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                                                  NOISE in NEURAL NETWORKS

Even today a good many distinguished minds seem unable to accept or even to understand that from

a source of noise natural selection could quite unaided have drawn all the music of the biosphere

(Jacques Monod)

  1. Diez A., Suazo V., Casado P., Martin-Loeches M., Victoria Perea M., Molina V.: Frontal gamma noise power and cognitive domains in schizophrenia. Psychiatry Research-Neuroimaging, Vol. 221, no. 1, 2014, pp. 104 – 113. DOI 10.1016/j.pscychresns.2013.11.001

  2. Wang Maosheng, Sun Runzhi : Cooperative effects of inherent stochasticity and random long-range connections on synchronization and coherence resonance in diffusively coupled calcium oscillators. Physica A - Statistical Mechanics and its Applications, Vol. 398, 2014, pp. 243 – 251. DOI 10.1016/j.physa.2013.12.024

  3. Agliari E., Barra A., Galluzzi A., Isopi M.: Multitasking attractor networks with neuronal threshold noise. Neural Networks, Vol. 49, 2014, pp. 19 – 29. DOI 10.1016/j.neunet.2013.09.008

  4. Yang X. L., Jia Y. B., Zhang L.: Impact of bounded noise and shortcuts on the spatiotemporal dynamics of neuronal networks. Physica A - Statistical Mechanics and its Applications, Vol. 393, 2014, pp. 617 – 623. DOI 10.1016/j.physa.2013.09.021

  5. Pisarchik A.N., Jaimes-Reategui R., Magallon-Garcia C.D.A., Castillo-Morales C.O.: Critical slowing down and noise-induced intermittency in bistable preception: bifurcation analysis. Biological Cybernetics, Vol. 108, no. 4, 2014, pp. 397 – 404. DOI 10.1007/s00422-014-0607-5

  6. Pang J.C.S., Monterola C.P., Bantang J.Y.: Noise-induced synchronization in a lattice Hodgkin-Huxley neural network. Physica A - Statistical Mechanics and its Applications, Vol. 393, 2014, pp. 638 – 645. DOI 10.1016/j.physa.2013.08.069

  7. Hui Q., Haddad W.M., Bailey J.M., Hayakawa T.: A Stochastic Mean Field Model for an Excitatory and Inhibitory Synaptic Drive Cortical Neuronal Network. IEEE Trans on Neural Networks and Learning Systems, Vol. 25, no. 4, 2014, pp. 751 – 763. DOI 10.1109/TNNLS.2013.2281065

  8. Guler Marifi: An Investigation of the Stochastic Hodgkin-Huxley Models Under Noisy Rate Functions. Neural Networks, Vol. 25, no. 9, 2013, pp. 2355 – 2372. DOI 10.1162/NECO_a_00487

  9. L'Esperance P.-Y., Labib R.: Model of an Excitatory Synapse Based on Stochastic Processes. IEEE Trans on Neural Networks and Learning Systems, Vol. 24, no. 9, 2013, pp. 1449 – 1458. DOI 10.1109/TNNLS.2013.2260559

  10. Sum J., Chi-Sing Leung, Ho K.: Effect of Input Noise and Output Node Stochastic on Wang's kWTA. IEEE Trans on Neural Networks and Learning Systems, Vol. 24, no. 9, 2013, pp 1472 – 1478. DOI 10.1109/TNNLS.2013.2257182

  11. El-Melegy M.T.: Random Sampler M-Estimator Algorithm With Sequential Probability Ratio Test for Robust Function Approximation Via Feed-Forward Neural Networks. IEEE Trans on Neural Networks and Learning Systems, Vol. 24, no. 7, 2013, pp. 1074 – 1085. DOI 10.1109/TNNLS.2013.2251001

  12. Medvedev G.S., Zhuravytska S.: Shaping bursting by electrical coupling and noise. Biological Cybernetics, Vol. 106, no. 2, 2012, pp. 67 – 88. DOI 10.1007/s00422-012-0481-y

  13. Zeldenrust F., Chameau P.J.P.; Wadman W.J.: Reliability of spike and burst firing in thalamocortical relay cells. Journal of Computational Neuroscience, Vol. 35, no. 3, 2013, pp. 317 – 334. DOI 10.1007/s10827-013-0454-8

