Some members and collaborators of the Mechatronics Laboratory. From left to right: Paulo Branco, Joaquim Dente, Rui Vilela Mendes, Vladimir Man'ko, Tanya Araújo, Rui Carvalho, João Martins, Margarita Man'ko, Armando Pires. |

Non-linear dynamics, Adaptive and intelligent control, Fuzzy systems, Multi-agent models and self-organization, Neural networks, Signal processing, Quantum computation

Does function determine form, when a society of agents organizes itself for some purpose, or is the organizing method more important than the functionality in determining the structure of the ensemble? To explore this question, a neural network learning the same function by two different learning methods was used. For sufficiently large networks, very different structures may indeed be obtained for the same functionality. Clustering, characteristic path length and hierarchy are structural differences, which in turn have implications on the robustness and adaptability of the networks. In networks, as opposed to simple graphs, the connections between the agents are not necessarily symmetric and may have positive or negative signs. New characteristic coefficients were introduced to characterize this richer connectivity structure (ZiF preprint 2000/002 - Complex Systems 12, 357, 2000).

Figure 1: Characteristic path length distribution for random, learning from mistakes and reinforcement learning networks |

The emergence of dynamical structures in multi-agent systems was also analysed. Three different mechanisms were identified, namely: (1) sensitive-dependence and convex coupling, (2) sensitive-dependence and extremal dynamics and (3) interaction through a collectively generated field. The dynamical origin of the emergent structures is traced back either to a modification, by interaction, of the Lyapunov spectrum or to multistable dynamics (ZiF preprint 2000/001 - Physica A295, 537, 2001).

Figure 2: One- and two-agent marginal distributions of distances to the "ghost weak repeller" and scaling of avalanches in a SOC model |

A correspondence was established between the basic elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the structure and dynamical evolution laws of neural networks. The correspondence is pictured as a translation dictionary

Logical System |
Network |
---|---|

Constant | Single node |

Atomic proposition (n arguments) |
Node with n-order synapses^{th} |

Rules | Synaptic intensity constrains |

Rule application (forward chaining) | Synaptic dynamics |

Queries | Node activation / Query tensor dynamics |

which allows to go back and forth between symbolic and network formulations, a desirable step in learning-oriented systems and multicomputer networks. In the framework of Horn clause logics, it was found that atomic propositions with *n* arguments correspond to nodes with *n*-th order synapses, rules to synaptic intensity constraints, forward chaining to synaptic dynamics and queries either to simple node activation or to a query tensor dynamics (ZiF preprint 2001/033, to appear in International Journal of Neural Systems).

To use formal language techniques to study controlled dynamical systems, one needs to distinguish between information generated by the system and input control. It was shown how the modelling framework for controlled dynamical systems leads naturally to a formulation in terms of context-dependent grammars. A learning algorithm was proposed for on-line generation of the grammar productions, this formulation being then used for modelling, control and anomaly detection. Practical applications were described for electromechanical drives. Grammatical interpolation techniques yield accurate results and the pattern detection capabilities of the language-based formulation is a promising technique for the early detection of anomalies or faulty behavior (ZiF preprint 2001/031, to appear in IEEE Transactions in Systems, Man and Cybernetics).

Figure 3: Learning algorithm for grammatical inference from the dynamical system |

The immune system is a cognitive system of complexity comparable to the brain and its computational algorithms suggest new solutions to engineering problems or new ways of looking at these problems. Using immunological principles, a two- (or three-)module algorithm was developed which is capable of launching a specific response to anomalous situations. Applications are being developed for electromechanical drives and network power transformers. Experimental results were obtained for fault detection in squirrel-cage electric motors (ZiF preprint 2001/057).

Figure 4: Cluster formation in the B-module |

Following previous work on the application of tomography techniques to the time-frequency analysis of noisy signals (Physics Letters A263, 53, 1999 and ZiF preprint 2000/006),

Figure 5: Detection of noisy signals by non-commutative tomography |

a general framework was developed, which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms were obtained and the case of transforms associated to the symplectic and affine groups was treated in some detail. Special emphasis was given to the properties of the scale-time and scale-frequency tomograms. Tomograms were interpreted as a tool to sample the signal space by a family of curves or as the matrix element of a projector (ZiF preprint 2001/032, to appear in Journal of Physics A).

Using a quantumlike description (ZiF preprint 2000/007) for light propagation in nonhomogeneous optical fibers, it was shown that quantum information processing may be implemented by optical means. Quantum-like bits (qulbits) are associated to light modes in the optical fiber and quantum gates to segments of the fiber providing an unitary transformation of the mode structure along a space direction. Simulation of nonlinear quantum effects was also discussed (ZiF preprint 2001/044, to appear in Physics Letters A).

The statistical properties of a stochastic process may be described (1) by the expectation values of the observables, (2) by the probability distribution functions or (3) by probability measures on path space. An analysis of level (3) was carried out for market fluctuation processes.

Figure 6: Detrended and rescaled market data |

Gibbs measures and chains with complete connections were considered. Some other topics were also discussed, in particular the asymptotic stationarity of the processes and the behavior of statistical indicators of level (1) and (2). Based on the theory of chains with complete connections, a variable-length Markov process is used for prediction and simulation. Some conclusions were obtained concerning the nature and origin of the market fluctuation process and its relation to the efficient market hypothesis (ZiF preprint 2001/042).

- Multiagent models with innovation
- Reconstruction of economic spaces from market data
- Chaos and complexity in quantum systems: Lyapunov exponents versus spectral properties