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Demographic modeling of transient amplifying cell population growth
Cooperative behavior in a jump diffusion model for a simple network of spiking neurons
1. | Department of Mathematics "G. Peano", University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy, Italy |
2. | Grenoble Institute of Neuroscience Inserm UMRS 836, University Joseph Fourier Grenoble, France |
References:
[1] |
L. Alili, P. Patie and J. L. Pedersen, Representations of the first hitting time density of an Ornstein-Uhlenbeck process, Stoch. Models, 21 (2005), 967-980.
doi: 10.1080/15326340500294702. |
[2] |
P. Baldi and L. Caramellino, Asymptotics of hitting probabilities for general one-dimensional pinned diffusions, Ann. Appl. Probab., 12 (2002), 1071-1095.
doi: 10.1214/aoap/1031863181. |
[3] |
A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen and K. Lindenberg, Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics, Phys. Rev. E, 53 (1996), 3958-3969.
doi: 10.1103/PhysRevE.53.3958. |
[4] |
A. R. Bulsara, S. B. Lowen and C. D. Rees, Cooperative behavior in the periodically modulated Wiener process: Noise-induced complexity in a model neutron, Phys. Rev. E, 49 (1994), 4989-5000.
doi: 10.1103/PhysRevE.49.4989. |
[5] |
W. H. Calvin and C. F. Stevens, Synaptic noise and other sources of randomness in motoneuron interspike intervals, J. Neurophysiol., 31 (1968), 574-587. |
[6] |
A. Capurro, K. Pakdaman, T. Nomura and S. Sato, Aperiodic stochastic resonance with correlated noise, Phys. Rev. E, 58 (1998), 4820-4827.
doi: 10.1103/PhysRevE.58.4820. |
[7] |
G. A. Cecchi, M. Sigman, J.-M. Alonso, L. Martínez, D. R. Chialvo and M. O. Magnasco, Noise in neurons is message dependent, Proceedings of the National Academy of Sciences, 97 (2000), 5557-5561.
doi: 10.1073/pnas.100113597. |
[8] |
J. J. Collins, C. C. Chow, A. C. Capela and T. T. Imhoff, Aperiodic stochastic resonance, Phys. Rev. E, 54 (1996), 5575-5584.
doi: 10.1103/PhysRevE.54.5575. |
[9] |
J. J. Collins, C. C. Chow and T. T. Imhoff, Aperiodic stochastic resonance in excitable systems, Phys. Rev. E, 52 (1995), R3321-R3324.
doi: 10.1103/PhysRevE.52.R3321. |
[10] |
I. Duguid, T. Branco, M. London, P. Chadderton and M. Häusser, Tonic inhibition enhances fidelity of sensory information transmission in the cerebellar cortex, The Journal of Neuroscience, 32 (2012), 11132-11143.
doi: 10.1523/JNEUROSCI.0460-12.2012. |
[11] |
M. Gernert, M. Bennay, M. Fedrowitz, J. H. Rehders and A. Richter, Altered discharge pattern of basal ganglia output neurons in an animal model of idiopathic dystonia, J. Neurosci., 22 (2002), 7244-7253. |
[12] |
M. T. Giraudo and L. Sacerdote, An improved technique for the simulation of first passage times for diffusion processes, Comm. Statist. Simulation Comput., 28 (1999), 1135-1163.
doi: 10.1080/03610919908813596. |
[13] |
L. L. Gollo, C. R. Mirasso and A. E. P. Villa, Dynamic control for synchronization of separated cortical areas through thalamic relay, NeuroImage, 52 (2010), 947-955.
doi: 10.1016/j.neuroimage.2009.11.058. |
[14] |
M. Häusser and B. A. Clark, Tonic synaptic inhibition modulates neuronal output pattern and spatiotemporal synaptic integration, Neuron, 19 (1997), 665-678. |
[15] |
E. R. Kandel, J. H. Schwartz and T. M. Jessell, Principles of Neural Science, Vol. 4, McGraw-Hill, New York, 2000. |
[16] |
P. Lánský, On approximations of Stein's neuronal model, J. Theor. Biol., 107 (1984), 631-647. |
[17] |
M. W. Levine and J. M. Shefner, A model for the variability of interspike intervals during sustained firing of a retinal neuron, Biophysical Journal, 19 (1977), 241-252.
doi: 10.1016/S0006-3495(77)85584-7. |
[18] |
Y. Loewenstein, S. Mahon, P. Chadderton, K. Kitamura, H. Sompolinsky, Y. Yarom and M. Häusser, Bistability of cerebellar Purkinje cells modulated by sensory stimulation, Nature Neuroscience, 8 (2005), 202-211.
doi: 10.1038/nn1393. |
[19] |
A. Longtin, Stochastic resonance in neuron models, Journal of Statistical Physics, 70 (1993), 309-327.
doi: 10.1007/BF01053970. |
[20] |
A. Longtin, A. Bulsara and F. Moss, Time interval sequences in the bistable systems and the noise-induced transmission of information by sensory neurons, Phys. Rev. Lett., 67 (1991), 656-659.
