incorporating spatio-temporal components given…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
Stochastic reduced models are an important tool in climate systems whose many spatial and temporal scales cannot be fully discretized or underlying physics may not be fully accounted for. One form of reduced model, the linear inverse model…
The aim of this paper is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. Our STMs…
We introduce a method of estimating parameters associated with a fractal random scattering medium, which utilizes the multiscale properties of the scattered field. The example of ray-density fluctuations beyond a phase screen with fractal…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…