随机相关输入的Integrate-and-Fire神经元模型
|
摘要
尽管随机输入的单一神经元模型已经在理论和计算神经科学中被广泛地研究,但大部分研究是在假定输入为独立的泊淞过程情况下进行的。因为神经元发出和接收放电脉冲一般是更新过程,因此这种假定是对生理学数据的一种很粗略的近似。我们将考虑更新输入的情况,它是对神经键输入的一种更精确的近似。本文主要研究了Integrate-and-Fire神经元模型随机更新输入的近似问题和相关更新输入对Integrate-and-Fire神经元模型输出和解码的影响,以及两个相关点过程之间相关性的描述,获得了一些有用的新结论。具体地说:
第一章介绍了问题研究的背景及本文的主要工作。
第二章研究了随机更新输入的Integrate-and-Fire神经元模型的近似问题,得到了两种新的近似方案。
第三章研究了低相关更新输入对Integrate-and-Fire模型输出的影响。对低的正相关,随着输入相关的增加,平均发放时间缩短。对低的负相关,平均发放时间独立于输入相关。
第四章研究了两个相关点过程之间相关性的描述。我们指出当两个点过程是泊淞过程时,相关系数能充分描述它们之间的相互关系。当两个点过程是更新过程时,相关系数随着时间窗口的变化而变化,是时间窗口的递增函数。于是我们提出用相关系数曲线来描述两个更新过程之间的相互关系。
第五章研究了随机相关输入的Integrate-and-Fire神经元模型的最优解码问题。使用Fisher信息,在理论上我们解决了这样一个问题:当抑制和兴奋输入的比(r)取何值时,神经元能最精确地解码Integrate-and-Fire神经元的输入。同时,我们指出相关输入整体上减小了解码的精确性。这些结论对优化神经网络的设计将是很有用的。
Although single neuron models with random inputs have been widely studied in theory and experiment, most such studies are done under the assumption that inputs are Poisson processes. Because spike trains which neuron fire and receive are commoly renewal processes. The assumption is a very rough approximation of physiological data. We will consider the case of renewal process inputs, which represents a more accurate approximation of synaptic inputs.In this paper, the issue how to approximate the integrate-and-fire(IF) with renewal inputs is studied, The effects of correlation between renewal process synaptic inputs are examined and the correlation relationship between two point processes is studied. A series of new results are obtained.Chapter 1 introduces the background of the problem-researching , the recent development of the neuron model and some research results we have obtained in this field.Chapter 2 focuses on the issue how to approximate the integrate-and-fire model with stochastic renewal inputs, two novel approximation schemes are proposed.Chapter 3 concerns the effect low correlation between renewal process synaptic inputs impacts on the output of the integrate-and-fire model. For low positive correlations, mean firing time is a decreasing function of input correlation . For low negative correlations, mean firing time is almost independent of input correlation.Chapter 4 concerns the correlation relationship between two point processes. We conclude: when the point process is Poisson, a single cofficient is enough to descibe the correlation relationship. However, for renewal processes, The correlation cofficient is a increasing function of time binsize. So we introduce the correlation coefficient curve to characterize the correlation relationship.
Chapter 5 discusses optimally decoding the inputs of integrate-and-fire neuron model with correlated inputs. Using the Fisher information,we theoretically solve the issue: what is the rate(r) between inhibitory and exicitatory inputs so that the neuron can most accurately decode input rate. Besides, we argue that correlation input in general reduces the accutacy. The conclusions should be useful for the design of neural networks.