doi: 10.1103/PhysRevLett.67.656. |
[21] |
M. Musila and P. Lánský, Generalized Stein's model for anatomically complex neurons, Biosystems, 25 (1991), 179-191.
doi: 10.1016/0303-2647(91)90004-5. |
[22] |
A. G. Nobile, L. M. Ricciardi and L. Sacerdote, Exponential trends of Ornstein-Uhlenbeck first-passage-time densities, J. Appl. Probab., 22 (1985), 360-369.
doi: 10.2307/3213779. |
[23] |
L. M. Ricciardi, Diffusion approximation for a multi-input model neuron, Biological Cybernetics, 24 (1976), 237-240.
doi: 10.1007/BF00335984. |
[24] |
L. Sacerdote and R. Sirovich, Multimodality of the interspike interval distribution in a simple jump-diffusion model, Sci. Math. Jpn., 58 (2003), 307-322. |
[25] |
J. P. Segundo, J. F. Vibert, K. Pakdaman, M. Stiber and O. Diez-Martinez, Noise and the neurosciences: A long history, a recent revival and some theory, Origins: Brain and Self Organization, (1994), 299-331. |
[26] |
T. Shimokawa, K. Pakdaman and S. Sato, Time-scale matching in the response of a leaky integrate-and-fire neuron model to periodic stimulus with additive noise, Phys. Rev. E, 59 (1999), 3427-3443.
doi: 10.1103/PhysRevE.59.3427. |
[27] |
H. C. Tuckwell, Introduction to Theoretical Neurobiology: Volume 2, Nonlinear and Stochastic Theories, Cambridge University Press, 2005. |
[28] |
C. Van Vreeswijk, L. F. Abbott and G. B. Ermentrout, When inhibition not excitation synchronizes neural firing, Journal of Computational Neuroscience, 1 (1994), 313-321. |
[29] |
F. Wan and H. C. Tuckwell, Neuronal firing and input variability, J. Theor. Neurobiol., 1 (1982), 197-218. |
[30] |
K. Wiesenfeld and F. Moss, Stochastic resonance and the benefits of noise: From ice ages to crayfish and squids, Nature, 373 (1995), 33-36.
doi: 10.1038/373033a0. |
[31] |
F. Wörgötter, E. Nelle, B. Li and K. Funke, The influence of corticofugal feedback on the temporal structure of visual responses of cat thalamic relay cells, J. Physiol., 509 (1998), 797-815.
doi: 10.1111/j.1469-7793.1998.797bm.x. |
show all references
References:
[1] |
L. Alili, P. Patie and J. L. Pedersen, Representations of the first hitting time density of an Ornstein-Uhlenbeck process, Stoch. Models, 21 (2005), 967-980.
doi: 10.1080/15326340500294702. |
[2] |
P. Baldi and L. Caramellino, Asymptotics of hitting probabilities for general one-dimensional pinned diffusions, Ann. Appl. Probab., 12 (2002), 1071-1095.
doi: 10.1214/aoap/1031863181. |
[3] |
A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen and K. Lindenberg, Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics, Phys. Rev. E, 53 (1996), 3958-3969.
doi: 10.1103/PhysRevE.53.3958. |
[4] |
A. R. Bulsara, S. B. Lowen and C. D. Rees, Cooperative behavior in the periodically modulated Wiener process: Noise-induced complexity in a model neutron, Phys. Rev. E, 49 (1994), 4989-5000.
doi: 10.1103/PhysRevE.49.4989. |
[5] |
W. H. Calvin and C. F. Stevens, Synaptic noise and other sources of randomness in motoneuron interspike intervals, J. Neurophysiol., 31 (1968), 574-587. |
[6] |
A. Capurro, K. Pakdaman, T. Nomura and S. Sato, Aperiodic stochastic resonance with correlated noise, Phys. Rev. E, 58 (1998), 4820-4827.
doi: 10.1103/PhysRevE.58.4820. |
[7] |
G. A. Cecchi, M. Sigman, J.-M. Alonso, L. Martínez, D. R. Chialvo and M. O. Magnasco, Noise in neurons is message dependent, Proceedings of the National Academy of Sciences, 97 (2000), 5557-5561.
doi: 10.1073/pnas.100113597. |
[8] |
J. J. Collins, C. C. Chow, A. C. Capela and T. T. Imhoff, Aperiodic stochastic resonance, Phys. Rev. E, 54 (1996), 5575-5584.
doi: 10.1103/PhysRevE.54.5575. |
[9] |
J. J. Collins, C. C. Chow and T. T. Imhoff, Aperiodic stochastic resonance in excitable systems, Phys. Rev. E, 52 (1995), R3321-R3324.
