-
Previous Article
Approximation of the first passage time density of a Wiener process to an exponentially decaying boundary by two-piecewise linear threshold. Application to neuronal spiking activity
- MBE Home
- This Issue
-
Next Article
On the properties of input-to-output transformations in neuronal networks
A new firing paradigm for integrate and fire stochastic neuronal models
1. | Department of Mathematics "G. Peano", University of Torino, Via Carlo Alberto 10, 10123 Torino |
2. | Department of Mathematics G. Peano, University of Torino, Via Carlo Alberto 10, 10123 - Torino, Italy |
References:
[1] |
J. Abate and W. Whitt, The fourier-series method for inverting transforms of probability distributions, Queueing Systems, 10 (1992), 5-87.
doi: 10.1007/BF01158520. |
[2] |
J. Abate and W. Whitt, Numerical inversion of laplace transforms of probability distributions, ORSA Journal on Computing, 7 (1995), 36-43.
doi: 10.1287/ijoc.7.1.36. |
[3] |
L. Alili, P. Patie and J. L. Pedersen, Representations of the first hitting time density of an Ornstein-Uhlenbeck process, Stochastic Models, 21 (2005), 967-980.
doi: 10.1080/15326340500294702. |
[4] |
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. |
[5] |
E. Bibbona and S. Ditlevsen, Estimation in discretely observed diffusions killed at a threshold, Scandinavian Journal of Statistics, 40 (2013), 274-293.
doi: 10.1111/j.1467-9469.2012.00810.x. |
[6] |
E. Bibbona, P. Lansky, L. Sacerdote and R. Sirovich, Errors in estimation of the input signal for integrate-and-fire euronal models, Physical Review E, 78 (2008), 011918. |
[7] |
E. Bibbona, P. Lansky, L. Sacerdote and R. Sirovich, Estimating input parameters from intracellular recordings in the Feller neuronal model, Physical Review E, 81 (2010), 031916.
doi: 10.1103/PhysRevE.81.031916. |
[8] |
A. Buonocore, L. Caputo, E. Pirozzi and M. F. Carfora, Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons, Mathematical Biosciences and Engineering, 11 (2014), 189-201. |
[9] |
A. Buonocore, A. G. Nobile and L. M. Ricciardi, A new integral equation for the evaluation of first-passage-time probability densities, Advances in Applied Probability, 19 (1987), 784-800.
doi: 10.2307/1427102. |
[10] |
A. N. Burkitt, A review of the integrate-and-fire neuron model. I. Homogeneous synaptic input, Biological Cybernetics, 95 (2006), 1-19.
doi: 10.1007/s00422-006-0068-6. |
[11] |
A. N. Burkitt, A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties, Biological Cybernetics, 95 (2006), 97-112.
doi: 10.1007/s00422-006-0082-8. |
[12] |
M. J. Caceres and B. Perthame, Beyond blow-up in excitatory integrate and fire neuronal networks: Refractory period and spontaneous activity, Journal of Theoretical Biology, 350 (2014), 81-89.
doi: 10.1016/j.jtbi.2014.02.005. |
[13] |
S. Cavallari, S. Panzeri and A. Mazzoni, Comparison of the dynamics of neural interactions between current-based and conductance-based integrate-and-fire recurrent networks, Frontiers in Neural Circuits, 8 (2014), p11.
doi: 10.3389/fncir.2014.00012. |
[14] |
M. Chesney, M. Jeanblanc-Picqué and M. Yor, Brownian excursions and Parisian barrier options, Advances in Applied Probabability, 29 (1997), 165-184.
doi: 10.2307/1427865. |
[15] |
S. Ditlevsen and O. Ditlevsen, Parameter estimation from observations of first-passage times of the Ornstein-Uhlenbeck process and the Feller process, Probabilistic Engineering Mechanics, 23 (2008), 170-179.
doi: 10.1016/j.probengmech.2007.12.024. |
[16] |
S. Ditlevsen and P. Lansky, Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model, Physical Review. E (3), 71 (2005), 011907, 9pp.
doi: 10.1103/PhysRevE.71.011907. |
[17] |
S. Ditlevsen and P. Lansky, Estimation of the input parameters in the Feller neuronal model, Physical Review E, 73 (2006), 061910, 9pp.
doi: 10.1103/PhysRevE.73.061910. |
[18] |
G. Dumont and J. Henry, Population density models of integrate-and-fire neurons with jumps: Well-posedness, Journal of Mathematical Biology, 67 (2013), 453-481.
doi: 10.1007/s00285-012-0554-5. |
[19] |
G. Dumont and J. Henry, Synchronization of an excitatory integrate-and-fire neural network, Bulletin of Mathematical Biology, 75 (2013), 629-648.
doi: 10.1007/s11538-013-9823-8. |
[20] |
A. Elbert and M. E. Muldoon, Inequalities and monotonicity properties for zeros of hermite functions, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 129 (1999), 57-75.
doi: 10.1017/S0308210500027463. |
[21] |
G. L. Gerstein and B. Mandelbrot, Random walk models for the spike activity of a single neuron, Biophysical Journal, 4 (1964), 41-68.
doi: 10.1016/S0006-3495(64)86768-0. |
[22] |
W. Gerstner and W. M. Kistler, Spiking Neuron Models: Single Neurons, Populations, Plasticity, Cambridge University Press, 2002.
doi: 10.1017/CBO9780511815706. |
[23] |
R. K. Getoor, Excursions of a Markov process, Annals of Probability, 7 (1979), 244-266.
doi: 10.1214/aop/1176995086. |
[24] |
V. Giorno, G. Nobile, L. M. Ricciardi and S. Sato, On the evaluation of first-passage-time probability densities via non-singular integral, Advances in Applied Probability, 21 (1989), 20-36.
doi: 10.2307/1427196. |
[25] |
M. T. Giraudo, P. Greenwood and L. Sacerdote, How sample paths of leaky integrate-and-fire models are influenced by the presence of a firing threshold, Neural Computation, 23 (2011), 1743-1767.
doi: 10.1162/NECO_a_00143. |
[26] |
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. |
[27] |
D. Grytskyy, T. Tetzlaff, M. Diesmann and M. Helias, A unified view on weakly correlated recurrent networks, Frontiers in Computational Neuroscience, 7 (2013), p131.
doi: 10.3389/fncom.2013.00131. |
[28] |
J. Inoue, S. Sato and L. M. Ricciardi, On the parameter estimation for diffusion models of single neuron's activities, Biological Cybernetics, 73 (1995), 209-221.
doi: 10.1007/BF00201423. |
[29] |
K. Itô, Poisson point processes attached to Markov processes, in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, Univ. California Press, Berkeley, Calif., 1972, 225-239. |
[30] |
R. Jolivet, A. Rauch, H. Lüscher and W. Gerstner, Integrate-and-fire models with adaptation are good enough, in Advances in Neural Information Processing Systems 18 (eds. Y. Weiss, B. Sch\"olkopf and J. Platt), MIT Press, 2006, 595-602. |
[31] |
I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Vol. 113, Springer-Verlag, 1991.
doi: 10.1007/978-1-4612-0949-2. |
[32] |
R. Kobayashi, Y. Tsubo and S. Shinomoto, Made-to-order spiking neuron model equipped with a multi-timescale adaptive threshold, Frontiers in Computational Neuroscience, 3 (2009), p9.
doi: 10.3389/neuro.10.009.2009. |
[33] |
A. Koutsou, J. Kanev and C. Christodoulou, Measuring input synchrony in the Ornstein-Uhlenbeck neuronal model through input parameter estimation, Brain Research, 1536 (2013), 97-106.
doi: 10.1016/j.brainres.2013.05.012. |
[34] |
P. Lansky, Inference for the diffusion models of neuronal activity, Mathematical Bioscience, 67 (1983), 247-260.
doi: 10.1016/0025-5564(83)90103-7. |
[35] |
P. Lansky and S. Ditlevsen, A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models, Biological Cybernetics, 99 (2008), 253-262.
doi: 10.1007/s00422-008-0237-x. |
[36] |
P. Lánskỳ, R. Rodriguez and L. Sacerdote, Mean instantaneous firing frequency is always higher than the firing rate, Neural Computation, 16 (2004), 477-489. |
[37] |
P. Lansky, P. Sanda and J. He, The parameters of the stochastic leaky integrate-and-fire neuronal model, Journal of Computational Neuroscence, 21 (2006), 211-223.
doi: 10.1007/s10827-006-8527-6. |
[38] |
N. Lebedev, Special Functions and Their Applications, Courier Corporation, 1972. |
[39] |
B. Lindner, M. J. Chacron and A. Longtin, Integrate-and-fire neurons with threshold noise: A tractable model of how interspike interval correlations affect neuronal signal transmission, Physical Review E, 72 (2005), 021911, 21pp.
doi: 10.1103/PhysRevE.72.021911. |
[40] |
B. Øksendal, Stochastic Differential Equations, Springer-Verlag, 2003.
doi: 10.1007/978-3-642-14394-6. |
[41] |
J. Pitman and M. Yor, Hitting, occupation and inverse local times of one-dimensional diffusions: Martingale and excursion approaches, Bernoulli, 9 (2003), 1-24.
doi: 10.3150/bj/1068129008. |
[42] |
L. M. Ricciardi, Diffusion Processes and Related Topics in Biology, Springer-Verlag, Berlin-New York, 1977. |
[43] |
L. M. Ricciardi and L. Sacerdote, The Ornstein-Uhlenbeck process as a model for neuronal activity, Biological Cybernetics, 35 (1979), 1-9.
doi: 10.1007/BF01845839. |
[44] |
M. J. Richardson, Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive, Physical Review E, 76 (2007), 021919.
doi: 10.1103/PhysRevE.76.021919. |
[45] |
L. C. G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales. Vol. 2, Cambridge University Press, Cambridge, 2000. |
[46] |
L. Sacerdote and M. T. Giraudo, Stochastic integrate and fire models: A review on mathematical methods and their applications, in Stochastic Biomathematical Models, Lecture Notes in Math., 2058, Springer, Heidelberg, 2013, 99-148.
doi: 10.1007/978-3-642-32157-3_5. |
[47] |
S. Sato, On the moments of the firing interval of the diffusion approximated model neuron, Mathematical Bioscience, 39 (1978), 53-70.
doi: 10.1016/0025-5564(78)90027-5. |
[48] |
M. Tamborrino, S. Ditlevsen and P. Lansky, Parameter inference from hitting times for perturbed Brownian motion, Lifetime Data Analysis, 21 (2015), 331-352.
doi: 10.1007/s10985-014-9307-7. |
[49] |
M. Tamborrino, L. Sacerdote and M. Jacobsen, Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Physica D: Nonlinear Phenomena, 288 (2014), 45-52.
doi: 10.1016/j.physd.2014.08.003. |
[50] |
H. C. Tuckwell, Introduction to Theoretical Neurobiology. Vol. 1. Linear Cable Theory and Dendritic Structure, Cambridge Studies in Mathematical Biology, 8, Cambridge University Press, Cambridge, 1988. |
[51] |
H. C. Tuckwell, Introduction to theoretical neurobiology. Vol. 2. Nonlinear and Stochastic Theories, Cambridge Studies in Mathematical Biology, 8, Cambridge University Press, Cambridge, 1988. |
[52] |
Y. Yu, Y. Xiong, Y. Chan and J. He, Corticofugal gating of auditory information in the thalamus: An in vivo intracellular recording study, The Journal of Neuroscience, 24 (2004), 3060-3069.
doi: 10.1523/JNEUROSCI.4897-03.2004. |
show all references
References:
[1] |
J. Abate and W. Whitt, The fourier-series method for inverting transforms of probability distributions, Queueing Systems, 10 (1992), 5-87.