第一章介绍了问题研究的背景及本文的主要工作。
第二章研究了随机更新输入的Integrate-and-Fire神经元模型的近似问题,得到了两种新的近似方案。
第三章研究了低相关更新输入对Integrate-and-Fire模型输出的影响。对低的正相关,随着输入相关的增加,平均发放时间缩短。对低的负相关,平均发放时间独立于输入相关。
第四章研究了两个相关点过程之间相关性的描述。我们指出当两个点过程是泊淞过程时,相关系数能充分描述它们之间的相互关系。当两个点过程是更新过程时,相关系数随着时间窗口的变化而变化,是时间窗口的递增函数。于是我们提出用相关系数曲线来描述两个更新过程之间的相互关系。
第五章研究了随机相关输入的Integrate-and-Fire神经元模型的最优解码问题。使用Fisher信息,在理论上我们解决了这样一个问题:当抑制和兴奋输入的比(r)取何值时,神经元能最精确地解码Integrate-and-Fire神经元的输入。同时,我们指出相关输入整体上减小了解码的精确性。这些结论对优化神经网络的设计将是很有用的。
Although single neuron models with random inputs have been widely studied in theory and experiment, most such studies are done under the assumption that inputs are Poisson processes. Because spike trains which neuron fire and receive are commoly renewal processes. The assumption is a very rough approximation of physiological data. We will consider the case of renewal process inputs, which represents a more accurate approximation of synaptic inputs.In this paper, the issue how to approximate the integrate-and-fire(IF) with renewal inputs is studied, The effects of correlation between renewal process synaptic inputs are examined and the correlation relationship between two point processes is studied. A series of new results are obtained.Chapter 1 introduces the background of the problem-researching , the recent development of the neuron model and some research results we have obtained in this field.Chapter 2 focuses on the issue how to approximate the integrate-and-fire model with stochastic renewal inputs, two novel approximation schemes are proposed.Chapter 3 concerns the effect low correlation between renewal process synaptic inputs impacts on the output of the integrate-and-fire model. For low positive correlations, mean firing time is a decreasing function of input correlation . For low negative correlations, mean firing time is almost independent of input correlation.Chapter 4 concerns the correlation relationship between two point processes. We conclude: when the point process is Poisson, a single cofficient is enough to descibe the correlation relationship. However, for renewal processes, The correlation cofficient is a increasing function of time binsize. So we introduce the correlation coefficient curve to characterize the correlation relationship.
Chapter 5 discusses optimally decoding the inputs of integrate-and-fire neuron model with correlated inputs. Using the Fisher information,we theoretically solve the issue: what is the rate(r) between inhibitory and exicitatory inputs so that the neuron can most accurately decode input rate. Besides, we argue that correlation input in general reduces the accutacy. The conclusions should be useful for the design of neural networks.
引文
[1] W. S. McCulloch and W. Pitts. A logical calculus the ideas imminet in nervous activity[J]. Bulletin of Mathematical biophysics., 1943, 5: 115-133.
[2] Brown, D., Feng, J., Feerick. S., Varibility of firing of Hodgkin-Huxley and FitzHugh Nagumo neurons with stochastic synaptic input[J]. Phys. Rev. Lett., 1999, 82: 4731- 4734.
[3] Feng, J., and Li G. Integrate-and-Fire and Hodgkin-Huxley models with current inputs[J]. J. Phys. A: Math. Gen., 2001, 34: 1649-1664.
[4] Softky and Koch. The highly irregular firing of cortical-cells is inconsistent with temporal integration of random EPSPs[J]. J. Neurosci., 1993, 13: 334-350.
[5] Shadlen M. N. and Newsome W. T., Noise, neural codes and cortical organization[J]. Curr. Opin. Neurobiol., 1994, 4: 569-579.
[6] Feng, J., Behaviours of spike output jitter in the integrate-and-fire model[J]. Phys. Rev. Lett., 1997, 79: 4505-4734.
[7] Feng, J., Brown, D., Impact of temporal variation and the balance between excitation and inhibition on the output of the perfect integrate-and-fire model[J]. Biol. Cybern., 1998b, 78: 369-376.
[8] Bernander O, Koch C, Usher M, The effects of synchronized inputs at the single neuron level[J]. Neural Comput., 1994, 6: 622-641.
[9] Feng J, Brown D, Coeffcient or variation greater than 0.5 how and when?[J]. Biol Cybern., 1999a, 80: 291-297.
[10] Brown D, Feng J, Is there a problem matching model and real CV(ISI)[J]. Neurocomputing., 1999, 26-7: 117-122.
[11] Cope, D. K.,and Tuckwell, H. C. Firing rates of neurons with random excitation and inhibion[J]. J. Theor. Biol., 1979, 80: 1-14.
[12] Yingchun Deng, Enrico Rossoni, Jianfeng Feng, Dynamics of moment neuronal networks I:Foundations[J]. Europe Phys lett., (in press).
[13] Zohary,E.,Shadlen,M.N.,and Newsome,W.T. Correlated neuronal discharge rate and its implications for psychophysical performance[J].Nature,1994,370:140-143.
[14] Stevens,C.F.,and Zador,A.M. Input synchrony and the irregular firing of cortical neurons [J].Nat.Neurosci., 1998,1:210-217.
[15] Salinas E. and Sejnowski T.J.,Correlated neuronal activity and the flow of neural information[J].Nat Rev Neurosci,2001,2:539-550.
[16] Feng J,Computational neuroscience -A comprehensive approach[M].ChapmanHall:CRC Press,2003.
[17] Salinas E. and Sejnowski T.J.,Impact of correlated synaptic input on output fir- ing rate and variability in simple neuronal models[J]. J.Neurosci.,2000,20(16):6193- 6209.
