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References and models cited by this paper  References and models that cite this paper  
Anzill W,Russer P (1993) A general method to simulate noise in oscillators based on frequency domain techniques IEEE Trans. Microw. Theory Tech. 41(12):22562263 Arthur JV,Merolla PA,Akopyan F,Alvarez R,Cassidy A,Chandra S,Esser S,Imam N,Risk W,Rubin D,Manohar R,Modha D (2012) Building block of a programmable neuromorphic substrate: A digital neurosynaptic core Proc. 2012 Int. Joint Conf. Neural Netw. :18 Ascher UM,Petzold LR (1998) Computer methods for ordinary differential equations and differentialalgebraic equations. Attwell D, Laughlin SB (2001) An energy budget for signaling in the grey matter of the brain. J Cereb Blood Flow Metab 21:113345 [Journal] [PubMed] Bartoloni N (1992) Markovian processes in aneuploids: I. Diploid populations. J Theor Biol 155:27380 [PubMed] Bower JM, Beeman D (1995) The Book of GENESIS: Exploring Realistic Neural Models with the GEneral NEural SImulation System. [Journal] Brown E, Moehlis J, Holmes P (2004) On the phase reduction and response dynamics of neural oscillator populations. Neural Comput 16:673715 [Journal] [PubMed] Cafaro J, Rieke F (2010) Noise correlations improve response fidelity and stimulus encoding. Nature 468:9647 [Journal] [PubMed] Cassidy A,Andreou AG (2008) Dynamical digital silicon neurons Proc. 2008 IEEE Biomed. Circuits Syst. Conf :28929 Chen YD, Hill TL (1973) Fluctuations and noise in kinetic systems. Application to K+ channels in the squid axon. Biophys J 13:127695 [Journal] [PubMed] Clay JR, DeFelice LJ (1983) Relationship between membrane excitability and single channel openclose kinetics. Biophys J 42:1517 [Journal] [PubMed] Cooley J, Dodge F, Cohen H (1965) Digital computer solutions for excitable membrane models J Cell Comp Physiol 66:99108 CruzAlbrecht JM, Yung MW, Srinivasa N (2012) Energyefficient neuron, synapse and STDP integrated circuits. IEEE Trans Biomed Circuits Syst 6:24656 [Journal] [PubMed] Daniel R, Rubens JR, Sarpeshkar R, Lu TK (2013) Synthetic analog computation in living cells. Nature 497:61923 [Journal] [PubMed] Dayan P, Abbott LF (2001) Theoretical Neuroscience. Computational and Mathematical Modeling of Neural Systems Demir A,Gu C,Roychowdhury J (2010) Phase equations for quasiperiodic oscillators IEEE/ACM International conference on computeraided design Demir A,Mehrotra A,Roychowdhury J (2000) Phase noise in oscillators: a unifying theory and numerical methods for characterization IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 47(5):655674 Demir A,SangiovanniVincentelli A (1998) Analysis and simulation of noise in nonlinear electronic circuits and systems Kluwer Academic Publishers 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 1:195230 [PubMed]
Destexhe A, Mainen ZF, Sejnowski TJ (1998) Kinetic models of synaptic transmission Methods In Neuronal Modeling, Koch C:Segev I, ed. pp.1
Elf J, Ehrenberg M (2003) Fast evaluation of fluctuations in biochemical networks with the linear noise approximation. Genome Res 13:247584 [Journal] [PubMed] Esfahani ZG, Gollo LL, Valizadeh A (2016) Stimulusdependent synchronization in delayedcoupled neuronal networks. Sci Rep 6:23471 [Journal] [PubMed] Faisal AA (2009) Stochastic simulation of neurons axons and action potentials Stochastic Methods in Neuroscience :297343 Faisal AA, Selen LP, Wolpert DM (2008) Noise in the nervous system. Nat Rev Neurosci 9:292303 [Journal] [PubMed] Fitzhugh R (1965) A kinetic model of the conductance changes in nerve membrane J Cell Comp Physiol 66:111118 Fox RF, Lu Yn (1994) Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 49:34213431 [PubMed] Gajic Z,Qureshi MTJ (2008) Lyapunov matrix equation in system stability and control Gardiner CW (1983) Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences Gardner WA (1990) Introduction to Random Processes: With