References and models cited by this paper

References and models that cite this paper

Acker CD, Antic SD (2009) Quantitative assessment of the distributions of membrane conductances involved in action potential backpropagation along basal dendrites. J Neurophysiol 101:1524-41 [Journal] [PubMed]

Andrásfalvy BK, Magee JC (2004) Changes in AMPA receptor currents following LTP induction on rat CA1 pyramidal neurones. J Physiol 559:543-54 [Journal] [PubMed]

Araya R, Eisenthal KB, Yuste R (2006) Dendritic spines linearize the summation of excitatory potentials. Proc Natl Acad Sci U S A 103:18799-804 [Journal] [PubMed]

Athanasios P,Unnikrishna PS (2002) Probability, Random Variables, and Stochastic Processes

Averbeck BB, Latham PE, Pouget A (2006) Neural correlations, population coding and computation. Nat Rev Neurosci 7:358-66 [Journal] [PubMed]

Bahl A, Stemmler MB, Herz AV, Roth A (2012) Automated optimization of a reduced layer 5 pyramidal cell model based on experimental data. J Neurosci Methods 210:22-34 [Journal] [PubMed]

Banitt Y, Martin KA, Segev I (2007) A biologically realistic model of contrast invariant orientation tuning by thalamocortical synaptic depression. J Neurosci 27:10230-9 [Journal] [PubMed]

Barak O, Tsodyks M, Romo R (2010) Neuronal population coding of parametric working memory. J Neurosci 30:9424-30 [Journal] [PubMed]

Baranauskas G, David Y, Fleidervish IA (2013) Spatial mismatch between the Na+ flux and spike initiation in axon initial segment. Proc Natl Acad Sci U S A 110:4051-6 [Journal] [PubMed]

Barber MJ, Clark JW, Anderson CH (2003) Neural representation of probabilistic information. Neural Comput 15:1843-64 [Journal] [PubMed]

Beck JM, Ma WJ, Kiani R, Hanks T, Churchland AK, Roitman J, Shadlen MN, Latham PE, Pouget A (2008) Probabilistic population codes for Bayesian decision making. Neuron 60:1142-52 [Journal] [PubMed]

Berger T,Levy WB (2010) A mathematical theory of energy efficient neural computation and communication IEEE Transactions on Information Theory 56(2):852-874

Bernander O, Koch C, Douglas RJ (1994) Amplification and linearization of distal synaptic input to cortical pyramidal cells. J Neurophysiol 72:2743-53 [Journal] [PubMed]

Berry MJ, Meister M (1998) Refractoriness and neural precision. J Neurosci 18:2200-11 [PubMed]

Bialek W, Rieke F, de Ruyter van Steveninck RR, Warland D (1991) Reading a neural code. Science 252:1854-7 [PubMed]

Brown EN, Barbieri R, Ventura V, Kass RE, Frank LM (2002) The time-rescaling theorem and its application to neural spike train data analysis. Neural Comput 14:325-46 [Journal] [PubMed]

Buracas GT, Zador AM, DeWeese MR, Albright TD (1998) Efficient discrimination of temporal patterns by motion-sensitive neurons in primate visual cortex. Neuron 20:959-69 [PubMed]

Calvin WH, Stevens CF (1968) Synaptic noise and other sources of randomness in motoneuron interspike intervals. J Neurophysiol 31:574-87 [Journal] [PubMed]

Capocelli RM, Ricciardi LM (1971) Diffusion approximation and first passage time problem for a model neuron. Kybernetik 8:214-23 [PubMed]

Carandini M, Ferster D (2000) Membrane potential and firing rate in cat primary visual cortex. J Neurosci 20:470-84 [PubMed]

Carandini M, Heeger DJ, Movshon JA (1997) Linearity and normalization in simple cells of the macaque primary visual cortex. J Neurosci 17:8621-44 [PubMed]

Carnevale NT, Hines ML (2006) The NEURON Book [Journal]

Cash S, Yuste R (1998) Input summation by cultured pyramidal neurons is linear and position-independent. J Neurosci 18:10-5 [PubMed]

Cash S, Yuste R (1999) Linear summation of excitatory inputs by CA1 pyramidal neurons. Neuron 22:383-94 [PubMed]

Chatelier A, Zhao J, Bois P, Chahine M (2010) Biophysical characterisation of the persistent sodium current of the Nav1.6 neuronal sodium channel: a single-channel analysis. Pflugers Arch 460:77-86 [Journal] [PubMed]

Chen LH (1975) Poisson approximation for dependent trials The Annals of Probability :534-545

Chikazoe J, Lee DH, Kriegeskorte N, Anderson AK (2014) Population coding of affect across stimuli, modalities and individuals. Nat Neurosci 17:1114-22 [Journal] [PubMed]

