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Many temporal networks exhibit multiple system states, such as weekday and weekend patterns in social contact networks. The detection of such distinct states in temporal network data has recently been explored as it helps reveal underlying…
We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
Linear finite dynamical systems play an important role, for example, in coding theory and simulations. Methods for analyzing such systems are often restricted to cases in which the system is defined over a field %and usually strive to…
Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem…
The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…
Comparing with traditional fixed formation for a group of dynamical systems, time-varying formation can produce the following benefits: i) covering the greater part of complex environments; ii) collision avoidance. This paper studies the…
In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…
In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear…
Given the large size and complexity of most biochemical regulation and signaling networks, there is a non-trivial relationship between the micro-level logic of component interactions and the observed macro-dynamics. Here we address this…
Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for…
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the…
This chapter provides a comprehensive overview of controlling collective behavior in complex systems comprising large ensembles of interacting dynamical agents. Building upon traditional control theory's foundation in individual systems, we…
Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable--derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency…
We introduce a novel approach to description of networks/graphs. It is based on an analogue physical model which is dynamically evolved. This evolution depends on the connectivity matrix and readily brings out many qualitative features of…
Biological networks have two modes. The first mode is static: a network is a passage on which something flows. The second mode is dynamic: a network is a pattern constructed by gluing functions of entities constituting the network. In this…
We introduce a program aimed to studying problems arising from the theory of complex networks with differential geometric means. We study the propagation of influences on manifolds assuming that at each point only a finite number of…
In this contribution we establish a dictionary between terms in two different areas in order to show that many of the topics studied are common ones - just with a different terminology. We further analyze the relations between the…