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Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information,…
People organize in groups and contagions spread across them. A simple process, but complex to model due to dynamical correlations within groups and between groups. Groups can also change as agents join and leave them to avoid infection. To…
In this paper we investigate composition operators on discrete spaces. We establish the classification of underlying graphs of such operators. For one class of such graphs, namely graphs with one cycle, we obtain a characterization of…
We wrote this paper as an example to show the way we pass from ordered semigroups to ordered hypersemigroups.
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
Graph-based analyses have gained a lot of relevance in the past years due to their high potential in describing complex systems by detailing the actors involved, their relations and their behaviours. Nevertheless, in scenarios where these…
It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To…
In this work, we address ergodicity of smooth actions of finitely generated semi-groups on an m-dimensional closed manifold M. We provide sufficient conditions for such an action to be ergodic with respect to the Lebesgue measure. Our…
In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
In this paper, we begin by reviewing a certain number of mathematical challenges posed by the modelling of collective dynamics and self-organization. Then, we focus on two specific problems, first, the derivation of fluid equations from…
Weighted graphs obtained from co-occurrence in user-item relations lead to non-metric topologies. We use this semi-metric behavior to issue recommendations, and discuss its relationship to transitive closure on fuzzy graphs. Finally, we…
Functional autonomous systems often realize complex tasks by utilizing state machines comprised of discrete primitive behaviors and transitions between these behaviors. This architecture has been widely studied in the context of…
We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$…
We consider dataflow architecture for two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We improve the earlier technique of almost continuous program…
Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…
We consider the class of semi-transitively orientable graphs, which is a much larger class of graphs compared to transitively orientable graphs, in other words, comparability graphs. Ever since the concept of a semi-transitive orientation…
The sine-Gordon model appears as the low-energy effective field theory of various one-dimensional gapped quantum systems. Here we investigate the dynamics of generic, non-integrable systems belonging to the sine-Gordon family at finite…
We study the action of a relatively hyperbolic group on its boundary, by methods of symbolic dynamics. Under a condition on the parabolic subgroups, we show that this dynamical system is finitely presented. We give examples where this…
Mesoscopic systems in a slowly fluctuating environment are often well described by superstatistical models. We develop a generalized statistical mechanics formalism for superstatistical systems, by mapping the superstatistical complex…