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Cognitive Neurodynamics
Erschienen in: Cognitive Neurodynamics 6/2012

01.12.2012 | Research Article

Combined effects of LTP/LTD and synaptic scaling in formation of discrete and line attractors with persistent activity from non-trivial baseline

verfasst von: Timothee Leleu, Kazuyuki Aihara

Erschienen in: Cognitive Neurodynamics | Ausgabe 6/2012

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Abstract

In this article, we analyze combined effects of LTP/LTD and synaptic scaling and study the creation of persistent activity from a periodic or chaotic baseline attractor. The bifurcations leading to the creation of new attractors have been detailed; this was achieved using a mean field approximation. Attractors encoding persistent activity can notably appear via generalized period-doubling bifurcations, tangent bifurcations of the second iterates or boundary crises, after which the basins of attraction become irregular. Synaptic scaling is shown to maintain the coexistence of a state of persistent activity and the baseline. According to the rate of change of the external inputs, different types of attractors can be formed: line attractors for rapidly changing external inputs and discrete attractors for constant external inputs.
Vorheriger Artikel Identifying type I excitability using dynamics of stochastic neural firing patterns
Nächster Artikel A new discriminant NMF algorithm and its application to the extraction of subtle emotional differences in speech

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Fußnoten
1
It is important to note that phenomena that are related to spike timing (such as synchrony of spikes) are not taken into account here; however, they may play an important role in cognition studies (a temporal-coding hypothesis). Synchronous firing may disrupt persistent activity (Compte 2006) because of the different time scales for the receptors (primarily AMPA and GABAA), and create oscillations (Compte et al. 2003). All receptors are assumed to have an identical time scale for simplicity; thus only asynchronous persistent activity is considered in the following.
 
2
Note that the chaos observed in this network is of a different nature than the one observed in Sompolinsky et al. (1988), Doyon et al. (1994). Here, the average activity over the population of neurons, which is given by the mean field approximation, is chaotic (see Appendix 4).
 
3
Otherwise, only LTP/LTD are active, see Eq. (7).
 
4
An infinite set of maps indexed by the step n are thus considered.
 
5
A soft bifurcation induces new stable attractors in a small neighborhood of the old one. For example, tangent bifurcations far from the cusp and subcritical pitchfork bifurcations are hard, whereas supercritical pitchfork bifurcations are soft (Hoppensteadt and Izhikevich 1997).
 
6
For a normally hyperbolic invariant manifold (NHIM), the contraction vectors orthogonal to the manifold are stronger than those along the manifold (Hoppensteadt and Izhikevich 1997). NHIM can be interpreted as the generalization of a hyperbolic fixed point to non-trivial attractors. Formal definitions can be found in Fenichel (1972); Hirsch and Shub (1977), Pesin (2004). A fundamental property of these manifolds is that they are persistent under perturbations, i.e., the perturbed invariant manifold has normal and tangent subspaces that are close to the original manifold. This structural stability assures that an attractor of the perturbed system lies near an attractor of the unperturbed system.
 
7
Note that the assumption in Eq. (19) does not hold for \(\Updelta^{T_s} X_i(n), T_s \ll T_0\). Indeed, the terms X i (n) and X i (n − T s ) average almost identical trajectories, and therefore do not describe the attractors of two different dynamical systems (perturbed \(\tilde{G}(n)\) and unperturbed \(\tilde{G}(n-T_1)\)), but the difference between consecutive steps of the same attractor. In that case, these consecutive steps could be at a distance that is equal to the size of the attractor.
 
8
These populations should not be confused with excitatory and inhibitory populations which are common in neuroscience; for example in the Wilson-Conwan model (1972).
 
9
For simplicity, we assume γ+ =  − γ− = γ > 0. Similar dynamics to the ones described in the following are also observed for other choices of γ− and are not restrained to this set of parameters.
 
10
These two curves are the equivalent of nullclines for a system of differential equations.
 
11
Other distribution functions that induce multiple discrete attractors could be considered. This article focus only on the uniform distribution to show the creation of line attractors.
 
12
Simply considering the symmetry of the change in weights, all neurons are similarly affected by synaptic plasticity.
 
13
“Complex” refers here to the Kolmogorov-Sinai entropy.
 
14
The creation of fractal basin boundaries is also observed for systems with continuous time (Ott 1993), and is not an artifact due to the discrete time used in the current article.
 
