An algorithmically random family of MultiAspect Graphs and its topological properties

This article presents a theoretical investigation of incompressibility and randomness in generalized representations of graphs along with its implications on network topological properties. We extend previous studies on plain algorithmically random classical graphs to plain and prefix algorithmically random MultiAspect Graphs (MAGs). First, we show that there is an infinite recursively labeled infinite family of nested MAGs (or, as a particular case, of nested classical graphs) that behaves like (and is determined by) an algorithmically random real number. Then, we study some of their important topological properties, in particular, vertex degree, connectivity, diameter, and rigidity

Algorithmic information and incompressibility of families of multidimensional networks

This article presents a theoretical investigation of string-based generalized representations of families of finite networks in a multidimensional space. First, we study the recursive labeling of networks with (finite) arbitrary node dimensions (or aspects), such as time instants or layers. In particular, we study these networks that are formalized in the form of multiaspect graphs. We show that, unlike classical graphs, the algorithmic information of a multidimensional network is not in general dominated by the algorithmic information of the binary sequence that determines the presence or absence of edges. This universal algorithmic approach sets limitations and conditions for irreducible information content analysis in comparing networks with a large number of dimensions, such as multilayer networks. Nevertheless, we show that there are particular cases of infinite nesting families of finite multidimensional networks with a unified recursive labeling such that each member of these families is incompressible. From these results, we study network topological properties and equivalences in irreducible information content of multidimensional networks in comparison to their isomorphic classical graph.Comment: Extended preprint version of the pape

Statistical Fusion of Multi-aspect Synthetic Aperture Radar Data for Automatic Road Extraction

In this dissertation, a new statistical fusion for automatic road extraction from SAR images taken from different looking angles (i.e. multi-aspect SAR data) was presented. The main input to the fusion is extracted line features. The fusion is carried out on decision-level and is based on Bayesian network theory

Algorithmically random generalized graphs and their topological properties

This article presents a theoretical investigation of incompressibility and randomness in generalized representations of graphs along with its implications on network topological properties. We extend previous studies on plain algorithmically random classical graphs to plain and prefix algorithmically random MultiAspect Graphs (MAGs), which are formal graph-like representations of arbitrary dyadic relations between $n$-ary tuples. In doing so, we define recursively labeled MAGs given a companion tuple and recursively labeled families of MAGs. In particular, we show that, unlike recursively labeled classical graphs, the algorithmic information of a MAG may be not equivalent to the algorithmic information of the binary string that determines the presence or absence of edges. Nevertheless, we show that there is a recursively labeled infinite family of nested MAGs (or, as a particular case, of nested classical graphs) that behaves like (and is determined by) an algorithmically random real number. Furthermore, by relating the algorithmic randomness of a MAG and the algorithmic randomness of its isomorphic graph, we study some important topological properties, in particular, vertex degree, connectivity, diameter, and rigidity