  14. Yang Tang, Wai Keung Wong: Distributed Synchronization of Coupled Neural Networks via Randomly Occurring Control. IEEE Trans on Neural Networks and Learning Systems, Vol. 24, no. 3, 2013, pp. 435 – 447. DOI 10.1109/TNNLS.2012.2236355

  15. di Volo M., Livi R.: The influence of noise on synchronous dynamics in a diluted neural network. Chaos Solitons & Fractals, Vol. 57, 2013, pp. 54 – 61. DOI 10.1016/j.chaos.2013.08.012

  16. Lundqvist M., Herman P., Palva M., Palva S., Silverstein D., Lansner A.: Stimulus detection rate and latency, firing rates and 1-40 Hz oscillatory power are modulated by infra-slow fluctuations in a bistable attractor network model. Neuroimage, Vol. 83, 2013, pp. 458 – 471. DOI 10.1016/j.neuroimage.2013.06.080

  17. Girardi-Schappo M., Tragtenberg M. H. R., Kinouchi O. : A brief history of excitable map-based neurons and neural networks. Journal of Neuroscience Methods, Vol. 220, no. 2, 2013, pp. 116 – 130. DOI 10.1016/j.jneumeth.2013.07.014

  18. Wang Q., Zheng Y., Ma Jun: Cooperative dynamics in neuronal networks. Chaos Solitons & Fractals, Vol. 56, Special no. SI, 2013, pp. 19 – 27.  DOI 10.1016/j.chaos.2013.05.003

  19. Uzuntarla M., Uzun R. ,Yilmaz E., Ozer M., Perc M.: Noise-delayed decay in the response of a scale-free neuronal network. Chaos Solitons & Fractals, Vol. 56, Special no. SI, 2013, pp. 202 – 208. DOI 10.1016/j.chaos.2013.08.009

  20. Yilmaz E., Ozer M.: Collective firing regularity of a scale-free Hodgkin-Huxley neuronal network in response to a subthreshold signal. Physics Lett. A, Vol. 377, no. 18, pp. 1301-1307, 2013 DOI 10.1016/j.physleta.2013.03.007

  21. Bordet M., Morfu S.: Experimental and numerical study of noise effects in a FitzHugh-Nagumo system driven by a biharmonic signal. Chaos Solitons & Fractals, Vol. 54, 2013,  pp. 82 – 89.  DOI 10.1016/j.chaos.2013.05.020

  22. Zare Marzieh, Grigolini P.: Criticality and avalanches in neural networks. Chaos Solitons & Fractals, Vol. 55,  Special issue SI, 2013, pp. 80 – 94. DOI 10.1016/j.chaos.2013.05.009

  23. Mueller F., Schimansky-Geier L., Postnov D. E.: Interaction of noise supported Ising-Bloch fronts with Dirichlet boundaries. Ecological Complexity, Vol. 14, Special Issue: SI, 2013, pp. 21 – 36. DOI 10.1016/j.ecocom.2012.11.002

  24. Park In Jun, Bobkov Y.V., Ache B.W., Principe J.C: Quantifying bursting neuron activity from calcium signals using blind deconvolution. Journal of Neuroscience Methods, Vol. 218, no. 2, 2013, pp. 196 – 205. DOI 10.1016/j.jneumeth.2013.05.007

  25. Djeundam S.R.D., Yamapi R., Kofane T.C., Aziz-Alaoui M.A: Deterministic and stochastic bifurcations in the Hindmarsh-Rose neuronal model. Chaos, Vol. 23, no. 3, 2013, Article # 033125. DOI 10.1063/1.4818545

  26. Gong Yubing, Xu Bo, Wu Yanan: Adaptive coupling optimized spiking coherence and synchronization in Newman-Watts neuronal networks. Chaos, Vol. 23, no. 3, 2013, Article # 033105. DOI 10.1063/1.4813224

  27. Cofre R., Cessac B.: Dynamics and spike trains statistics in conductance-based integrate-and-fire neural networks with chemical and electric synapses. Chaos Solitons & Fractals, Vol. 50, Special Issue SI, 2013, pp. 13 – 31. DOI 10.1016/j.chaos.2012.12.006

