1932

Abstract

Mathematical and statistical models have played important roles in neuroscience, especially by describing the electrical activity of neurons recorded individually, or collectively across large networks. As the field moves forward rapidly, new challenges are emerging. For maximal effectiveness, those working to advance computational neuroscience will need to appreciate and exploit the complementary strengths of mechanistic theory and the statistical paradigm.

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2018-03-07
2024-04-16
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Literature Cited

  1. Abbott LF. 1999. Lapicque's introduction of the integrate-and-fire model neuron (1907).. Brain Res. Bull. 50:303–4 [Google Scholar]
  2. Abeles M. 1982. Role of the cortical neuron: integrator or coincidence detector?. Israel J. Med. Sci. 18:83–92 [Google Scholar]
  3. Adrian ED, Zotterman Y. 1926. The impulses produced by sensory nerve endings. J. Physiol. 61:465–83 [Google Scholar]
  4. Agresti A. 1996. Categorical Data Analysis New York: Wiley
  5. Albert M, Bouret Y, Fromont M, Reynaud-Bouret P. 2016. Surrogate data methods based on a shuffling of the trials for synchrony detection: the centering issue. Neural Comput 28:2352–92 [Google Scholar]
  6. Aljadeff J, Lansdell BJ, Fairhall AL, Kleinfeld D. 2016. Analysis of neuronal spike trains, deconstructed. Neuron 91:221–59 [Google Scholar]
  7. Amarasingham A, Geman S, Harrison MT. 2015. Ambiguity and nonidentifiability in the statistical analysis of neural codes. PNAS 112:6455–60 [Google Scholar]
  8. Amari SI. 1977.a Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern. 27:77–87 [Google Scholar]
  9. Amari SI. 1977.b Neural theory of association and concept-formation. Biol. Cybern. 26:175–85 [Google Scholar]
  10. Amari SI, Nakahara H, Wu S, Sakai Y. 2003. Synchronous firing and higher-order interactions in neuron pool. Neural Comput 15:127–42 [Google Scholar]
  11. Amit DJ, Brunel N. 1997. Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cereb. Cortex 7:237–52 [Google Scholar]
  12. Amit DJ, Gutfreund H, Sompolinsky H. 1987. Information storage in neural networks with low levels of activity. Phys. Rev. A Gen. Phys. 35:2293–303 [Google Scholar]
  13. Anderson JR. 2009. How Can the Human Mind Occur in the Physical Universe? Oxford, UK: Oxford Univ. Press
  14. Bailey DL, Townsend DW, Valk PE, Maisey MN. 2005. Positron Emission Tomography New York: Springer
  15. Bassett DS, Bullmore ET. 2016. Small-world brain networks revisited. Neuroscientist 23:499–516 [Google Scholar]
  16. Beggs JM, Plenz D. 2003. Neuronal avalanches in neocortical circuits. J. Neurosci. 23:11167–77 [Google Scholar]
  17. Bengio Y, Lamblin P, Popovici D, Larochelle H. 2007. Greedy layer-wise training of deep networks. Advances in Neural Information Processing Systems 19, ed PB Schölkopf, JC Platt, T Hoffman 153–60 Cambridge, MA: MIT Press [Google Scholar]
  18. Boole G. 1854. An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities London: Walton and Maberly
  19. Bos H, Diesmann M, Helias M. 2016. Identifying anatomical origins of coexisting oscillations in the cortical microcircuit. PLOS Comput. Biol. 12:1–34 [Google Scholar]
  20. Bressloff PC. 2012. Spatiotemporal dynamics of continuum neural fields. J. Phys. A Math. Theor. 45:3 [Google Scholar]
  21. Bressloff PC, Cowan JD, Golubitsky M, Thomas PJ, Wiener MC. 2001. Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex. Philos. Trans. R. Soc. B 356:299–330 [Google Scholar]
  22. Brown EN, Purdon PL, Van Dort CJ. 2011. General anesthesia and altered states of arousal: a systems neuroscience analysis. Annu. Rev. Neurosci. 34:601–28 [Google Scholar]
  23. Brunel N. 2000. Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J. Comput. Neurosci. 8:183–208 [Google Scholar]
  24. Brunel N, Van Rossum MC. 2007. Lapicque's 1907 paper: from frogs to integrate-and-fire. Biol. Cybern. 97:337–39 [Google Scholar]
