相关论文: Introduction aux dynamiques cat\'egoriques connect…

The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…

We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…

We give a description of simple functors taking finitely generated values, from a small additive category to the category of vector spaces over a field. This result is analogous to Steinberg's tensor product theorems in group representation…

We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…

In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…

The "theory of open sub-functorial dynamics" is a new theory that defines interacting generalized dynamical systems. The interactions between these dynamics produce new dynamics which, of course, can then enter into other interactions. A…

We try to perform geometrization of cognitive science and psychology by representing information states of cognitive systems by points of {\it mental space} given by a hierarchic $m$-adic tree. Associations are represented by balls and…

This paper gives an introduction to \textit{Cognidynamics}, that is to the dynamics of cognitive systems driven by optimal objectives imposed over time when they interact either with a defined virtual or with a real-world environment. The…

The information implicitly represented in the state of physical systems allows one to analyze them with analytical techniques from statistical mechanics and information theory. In the case of complex networks such techniques are inspired by…

Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a '{\it cellular network}'…

A novel field theoretical approach towards modelling dynamic networking in complex systems is presented. An equilibrium networking formalism which utilises Gaussian fields is adapted to model the dynamics of particles that can bind and…

Most generally, dynamic functional connectivity (FC) refers to the non-instantaneous couplings across timeseries from a set of brain areas, here as measured by fMRI. This is in contrast to static FC, which is defined as purely instantaneous…

We characterize synchronization phenomenon in discrete-time, discrete-state random dynamical systems, with random and probabilistic Boolean networks as particular examples. In terms of multiplicative ergodic properties of the induced linear…

An analytic approach to phenomenological models inspired by cubic string field theory is introduced and applied to some examples. We study a class of actions for a minimally coupled, homogeneous scalar field whose energy density contains…

Many natural systems are organized as networks, in which the nodes interact in a time-dependent fashion. The object of our study is to relate connectivity to the temporal behavior of a network in which the nodes are (real or complex)…

Many complex systems are representable as macroscopic set of elements which interact by simple rules. The complex macroscopically relevant phenomena are then the result of the generic emergence of a space-time multi-scale dynamics. Critical…

Information to be stored and transported requires physical carriers. The quantum bit of information (qubit) can for instance be realised as the spin 1/2 degree of freedom of a massive particle like an electron or as the spin 1 polarisation…

Actors are embedded in networks of communication: the relations of the actors can be represented as the rows of a matrix, while the column vectors represent their communications. The two systems are structurally coupled in the co-variation:…

This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result…

In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer…