Bibliography

Major publications by the team in recent years

• 1B. Aymard, F. Clément, F. Coquel, M. Postel.
  
  Numerical simulation of the selection process of the ovarian follicles, in: ESAIM Proc., 2012, vol. 28, pp. 99-117.
• 2B. Aymard, F. Clément, F. Coquel, M. Postel.
  
  A numerical method for cell dynamics; kinetic equations with discontinuous coefficients, in: SIAM J. Sci. Comput., 2013, vol. 35, pp. A2442-A2468.
• 3B. Aymard, F. Clément, M. Postel.
  
  Adaptive mesh refinement strategy for a non conservative transport problem, in: ESAIM Math. Model. Numer. Anal., 2014, vol. 90, 4 p.
• 4J. Burke, M. Desroches, A. Barry, T. Kaper, M. Kramer.
  
  A showcase of torus canards in neuronal bursters, in: J. Math. Neurosci., 2012, vol. 2.
• 5F. Clément, J.-M. Coron, P. Shang.
  
  Optimal control of cell mass and maturity in a model of follicular ovulation, in: SIAM J. Control Optim., 2013, vol. 51, n^o 2, pp. 824-847.
• 6F. Clément, P. Michel, D. Monniaux, T. Stiehl.
  
  Coupled somatic cell kinetics and germ cell growth: multiscale model-based insight on ovarian follicular development, in: Multiscale Model. Simul., 2013, vol. 11, n^o 3, pp. 719-746.
• 7F. Clément, D. Monniaux.
  
  Multiscale modelling of follicular selection, in: Prog. Biophys. Mol. Biol., 2013, vol. 113, pp. 398-408.
• 8M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. Osinga, M. Wechselberger.
  
  Mixed-mode oscillations with multiple time scales, in: SIAM Rev., 2012, vol. 54, pp. 211–288.
• 9D. Heitzler, G. Durand, A. Rizk, S. Ahn, J. Kim, J. Violin, L. Dupuy, C. Gauthier, V. Piketty, P. Crépieux, A. Poupon, F. Clément, F. Fages, R. Lefkowitz, E. Reiter.
  
  Competing G protein-coupled receptor kinases balance G protein and $\beta$-arrestin signaling, in: Mol. Syst. Biol., 2012, vol. 8, n^o 590.
• 10M. Krupa, A. Vidal, F. Clément.
  
  A network model of the periodic synchronization process in the dynamics of calcium concentration in GnRH neurons, in: J. Math. Neurosci., 2013, vol. 3, 4 p.
• 11P. Shang.
  
  Cauchy problem for multiscale conservation laws: Application to structured cell populations, in: J. Math. Anal. Appl., 2013, vol. 401, n^o 2, pp. 896-920.
• 12J. Touboul.
  
  Limits and dynamics of stochastic neuronal networks with random delays, in: J. Stat. Phys., 2012, n^o 149, pp. 569–597.
• 13J. Touboul.
  
  Mean-Field equations for stochastic firing-rate neural fields with delays: derivation and noise-induced transitions, in: Phys. D, 2012, vol. 241, pp. 1223–1244.
• 14J. Touboul.
  
  Propagation Of Chaos In Neural Fields, in: Ann. Appl. Probab., 2014, vol. 24, n^o 3, pp. 1298–1327.
• 15A. Vidal, Q. Zhang, C. Médigue, S. Fabre, F. Clément.
  
  DynPeak: An algorithm for pulse detection and frequency analysis in hormonal time series, in: PloS One, 2012, vol. 7, e39001.

Publications of the year

Articles in International Peer-Reviewed Journals

• 16M. Desroches, J.-P. Françoise, L. Mégret.
  
  Canard-induced loss of stability across a homoclinic bifurcation, in: Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, June 2015, vol. 20, 15 p.
  
  https://hal.inria.fr/hal-01093445
• 17S. Fernández-García, M. Desroches, M. Krupa, F. Clément.
  
  A Multiple Time Scale Coupling of Piecewise Linear Oscillators. Application to a Neuroendocrine System, in: SIAM Journal on Applied Dynamical Systems, April 2015, vol. 14, n^o 2, 31 p. [ DOI : 10.1137/140984464 ]
  
  https://hal.inria.fr/hal-01146225
• 18S. Fernández-García, M. Desroches, M. Krupa, A. Teruel.
  
  Canard solutions in planar piecewise linear systems with three zones, in: Dynamical Systems, September 2015, 25 p. [ DOI : 10.1080/14689367.2015.1079304 ]
  
  https://hal.inria.fr/hal-01244978
• 19L.-C.-L. Hsu, S. Nam, Y. Cui, C.-P. Chang, C.-F. Wang, H.-C. Kuo, J. Touboul, S.-J. Chou.
  
  Lhx2 regulates the timing of β-catenin-dependent cortical neurogenesis, in: Proceeding of the national academy of sciences, 2015, vol. 112, n^o 39, pp. 12199-204. [ DOI : 10.1073/pnas.1507145112 ]
  
  https://hal.archives-ouvertes.fr/hal-01253416
• 20M. Krupa, J. Touboul.
  
  Canard explosion in delayed equations with multiple timescales, in: Journal of Dynamics and Differential Equations, 2015, 21 p.
  
  https://hal.archives-ouvertes.fr/hal-01253412
• 21M. Krupa, J. Touboul.
  
  Complex oscillations in the delayed van der Pol equation, in: Journal of Nonlinear Science, 2015, vol. 26, n^o 1, 38 p.
  
  https://hal.archives-ouvertes.fr/hal-01253413
• 22B. Perthame, C. Quiñinao, J. Touboul.
  
