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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].
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 http://camaraclara.rtp.pt/#/arquivo/131 ). 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.
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.
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.
“It takes you 500,000 microseconds just to click a mouse. But if you’re a Wall Street algorithm and you’re five microseconds behind, you’re a loser.” ~ Kevin Slavin.
TED video lecture – Kevin Slavin (link) argues that we’re living in a world designed for – and increasingly controlled by – algorithms. In this riveting talk from TEDGlobal, he shows how these complex computer programs determine: espionage tactics, stock prices, movie scripts, and architecture. And he warns that we are writing code we can’t understand, with implications we can’t control. Kevin Slavin navigates in the “algoworld“, the expanding space in our lives that’s determined and run by algorithms (link at TED).
Figs. – Check animated pictures in here. (a) A 3D toroidal fast changing landscape describing a Dynamic Optimization (DO) Control Problem (8 frames in total). (b) A self-organized swarm emerging a characteristic flocking migration behaviour surpassing in intermediate steps some local optima over the 3D toroidal landscape (left), describing a Dynamic Optimization (DO) Control Problem. Over each foraging step, the swarm self-regulates his population and keeps tracking the extrema (44 frames in total).
 Vitorino Ramos, Carlos Fernandes, Agostinho C. Rosa, On Self-Regulated Swarms, Societal Memory, Speed and Dynamics, in Artificial Life X – Proc. of the Tenth Int. Conf. on the Simulation and Synthesis of Living Systems, L.M. Rocha, L.S. Yaeger, M.A. Bedau, D. Floreano, R.L. Goldstone and A. Vespignani (Eds.), MIT Press, ISBN 0-262-68162-5, pp. 393-399, Bloomington, Indiana, USA, June 3-7, 2006.
Wasps, bees, ants and termites all make effective use of their environment and resources by displaying collective “swarm” intelligence. Termite colonies – for instance – build nests with a complexity far beyond the comprehension of the individual termite, while ant colonies dynamically allocate labor to various vital tasks such as foraging or defense without any central decision-making ability. Recent research suggests that microbial life can be even richer: highly social, intricately networked, and teeming with interactions, as found in bacteria. What strikes from these observations is that both ant colonies and bacteria have similar natural mechanisms based on Stigmergy and Self-Organization in order to emerge coherent and sophisticated patterns of global foraging behavior. Keeping in mind the above characteristics we propose a Self-Regulated Swarm (SRS) algorithm which hybridizes the advantageous characteristics of Swarm Intelligence as the emergence of a societal environmental memory or cognitive map via collective pheromone laying in the landscape (properly balancing the exploration/exploitation nature of our dynamic search strategy), with a simple Evolutionary mechanism that trough a direct reproduction procedure linked to local environmental features is able to self-regulate the above exploratory swarm population, speeding it up globally. In order to test his adaptive response and robustness, we have recurred to different dynamic multimodal complex functions as well as to Dynamic Optimization Control problems, measuring reaction speeds and performance. Final comparisons were made with standard Genetic Algorithms (GAs), Bacterial Foraging strategies (BFOA), as well as with recent Co-Evolutionary approaches. SRS’s were able to demonstrate quick adaptive responses, while outperforming the results obtained by the other approaches. Additionally, some successful behaviors were found: SRS was able to maintain a number of different solutions, while adapting to unforeseen situations even when over the same cooperative foraging period, the community is requested to deal with two different and contradictory purposes; the possibility to spontaneously create and maintain different sub-populations on different peaks, emerging different exploratory corridors with intelligent path planning capabilities; the ability to request for new agents (division of labor) over dramatic changing periods, and economizing those foraging resources over periods of intermediate stabilization. Finally, results illustrate that the present SRS collective swarm of bio-inspired ant-like agents is able to track about 65% of moving peaks traveling up to ten times faster than the velocity of a single individual composing that precise swarm tracking system. This emerged behavior is probably one of the most interesting ones achieved by the present work.