doi: 10.1103/PhysRevE.52.R3321. |
[10] |
I. Duguid, T. Branco, M. London, P. Chadderton and M. Häusser, Tonic inhibition enhances fidelity of sensory information transmission in the cerebellar cortex, The Journal of Neuroscience, 32 (2012), 11132-11143.
doi: 10.1523/JNEUROSCI.0460-12.2012. |
[11] |
M. Gernert, M. Bennay, M. Fedrowitz, J. H. Rehders and A. Richter, Altered discharge pattern of basal ganglia output neurons in an animal model of idiopathic dystonia, J. Neurosci., 22 (2002), 7244-7253. |
[12] |
M. T. Giraudo and L. Sacerdote, An improved technique for the simulation of first passage times for diffusion processes, Comm. Statist. Simulation Comput., 28 (1999), 1135-1163.
doi: 10.1080/03610919908813596. |
[13] |
L. L. Gollo, C. R. Mirasso and A. E. P. Villa, Dynamic control for synchronization of separated cortical areas through thalamic relay, NeuroImage, 52 (2010), 947-955.
doi: 10.1016/j.neuroimage.2009.11.058. |
[14] |
M. Häusser and B. A. Clark, Tonic synaptic inhibition modulates neuronal output pattern and spatiotemporal synaptic integration, Neuron, 19 (1997), 665-678. |
[15] |
E. R. Kandel, J. H. Schwartz and T. M. Jessell, Principles of Neural Science, Vol. 4, McGraw-Hill, New York, 2000. |
[16] |
P. Lánský, On approximations of Stein's neuronal model, J. Theor. Biol., 107 (1984), 631-647. |
[17] |
M. W. Levine and J. M. Shefner, A model for the variability of interspike intervals during sustained firing of a retinal neuron, Biophysical Journal, 19 (1977), 241-252.
doi: 10.1016/S0006-3495(77)85584-7. |
[18] |
Y. Loewenstein, S. Mahon, P. Chadderton, K. Kitamura, H. Sompolinsky, Y. Yarom and M. Häusser, Bistability of cerebellar Purkinje cells modulated by sensory stimulation, Nature Neuroscience, 8 (2005), 202-211.
doi: 10.1038/nn1393. |
[19] |
A. Longtin, Stochastic resonance in neuron models, Journal of Statistical Physics, 70 (1993), 309-327.
doi: 10.1007/BF01053970. |
[20] |
A. Longtin, A. Bulsara and F. Moss, Time interval sequences in the bistable systems and the noise-induced transmission of information by sensory neurons, Phys. Rev. Lett., 67 (1991), 656-659.
doi: 10.1103/PhysRevLett.67.656. |
[21] |
M. Musila and P. Lánský, Generalized Stein's model for anatomically complex neurons, Biosystems, 25 (1991), 179-191.
doi: 10.1016/0303-2647(91)90004-5. |
[22] |
A. G. Nobile, L. M. Ricciardi and L. Sacerdote, Exponential trends of Ornstein-Uhlenbeck first-passage-time densities, J. Appl. Probab., 22 (1985), 360-369.
doi: 10.2307/3213779. |
[23] |
L. M. Ricciardi, Diffusion approximation for a multi-input model neuron, Biological Cybernetics, 24 (1976), 237-240.
doi: 10.1007/BF00335984. |
[24] |
L. Sacerdote and R. Sirovich, Multimodality of the interspike interval distribution in a simple jump-diffusion model, Sci. Math. Jpn., 58 (2003), 307-322. |
[25] |
J. P. Segundo, J. F. Vibert, K. Pakdaman, M. Stiber and O. Diez-Martinez, Noise and the neurosciences: A long history, a recent revival and some theory, Origins: Brain and Self Organization, (1994), 299-331. |
[26] |
T. Shimokawa, K. Pakdaman and S. Sato, Time-scale matching in the response of a leaky integrate-and-fire neuron model to periodic stimulus with additive noise, Phys. Rev. E, 59 (1999), 3427-3443.
doi: 10.1103/PhysRevE.59.3427. |
[27] |
H. C. Tuckwell, Introduction to Theoretical Neurobiology: Volume 2, Nonlinear and Stochastic Theories, Cambridge University Press, 2005. |
[28] |
C. Van Vreeswijk, L. F. Abbott and G. B. Ermentrout, When inhibition not excitation synchronizes neural firing, Journal of Computational Neuroscience, 1 (1994), 313-321. |
[29] |
F. Wan and H. C. Tuckwell, Neuronal firing and input variability, J. Theor. Neurobiol., 1 (1982), 197-218. |
[30] |
K. Wiesenfeld and F. Moss, Stochastic resonance and the benefits of noise: From ice ages to crayfish and squids, Nature, 373 (1995), 33-36.
doi: 10.1038/373033a0. |
[31] |
F. Wörgötter, E. Nelle, B. Li and K. Funke, The influence of corticofugal feedback on the temporal structure of visual responses of cat thalamic relay cells, J. Physiol., 509 (1998), 797-815.
doi: 10.1111/j.1469-7793.1998.797bm.x. |
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