  25. Bullmore E, Sporns O. 2009. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10:186–98 [Google Scholar]
  26. Bush RR, Mosteller F. 1955. Stochastic Models for Learning New York: Wiley
  27. Buzsáki G, Mizuseki K. 2014. The log-dynamic brain: how skewed distributions affect network operations. Nat. Rev. Neurosci. 15:264–78 [Google Scholar]
  28. Cain N, Shea-Brown E. 2012. Computational models of decision making: integration, stability, and noise. Curr. Opin. Neurobiol. 22:1047–53 [Google Scholar]
  29. Carlson DE, Vogelstein JT, Wu Q, Lian W, Zhou M. et al. 2014. Multichannel electrophysiological spike sorting via joint dictionary learning and mixture modeling. IEEE Trans. Biomed. Eng. 61:41–54 [Google Scholar]
  30. Ching S, Cimenser A, Purdon PL, Brown EN, Kopell NJ. 2010. Thalamocortical model for a propofol-induced-rhythm associated with loss of consciousness. PNAS 107:22665–70 [Google Scholar]
  31. Churchland MM, Yu BM, Sahani M, Shenoy KV. 2007. Techniques for extracting single-trial activity patterns from large-scale neural recordings. Curr. Opin. Neurobiol. 17:609–18 [Google Scholar]
  32. Cimenser A, Purdon PL, Pierce ET, Walsh JL, Salazar-Gomez AF. et al. 2011. Tracking brain states under general anesthesia by using global coherence analysis. PNAS 108:8832–37 [Google Scholar]
  33. Cohen MR, Kohn A. 2011. Measuring and interpreting neuronal correlations. Nat. Neurosci. 14:811–19 [Google Scholar]
  34. Colquhoun D, Sakmann B. 1998. From muscle endplate to brain synapses: a short history of synapses and agonist-activated ion channels. Neuron 20:381–87 [Google Scholar]
  35. Craik K. 1943. The Nature of Explanation Cambridge, UK: Cambridge Univ. Press
  36. Cunningham JP, Yu BM. 2014. Dimensionality reduction for large-scale neural recordings. Nat. Neurosci. 17:1500–9 [Google Scholar]
  37. Dayan P, Abbott LF. 2001. Theoretical Neuroscience Cambridge, MA: MIT Press
  38. Dayan P, Nakahara H. 2017. Reconstruction of recurrent synaptic connectivity of thousands of neurons from simulated spiking activity. press
  39. De La Rocha J, Doiron B, Shea-Brown E, Josić K, Reyes A. 2007. Correlation between neural spike trains increases with firing rate. Nature 448:802–6 [Google Scholar]
  40. Deger M, Schwalger T, Naud R, Gerstner W. 2014. Fluctuations and information filtering in coupled populations of spiking neurons with adaptation. Phys. Rev. E 90:062704 [Google Scholar]
  41. Deng J, Dong W, Socher R, Li LJ, Li K, Fei-Fei L. 2009. ImageNet: A large-scale hierarchical image database. Proc. 2009 IEEE Conf. Comput. Vis. Pattern Recognit.248–55 New York: IEEE [Google Scholar]
  42. Destexhe A, Mainen ZF, Sejnowski TJ. 1994. Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. J. Comput. Neurosci. 1:195–230 [Google Scholar]
  43. Doiron B, Litwin-Kumar A, Rosenbaum R, Ocker GK, Josić K. 2016. The mechanics of state-dependent neural correlations. Nat. Neurosci. 19:383–93 [Google Scholar]
  44. Doiron B, Rinzel J, Reyes A. 2006. Stochastic synchronization in finite size spiking networks. Phys. Rev. E 74:030903 [Google Scholar]
  45. Ermentrout GB, Terman DH. 2010. Foundations of Mathematical Neuroscience New York: Springer
  46. Faisal AA, Selen LP, Wolpert DM. 2008. Noise in the nervous system. Nat. Rev. Neurosci. 9:292–303 [Google Scholar]
  47. Famulare M, Fairhall A. 2010. Feature selection in simple neurons: how coding depends on spiking dynamics. Neural Comput 22:581–98 [Google Scholar]
  48. Fienberg SE. 2012. A brief history of statistical models for network analysis and open challenges. J. Comput. Graph. Stat. 21:825–39 [Google Scholar]
  49. Fischl B, Salat DH, Busa E, Albert M, Dieterich M. et al. 2002. Whole brain segmentation: automated labeling of neuroanatomical structures in the human brain. Neuron 33:341–55 [Google Scholar]
  50. Fitzhugh R. 1960. Thresholds and plateaus in the Hodgkin-Huxley nerve equations. J. Gen. Physiol. 43:867–96 [Google Scholar]
  51. Foster M, Sherrington CS. 1897. A Text Book of Physiology. Part III. The Central Nervous System New York: Macmillan
  52. Galvani L, Aldini G. 1792. De Viribus Electricitatis In Motu Musculari Commentarius Cum Joannis Aldini Dissertatione Et Notis. Accesserunt Epistolae ad animalis electricitatis theoriam pertinentes. Florence, Italy: Apud Societatem Typographicam
  53. Geisler WS. 2011. Contributions of ideal observer theory to vision research. Vis. Res. 51:771–81 [Google Scholar]
  54. Geman S. 2006. Invariance and selectivity in the ventral visual pathway. J. Physiol. Paris 100:212–24 [Google Scholar]
  55. Geman S, Geman D. 1984. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6:721–41 [Google Scholar]
  56. Gerhard F, Kispersky T, Gutierrez GJ, Marder E, Kramer M, Eden U. 2013. Successful reconstruction of a physiological circuit with known connectivity from spiking activity alone. PLOS Comput. Biol. 9:e1003138 [Google Scholar]
  57. Gerstein GL, Mandelbrot B. 1964. Random walk models for the spike activity of a single neuron. Biophys. J. 4:41–68 [Google Scholar]
  58. Gerstner W, Kistler WM, Naud R, Paninski L. 2014. Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition Cambridge, UK: Cambridge Univ. Press
  59. Gerstner W, Naud R. 2009. How good are neuron models?. Science 326:379–80 [Google Scholar]
  60. Ginzburg I, Sompolinsky H. 1994. Theory of correlations in stochastic neural networks. Phys. Rev. E 50:3171–91 [Google Scholar]
  61. Goedeke S, Diesmann M. 2008. The mechanism of synchronization in feed-forward neuronal networks. New J. Phys. 10:015007 [Google Scholar]
  62. Gold JI, Shadlen MN. 2007. The neural basis of decision making. Annu. Rev. Neurosci. 30:535–74 [Google Scholar]
  63. Grienberger C, Konnerth A. 2012. Imaging calcium in neurons. Neuron 73:862–85 [Google Scholar]
  64. Griffiths TL, Chater N, Norris D, Pouget A. 2012. How the Bayesians got their beliefs (and what those beliefs actually are): comment on Bowers and Davis (2012)..
  65. Grillner S, Jessell TM. 2009. Measured motion: searching for simplicity in spinal locomotor networks. Curr. Opin. Neurobiol. 19:572–86 [Google Scholar]
  66. Grün S. 2009. Data-driven significance estimation for precise spike correlation. J. Neurophysiol. 101:1126–40 [Google Scholar]
  67. Grytskyy D, Tetzlaff T, Diesmann M, Helias M. 2013. A unified view on weakly correlated recurrent networks. Front. Comput. Neurosci. 7:131 [Google Scholar]
  68. Gugerty L. 2006. Newell and Simon's logic theorist: historical background and impact on cognitive modeling. Proc. Hum. Fact. Ergon. Soc. Annu. Meet. 50:880–84 [Google Scholar]
  69. Hämäläinen M, Hari R, Ilmoniemi RJ, Knuutila J, Lounasmaa OV. 1993. Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev. Mod. Phys. 65:413 [Google Scholar]
  70. Harrison MT, Amarasingham A, Kass RE. 2013. Statistical identification of synchronous spiking. Spike Timing: Mechanisms and Function, PM DiLorenzo, JD Victor 77–120 Boca Raton, FL: CRC [Google Scholar]
  71. Harrison MT, Amarasingham A, Truccolo W. 2015. Spatiotemporal conditional inference and hypothesis tests for neural ensemble spiking precision. Neural Comput 27:104–50 [Google Scholar]
  72. Hartline HK, Graham CH. 1932. Nerve impulses from single receptors in the eye. J. Cell. Physiol. 1:277–95 [Google Scholar]
  73. Hebb DO. 1949. The Organization of Behavior: A Neuropsychological Approach New York: Wiley
  74. Helias M, Tetzlaff T, Diesmann M. 2013. Echoes in correlated neural systems. New J. Phys. 15:023002 [Google Scholar]
  75. Helias M, Tetzlaff T, Diesmann M. 2014. The correlation structure of local cortical networks intrinsically results from recurrent dynamics. PLOS Comput. Biol. 10:e1003428 [Google Scholar]
  76. Hertz J. 2010. Cross-correlations in high-conductance states of a model cortical network. Neural Comput 22:427–47 [Google Scholar]
  77. Hille B. 2001. Ionic Channels of Excitable Membranes Sunderland, MA: Sinauer
