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Vitorino Ramos - Citations2016Jan

2016 – Up now, an overall of 1567 citations among 74 works (including 3 books) on GOOGLE SCHOLAR ( [with an Hirsh h-index=19, and an average of 160.2 citations each for any work on my top five] + 900 citations among 57 works on the new RESEARCH GATE site (

Refs.: Science, Artificial Intelligence, Swarm Intelligence, Data-Mining, Big-Data, Evolutionary Computation, Complex Systems, Image Analysis, Pattern Recognition, Data Analysis.

Complete circuit diagram with pheromone - Cristian Jimenez-Romero, David Sousa-Rodrigues, Jeffrey H. Johnson, Vitorino Ramos; Figure – Neural circuit controller of the virtual ant (page 3, fig. 2). [URL: ]

Intelligence and decision in foraging ants. Individual or Collective? Internal or External? What is the right balance between the two. Can one have internal intelligence without external intelligence? Can one take examples from nature to build in silico artificial lives that present us with interesting patterns? We explore a model of foraging ants in this paper that will be presented in early September in Exeter, UK, at UKCI 2015. (available on arXiv [PDF] and ResearchGate)

Cristian Jimenez-Romero, David Sousa-Rodrigues, Jeffrey H. Johnson, Vitorino Ramos; “A Model for Foraging Ants, Controlled by Spiking Neural Networks and Double Pheromones“, UKCI 2015 Computational Intelligence – University of Exeter, UK, September 2015.

Abstract: A model of an Ant System where ants are controlled by a spiking neural circuit and a second order pheromone mechanism in a foraging task is presented. A neural circuit is trained for individual ants and subsequently the ants are exposed to a virtual environment where a swarm of ants performed a resource foraging task. The model comprises an associative and unsupervised learning strategy for the neural circuit of the ant. The neural circuit adapts to the environment by means of classical conditioning. The initially unknown environment includes different types of stimuli representing food (rewarding) and obstacles (harmful) which, when they come in direct contact with the ant, elicit a reflex response in the motor neural system of the ant: moving towards or away from the source of the stimulus. The spiking neural circuits of the ant is trained to identify food and obstacles and move towards the former and avoid the latter. The ants are released on a landscape with multiple food sources where one ant alone would have difficulty harvesting the landscape to maximum efficiency. In this case the introduction of a double pheromone mechanism (positive and negative reinforcement feedback) yields better results than traditional ant colony optimization strategies. Traditional ant systems include mainly a positive reinforcement pheromone. This approach uses a second pheromone that acts as a marker for forbidden paths (negative feedback). This blockade is not permanent and is controlled by the evaporation rate of the pheromones. The combined action of both pheromones acts as a collective stigmergic memory of the swarm, which reduces the search space of the problem. This paper explores how the adaptation and learning abilities observed in biologically inspired cognitive architectures is synergistically enhanced by swarm optimization strategies. The model portraits two forms of artificial intelligent behaviour: at the individual level the spiking neural network is the main controller and at the collective level the pheromone distribution is a map towards the solution emerged by the colony. The presented model is an important pedagogical tool as it is also an easy to use library that allows access to the spiking neural network paradigm from inside a Netlogo—a language used mostly in agent based modelling and experimentation with complex systems.