Literatur
Abbott LF, Nelson SB (2000) Synaptic plasticity: taming the beast. Nat Neurosci 3:1178–1183PubMedCrossRef
Aihara K, Takabe T, Toyoda M (1990) Chaotic neural networks. Phys Lett A 144(6–7):333–340CrossRef
Amari S-I (1971) Characteristics of randomly connected threshold-element networks and network systems. Proc IEEE 59(1):35–47CrossRef
Amari S-I (1972) Learning patterns and pattern sequences by self-organizing nets of threshold elements. IEEE Trans Comput C-21(11):1197–1206CrossRef
Artola A, Singer W (1993) Long-term depression of excitatory synaptic transmission and its relationship to long-term potentiation. Trends Neurosci 16:480–487PubMedCrossRef
Bartos M, Vida I, Jonas P (2007) Synaptic mechanisms of synchronized gamma oscillations in inhibitory interneuron networks. Nat Rev Neurosci 8(1):45–56PubMedCrossRef
Bienenstock EL, Cooper LN, Munro PW (1982) Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J Neurosci 2:32–48PubMed
Brody CD, Romo R, Kepecs A (2003) Basic mechanisms for graded persistent activity: discrete attractors, continuous attractors, and dynamic representations. Curr Opin Neurobiol 13(2):204–211PubMedCrossRef
Brunel N (1996) Hebbian learning of context in recurrent neural networks. Neural Comput Appl 8:1677–1710PubMedCrossRef
Brunel N (2003) Dynamics and plasticity of stimulus-selective persistent activity in cortical network models. Cereb Cortex 13(11):1151–1161PubMedCrossRef
Buonomano DV, Maass W (2009) State-dependent computations: spatiotemporal processing in cortical networks. Nat Rev Neurosci 10(2):113–125PubMedCrossRef
Burkitt AN, Meffin H, Grayden DB (2004) Spike-timing-dependent plasticity: the relationship to rate-based learning for models with weight dynamics determined by a stable fixed point. Neural Comput Appl 16(5):885–940PubMedCrossRef
Buxhoeveden DP, Casanova MF (2002) The minicolumn hypothesis in neuroscience. Brain Behav Evol 125:935–951PubMedCrossRef
Buzsaki G (2010) Neural syntax: Cell assemblies, synapsembles, and readers. Neuron 68(3):362–385PubMedCrossRef
Caianiello ER (1961) Outline of a theory of thought-processes and thinking machines. J Theor Biol 1:204–235PubMedCrossRef
Cessac B, Doyon B, Quoy M, Samuelides M (1994) Mean-field equations, bifurcation map and route to chaos in discrete time neural networks. Phys D 74:24–44CrossRef
Churchland M et al (2010) Stimulus onset quenches neural variability: a widespread cortical phenomenon. Nat Neurosci 13:369–378PubMedCrossRef
Compte A (2006) Computational and in vitro studies of persistent activity: edging towards cellular and synaptic mechanisms of working memory. Neurosci Behav Physiol 139:135–151PubMedCrossRef
Compte A, Brunel N, Goldman-Rakic PS, Wang X-J (2000) Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model. Cereb Cortex 10(9):910–923PubMedCrossRef
Compte A, Constantinidis C, Tegner J, Raghavachari S, Chafee MV, Goldman-Rakic PS, Wang X-J (2003) Temporally irregular mnemonic persistent activity in prefrontal neurons of monkeys during a delayed response task. J Neurophysiol 90:3441–3454PubMedCrossRef
Dauce E, Quoy M, Cessac B, Doyon B, Samuelides M (1998) Self-organization and dynamics reduction in recurrent networks: stimulus presentation and learning. Neural Networks 11(3):521–533PubMedCrossRef
Doyon B, Cessac B, Quoy M, Samuelides M (1994) On bifurcations and chaos in random neural networks. Acta Biotheor 42(2):215–225CrossRef
Durstewitz D, Seamans JK, Sejnowski TJ (2000) Neurocomputational models of working memory. Nat Neurosci 3:1184–1191PubMedCrossRef
Faisal AA, Selen LPJ, Wolpert DM (2008) Noise in the nervous system. Nat Rev Neurosci 9(4):292–303PubMedCrossRef
Fenichel N (1972) Persistence and smoothness of invariant manifolds for flows. Indiana Univ Math J 21(3):193–226CrossRef