  78. Hinton GE, Sejnowski TJ. 1983. Optimal perceptual inference. Proc. IEEE Conf. Comput. Vis. Pattern Recognit.448–53 New York: IEEE [Google Scholar]
  79. Hochreiter S, Schmidhuber J. 1997. Long short-term memory. Neural Comput 9:1735–80 [Google Scholar]
  80. Hodgkin AL, Huxley AF. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117:500–44 [Google Scholar]
  81. Hong S, y Arcas BA, Fairhall AL. 2007. Single neuron computation: from dynamical system to feature detector. Neural Comput 19:3133–72 [Google Scholar]
  82. Hopfield JJ. 1982. Neural networks and physical systems with emergent collective computational abilities. PNAS 79:2554–58 [Google Scholar]
  83. Hubel DH, Wiesel TN. 1959. Receptive fields of single neurones in the cat's striate cortex. J. Physiol. 148:574–91 [Google Scholar]
  84. Izhikevich EM. 2007. Dynamical Systems in Neuroscience Cambridge, MA: MIT Press
  85. Jovanović S, Hertz J, Rotter S. 2015. Cumulants of Hawkes point processes. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91:042802 [Google Scholar]
  86. Kandel ER, Schwartz JH, Jessell TM, Siegelbaum SA, Hudspeth AJ. 2013. Principles of Neural Science New York: McGraw-Hill. , 5th ed..
  87. Kass RE, Eden UT, Brown EN. 2014. Analysis of Neural Data Springer Ser. Stat New York: Springer
  88. Kass RE, Ventura V. 2001. A spike-train probability model. Neural Comput 13:1713–20 [Google Scholar]
  89. Kaufman MT, Churchland MM, Ryu SI, Shenoy KV. 2014. Cortical activity in the null space: permitting preparation without movement. Nat. Neurosci. 17:440–48 [Google Scholar]
  90. Kelly RC, Kass RE. 2012. A framework for evaluating pairwise and multiway synchrony among stimulus-driven neurons. Neural Comput 24:2007–32 [Google Scholar]
  91. Kobayashi R, Tsubo Y, Shinomoto S. 2009. Made-to-order spiking neuron model equipped with a multi-timescale adaptive threshold. Front. Comput. Neurosci. 3:9 [Google Scholar]
  92. Kopell N, Ermentrout GB. 2002. Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators. Handbook of Dynamical Systems, Volume 2: Toward Applications B Fielder 3–54 Amsterdam: Elsevier [Google Scholar]
  93. Körding K. 2007. Decision theory: What “should” the nervous system do?. Science 318:606–10 [Google Scholar]
  94. Kriegeskorte N. 2015. Deep neural networks: a new framework for modeling biological vision and brain information processing. Annu. Rev. Vis. Sci. 1:417–46 [Google Scholar]
  95. Krizhevsky A, Sutskever I, Hinton GE. 2012. ImageNet classification with deep convolutional neural networks. Advances in Neural Information Processing Systems 25 (NIPS 2012) F Pereira, CJC Burges, L Bottou, KQ Weinberger 1097–105 Red Hook, NY: Curran [Google Scholar]
  96. Lansky P, Ditlevsen S. 2008. A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models. Biol. Cybern. 99:253–62 [Google Scholar]
  97. Lapique L. 1907. Recherches quantitatives sur l'excitation électrique des nerfs traitée comme une polarisation. J. Physiol. Pathol. Gen. 9:620–35 [Google Scholar]
  98. Lazar N. 2008. The Statistical Analysis of Functional MRI Data New York: Springer
  99. le Cun Y. 1989. Generalization and network design strategies. Connectionism in Perspective R Pfeifer, Z Schreter, F Fogelman-Soulié, L Steels 143–55 Amsterdam: Elsevier [Google Scholar]
  100. le Cun Y, Bengio Y, Hinton G. 2015. Deep learning. Nature 521:436–44 [Google Scholar]
  101. Litwin-Kumar A, Doiron B. 2012. Slow dynamics and high variability in balanced cortical networks with clustered connections. Nat. Neurosci. 15:1498–505 [Google Scholar]
  102. Mainen ZF, Sejnowski TJ. 1995. Reliability of spike timing in neocortical neurons. Science 268:1503–6 [Google Scholar]
  103. Mante V, Sussillo D, Shenoy KV, Newsome WT. 2013. Context-dependent computation by recurrent dynamics in prefrontal cortex. Nature 503:78–84 [Google Scholar]
  104. Marder E, Bucher D. 2001. Central pattern generators and the control of rhythmic movements. Curr. Biol. 11:R986–96 [Google Scholar]