[1] C. G. Langton, “Studying artificial life with cellular automata,” Physica D: Nonlinear Phenomena, vol. 22, no. 1–3, pp. 120 – 149, 1986, proceedings of the Fifth Annual International Conference. [Online]. Available: science/article/pii/016727898690237X
[2] A. Abraham and V. Ramos, “Web usage mining using artificial ant colony clustering and linear genetic programming,” in Proceedings of the Congress on Evolutionary Computation. Australia: IEEE Press, 2003, pp. 1384–1391.
[3] V. Ramos, F. Muge, and P. Pina, “Self-organized data and image retrieval as a consequence of inter-dynamic synergistic relationships in artificial ant colonies,” Hybrid Intelligent Systems, vol. 87, 2002.
[4] V. Ramos and J. J. Merelo, “Self-organized stigmergic document maps: Environment as a mechanism for context learning,” in Proceddings of the AEB, Merida, Spain, February 2002. ´
[5] D. Sousa-Rodrigues and V. Ramos, “Traversing news with ant colony optimisation and negative pheromones,” in European Conference in Complex Systems, Lucca, Italy, Sep 2014.
[6] E. Bonabeau, G. Theraulaz, and M. Dorigo, Swarm Intelligence: From Natural to Artificial Systems, 1st ed., ser. Santa Fe Insitute Studies In The Sciences of Complexity. 198 Madison Avenue, New York: Oxford University Press, USA, Sep. 1999.
[7] M. Dorigo and L. M. Gambardella, “Ant colony system: A cooperative learning approach to the traveling salesman problem,” Universite Libre de Bruxelles, Tech. Rep. TR/IRIDIA/1996-5, ´ 1996.
[8] M. Dorigo, G. Di Caro, and L. M. Gambardella, “Ant algorithms for discrete optimization,” Artif. Life, vol. 5, no. 2, pp. 137– 172, Apr. 1999. [Online]. Available: 106454699568728
[9] L. M. Gambardella and M. Dorigo, “Ant-q: A reinforcement learning approach to the travelling salesman problem,” in Proceedings of the ML-95, Twelfth Intern. Conf. on Machine Learning, M. Kaufman, Ed., 1995, pp. 252–260.
[10] A. Gupta, V. Nagarajan, and R. Ravi, “Approximation algorithms for optimal decision trees and adaptive tsp problems,” in Proceedings of the 37th international colloquium conference on Automata, languages and programming, ser. ICALP’10. Berlin, Heidelberg: Springer-Verlag, 2010, pp. 690–701. [Online]. Available:
[11] V. Ramos, D. Sousa-Rodrigues, and J. Louçã, “Second order ˜ swarm intelligence,” in HAIS’13. 8th International Conference on Hybrid Artificial Intelligence Systems, ser. Lecture Notes in Computer Science, J.-S. Pan, M. Polycarpou, M. Wozniak, A. Carvalho, ´ H. Quintian, and E. Corchado, Eds. Salamanca, Spain: Springer ´ Berlin Heidelberg, Sep 2013, vol. 8073, pp. 411–420.
[12] W. Maass and C. M. Bishop, Pulsed Neural Networks. Cambridge, Massachusetts: MIT Press, 1998.
[13] E. M. Izhikevich and E. M. Izhikevich, “Simple model of spiking neurons.” IEEE transactions on neural networks / a publication of the IEEE Neural Networks Council, vol. 14, no. 6, pp. 1569–72, 2003. [Online]. Available: http://www.ncbi.nlm.nih. gov/pubmed/18244602
[14] C. Liu and J. Shapiro, “Implementing classical conditioning with spiking neurons,” in Artificial Neural Networks ICANN 2007, ser. Lecture Notes in Computer Science, J. de S, L. Alexandre, W. Duch, and D. Mandic, Eds. Springer Berlin Heidelberg, 2007, vol. 4668, pp. 400–410. [Online]. Available: 41
[15] J. Haenicke, E. Pamir, and M. P. Nawrot, “A spiking neuronal network model of fast associative learning in the honeybee,” Frontiers in Computational Neuroscience, no. 149, 2012. [Online]. Available: neuroscience/10.3389/conf.fncom.2012.55.00149/full
[16] L. I. Helgadottir, J. Haenicke, T. Landgraf, R. Rojas, and M. P. Nawrot, “Conditioned behavior in a robot controlled by a spiking neural network,” in International IEEE/EMBS Conference on Neural Engineering, NER, 2013, pp. 891–894.
[17] A. Cyr and M. Boukadoum, “Classical conditioning in different temporal constraints: an STDP learning rule for robots controlled by spiking neural networks,” pp. 257–272, 2012.
[18] X. Wang, Z. G. Hou, F. Lv, M. Tan, and Y. Wang, “Mobile robots’ modular navigation controller using spiking neural networks,” Neurocomputing, vol. 134, pp. 230–238, 2014.
[19] C. Hausler, M. P. Nawrot, and M. Schmuker, “A spiking neuron classifier network with a deep architecture inspired by the olfactory system of the honeybee,” in 2011 5th International IEEE/EMBS Conference on Neural Engineering, NER 2011, 2011, pp. 198–202.
[20] U. Wilensky, “Netlogo,” Evanston IL, USA, 1999. [Online]. Available:
[21] C. Jimenez-Romero and J. Johnson, “Accepted abstract: Simulation of agents and robots controlled by spiking neural networks using netlogo,” in International Conference on Brain Engineering and Neuro-computing, Mykonos, Greece, Oct 2015.
[22] W. Gerstner and W. M. Kistler, Spiking Neuron Models: Single Neurons, Populations, Plasticity. Cambridge: Cambridge University Press, 2002.
[23] J. v. H. W Gerstner, R Kempter and H. Wagner, “A neuronal learning rule for sub-millisecond temporal coding,” Nature, vol. 386, pp. 76–78, 1996.
[24] I. P. Pavlov, “Conditioned reflexes: An investigation of the activity of the cerebral cortex,” New York, 1927.
[25] E. J. H. Robinson, D. E. Jackson, M. Holcombe, and F. L. W. Ratnieks, “Insect communication: ‘no entry’ signal in ant foraging,” Nature, vol. 438, no. 7067, pp. 442–442, 11 2005. [Online]. Available:
[26] E. J. Robinson, D. Jackson, M. Holcombe, and F. L. Ratnieks, “No entry signal in ant foraging (hymenoptera: Formicidae): new insights from an agent-based model,” Myrmecological News, vol. 10, no. 120, 2007.
[27] D. Sousa-Rodrigues, J. Louçã, and V. Ramos, “From standard ˜ to second-order swarm intelligence phase-space maps,” in 8th European Conference on Complex Systems, S. Thurner, Ed., Vienna, Austria, Sep 2011.
[28] V. Ramos, D. Sousa-Rodrigues, and J. Louçã, “Spatio-temporal ˜ dynamics on co-evolved stigmergy,” in 8th European Conference on Complex Systems, S. Thurner, Ed., Vienna, Austria, 9 2011.
[29] S. Tisue and U. Wilensky, “Netlogo: A simple environment for modeling complexity,” in International conference on complex systems. Boston, MA, 2004, pp. 16–21.

David MS Rodrigues Reading the News Through its Structure New Hybrid Connectivity Based ApproachesFigure – Two simplicies a and b connected by the 2-dimensional face, the triangle {1;2;3}. In the analysis of the time-line of The Guardian newspaper (link) the system used feature vectors based on frequency of words and them computed similarity between documents based on those feature vectors. This is a purely statistical approach that requires great computational power and that is difficult for problems that have large feature vectors and many documents. Feature vectors with 100,000 or more items are common and computing similarities between these documents becomes cumbersome. Instead of computing distance (or similarity) matrices between documents from feature vectors, the present approach explores the possibility of inferring the distance between documents from the Q-analysis description. Q-analysis is a very natural notion of connectivity between the simplicies of the structure and in the relation studied, documents are connected to each other through shared sets of tags entered by the journalists. Also in this framework, eccentricity is defined as a measure of the relatedness of one simplex in relation to another [7].

David M.S. Rodrigues and Vitorino Ramos, “Traversing News with Ant Colony Optimisation and Negative Pheromones” [PDF], accepted as preprint for oral presentation at the European Conference on Complex SystemsECCS14 in Lucca, Sept. 22-26, 2014, Italy.

Abstract: The past decade has seen the rapid development of the online newsroom. News published online are the main outlet of news surpassing traditional printed newspapers. This poses challenges to the production and to the consumption of those news. With those many sources of information available it is important to find ways to cluster and organise the documents if one wants to understand this new system. Traditional approaches to the problem of clustering documents usually embed the documents in a suitable similarity space. Previous studies have reported on the impact of the similarity measures used for clustering of textual corpora [1]. These similarity measures usually are calculated for bag of words representations of the documents. This makes the final document-word matrix high dimensional. Feature vectors with more than 10,000 dimensions are common and algorithms have severe problems with the high dimensionality of the data. A novel bio inspired approach to the problem of traversing the news is presented. It finds Hamiltonian cycles over documents published by the newspaper The Guardian. A Second Order Swarm Intelligence algorithm based on Ant Colony Optimisation was developed [2, 3] that uses a negative pheromone to mark unrewarding paths with a “no-entry” signal. This approach follows recent findings of negative pheromone usage in real ants [4].

