P. J. Attwell, S. Rahman, and C. H. Yeo, Acquisition of Eyeblink Conditioning Is Critically Dependent on Normal Function in Cerebellar Cortical Lobule HVI, The Journal of Neuroscience, vol.21, issue.15, pp.5715-5722, 2001.
DOI : 10.1523/JNEUROSCI.21-15-05715.2001

R. Brette and W. Gerstner, Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity, Journal of Neurophysiology, vol.94, issue.5, pp.3637-3642, 2005.
DOI : 10.1038/nrn1325

C. Clopath, R. Jolivet, A. Rauch, H. R. Lüscher, and W. Gerstner, Predicting neuronal activity with simple models of the threshold type: Adaptive Exponential Integrate-and-Fire model with two compartments, Neurocomputing, vol.70, issue.10-12, pp.70-1668, 2007.
DOI : 10.1016/j.neucom.2006.10.047

J. Couto, D. Linaro, D. Schutter, E. Giugliano, and M. , On the Firing Rate Dependency of the Phase Response Curve of Rat Purkinje Neurons In Vitro, PLOS Computational Biology, vol.63, issue.3, p.1004112, 2015.
DOI : 10.1371/journal.pcbi.1004112.s005

J. T. Davie, M. H. Kole, J. J. Letzkus, E. A. Rancz, N. Spruston et al., Dendritic patch-clamp recording, Nature Protocols, vol.2, issue.3, pp.1235-1247, 2006.
DOI : 10.1113/jphysiol.1994.sp020303

J. T. Davie, A. Beverley, M. Clark, and . Häusser, The Origin of the Complex Spike in Cerebellar Purkinje Cells, Journal of Neuroscience, vol.28, issue.30, pp.7599-7609, 2008.
DOI : 10.1523/JNEUROSCI.0559-08.2008

P. Dean and J. Porrill, Evaluating the adaptive-filter model of the cerebellum, The Journal of Physiology, vol.2, issue.14, pp.3459-3470, 2011.
DOI : 10.1016/S1364-6613(98)01219-4

P. Dean, J. Porrill, C. F. Ekerot, and H. Jörntell, The cerebellar microcircuit as an adaptive filter: experimental and computational evidence, Nature Reviews Neuroscience, vol.68, issue.1, pp.30-43, 2010.
DOI : 10.3389/neuro.06.002.2009

M. Dipoppa and B. S. Gutkin, Correlations in background activity control persistent state stability and allow execution of working memory tasks, Frontiers in Computational Neuroscience, vol.7, 2013.
DOI : 10.3389/fncom.2013.00139

URL : https://hal.archives-ouvertes.fr/hal-01551303

F. R. Fernandez, J. D. Engbers, and R. W. Turner, Firing Dynamics of Cerebellar Purkinje Cells, Journal of Neurophysiology, vol.98, issue.1, pp.278-294, 2007.
DOI : 10.1111/j.1469-7793.1997.689ba.x

N. Fourcaud-trocmé, D. Hansel, C. Van-vreeswijk, and N. Brunel, How Spike Generation Mechanisms Determine the Neuronal Response to Fluctuating Inputs, The Journal of Neuroscience, vol.23, issue.37, pp.11628-11640, 2003.
DOI : 10.1523/JNEUROSCI.23-37-11628.2003

W. Gerstner and W. M. Kistler, Spiking neuron models: Single neurons, populations, plasticity, 2002.
DOI : 10.1017/CBO9780511815706

D. Guo, Inhibition of rhythmic spiking by colored noise in neural systems, Cognitive Neurodynamics, vol.80, issue.3, pp.293-300, 2011.
DOI : 10.1103/PhysRevE.80.031907

B. S. Gutkin, J. Jost, and H. C. Tuckwell, Transient termination???of spiking by noise in coupled neurons, EPL (Europhysics Letters), vol.81, issue.2, p.81, 2008.
DOI : 10.1209/0295-5075/81/20005

B. S. Gutkin, J. Jost, and H. C. Tuckwell, Inhibition of rhythmic neural spiking by noise: the occurrence of a minimum in activity with increasing noise, Naturwissenschaften, vol.36, issue.9, pp.96-1091, 2009.
DOI : 10.1113/jphysiol.1952.sp004764

B. Gutkin, J. Jost, and H. C. Tuckwell, Random perturbations of spiking activity in a pair of coupled neurons, Theory in Biosciences, vol.36, issue.60, pp.135-139, 2008.
DOI : 10.1137/1.9781611970159

M. Häusser and B. A. Clark, Tonic Synaptic Inhibition Modulates Neuronal Output Pattern and Spatiotemporal Synaptic Integration, Neuron, vol.19, issue.3, pp.665-678, 1997.
DOI : 10.1016/S0896-6273(00)80379-7

F. Johansson, D. A. Jirenhed, A. Rasmussen, R. Zucca, and G. Hesslow, Memory trace and timing mechanism localized to cerebellar Purkinje cells, Proceedings of the National Academy of Sciences, pp.111-14930, 2014.
DOI : 10.1046/j.1460-9568.1999.00862.x

URL : http://www.pnas.org/content/111/41/14930.full.pdf

Z. M. Khaliq, N. W. Gouwens, and I. M. Raman, The Contribution of Resurgent Sodium Current to High-Frequency Firing in Purkinje Neurons: An Experimental and Modeling Study, The Journal of Neuroscience, vol.23, issue.12, pp.4899-4912, 2003.
DOI : 10.1523/JNEUROSCI.23-12-04899.2003

J. Leigh, D. Schutter, E. Lee, M. Bower, J. Defanti et al., Realistic modeling of brain structures with remote interaction between simulations of an inferior olivary neuron and a cerebellar Purkinje cell, Proceedings of the Society for Computing Simulation, 1993.

R. Llinas and M. Sugimori, Electrophysiological properties of in vitro Purkinje cell somata in mammalian cerebellar slices., The Journal of Physiology, vol.305, issue.1, pp.171-195, 1980.
DOI : 10.1113/jphysiol.1980.sp013357

Y. Loewenstein, S. Mahon, P. Chadderton, K. Kitamura, H. Sompolinsky et al., Bistability of cerebellar Purkinje cells modulated by sensory stimulation, Nature Neuroscience, vol.19, issue.2, pp.202-211, 2005.
DOI : 10.1007/s00424-002-0831-z

M. London, A. Schreibman, M. Häusser, M. E. Larkum, and I. Segev, The information efficacy of a synapse, Nature Neuroscience, vol.78, issue.4, pp.332-340, 2002.
DOI : 10.1103/PhysRevLett.86.5823

Z. F. Mainen and T. J. Sejnowski, Reliability of spike timing in neocortical neurons, Science, vol.268, issue.5216, pp.268-1503, 1995.
DOI : 10.1126/science.7770778

S. A. Norris, B. Greger, E. N. Hathaway, and W. T. Thach, Purkinje Cell Spike Firing in the Posterolateral Cerebellum: Correlation With Visual Stimulus, Oculomotor Response, and Error Feedback, Journal of Neurophysiology, vol.92, issue.3, pp.1867-1879, 2004.
DOI : 10.1016/0006-8993(87)90331-3

C. S. Oldfield, A. Marty, and B. M. Stell, Interneurons of the cerebellar cortex toggle Purkinje cells between up and down states, Proceedings of the National Academy of Sciences, pp.13153-13158, 2010.
DOI : 10.1113/jphysiol.2004.075028

D. Paydafar, D. B. Forger, and J. R. Clay, Noisy Inputs and the Induction of On???Off Switching Behavior in a Neuronal Pacemaker, Journal of Neurophysiology, vol.96, issue.6, pp.3338-3348, 2006.
DOI : 10.1007/978-3-662-22492-2

E. Phoka, H. Cuntz, A. Roth, and M. Häusser, A New Approach for Determining Phase Response Curves Reveals that Purkinje Cells Can Act as Perfect Integrators, PLoS Computational Biology, vol.23, issue.12, pp.1000768-1000768, 2010.
DOI : 10.1371/journal.pcbi.1000768.s003

I. M. Raman and B. P. Bean, Resurgent Sodium Current and Action Potential Formation in Dissociated Cerebellar Purkinje Neurons, The Journal of Neuroscience, vol.17, issue.12, pp.4517-4526, 1997.
DOI : 10.1523/JNEUROSCI.17-12-04517.1997

A. V. Roitman, S. Pasalar, and T. J. Ebner, Single trial coupling of Purkinje cell activity to speed and error signals during circular manual tracking, Experimental Brain Research, vol.2, issue.2, pp.241-251, 2009.
DOI : 10.1113/jphysiol.1993.sp019837

D. Rokni and Y. Yarom, State-dependence of climbing fiber???driven calcium transients in Purkinje cells, Neuroscience, vol.162, issue.3, pp.694-701, 2009.
DOI : 10.1016/j.neuroscience.2008.12.044

A. Roth and M. Häusser, Compartmental models of rat cerebellar Purkinje cells based on simultaneous somatic and dendritic patch-clamp recordings, The Journal of Physiology, vol.522, issue.2, pp.445-472, 2001.
DOI : 10.1111/j.1469-7793.2000.0059m.x

M. Schonewille, S. Khosrovani, B. H. Winkelman, F. E. Hoebeek, M. T. De-jeu et al., Purkinje cells in awake behaving animals operate at the upstate membrane potential, Nature Neuroscience, vol.68, issue.suppl., pp.459-461, 2006.
DOI : 10.1152/jn.01251.2003

S. L. Shin, S. Rotter, A. Aertsen, and E. De-schutter, Stochastic description of complex and simple spike firing in cerebellar Purkinje cells, European Journal of Neuroscience, vol.978, issue.3, pp.785-794, 2007.
DOI : 10.1137/1.9781611970159

J. Touboul and R. Brette, Dynamics and bifurcations of the adaptive exponential integrate-and-fire model, Biological Cybernetics, vol.62, issue.5, pp.4-5, 2008.
DOI : 10.1017/CBO9780511815706

URL : https://hal.archives-ouvertes.fr/inria-00422701

H. C. Tuckwell and J. Jost, Weak Noise in Neurons May Powerfully Inhibit the Generation of Repetitive Spiking but Not Its Propagation, PLoS Computational Biology, vol.38, issue.5, 2010.
DOI : 10.1371/journal.pcbi.1000794.g011

H. C. Tuckwell, J. Jost, and B. S. Gutkin, Inhibition and modulation of rhythmic neuronal spiking by noise, Physical Review E, vol.5, issue.3, p.31907, 2009.
DOI : 10.1073/pnas.88.20.9107

F. J. Urbano, J. I. Simpson, and R. R. Llinás, Somatomotor and oculomotor inferior olivary neurons have distinct electrophysiological phenotypes, Proceedings of the National Academy of Sciences, pp.16550-16555, 2006.
DOI : 10.1073/pnas.83.17.6651

URL : http://www.pnas.org/content/103/44/16550.full.pdf

J. T. Walter, K. Alvina, M. D. Womack, C. Chevez, and K. Khodakhah, Decreases in the precision of Purkinje cell pacemaking cause cerebellar dysfunction and ataxia, Nature Neuroscience, vol.25, issue.3, pp.389-397, 2006.
DOI : 10.1523/JNEUROSCI.0098-05.2005

F. Wang, Q. Xu, W. Wang, T. Takano, and M. Nedergaard, Bergmann glia modulate cerebellar Purkinje cell bistability via Ca2+-dependent K+ uptake, Proceedings of the National Academy of Sciences, pp.7911-7916, 2012.
DOI : 10.1093/cercor/bhn040

URL : http://www.pnas.org/content/109/20/7911.full.pdf

F. M. Willems, Y. M. Shtarkov, and T. J. Tjalkens, The context-tree weighting method: basic properties. Information Theory, IEEE Transactions on, issue.3, pp.41-653, 1995.
DOI : 10.1109/18.382012

URL : http://cs.haifa.ac.il/courses/src_coding/ContextTreeW-Basic.pdf

M. M. Yartsev, R. Givon-mayo, M. Maller, and O. Donchin, Pausing Purkinje cells in the cerebellum of the awake cat. Frontiers in systems neuroscience, 2009.

H. Zhou, K. Voges, Z. Lin, C. Ju, and M. Schonewille, Differential Purkinje cell simple spike activity and pausing behavior related to cerebellar modules, Journal of Neurophysiology, vol.31, issue.7, pp.2524-2536, 2015.
DOI : 10.7554/eLife.02536

URL : http://jn.physiology.org/content/jn/113/7/2524.full.pdf

M. Bazhenov, I. Timofeev, M. Steriade, and T. J. Sejnowski, Potassium Model for Slow (2-3 Hz) In Vivo Neocortical Paroxysmal Oscillations, Journal of Neurophysiology, vol.92, issue.2, pp.1116-1132, 2004.
DOI : 10.1016/S0166-2236(98)01341-1

J. Benda and A. V. Herz, A Universal Model for Spike-Frequency Adaptation, Neural Computation, vol.79, issue.11, pp.2523-2564, 2003.
DOI : 10.1038/26758

N. Brunel, Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons, Journal of Computational Neuroscience, vol.8, issue.3, pp.183-208, 2000.
DOI : 10.1023/A:1008925309027

N. Brunel and M. C. Van-rossum, Lapicque's 1907 paper: from frogs to integrate-andfire, Biological cybernetics, vol.97, pp.5-6, 2007.
DOI : 10.1007/s00422-007-0190-0

N. Brunel and X. J. Wang, Erratum to: Effects of neuromodulation in a cortical network model of object working memory dominated by recurrent inhibition, Journal of Computational Neuroscience, vol.37, issue.3, pp.63-85, 2001.
DOI : 10.1007/s10827-014-0506-8

A. Y. Buchin and A. V. Chizhov, Firing-rate model of a population of adaptive neurons, Biophysics, vol.19, issue.1???2, pp.592-599, 2010.
DOI : 10.1007/978-3-642-87596-0_11

A. V. Chizhov, E. Y. Smirnova, K. K. Kim, and A. V. Zaitsev, A simple Markov model of sodium channels with a dynamic threshold, Journal of Computational Neuroscience, vol.28, issue.29, pp.181-191, 2014.
DOI : 10.1523/JNEUROSCI.1613-08.2008

P. Dean and J. Porrill, Evaluating the adaptive-filter model of the cerebellum, The Journal of Physiology, vol.2, issue.14, pp.3459-3470, 2011.
DOI : 10.1016/S1364-6613(98)01219-4

E. Boustani, S. Pospischil, M. Rudolph-lilith, M. Destexhe, and A. , Activated cortical states: Experiments, analyses and models, Journal of Physiology-Paris, vol.101, issue.1-3, pp.99-109, 2007.
DOI : 10.1016/j.jphysparis.2007.10.001

URL : https://hal.archives-ouvertes.fr/hal-00207715

A. L. Fairhall, G. D. Lewen, W. Bialek, and R. R. Van-steveninck, Efficiency and ambiguity in an adaptive neural code, Nature, vol.379, issue.6849, pp.412-787, 2001.
DOI : 10.1038/379642a0

A. Fairhall and H. Sompolinsky, Editorial overview: Theoretical and computational neuroscience, Current Opinion in Neurobiology, vol.25, issue.25, pp.v-viii, 2014.
DOI : 10.1016/j.conb.2014.02.010

F. Fröhlich, M. Bazhenov, V. Iragui-madoz, and T. J. Sejnowski, Potassium Dynamics in the Epileptic Cortex: New Insights on an Old Topic, The Neuroscientist, vol.56, issue.2, pp.422-433, 2008.
DOI : 10.1152/jn.1986.56.2.424

B. Grafstein, MECHANISM OF SPREADING CORTICAL DEPRESSION, Journal of Neurophysiology, vol.19, issue.2, pp.154-171, 1956.
DOI : 10.1152/jn.1956.19.2.154

B. Gutkin and F. Zeldenrust, Spike frequency adaptation, Scholarpedia, vol.9, issue.2, p.30643, 2014.
DOI : 10.4249/scholarpedia.30643

URL : https://hal.archives-ouvertes.fr/hal-01686451

J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proceedings of the national academy of sciences, pp.79-2554, 1982.

E. M. Izhikevich, Simple model of spiking neurons, IEEE Transactions on Neural Networks, vol.14, issue.6, pp.1569-1572, 2003.
DOI : 10.1109/TNN.2003.820440

P. Jedli?ka and K. H. Backus, Inhibitory transmission, activity-dependent ionic changes and neuronal network oscillations, Physiol. Res, vol.55, pp.139-149, 2006.

G. P. Krishnan and M. Bazhenov, Ionic Dynamics Mediate Spontaneous Termination of Seizures and Postictal Depression State, Journal of Neuroscience, vol.31, issue.24, pp.31-8870, 2011.
DOI : 10.1523/JNEUROSCI.6200-10.2011

M. Maravall, R. S. Petersen, A. L. Fairhall, E. Arabzadeh, and M. E. Diamond, Shifts in Coding Properties and Maintenance of Information Transmission during Adaptation in Barrel Cortex, PLoS Biology, vol.80, issue.2, p.19, 2007.
DOI : 10.1371/journal.pbio.0050019.sg002

E. Marder and A. L. Taylor, Multiple models to capture the variability in biological neurons and networks, Nature Neuroscience, vol.13, issue.27, pp.133-138, 2011.
DOI : 10.1038/nn.2630

H. Markram, The Blue Brain Project, Nature Reviews Neuroscience, vol.10, issue.2, pp.153-160, 2006.
DOI : 10.1162/089976698300017502

J. Platkiewicz and R. Brette, Impact of Fast Sodium Channel Inactivation on Spike Threshold Dynamics and Synaptic Integration, PLoS Computational Biology, vol.81, issue.1, pp.1001129-1001129, 2011.
DOI : 10.1371/journal.pcbi.1001129.s003

A. A. Prinz, D. Bucher, and E. Marder, Similar network activity from disparate circuit parameters, Nature Neuroscience, vol.7, issue.12, pp.1345-1352, 2004.
DOI : 10.1016/0301-0082(76)90008-3

J. V. Raimondo, H. Markram, and C. J. Akerman, Short-term ionic plasticity at GABAergic synapses, Frontiers in synaptic neuroscience, 2012.
DOI : 10.3389/fnsyn.2012.00005

URL : https://www.frontiersin.org/articles/10.3389/fnsyn.2012.00005/pdf

C. A. Schevon, S. A. Weiss, G. Mckhann-jr, R. R. Goodman, R. Yuste et al., Evidence of an inhibitory restraint of seizure activity in humans, Nature Communications, vol.55, issue.1, p.1060, 2012.
DOI : 10.1016/j.neuroimage.2011.01.055

G. W. Sypert and A. A. Ward, Changes in extracellular potassium activity during neocortical propagated seizures, Experimental Neurology, vol.45, issue.1, pp.19-41, 1974.
DOI : 10.1016/0014-4886(74)90097-1

R. D. Traub, R. K. Wong, R. Miles, and H. Michelson, A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances, Journal of Neurophysiology, vol.66, issue.2, pp.635-650, 1991.
DOI : 10.1152/jn.1991.66.2.635

A. J. Trevelyan, D. Sussillo, and R. Yuste, Feedforward Inhibition Contributes to the Control of Epileptiform Propagation Speed, Journal of Neuroscience, vol.27, issue.13, pp.3383-3387, 2007.
DOI : 10.1523/JNEUROSCI.0145-07.2007

C. Van-vreeswijk and H. Sompolinsky, Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity, Science, vol.274, issue.5293, pp.274-1724, 1996.
DOI : 10.1126/science.274.5293.1724

C. D. Wilms and M. Häusser, Reading out a spatiotemporal population code by imaging neighbouring parallel fibre axons in vivo, Nature Communications, vol.219, issue.1, 2015.
DOI : 10.1007/s00424-007-0234-2

B. A. Arcas, A. L. Fairhall, and W. Bialek, Computation in a Single Neuron: Hodgkin and Huxley Revisited, Neural Computation, vol.20, issue.18, pp.1715-1749, 2003.
DOI : 10.1103/PhysRevE.62.8413