doi: 10.1007/BF01158520. |
[2] |
J. Abate and W. Whitt, Numerical inversion of laplace transforms of probability distributions, ORSA Journal on Computing, 7 (1995), 36-43.
doi: 10.1287/ijoc.7.1.36. |
[3] |
L. Alili, P. Patie and J. L. Pedersen, Representations of the first hitting time density of an Ornstein-Uhlenbeck process, Stochastic Models, 21 (2005), 967-980.
doi: 10.1080/15326340500294702. |
[4] |
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. |
[5] |
E. Bibbona and S. Ditlevsen, Estimation in discretely observed diffusions killed at a threshold, Scandinavian Journal of Statistics, 40 (2013), 274-293.
doi: 10.1111/j.1467-9469.2012.00810.x. |
[6] |
E. Bibbona, P. Lansky, L. Sacerdote and R. Sirovich, Errors in estimation of the input signal for integrate-and-fire euronal models, Physical Review E, 78 (2008), 011918. |
[7] |
E. Bibbona, P. Lansky, L. Sacerdote and R. Sirovich, Estimating input parameters from intracellular recordings in the Feller neuronal model, Physical Review E, 81 (2010), 031916.
doi: 10.1103/PhysRevE.81.031916. |
[8] |
A. Buonocore, L. Caputo, E. Pirozzi and M. F. Carfora, Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons, Mathematical Biosciences and Engineering, 11 (2014), 189-201. |
[9] |
A. Buonocore, A. G. Nobile and L. M. Ricciardi, A new integral equation for the evaluation of first-passage-time probability densities, Advances in Applied Probability, 19 (1987), 784-800.
doi: 10.2307/1427102. |
[10] |
A. N. Burkitt, A review of the integrate-and-fire neuron model. I. Homogeneous synaptic input, Biological Cybernetics, 95 (2006), 1-19.
doi: 10.1007/s00422-006-0068-6. |
[11] |
A. N. Burkitt, A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties, Biological Cybernetics, 95 (2006), 97-112.
doi: 10.1007/s00422-006-0082-8. |
[12] |
M. J. Caceres and B. Perthame, Beyond blow-up in excitatory integrate and fire neuronal networks: Refractory period and spontaneous activity, Journal of Theoretical Biology, 350 (2014), 81-89.
doi: 10.1016/j.jtbi.2014.02.005. |
[13] |
S. Cavallari, S. Panzeri and A. Mazzoni, Comparison of the dynamics of neural interactions between current-based and conductance-based integrate-and-fire recurrent networks, Frontiers in Neural Circuits, 8 (2014), p11.
doi: 10.3389/fncir.2014.00012. |
[14] |
M. Chesney, M. Jeanblanc-Picqué and M. Yor, Brownian excursions and Parisian barrier options, Advances in Applied Probabability, 29 (1997), 165-184.
doi: 10.2307/1427865. |
[15] |
S. Ditlevsen and O. Ditlevsen, Parameter estimation from observations of first-passage times of the Ornstein-Uhlenbeck process and the Feller process, Probabilistic Engineering Mechanics, 23 (2008), 170-179.
doi: 10.1016/j.probengmech.2007.12.024. |
[16] |
S. Ditlevsen and P. Lansky, Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model, Physical Review. E (3), 71 (2005), 011907, 9pp.
doi: 10.1103/PhysRevE.71.011907. |
[17] |
S. Ditlevsen and P. Lansky, Estimation of the input parameters in the Feller neuronal model, Physical Review E, 73 (2006), 061910, 9pp.
doi: 10.1103/PhysRevE.73.061910. |
[18] |
G. Dumont and J. Henry, Population density models of integrate-and-fire neurons with jumps: Well-posedness, Journal of Mathematical Biology, 67 (2013), 453-481.
doi: 10.1007/s00285-012-0554-5. |
[19] |
G. Dumont and J. Henry, Synchronization of an excitatory integrate-and-fire neural network, Bulletin of Mathematical Biology, 75 (2013), 629-648.