In this case study the corpus of data is represented as a bipartite relation between documents and keywords entered by the journalists to characterise the news. A new similarity measure between documents is presented based on the Q-analysis description [5, 6, 7] of the simplicial complex formed between documents and keywords. The eccentricity between documents (two simplicies) is then used as a novel measure of similarity between documents. The results prove that the Second Order Swarm Intelligence algorithm performs better in benchmark problems of the travelling salesman problem, with faster convergence and optimal results. The addition of the negative pheromone as a non-entry signal improves the quality of the results. The application of the algorithm to the corpus of news of The Guardian creates a coherent navigation system among the news. This allows the users to navigate the news published during a certain period of time in a semantic sequence instead of a time sequence. This work as broader application as it can be applied to many cases where the data is mapped to bipartite relations (e.g. protein expressions in cells, sentiment analysis, brand awareness in social media, routing problems), as it highlights the connectivity of the underlying complex system.

Keywords: Self-Organization, Stigmergy, Co-Evolution, Swarm Intelligence, Dynamic Optimization, Foraging, Cooperative Learning, Hamiltonian cycles, Text Mining, Textual Corpora, Information Retrieval, Knowledge Discovery, Sentiment Analysis, Q-Analysis, Data Mining, Journalism, The Guardian.


[1] Alexander Strehl, Joydeep Ghosh, and Raymond Mooney. Impact of similarity measures on web-page clustering.  In Workshop on Artifcial Intelligence for Web Search (AAAI 2000), pages 58-64, 2000.
[2] David M. S. Rodrigues, Jorge Louçã, and Vitorino Ramos. From standard to second-order Swarm Intelligence  phase-space maps. In Stefan Thurner, editor, 8th European Conference on Complex Systems, Vienna, Austria,  9 2011.
[3] Vitorino Ramos, David M. S. Rodrigues, and Jorge Louçã. Second order Swarm Intelligence. In Jeng-Shyang  Pan, Marios M. Polycarpou, Micha l Wozniak, André C.P.L.F. Carvalho, Hector Quintian, and Emilio Corchado,  editors, HAIS’13. 8th International Conference on Hybrid Artificial Intelligence Systems, volume 8073 of Lecture  Notes in Computer Science, pages 411-420. Springer Berlin Heidelberg, Salamanca, Spain, 9 2013.
[4] Elva J.H. Robinson, Duncan Jackson, Mike Holcombe, and Francis L.W. Ratnieks. No entry signal in ant  foraging (hymenoptera: Formicidae): new insights from an agent-based model. Myrmecological News, 10(120), 2007.
[5] Ronald Harry Atkin. Mathematical Structure in Human A ffairs. Heinemann Educational Publishers, 48 Charles  Street, London, 1 edition, 1974.
[6] J. H. Johnson. A survey of Q-analysis, part 1: The past and present. In Proceedings of the Seminar on Q-analysis  and the Social Sciences, Universty of Leeds, 9 1983.
[7] David M. S. Rodrigues. Identifying news clusters using Q-analysis and modularity. In Albert Diaz-Guilera,  Alex Arenas, and Alvaro Corral, editors, Proceedings of the European Conference on Complex Systems 2013, Barcelona, 9 2013.

In order to solve hard combinatorial optimization problems (e.g. optimally scheduling students and teachers along a week plan on several different classes and classrooms), one way is to computationally mimic how ants forage the vicinity of their habitats searching for food. On a myriad of endless possibilities to find the optimal route (minimizing the travel distance), ants, collectively emerge the solution by using stigmergic signal traces, or pheromones, which also dynamically change under evaporation.

Current algorithms, however, make only use of a positive feedback type of pheromone along their search, that is, if they collectively visit a good low-distance route (a minimal pseudo-solution to the problem) they tend to reinforce that signal, for their colleagues. Nothing wrong with that, on the contrary, but no one knows however if a lower-distance alternative route is there also, just at the corner. On his global search endeavour, like a snowballing effect, positive feedbacks tend up to give credit to the exploitation of solutions but not on the – also useful – exploration side. The upcoming potential solutions can thus get crystallized, and freeze, while a small change on some parts of the whole route, could on the other-hand successfully increase the global result.

Influence of Negative Pheromone in Swarm IntelligenceFigure – Influence of negative pheromone on kroA100.tsp problem (fig.1 – page 6) (values on lines represent 1-ALPHA). A typical standard ACS (Ant Colony System) is represented here by the line with value 0.0, while better results could be found by our approach, when using positive feedbacks (0.95) along with negative feedbacks (0.05). Not only we obtain better results, as we found them earlier.

There is, however, an advantage when a second type of pheromone (a negative feedback one) co-evolves with the first type. And we decided to research for his impact. What we found out, is that by using a second type of global feedback, we can indeed increase a faster search while achieving better results. In a way, it’s like using two different types of evaporative traffic lights, in green and red, co-evolving together. And as a conclusion, we should indeed use a negative no-entry signal pheromone. In small amounts (0.05), but use it. Not only this prevents the whole system to freeze on some solutions, to soon, as it enhances a better compromise on the search space of potential routes. The pre-print article is available here at arXiv. Follows the abstract and keywords:

Vitorino Ramos, David M. S. Rodrigues, Jorge Louçã, “Second Order Swarm Intelligence” [PDF], in Hybrid Artificial Intelligent Systems, Lecture Notes in Computer Science, Springer-Verlag, Volume 8073, pp. 411-420, 2013.

Abstract: An artificial Ant Colony System (ACS) algorithm to solve general purpose combinatorial Optimization Problems (COP) that extends previous AC models [21] by the inclusion of a negative pheromone, is here described. Several Travelling Salesman Problem‘s (TSP) were used as benchmark. We show that by using two different sets of pheromones, a second-order co-evolved compromise between positive and negative feedbacks achieves better results than single positive feedback systems. The algorithm was tested against known NP complete combinatorial Optimization Problems, running on symmetrical TSPs. We show that the new algorithm compares favourably against these benchmarks, accordingly to recent biological findings by Robinson [26,27], and Grüter [28] where “No entry” signals and negative feedback allows a colony to quickly reallocate the majority of its foragers to superior food patches. This is the first time an extended ACS algorithm is implemented with these successful characteristics.

Keywords: Self-Organization, Stigmergy, Co-Evolution, Swarm Intelligence, Dynamic Optimization, Foraging, Cooperative Learning, Combinatorial Optimization problems, Symmetrical Travelling Salesman Problems (TSP).