Applications to Signals and Systems Gillespie DT (1976) A General method for numerically simulating the stochastic time evolution of coupledchemical reactions J Comput Phys 22:403434 Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. Journal Of Physical Chemistry 81:23402361 Gillespie DT (2000) The chemical Langevin equation J Chem Phys 113:297306 Gillespie DT (2007) Stochastic simulation of chemical kinetics. Annu Rev Phys Chem 58:3555 [Journal] [PubMed] Goldwyn JH, Imennov NS, Famulare M, SheaBrown E (2011) Stochastic differential equation models for ion channel noise in HodgkinHuxley neurons. Phys Rev E Stat Nonlin Soft Matter Phys 83:041908 [Journal] [PubMed]
Goldwyn JH, SheaBrown E (2011) The what and where of adding channel noise to the HodgkinHuxley equations. PLoS Comput Biol 7:e1002247 [Journal] [PubMed]
Gu C, Xu J, Rohling J, Yang H, Liu Z (2015) Noise Induces Oscillation and Synchronization of the Circadian Neurons. PLoS One 10:e0145360 [Journal] [PubMed] Higham DJ (2008) Modeling and simulating chemical reactions SIAM Review 50(2):347368 Hille B (2001) Ionic Channels of Excitable Membranes Hines ML, Carnevale NT (2001) NEURON: a tool for neuroscientists. Neuroscientist 7:12335 [Journal] [PubMed]
HODGKIN AL, HUXLEY AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:50044 [Journal] [PubMed] Indiveri G, LinaresBarranco B, Hamilton TJ, van Schaik A, EtienneCummings R, Delbruck T, Liu SC, Dudek P, Häfliger P, Renaud S, Schemmel J, Cauwenberghs G, Arthur J, Hynna K, Folowosele F, Saighi S, SerranoGotarredona T, Wijekoon J, Wang Y, Boahen K (2011) Neuromorphic silicon neuron circuits. Front Neurosci 5:73 [Journal] [PubMed] Izhikevich EM (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting [Journal]
Kandel ER, Schwartz JH, Jessell TM (2000) Principles of neural science (4th ed), Kandel ER:Schwartz JH:Jessell TM, ed. Kärtner FX (1990) Analysis of white and f^alpha noise in oscillators Int. J. Circuit Theory Appl. 18(5):485519 Kilinc D,Demir A (2015) Simulation of noise in neurons and neuronal circuits Proceedings of the IEEE/ACM international conference on computeraided design (ICCAD) :589596 [Journal]
Koickal TJ,Hamilton JA,Tan SL,Covington JA,Gardner JW,Pearce TC (2007) Analog VLSI circuit implementation of an adaptive neuromorphic olfaction chip IEEE Trans. Circuits Syst. I Reg. Papers :6073 Lennie P (2003) The cost of cortical computation. Curr Biol 13:4937 [PubMed] Linaro D, Storace M, Giugliano M (2011) Accurate and fast simulation of channel noise in conductancebased model neurons by diffusion approximation. PLoS Comput Biol 7:e1001102 [Journal] [PubMed]
Mahmutoglu AG,Demir A,Roychowdhury J (2013) Modeling and analysis of (nonstationary) low frequency noise in nano devices: A synergistic approach based on stochastic chemical kinetics Proc. 2013 IEEE/ACM Int. Conf. Comput.Aided Design :500507 Mahmutoglu AG, Demir A (2013) CIRSIUM: A circuit simulator in MATLAB® with object oriented design Proceedings of the 2013 9th Conference on Ph.D. Research in Microelectronics and Electronics (PRIME) :173176 [Journal]
Mahmutoglu AG,Demir A (2014) Modeling and analysis of nonstationary lowfrequency noise in circuit simulators: enabling non Monte Carlo techniques Proceedings of the international conference on computeraided design :309315 Mahmutoglu AG,Demir A (2015) Modeling and simulation of lowfrequency noise in nano devices: Stochastically correct and carefully crafted numerical techniques IEEE Trans. Comput.Aided Design Integr. Circuits Syst. 34(5):794807 Mahmutoglu AG,Demir A (2016) Non Monte Carlo analysis of lowfrequency noise: Exposition of intricate nonstationary behavior and comparison with legacy models IEEE Trans. Comput.Aided Design Integr. Circuits Syst. 35(11):18251835 Mainen ZF, Sejnowski TJ (1995) Reliability of spike timing in neocortical neurons. Science 268:15036 [PubMed] MATLAB version (2015) "MATLAB” version 2015b", 2015, [online] Available: http://www.mathworks.com/products/matlab. [Journal] Mead C (1989) Analog VLSI and neural systems. Mead C (1990) Neuromorphic electronic systems Proc IEEE 78:16291636 Mitra S, Fusi S, Indiveri G (2009) RealTime Classification of Complex Patterns Using SpikeBased Learning in Neuromorphic VLSI. IEEE Trans Biomed Circuits Syst 3:3242 [Journal] [PubMed] Nastov OJ (1999) Spectral methods for circuit analysis Okumura M,Tanimoto H (1997) A timedomain method for numerical noise analysis of oscillators Proc. 1997 Asia South Pacific Design Autom. Conf. :477482 Orio P, Soudry D (2012) Simple, fast and accurate implementation of the diffusion approximation algorithm for stochastic ion channels with multiple states. PLoS One 7:e36670 [Journal] [PubMed]
Ramakrishnan S, Hasler PE, Gordon C (2011) Floating gate synapses with spiketimedependent plasticity. IEEE Trans Biomed Circuits Syst 5:24452 [Journal] [PubMed] Roychowdhury J,Long D,Feldmann P (1998) Cyclostationary noise analysis of large RF circuits with multitone excitations IEEE J. SolidState Circuits 33(3):324336 Sakmann B, Neher E (1995) Singlechannel Recording 2:487 Sarpeshkar R (2014) Analog synthetic biology Philosoph. Trans. Roy. Soc. A Shanthikumar JG (1986) Uniformization and hybrid simulation/analytic models of renewal processes Oper. Res. 34(4):573580 Sharpeshkar R (2010) Ultra low power bioelectronics: fundamentals, biomedical applications, and bioinspired system Stein RB, Gossen ER, Jones KE (2005) Neuronal variability: noise or part of the signal? Nat Rev Neurosci 6:38997 [Journal] [PubMed] Subrahmanyam M (1986) On a numerical method of solving the Lyapunov and Sylvester equations International Journal of Control 43(2):433439 Tank DW, Hopfield JJ (1987) Collective computation in neuronlike circuits. Sci Am 257:10414 [PubMed] Teo JJ, Woo SS, Sarpeshkar R (2015) Synthetic Biology: A Unifying View and Review Using Analog Circuits. IEEE Trans Biomed Circuits Syst 9:45374 [Journal] [PubMed] Welsh DK, Takahashi JS, Kay SA (2010) Suprachiasmatic nucleus: cell autonomy and network properties. Annu Rev Physiol 72:55177 [Journal] [PubMed] White JA, Rubinstein JT, Kay AR (2000) Channel noise in neurons. Trends Neurosci 23:1317 [PubMed] Yu T,Cauwenberghs TG (2010) Analog VLSI biophysical neurons and synapses with programmable membrane channel kinetics IEEE Trans. Biomed. Circuits Syst. 4(3):139148  Kilinc D, Demir A (2018) Spike timing precision of neuronal circuits. J Comput Neurosci 44:341362 [Journal] [PubMed]

References and models cited by this paper  References and models that cite this paper  
Adler R (1973) A study of locking phenomena in oscillators Proceedings of the IEEE 61(10):13801385 Attwell D, Laughlin SB (2001) An energy budget for signaling in the grey matter of the brain. J Cereb Blood Flow Metab 21:113345 [Journal] [PubMed] Bacci A, Huguenard JR (2006) Enhancement of spiketiming precision by autaptic transmission in neocortical inhibitory interneurons. Neuron 49:11930 [Journal] [PubMed] Brown E, Moehlis J, Holmes P (2004) On the phase reduction and response dynamics of neural oscillator populations. Neural Comput 16:673715 [Journal] [PubMed] Buzsáki G, Draguhn A (2004) Neuronal oscillations in cortical networks. Science 304:19269 [Journal] [PubMed] Chiu CS, Jensen K, Sokolova I, Wang D, Li M, Deshpande P, Davidson N, Mody I, Quick MW, Quake SR, Lester HA (2002) Number, density, and surface/cytoplasmic distribution of GABA transporters at presynaptic structures of knockin mice carrying GABA transporter subtype 1green fluorescent protein fusions. J Neurosci 22:1025166 [PubMed] Cover TM,Thomas JA (2012) Elements of information theory Dayan P, Abbott LF (2001) Theoretical Neuroscience. Computational and Mathematical Modeling of Neural Systems de la Casa MA, de la Rubia FJ, Ivanov PCh (2007) Patterns of spiral wave attenuation by lowfrequency periodic planar fronts. Chaos 17:015109 [Journal] [PubMed] De Smedt V,Gielen