doi: 10.1007/s11538-013-9823-8. |
[20] |
A. Elbert and M. E. Muldoon, Inequalities and monotonicity properties for zeros of hermite functions, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 129 (1999), 57-75.
doi: 10.1017/S0308210500027463. |
[21] |
G. L. Gerstein and B. Mandelbrot, Random walk models for the spike activity of a single neuron, Biophysical Journal, 4 (1964), 41-68.
doi: 10.1016/S0006-3495(64)86768-0. |
[22] |
W. Gerstner and W. M. Kistler, Spiking Neuron Models: Single Neurons, Populations, Plasticity, Cambridge University Press, 2002.
doi: 10.1017/CBO9780511815706. |
[23] |
R. K. Getoor, Excursions of a Markov process, Annals of Probability, 7 (1979), 244-266.
doi: 10.1214/aop/1176995086. |
[24] |
V. Giorno, G. Nobile, L. M. Ricciardi and S. Sato, On the evaluation of first-passage-time probability densities via non-singular integral, Advances in Applied Probability, 21 (1989), 20-36.
doi: 10.2307/1427196. |
[25] |
M. T. Giraudo, P. Greenwood and L. Sacerdote, How sample paths of leaky integrate-and-fire models are influenced by the presence of a firing threshold, Neural Computation, 23 (2011), 1743-1767.
doi: 10.1162/NECO_a_00143. |
[26] |
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. |
[27] |
D. Grytskyy, T. Tetzlaff, M. Diesmann and M. Helias, A unified view on weakly correlated recurrent networks, Frontiers in Computational Neuroscience, 7 (2013), p131.
doi: 10.3389/fncom.2013.00131. |
[28] |
J. Inoue, S. Sato and L. M. Ricciardi, On the parameter estimation for diffusion models of single neuron's activities, Biological Cybernetics, 73 (1995), 209-221.
doi: 10.1007/BF00201423. |
[29] |
K. Itô, Poisson point processes attached to Markov processes, in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, Univ. California Press, Berkeley, Calif., 1972, 225-239. |
[30] |
R. Jolivet, A. Rauch, H. Lüscher and W. Gerstner, Integrate-and-fire models with adaptation are good enough, in Advances in Neural Information Processing Systems 18 (eds. Y. Weiss, B. Sch\"olkopf and J. Platt), MIT Press, 2006, 595-602. |
[31] |
I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Vol. 113, Springer-Verlag, 1991.
doi: 10.1007/978-1-4612-0949-2. |
[32] |
R. Kobayashi, Y. Tsubo and S. Shinomoto, Made-to-order spiking neuron model equipped with a multi-timescale adaptive threshold, Frontiers in Computational Neuroscience, 3 (2009), p9.
doi: 10.3389/neuro.10.009.2009. |
[33] |
A. Koutsou, J. Kanev and C. Christodoulou, Measuring input synchrony in the Ornstein-Uhlenbeck neuronal model through input parameter estimation, Brain Research, 1536 (2013), 97-106.
doi: 10.1016/j.brainres.2013.05.012. |
[34] |
P. Lansky, Inference for the diffusion models of neuronal activity, Mathematical Bioscience, 67 (1983), 247-260.
doi: 10.1016/0025-5564(83)90103-7. |
[35] |
P. Lansky and S. Ditlevsen, A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models, Biological Cybernetics, 99 (2008), 253-262.
doi: 10.1007/s00422-008-0237-x. |
[36] |
P. Lánskỳ, R. Rodriguez and L. Sacerdote, Mean instantaneous firing frequency is always higher than the firing rate, Neural Computation, 16 (2004), 477-489. |
[37] |
P. Lansky, P. Sanda and J. He, The parameters of the stochastic leaky integrate-and-fire neuronal model, Journal of Computational Neuroscence, 21 (2006), 211-223.
doi: 10.1007/s10827-006-8527-6. |
[38] |
N. Lebedev, Special Functions and Their Applications, Courier Corporation, 1972. |
[39] |
B. Lindner, M. J. Chacron and A. Longtin, Integrate-and-fire neurons with threshold noise: A tractable model of how interspike interval correlations affect neuronal signal transmission, Physical Review E, 72 (2005), 021911, 21pp.