Saramago Caos quote - Lisbon, Vitorino Ramos 2013Photo – “O caos é uma ordem por decifrar” (Portuguese), that is… “Chaos is an order yet to be deciphered“, a quote from the Nobel Prize in Literature (1998) José Saramago [Lisbon, V. Ramos, 2013].

In 1990 (*), on one of his now famous works, Christopher Langton (link) decided to ask an important question. In order for computation to emerge spontaneously and become an important factor in the dynamics of a system, the material substrate must support the primitive functions required for computation: the transmission, storage, and modification of information. He then asked: Under what conditions might we expect physical systems to support such computational primitives?

Naturally, the question is difficult to address directly. Instead, he decided to reformulate the question in the context of a class of formal abstractions of physical systems: cellular automata (CAs). First, he introduce cellular automata and a simple scheme for parametrising (lambda parameter, λ) the space of all possible CA rules. Then he applied this parametrisation scheme to the space of possible one-dimensional CAs in a qualitative survey of the different dynamical regimes existing in CA rule space and their relationship to one another.

By presenting a quantitative picture of these structural relationships, using data from an extensive survey of two-dimensional CAs, he finally review the observed relationships among dynamical regimes, discussing their implications for the more general question raised above.  Langton found out that for a 2-state, 1-r neighbourhood, 1D cellular automata the optimal λ value is close to 0.5. For a 2-state, Moore neighbourhood, 2D cellular automata, like Conway’s Life, the λ value is then 0.273.

We then find that by selecting an appropriate parametrisation of the space of CAs, one observes a phase transition between highly ordered and highly disordered dynamics, analogous to the phase transition between the solid and fluid states of matter. Furthermore, Langton observed that CAs exhibiting the most complex behaviour – both qualitatively and quantitatively- are found generically in the vicinity of this phase transition. Most importantly, he observed that CAs in the transition region have the greatest potential for the support of information storage, transmission, and modification, and therefore for the emergence of computation. He concludes:

(…) These observations suggest that  there is  a fundamental connection between phase transitions and computation, leading to the following hypothesis concerning the emergence of computation in  physical systems: Computation may emerge spontaneously and come to dominate the dynamics of physical systems when those systems are at or near a transition between their solid and fluid phases, especially in the vicinity of a second-order or “critical” transition. (…)

Moreover, we observe surprising similarities between the behaviours of computations and systems near phase transitions, finding analogs of computational complexity classes and the halting problem (Turing) within the phenomenology of phase transitions. Langton, concludes that there is a fundamental connection between computation and phase transitions, especially second-order or “critical” transitions, discussing some of the implications for our understanding of nature if such a connection is borne out.

The full paper (*), Christopher G. Langton. “Computation at the edge of chaos”. Physica D, 42, 1990, is available online, here [PDF].

Portugal at World Expo 1998 by Vitorino Ramos

Images – Portugal (1A – top left, original input satellite image below), geodesically stretched by one of my Mathematical Morphology algorithms, in order to represent real travel times from each of the 18 regional districts in Portugal, to the rest of the territory.  From the 18, three capital districts are represented here. As departing from Lisbon (1B – top right), from Faro (1C – South of Portugal, bottom left), and from Bragança (1D – North-East region, bottom right). [World Exposition, Lisbon, Territory pavilion, 1998].

Recently one of my colleagues who knows I love maps, pointed me to an old TV show “Câmara Clara“, a cultural TV show by RTP2, at one of the main public Portuguese TV stations. Main reason for my interest was his current theme: Maps. My second reason was their guests: Joaquim Ferreira do Amaral (an ex-Minister with a passion for maps) and Manuel Lima, which wonderful work on information visualization I know for a long time (on one of my past posts I referred to one of his ongoing working sites: visualcomplexity).

For my complete and positive surprise, their interview ended with some new examples, being one of my old works referred (from 57m 12s up to 60m 26s on ). It’s a long story on how I ended doing these kind of maps. Part of it, it’s here. During 1998, the World Exposition was in Portugal, and I got invited to present a set of 18 different maps from the Portuguese territory. So I decided to geodesically stretch the travel distances from any of the 18 different capital districts, to the rest of the territory, in order to represent travel Time not Distance, or Distance as time. For that,  I have coded new algorithms based on Mathematical Morphology (MM), taking in account every road (from main roads to regional, check some images below), from which I applied different MM operators.

Unfortunately, many of those maps are now lost. I did tried hard to find them from my old digital archives, but only found those above, which represent the departure from Lisbon (the Capital), Faro and Bragança. So, if by any reason you happen to have some photos from the 1998’s World Exposition in Lisbon, inside the Territory pavilion, I would love to receive them.

Os Portugueses e a Arte dos Mapas - Câmara Clara 131 - Maio 10 2009Video (LINK) – “Câmara Clara” TV show by journalist Paula Moura Pinheiro dedicated to maps (nº 131), at one of the main public Portuguese TV stations (RTP2), broadcasted on May 3 2009, in Portuguese.

A sketchy summary of this TV program went on something like this (the poor translation is mine): At the year Google promises to launch his first and exhaustive world-wide open-access digital cartography of the African continent, Joaquim Ferreira do Amaral, passioned by the Portuguese World Discover History and collector of historical maps, joins as guest with Manuel Lima, the Portuguese information designer that recently Creativity magazine has considered one of the top bright minds along with Google and Amazon founders, debating the importance of “navigating” reality with a map. From the Portuguese cartographic history, know to be the best in the XV and XVI centuries, up to the actual state-of-the-art in this area, from which Manuel Lima is considered to be one of the top researchers at global scale.

Original + Layers Portugal at World Expo 1998 by Vitorino Ramos

Signal Traces - Sept. 2013 Vitorino RamosPhoto – Signal traces, September 2013, Vitorino Ramos.

[…] While pheromone reinforcement plays a role as system’s memory, evaporation allows the system to adapt and dynamically decide, without any type of centralized or hierarchical control […], below.

“[…] whereas signals tends to be conspicuous, since natural selection has shaped signals to be strong and effective displays, information transfer via cues is often more subtle and based on incidental stimuli in an organism’s social environment […]”, Seeley, T.D., “The Honey Bee Colony as a Super-Organism”, American Scientist, 77, pp.546-553, 1989.