Funahashi S, Bruce CJ, Goldman-Rakic PS (1989) Mnemonic coding of visual space in the monkey’s dorsolateral prefrontal cortex. J Neurophysiol 61:331–349PubMed
Grebogi C, Ott E, Yorke JA (1983) Crises, sudden changes in chaotic attractors, and transient chaos. Physica D 7(1–3):181–200CrossRef
Grebogi C, Ott E, Yorke JA (1986) Metamorphoses of basin boundaries in nonlinear dynamical systems. Phys Rev Lett 56:1011–1014PubMedCrossRef
Hansel D, Sompolinsky H (1998) Modeling feature selectivity in local cortical circuits. In: Methods in neuronal modeling: from synapse to networks. MIT Press, Cambridge
Hebb D (1949) The organization of behavior. Wiley, New York
Heemels W, Lehmann D, Lunze J, De Schutter B (2009) Introduction to hybrid systems. In: Lunze J, Lamnabhi-Lagarrigue F (eds) Handbook of hybrid systems control—theory tools applications, Cambridge University Press, Cambridge
Hertz J, Krogh A, Palmer RG (1991) Introduction to the theory of neural computation. Addison-Wesley Longman Publishing Co, Inc, Boston
Hirsch MW, Pugh CC, Shub M (1977) Invariant manifolds. Springer, New York
Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Nat Acad Sci 79(8):2554–2558PubMedCrossRef
Hoppensteadt FC, Izhikevich EM (1997) Weakly connected neural networks. Springer, New YorkCrossRef
Ikegaya Y (2004) Synfire chains and cortical songs: temporal modules of cortical activity. Sci Agric 304:559–564PubMedCrossRef
Ibarz B, Casado J, Sanjuan M (2011) Map-based models in neuronal dynamics. Phys Rep 501:1–74CrossRef
Katori Y, Sakamoto K, Saito N, Tanji J, Mushiake H, Aihara K (2011) Representational switching by dynamical reorganization of attractor structure in a network model of the prefrontal cortex. PLoS Comput Biol 7(11):e1002266PubMedCrossRef
Korn H (2003) Is there chaos in the brain? ii. Experimental evidence and related models. CR Biol 326(9):787–840CrossRef
Kuznetsov YA (1998) Elements of applied bifurcation theory. 2nd edn. Springer, New York
Leleu T, Aihara K (2011) Sequential memory retention by stabilization of cell assemblies. In: Post-conference proceedings of the 3rd international conference on cognitive neurodynamics, 9–13 June 2011 (in press)
Li Y, Nara S (2008) Novel tracking function of moving target using chaotic dynamics in a recurrent neural network model. Cogn Neurodyn 2(1):39–48PubMedCrossRef
Major G, Tank D (2004) Persistent neural activity: prevalence and mechanisms. Curr Opin Neurobiol 14(6):675–684PubMedCrossRef
Matsumoto G, Aihara K, Hanyu Y, Takahashi N, Yoshizawa S, Nagumo J-I (1987) Chaos and phase locking in normal squid axons. Phys Lett A 123(4):162–166CrossRef
McCulloch W, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 7:115–133CrossRef
Miyashita Y (1988) Neuronal correlate of visual associative long-term memory in the primate temporal cortex. Nat Biotechnol 335(6193):817–820PubMedCrossRef
Mongillo G, Amit DJ, Brunel N (2003) Retrospective and prospective persistent activity induced by hebbian learning in a recurrent cortical network. Eur J Neurosci 18(7):2011–2024PubMedCrossRef
Moynot O, Samuelides M (2002) Large deviations and mean-field theory for asymmetric random recurrent neural networks. Probab Theory Relat Fields 123:41–75CrossRef
Mushiake H, Saito N, Sakamoto K, Itoyama Y, Tanji J (2006) Activity in the lateral prefrontal cortex reflects multiple steps of future events in action plans. Neuron 50(4):631–641PubMedCrossRef
Nagumo J, Sato S (1972) On a response characteristic of a mathematical neuron model. Biol Cybern 10:155–164
Naya Y, Sakai K, Miyashita Y (1996) Activity of primate inferotemporal neurons related to a sought target in pair-association task. Proc Nat Acad Sci 93:2664–2669PubMedCrossRef
Ott E (1993) Chaos in dynamical systems. Cambridge University Press, New York
Ozaki TJ et al (2012) Traveling EEG slow oscillation along the dorsal attention network initiates spontaneous perceptual switching. Cogn Neurodyn 6(2):185–198PubMedCrossRef