  105. Markram H, Muller E, Ramaswamy S, Reimann MW, Abdellah M. et al. 2015. Reconstruction and simulation of neocortical microcircuitry. Cell 163:456–92 [Google Scholar]
  106. Marr D. 1982. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information San Francisco: W.H. Freeman
  107. McClelland JL, Rumelhart DE. 1981. An interactive activation model of context effects in letter perception: I. An account of basic findings. Psychol. Rev. 88:375 [Google Scholar]
  108. McCulloch WS, Pitts W. 1943. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5:115–33 [Google Scholar]
  109. McGrayne SB. 2011. The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy New Haven, CT: Yale Univ. Press
  110. Medler DA. 1998. A brief history of connectionism. Neural Comput. Surv. 1:18–72 [Google Scholar]
  111. Meliza CD, Kostuk M, Huang H, Nogaret A, Margoliash D, Abarbanel HD. 2014. Estimating parameters and predicting membrane voltages with conductance-based neuron models. Biol. Cybern. 108:495–516 [Google Scholar]
  112. Meng L, Kramer MA, Middleton SJ, Whittington MA, Eden UT. 2014. A unified approach to linking experimental, statistical and computational analysis of spike train data. PLOS ONE 9:e85269 [Google Scholar]
  113. Meyer C, van Vreeswijk C. 2002. Temporal correlations in stochastic networks of spiking neurons. Neural Comput 14:369–404 [Google Scholar]
  114. Mnih V, Kavukcuoglu K, Silver D, Rusu AA, Veness J. et al. 2015. Human-level control through deep reinforcement learning. Nature 518:529–33 [Google Scholar]
  115. Monteforte M, Wolf F. 2012. Dynamic flux tubes form reservoirs of stability in neuronal circuits. Phys. Rev. X. 2:041007 [Google Scholar]
  116. Moreno-Bote R, Parga N. 2010. Response of integrate-and-fire neurons to noisy inputs filtered by synapses with arbitrary timescales: firing rate and correlations. Neural Comput 22:1528–72 [Google Scholar]
  117. Nagumo J, Arimoto S, Yoshizawa S. 1962. An active pulse transmission line simulating nerve axon. Proc. IRE 50:2061–70 [Google Scholar]
  118. Nakahara H, Amari S, Richmond BJ. 2006. A comparison of descriptive models of a single spike train by information-geometric measure. Neural Comput 18:545–68 [Google Scholar]
  119. Newell A, Simon H. 1956. The logic theory machine–a complex information processing system. IEEE Trans. Inf. Theory 2:61–79 [Google Scholar]
  120. Nguyen A, Yosinski J, Clune J. 2015. Deep neural networks are easily fooled: high confidence predictions for unrecognizable images. Proc. IEEE Conf. Comput. Vis. Pattern Recognit.427–36 New York: IEEE [Google Scholar]
  121. Nunez PL, Srinivasan R. 2006. Electric Fields of the Brain: The Neurophysics of EEG New York: Oxford Univ Press
  122. Ohiorhenuan IE, Mechler F, Purpura KP, Schmid AM, Hu Q, Victor JD. 2010. Sparse coding and high-order correlations in fine-scale cortical networks. Nature 466:617–21 [Google Scholar]
  123. Okun M, Lampl I. 2008. Instantaneous correlation of excitation and inhibition during ongoing and sensory-evoked activities. Nat. Neurosci. 11:535–37 [Google Scholar]
  124. Ostojic S, Brunel N. 2011. From spiking neuron models to linear-nonlinear models. PLOS Comput. Biol. 7:e1001056 [Google Scholar]
  125. Ostojic S, Brunel N, Hakim V. 2009. How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains. J. Neurosci. 29:10234–53 [Google Scholar]
  126. Paninski L, Brown EN, Iyengar S, Kass RE. 2009. Statistical models of spike trains. Stoch. Methods Neurosci.278–303 [Google Scholar]
  127. Papo D, Zanin M, Martnez JH, Buldú JM. 2016. Beware of the small-world neuroscientist! Front. Hum. Neurosci. 10:96 [Google Scholar]
  128. Pelillo M, Scantamburlo T, Schiaffonati V. 2015. Pattern recognition between science and engineering: a red herring?. Pattern Recognit. Lett. 64:3–10 [Google Scholar]
  129. Perkel DH, Bullock TH. 1968. Neural coding. Neurosci. Res. Program Bull. 6:219–349 [Google Scholar]