[…] If an ant colony on his cyclic way from the nest to a food source (and back again), has only two possible branches around an obstacle, one bigger and the other smaller (the bridge experiment [7,52]), pheromone will accumulate – as times passes – on the shorter path, simple because any ant that sets out on that path will return sooner, passing the same points more frequently, and via that way, reinforcing the signal of that precise branch. Even if as we know, the pheromone evaporation rate is the same in both branches, the longer branch will faster vanish his pheromone, since there is not enough critical mass of individuals to keep it. On the other hand – in what appears to be a vastly pedagogic trick of Mother Nature – evaporation plays a critical role on the society. Without it, the final global decision or the phase transition will never happen. Moreover, without it, the whole colony can never adapt if the environment suddenly changes (e.g., the appearance of a third even shorter branch). While pheromone reinforcement plays a role as system’s memory, evaporation allows the system to adapt and dynamically decide, without any type of centralized or hierarchical control. […], in “Social Cognitive Maps, Swarm Collective Perception and Distributed Search on Dynamic Landscapes“, V. Ramos et al., available as pre-print on arXiV, 2005.

[…] There is some degree of communication among the ants, just enough to keep them from wandering of completely at random. By this minimal communication they can remind each other that they are not alone but are cooperating with team-mates. It takes a large number of ants, all reinforcing each other this way, to sustain any activity – such as trail building – for any length of time. Now my very hazy understanding of the operation of brain leads me to believe that something similar pertains to the firing of neurons… […] in, p. 316, Hofstadter, D.R., “Gödel, Escher, Bach: An Eternal Golden Braid“, New York: Basic Books, 1979).

[…] Since in Self-Organized (SO) systems their organization arises entirely from multiple interactions, it is of critical importance to question how organisms acquire and act upon information [9]. Basically through two forms: a) information gathered from one’s neighbours, and b) information gathered from work in progress, that is, stigmergy. In the case of animal groups, these internal interactions typically involve information transfers between individuals. Biologists have recently recognized that information can flow within groups via two distinct pathways – signals and cues. Signals are stimuli shaped by natural selection specifically to convey information, whereas cues are stimuli that convey information only incidentally [9]. The distinction between signals and cues is illustrated by the difference on ant and deer trails. The chemical trail deposited by ants as they return from a desirable food source is a signal. Over evolutionary time such trails have been moulded by natural selection for the purpose of sharing with nest mates information about the location of rich food sources. In contrast, the rutted trails made by deer walking through the woods is a cue, not shaped by natural selection for communication among deer but are a simple by-product of animals walking along the same path. SO systems are based on both, but whereas signals tends to be conspicuous, since natural selection has shaped signals to be strong and effective displays, information transfer via cues is often more subtle and based on incidental stimuli in an organism’s social environment [45] […], in “Social Cognitive Maps, Swarm Collective Perception and Distributed Search on Dynamic Landscapes“, V. Ramos et al., available as pre-print on arXiV, 2005.

Hybrid Artificial Intelligent Systems HAIS 2013 (pp. 411-420 Second Order Swarm Intelligence)Figure – Hybrid Artificial Intelligent Systems new LNAI (Lecture Notes on Artificial Intelligence) series volume 8073, Springer-Verlag Book [original photo by my colleague David M.S. Rodrigues].

New work, new book. Last week one of our latest works come out published on Springer. Edited by Jeng-Shyang Pan, Marios M. Polycarpou, Emilio Corchado et al. “Hybrid Artificial Intelligent Systems” comprises a full set of new papers on this hybrid area on Intelligent Computing (check the full articles list at Springer). Our new paper “Second Order Swarm Intelligence” (pp. 411-420, Springer books link) was published on the Bio-inspired Models and Evolutionary Computation section.

Nocturnal swarm

Nocturnal moth trails – Fluttering wings leave lacy trails as moths beat their way to a floodlight on a rural Ontario lawn. The midsummer night’s exposure, held for 20 seconds, captured some of the hundreds of insects engaged in a nocturnal swarm. [Photo: Steve Irvine, National Geographic, 2013, link]

Surfaces and Essences - Hofstadter Sander 2013

[…] Analogy is the core of all thinking. – This is the simple but unorthodox premise that Pulitzer Prize-winning author Douglas Hofstadter and French psychologist Emmanuel Sander defend in their new work. Hofstadter has been grappling with the mysteries of human thought for over thirty years. Now, with his trademark wit and special talent for making complex ideas vivid, he has partnered with Sander to put forth a highly novel perspective on cognition. We are constantly faced with a swirling and intermingling multitude of ill-defined situations. Our brain’s job is to try to make sense of this unpredictable, swarming chaos of stimuli. How does it do so? The ceaseless hail of input triggers analogies galore, helping us to pinpoint the essence of what is going on. Often this means the spontaneous evocation of words, sometimes idioms, sometimes the triggering of nameless, long-buried memories.

Why did two-year-old Camille proudly exclaim, “I undressed the banana!”? Why do people who hear a story often blurt out, “Exactly the same thing happened to me!” when it was a completely different event? How do we recognize an aggressive driver from a split-second glance in our rear-view mirror? What in a friend’s remark triggers the offhand reply, “That’s just sour grapes”?  What did Albert Einstein see that made him suspect that light consists of particles when a century of research had driven the final nail in the coffin of that long-dead idea? The answer to all these questions, of course, is analogy-making – the meat and potatoes, the heart and soul, the fuel and fire, the gist and the crux, the lifeblood and the wellsprings of thought. Analogy-making, far from happening at rare intervals, occurs at all moments, defining thinking from top to toe, from the tiniest and most fleeting thoughts to the most creative scientific insights.

Like Gödel, Escher, Bach before it, Surfaces and Essences will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core – the incessant, unconscious quest for strong analogical links to past experiences – this book puts forth a radical and deeply surprising new vision of the act of thinking. […] intro to “Surfaces and Essences – Analogy as the fuel and fire of thinking” by Douglas Hofstadter and Emmanuel Sander, Basic Books, NY, 2013 [link] (to be released May 1, 2013).

Image – The frontispiece of William King Gregory’s two-volume Evolution Emerging. Gregory, 1951, Evolution Emerging: A Survey of Changing Patterns from Primeval Life to Man, vol. 2, p. 757; fig. 20.33; [courtesy of Mary DeJong, Mai Qaraman, and the American Museum of Natural History].

Fig. – (book cover) “Emergence: The Connected Lives of Ants, Brains, Cities, and Software” (additional link) is a book written by media theorist Steven Berlin Johnson, published in 2001,  Scribner. New York, NY.