Colbert CM, Levy WB (1992) Electrophysiological and pharmacological characterization of perforant path synapses in CA1: mediation by glutamate receptors. J Neurophysiol 68:1-8 [Journal] [PubMed]

Colbert CM, Pan E (2002) Ion channel properties underlying axonal action potential initiation in pyramidal neurons. Nat Neurosci 5:533-8 [Journal] [PubMed]

Conti F, Hille B, Neumcke B, Nonner W, Stämpfli R (1976) Measurement of the conductance of the sodium channel from current fluctuations at the node of Ranvier. J Physiol 262:699-727 [PubMed]

Cook EP, Wilhelm AC, Guest JA, Liang Y, Masse NY, Colbert CM (2007) The neuronal transfer function: contributions from voltage- and time-dependent mechanisms. Prog Brain Res 165:1-12 [Journal] [PubMed]

Deneve S (2008) Bayesian spiking neurons I: inference. Neural Comput 20:91-117 [Journal] [PubMed]

Deneve S, Pouget A (2004) Bayesian multisensory integration and cross-modal spatial links. J Physiol Paris 98:249-58 [Journal] [PubMed]

Ermentrout GB, Terman DH (2010) Mathematical Foundations of Neuroscience Interdisciplinary Applied Mathematics, Antman SS:Marsden JE:Sirovich L:Wiggins, ed. pp.1 [Journal]

Faisal AA (2012) Noise in neurons and other constraints Computational Systems Neurobiology :227-257

Faisal AA, Laughlin SB (2007) Stochastic simulations on the reliability of action potential propagation in thin axons. PLoS Comput Biol 3:e79 [Journal] [PubMed]

Faisal AA, Selen LP, Wolpert DM (2008) Noise in the nervous system. Nat Rev Neurosci 9:292-303 [Journal] [PubMed]

Ferster D (1994) Linearity of synaptic interactions in the assembly of receptive fields in cat visual cortex. Curr Opin Neurobiol 4:563-8 [PubMed]

Gentet LJ, Stuart GJ, Clements JD (2000) Direct measurement of specific membrane capacitance in neurons. Biophys J 79:314-20 [Journal] [PubMed]

GERSTEIN GL, MANDELBROT B (1964) RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. Biophys J 4:41-68 [PubMed]

Gerwinn S, Macke JH, Bethge M (2010) Bayesian inference for generalized linear models for spiking neurons. Front Comput Neurosci 4:12 [Journal] [PubMed]

Gillespie DC, Lampl I, Anderson JS, Ferster D (2001) Dynamics of the orientation-tuned membrane potential response in cat primary visual cortex. Nat Neurosci 4:1014-9 [Journal] [PubMed]

Giorno V, Lánský P, Nobile AG, Ricciardi LM (1988) Diffusion approximation and first-passage-time problem for a model neuron. III. A birth-and-death process approach. Biol Cybern 58:387-404 [PubMed]

Hallermann S, de Kock CP, Stuart GJ, Kole MH (2012) State and location dependence of action potential metabolic cost in cortical pyramidal neurons. Nat Neurosci 15:1007-14 [Journal] [PubMed]

He H (2016) IEEE Transactions on Neural Networks and Learning Systems 2016 and Beyond. IEEE Trans Neural Netw Learn Syst 27:1-7 [PubMed]

Hille B (1978) Ionic channels in excitable membranes. Current problems and biophysical approaches. Biophys J 22:283-94 [Journal] [PubMed]

Hille B (2001) Ionic Channels of Excitable Membranes

Hines ML, Morse T, Migliore M, Carnevale NT, Shepherd GM (2004) ModelDB: A Database to Support Computational Neuroscience. J Comput Neurosci 17:7-11 [Journal] [PubMed]

Hu W, Tian C, Li T, Yang M, Hou H, Shu Y (2009) Distinct contributions of Na(v)1.6 and Na(v)1.2 in action potential initiation and backpropagation. Nat Neurosci 12:996-1002 [Journal] [PubMed]

Iyengar S, Liao Q (1997) Modeling neural activity using the generalized inverse Gaussian distribution. Biol Cybern 77:289-95 [Journal] [PubMed]

Jagadeesh B, Wheat HS, Ferster D (1993) Linearity of summation of synaptic potentials underlying direction selectivity in simple cells of the cat visual cortex. Science 262:1901-4 [PubMed]

Johnston D, Magee JC, Colbert CM, Cristie BR (1996) Active properties of neuronal dendrites. Annu Rev Neurosci 19:165-86 [Journal] [PubMed]

Kole MH, Hallermann S, Stuart GJ (2006) Single Ih channels in pyramidal neuron dendrites: properties, distribution, and impact on action potential output. J Neurosci 26:1677-87 [Journal] [PubMed]

Kole MH, Ilschner SU, Kampa BM, Williams SR, Ruben PC, Stuart GJ (2008) Action potential generation requires a high sodium channel density in the axon initial segment. Nat Neurosci 11:178-86 [Journal] [PubMed]

Lánsky P,Rospars JP (1995) Ornstein-Uhlenbeck model neuron revisited Biological cybernetics 72(5):397-406

Lansky P,Smith C,Ricciardi LM (1990) One-dimensional stochastic diffusion models of neuronal activity and related first passage time problems Trends in Biological Cybernetics 1:153-162

Lee C, Rohrer WH, Sparks DL (1988) Population coding of saccadic eye movements by neurons in the superior colliculus. Nature 332:357-60 [Journal] [PubMed]

Léger JF, Stern EA, Aertsen A, Heck D (2005) Synaptic integration in rat frontal cortex shaped by network activity. J Neurophysiol 93:281-93 [Journal] [PubMed]

Levy W (1988) A theory of the hippocampus based on reinforced synaptic modification in CA1 Society for Neuroscience Abstracts. vol. 14 :168

Levy WB, Baxter RA (2002) Energy-efficient neuronal computation via quantal synaptic failures. J Neurosci 22:4746-55 [Journal] [PubMed]

Levy WB,Berger T,Sungkar M (2016) Neural Computation From First Principles: Using the Maximum Entropy Method to Obtain an Optimal Bits-Per-Joule Neuron. T-MBMC 2:154-165

Levy WB,Colbert CM,Desmond NL (1990) Elemental adaptive processes of neurons and synapses: a statistical/computational perspective. vol. 187

Lindley D (1956) On a measure of information provided by an experiment Ann Math Stat 29:986-1005

Ma WJ, Beck JM, Latham PE, Pouget A (2006) Bayesian inference with probabilistic population codes. Nat Neurosci 9:1432-8 [Journal] [PubMed]

Mainen ZF, Sejnowski TJ (1995) Reliability of spike timing in neocortical neurons. Science 268:1503-6 [PubMed]

Mainen ZF, Sejnowski TJ (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382:363-6 [Journal] [PubMed]

McCulloch WS, Pitts W (1990) A logical calculus of the ideas immanent in nervous activity. 1943. Bull Math Biol 52:99-115; discussion 73-97 [PubMed]

McDonnell MD, Ikeda S, Manton JH (2011) An introductory review of information theory in the context of computational neuroscience. Biol Cybern 105:55-70 [Journal] [PubMed]

Morel D,Levy WB (2007) Persistent sodium is a better linearizing mechanism than the hyperpolarization-activated current. Neurocomputing 70(10):1635-1639

Morel D,Levy WB (2008) Cost of linearization for different time constants BMC Neuroscience 9(1):1

Nettleton JS, Spain WJ (2000) Linear to supralinear summation of AMPA-mediated EPSPs in neocortical pyramidal neurons. J Neurophysiol 83:3310-22 [Journal] [PubMed]

Palmer LM, Stuart GJ (2006) Site of action potential initiation in layer 5 pyramidal neurons. J Neurosci 26:1854-63 [Journal] [PubMed]

Priebe NJ, Ferster D (2005) Direction selectivity of excitation and inhibition in simple cells of the cat primary visual cortex. Neuron 45:133-45 [Journal] [PubMed]

Reinagel P,Reid R (1998) Visual stimulus statistics and the reliability of spike timing in the LGN Soc Neurosci Abstr. vol. 24 :139

Revah O, Libman L, Fleidervish IA, Gutnick MJ (2015) The Outwardly Rectifying Current of Layer 5 Neocortical Neurons that was Originally Identified as "Non-Specific Cationic" Is Essentially a Potassium Current. PLoS One 10:e0132108 [Journal] [PubMed]

Ricciardi LM, Sacerdote L (1979) The Ornstein-Uhlenbeck process as a model for neuronal activity. I. Mean and variance of the firing time. Biol Cybern 35:1-9 [PubMed]

Rieke F, Bodnar DA, Bialek W (1995) Naturalistic stimuli increase the rate and efficiency of information transmission by primary auditory afferents. Proc Biol Sci 262:259-65 [Journal] [PubMed]

Rieke F, Warland D, de Ruyter van Steveninck, R, Bialek B (1997) Spikes: Exploring The Neural Code

Rieke F,Warland D,Bialek W (1993) Coding efficiency and information rates in sensory neurons EPL (Europhysics Letters) 22(2):151

Roelfsema PR, Lamme VA, Spekreijse H (1998) Object-based attention in the primary visual cortex of the macaque monkey. Nature 395:376-81 [Journal] [PubMed]

Rotaru DC, Lewis DA, Gonzalez-Burgos G (2007) Dopamine D1 receptor activation regulates sodium channel-dependent EPSP amplification in rat prefrontal cortex pyramidal neurons. J Physiol 581:981-1000 [Journal] [PubMed]