  130. Piccinini G. 2004. The first computational theory of mind and brain: a close look at McCulloch and Pitts's logical calculus of ideas immanent in nervous activity. Synthese 141:175–215 [Google Scholar]
  131. Piccolino M. 1998. Animal electricity and the birth of electrophysiology: the legacy of Luigi Galvani. Brain Res. Bull. 46:381–407 [Google Scholar]
  132. Pillow JW, Shlens J, Paninski L, Sher A, Litke AM. et al. 2008. Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature 454:995–99 [Google Scholar]
  133. Platkiewicz J, Stark E, Amarasingham A. 2017. Spike-centered jitter can mistake temporal structure. Neural Comput 29:783–803 [Google Scholar]
  134. Pnevmatikakis EA, Soudry D, Gao Y, Machado TA, Merel J. et al. 2016. Simultaneous denoising, deconvolution, and demixing of calcium imaging data. Neuron 89:285–99 [Google Scholar]
  135. Prinz AA, Bucher D, Marder E. 2004. Similar network activity from disparate circuit parameters. Nat. Neurosci. 7:1345–52 [Google Scholar]
  136. Qin F, Auerbach A, Sachs F. 1997. Maximum likelihood estimation of aggregated Markov processes. Proc. R. Soc. Lond. B 264:375–83 [Google Scholar]
  137. Rall W. 1962. Theory of physiological properties of dendrites. Ann. N.Y. Acad. Sci. 96:1071–92 [Google Scholar]
  138. Renart A, De La Rocha J Bartho P, Hollender L, Parga N. et al. 2010. The asynchronous state in cortical circuits. Science 327:587–90 [Google Scholar]
  139. Rescorla RA, Wagner AR. 1972. A theory of Pavlovian conditioning: variations in the effectiveness of reinforcement and nonreinforcement. Classical Conditioning II: Current Research and Theory AH Black, WF Prokasy 64–99 New-York: Appleton-Century-Crofts [Google Scholar]
  140. Rey HG, Pedreira C, Quiroga RQ. 2015. Past, present and future of spike sorting techniques. Brain Res. Bull. 119:106–17 [Google Scholar]
  141. Richardson MJE. 2008. Spike-train spectra and network response functions for non-linear integrate-and-fire neurons. Biol. Cybern. 99:381–92 [Google Scholar]
  142. Riehle A, Grün S, Diesmann M, Aertsen A. 1997. Spike synchronization and rate modulation differentially involved in motor cortical function. Science 278:1950–53 [Google Scholar]
  143. Rinzel J. 1985. Excitation dynamics: insights from simplified membrane models. Fed. Proc. 44:2944–46 [Google Scholar]
  144. Rosenblatt F. 1958. The perceptron: a probabilistic model for information storage and organization in the brain. Psychol. Rev. 65:386–408 [Google Scholar]
  145. Rosenblueth A, Wiener N, Bigelow J. 1943. Behavior, purpose and teleology. Philos. Sci. 10:18–24 [Google Scholar]
  146. Rotstein HG. 2015. Subthreshold amplitude and phase resonance in models of quadratic type: nonlinear effects generated by the interplay of resonant and amplifying currents. J. Comput. Neurosci. 38:325–54 [Google Scholar]
  147. Rotstein HG, Oppermann T, White JA, Kopell N. 2006. A reduced model for medial entorhinal cortex stellate cells: subthreshold oscillations, spiking and synchronization. J. Comput. Neurosci. 21:271–92 [Google Scholar]
  148. Roxin A, Brunel N, Hansel D. 2006. Rate models with delays and the dynamics of large networks of spiking neurons. Prog. Theor. Phys. Suppl. 161:68–85 [Google Scholar]
  149. Roxin A, Brunel N, Hansel D, Mongillo G, van Vreeswijk C. 2011. On the distribution of firing rates in networks of cortical neurons. J. Neurosci. 31:16217–26 [Google Scholar]
  150. Rumelhart DE, McClelland JL, Research Group PDP. 1986. Parallel Distributed Processing: Explorations in the Microstructures of Cognition, Vol. 1: Foundations Cambridge, MA: MIT Press [Google Scholar]
  151. Sadtler PT, Quick KM, Golub MD, Chase SM, Ryu SI. et al. 2014. Neural constraints on learning. Nature 512:423–26 [Google Scholar]
  152. Sakmann B, Neher E. 1984. Patch clamp techniques for studying ionic channels in excitable membranes. Annu. Rev. Physiol. 46:455–72 [Google Scholar]