The patterns are simple, but followed together, they make for a whole that is wiser than the sum of its parts. Go for a walk; cultivate hunches; write everything down, but keep your folders messy; embrace serendipity; make generative mistakes; take on multiple hobbies; frequent coffee houses and other liquid networks; follow the links; let others build on your ideas; borrow, recycle; reinvent. Build a tangled bank.” — Steven Johnson.

Recent research have increasingly being focused on the relationship between Human-Human interaction, social networks (no, not the Facebook) and other Human-activity areas, like health. Nicholas Christakis (Harvard Univ. research link) points us that, people are inter-connected, and so as well, their health is inter-connected. This research engages two types of phenomena: the social, mathematical, and biological rules governing how social networks form (“Connection“) and the biological and social implications of how they operate to influence thoughts, feelings, and behaviours (“Contagion“), as in the self-organized stigmergy-like dynamics of Cognitive Collective Perception (link).

Above, Nicholas Christakis (in a 56m. documentary lecture produced by The Floating University, Sept. 2011) discusses the obvious tension and delicate balance between agency (one individual choices and actions) and structure (our collective responsibility), where here, structure refers not only to our co-evolving dynamic societal environment as well as to the permanent unfolding entangled nature of topological structure on complex networks, such as in human-human social networks, while asking: If you’re so free, why do you follow others? The documentary (YouTube link) resume states:

If you think you’re in complete control of your destiny or even your own actions, you’re wrong. Every choice you make, every behaviour you exhibit, and even every desire you have finds its roots in the social universe. Nicholas Christakis explains why individual actions are inextricably linked to sociological pressures; whether you’re absorbing altruism performed by someone you’ll never meet or deciding to jump off the Golden Gate Bridge, collective phenomena affect every aspect of your life. By the end of the lecture Christakis has revealed a startling new way to understand the world that ranks sociology as one of the most vitally important social sciences.”

While cooperation is central to the success of human societies and is widespread, cooperation in itself, however, poses a challenge in both the social and biological sciences: How can this high level of cooperation be maintained in the face of possible exploitation? One answer involves networked interactions and population structure.

As perceived, the balance between homophily (where “birds of a feather flock together”) and heterophily (one where most of genotypes are negatively correlated), do requires further research. In fact, in humans, one of the most replicated findings in the social sciences is that people tend to associate with other people that they resemble, a process precisely known as homophily. As Christakis points out, although phenotypic resemblance between friends might partly reflect the operation of social influence, our genotypes are not materially susceptible to change. Therefore, genotypic resemblance could result only from a process of selection. Such genotypic selection might in turn take several forms. For short, let me stress you two examples. What follows are two papers, as well as a quick reference (image below) to a recent general-audience of his books:

1) Rewiring your network fosters cooperation:

“Human populations are both highly cooperative and highly organized. Human interactions are not random but rather are structured in social networks. Importantly, ties in these networks often are dynamic, changing in response to the behavior of one’s social partners. This dynamic structure permits an important form of conditional action that has been explored theoretically but has received little empirical attention: People can respond to the cooperation and defection of those around them by making or breaking network links. Here, we present experimental evidence of the power of using strategic link formation and dissolution, and the network modification it entails, to stabilize cooperation in sizable groups. Our experiments explore large-scale cooperation, where subjects’ cooperative actions are equally beneficial to all those with whom they interact. Consistent with previous research, we find that cooperation decays over time when social networks are shuffled randomly every round or are fixed across all rounds. We also find that, when networks are dynamic but are updated only infrequently, cooperation again fails. However, when subjects can update their network connections frequently, we see a qualitatively different outcome: Cooperation is maintained at a high level through network rewiring. Subjects preferentially break links with defectors and form new links with cooperators, creating an incentive to cooperate and leading to substantial changes in network structure. Our experiments confirm the predictions of a set of evolutionary game theoretic models and demonstrate the important role that dynamic social networks can play in supporting large-scale human cooperation.”, abstract in D.G. Rand, S. Arbesman, and N.A. Christakis, “Dynamic Social Networks Promote Cooperation in Experiments with Humans,” PNAS: Proceedings of the National Academy of Sciences (October 2011). [full PDF];

Picture – (book cover) Along with James Fowler, Christakis has authored also a general-audience book on social networks: Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives, 2011 (book link). For a recent book review, access here.

2) We are surrounded by a sea of our friends’ genes:

“It is well known that humans tend to associate with other humans who have similar characteristics, but it is unclear whether this tendency has consequences for the distribution of genotypes in a population. Although geneticists have shown that populations tend to stratify genetically, this process results from geographic sorting or assortative mating, and it is unknown whether genotypes may be correlated as a consequence of nonreproductive associations or other processes. Here, we study six available genotypes from the National Longitudinal Study of Adolescent Health to test for genetic similarity between friends. Maps of the friendship networks show clustering of genotypes and, after we apply strict controls for population strati!cation, the results show that one genotype is positively correlated (homophily) and one genotype is negatively correlated (heterophily). A replication study in an independent sample from the Framingham Heart Study veri!es that DRD2 exhibits signi!cant homophily and that CYP2A6 exhibits signi!cant heterophily. These unique results show that homophily and heterophily obtain on a genetic (indeed, an allelic) level, which has implications for the study of population genetics and social behavior. In particular, the results suggest that association tests should include friends’ genes and that theories of evolution should take into account the fact that humans might, in some sense, be metagenomic with respect to the humans around them.”, abstract in J.H. Fowler, J.E. Settle, and N.A. Christakis, “Correlated Genotypes in Friendship Networks,” PNAS: Proceedings of the National Academy of Sciences (January 2011). [full PDF].

Four different snapshots (click to enlarge) from one of my latest books, recently published in Japan: Ajith Abraham, Crina Grosan, Vitorino Ramos (Eds.), “Swarm Intelligence in Data Mining” (群知能と  データマイニング), Tokyo Denki University press [TDU], Tokyo, Japan, July 2012.

Figure – Attractor basins (fig.2 pp.6 on Mária Ercsey-Ravasz and Zoltán Toroczkai, “Optimization hardness as transient chaos in an analog approach to constraint satisfaction“, Nature Physics, vol. 7, p. 966-970, 2011.)

Mária Ercsey-Ravasz and Zoltán Toroczkai have proposed a way of mapping satisfiability problems to differential equations and a deterministic algorithm that solves them in polynomial continuous time at the expense of exponential energy functions (so the discrete approximation of the algorithm does not run in polynomial time, and an analogue system would need exponential resources).

