Spatio-Temporal Patterns act as Computational Mechanisms governing Emergent behavior in Robotic Swarms

open access articleOur goal is to control a robotic swarm without removing its swarm-like nature. In other words, we aim to intrinsically control a robotic swarm emergent behavior. Past attempts at governing robotic swarms or their selfcoordinating emergent behavior, has proven ineffective, largely due to the swarm’s inherent randomness (making it difficult to predict) and utter simplicity (they lack a leader, any kind of centralized control, long-range communication, global knowledge, complex internal models and only operate on a couple of basic, reactive rules). The main problem is that emergent phenomena itself is not fully understood, despite being at the forefront of current research. Research into 1D and 2D Cellular Automata has uncovered a hidden computational layer which bridges the micromacro gap (i.e., how individual behaviors at the micro-level influence the global behaviors on the macro-level). We hypothesize that there also lie embedded computational mechanisms at the heart of a robotic swarm’s emergent behavior. To test this theory, we proceeded to simulate robotic swarms (represented as both particles and dynamic networks) and then designed local rules to induce various types of intelligent, emergent behaviors (as well as designing genetic algorithms to evolve robotic swarms with emergent behaviors). Finally, we analysed these robotic swarms and successfully confirmed our hypothesis; analyzing their developments and interactions over time revealed various forms of embedded spatiotemporal patterns which store, propagate and parallel process information across the swarm according to some internal, collision-based logic (solving the mystery of how simple robots are able to self-coordinate and allow global behaviors to emerge across the swarm)

Evolution: Complexity, uncertainty and innovation

Complexity science provides a general mathematical basis for evolutionary thinking. It makes us face the inherent, irreducible nature of uncertainty and the limits to knowledge and prediction. Complex, evolutionary systems work on the basis of on-going, continuous internal processes of exploration, experimentation and innovation at their underlying levels. This is acted upon by the level above, leading to a selection process on the lower levels and a probing of the stability of the level above. This could either be an organizational level above, or the potential market place. Models aimed at predicting system behaviour therefore consist of assumptions of constraints on the micro-level – and because of inertia or conformity may be approximately true for some unspecified time. However, systems without strong mechanisms of repression and conformity will evolve, innovate and change, creating new emergent structures, capabilities and characteristics. Systems with no individual freedom at their lower levels will have predictable behaviour in the short term – but will not survive in the long term. Creative, innovative, evolving systems, on the other hand, will more probably survive over longer times, but will not have predictable characteristics or behaviour. These minimal mechanisms are all that are required to explain (though not predict) the co-evolutionary processes occurring in markets, organizations, and indeed in emergent, evolutionary communities of practice. Some examples will be presented briefly

Mesoscopic Biochemical Basis of Isogenetic Inheritance and Canalization: Stochasticity, Nonlinearity, and Emergent Landscape

Biochemical reaction systems in mesoscopic volume, under sustained environmental chemical gradient(s), can have multiple stochastic attractors. Two distinct mechanisms are known for their origins: ($a$) Stochastic single-molecule events, such as gene expression, with slow gene on-off dynamics; and ($b$) nonlinear networks with feedbacks. These two mechanisms yield different volume dependence for the sojourn time of an attractor. As in the classic Arrhenius theory for temperature dependent transition rates, a landscape perspective provides a natural framework for the system's behavior. However, due to the nonequilibrium nature of the open chemical systems, the landscape, and the attractors it represents, are all themselves {\em emergent properties} of complex, mesoscopic dynamics. In terms of the landscape, we show a generalization of Kramers' approach is possible to provide a rate theory. The emergence of attractors is a form of self-organization in the mesoscopic system; stochastic attractors in biochemical systems such as gene regulation and cellular signaling are naturally inheritable via cell division. Delbr\"{u}ck-Gillespie's mesoscopic reaction system theory, therefore, provides a biochemical basis for spontaneous isogenetic switching and canalization.Comment: 24 pages, 6 figure

Transformations in the Scale of Behaviour and the Global Optimisation of Constraints in Adaptive Networks