  28. Zeldenrust F., Wadman W. J.: Modulation of spike and burst rate in a minimal neuronal circuit with feed-forward inhibition. Neural Networks, Vol. 40, 2013, pp. 1 – 17. DOI 10.1016/j.neunet.2012.12.008

  29. Xiaoming Liang, Liang Zhao: Phase-Noise-Induced Resonance in Arrays of Coupled Excitable Neural Models. IEEE Trans on Neural Networks and Learning Systems, Vol. 24, no. 8, 2013, pp.1339 – 1345. DOI 10.1109/TNNLS.2013.2254126

  30. M. G. Riedler, E. Buckwar: Laws of Large Numbers and Langevin Approximations for Stochastic Neural Field Equations. Journal of Mathematical Neuroscience, Vol. 3, no 1, 2013. DOI 10.1186/2190-8567-3-1

  31. D. Holstein, A. V. Goltsev, J. F. F. Mendes: Impact of noise and damage on collective dynamics of scale-free neuronal networks. Phys. Rev. E, Vol. 87, no. 3, 2013, pp 032717-1 – 032717-13. DOI 10.1103/PhysRevE.87.032717

  32. John Sum, Chi-sing Leung, Kevin Ho: Convergence Analyses on On-Line Weight Noise Injection-Based Training Algorithms for MLPs. IEEE Trans on Neural Networks and Learning Systems, Vol. 23, no. 11, 2012, 1827 – 1840. DOI 10.1109/TNNLS.2012.2210243

  33. John Sum, Chi-sing Leung, Kevin Ho: On-Line Node Fault Injection Training Algorithm for MLP Networks: Objective Function and Convergence Analysis. IEEE Trans on Neural Networks and Learning Systems, Vol. 23, no. 2, 2012, pp. 211 – 222. DOI 10.1109/TNNLS.2011.2178477

  34. Lopez C. M., Welkenhuysen M., Musa S., Eberle W., Bartic C., Puers R., Gielen G.: Towards a noise prediction model for in vivo neural recording. IEEE Annual Int. Conf. of Engineering in Medicine and Biology Society (EMBC), 2012, pp. 759 – 762. DOI 10.1109/EMBC.2012.6346042

  35. P. C. Bressloff, M. A. Webber: Front propagation in stochastic neural fields. SIAM J. Appl. Dyn. Syst., Vol. 11, no. 2, 2012, pp 708 – 740. DOI 10.1137/110851031

  36. Chen Hsin, Lu Chih-Chen, Wu Yi-Da, Chiu Tang-Jung: Learning from biological neurons to compute with electronic noise special. IEEE/ACM Int. Conf. on Computer-Aided Design (ICCAD), 2012, pp. 168 – 171. URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6386605&isnumber=6386569

  37. Alijani A. K., Richardson M. J. E.: Rate response of neurons subject to fast or frozen noise: From stochastic and homogeneous to deterministic and heterogeneous populations. Physical Review E, Vol. 84, no. 1, 2011, Article # 011919. DOI 10.1103/PhysRevE.84.011919

  38. Kevin Ho, Chi-sing Leung, John Sum: Objective Functions of the Online Weight noise injection training algorithms for MLP. IEEE Trans on Neural Networks, Vol. 22, no. 2, 2011, pp. 317 – 323. DOI 10.1109/TNN.2010.2095881

  39. Medina J.M., Carvalho J., Franco S.: Properties of neural noise in amblyopia. 21st Int. Conf. on Noise and Fluctuations (ICNF), 2011, pp. 421 – 424. DOI 10.1109/ICNF.2011.5994360

  40. T. Wyckhuys, P. Boon, R. Raedt, B. Van Nieuwenhuyse, K. Vonck, W. Wadman: Suppression of hippocampal epileptic seizures in the kainate rat by Poisson distributed stimulation. Epilepsia, Vol. 51, no. 11, 2010, pp. 2297 – 2304. DOI 10.1111/j.1528-1167.2010.02750.x

  41. P. C. Bressloff: Metastable states and quasicycles in a stochastic Wilson-Cowan model of neural population dynamics. Phys. Rev. E., Vol. 82, no. 5, 2010, pp 051903-1 – 051903-13. DOI 10.1103/PhysRevE.82.051903