The map assigns a phase space to a problem; the algorithm chooses random initial conditions from within that phase space.  In the graphs above and below, they pick a 2-d subspace of the phase space and for each initial point in that space they illustrate 1) the particular solution the algorithm finds, 2) the corresponding “solution cluster”, an equivalence class of solutions that identifies two solutions if they differ in exactly one variable assignment, and 3) the time it takes to solve the problem.  Each row adds another clause to satisfy.

The especially interesting part of the paper is the notion of an escape rate,  the proportion of the trajectories still searching for a solution after a time t.  In a companion paper, they show that the escape rate for Sudoku combinatorial instances (The Chaos Within Sudoku, Nature, August 2012)  correlates strongly with human judgements of hardness. This escape rate is similar to the Kolmogorov complexity in that it gives a notion of hardness to individual problem instances rather than to classes of problems. Full paper could be retrieved from arXiv: Mária Ercsey-Ravasz and Zoltán Toroczkai, “Optimization hardness as transient chaos in an analog approach to constraint satisfaction“, Nature Physics, vol. 7, p. 966-970, 2011. (at arXiv on August 2012).

Figure – Attractor basins for 3-XORSAT (fig.8 pp.18 on Mária Ercsey-Ravasz and Zoltán Toroczkai, “Optimization hardness as transient chaos in an analog approach to constraint satisfaction“, Nature Physics, vol. 7, p. 966-970, 2011.)

Figure (click to enlarge) – Orders of common functions (via Wikipedia): A list of classes of functions that are commonly encountered when analyzing the running time of an algorithm. In each case, c is a constant and n increases without bound. The slower-growing functions are generally listed first. For each case, several examples are given.

Fig.1 – (click to enlarge) The optimal shortest path among N=1265 points depicting a Portuguese Navalheira crab as a result of one of our latest Swarm-Intelligence based algorithms. The problem of finding the shortest path among N different points in space is NP-hard, known as the Travelling Salesmen Problem (TSP), being one of the major and hardest benchmarks in Combinatorial Optimization (link) and Artificial Intelligence. (V. Ramos, D. Rodrigues, 2012)

This summer my kids just grab a tiny Portuguese Navalheira crab on the shore. After a small photo-session and some baby-sitting with a lettuce leaf, it was time to release it again into the ocean. He not only survived my kids, as he is now entitled into a new World Wide Web on-line life. After the Shortest path Sardine (link) with 1084 points, here is the Crab with 1265 points. The algorithm just run as little as 110 iterations.

Fig. 2 – (click to enlarge) Our 1265 initial points depicting a TSP Portuguese Navalheira crab. Could you already envision a minimal tour between all these points?

As usual in Travelling Salesmen problems (TSP) we start it with a set of points, in our case 1084 points or cities (fig. 2). Given a list of cities and their pairwise distances, the task is now to find the shortest possible tour that visits each city exactly once. The problem was first formulated as a mathematical problem in 1930 and is one of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods.

Fig. 3 – (click to enlarge) Again the shortest path Navalheira crab, where the optimal contour path (in black: first fig. above) with 1265 points (or cities) was filled in dark orange.

TSP has several applications even in its purest formulation, such as planning, logistics, and the manufacture of microchips. Slightly modified, it appears as a sub-problem in many areas, such as DNA sequencing. In these applications, the concept city represents, for example, customers, soldering points, or DNA fragments, and the concept distance represents travelling times or cost, or a similarity measure between DNA fragments. In many applications, additional constraints such as limited resources or time windows make the problem considerably harder.

What follows (fig. 4) is the original crab photo after image segmentation and just before adding Gaussian noise in order to retrieve several data points for the initial TSP problem. The algorithm was then embedded with the extracted x,y coordinates of these data points (fig. 2) in order for him to discover the minimal path, in just 110 iterations. For extra details, pay a visit onto the Shortest path Sardine (link) done earlier.

Fig. 4 – (click to enlarge) The original crab photo after some image processing as well as segmentation and just before adding Gaussian noise in order to retrieve several data points for the initial TSP problem.

Figure – A classic example of emergence: The exact shape of a termite mound is not reducible to the actions of individual termites. Even if, there are already computer models who could achieve it (Check for more on “Stigmergic construction” or the full current blog Stigmergy tag)

The world can no longer be understood like a chessboard… It’s a Jackson Pollack painting” ~ Carne Ross, 2012.

[…] As pointed by Langton, there is more to life than mechanics – there is also dynamics. Life depends critically on principles of dynamical self-organization that have remained largely untouched by traditional analytic methods. There is a simple explanation for this – these self-organized dynamics are fundamentally non-linear phenomena, and non-linear phenomena in general depend critically on the interactions between parts: they necessarily disappear when parts are treated in isolation from one another, which is the basis for any analytic method. Rather, non-linear phenomena are most appropriately treated by a synthetic approach, where synthesis means “the combining of separate elements or substances to form a coherent whole”. In non-linear systems, the parts must be treated in each other’s presence, rather than independently from one another, because they behave very differently in each other’s presence than we would expect from a study of the parts in isolation. […] in Vitorino Ramos, 2002, /0412077.

What follows are passages from an important article on the consequences for Science at the moment of the recent discovery of the Higgs boson. Written by Ashutosh Jogalekar, “The Higgs boson and the future of science” (link) the article appeared at the Scientific American blog section (July 2012). And it starts discussing reductionism or how the Higgs boson points us to the culmination of reductionist thinking:

[…] And I say this with a suspicion that the Higgs boson may be the most fitting tribute to the limitations of what has been the most potent philosophical instrument of scientific discovery – reductionism. […]

[…] Yet as we enter the second decade of the twenty-first century, it is clear that reductionism as a principal weapon in our arsenal of discovery tools is no longer sufficient. Consider some of the most important questions facing modern science, almost all of which deal with complex, multi factorial systems. How did life on earth begin? How does biological matter evolve consciousness? What are dark matter and dark energy? How do societies cooperate to solve their most pressing problems? What are the properties of the global climate system? It is interesting to note at least one common feature among many of these problems; they result from the build-up rather than the breakdown of their operational entities. Their signature is collective emergence, the creation of attributes which are greater than the sum of their constituent parts. Whatever consciousness is for instance, it is definitely a result of neurons acting together in ways that are not obvious from their individual structures. Similarly, the origin of life can be traced back to molecular entities undergoing self-assembly and then replication and metabolism, a process that supersedes the chemical behaviour of the isolated components. The puzzle of dark matter and dark energy also have as their salient feature the behaviour of matter at large length and time scales. Studying cooperation in societies essentially involves studying group dynamics and evolutionary conflict. The key processes that operate in the existence of all these problems seem to almost intuitively involve the opposite of reduction; they all result from the agglomeration of molecules, matter, cells, bodies and human beings across a hierarchy of unique levels. In addition, and this is key, they involve the manifestation of unique principles emerging at every level that cannot be merely reduced to those at the underlying level. […]

