Related papers: Robust Morphological Measures for Large-Scale Stru…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
I present here a review of Large-Scale Structure (LSS) studies using clusters of galaxies. First, I re-evaluate the `pros' and `cons' of using clusters for such studies, especially in this era of large galaxy redshift surveys. Secondly, I…
We propose a variational framework for analyzing dependence structures of convex compact random sets based on their support functions. The approach relies on the canonical even--odd decomposition on the unit sphere, which separates…
We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type…
The conformal compactification is considered in a hierarchy of hypercomplex projective spaces with relevance in physics including Minkowski and Anti-de Sitter space. The geometries are expressed in terms of bicomplex Vahlen matrices and…
We revise the Bayesian inference steps required to analyse the cosmological large-scale structure. Here we make special emphasis in the complications which arise due to the non-Gaussian character of the galaxy and matter distribution. In…
The traditional Minkowski distances are induced by the corresponding Minkowski norms in real-valued vector spaces. In this work, we propose novel statistical symmetric distances based on the Minkowski's inequality for probability densities…
We apply the scale-length method to several three dimensional samples of the Two degree Field Galaxy Redshift Survey. This method allows us to map in a quantitative and powerful way large scale structures in the distribution of galaxies…
A list of all possible causal relations in the $2$-dimensional Minkowski space $M$ is exhausted, based on the duality between timelike and spacelike in this particular case, and thirty topologies are introduced, all of them encapsulating…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
We present a new method of analysing and quantifying velocity structure in star forming regions suitable for the rapidly increasing quantity and quality of stellar position-velocity data. The method can be applied to data in any number of…
We introduce a multiscale topological description of the Megaparsec weblike cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of…
Observations reveal that on large scales the universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions -- voids. This thesis reports the construction of a sophisticated computational…
We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use…
This paper investigates the relationship between various measure-theoretic properties of U-statistics with fixed sample size $N$ and the same properties of their kernels. Specifically, the random variables are replaced with elements in some…
Let $\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism $f\in\Diff(M)$. We show that the space of invariant measures supported on $\Lambda$ coincides with the space of accumulation measures of time averages…
We consider the possibility of obtaining emergent properties of physical spaces endowed with structures analogous to that of collective models put forward by classical statistical physics. We show that, assuming that a so-called "metric…
The concept of robustness of regulatory networks has been closely related to the nature of the interactions among genes, and the capability of pattern maintenance or reproducibility. Defining this robustness property is a challenging task,…
The problem of estimating, from a random sample of points, the dimension of a compact subset $S$ of the Euclidean space is considered. The emphasis is put on consistency results in the statistical sense. That is, statements of convergence…
Using modifications of Lindeberg's interpolation technique, I propose a new identification-robust test for the structural parameter in a heteroskedastic instrumental variables model. While my analysis allows the number of instruments to be…