Low rattling: A predictive principle for self-organization in active collectives

Self-organization is frequently observed in active collectives as varied as ant rafts and molecular motor assemblies. General principles describing self-organization away from equilibrium have been challenging to identify. We offer a unifying framework that models the behavior of complex systems as largely random while capturing their configuration-dependent response to external forcing. This allows derivation of a Boltzmann-like principle for understanding and manipulating driven self-organization. We validate our predictions experimentally, with the use of shape-changing robotic active matter, and outline a methodology for controlling collective behavior. Our findings highlight how emergent order depends sensitively on the matching between external patterns of forcing and internal dynamical response properties, pointing toward future approaches for the design and control of active particle mixtures and metamaterials.

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In-Between and Through: Architecture and Complexity

International Journal of Architectural Computing ◽

10.1260/147807705775377311 ◽

2005 ◽

Vol 3 (3) ◽

pp. 335-354 ◽

Cited By ~ 2

Author(s):

Clarissa Ribeiro Pereira de Almeida ◽

Anja Pratschke ◽

Renata La Rocca

Keyword(s):

Complex System ◽

Software Engineering ◽

Complex Systems ◽

Design Process ◽

Three Dimensional ◽

Self Organization ◽

Three Dimensional Modeling ◽

Dimensional Modeling ◽

Complex Thought ◽

Basic Characteristics

This paper draws on current research on complexity and design process in architecture and offers a proposal for how architects might bring complex thought to bear on the understanding of design process as a complex system, to understand architecture as a way of organizing events, and of organizing interaction. Our intention is to explore the hypothesis that the basic characteristics of complex systems – emergence, nonlinearity, self-organization, hologramaticity, and so forth – can function as effective tools for conceptualization that can usefully extend the understanding of the way architects think and act throughout the design process. To illustrate the discussions, we show how architects might bring complex thought inside a transdisciplinary design process by using models such as software engineering diagrams, and three-dimensional modeling network environments such as media to integrate, connect and ‘trans–act’.

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Sparse stabilization and control of alignment models

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202515400059 ◽

2014 ◽

Vol 25 (03) ◽

pp. 521-564 ◽

Cited By ~ 48

Author(s):

Marco Caponigro ◽

Massimo Fornasier ◽

Benedetto Piccoli ◽

Emmanuel Trélat

Keyword(s):

Policy Maker ◽

Research Direction ◽

Fundamental Question ◽

Self Organization ◽

Group Consensus ◽

Future Developments ◽

Consensus Dynamics ◽

Time Optimal ◽

And Control ◽

Mathematical Justification

Starting with the seminal papers of Reynolds (1987), Vicsek et al. (1995), Cucker–Smale (2007), there has been a lot of recent works on models of self-alignment and consensus dynamics. Self-organization has so far been the main driving concept of this research direction. However, the evidence that in practice self-organization does not necessarily occur (for instance, the achievement of unanimous consensus in government decisions) leads to the natural question of whether it is possible to externally influence the dynamics in order to promote the formation of certain desired patterns. Once this fundamental question is posed, one is also faced with the issue of defining the best way of obtaining the result, seeking for the most "economical" way to achieve a certain outcome. Our paper precisely addressed the issue of finding the sparsest control strategy in order to lead us optimally towards a given outcome, in this case the achievement of a state where the group will be able by self-organization to reach an alignment consensus. As a consequence, we provide a mathematical justification to the general principle according to which "sparse is better": in order to achieve group consensus, a policy maker not allowed to predict future developments should decide to control with stronger action the fewest possible leaders rather than trying to act on more agents with minor strength. We then establish local and global sparse controllability properties to consensus. Finally, we analyze the sparsity of solutions of the finite time optimal control problem where the minimization criterion is a combination of the distance from consensus and of the ℓ1-norm of the control. Such an optimization models the situation where the policy maker is actually allowed to observe future developments. We show that the lacunarity of sparsity is related to the codimension of certain manifolds in the space of cotangent vectors.

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SELF-ORGANIZATION IN COMPLEX SYSTEMS AS DECISION MAKING

Advances in Complex Systems ◽

10.1142/s0219525914500167 ◽

2014 ◽

Vol 17 (03n04) ◽

pp. 1450016 ◽

Cited By ~ 16

Author(s):

V. I. YUKALOV ◽

D. SORNETTE

Keyword(s):

Decision Making ◽

Complex Systems ◽

Mathematical Formulation ◽

Conditional Entropy ◽

Self Organization ◽

Entropy Maximization ◽

Natural Systems ◽

Macroscopic States ◽

System States ◽

Statistical Systems

The idea is advanced that self-organization in complex systems can be treated as decision making (as it is performed by humans) and, vice versa, decision making is nothing but a kind of self-organization in the decision maker nervous systems. A mathematical formulation is suggested based on the definition of probabilities of system states, whose particular cases characterize the probabilities of structures, patterns, scenarios, or prospects. In this general framework, it is shown that the mathematical structures of self-organization and of decision making are identical. This makes it clear how self-organization can be seen as an endogenous decision making process and, reciprocally, decision making occurs via an endogenous self-organization. The approach is illustrated by phase transitions in large statistical systems, crossovers in small statistical systems, evolutions and revolutions in social and biological systems, structural self-organization in dynamical systems, and by the probabilistic formulation of classical and behavioral decision theories. In all these cases, self-organization is described as the process of evaluating the probabilities of macroscopic states or prospects in the search for a state with the largest probability. The general way of deriving the probability measure for classical systems is the principle of minimal information, that is, the conditional entropy maximization under given constraints. Behavioral biases of decision makers can be characterized in the same way as analogous to quantum fluctuations in natural systems.

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