G,Dehaene W (2015) Injectionlocked oscillators Temperatureand supply voltageindependent time references for wireless sensor networks :209256 Deleuze C, Pazienti A, Bacci A (2014) Autaptic selfinhibition of cortical GABAergic neurons: synaptic narcissism or useful introspection? Curr Opin Neurobiol 26:6471 [Journal] [PubMed] Demir A,Gu C,Roychowdhury J (2010) Phase equations for quasiperiodic oscillators IEEE/ACM International conference on computeraided design Demir A (2000) Floquet theory and nonlinear perturbation analysis for oscillators with differentialalgebraic equations International Journal of Circuit Theory and Applications 28(2):163185 Demir A (2006) Computing timing jitter from phase noise spectra for oscillators and phaselocked loops with white and 1/f noise IEEE Transactions on Circuits and SystemsI: Regular Papers Demir A,Mehrotra A,Roychowdhury J (2000) Phase noise in oscillators: a unifying theory and numerical methods for characterization IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 47(5):655674 Demir A,Roychowdhury J (2003) A reliable and efficient procedure for oscillator PPV computation, with phase noise macromodelling applications IEEE Transaction on CAD of ICs and Systems Demir A,SangiovanniVincentelli A (1998) Analysis and simulation of noise in nonlinear electronic circuits and systems Kluwer Academic Publishers Destexhe A, Contreras D, Steriade M (1998) Mechanisms underlying the synchronizing action of corticothalamic feedback through inhibition of thalamic relay cells. J Neurophysiol 79:9991016 [Journal] [PubMed]
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 1:195230 [PubMed]
Destexhe A, Mainen ZF, Sejnowski TJ (1998) Kinetic models of synaptic transmission Methods In Neuronal Modeling, Koch C:Segev I, ed. pp.1
DiGiovanna J, Nguyen TA, Guinand N, PérezFornos A, Micera S (2016) Neural Network Model of Vestibular Nuclei Reaction to Onset of Vestibular Prosthetic Stimulation. Front Bioeng Biotechnol 4:34 [Journal] [PubMed] Esfahani ZG, Gollo LL, Valizadeh A (2016) Stimulusdependent synchronization in delayedcoupled neuronal networks. Sci Rep 6:23471 [Journal] [PubMed] Faisal AA, Selen LP, Wolpert DM (2008) Noise in the nervous system. Nat Rev Neurosci 9:292303 [Journal] [PubMed] Fitzhugh R (1965) A kinetic model of the conductance changes in nerve membrane J Cell Comp Physiol 66:111118 Fox RF, Lu Yn (1994) Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 49:34213431 [PubMed] Gajic Z,Qureshi MTJ (2008) Lyapunov matrix equation in system stability and control Gardiner CW (1983) Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences Ghazanfar AA, Schroeder CE (2006) Is neocortex essentially multisensory? Trends Cogn Sci 10:27885 [Journal] [PubMed] Gillespie DT (2007) Stochastic simulation of chemical kinetics. Annu Rev Phys Chem 58:3555 [Journal] [PubMed] Goldwyn JH, Imennov NS, Famulare M, SheaBrown E (2011) Stochastic differential equation models for ion channel noise in HodgkinHuxley neurons. Phys Rev E Stat Nonlin Soft Matter Phys 83:041908 [Journal] [PubMed]
Grothe B, Klump GM (2000) Temporal processing in sensory systems. Curr Opin Neurobiol 10:46773 [PubMed] Gu C, Xu J, Rohling J, Yang H, Liu Z (2015) Noise Induces Oscillation and Synchronization of the Circadian Neurons. PLoS One 10:e0145360 [Journal] [PubMed] Gupta SC (1975) Phaselocked loops Proceedings of the IEEE 63(2):291306 Hasenstaub A, Shu Y, Haider B, Kraushaar U, Duque A, McCormick DA (2005) Inhibitory postsynaptic potentials carry synchronized frequency information in active cortical networks. Neuron 47:42335 [Journal] [PubMed] Higham DJ (2008) Modeling and simulating chemical reactions SIAM Review 50(2):347368 Isaacson JS, Scanziani M (2011) How inhibition shapes cortical activity. Neuron 72:23143 [Journal] [PubMed] Izhikevich EM (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting [Journal]
