Joseph Rushton Wakeling 
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Papers by me

All papers are in reverse chronological order (i.e. most recent first)...

Dietmar Plenz, Craig V. Stewart, Joseph Rushton Wakeling, Dante R. Chialvo and David S. Greenberg (2004), ‘Synfire chains’ and ‘neuronal avalanches’ governed by power laws in balanced cortical networks. Soc. Neurosci. Abstr. 970.2
Joseph Rushton Wakeling (2004), Adaptivity and ‘Per learning’. Physica A 340, 766–773.
Physica A 340 (2004), 766–773    q-bio.NC/0403025
A little tribute to a dear friend. This is a playful paper discussing the idea put forward by Per Bak and Dante Chialvo that potentiation (strengthening) of synapses as a reward for good behaviour carries with it the possibility of addiction and inability to adapt. (It also marks the public debut of my middle name...;-)
Paolo Laureti, Peter Ruch, Joseph Wakeling and Yi-Cheng Zhang (2004), The Interactive Minority Game: a Web-based investigation of human market interactions. Physica A 331, 651–659.
Physica A 331 (2004), 651–659    nlin.AO/0309033
Technically this is not a neural systems paper; it’s really a psychology/economics experiment. But it’s still fun, so I’m listing it here anyway. By using a Web-based interface we allow humans to interact with a simple economic game (the Minority Game), and we study how they make use of information contained in the market history. The game itself can be found at An article on the work appeared in Technology Research News Magazine (5 November 2003), and it was mentioned in Mark Buchanan’s New Scientist article ‘It’s the economy, stupid’ (10 April, pp. 35–37).
Joseph Wakeling (2003), Order-disorder transition in the Chialvo-Bak ‘minibrain’ controlled by network geometry. Physica A 325, 561–569.
Physica A 325 (2003), 561–569    cond-mat/0204562
A snappy title I’m sure you’ll agree!-) This paper ‘does exactly what it says on the tin’, demonstrating a phase transition in the minibrain neural network between an ordered phase where learning is possible, and a disordered phase where there is a limit on learning ability. The transition occurs subject to the ratios of the size of different layers of neurons (rather like the phase transition observed in Hopfield networks on the basis of neural connectivity). Mostly numerical work here but an analytical justification is on its way.
Joseph Wakeling and Per Bak (2001), Intelligent systems in the context of surrounding environment. Phys. Rev. E 64, 051920.
Phys. Rev. E 64 (2001), 051920    wakeling_bak_2001.pdf (93kB) (88kB)
This fun and rather philosophical paper discusses the need to take into account the surrounding environment when investigating intelligence (and thus neural systems). A lot of people seemed to think this was rather an important paper (and others were rather annoyed by it!). Articles on this work were published in Physics News Update 563 (31 October 2001), New Scientist (17 November 2001), (26 November 2001) and Technology Research News Magazine (5 December 2001), and it was selected as the Econophysics Forum Paper of the Month (February 2002).

Papers by others

These are papers by other authors which I find of particular interest. For obvious copyright reasons they can’t be downloaded from here; links are provided to the relevant journals and/or preprints. As before they’re in reverse chronological order. N.B. — journals may require registration and/or subscription to view the full text of articles.

experimental work

Victor M. Eguíluz, Dante R. Chialvo, Guillermo A. Cecchi, Marwan Baliki and A. Vania Apkarian (2005), Scale-free brain functional networks. Phys. Rev. Lett. 94, 018102.
Phys. Rev. Lett. 94 (2005), 018102    cond-mat/0309092
This is an experimental paper using fMRI to examine correlations in activity between different neural regions. It is shown that the resulting functional network displays scaling both in its topology and in its physical size.
John M. Beggs and Dietmar Plenz (2003), Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11177.
J. Neurosci. 23 (2003), 11167–11177
This is a very exciting paper describing experiments in which cultures of cortical neurons are grown on a multi-electrode array (MEA). This allows for fairly high-resolution spatial and temporal measuring of electrical activity. The present work demonstrates that spontaneous neural activity propagates in ‘avalanches’ with a scale-free distribution, characteristic of self-organized criticality.
Klaus Linkenkaer-Hansen, Vadim V. Nikouline, J. Matias Palva and Risto J. Ilmoniemi (2001), Long-range temporal correlations and scaling behavior in human brain oscillations. J. Neurosci. 21, 1370–1377.
J. Neurosci. 21 (2001), 1370–1377
This is an experimental paper using EEG analysis to examine neural oscillations. Long-range temporal correlations and power-law distribution of oscillation amplitude are observed, suggesting that SOC may be present.

