Related papers: Space-Time Geostatistical Models with both Linear …
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
Geometric continuum models for fluid lipid membranes are considered using classical field theory, within a covariant variational approach. The approach is cast as a higher-derivative Lagrangian formulation of continuum classical field…
This is intended as an analysis of the global properties of static and stationary spacetimes with complete (timelike) Killing field, with particular attention to quotients by group actions. This is presented in terms of algebraic structures…
Explosive growth in spatio-temporal data and its wide range of applications have attracted increasing interests of researchers in the statistical and machine learning fields. The spatio-temporal regression problem is of paramount importance…
Atmospheric inverse modelling is a method for reconstructing historical fluxes of green-house gas between land and atmosphere, using observed atmospheric concentrations and an atmospheric tracer transport model. The small number of observed…
We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…
The analysis of spatio-temporal data has been the object of research in several areas of knowledge. One of the main objectives of such research is the need to evaluate the behavior of climate effects in certain regions across a period of…
Weather radar echoes, correlated in both space and time, are the most important input data for short-term precipitation forecast. Motivated by real datasets, this paper is concerned with the spatio-temporal modeling of two-dimensional radar…
We make a perturbative analysis of the number of degrees of freedom in a large class of metric theories respecting spatial symmetries, of which the Lagrangian includes kinetic terms of both the spatial metric and the lapse function. We show…
Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
This paper presents a "historical" formalism for dynamical systems, in its Hamiltonian version (Lagrangian version was presented in a previous paper). It is universal, in the sense that it applies equally well to time dynamics and to field…
We study covariant models for vacuum spherical gravity within a canonical setting. Starting from a general ansatz, we derive the most general family of Hamiltonian constraints that are quadratic in first-order and linear in second-order…
Scalar fields play an important role in constructing modified gravity theories. In the case of a single scalar field with timelike gradient, the corresponding Lagrangian in the unitary gauge takes the form of spatially covariant gravity…
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the non-linear evolution of…
In this article, we argue that two distinct types of time should be taken into account in relativistic physics: a geometric time, which emanates from the structure of spacetime and its metrics, and a causal time, indicating the flow from…
A novel approach for Lagrange formulation for field theories is proposed in terms of Kawaguchi geometry (areal metric space). On the extended configuration space M for classical field theory composed of spacetime and field configuration…
We study how sampling geometry contributes to uncertainty in modeling spatial geophysical observations as sampled random fields characterized by stationary, isotropic, parametric covariance functions. We incorporate the signature of…
Spatiotemporal simulation of minimum and maximum temperature is a fundamental requirement for climate impact studies and hydrological or agricultural models. Particularly over regions with variable orography, these simulations are difficult…
There has been recent interest in identifying entanglement as the fundamental concept from which space may emerge. We note that the particular way that a Hilbert space is decomposed into tensor factors is important in what the resulting…