Kilinc D, Demir A (2017) Noise in Neuronal and Electronic Circuits: A General Modeling Framework and NonMonte Carlo Simulation Techniques. IEEE Trans Biomed Circuits Syst 11:958974 [Journal] [PubMed]
Kilinc D,Demir A (2015) Simulation of noise in neurons and neuronal circuits Proceedings of the IEEE/ACM international conference on computeraided design (ICCAD) :589596 [Journal]
Kundert KS,White JK,SangiovanniVincentelli A (1990) Steadystate methods for simulating analog and microwave circuits Lennie P (2003) The cost of cortical computation. Curr Biol 13:4937 [PubMed] Linaro D, Storace M, Giugliano M (2011) Accurate and fast simulation of channel noise in conductancebased model neurons by diffusion approximation. PLoS Comput Biol 7:e1001102 [Journal] [PubMed]
Mahmutoglu AG,Demir A (2014) Modeling and analysis of nonstationary lowfrequency noise in circuit simulators: enabling non Monte Carlo techniques Proceedings of the international conference on computeraided design :309315 Mainen ZF, Sejnowski TJ (1995) Reliability of spike timing in neocortical neurons. Science 268:15036 [PubMed] MasugiTokita M, Tarusawa E, Watanabe M, Molnár E, Fujimoto K, Shigemoto R (2007) Number and density of AMPA receptors in individual synapses in the rat cerebellum as revealed by SDSdigested freezefracture replica labeling. J Neurosci 27:213544 [Journal] [PubMed] Miller EK (2000) The prefrontal cortex and cognitive control. Nat Rev Neurosci 1:5965 [Journal] [PubMed] Moujahid A, d'Anjou A, Torrealdea FJ, Torrealdea F (2011) Energy and information in HodgkinHuxley neurons. Phys Rev E Stat Nonlin Soft Matter Phys 83:031912 [Journal] [PubMed] Nowak LG, SanchezVives MV, McCormick DA (1997) Influence of low and high frequency inputs on spike timing in visual cortical neurons. Cereb Cortex 7:487501 [PubMed] Orio P, Soudry D (2012) Simple, fast and accurate implementation of the diffusion approximation algorithm for stochastic ion channels with multiple states. PLoS One 7:e36670 [Journal] [PubMed]
Perrais D, Veran J, Mulle C (2010) Gating and permeation of kainate receptors: differences unveiled. Trends Pharmacol Sci 31:51622 [Journal] [PubMed] Pouille F, Scanziani M (2001) Enforcement of temporal fidelity in pyramidal cells by somatic feedforward inhibition. Science 293:115963 [Journal] [PubMed] Razavi B (2004) A study of injection locking and pulling in oscillators IEEE Journal of SolidState Circuits 39(9):14151424 Sharpeshkar R (2010) Ultra low power bioelectronics: fundamentals, biomedical applications, and bioinspired system Subrahmanyam M (1986) On a numerical method of solving the Lyapunov and Sylvester equations International Journal of Control 43(2):433439 Suvak O,Demir A (2011) On phase models for oscillators IEEE Transactions On ComputerAided Design of Integrated Circuits and Systems 30(7):972985 Tank DW, Hopfield JJ (1987) Collective computation in neuronlike circuits. Sci Am 257:10414 [PubMed] VanRullen R, Guyonneau R, Thorpe SJ (2005) Spike times make sense. Trends Neurosci 28:14 [Journal] [PubMed] Varga Z, Jia H, Sakmann B, Konnerth A (2011) Dendritic coding of multiple sensory inputs in single cortical neurons in vivo. Proc Natl Acad Sci U S A 108:154205 [Journal] [PubMed] White JA, Rubinstein JT, Kay AR (2000) Channel noise in neurons. Trends Neurosci 23:1317 [PubMed] 
References and models cited by this paper  References and models that cite this paper  
Ascher UM,Petzold LR (1998) Computer methods for ordinary differential equations and differentialalgebraic equations. Bartoloni N (1992) Markovian processes in aneuploids: I. Diploid populations. J Theor Biol 155:27380 [PubMed] Bower J, Beeman D (1994) The Book of GENESIS: exploring realistic neural models with the GEneral NEural Simulation System Bruce IC, Irlicht LS, White MW, O'Leary SJ, Dynes S, Javel E, Clark GM (1999) A stochastic model of the electrically stimulated auditory nerve: pulsetrain response. IEEE Trans Biomed Eng 46:6307 [PubMed]
