Related papers: Solving the Observer Metric
We present a numerical solution on a 5-dimensional spherically symmetric space time, in Einstein-Yang-Mills-Gauss-Bonnet theory using a two point boundary value routine. It turns out that the Gauss-Bonnet contribution has a profound…
A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation…
Over the past decade advancements in the understanding of several astrophysical phenomena have allowed us to infer a concordance cosmological model that successfully accounts for most of the observations of our universe. This has opened up…
A new approach for arbitrary dimension to the Friedmann cosmological models is presented. Taking suitable changes of the parameters of the spacetime the harmonic motion equations appear, where the curvature determines the angular frequency.…
The general idea of determining cosmological parameters with gravitational lensing statistics is outlined, and then recent work---with an emphasis on applicability to all cosmological models, observational bias, better statistics and…
Fitting concentric geometric objects to digitized data is an important problem in many areas such as iris detection, autonomous navigation, and industrial robotics operations. There are two common approaches to fitting geometric shapes to…
Standard methods of data assimilation assume prior knowledge of a model that describes the system dynamics and an observation function that maps the model state to a predicted output. An accurate mapping from model state to observation…
A Newtonian matrix cosmology, correspoding to the BFSS model of eleven-dimensional M-theory in the IMF as a (0+1) M(atrix) model is constructed. Interesting new results are obtained, such as the existence of (much sought for in the past)…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
Sky surveys represent a fundamental data basis for astronomy. We use them to map in a systematic way the universe and its constituents, and to discover new types of objects or phenomena. We review the subject, with an emphasis on the…
We study observability for the one-dimensional wave equation on the torus from spacetime measurable observation sets. While the Geometric Control Condition (GCC) provides a sufficient criterion in many classical settings, it is no longer…
When dealing with highly accurate modeling of time and frequency transfers into arbitrarily moving dielectrics medium, it may be convenient to work with Gordon's optical spacetime metric rather than the usual physical spacetime metric.…
Over the past decade, sky surveys such as the Sloan Digital Sky Survey have proven the power of large data sets for answering fundamental astrophysical questions. This observational progress, based on a synergy of advances in telescope…
In the Bondi-Sachs formulation of General Relativity space-time is foliated via a family of null cones. If these null cones are defined such that their vertices are traced by a regular world-line then the metric tensor has to obey…
We present an analytical method to extract observational predictions about non linear evolution of perturbations in a Tolman Universe. We assume no a priori profile for them. We solve perturbatively a Hamilton - Jacobi equation for a…
We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimised for a specific cosmological model or for an ensemble of models, even if based on drastically different physical…
In these lectures I cover a number of topics in cosmological data analysis. I concentrate on general techniques which are common in cosmology, or techniques which have been developed in a cosmological context. In fact they have very general…
The bimetric generalization of general relativity has been proven to be able to give an accelerated background expansion consistent with observations. Apart from the energy densities coupling to one or both of the metrics, the expansion…
The concept of an observer and their associated rest space is defined in a pre-metric (i.e., projective-geometric) context that relates to time+space decompositions of the tangent bundle to space-time. The transformation from one observer…
The general world model for homogeneous and isotropic universe has been roposed. For this purpose, we introduce a global and fiducial system of reference (world reference frame) constructed on a 5-dimensional space-time that is embedding…