The natural energy minimisation behaviour of a dynamical system can be interpreted as a simple optimisation process, finding a locally optimal resolution of problem constraints. In human problem solving, high-dimensional problems are often made much easier by inferring a low-dimensional model of the system in which search is more effective. But this is an approach that seems to require top-down domain knowledge; not one amenable to the spontaneous energy minimisation behaviour of a natural dynamical system. However, in this paper we investigate the ability of distributed dynamical systems to improve their constraint resolution ability over time by self-organisation. We use a ‘self-modelling’ Hopfield network with a novel type of associative connection to illustrate how slowly changing relationships between system components can result in a transformation into a new system which is a low-dimensional caricature of the original system. The energy minimisation behaviour of this new system is significantly more effective at globally resolving the original system constraints. This model uses only very simple, and fully-distributed positive feedback mechanisms that are relevant to other ‘active linking’ and adaptive networks. We discuss how this neural network model helps us to understand transformations and emergent collective behaviour in various non-neural adaptive networks such as social, genetic and ecological networks

A renormalization procedure for tensor models and scalar-tensor theories of gravity

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian configurations are parameterized by a scalar and a symmetric two-tensor, it is argued that, in general situations, the infrared dynamics of the tensor models should be described by scalar-tensor theories of gravity.Comment: 20 pages, 3 figures, references added, minor correction

From Holistic to Discrete Speech Sounds: The Blind Snow-Flake Maker Hypothesis

Sound is a medium used by humans to carry information. The existence of this kind of medium is a pre-requisite for language. It is organized into a code, called speech, which provides a repertoire of forms that is shared in each language community. This code is necessary to support the linguistic interactions that allow humans to communicate. How then may a speech code be formed prior to the existence of linguistic interactions? Moreover, the human speech code is characterized by several properties: speech is digital and compositional (vocalizations are made of units re-used systematically in other syllables); phoneme inventories have precise regularities as well as great diversity in human languages; all the speakers of a language community categorize sounds in the same manner, but each language has its own system of categorization, possibly very different from every other. How can a speech code with these properties form? These are the questions we will approach in the paper. We will study them using the method of the artificial. We will build a society of artificial agents, and study what mechanisms may provide answers. This will not prove directly what mechanisms were used for humans, but rather give ideas about what kind of mechanism may have been used. This allows us to shape the search space of possible answers, in particular by showing what is sufficient and what is not necessary. The mechanism we present is based on a low-level model of sensory-motor interactions. We show that the integration of certain very simple and non language-specific neural devices allows a population of agents to build a speech code that has the properties mentioned above. The originality is that it pre-supposes neither a functional pressure for communication, nor the ability to have coordinated social interactions (they do not play language or imitation games). It relies on the self-organizing properties of a generic coupling between perception and production both within agents, and on the interactions between agents

Quantitative modelling of the human–Earth System a new kind of science?

The five grand challenges set out for Earth System Science by the International Council for Science in 2010 require a true fusion of social science, economics and natural science—a fusion that has not yet been achieved. In this paper we propose that constructing quantitative models of the dynamics of the human–Earth system can serve as a catalyst for this fusion. We confront well-known objections to modelling societal dynamics by drawing lessons from the development of natural science over the last four centuries and applying them to social and economic science. First, we pose three questions that require real integration of the three fields of science. They concern the coupling of physical planetary boundaries via social processes; the extension of the concept of planetary boundaries to the human–Earth System; and the possibly self-defeating nature of the United Nation’s Millennium Development Goals. Second, we ask whether there are regularities or ‘attractors’ in the human–Earth System analogous to those that prompted the search for laws of nature. We nominate some candidates and discuss why we should observe them given that human actors with foresight and intentionality play a fundamental role in the human–Earth System. We conclude that, at sufficiently large time and space scales, social processes are predictable in some sense. Third, we canvass some essential mathematical techniques that this research fusion must incorporate, and we ask what kind of data would be needed to validate or falsify our models. Finally, we briefly review the state of the art in quantitative modelling of the human–Earth System today and highlight a gap between so-called integrated assessment models applied at regional and global scale, which could be filled by a new scale of model