Cafaro J, Rieke F (2010) Noise correlations improve response fidelity and stimulus encoding. Nature 468:9647 [Journal] [PubMed] Chen YD, Hill TL (1973) Fluctuations and noise in kinetic systems. Application to K+ channels in the squid axon. Biophys J 13:127695 [Journal] [PubMed] Clay JR, DeFelice LJ (1983) Relationship between membrane excitability and single channel openclose kinetics. Biophys J 42:1517 [Journal] [PubMed] Cooley J, Dodge F, Cohen H (1965) Digital computer solutions for excitable membrane models J Cell Comp Physiol 66:99108 Dangerfield CE,Kay D,Burrage K (2011) Comparison of continuous and discrete stochastic ion channel models Engineering in Medicine and Biology Society EMBC 2011 Annual International Conference of the IEEE :704707 Dayan P, Abbott LF (2001) Theoretical Neuroscience. Computational and Mathematical Modeling of Neural Systems Deelstra G,Delbaen F (1998) Convergence of discretized stochastic (interest rate) processes with stochastic drift term Applied stochastic models and data analysis 14(1):7784 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 1:195230 [PubMed]
Destexhe A, Mainen ZF, Sejnowski TJ (1998) Kinetic models of synaptic transmission Methods In Neuronal Modeling, Koch C:Segev I, ed. pp.1
Faisal AA (2009) Stochastic simulation of neurons axons and action potentials Stochastic Methods in Neuroscience :297343 Faisal AA, Selen LP, Wolpert DM (2008) Noise in the nervous system. Nat Rev Neurosci 9:292303 [Journal] [PubMed] Fitzhugh R (1965) A kinetic model of the conductance changes in nerve membrane J Cell Comp Physiol 66:111118 Fox RF, Lu Yn (1994) Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 49:34213431 [PubMed] Gardiner CW (1983) Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences Gillespie DT (1976) A General method for numerically simulating the stochastic time evolution of coupledchemical reactions J Comput Phys 22:403434 Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. Journal Of Physical Chemistry 81:23402361 Gillespie DT (2000) The chemical Langevin equation J Chem Phys 113:297306 Gillespie DT (2007) Stochastic simulation of chemical kinetics. Annu Rev Phys Chem 58:3555 [Journal] [PubMed] Goldwyn JH, Imennov NS, Famulare M, SheaBrown E (2011) Stochastic differential equation models for ion channel noise in HodgkinHuxley neurons. Phys Rev E Stat Nonlin Soft Matter Phys 83:041908 [Journal] [PubMed]
Goldwyn JH, SheaBrown E (2011) The what and where of adding channel noise to the HodgkinHuxley equations. PLoS Comput Biol 7:e1002247 [Journal] [PubMed]
Grimmett G,Stirzaker D (1992) Probability and random processes Oxford University Press Higham DJ (2001) An algorithmic introduction to numerical simulation of stochastic differential equation Siam Review 43:525546 Higham DJ (2008) Modeling and simulating chemical reactions SIAM Review 50(2):347368 Higham DJ,Mao X (2005) Convergence of Monte Carlo simulations involving the meanreverting square root process Journal of Computational Finance 8(3):3561 Hille B (2001) Ionic Channels of Excitable Membranes Hines ML, Carnevale NT (2001) NEURON: a tool for neuroscientists. Neuroscientist 7:12335 [Journal] [PubMed]
HODGKIN AL, HUXLEY AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:50044 [Journal] [PubMed] Huang Y, Rudiger S, Shuai J (2013) Phys Rev E 87:012716 Kandel ER, Jessell TM, Schwartz JH (2008) Principles of Neural Science Kloeden PE, Platen E (1992) Numerical Solution Of Stochastic Differential Equations Linaro D, Storace M, Giugliano M (2011) Accurate and fast simulation of channel noise in conductancebased model neurons by diffusion approximation. PLoS Comput Biol 7:e1001102 [Journal] [PubMed]