doi: 10.1103/PhysRevE.72.021911. |
[40] |
B. Øksendal, Stochastic Differential Equations, Springer-Verlag, 2003.
doi: 10.1007/978-3-642-14394-6. |
[41] |
J. Pitman and M. Yor, Hitting, occupation and inverse local times of one-dimensional diffusions: Martingale and excursion approaches, Bernoulli, 9 (2003), 1-24.
doi: 10.3150/bj/1068129008. |
[42] |
L. M. Ricciardi, Diffusion Processes and Related Topics in Biology, Springer-Verlag, Berlin-New York, 1977. |
[43] |
L. M. Ricciardi and L. Sacerdote, The Ornstein-Uhlenbeck process as a model for neuronal activity, Biological Cybernetics, 35 (1979), 1-9.
doi: 10.1007/BF01845839. |
[44] |
M. J. Richardson, Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive, Physical Review E, 76 (2007), 021919.
doi: 10.1103/PhysRevE.76.021919. |
[45] |
L. C. G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales. Vol. 2, Cambridge University Press, Cambridge, 2000. |
[46] |
L. Sacerdote and M. T. Giraudo, Stochastic integrate and fire models: A review on mathematical methods and their applications, in Stochastic Biomathematical Models, Lecture Notes in Math., 2058, Springer, Heidelberg, 2013, 99-148.
doi: 10.1007/978-3-642-32157-3_5. |
[47] |
S. Sato, On the moments of the firing interval of the diffusion approximated model neuron, Mathematical Bioscience, 39 (1978), 53-70.
doi: 10.1016/0025-5564(78)90027-5. |
[48] |
M. Tamborrino, S. Ditlevsen and P. Lansky, Parameter inference from hitting times for perturbed Brownian motion, Lifetime Data Analysis, 21 (2015), 331-352.
doi: 10.1007/s10985-014-9307-7. |
[49] |
M. Tamborrino, L. Sacerdote and M. Jacobsen, Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Physica D: Nonlinear Phenomena, 288 (2014), 45-52.
doi: 10.1016/j.physd.2014.08.003. |
[50] |
H. C. Tuckwell, Introduction to Theoretical Neurobiology. Vol. 1. Linear Cable Theory and Dendritic Structure, Cambridge Studies in Mathematical Biology, 8, Cambridge University Press, Cambridge, 1988. |
[51] |
H. C. Tuckwell, Introduction to theoretical neurobiology. Vol. 2. Nonlinear and Stochastic Theories, Cambridge Studies in Mathematical Biology, 8, Cambridge University Press, Cambridge, 1988. |
[52] |
Y. Yu, Y. Xiong, Y. Chan and J. He, Corticofugal gating of auditory information in the thalamus: An in vivo intracellular recording study, The Journal of Neuroscience, 24 (2004), 3060-3069.