  42. Kevin Ho, Chi-sing Leung, John Sum: Analysis on the Convergence and Objective Functions of Some Fault/Noise Injection-Based On-line Learning Algorithms for RBF Networks. IEEE Trans on Neural Networks, Vol. 21, no. 6, 2010, pp. 938 – 947. DOI 10.1109/TNN.2010.2046179

  43. Benayoun M., Cowan J.D., van Drongelen W., Wallace E.: Avalanches in a Stochastic Model of Spiking Neurons. PLoS Comput. Biol., Vol. 6, no. 7, 2010, pp. e1000846. DOI 10.1371/journal.pcbi.1000846

  44. Zeldenrust F., Wadman W. J.: Two forms of feedback inhibition determine the dynamical state of a small hippocampal network. Neural Networks, Vol. 22, no. 8, 2009, pp. 1139 – 1158. DOI 10.1016/j.neunet.2009.07.015

  45. Patel A., Kosko B.: Neural signal-detection noise benefits based on error probability. IJCNN 2009 (Int. Joint Conf. on Neural Networks), 2009, pp. 2423 – 2430. DOI 10.1109/IJCNN.2009.5179058

  46. Ryota Kobayashi: The influence of firing mechanisms on gain modulation. J. Stat. Mech., 2009, P01017. DOI 10.1088/1742-5468/2009/01/P01017

  47. O. C. Akin, P. Paradisi, P. Grigolini: Perturbation-induced emergence of Poisson-like behavior in non-Poisson systems. J. Stat. Mech., 2009, P01013. DOI 10.1088/1742-5468/2009/01/P01013

  48. P. C. Bressloff: Stochastic neural field theory and the system-size expansion. SIAM J. Appl. Math., Vol. 70, no. 5, 2009, pp. 1488 – 1521. DOI 10.1137/090756971

  49. A. A. Faisal, L. P. J. Selen, D. M. Wolpert: Noise in the nervous system. Nature Reviews Neuroscience, Vol. 9, 2008, pp. 292 – 303. DOI 10.1038/nrn2258

  50. P. S. Swain, A. Longtin: Noise in genetic and neural networks. Chaos, Vol. 16, no 2, 2006, pp 026101 (6 pages). DOI 10.1063/1.2213613

  51. G Schmid, I Goychuk, P Hänggi: Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin–Huxley systems. Physical Biology, Vol. 3, no 4, 2006, pp. 248 – 254. DOI 10.1088/1478-3975/3/4/002

  52. Gianni M., Maggio F., Liberti M., Paffi A., Apollonio F., d'Inzeo G.: Modeling Biological Noise in Firing and Bursting Neurons in the Presence of an Electromagnetic Field. IEEE Int. EMBS Conf. on Neural Engineering, 2005, pp. 237 – 240. DOI 10.1109/CNE.2005.1419600

  53. M. J. Richardson, W. Gerstner: Statistics of subthreshold neuronal voltage fluctuations due to conductance-based synaptic shot noise. Chaos, Vol. 16, no. 2, 2006, 026106 (10 pages). DOI 10.1063/1.2203409

  54. P. Balenzuela, J. Garcia-Ojalvo: Role of chemical synapses in coupled neurons with noise. Physical Review E, Vol. 72, 2005, pp. 021901-1 – 021901-7. DOI 10.1103/PhysRevE.72.021901

  55. J.-M. Fellous, M. Rudolph, A. Destexhe, T. J. Sejnowski: Synaptic Background Noise Controls the Input/Output Characteristics of Single Cells in an In Vitro Model of In Vivo Activity. Neuroscience, Vol. 122, 2003, pp. 811 – 829. doi:10.1016/j.neuroscience.2003.08.027

  56. Parnas B.R.: Noise and neuronal populations conspire to encode simple waveforms reliably. IEEE Trans. on Biomedical Engineering, Vol. 43, no. 3, 1996, pp. 313 – 318. DOI 10.1109/10.486289

  57. Ginzburg I., H. Sompolinsky: Theory of correlations in stochastic neural networks. Physical Review E , Vol. 50, no. 4, 1994, pp. 3171 – 3191. DOI 10.1103/PhysRevE.50.3171

Links:

http://www.nslij-genetics.org/wli/1fnoise/ (A bibliography on 1/f noise in biosystems)

http://papers.cnl.salk.edu/PDFs/

http://iopscience.iop.org/1742-5468/focus/extra.focus5

 

 


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