[…] While emergence had been implicitly appreciated by scientists for a long time, its modern salvo was undoubtedly a 1972 paper in Science by the Nobel Prize winning physicist Philip Anderson (link) titled “More is Different” (PDF), a title that has turned into a kind of clarion call for emergence enthusiasts. In his paper Anderson (who incidentally first came up with the so-called Higgs mechanism) argued that emergence was nothing exotic; for instance, a lump of salt has properties very different from those of its highly reactive components sodium and chlorine. A lump of gold evidences properties like color that don’t exist at the level of individual atoms. Anderson also appealed to the process of broken symmetry, invoked in all kinds of fundamental events – including the existence of the Higgs boson – as being instrumental for emergence. Since then, emergent phenomena have been invoked in hundreds of diverse cases, ranging from the construction of termite hills to the flight of birds. The development of chaos theory beginning in the 60s further illustrated how very simple systems could give rise to very complicated and counter-intuitive patterns and behaviour that are not obvious from the identities of the individual components. […]

[…] Many scientists and philosophers have contributed to considered critiques of reductionism and an appreciation of emergence since Anderson wrote his paper. (…) These thinkers make the point that not only does reductionism fail in practice (because of the sheer complexity of the systems it purports to explain), but it also fails in principle on a deeper level. […]

[…] An even more forceful proponent of this contingency-based critique of reductionism is the complexity theorist Stuart Kauffman who has laid out his thoughts in two books. Just like Anderson, Kauffman does not deny the great value of reductionism in illuminating our world, but he also points out the factors that greatly limit its application. One of his favourite examples is the role of contingency in evolution and the object of his attention is the mammalian heart. Kauffman makes the case that no amount of reductionist analysis could explain tell you that the main function of the heart is to pump blood. Even in the unlikely case that you could predict the structure of hearts and the bodies that house them starting from the Higgs boson, such a deductive process could never tell you that of all the possible functions of the heart, the most important one is to pump blood. This is because the blood-pumping action of the heart is as much a result of historical contingency and the countless chance events that led to the evolution of the biosphere as it is of its bottom-up construction from atoms, molecules, cells and tissues. […]

[…] Reductionism then falls woefully short when trying to explain two things; origins and purpose. And one can see that if it has problems even when dealing with left-handed amino acids and human hearts, it would be in much more dire straits when attempting to account for say kin selection or geopolitical conflict. The fact is that each of these phenomena are better explained by fundamental principles operating at their own levels. […]

[…] Every time the end of science has been announced, science itself proved that claims of its demise were vastly exaggerated. Firstly, reductionism will always be alive and kicking since the general approach of studying anything by breaking it down into its constituents will continue to be enormously fruitful. But more importantly, it’s not so much the end of reductionism as the beginning of a more general paradigm that combines reductionism with new ways of thinking. The limitations of reductionism should be seen as a cause not for despair but for celebration since it means that we are now entering new, uncharted territory. […]

Figure (click to enlarge) – Time dependence of FAO Food Price Index from January 2004 to May 2011. Red dashed vertical lines correspond to beginning dates of “food riots” and protests associated with the major recent unrest in North Africa and the Middle East. The overall death toll is reported in parentheses [26-55]. Blue vertical line indicates the date, December 13, 2010, on which we submitted a report to the U.S. government, warning of the link between food prices, social unrest and political instability [56]. Inset shows FAO Food Price Index from 1990 to 2011. [From arXiv:1108.2455, page 3]

Poverty is the parent of revolution and crime.” ~ Aristotle.

By crossing data on food price, and food price peaks with an ongoing trend of increasing prices, as well as the date of riots around the world, 3 of my colleagues at NECSI – the New England Complex Systems Institute (link), Boston,  found out a specific food price threshold above which protests become likely. By doing so, unveiled a model that accurately explained why the waves of unrest that swept the world in 2008 and 2011 crashed when they did. That was the past. NECSI team however, expects a perilous trend in rising food prices to continue (link). Even before the extreme weather scrambled food prices this year, their 2011 report predicted that the next great breach would occur in August 2013, and that the risk of more worldwide rioting would follow. So, if trends hold, these complex systems model say we’re less than one year and counting from a fireball of global unrest riots.

The abstract and PDF link into their work follows:

[…] Social unrest may reflect a variety of factors such as poverty, unemployment, and social injustice. Despite the many possible contributing factors, the timing of violent protests in North Africa and the Middle East in 2011 as well as earlier riots in 2008 coincides with large peaks in global food prices. We identify a specific food price threshold above which protests become likely. These observations suggest that protests may reflect not only long-standing political failings of governments, but also the sudden desperate straits of vulnerable populations. If food prices remain high, there is likely to be persistent and increasing global social disruption. Underlying the food price peaks we also found an ongoing trend of increasing prices. We extrapolate these trends and identify a crossing point to the domain of high impacts, even without price peaks, in 2012-2013. This implies that avoiding global food crises and associated social unrest requires rapid and concerted action. […] in Marco Lagi, Karla Z. Bertrand and Yaneer Bar-Yam, “The Food Crises and Political Instability in North Africa and the Middle East“, arXiv:1108.2455, August 10, 2011. [PDF link]

Remove one network edge and see what happens. Then, two… etc. This is the first illustration on Mark BuchananNexus: Small-worlds and the ground-breaking science of networks” 2002 book – Norton, New York (Prelude, page 17), representing a portion of the food web for the Benguela ecosystem, located off the western coast of South Africa (from Peter Yodzis). For a joint review of 3 general books in complex networks, including Barabási‘s “Linked“, Duncan WattsSmall-Worlds” and Buchanan‘s “Nexus” pay a visit into JASSSJournal of Artificial Societies and Social Simulation, ‘a review of three books’ entry by Frédéric Amblard (link).

[...] People should learn how to play Lego with their minds. Concepts are building bricks [...] V. Ramos, 2002.

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