  Competition and boundary formation in heterogeneous media: Application to neuronal differentiation, in: Mathematical Models and Methods in Applied Sciences (M3AS), 2015, vol. 25, n^o 13, pp. 2477–2502. [ DOI : 10.1142/S0218202515400151 ]
  
  https://hal.archives-ouvertes.fr/hal-01054813
• 23C. Quiñinao, A. Prochiantz, J. Touboul.
  
  Local homeoprotein diffusion can stabilize boundaries generated by graded positional cues, in: Development, 2015, vol. 142, n^o 10, 8 p.
  
  https://hal.archives-ouvertes.fr/hal-01253419
• 24C. Quiñinao, J. Touboul.
  
  Limits and dynamics of randomly connected neuronal networks, in: Acta Applicandae Mathematicae, 2015, vol. 136, n^o 1, pp. 167-192.
  
  https://hal.archives-ouvertes.fr/hal-01054802
• 25J. Ribot, A. Romagnoni, C. Milleret, D. Bennequin, J. Touboul.
  
  Pinwheel-dipole configuration in cat early visual cortex, in: NeuroImage, 2015, vol. 128, pp. 63–73. [ DOI : 10.1016/j.neuroimage.2015.12.022 ]
  
  https://hal.archives-ouvertes.fr/hal-01253408
• 26A. Romagnoni, J. Ribot, D. Bennequin, J. Touboul.
  
  Parsimony, exhaustivity and balanced detection in neocortex, in: PLoS Computational Biology, 2015, vol. 11, n^o 11, 17 p. [ DOI : 10.1371/journal.pcbi.1004623 ]
  
  https://hal.archives-ouvertes.fr/hal-01253410
• 27J. Signerska-Rynkowska.
  
  Analysis of Interspike-Intervals for the General Class of Integrate-and-Fire Models with Periodic Drive, in: Mathematical Modelling and Numerical Analysis, September 2015, vol. 20, n^o 5, 22 p. [ DOI : 10.3846/13926292.2015.1085459 ]
  
  https://hal.inria.fr/hal-01256353
• 28J. Touboul, M. Krupa, M. Desroches.
  
  Noise-induced canard and mixed-mode oscillations in large stochastic networks with multiple timescales , in: SIAM Journal on Applied Mathematics, 2015, vol. 75, n^o 5, 26 p.
  
  https://hal.archives-ouvertes.fr/hal-01253417
• 29J. Touboul, G. Wainrib.
  
  Absorption properties of stochastic equations with Hölder diffusion coefficients, in: Physica D: Nonlinear Phenomena, 2015, vol. 307, 18 p.
  
  https://hal.archives-ouvertes.fr/hal-01253418

Other Publications

• 30B. Aymard, F. Clément, D. Monniaux, M. Postel.
  
  Cell-kinetics based calibration of a multiscale model: Application to cell population dynamics in ovarian follicles, August 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01186381
• 31M. Desroches, S. Fernández-García, M. Krupa.
  
  Canards and spike-adding transitions in a minimal piecewise-linear Hindmarsh-Rose square-wave burster, December 2015, submitted for publication.
  
  https://hal.inria.fr/hal-01243302
• 32E. Köksal-Ersöz, M. Desroches, M. Krupa, F. Clément.
  
  Canard-Mediated (De)Synchronization in Coupled Phantom Bursters, January 2016, To appear in SIAM Journal on Applied Dynamical Systems.
  
  https://hal.inria.fr/hal-01256389
• 33S. Mischler, C. Quiñinao, J. Touboul.
  
  On a Kinetic Fitzhugh–Nagumo Model of Neuronal Network, January 2016, working paper or preprint. [ DOI : 10.1007/s00220-015-2556-9 ]
  
  https://hal.archives-ouvertes.fr/hal-01108872
• 34P. Robert, J. Touboul.
  
  On the dynamics of random neuronal networks, May 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01075242
• 35J. Signerska-Rynkowska, J. Touboul, A. Vidal.
  
  A geometric mechanism for mixed-mode bursting oscillations in a hybrid neuron model, January 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01256368

References in notes

• 36P. Bressloff.
  
  Spatiotemporal dynamics of continuum neural fields, in: J. Phys. A: Math. Theor., 2012, vol. 45, pp. 033001–.
• 37F. Clément, A. Vidal.
  
  Foliation-based parameter tuning in a model of the GnRH pulse and surge generator, in: SIAM J. Appl. Dyn. Syst., 2009, vol. 8, n^o 4, pp. 1591–1631.
• 38F. Clément, J.-P. Françoise.
  
  Mathematical modeling of the GnRH-pulse and surge generator, in: SIAM J. Appl. Dyn. Syst., 2007, vol. 6, pp. 441-456.
• 39N. Echenim, D. Monniaux, M. Sorine, F. Clément.
  
  Multi-scale modeling of the follicle selection process in the ovary, in: Math. Biosci., 2005, vol. 198, pp. 57-79.
• 40J. Ribot, A. Romagnoni, C. Milleret, D. Bennequin, J. Touboul.
  
  Pinwheel-dipole configuration in cat early visual cortex, 2014, pp. 63–73.
• 41T. Vo, R. Bertram, J. Tabak, M. Wechselberger.
  
  Mixed mode oscillations as a mechanism for pseudo-plateau bursting, in: J. Comput. Neurosci., 2010, vol. 28, n^o 3, pp. 443–458.
• 42H. Wilson, J. Cowan.
  
  Excitatory and inhibitory interactions in localized populations of model neurons, in: Biophys. J., 1972, vol. 12, pp. 1–24.