  153. Santos GS, Gireesh ED, Plenz D, Nakahara H. 2010. Hierarchical interaction structure of neural activities in cortical slice cultures. J. Neurosci. 30:8720–33 [Google Scholar]
  154. Schultz W. 2015. Neuronal reward and decision signals: from theories to data. Physiol. Rev. 95:853–951 [Google Scholar]
  155. Schultz W, Dayan P, Montague PR. 1997. A neural substrate of prediction and reward. Science 275:1593–99 [Google Scholar]
  156. Shadlen MN, Movshon JA. 1999. Synchrony unbound. Neuron 24:67–77 [Google Scholar]
  157. Shadlen MN, Newsome WT. 1998. The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J. Neurosci. 18:3870–96 [Google Scholar]
  158. Shannon CE, Weaver W. 1949. The Mathematical Theory of Communication Urbana: Univ. Ill. Press
  159. Shea-Brown E, Josic K, de la Rocha J, Doiron B. 2008. Correlation and synchrony transfer in integrate-and-fire neurons: basic properties and consequences for coding. Phys. Rev. Lett. 100:108102 [Google Scholar]
  160. Shimazaki H, Amari SI, Brown EN, Grün S. 2012. State-space analysis of time-varying higher-order spike correlation for multiple neural spike train data. PLOS Comput. Biol. 8:e1002385 [Google Scholar]
  161. Shimazaki H, Sadeghi K, Ishikawa T, Ikegaya Y, Toyoizumi T. 2015. Simultaneous silence organizes structured higher-order interactions in neural populations. Sci. Rep. 5:9821 [Google Scholar]
  162. Sigworth F. 1977. Sodium channels in nerve apparently have two conductance states. Nature 270:265–67 [Google Scholar]
  163. Sigworth F. 1980. The variance of sodium current fluctuations at the node of Ranvier. J. Physiol. 307:97–129 [Google Scholar]
  164. Singer W. 1999. Neuronal synchrony: a versatile code for the definition of relations?. Neuron 24:49–65111–25 [Google Scholar]
  165. Singer W, Gray CM. 1995. Visual feature integration and the temporal correlation hypothesis. Annu. Rev. Neurosci. 18:555–86 [Google Scholar]
  166. Somjen GG. 2004. Ions in the Brain: Normal Function, Seizures, and Stroke Oxford, UK: Oxford Univ. Press
  167. Staude B, Rotter S, Grün S. 2010. CuBIC: cumulant based inference of higher-order correlations in massively parallel spike trains. J. Comput. Neurosci. 29:327–50 [Google Scholar]
  168. Stigler SM. 1986. The History of Statistics: The Measurement of Uncertainty Before 1900 Cambridge, MA: Harvard Univ. Press
  169. Sutton RS, Barto AG. 1998. Reinforcement Learning: An Introduction Cambridge, MA: MIT Press
  170. Swanson LW. 2012. Brain Architecture: Understanding the Basic Plan Oxford, UK: Oxford Univ. Press
  171. Teramae JN, Tsubo Y, Fukai T. 2012. Optimal spike-based communication in excitable networks with strong-sparse and weak-dense links. Sci. Rep. 2:485 [Google Scholar]
  172. Tetzlaff T, Helias M, Einevoll G, Diesmann M. 2012. Decorrelation of neural-network activity by inhibitory feedback. PLOS Comput. Biol. 8:e1002596 [Google Scholar]
  173. Thorndike EL. 1911. Animal Intelligence: Experimental Studies New York: Macmillan
  174. Tien JH, Guckenheimer J. 2008. Parameter estimation for bursting neural models. J. Comput. Neurosci. 24:358–73 [Google Scholar]
  175. Torre E, Quaglio P, Denker M, Brochier T, Riehle A, Grün S. 2016. Synchronous spike patterns in macaque motor cortex during an instructed-delay reach-to-grasp task. J. Neurosci. 36:8329–40 [Google Scholar]
  176. Tranchina D. 2010. Population density methods in large-scale neural network modelling. Stochastic Methods in Neuroscience C Laing, GH Lord 181–216 Oxford, UK: Oxford Univ. Press [Google Scholar]
  177. Traub RD, Contreras D, Cunningham MO, Murray H, LeBeau FEN. et al. 2005. Single-column thalamocortical network model exhibiting gamma oscillations, sleep spindles, and epileptogenic bursts. J. Neurophysiol. 93:2194–232 [Google Scholar]
  178. Trousdale J, Hu Y, Shea-Brown E, Josic K. 2012. Impact of network structure and cellular response on spike time correlations. PLOS Comput. Biol. 8:e1002408 [Google Scholar]