Royeck M, Horstmann MT, Remy S, Reitze M, Yaari Y, Beck H (2008) Role of axonal NaV1.6 sodium channels in action potential initiation of CA1 pyramidal neurons. J Neurophysiol 100:2361-80 [Journal] [PubMed]

Sacerdote L, Lánský P (2002) Interspike interval statistics in the Ornstein-Uhlenbeck neuronal model with signal-dependent noise. Biosystems 67:213-9 [PubMed]

Schmidt-Hieber C, Bischofberger J (2010) Fast sodium channel gating supports localized and efficient axonal action potential initiation. J Neurosci 30:10233-42 [Journal] [PubMed]

Schneidman E, Freedman B, Segev I (1998) Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput 10:1679-703 [PubMed]

Schrodinger E (1968) Statistical Thermodynamics

Sengupta B, Laughlin SB, Niven JE (2014) Consequences of converting graded to action potentials upon neural information coding and energy efficiency. PLoS Comput Biol 10:e1003439 [Journal] [PubMed]

Simen P, Balci F, de Souza L, Cohen JD, Holmes P (2011) A model of interval timing by neural integration. J Neurosci 31:9238-53 [Journal] [PubMed]

Sompolinsky H, Yoon H, Kang K, Shamir M (2001) Population coding in neuronal systems with correlated noise. Phys Rev E Stat Nonlin Soft Matter Phys 64:051904 [Journal] [PubMed]

STEIN RB (1965) A THEORETICAL ANALYSIS OF NEURONAL VARIABILITY. Biophys J 5:173-94 [PubMed]

Stein RB, Gossen ER, Jones KE (2005) Neuronal variability: noise or part of the signal? Nat Rev Neurosci 6:389-97 [Journal] [PubMed]

Steinmetz PN, Manwani A, Koch C, London M, Segev I (2000) Subthreshold voltage noise due to channel fluctuations in active neuronal membranes. J Comput Neurosci 9:133-48 [PubMed]

Stevens CF, Zador AM (1998) Input synchrony and the irregular firing of cortical neurons. Nat Neurosci 1:210-7 [Journal] [PubMed]

Strong SP, Koberle R, de Ruyter van Steveninck R, Bialek W (1997) Entropy and information in neuronal spike trains. Phys Rev Lett 80:197-201

Sugihara T, Qiu FT, von der Heydt R (2011) The speed of context integration in the visual cortex. J Neurophysiol 106:374-85 [Journal] [PubMed]

Sungkar M,Berger T,Levy WB (2016) Mutual Information and Parameter Estimation in the Generalized Inverse Gaussian Diffusion Model of Cortical Neurons IEEE Transactions on Molecular, Biological and Multi-Scale Communications 2(2):166-182

Tripathy SJ, Padmanabhan K, Gerkin RC, Urban NN (2013) Intermediate intrinsic diversity enhances neural population coding. Proc Natl Acad Sci U S A 110:8248-53 [Journal] [PubMed]

Tuckwell HC (2005) Introduction to theoretical neurobiology: volume 2, nonlinear and stochastic theories. vol. 8

Tuckwell HC, Ditlevsen S (2016) The Space-Clamped Hodgkin-Huxley System with Random Synaptic Input: Inhibition of Spiking by Weak Noise and Analysis with Moment Equations. Neural Comput 28:2129-61 [Journal] [PubMed]

van Rossum MC, O'Brien BJ, Smith RG (2003) Effects of noise on the spike timing precision of retinal ganglion cells. J Neurophysiol 89:2406-19 [Journal] [PubMed]

Wald A (1973) Sequential analysis

Warland DK (1991) Reading Between the Spikes: Real-Time Signal Processing in Neural Systems

Warland DK, Reinagel P, Meister M (1997) Decoding visual information from a population of retinal ganglion cells. J Neurophysiol 78:2336-50 [Journal] [PubMed]

White JA, Rubinstein JT, Kay AR (2000) Channel noise in neurons. Trends Neurosci 23:131-7 [PubMed]

Woolley SM, Gill PR, Theunissen FE (2006) Stimulus-dependent auditory tuning results in synchronous population coding of vocalizations in the songbird midbrain. J Neurosci 26:2499-512 [Journal] [PubMed]

Xing J,Berger T,Sejnowski TJ (2012) A Berger-Levy energy efficient neuron model with unequal synaptic weights Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on. IEEE :2964-2968

Yarom Y, Hounsgaard J (2011) Voltage fluctuations in neurons: signal or noise? Physiol Rev 91:917-29 [Journal] [PubMed]

Yu Y, Shu Y, McCormick DA (2008) Cortical action potential backpropagation explains spike threshold variability and rapid-onset kinetics. J Neurosci 28:7260-72 [Journal] [PubMed]