theoretical work

R. J. C. Bosman, W. A. van Leeuwen and B. Wemmenhove (2004), Combining Hebbian and reinforcement learning in a minibrain model. Neural Networks 17, 29–36.
Neural Networks 17 (2004), 29–36    cond-mat/0301627
The authors demonstrate that including a positive feedback term in the minibrain’s learning dynamics improves its once-off learning ability, helping overcome path interference in the ‘disordered’ phase, and thus allowing for the possibility of multi-neuron firings in each layer. However, they do not consider adaptive learning.
Stefan Bornholdt and Torsten Röhl (2003), Self-organized critical neural networks. Phys. Rev. E 67, 066118.
Phys. Rev. E 67 (2003), 066118    cond-mat/0109256
This paper proposes a way for a neural network to modify connectivity, using a Hebbian-style activity-based mechanism, so as to tune itself to criticality. The model is ‘stand-alone’ and does not interact with an outside environment — this is purely spontaneous activity. So there is an opening for any clever person who wants to link this to a learning rule...
Eytan Ruppin (2002), Evolutionary autonomous agents: a neuroscience perspective. Nat. Rev. Neurosci. 3, 132–141.
Nat. Rev. Neurosci. 3 (2002), 132–141    ~ruppin/ (128kB)
This review paper on the importance of modelling ‘embodied’ agents for neuroscience research came out a few months after the paper by Per and I.
Per Bak and Dante R. Chialvo (2001), Adaptive learning by extremal dynamics and negative feedback. Phys. Rev. E 63, 031912.
Phys. Rev. E 63 (2001), 031912    xx-2001-bak.pdf (139kB)
The second of Dante and Per’s papers on the minibrain model (still not called by this name, though). This paper addresses some more complicated problems such as the xor and (more general) parity problem, learning of sequences of responses to a single input, and so on. It also introduces the idea of ‘selective punishment’ of connections that have been involved in good decisions in the past, which helps create a memory of past good responses that are favoured over responses that have never been successful.
Arjen van Ooyen (2001), Competition in the development of nerve connections: a review of models. Network: Comput. Neural Syst. 12, R1–R47.
Network: Comput. Neural Syst. 12 (2001), R1–R47
A review paper on different models of neural development based around the idea of competition between nerve cells.
Tanya Araújo and R. Vilela Mendes (2000), Function and form in networks of interacting agents. Complex Systems 12, 357–378.
This paper investigates the different network structures that result from learning by suppression of ‘bad’ connections, and learning by reinforcement of ‘good’ connections.
J. C. Astor and C. Adami (2000), A developmental model for the evolution of artificial neural networks. Artificial Life 6, 189–218.
Artificial Life 64 (2000), 189–218    adap-org/9807003
A fun paper on evolving neural networks in A-life simulations.
Konstantin Klemm, Stefan Bornholdt and Heinz Georg Schuster (2000), Beyond Hebb: exclusive-or and biological learning. Phys. Rev. Lett. 84, 3013–3016.
Phys. Rev. Lett. 84 (2000), 3013–3016    adap-org/9909005
This letter proposes some revisions/generalisations of the minibrain model, in particular using stochastic rather than deterministic dynamics to determine which neurons fire, and including a ‘forgiveness’ parameter which means that synapses are punished only if they show consistent failure. These revisions allow the network to learn the xor problem with very few neurons.
Dante R. Chialvo and Per Bak (1999), Learning from mistakes. Neurosci. 90, 1137–1148.
Neurosci. 90 (1999), 1137–1148    xx-1999-chialvo.pdf (238kB)
This is the original paper on the ‘minibrain’ neural network, although of course it wasn’t called that at the time. Dante and Per put forward the view that it is weakening (depression) of synaptic strength, rather than strengthening (potentiation), that forms the basis of biological learning. Essentially the picture is one of Darwinian selection of successful behavioural patterns. They note that this allows greater adaptive ability than traditional reinforcement learning.
Andreas V. M. Herz and John J. Hopfield (1995), Earthquake cycles and neural reverberations: collective oscillations in systems with pulse-coupled threshold elements. Phys. Rev. Lett. 75, 1222–1225.
Phys. Rev. Lett. 75 (1995), 1222–1225
Together with the previous papers by Corral et al. and Usher et al., this paper forms a trio of different models drawing an analogy between the dynamics of ‘earthquake’ models of SOC and neural dynamics.
Marius Usher, Martin Stemmler and Zeev Olami (1995), Dynamic pattern formation leads to 1/f noise in neural populations. Phys. Rev. Lett. 74, 326–329.
Phys. Rev. Lett. 74 (1995), 326–329
A second paper examining self-organized criticality in coupled nonlinear oscillators.
Álvaro Corral, Conrad J. Pérez, Albert Díaz-Guilera and Alex Arenas (1995), Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators. Phys. Rev. Lett. 74, 118–121.
Phys. Rev. Lett. 74 (1995), 118–121
This paper shows a link between the ‘stick-slip’ SOC models inspired by earthquakes, and models of ‘integrate-and-fire’ neurons.


For details of interesting and relevant journals, see the links page.

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