Mathematical Neuroscience and Applications - Latest Publications Latest articles https://mna.episciences.org/img/episciences_sign_50x50.png episciences.org https://mna.episciences.org Sun, 15 Mar 2026 05:17:16 +0000 episciences.org https://mna.episciences.org Mathematical Neuroscience and Applications Mathematical Neuroscience and Applications Ordinal Characterization of Similarity Judgments Thu, 07 Aug 2025 07:43:10 +0000 https://doi.org/10.46298/mna.12457 https://doi.org/10.46298/mna.12457 Victor, Jonathan D. Aguilar, Guillermo Waraich, Suniyya A. Victor, Jonathan D. Aguilar, Guillermo Waraich, Suniyya A. 0 A Quasi-Stationary Approach to Metastability in a System of Spiking Neurons with Synaptic Plasticity Thu, 02 Jan 2025 17:01:25 +0000 https://doi.org/10.46298/mna.7668 https://doi.org/10.46298/mna.7668 André, Morgan Pouzat, Christophe André, Morgan Pouzat, Christophe 0 A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutions Fri, 27 Sep 2024 12:15:32 +0000 https://doi.org/10.46298/mna.12583 https://doi.org/10.46298/mna.12583 Cormier, Quentin Cormier, Quentin 0 Neural Coding as a Statistical Testing Problem Fri, 29 Dec 2023 10:36:36 +0000 https://doi.org/10.46298/mna.10002 https://doi.org/10.46298/mna.10002 Ost, Guilherme Reynaud-Bouret, Patricia Ost, Guilherme Reynaud-Bouret, Patricia 0 Propagation of chaos in mean field networks of FitzHugh-Nagumo neurons Mon, 19 Jun 2023 08:04:38 +0000 https://doi.org/10.46298/mna.9748 https://doi.org/10.46298/mna.9748 Colombani, Laetitia Bris, Pierre Le Colombani, Laetitia Bris, Pierre Le 0 Gabor frames from contact geometry in models of the primary visual cortex Tue, 06 Jun 2023 13:56:08 +0000 https://doi.org/10.46298/mna.9766 https://doi.org/10.46298/mna.9766 Liontou, Vasiliki Marcolli, Matilde Liontou, Vasiliki Marcolli, Matilde 0 On the long time behaviour of single stochastic Hodgkin-Huxley neurons with constant signal, and a construction of circuits of interacting neurons showing self-organized rhythmic oscillations 0$ and backdriving force $\tau>0$, and we call $\vartheta>0$ the signal. We have ergodicity and strong laws of large numbers for various functionals of the process, and characterize 'quiet behaviour' and 'regular spiking' as events whose probability depends on the parameters $(\tau,\sigma)$ and on the signal $\vartheta$. The notions of quiet behaviour and regular spiking allow for a construction of circuits of interacting stochastic Hodgkin-Huxley neurons, combining excitation with inhibition according to a bloc structure along the circuit, on which self-organized rhythmic oscillations can be observed.]]> Mon, 30 Jan 2023 08:47:01 +0000 https://doi.org/10.46298/mna.9279 https://doi.org/10.46298/mna.9279 Höpfner, Reinhard Höpfner, Reinhard 0$ and backdriving force $\tau>0$, and we call $\vartheta>0$ the signal. We have ergodicity and strong laws of large numbers for various functionals of the process, and characterize 'quiet behaviour' and 'regular spiking' as events whose probability depends on the parameters $(\tau,\sigma)$ and on the signal $\vartheta$. The notions of quiet behaviour and regular spiking allow for a construction of circuits of interacting stochastic Hodgkin-Huxley neurons, combining excitation with inhibition according to a bloc structure along the circuit, on which self-organized rhythmic oscillations can be observed.]]> 0 Theoretical study of the emergence of periodic solutions for the inhibitory NNLIF neuron model with synaptic delay Wed, 26 Oct 2022 14:57:14 +0000 https://doi.org/10.46298/mna.7256 https://doi.org/10.46298/mna.7256 Ikeda, Kota Roux, Pierre Salort, Delphine Smets, Didier Ikeda, Kota Roux, Pierre Salort, Delphine Smets, Didier 0 Mean field system of a two-layers neural model in a diffusive regime Thu, 25 Aug 2022 17:55:31 +0000 https://doi.org/10.46298/mna.7570 https://doi.org/10.46298/mna.7570 Erny, Xavier Erny, Xavier 0 Neural Field Models: A mathematical overview and unifying framework Sat, 19 Mar 2022 15:24:28 +0000 https://doi.org/10.46298/mna.7284 https://doi.org/10.46298/mna.7284 Cook, Blake J. Peterson, Andre D. H. Woldman, Wessel Terry, John R. Cook, Blake J. Peterson, Andre D. H. Woldman, Wessel Terry, John R. 0 Analysis of Activity Dependent Development of Topographic Maps in Neural Field Theory with Short Time Scale Dependent Plasticity Fri, 11 Mar 2022 08:48:32 +0000 https://doi.org/10.46298/mna.8390 https://doi.org/10.46298/mna.8390 Gale, Nicholas Rodger, Jennifer Small, Michael Eglen, Stephen Gale, Nicholas Rodger, Jennifer Small, Michael Eglen, Stephen 0 Investigating the integrate and fire model as the limit of a random discharge model: a stochastic analysis perspective Tue, 30 Nov 2021 09:12:22 +0000 https://doi.org/10.46298/mna.7203 https://doi.org/10.46298/mna.7203 Liu, Jian-Guo Wang, Ziheng Xie, Yantong Zhang, Yuan Zhou, Zhennan Liu, Jian-Guo Wang, Ziheng Xie, Yantong Zhang, Yuan Zhou, Zhennan 0 Perceptual spaces and their symmetries: The geometry of color space Thu, 15 Jul 2021 14:46:02 +0000 https://doi.org/10.46298/mna.7108 https://doi.org/10.46298/mna.7108 Vattuone, Nicolás Wachtler, Thomas Samengo, Inés Vattuone, Nicolás Wachtler, Thomas Samengo, Inés 0