  179. Truccolo W. 2010. Stochastic models for multivariate neural point processes: collective dynamics and neural decoding. Analysis of Parallel Spike Trains S Grün, S Rotter 321–41 New York: Springer [Google Scholar]
  180. Tuckwell HC. 1988. Introduction to Theoretical Neurobiology 1 Cambridge, UK: Cambridge Univ. Press
  181. Turing AM. 1937. On computable numbers, with an application to the Entscheidungsproblem. Proc. Lond. Math. Soc. 2:230–65 [Google Scholar]
  182. Ullman S, Assif L, Fetaya E, Harari D. 2016. Atoms of recognition in human and computer vision. PNAS 113:2744–49 [Google Scholar]
  183. Van Vreeswijk C, Sompolinsky H. 1996. Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274:1724–26 [Google Scholar]
  184. Van Vreeswijk C, Sompolinsky H. 1998. Chaotic balanced state in a model of cortical circuits. Neural Comput 10:1321–71 [Google Scholar]
  185. Vavoulis DV, Straub VA, Aston JA, Feng J. 2012. A self-organizing state-space-model approach for parameter estimation in Hodgkin-Huxley-type models of single neurons. PLOS Comput. Biol. 8:e1002401 [Google Scholar]
  186. Ventura V, Todorova S. 2015. A computationally efficient method for incorporating spike waveform information into decoding algorithms. Neural Comput 27:1033–50 [Google Scholar]
  187. Villringer A, Planck J, Hock C, Schleinkofer L, Dirnagl U. 1993. Near infrared spectroscopy (NIRS): a new tool to study hemodynamic changes during activation of brain function in human adults. Neurosci. Lett. 154:101–4 [Google Scholar]
  188. Walch OJ, Eisenberg MC. 2016. Parameter identifiability and identifiable combinations in generalized Hodgkin-Huxley models. Neurocomputing 199:137–43 [Google Scholar]
  189. Wang W, Tripathy SJ, Padmanabhan K, Urban NN, Kass RE. 2015. An empirical model for reliable spiking activity. Neural Comput 27:1609–23 [Google Scholar]
  190. Watts DJ, Strogatz SH. 1998. Collective dynamics of small-world networks. Nature 393:440–42 [Google Scholar]
  191. Weber AI, Pillow JW. 2016. Capturing the dynamical repertoire of single neurons with generalized linear models. arXiv:1602.07389 [q-bio.NC]
  192. Wei Y, Ullah G, Schiff SJ. 2014. Unification of neuronal spikes, seizures, and spreading depression. J. Neurosci. 34:11733–43 [Google Scholar]
  193. Whitehead AN, Russell B. 1935. Principia Mathematica 1 Cambridge, UK: Cambridge Univ. Press, 2nd ed..
  194. Wiener N. 1948. Cybernetics: Control and Communication in the Animal and the Machine New York: Wiley
  195. Williamson RC, Cowley BR, Litwin-Kumar A, Doiron B, Kohn A, Smith MA, Yu BM. 2016. Scaling properties of dimensionality reduction for neural populations and network models. PLOS Comput. Biol. 12:e1005141 [Google Scholar]
  196. Wilson HR, Cowan JD. 1972. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12:1–24 [Google Scholar]
  197. Wolpert DM, Diedrichsen J, Flanagan JR. 2011. Principles of sensorimotor learning. Nat. Rev. Neurosci. 12:739–51 [Google Scholar]
  198. Yamins DLK, DiCarlo JJ. 2016. Using goal-driven deep learning models to understand sensory cortex. Nat. Neurosci. 19:356–65 [Google Scholar]
  199. Yu BM, Cunningham JP, Santhanam G, Ryu SI, Shenoy KV, Sahani M. 2009. Gaussian-process factor analysis for low-dimensional single-trial analysis of neural population activity. J. Neurophysiol. 102:614–35 [Google Scholar]
  200. Zaytsev YV, Morrison A, Deger M. 2015. Reconstruction of recurrent synaptic connectivity of thousands of neurons from simulated spiking activity. J. Comput. Neurosci. 39:77–103 [Google Scholar]
  201. Zhou P, Burton SD, Snyder AC, Smith MA, Urban NN, Kass RE. 2015. Establishing a statistical link between network oscillations and neural synchrony. PLOS Comput. Biol. 11:e1004549 [Google Scholar]
  202. Zylberberg J, Cafaro J, Turner MH, Shea-Brown E, Rieke F. 2016. Direction-selective circuits shape noise to ensure a precise population code. Neuron 89:369–83 [Google Scholar]
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