Pesin YB (2004) Lectures on partial hyperbolicity and stable ergodicity. Zurich Lect Adv Math
Pool RR, Mato G (2010) Hebbian plasticity and homeostasis in a model of hypercolumn of the visual cortex. Neural Comput Appl 22:1837–1859PubMedCrossRef
Pulvermler F (1996) Hebb’s concept of cell assemblies an the psychophysiology of word processing. Psychophysiology 33(4):317–333CrossRef
Rajan K, Abbott LF, Sompolinsky H (2010) Stimulus-dependent suppression of chaos in recurrent neural networks. Phys Rev E 82:011903CrossRef
Ranck JB Jr (1985) Head direction cells in the deep cell layer of dorsal presubiculum in freely moving rats. In: Electrical activity of the archicortex. Publishing House of the Hungarian Academy of Sciences
Renart A, Moreno-Bote R, Wang X-J, Parga N (2007) Mean-driven and fluctuation-driven persistent activity in recurrent networks. Neural Comput Appl 19:1–46PubMedCrossRef
Renart A, Song P, Wang X-J (2003) Robust spatial working memory through homeostatic synaptic scaling in heterogeneous cortical networks. Neuron 38(3):473–485PubMedCrossRef
Romo R, Brody CD, Hernandez A, Lemus L (1999) Neuronal correlates of parametric working memory in the prefrontal cortex. Nat Biotechnol 399:470–473PubMedCrossRef
Sakai K, Miyashita Y (1991) Neural organization for the long-term memory of paired associates. Nat Biotechnol 354:152–155PubMedCrossRef
Siri B, Berry H, Cessac B, Delord B, Quoy M (2008) A mathematical analysis of the effects of hebbian learning rules on the dynamics and structure of discrete-time random recurrent neural networks. Neural Comput Appl 20(12):2937–2966PubMedCrossRef
Skarda C, Freeman W (1987) How brains make chaos in order to make sense of the world. Behav Brain Sci 10:161–195CrossRef
Softky WR, Koch C (1992) Cortical cells should fire regularly, but do not. Neural Comput Appl 4:643–646CrossRef
Sompolinsky H, Crisanti A, Sommers HJ (1988) Chaos in random neural networks. Phys Rev Lett 61(3):259–262PubMedCrossRef
Tsuda I (2001) Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems. Behav Brain Sci 24:793–810PubMedCrossRef
Turrigiano GG (2008) The self-tuning neuron: synaptic scaling of excitatory synapses. Cell (Cambridge, MA, US) 135(3):422–435PubMedCrossRef
Turrigiano GG, Leslie KR, Desai NS, Rutherford LC, Nelson SB (1998) Activity-dependent scaling of quantal amplitude in neocortical neurons. Nat Biotechnol 391(6670):892–896PubMedCrossRef
Turrigiano GG, Nelson SB (2004) Homeostatic plasticity in the developing nervous system. Nat Rev Neurosci 5(2):97–107PubMedCrossRef
Wang L (2007) Interactions between neural networks: a mechanism for tuning chaos and oscillations. Cogn Neurodyn 1(2):185–188PubMedCrossRef
Wang X-J (2001) Synaptic reverberation underlying mnemonic persistent activity. Trends Neurosci 24(8):455–463PubMedCrossRef
Wennekers T, Palm G (2009) Syntactic sequencing in Hebbian cell assemblies. Cogn Neurodyn 3(4):429–441PubMedCrossRef
Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 12(1):1–24PubMedCrossRef
Yoshida H, Kurata S, Li Y, Nara S (2010) Chaotic neural network applied to two-dimensional motion control. Cogn Neurodyn 4(1):69–80PubMedCrossRef
Zheng G, Tonnelier A (2008) Chaotic solutions in the quadratic integrate-and-fire neuron with adaptation. Cogn Neurodyn 3(3):197–204PubMedCrossRef
Metadaten
Titel
Combined effects of LTP/LTD and synaptic scaling in formation of discrete and line attractors with persistent activity from non-trivial baseline
verfasst von
Timothee Leleu
Kazuyuki Aihara
Publikationsdatum
01.12.2012
Verlag
Springer Netherlands
Erschienen in
Cognitive Neurodynamics / Ausgabe 6/2012
Print ISSN: 1871-4080
Elektronische ISSN: 1871-4099
DOI
https://doi.org/10.1007/s11571-012-9211-3

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