Related papers: Harmonic evolutions on graphs
Higher dimensional automata, i.e. labelled precubical sets, model concurrent systems. We introduce the homology graph of an HDA, which is a directed graph whose nodes are the homology classes of the HDA. We show that the homology graph is…
The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section,…
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…
For Paradigm models, evolution is just-in-time specified coordination conducted by a special reusable component McPal. Evolution can be treated consistently and on-the-fly through Paradigm's constraint orchestration, also for originally…
Schemata theory, Markov chains, and statistical mechanics have been used to explain how evolutionary algorithms (EAs) work. Incremental success has been achieved with all of these methods, but each has been stymied by limitations related to…
The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…
Graphs offer a generic abstraction for modeling entities, and the interactions and relationships between them. Most real world graphs, such as social and cooperation networks evolve over time, and exploring their evolution may reveal…
Persistent homology is a topological data analysis tool that has been widely generalized, extending its scope beyond the field of topology. Among its extensions, steady and ranging persistence were developed to study a wide variety of graph…
Evolutionary complexity is here measured by the number of trials/evaluations needed for evolving a logical gate in a non-linear medium. Behavioural complexity of the gates evolved is characterised in terms of cellular automata behaviour. We…
Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections…
In this paper we investigate the growth rate of the number of all possible paths in graphs with respect to their length in an exact analytical way. Apart from the typical rates of growth, i.e. exponential or polynomial, we identify…
While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
Discrete interaction models for the classical harmonic oscillator are used for introducing new mathematical generalizations in the usual continuous formalism. The inverted harmonic potential and generalized discrete hyperbolic and…
Capturing complex high-order interactions among data is an important task in many scenarios. A common way to model high-order interactions is to use hypergraphs whose topology can be mathematically represented by tensors. Existing methods…
Proper vertex colorings of a graph are related to its boundary map, also called its signed vertex-edge incidence matrix. The vertex Laplacian of a graph, a natural extension of the boundary map, leads us to introduce nowhere-harmonic…
We introduce and study cellular automata whose cell spaces are left-homogeneous spaces. Examples of left-homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spaces acted on by isometries; uniform tilings acted on by…
Bigraphs are a versatile modelling formalism that allows easy expression of placement and connectivity relations in a graphical format. System evolution is user defined as a set of rewrite rules. This paper presents a practical, yet…
In network science, the interplay between dynamical processes and the underlying topologies of complex systems has led to a diverse family of models with different interpretations. In graph signal processing, this is manifested in the form…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…