Related papers: The Meaning of Structure in Interconnected Dynamic…
This presentation explains why models with a dynamical symmetry often work extraordinarily well even in the presence of large symmetry breaking interactions. A model may be a caricature of a more realistic system with a "quasi-dynamical"…
A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast inversion (or solution), and reduced…
The concept of structured occurrence nets is an extension of that of occurrence nets which are directed acyclic graphs that represent causality and concurrency information concerning a single execution of a distributed system. The formalism…
This paper addresses problems on the structural design of control systems taking explicitly into consideration the possible application to large-scale systems. We provide an efficient and unified framework to solve the following major…
A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields…
This chapter provides an overview of the different techniques and methods that exist for the analysis and visualization of dynamic networks. Basic definitions and formal notations are discussed and important references are cited. A major…
Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…
In many cases we need to represent on the same abstraction level not only system components but also processes within the system, and if for both representation different frameworks are used, the system model becomes hard to read and to…
This paper leverages linear systems theory to propose a principled measure of complexity for network systems. We focus on a network of first-order scalar linear systems interconnected through a directed graph. By locally filtering out the…
We show that mixtures comprised of multicomponent systems typically are much more structurally complex than the sum of their parts; sometimes, infinitely more complex. We contrast this with the more familiar notion of statistical mixtures,…
From the complex motions of robots to the oxygen binding of hemoglobin, the function of many mechanical systems depends on large, coordinated movements of their components. Such movements arise from a network of physical interactions in the…
A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems has proven incredibly useful in those sciences that can…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
In a sequential decision-making problem, the information structure is the description of how events in the system occurring at different points in time affect each other. Classical models of reinforcement learning (e.g., MDPs, POMDPs)…
Linear matrix Inequalities (LMIs) have had a major impact on control but formulating a problem as an LMI is an art. Recently there is the beginnings of a theory of which problems are in fact expressible as LMIs. For optimization purposes it…
Biological phenomena differ significantly from physical phenomena. At the heart of this distinction is the fact that biological entities have computational abilities and thus they are inherently difficult to predict. This is the reason why…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional…
Linear diagrams are used to visualize set systems by depicting set memberships as horizontal line segments in a matrix, where each set is represented as a row and each element as a column. Each such line segment of a set is shown in a…