Computation beyond the Boolean world

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Background

Understanding how computational tasks are performed in the brain is a challenging task. This is clearly due to the intrinsic complexity of the brain, but also to the presence of three elements that are usually not part of an engineering view of computation.

First, while it is believed that synchronization is central to neural computation, the exact mechanisms behind this are not completely understood. The synchronous dynamics of two brain regions might indeed mark some kind of information sharing, yet strong synchronization is not compatible with a process of transformation (or integration) of different information sources.

Second, neural dynamics is characterized by high amounts of noise. Noise is considered a nuisance in standard Boolean computation, or even the major obstacle towards the implementation of quantum circuits: creating a noise-robust computation is a problem known since von Neumann (1956). In contrast to digital man-made circuits, neurons are biological entities with an intrinsically noisy dynamics; furthermore, such dynamics is highly non-linear, making them even more sensitive to small perturbations. In spite of the unreliability of the individual computational elements, the brain is able to consistently compute information, using large-scale unknown noise suppression mechanisms.

Finally, neurons do not assemble following pre-defined patterns, but instead self-organize into complex structures. While mechanisms for spatial self-organization and patterns formation have been studied extensively in the last decades, how these neural patterns are guided and formed is still insufficiently understood.

This research topic aims at investigating forms of computation beyond the Boolean paradigm: for instance, based on chaotic oscillators (Ditto et al., 2008; Zanin et al., 2011), synchronization between oscillators (Murali and Sinha, 2007; Zanin et al., 2013), and complex networks (Neves and Timme, 2012) among others. Furthermore, it aims at creating a bridge between these techniques and the human brain, i.e. at shedding light on the actual mechanisms behind brain computation, and at understanding how some elements, like noise and chaotic dynamics, contribute to creating human intelligence.


Non-exhaustive list of topics:
Unconventional computing - including natural, chaos, neuromorphic, DNA, and membrane computing.
Non-linear and chaotic dynamical system theory, and its application to neural computation.
Pattern formation and self-organization of neural circuits.


W. L. Ditto, K. Murali & S. Sinha (2008). Chaos computing: ideas and implementations. Philosophical Transactions of the Royal Society A 366 (1865), 653-664.
K. Murali & S. Sinha (2007). Using synchronization to obtain dynamic logic gates. Physical Review E 75 (2), 025201.
F. S. Neves & M. Timme (2012). Computation by switching in complex networks of states. Physical Review Letters 109 (1), 018701.
J. von Neumann (1956). Probabilistic logics and the synthesis of reliable organisms from unreliable components. Automata studies 34, 43-98.
M. Zanin, F. Del Pozo & S. Boccaletti (2011). Computation emerges from adaptive synchronization of networking neurons. PloS one 6 (11), e26467.
M. Zanin, D. Papo & S. Boccaletti (2013). Computing with complex-valued networks of phase oscillators. Europhysics Letters 102 (4), 40007.

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