doi: 10.1523/JNEUROSCI.4897-03.2004. |
[1] |
Gengen Zhang. Time splitting combined with exponential wave integrator Fourier pseudospectral method for quantum Zakharov system. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2587-2606. doi: 10.3934/dcdsb.2021149 |
[2] |
Qiuying Li, Lifang Huang, Jianshe Yu. Modulation of first-passage time for bursty gene expression via random signals. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1261-1277. doi: 10.3934/mbe.2017065 |
[3] |
Massimiliano Tamborrino. Approximation of the first passage time density of a Wiener process to an exponentially decaying boundary by two-piecewise linear threshold. Application to neuronal spiking activity. Mathematical Biosciences & Engineering, 2016, 13 (3) : 613-629. doi: 10.3934/mbe.2016011 |
[4] |
Emmanuel Frénod, Sever A. Hirstoaga, Eric Sonnendrücker. An exponential integrator for a highly oscillatory vlasov equation. Discrete and Continuous Dynamical Systems - S, 2015, 8 (1) : 169-183. doi: 10.3934/dcdss.2015.8.169 |
[5] |
Omer Gursoy, Kamal Adli Mehr, Nail Akar. Steady-state and first passage time distributions for waiting times in the $ MAP/M/s+G $ queueing model with generally distributed patience times. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021078 |
[6] |
Jinglai Qiao, Li Yang, Jiawei Yao. Passive control for a class of Nonlinear systems by using the technique of Adding a power integrator. Numerical Algebra, Control and Optimization, 2020, 10 (3) : 381-389. doi: 10.3934/naco.2020009 |
[7] |
Adrian Viorel, Cristian D. Alecsa, Titus O. Pinţa. Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems. Discrete and Continuous Dynamical Systems, 2021, 41 (7) : 3319-3341. doi: 10.3934/dcds.2020407 |
[8] |
Mei Luo, Jinrong Wang, Yumei Liao. Bounded consensus of double-integrator stochastic multi-agent systems. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022088 |
[9] |
Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora. A simple algorithm to generate firing times for leaky integrate-and-fire neuronal model. Mathematical Biosciences & Engineering, 2014, 11 (1) : 1-10. doi: 10.3934/mbe.2014.11.1 |
[10] |
Achilleas Koutsou, Jacob Kanev, Maria Economidou, Chris Christodoulou. Integrator or coincidence detector --- what shapes the relation of stimulus synchrony and the operational mode of a neuron?. Mathematical Biosciences & Engineering, 2016, 13 (3) : 521-535. doi: 10.3934/mbe.2016005 |
[11] |
Antoine Tambue, Jean Daniel Mukam. Magnus-type integrator for non-autonomous SPDEs driven by multiplicative noise. Discrete and Continuous Dynamical Systems, 2020, 40 (8) : 4597-4624. doi: 10.3934/dcds.2020194 |
[12] |
Zsolt Saffer, Wuyi Yue. A dual tandem queueing system with GI service time at the first queue. Journal of Industrial and Management Optimization, 2014, 10 (1) : 167-192. doi: 10.3934/jimo.2014.10.167 |
[13] |
Canghua Jiang, Zhiqiang Guo, Xin Li, Hai Wang, Ming Yu. An efficient adjoint computational method based on lifted IRK integrator and exact penalty function for optimal control problems involving continuous inequality constraints. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1845-1865. doi: 10.3934/dcdss.2020109 |
[14] |
Guoliang Zhang, Shaoqin Zheng, Tao Xiong. A conservative semi-Lagrangian finite difference WENO scheme based on exponential integrator for one-dimensional scalar nonlinear hyperbolic equations. Electronic Research Archive, 2021, 29 (1) : 1819-1839. doi: 10.3934/era.2020093 |
[15] |
Fabio Giannoni, Paolo Piccione, Daniel V. Tausk. Morse theory for the travel time brachistochrones in stationary spacetimes. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 697-724. doi: 10.3934/dcds.2002.8.697 |
[16] |
Ernst Eberlein, Dilip B. Madan. Portfolio theory for squared returns correlated across time. Probability, Uncertainty and Quantitative Risk, 2016, 1 (0) : 1-. doi: 10.1186/s41546-016-0001-4 |
[17] |
Meiqiao Ai, Zhimin Zhang, Wenguang Yu. First passage problems of refracted jump diffusion processes and their applications in valuing equity-linked death benefits. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1689-1707. doi: 10.3934/jimo.2021039 |
[18] |
Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control and Related Fields, 2012, 2 (2) : 195-215. doi: 10.3934/mcrf.2012.2.195 |
[19] |
Laurenz Göllmann, Helmut Maurer. Theory and applications of optimal control problems with multiple time-delays. Journal of Industrial and Management Optimization, 2014, 10 (2) : 413-441. doi: 10.3934/jimo.2014.10.413 |
[20] |
David Grant, Mahesh K. Varanasi. Duality theory for space-time codes over finite fields. Advances in Mathematics of Communications, 2008, 2 (1) : 35-54. doi: 10.3934/amc.2008.2.35 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]