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In these notes we review emergent phenomena in complex systems, emphasizing ways to identify potential underlying universal mechanisms that generates complexity. The discussion is centered around the emergence of collective behavior in…

Disordered Systems and Neural Networks · Physics 2008-04-02 Dante R. Chialvo

Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…

Physics and Society · Physics 2024-03-06 Santiago Núñez-Corrales , Eric Jakobsson

Understanding and modelling the complexity of the immune system is a challenge that is shared by the ImmunoComplexiT$^1$ thematic network from the RNSC. The immune system is a complex biological, adaptive, highly diversified, self-organized…

Quantitative Methods · Quantitative Biology 2020-08-27 Véronique Thomas-Vaslin

Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…

Logic in Computer Science · Computer Science 2018-02-12 Daniel Leivant , Jean-Yves Marion

Biological systems are generally complicated and/or complex. In the former approach, one sets up a model with a large number of parameters to describe the system in detail. The latter approach focuses on understanding the universal aspects…

Biological Physics · Physics 2026-03-19 Kunihiko Kaneko

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…

Systems and Control · Electrical Eng. & Systems 2025-07-10 Giacomo Baggio , Marco Fabris

Desirable system performance in the face of threats and disruptions has been characterized by various management concepts. Through semi-structured interviews with editors of journals in the fields of emergency response and systems…

Physics and Society · Physics 2020-08-25 Stephanie Galaitsi , Benjamin D. Trump , Jeffrey M. Keisler , Igor Linkov

In this paper, we analyze the complexity of functional programs written in the interaction-net computation model, an asynchronous, parallel and confluent model that generalizes linear-logic proof nets. Employing user-defined sized and…

Programming Languages · Computer Science 2015-11-06 Stéphane Gimenez , Georg Moser

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…

Societal complexity may be at a historical peak. Distinct from entropy, complexity tends to rise as systems move away from order, crest at an intermediate state, and decline as entropy continues increasing. The use of a thermodynamic…

Physics and Society · Physics 2026-05-08 Theodore Modis

In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number…

Information Theory · Computer Science 2025-01-20 Thomas F. Varley

Intricate interactions among firms, institutions, and spatial structures shape urban economic systems. In this study, we propose a framework based on three structural dimensions -- abundance, diversity, and longevity (ADL) of economic units…

Physics and Society · Physics 2026-01-28 Marco A. Rosas Pulido , Roberto Murcio , Omar R. Vázquez , Carlos Gershenson

In this paper we revisit the concept of mobility entropy. Over time, the structure of spatial interactions among urban centres tends to become more complex and evolves from centralised models to more scattered origin and destination…

Physics and Society · Physics 2021-06-30 Valentina Marin , Carlos Molinero , Elsa Arcaute

Empirical evidence suggesting that living systems might operate in the vicinity of critical points, at the borderline between order and disorder, has proliferated in recent years, with examples ranging from spontaneous brain activity to…

Statistical Mechanics · Physics 2014-07-25 Jorge Hidalgo , Jacopo Grilli , Samir Suweis , Miguel A. Munoz , Jayanth R. Banavar , Amos Maritan

Building software-driven systems that are easily understood becomes a challenge, with their ever-increasing complexity and autonomy. Accordingly, recent research efforts strive to aid in designing explainable systems. Nevertheless, a common…

Artificial Intelligence · Computer Science 2019-02-11 Dimitri Bohlender , Maximilian A. Köhl

We apply measures of complexity, emergence and self-organization to an abstract city traffic model for comparing a traditional traffic coordination method with a self-organizing method in two scenarios: cyclic boundaries and non-orientable…

Similarities between entities occur frequently in many real-world scenarios. For over a century, researchers in different fields have proposed a range of approaches to measure the similarity between entities. More recently, inspired by…

Artificial Intelligence · Computer Science 2023-03-21 Giovanni Amendola , Marco Manna , Aldo Ricioppo

Complexity matching characterizes the role of information in interactions between systems and can be traced back to the 1957 Introduction to Cybernetics by Ross Ashby. We argue that complexity can be expressed in terms of crucial events,…

Adaptation and Self-Organizing Systems · Physics 2019-09-24 Korosh Mahmoodi , Bruce J. West , Paolo Grigolini

A number of elements towards a classification of the quality of emergence in emergent collective systems are provided. By using those elements, several classes of emergent systems are exemplified, ranging from simple aggregations of simple…

Other Computer Science · Computer Science 2016-08-12 Vincenzo De Florio

Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the…

Pattern Formation and Solitons · Physics 2013-06-03 Yavni Bar-Yam , Dion Harmon , Yaneer Bar-Yam