Lord R, Koekkoek R, Dijk DV (2010) A comparison of biased simulation schemes for stochastic volatility models Quantitative Finance 10(2):177194 Mahmutoglu AG,Demir A,Roychowdhury J (2013) Modeling and analysis of (nonstationary) low frequency noise in nano devices: A synergistic approach based on stochastic chemical kinetics Proc. 2013 IEEE/ACM Int. Conf. Comput.Aided Design :500507 Mahmutoglu AG,Demir A (2015) Modeling and simulation of lowfrequency noise in nano devices: Stochastically correct and carefully crafted numerical techniques IEEE Trans. Comput.Aided Design Integr. Circuits Syst. 34(5):794807 Orio P, Soudry D (2012) Simple, fast and accurate implementation of the diffusion approximation algorithm for stochastic ion channels with multiple states. PLoS One 7:e36670 [Journal] [PubMed]
Pezo D, Soudry D, Orio P (2014) Diffusion approximationbased simulation of stochastic ion channels: which method to use? Front Comput Neurosci 8:139 [Journal] [PubMed]
Sakmann B, Neher E (1995) Singlechannel Recording 2:487 Schmid G,Goychuk I,Hanggi P (2001) Stochastic resonance as a collective property of ion channel assemblies EPL (Europhysics Letters) 56(1):22 Sengupta B, Laughlin SB, Niven JE (2010) Comparison of Langevin and Markov channel noise models for neuronal signal generation. Phys Rev E Stat Nonlin Soft Matter Phys 81:011918 [Journal] [PubMed] Shanthikumar JG (1986) Uniformization and hybrid simulation/analytic models of renewal processes Oper. Res. 34(4):573580 Stein RB, Gossen ER, Jones KE (2005) Neuronal variability: noise or part of the signal? Nat Rev Neurosci 6:38997 [Journal] [PubMed] van Moorsel AP,Sanders WH (1994) Adaptive uniformization Stochastic Models 10(3):619647 White JA, Rubinstein JT, Kay AR (2000) Channel noise in neurons. Trends Neurosci 23:1317 [PubMed]  Kilinc D, Demir A (2017) Noise in Neuronal and Electronic Circuits: A General Modeling Framework and NonMonte Carlo Simulation Techniques. IEEE Trans Biomed Circuits Syst 11:958974 [Journal] [PubMed]
Kilinc D, Demir A (2018) Spike timing precision of neuronal circuits. J Comput Neurosci 44:341362 [Journal] [PubMed]

References and models cited by this paper  References and models that cite this paper  
Lemaitre L,McAndrew C,Hamm S (2002) ADMSautomatic device model synthesizer Custom Integrated Circuits Conference :2730 Aadithya K,Demir A,Venugopalan S,Roychowdhury J (2013) Accurate prediction of random telegraph noise effects in SRAMs and DRAMs IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems 32(1):7386 Gildenblat G,Li X,Wang H,Wu W,Van Langevelde R,Scholten AJ,Smit GDJ,Klaassen DBM (2005) Introduction to PSP MOSFET model Proc. the MSM 2005 Int. Conf., Nanotech 2005 Gildenblat G,Li X,Wu W,Wang H,Jha A,van Langevelde R,Smit G,Scholten A,Klaassen D (2006) PSP: an advanced surfacepotentialbased MOSFET model for circuit simulation IEEE Transactions on Electron Devices 53(9):19791993 Hindmarsh AC, Brown PN, Grant KE, Lee SL, Serban R, Shumaker DE, Woodward C (2005) SUNDIALS: Suite of nonlinear and differentialalgebraic equation solvers ACM Trans Math Software 31:363396 Kirton MJ,Uren MJ (1989) Noise in solidstate microstructures: A new perspective on individual defects, interface states and low frequency (1/f) noise Advances in Physics 38(4):367468 Kundert KS (1995) The Designer's Guide to Spice and Spectre Martin S,Li G,Worley E;White J (1997) The gate bias and geometry dependence of random telegraph signal amplitudes [MOSFET] IEEE Electron Device Letters 18(9):444446 Miller I,FitzPatrick D (1998) Analog Behavioral Modeling with the VerilogA Language Roychowdhury J,Amsallem D (2011) ModSpec: an open, flexible specification framework for multidomain device modelling 2011 IEEE/ACM International Conference on ComputerAided Design (ICCAD) :367374 Schwarz S,Russek S (1983) Semiempirical equations for electron velocity in silicon: Part IIMOS inversion layer IEEE Transactions on Electron Devices 30(12):16341639 van Moorsel AP,Sanders WH (1994) Adaptive uniformization Stochastic Models 10(3):619647  Kilinc D, Demir A (2017) Noise in Neuronal and Electronic Circuits: A General Modeling Framework and NonMonte Carlo Simulation Techniques. IEEE Trans Biomed Circuits Syst 11:958974 [Journal] [PubMed]
