Related papers: A Characterization of Model Multi-colour Sets
Diagrammatic sets are presheaves on a rich category of shapes, whose definition is motivated by combinatorial topology and higher-dimensional diagram rewriting. These shapes include representatives of oriented simplices, cubes, and positive…
Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…
Let $M$ be a model set meeting two simple conditions: (1) the internal space $H$ is a product of $R^n$ and a finite group, and (2) the window $W$ is a finite union of disjoint polyhedra. Then any point pattern with finite local complexity…
We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…
We study a Weiner process that is conditioned to pass through a finite set of points and consider the dynamics generated by iterating a sample path from this process. Using topological techniques we are able to characterize the global…
We show that any translate of a model set is a model set in some modified cut-and-project scheme. Restricting to Euclidean direct space, we show that any translate of an inter model set is a model set in some modified cut-and-project scheme…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
Understanding the morphology of an urban system is an important step toward unveiling the dynamical processes of its growth and development. At the foundation of every urban system, transportation system is undeniably a crucial component in…
Model sets (also called cut and project sets) are generalizations of lattices. Here we show how the self-similarities of model sets are a natural replacement for the group of translations of a lattice. This leads us to the concept of…
Set-coloring a graph means giving each vertex a subset of a fixed color set so that no two adjacent subsets have the same cardinality. When the graph is complete one gets a new distribution problem with an interesting generating function.…
Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each…
One of the aims of systems biology is to build multiple layered and multiple scale models of living systems which can efficiently describe phenomena occurring at various level of resolution. Such models should consist of layers of various…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
To each colored graph, one can associate its closure in the universal space of isomorphism classes of pointed colored graphs, and this subspace can be regarded as a generalized subshift. Based on this correspondence, we extend the notion of…
During modeling of dynamical systems, often two or more model architectures are combined to obtain a more powerful or efficient model regarding a specific application area. This covers the combination of multiple machine learning…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
Biological systems are generally complicated and/or complex. In the former approach, one sets up a model with a large number of parameters to describe the system in detail. The latter approach focuses on understanding the universal aspects…
In this survey we describe how the so-called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.
Soft set theory provides a direct framework for parameterized decision modeling by assigning to each attribute (parameter) a subset of a given universe, thereby representing uncertainty in a structured way [1, 2]. Over the past decades, the…
Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect…