A. C. Shot, M. Noise-bibliography-abramowitz, and I. A. Stegun, Tables of mathematical functions, p.75, 1970.

H. Akaike, A new look at the statistical model identification, IEEE Transactions on Automatic Control, vol.196, pp.716-723, 1974.

C. Albers, J. T. Schmiedt, and K. R. Pawelzik, Theta-specific susceptibility in a model of adaptive synaptic plasticity, Frontiers in Computational Neuroscience, vol.7, issue.103, p.170, 2013.
DOI : 10.3389/fncom.2013.00170

J. S. Albus, A theory of cerebellar function, Mathematical Biosciences, vol.10, issue.1-2, pp.25-61, 1971.
DOI : 10.1016/0025-5564(71)90051-4

D. Amit and N. Brunel, Dynamics of a recurrent network of spiking neurons before and following learning, Network: Computation in Neural Systems 8.4, pp.373-404, 1997.
DOI : 10.1088/0954-898X_8_4_003

D. J. Amit and M. V. Tsodyks, Quantitative study of attractor neural network retrieving at low spike rates: I. substrate???spikes, rates and neuronal gain, Network: Computation in Neural Systems, vol.2, issue.3, pp.259-274, 1991.
DOI : 10.1088/0954-898X_2_3_003

D. J. Amit, N. Brunel, and M. V. Tsodyks, Correlations of cortical Hebbian reverberations: experiment vs theory, J. Neurosci, vol.14, pp.6435-6445, 1994.

D. J. Amit, H. Hanoch-gutfreund, and . Sompolinsky, Storing Infinite Numbers of Patterns in a Spin-Glass Model of Neural Networks, Physical Review Letters, vol.55, issue.14, pp.1530-1533, 1985.
DOI : 10.1103/PhysRevLett.55.1530

N. Aslam, Y. Kubota, D. Wells, and H. Z. Shouval, Translational switch for long-term maintenance of synaptic plasticity, In: Mol Syst Biol, vol.5, p.284, 2009.

B. Barbour, N. Brunel, V. Hakim, and J. Nadal, What can we learn from synaptic weight distributions?, Trends in Neurosciences, vol.30, issue.12, pp.622-629, 2007.
DOI : 10.1016/j.tins.2007.09.005

C. Bell and G. Von-der-emde, Electric organ corollary discharge pathways in mormyrid fish, Journal of Comparative Physiology A 177, pp.463-479, 1995.

A. Belmeguenai and C. Hansel, A Role for Protein Phosphatases 1, 2A, and 2B in Cerebellar Long-Term Potentiation, Journal of Neuroscience, vol.25, issue.46, pp.10768-10772, 2005.
DOI : 10.1523/JNEUROSCI.2876-05.2005

U. S. Bhalla and R. Iyengar, Emergent Properties of Networks of Biological Signaling Pathways, pp.381-387, 1999.

G. Q. Bi and M. Poo, Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type, In: The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, vol.1824, pp.10464-10472, 1998.

C. Bidoret, A. Ayon, B. Barbour, and M. Casado, Presynaptic NR2A-containing NMDA receptors implement a high-pass filter synaptic plasticity rule, Proceedings of the National Academy of Sciences 106.33, pp.14126-14131, 2009.
DOI : 10.1073/pnas.0904284106

E. Bienenstock, P. Cooper, and . Munro, THEORY FOR THE DEVELOPMENT OF NEURON SELECTIVITY: ORIENTATION SPECIFICITY AND BINOCULAR INTERACTION IN VISUAL CORTEX, J. Neurosci, vol.2, issue.13, pp.32-48, 1982.
DOI : 10.1142/9789812795885_0006

G. Billings and M. C. Van-rossum, Memory Retention and Spike-Timing-Dependent Plasticity, Journal of Neurophysiology, vol.101, issue.6, pp.2775-2788, 2009.
DOI : 10.1152/jn.91007.2008
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2694112

T. V. Bliss and A. R. Gardner-medwin, Long-lasting potentiation of synaptic transmission in the dentate area of the unanaesthetized rabbit following stimulation of the perforant path, The Journal of Physiology, vol.232, issue.2, pp.357-374, 1973.
DOI : 10.1113/jphysiol.1973.sp010274

T. V. Bliss and T. Lømo, Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path, The Journal of Physiology, vol.232, issue.2, pp.331-356, 1973.
DOI : 10.1113/jphysiol.1973.sp010273

T. Bliss, . Vp, L. Graham, and . Collingridge, A synaptic model of memory: long-term potentiation in the hippocampus, Nature, vol.361, issue.6407, pp.31-39, 1993.
DOI : 10.1038/361031a0

N. Brunel, Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons, Journal of computational neuroscience, vol.83, issue.84, pp.183-208, 2000.

N. Brunel, V. Hakim, P. Isope, J. Nadal, and B. Barbour, Optimal Information Storage and the Distribution of Synaptic Weights, Neuron, vol.43, issue.5, pp.745-757, 2004.
DOI : 10.1016/j.neuron.2004.08.023
URL : https://hal.archives-ouvertes.fr/hal-00143779

B. D. Burns and A. C. Webb, The spontaneous activity of neurons in the cat's cerebral cortex, Proc. R. Soc. Lond. B 194, pp.211-223, 1976.

S. Cajal and . Ramón, Histologie du Système Nerveux de l'Homme et des Vertébrés, 1911.

E. Campanac and D. Debanne, Spike timing-dependent plasticity: a learning rule for dendritic integration in rat CA1 pyramidal neurons, The Journal of Physiology, vol.561, issue.3, pp.779-793, 2008.
DOI : 10.1113/jphysiol.2007.147017

M. Casado, P. Dieudonné, and . Ascher, Presynaptic N-methyl-Daspartate receptors at the parallel fiber-Purkinje cell synapse, Proceedings of the National Academy of Sciences 97.21. PMID: 11016958, pp.11593-11597, 2000.

M. Casado, P. Isope, and P. Ascher, Involvement of Presynaptic N-Methyl-D-Aspartate Receptors in Cerebellar Long-Term Depression, Neuron, vol.33, issue.1, pp.123-130, 2002.
DOI : 10.1016/S0896-6273(01)00568-2

G. C. Castellani, A. Bazzani, and L. N. Cooper, Toward a microscopic model of bidirectional synaptic plasticity, Proceedings of the National Academy of Sciences, vol.106, issue.33, pp.14091-14095, 2009.
DOI : 10.1073/pnas.0905988106

V. Castellucci, H. Pinsker, I. Kupfermann, and E. R. Kandel, Neuronal Mechanisms of Habituation and Dishabituation of the Gill-Withdrawal Reflex in Aplysia, Science, vol.167, issue.3926, pp.1745-1748, 1970.
DOI : 10.1126/science.167.3926.1745

C. Chen and R. F. Thompson, Temporal specificity of long-term depression in parallel fiber--Purkinje synapses in rat cerebellar slice., Learning & Memory, vol.2, issue.3-4, pp.185-198, 1995.
DOI : 10.1101/lm.2.3-4.185

M. M. Churchland, Stimulus onset quenches neural variability: a widespread cortical phenomenon, Nature Neuroscience, vol.21, issue.3, pp.369-378, 2010.
DOI : 10.1038/nn.2501

C. Clopath, J. P. Nadal, and N. Brunel, Storage of Correlated Patterns in Standard and Bistable Purkinje Cell Models, PLoS Computational Biology, vol.4, issue.4, p.1002448, 2012.
DOI : 10.1371/journal.pcbi.1002448.g005

C. Clopath and N. Brunel, Optimal Properties of Analog Perceptrons with Excitatory Weights, PLoS Computational Biology, vol.21, issue.2, p.1002919, 2013.
DOI : 10.1371/journal.pcbi.1002919.g003

C. Clopath, L. Ziegler, E. Vasilaki, L. Büsing, and W. Gerstner, Tag-Trigger-Consolidation: A Model of Early and Late Long-Term-Potentiation and Depression, PLoS Computational Biology, vol.99, issue.12, pp.1-14, 2008.
DOI : 10.1371/journal.pcbi.1000248.t001

C. Clopath, L. Busing, E. Vasilaki, and W. Gerstner, Connectivity reflects coding: a model of voltage-based STDP with homeostasis, Nature Neuroscience, vol.99, issue.3, 2010.
DOI : 10.1038/nn.2479

M. Coesmans, J. T. Weber, C. I. De-zeeuw, and C. Hansel, Bidirectional Parallel Fiber Plasticity in the Cerebellum under Climbing Fiber Control, Neuron, vol.44, issue.4, pp.691-700, 2004.
DOI : 10.1016/j.neuron.2004.10.031

G. L. Collingridge, S. J. Kehl, and H. Mclennan, Excitatory amino acids in synaptic transmission in the Schaffer collateral-commissural pathway of the rat hippocampus., The Journal of Physiology, vol.334, issue.1, pp.33-46, 1983.
DOI : 10.1113/jphysiol.1983.sp014478

J. J. Couey, R. M. Meredith, S. Spijker, R. B. Poorthuis, A. B. Smit et al., Distributed Network Actions by Nicotine Increase the Threshold for Spike-Timing-Dependent Plasticity in Prefrontal Cortex, Neuron, vol.54, issue.1, pp.73-87, 2007.
DOI : 10.1016/j.neuron.2007.03.006

F. Crepel and D. Jaillard, Pairing of pre- and postsynaptic activities in cerebellar Purkinje cells induces long-term changes in synaptic efficacy in vitro., The Journal of Physiology, vol.432, issue.1, pp.123-141, 1991.
DOI : 10.1113/jphysiol.1991.sp018380

J. A. Cummings, M. Rosel, . Mulkey, A. Roger, . Nicoll et al., Ca2+ Signaling Requirements for Long-Term Depression in the Hippocampus, Neuron, vol.16, issue.4, pp.825-833, 1996.
DOI : 10.1016/S0896-6273(00)80102-6

G. Daoudal and D. Debanne, Long-Term Plasticity of Intrinsic Excitability: Learning Rules and Mechanisms, Learning & Memory 10.6. PMID: 14657257, pp.456-465, 2003.
DOI : 10.1101/lm.64103

D. Debanne, B. H. Gähwiler, and S. M. Thompson, Asynchronous preand postsynaptic activity induces associative long-term depression in area CA1 of the rat hippocampus in vitro, Proceedings of the National Academy of Sciences 91.3, pp.1148-1152, 1994.

D. Debanne, S. Gähwiler, and . Thompson, Cooperative interactions in the induction of long-term potentiation and depression of synaptic excitation between hippocampal CA3-CA1 cell pairs in vitro., Proceedings of the National Academy of Sciences 93.20. PMID: 8855337 PMCID: 38312, pp.11225-11230, 1996.
DOI : 10.1073/pnas.93.20.11225

B. Delord, H. Berry, E. Guigon, and S. Genet, A new principle for information storage in an enzymatic pathway model, PLoS Comput Biol, vol.36, p.124, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00149083

T. Doi, S. Kuroda, T. Michikawa, and M. Kawato, Inositol 1,4,5-Trisphosphate-Dependent Ca2+ Threshold Dynamics Detect Spike Timing in Cerebellar Purkinje Cells, Journal of Neuroscience, vol.25, issue.4, pp.950-961, 2005.
DOI : 10.1523/JNEUROSCI.2727-04.2005

S. M. Dudek and M. Bear, Homosynaptic long-term depression in area CA1 of hippocampus and effects of N-methyl-D-aspartate receptor blockade, Proceedings of the National Academy of Sciences 89.10, pp.4363-4367, 1992.

S. M. Dudek and M. F. Bear, Bidirectional long-term modification of synaptic effectiveness in the adult and immature hippocampus, The Journal of Neuroscience, vol.137, issue.7, pp.2910-2918, 1993.

J. C. Eccles, M. Ito, and J. Szentágothai, The Cerebellum as a Neuronal Machine, 1967.
DOI : 10.1007/978-3-662-13147-3

J. Eilers, G. Callewaert, C. Armstrong, and A. Konnerth, Calcium signaling in a narrow somatic submembrane shell during synaptic activity in cerebellar Purkinje neurons., Proceedings of the National Academy of Sciences 92.22, p.10272, 1995.
DOI : 10.1073/pnas.92.22.10272

C. Ekerot and M. Kano, Stimulation parameters influencing climbing fibre induced long-term depression of parallel fibre synapses, Neuroscience Research, vol.6, issue.3, pp.264-268, 1989.
DOI : 10.1016/0168-0102(89)90065-5

E. Boustani, S. , P. Yger, Y. Fregnac, and A. Destexhe, Stable Learning in Stochastic Network States, Journal of Neuroscience, vol.32, issue.1, pp.194-214, 2012.
DOI : 10.1523/JNEUROSCI.2496-11.2012
URL : https://hal.archives-ouvertes.fr/hal-00684084

E. A. Finch and G. J. Augustine, Local calcium signalling by inositol-1,4,5-trisphosphate in Purkinje cell dendrites " . en. In: Nature 396, pp.753-756, 1998.

R. C. Froemke and Y. Dan, Spike-timing-dependent synaptic modification induced by natural spike trains, Nature, vol.20, issue.6879, pp.433-438, 2002.
DOI : 10.1038/416433a

R. C. Froemke, A. Ishan, M. Tsay, J. D. Raad, Y. Long et al., Contribution of Individual Spikes in Burst-Induced Long-Term Synaptic Modification, Journal of Neurophysiology 95.3. PMID: 16319206, pp.1620-1629, 2006.
DOI : 10.1152/jn.00910.2005

S. Fusi, P. J. Drew, and L. F. Abbott, Cascade Models of Synaptically Stored Memories, Neuron, vol.45, issue.4, pp.599-611, 2005.
DOI : 10.1016/j.neuron.2005.02.001

M. Galassi, GNU scientific library: reference manual. Bristol: Network Theory (cit, p.46, 2009.

C. W. Gardiner, Handbook of stochastic methods for physics, chemistry and the natural sciences, 1986.

W. Gerstner, R. Ritz, and J. Leo-van-hemmen, Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns, Biological Cybernetics, vol.76, issue.5-6, pp.5-6, 1993.
DOI : 10.1007/BF00199450

W. Gerstner, R. Kempter, J. Leo-van-hemmen, and H. Wagner, A neuronal learning rule for sub-millisecond temporal coding, Nature, vol.383, issue.6595, pp.76-78, 1996.
DOI : 10.1038/383076a0

E. N. Gilbert and H. O. Pollak, Amplitude Distribution of Shot Noise, Bell System Technical Journal, vol.39, issue.2, pp.333-350, 1960.
DOI : 10.1002/j.1538-7305.1960.tb01603.x

M. Gilson, A. Burkitt, and J. Leo-van-hemmen, STDP in recurrent neuronal networks, Frontiers in Computational Neuroscience, vol.4, p.23, 2010.
DOI : 10.3389/fncom.2010.00023

N. L. Golding, P. Nathan, N. Staff, and . Spruston, Dendritic spikes as a mechanism for cooperative long-term potentiation, Nature, vol.29, issue.6895, pp.326-331, 2002.
DOI : 10.1002/(SICI)1098-1063(1998)8:3<244::AID-HIPO7>3.3.CO;2-M

D. F. Goodman and R. Brette, The Brian Simulator, Frontiers in Neuroscience 3.2. PMID: 20011141 PMCID: PMC2751620, pp.192-197, 2009.

M. Graupner and N. Brunel, Calcium-based plasticity model explains sensitivity of synaptic changes to spike pattern, rate, and dendritic location, Proceedings of the National Academy of Sciences, vol.109, issue.10, pp.67-70, 2012.
DOI : 10.1073/pnas.1109359109

C. Hansel, When the B-team runs plasticity: GluR2 receptor trafficking in cerebellar long-term potentiation, Proceedings of the National Academy of Sciences 102.51, pp.18245-18246, 2005.
DOI : 10.1073/pnas.0509686102

N. A. Hartell, Strong Activation of Parallel Fibers Produces Localized Calcium Transients and a Form of LTD That Spreads to Distant Synapses, Neuron, vol.16, issue.3, pp.601-610, 1996.
DOI : 10.1016/S0896-6273(00)80079-3

A. Hayer and U. S. Bhalla, Molecular Switches at the Synapse Emerge from Receptor and Kinase Traffic, PLoS Computational Biology, vol.8, issue.2, pp.137-154, 2005.
DOI : 10.1371/journal.pcbi.0010020.sg002

D. Hebb and . Olding, The organisation of behavior: a neuropsychological theory, 1949.

V. M. Ho, J. Lee, and K. C. Martin, The Cell Biology of Synaptic Plasticity, Science, vol.334, issue.6056, pp.623-628, 2011.
DOI : 10.1126/science.1209236

C. Holmgren, T. Harkany, B. Svennenfors, and Y. Zilberter, Pyramidal cell communication within local networks in layer 2/3 of rat neocortex, The Journal of Physiology, vol.551, issue.1, pp.139-153, 2003.
DOI : 10.1113/jphysiol.2003.044784

J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities " . en, Proceedings of the National Academy of Sciences 79.8. PMID: 6953413, pp.2554-2558, 1982.

I. Ismailov, D. Kalikulov, T. Inoue, and M. J. Friedlander, The Kinetic Profile of Intracellular Calcium Predicts Long-Term Potentiation and Long-Term Depression, Journal of Neuroscience, vol.24, issue.44, pp.9847-9861, 2004.
DOI : 10.1523/JNEUROSCI.0738-04.2004

P. Isope, R. Franconville, B. Barbour, and P. Ascher, Repetitive firing of rat cerebellar parallel fibres after a single stimulation " . en, The Journal of Physiology, vol.5543, pp.829-839, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00145477

M. Ito and L. Karachot, Receptor subtypes involved in, and time course of, the long-term desensitization of glutamate receptors in cerebellar Purkinje cells, Neuroscience Research, vol.8, issue.4, pp.303-307, 1990.
DOI : 10.1016/0168-0102(90)90036-E

M. Ito, M. Sakurai, and P. Tongroach, Climbing fibre induced depression of both mossy fibre responsiveness and glutamate sensitivity of cerebellar Purkinje cells, The Journal of Physiology, vol.324, issue.1, pp.113-134, 1982.
DOI : 10.1113/jphysiol.1982.sp014103

H. Jörntell and C. Hansel, Synaptic Memories Upside Down: Bidirectional Plasticity at Cerebellar Parallel Fiber-Purkinje Cell Synapses, Neuron 52.2, pp.227-238, 2006.

W. Kakegawa and M. Yuzaki, From The Cover: A mechanism underlying AMPA receptor trafficking during cerebellar long-term potentiation, Proceedings of the National Academy of Sciences of the United States of America 102, pp.17846-17873, 2005.
DOI : 10.1073/pnas.0508910102

L. Karachot, R. T. Kado, and M. Ito, Stimulus parameters for induction of long-term depression in in vitro rat Purkinje cells, Neuroscience Research, vol.21, issue.2, pp.161-168, 1994.
DOI : 10.1016/0168-0102(94)90158-9

J. A. Kauer and R. C. Malenka, Synaptic plasticity and addiction, Nature Reviews Neuroscience, vol.30, issue.11, pp.844-858, 2007.
DOI : 10.1038/nrn2234

S. Kawaguchi and T. Hirano, /calmodulin-dependent protein kinase??II through enhanced cGMP signalling in cerebellar Purkinje cells, The Journal of Physiology, vol.102, issue.7, pp.1707-1730, 2013.
DOI : 10.1113/jphysiol.2012.245787

R. Kempter, W. Gerstner, and J. Leo-van-hemmen, Hebbian learning and spiking neurons, Physical Review E, vol.59, issue.4, pp.4498-4514, 1999.
DOI : 10.1103/PhysRevE.59.4498

T. Kenet, D. Bibitchkov, M. Tsodyks, A. Grinvald, and A. Arieli, Spontaneously emerging cortical representations of visual attributes, Nature, vol.425, issue.6961, pp.954-956, 2003.
DOI : 10.1038/nature02078

K. Khodakhah and C. M. Armstrong, Induction of long-term depression and rebound potentiation by inositol trisphosphate in cerebellar Purkinje neurons, Proceedings of the National Academy of Sciences 94.25. PMID: 9391143, pp.14009-14014, 1997.
DOI : 10.1073/pnas.94.25.14009

T. Kohonen, Self-organized formation of topologically correct feature maps, Biological Cybernetics, vol.13, issue.1, pp.59-69, 1982.
DOI : 10.1007/BF00337288

A. Konnerth, J. Dreessen, and G. J. Augustine, Brief dendritic calcium signals initiate long-lasting synaptic depression in cerebellar Purkinje cells., Proceedings of the National Academy of Sciences 89.15, p.7051, 1992.
DOI : 10.1073/pnas.89.15.7051

H. A. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions, Physica, vol.7, issue.4, pp.284-304, 1940.
DOI : 10.1016/S0031-8914(40)90098-2

A. Kumar and M. R. Mehta, Frequency-Dependent Changes in NMDAR-Dependent Synaptic Plasticity, Frontiers in Computational Neuroscience, vol.5, issue.104, p.38, 2011.
DOI : 10.3389/fncom.2011.00038

S. Kuroda, N. Schweighofer, and M. Kawato, Exploration of Signal Transduction Pathways in Cerebellar Long-Term Depression by Kinetic Simulation, The Journal of Neuroscience, vol.2115, pp.5693-5702, 2001.

L. Ecuyer, P. , and R. Simard, TestU01: A C library for empirical testing of random number generators, In: ACM Transactions on Mathematical Software (TOMS), vol.334, issue.122, p.22, 2007.

. Lev-ram, L. R. Varda, P. F. Makings, J. P. Keitz, R. Y. Kao et al., Long-term depression in cerebellar Purkinje neurons results from coincidence of nitric oxide and depolarization-induced Ca2+ transients, Neuron 15.2, pp.407-415, 1995.
DOI : 10.1016/0896-6273(95)90044-6

. Lev-ram, T. Varda, J. Jiang, . Wood, S. David et al., Synergies and Coincidence Requirements between NO, cGMP, and Ca2+ in the Induction of Cerebellar Long-Term Depression, Neuron 18.6, pp.1025-1038, 1997.
DOI : 10.1016/S0896-6273(00)80340-2

. Lev-ram, S. T. Varda, D. R. Wong, R. Y. Storm, and . Tsien, A new form of cerebellar long-term potentiation is postsynaptic and depends on nitric oxide but not cAMP, Proceedings of the National Academy of Sciences 99.12, pp.8389-8393, 2002.
DOI : 10.1073/pnas.122206399

. Lev-ram, S. B. Varda, D. Mehta, R. Y. Kleinfeld, and . Tsien, Reversing cerebellar long-term depression, Proceedings of the National Academy of Sciences 100.26. PMID: 14671315, pp.15989-15993, 2003.
DOI : 10.1073/pnas.2636935100
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC307680

Y. W. Lin, M. Y. Min, T. H. Chiu, and H. W. Yang, Enhancement of associative long-term potentiation by activation of beta-adrenergic receptors at CA1 synapses in rat hippocampal slices, J. Neurosci, vol.23, pp.4173-4181, 2003.

J. E. Lisman, A mechanism for memory storage insensitive to molecular turnover: a bistable autophosphorylating kinase., Proceedings of the National Academy of Sciences, pp.3055-3057, 1985.
DOI : 10.1073/pnas.82.9.3055

J. Lisman and N. Spruston, Postsynaptic depolarization requirements for LTP and LTD: a critique of spike timing-dependent plasticity, Nature Neuroscience, vol.46, issue.7, pp.839-841, 2005.
DOI : 10.1038/nn0705-839

A. Litwin-kumar and B. Doiron, Slow dynamics and high variability in balanced cortical networks with clustered connections, Nature Neuroscience, vol.15, issue.11, pp.1498-1505, 2012.
DOI : 10.1063/1.1703954

Y. Loewenstein, A. Kuras, and S. Rumpel, Multiplicative Dynamics Underlie the Emergence of the Log-Normal Distribution of Spine Sizes in the Neocortex In Vivo, Journal of Neuroscience, vol.31, issue.26, pp.9481-9488, 2011.
DOI : 10.1523/JNEUROSCI.6130-10.2011

A. Luczak, P. Bartho, and K. D. Harris, Spontaneous Events Outline the Realm of Possible Sensory Responses in Neocortical Populations, Neuron, vol.62, issue.3, pp.413-425, 2009.
DOI : 10.1016/j.neuron.2009.03.014

N. R. Luque, J. A. Garrido, R. R. Carrillo, S. Tolu, and E. Ros, ADAPTIVE CEREBELLAR SPIKING MODEL EMBEDDED IN THE CONTROL LOOP: CONTEXT SWITCHING AND ROBUSTNESS AGAINST NOISE, International Journal of Neural Systems 21.05, pp.385-401, 2011.
DOI : 10.1142/S0129065711002900

G. S. Lynch, T. Dunwiddie, and V. Gribkoff, Heterosynaptic depression: a postsynaptic correlate of long-term potentiation, Nature, vol.13, issue.5604, pp.737-739, 1977.
DOI : 10.1038/263251a0

G. Lynch, J. Larson, S. Kelso, G. Barrionuevo, and F. Schottler, Intracellular injections of EGTA block induction of hippocampal longterm potentiation, Nature 305.5936, pp.719-721, 1983.

R. C. Malenka, J. A. Kauer, S. Robert, . Zucker, A. Roger et al., Postsynaptic calcium is sufficient for potentiation of hippocampal synaptic transmission, Science, vol.242, issue.4875, pp.81-84, 1988.
DOI : 10.1126/science.2845577

P. Marcaggi and D. Attwell, Short- and long-term depression of rat cerebellar parallel fibre synaptic transmission mediated by synaptic crosstalk, The Journal of Physiology, vol.3, issue.2, pp.545-550, 2007.
DOI : 10.1113/jphysiol.2006.115014

H. Markram, J. Lübke, M. Frotscher, and B. Sakmann, Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EP- SPs, In: Science, vol.2755297, issue.103, pp.213-215, 1997.

D. W. Marquardt, An Algorithm for Least-Squares Estimation of Nonlinear Parameters, Journal of the Society for Industrial and Applied Mathematics, vol.11, issue.2, pp.431-441, 1963.
DOI : 10.1137/0111030

D. Marr, A theory of cerebellar cortex, The Journal of Physiology 202.2. PMID: 5784296, pp.437-470, 1969.

G. Marsaglia, DIEHARD: a battery of tests of randomness (cit, p.121, 1996.

G. Marsaglia and A. Zaman, The KISS generator, 1993.

J. Martens, Deep learning via Hessian-free optimization, Proceedings of the 27th International Conference on Machine Learning (ICML-10), pp.735-742, 2010.
DOI : 10.1007/978-3-642-35289-8_27
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.296.4704

S. Matsuda, T. Launey, S. Mikawa, and H. Hirai, Disruption of AMPA receptor GluR2 clusters following long-term depression induction in cerebellar Purkinje neurons, The EMBO Journal, vol.19, issue.12, pp.2765-2774, 2000.
DOI : 10.1093/emboj/19.12.2765

M. Matsumoto and T. Nishimura, Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator, ACM Transactions on Modeling and Computer Simulation, vol.8, issue.1, pp.3-30, 1998.
DOI : 10.1145/272991.272995
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.215.1141

P. Miller, A. M. Zhabotinsky, J. E. Lisman, and X. Wang, The Stability of a Stochastic CaMKII Switch: Dependence on the Number of Enzyme Molecules and Protein Turnover, PLoS Biology, vol.35, issue.4, p.107, 2005.
DOI : 10.1371/journal.pbio.0030107.t001

M. Miyata, E. A. Finch, L. Khiroug, K. Hashimoto, S. Hayasaka et al., Local Calcium Release in Dendritic Spines Required for Long-Term Synaptic Depression, English. In: Neuron 28.1. PMID: 11086997, pp.233-244, 2000.
DOI : 10.1016/S0896-6273(00)00099-4

T. Mizuno, I. Kanazawa, and M. Sakurai, Differential induction of LTP and LTD is not determined solely by instantaneous calcium concentration: an essential involvement of a temporal factor, European Journal of Neuroscience, vol.6, issue.4, pp.701-708, 2001.
DOI : 10.1038/35046067

G. Mongillo, E. Curti, S. Romani, and D. J. Amit, Learning in realistic networks of spiking neurons and spike-driven plastic synapses, European Journal of Neuroscience, vol.265, issue.RC50, pp.3143-3160, 2005.
DOI : 10.1111/j.1460-9568.2005.04087.x

G. Mongillo, O. Barak, and M. Tsodyks, Synaptic Theory of Working Memory, Science 319.5869. PMID: 18339943, pp.1543-1546, 2008.
DOI : 10.1126/science.1150769

S. Nabavi, H. W. Kessels, S. Alfonso, J. Aow, R. Fox et al., Metabotropic NMDA receptor function is required for NMDA receptor-dependent long-term depression, Proceedings of the National Academy of Sciences, vol.110, issue.10, pp.4027-4032, 2013.
DOI : 10.1073/pnas.1219454110

J. P. Nadal, G. Toulouse, J. P. Changeux, and S. Dehaene, Networks of Formal Neurons and Memory Palimpsests, In: EPL (Europhysics Letters), vol.110, p.535, 1986.

J. A. Nelder and R. Mead, A Simplex Method for Function Minimization, Computer journal 7, pp.308-313, 1965.
DOI : 10.1093/comjnl/7.4.308

D. Neveu and R. S. Zucker, Postsynaptic Levels of [Ca2+]i Needed to Trigger LTD and LTP, Neuron, vol.16, issue.3, pp.619-629, 1996.
DOI : 10.1016/S0896-6273(00)80081-1

T. Nevian and B. Sakmann, Spine Ca2+ signaling in spiketiming-dependent plasticity, The Journal of Neuroscience, vol.2643, pp.11001-11013, 2006.

O. Connor, H. Daniel, M. Gayle, . Wittenberg, S. Samuel et al., Dissection of Bidirectional Synaptic Plasticity into Saturable Unidirectional Processes, Proceedings of the National Academy of Sciences, 2005.

O. Connor, D. H. Gayle, M. Wittenberg, and S. Wang, Graded bidirectional synaptic plasticity is composed of switch-like unitary events, 2005.

E. Oja, Simplified neuron model as a principal component analyzer " . en, Journal of Mathematical Biology, vol.153, issue.67, pp.267-273, 1982.

V. Pawlak, J. R. Wickens, A. Kirkwood, and J. N. Kerr, Timing is not everything: neuromodulation opens the STDP gate, Front Synaptic Neurosci 2, p.146, 2010.
DOI : 10.3389/fnsyn.2010.00146

C. C. Petersen, C. Robert, R. A. Malenka, J. J. Nicoll, and . Hopfield, All-or-none potentiation at CA3-CA1 synapses, Proceedings of the National Academy of Sciences 95.8, pp.4732-4737, 1998.
DOI : 10.1073/pnas.95.8.4732
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC22559

J. Pfister and W. Gerstner, Triplets of Spikes in a Model of Spike Timing-Dependent Plasticity, Journal of Neuroscience, vol.26, issue.38, pp.9673-9682, 2006.
DOI : 10.1523/JNEUROSCI.1425-06.2006

H. Pi, J. E. Jae, and . Lisman, Coupled phosphatase and kinase switches produce the tristability required for long-term potentiation and longterm depression, In: J Neurosci, vol.2849, pp.13132-13138, 2008.

C. Piochon, C. Levenes, G. Ohtsuki, and C. Hansel, Purkinje Cell NMDA Receptors Assume a Key Role in Synaptic Gain Control in the Mature Cerebellum, Journal of Neuroscience, vol.30, issue.45, pp.15330-15335, 2010.
DOI : 10.1523/JNEUROSCI.4344-10.2010

E. Polak and G. Ribiere, Note sur la convergence de m??thodes de directions conjugu??es, ESAIM: Mathematical Modelling and Numerical Analysis -Modélisation Mathématique et Analyse Numérique 3.R1, pp.35-43, 1969.
DOI : 10.1051/m2an/196903R100351
URL : http://archive.numdam.org/article/M2AN_1969__3_1_35_0.pdf

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 1992.

S. O. Rice, Mathematical Analysis of Random Noise, The Bell System technical journal, p.282, 1944.

G. Rose, KISS: A Bit Too Simple In: IACR Cryptology ePrint Archive, p.7, 2011.

A. Roxin, The Role of Degree Distribution in Shaping the Dynamics in Networks of Sparsely Connected Spiking Neurons, Frontiers in Computational Neuroscience, vol.5, pp.8-85, 2011.
DOI : 10.3389/fncom.2011.00008

A. Roxin and S. Fusi, Efficient Partitioning of Memory Systems and Its Importance for Memory Consolidation, PLoS Computational Biology, vol.6, issue.7, p.1003146, 2013.
DOI : 10.1371/journal.pcbi.1003146.s001

J. Rubin, D. D. Lee, and H. Sompolinsky, Equilibrium Properties of Temporally Asymmetric Hebbian Plasticity, Physical Review Letters, vol.86, issue.2, pp.364-367, 2001.
DOI : 10.1103/PhysRevLett.86.364

J. E. Rubin, C. Richard, G. Gerkin, . Bi, C. Carson et al., Calcium Time Course as a Signal for Spike-Timing-Dependent Plasticity, Journal of neurophysiology 93.5, pp.2600-2613, 2005.
DOI : 10.1152/jn.00803.2004

B. L. Sabatini, T. G. Oertner, and K. Svoboda, The life cycle of Ca(2+) ions in dendritic spines, pp.439-452, 2002.

P. Safo, G. Wade, and . Regehr, Timing dependence of the induction of cerebellar LTD, Neuropharmacology, vol.54, issue.1, pp.213-218, 2008.
DOI : 10.1016/j.neuropharm.2007.05.029

M. Sakurai, Synaptic modification of parallel fibre-Purkinje cell transmission in in vitro guinea-pig cerebellar slices., The Journal of Physiology, vol.394, issue.1, pp.463-480, 1987.
DOI : 10.1113/jphysiol.1987.sp016881

J. K. Salmon, M. A. Moraes, R. O. Dror, and D. E. Shaw, Parallel random numbers, Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis on, SC '11, pp.1-12, 2011.
DOI : 10.1145/2063384.2063405

D. V. Sarkisov and S. S. Wang, Order-Dependent Coincidence Detection in Cerebellar Purkinje Neurons at the Inositol Trisphosphate Receptor, Journal of Neuroscience, vol.28, issue.1, pp.133-142, 2008.
DOI : 10.1523/JNEUROSCI.1729-07.2008

K. Schermelleh-engel, H. Moosbrugger, and H. Müller, Evaluating the fit of structural equation models: Tests of significance and descriptive goodness-of-fit measures, Methods of psychological research online 8, pp.23-74, 2003.

G. Schwarz, Estimating the Dimension of a Model, The Annals of Statistics 6.2, pp.461-464, 1978.
DOI : 10.1214/aos/1176344136

T. J. Sejnowski, Storing covariance with nonlinearly interacting neurons, Journal of Mathematical Biology, vol.12, issue.4, pp.303-321, 1977.
DOI : 10.1007/BF00275079

G. H. Seol, J. Ziburkus, S. Huang, L. Song, I. T. Kim et al., Neuromodulators Control the Polarity of Spike-Timing-Dependent Synaptic Plasticity, Neuron, vol.55, issue.6, pp.919-929, 2007.
DOI : 10.1016/j.neuron.2007.08.013

J. Shin, D. J. Hoon, and . Linden, An NMDA Receptor/Nitric Oxide Cascade Is Involved in Cerebellar LTD But Is Not Localized to the Parallel Fiber Terminal, Journal of Neurophysiology, vol.94, issue.6, pp.4281-4289, 2005.
DOI : 10.1152/jn.00661.2005

H. Z. Shouval, Clusters of interacting receptors can stabilize synaptic efficacies, Proceedings of the National Academy of Sciences, vol.102, issue.40, pp.14440-14445, 2005.
DOI : 10.1073/pnas.0506934102

. Shouval, Z. Harel, F. Mark, L. Bear, and . Cooper, A unified model of NMDA receptor-dependent bidirectional synaptic plasticity, Proceedings of the National Academy of Sciences of the United States of America 99, pp.10831-10836, 2002.
DOI : 10.1073/pnas.152343099

A. J. Siegert, On the First Passage Time Probability Problem, Physical Review, vol.81, issue.4, pp.617-623, 1951.
DOI : 10.1103/PhysRev.81.617

I. A. Silver and M. Ereci?ska, Intracellular and extracellular changes of [Ca2+] in hypoxia and ischemia in rat brain in vivo, The Journal of General Physiology, vol.95, issue.5, pp.837-866, 1990.
DOI : 10.1085/jgp.95.5.837

R. E. Sims and N. A. Hartell, Differential Susceptibility to Synaptic Plasticity Reveals a Functional Specialization of Ascending Axon and Parallel Fiber Synapses to Cerebellar Purkinje Cells, Journal of Neuroscience, vol.26, issue.19, pp.5153-5159, 2006.
DOI : 10.1523/JNEUROSCI.4121-05.2006

P. J. Sjöström, G. G. Turrigiano, and S. B. Nelson, Rate, Timing, and Cooperativity Jointly Determine Cortical Synaptic Plasticity, Neuron, vol.32, issue.6, pp.1149-1164, 2001.
DOI : 10.1016/S0896-6273(01)00542-6

S. Song, K. D. Miller, and L. F. Abbott, Competitive Hebbian learning through spike-timing-dependent synaptic plasticity, Nat Neurosci, vol.39, issue.102, pp.919-926, 2000.

. Song, P. J. Sen, M. Sjostrom, S. Reigl, D. B. Nelson et al., Highly Nonrandom Features of Synaptic Connectivity in Local Cortical Circuits, PLoS Biology, vol.1, issue.3, p.68, 2005.
DOI : 10.1371/journal.pbio.0030068.st001

J. H. Steiger, A. Shapiro, and M. W. Browne, On the multivariate asymptotic distribution of sequential Chi-square statistics " . en, pp.253-263, 1985.

L. Takacs, On secondary stochastic processes generated by recurrent processes, Acta Mathematica Academiae Scientiarum Hungarica 7, pp.17-29, 1956.
DOI : 10.1007/BF02022961

K. Tanaka, L. Khiroug, F. Santamaria, T. Doi, H. Ogasawara et al., Ca2+ Requirements for Cerebellar Long-Term Synaptic Depression: Role for a Postsynaptic Leaky Integrator, Neuron, vol.54, issue.5, pp.787-800, 2007.
DOI : 10.1016/j.neuron.2007.05.014

T. Toyoizumi, . Pfister, W. Aihara, and . Gerstner, Generalized Bienenstock-Cooper-Munro rule for spiking neurons that maximizes information transmission, Proceedings of the National Academy of Sciences 102.14, pp.5239-5283, 2005.
DOI : 10.1073/pnas.0500495102

M. Tsodyks, T. Kenet, A. Grinvald, and A. Arieli, Linking Spontaneous Activity of Single Cortical Neurons and the Underlying Functional Architecture, Science, vol.286, issue.5446, pp.1943-1946, 1999.
DOI : 10.1126/science.286.5446.1943

M. V. Tsodyks and M. V. Feigel-'man, The Enhanced Storage Capacity, Neural Networks with Low Activity Level " . en. In: EPL (Europhysics Letters) 6.2, p.101, 1988.

M. Tsodyks, K. Pawelzik, and H. Markram, Neural Networks with Dynamic Synapses, Neural Computation 10.4, pp.821-835, 1998.
DOI : 10.1085/jgp.80.4.583
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.8981

M. V. Tsodyks and H. Markram, The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability, Proceedings of the National Academy of Sciences 94.2, pp.719-723, 1997.
DOI : 10.1073/pnas.94.2.719

G. G. Turrigiano, B. Sacha, and . Nelson, Hebb and homeostasis in neuronal plasticity, Current Opinion in Neurobiology, vol.10, issue.3, pp.358-364, 2000.
DOI : 10.1016/S0959-4388(00)00091-X

G. G. Turrigiano and S. B. Nelson, Homeostatic plasticity in the developing nervous system, Nature Reviews Neuroscience, vol.5, issue.2, pp.97-107, 2004.
DOI : 10.1038/nrn1327

M. C. Van-rossum and G. G. Turrigiano, Correlation based learning from spike timing dependent plasticity, Neurocomputing, vol.38, issue.40, pp.409-415, 2001.
DOI : 10.1016/S0925-2312(01)00360-5

M. C. Van-rossum, G. Q. Bi, and G. G. Turrigiano, Stable Hebbian Learning from Spike Timing-Dependent Plasticity, J. Neurosci, vol.2023, issue.102, pp.8812-8821, 2000.

T. P. Vogels, H. Sprekeler, F. Zenke, C. Clopath, and W. Gerstner, Inhibitory Plasticity Balances Excitation and Inhibition in Sensory Pathways and Memory Networks, Science, vol.334, issue.6062, pp.1569-1573, 2011.
DOI : 10.1126/science.1211095

. Wang, R. C. Huai-xing, D. W. Gerkin, G. Nauen, and . Bi, Coactivation and timing-dependent integration of synaptic potentiation and depression, Nature Neuroscience, vol.23, issue.2, pp.187-193, 2005.
DOI : 10.1126/science.1082212

S. S. Wang, W. Denk, and M. Hausser, Coincidence detection in single dendritic spines mediated by calcium release, Nat Neurosci, vol.312, issue.32, pp.1266-1273, 2000.

Y. Wang, D. J. Tian, and . Linden, Expression of Cerebellar Long-Term Depression Requires Postsynaptic Clathrin-Mediated Endocytosis, Neuron, vol.25, issue.3, pp.635-647, 2000.
DOI : 10.1016/S0896-6273(00)81066-1

G. M. Wittenberg, S. Samuel, and . Wang, Malleability of Spike-Timing-Dependent Plasticity at the CA3-CA1 Synapse, Journal of Neuroscience, vol.26, issue.24, pp.6610-6617, 2006.
DOI : 10.1523/JNEUROSCI.5388-05.2006

J. Xia, H. J. Chung, C. Wihler, L. Richard, . Huganir et al., Cerebellar Long-Term Depression Requires PKC-Regulated Interactions between GluR2/3 and PDZ Domain???Containing Proteins, Neuron 28.2, pp.499-510, 2000.
DOI : 10.1016/S0896-6273(00)00128-8
URL : http://doi.org/10.1016/s0896-6273(00)00128-8

. Yang, Y. Shao-nian, R. S. Tang, and . Zucker, Selective Induction of LTP and LTD by Postsynaptic [Ca2+]i Elevation, Journal of Neurophysiology, vol.81, issue.68, pp.781-787, 1999.

Y. Yang and S. G. Lisberger, Purkinje-cell plasticity and cerebellar motor learning are graded by complex-spike duration " . en. In: Nature advance online publication (cit, p.107, 2014.

P. Yger and K. D. Harris, The Convallis Rule for Unsupervised Learning in Cortical Networks, PLoS Computational Biology, vol.12, issue.10, pp.1003272-67, 2013.
DOI : 10.1371/journal.pcbi.1003272.s006

F. Zenke, G. Hennequin, and W. Gerstner, Synaptic Plasticity in Neural Networks Needs Homeostasis with a Fast Rate Detector, PLoS Computational Biology, vol.2, issue.11, p.1003330, 2013.
DOI : 10.1371/journal.pcbi.1003330.s002