[18] Deng Y C,Ding M,Feng,J, Synchronization in stochastic coupled systems[J].J.Phys A: Math and Gen.,1999, 11:91-101.
[19] Tuckwell H C, Stochastic processes in the neuroscience[M].SIAM: Philadel-phia, 1989.
[20] Cox P.R.,and Lewis P.A.W. The statistical analysis of series of events[M].Latimer Trend & Co.Ltd Whitstable,1966.
[21] Hunter J.J. Renewal theory in two dimensions:Basic results.[J].Adv.Appl.Probab., 1974,6:376-391.
[22] Hunter J.J. Renewal theory in two dimensions:asymptotic results[J]. Adv. Appl. Pr obab.,1974,6: 546-562.
[23] Gawne TJ,Richmond BJ ,How independent are the messages carried by adjacent inferior temporal cortical neurons?[J].J Neurosci.,1993, 13:2758-2772.
[24] Abbott L.F., Varela J.A.,Sen K. and Nelson S.B. Synaptic depression and cor- tical gain control[J].Science.,1997,275:220-223.
[25] Yingchun Deng, Peter Williams, Feng Liu and Jianfeng Feng, Neuronal discrimination capacity [J]. J. Phys. A: Math. Gen., 2003, 36: 1-20.
[26] Decharms RC, Merxenich MM. Primary cortical representation of sounds by the coordination of action potential timing[J]. Nature., 1995, 381: 610-613.
[27] Dan Yet al., Coding of visual information by precisely correlated spikes in the lateral geniculate nucleus[J]. Nat Neurosci., 1998, 1: 501-507.
[28] Engel AK et al., Why does the cortex oscillate? [J]. Curt Biol., 1992, 2: 332-334.
[29] Leng G. et al., Responses of magnocellular neurons to osmotic stimulation involves coactivation of excitatory and inhibitory input: an experimental and theoretical analysis[J]. J Neurosci., 2001, 21: 6967-6977.
[30] Knight B. W. Dynamics of encoding in a population of neurons[J]. J. Gen. Physiol., 1972, 59: 734-766.
[31] Sompolinsky H., Yoon H., Kang K. J., Population coding in neuronal systems with correlated noise. [J]. Phy. Rev. E., 2001, 64(5)no.051904.
[32] Treves A. Mean-field analysis of neuronal spike dynamics[J]. Network., 1993, 4: 259-284.
[33] Nirenberg S, Latham PE, Decoding neuronal spike trains: How important are correlation?[J]. P Natl Acad Sci USA., 2003, 100: 7348-7353.
[34] Strong SP, Koberle R, Entropy and information in neural spike trains[J]. Phys Rev lett., 1998, 80: 197-200.
[35] Amit D. J.and Brunel N, Dynamics of a recurrent network of spiking neurons before and following learning[J]. Network: Computation in Neural Systems., 1997, 8: 373-404.
[36] Abbott L F, Dayan P, The effect of correlated activity on the accuracy of a population code[J]. Neural Comput., 1999, 11: 91-101.
[37] 茆诗松,王静龙,濮晓龙.高等数理统计[M].北京;高等教育出版社,1998.
[38] Ping Zhang,Jianfeng Feng,Ideal observer of single neuron activity [J]. Neurocomputing., 2002, 44-46:243-247.
[39] Feng J,Brown D,and Li G.Synchronization due to common pulsed input in steins model[J].Phys.Rev.E., 2000, 61:2987-2995.
[40] Feng,J.F.Is the integrate-and-fire model good enough?-a review.[J].Neural Net- works., 2001, 14:955-975.
[41] Aldous D, Probability approxmation via the poisson clumping heuristic[M]. Berlin:Springer,1989.
[2] Brown, D., Feng, J., Feerick. S., Varibility of firing of Hodgkin-Huxley and FitzHugh Nagumo neurons with stochastic synaptic input[J]. Phys. Rev. Lett., 1999, 82: 4731- 4734.
[3] Feng, J., and Li G. Integrate-and-Fire and Hodgkin-Huxley models with current inputs[J]. J. Phys. A: Math. Gen., 2001, 34: 1649-1664.
[4] Softky and Koch. The highly irregular firing of cortical-cells is inconsistent with temporal integration of random EPSPs[J]. J. Neurosci., 1993, 13: 334-350.
[5] Shadlen M. N. and Newsome W. T., Noise, neural codes and cortical organization[J]. Curr. Opin. Neurobiol., 1994, 4: 569-579.
[6] Feng, J., Behaviours of spike output jitter in the integrate-and-fire model[J]. Phys. Rev. Lett., 1997, 79: 4505-4734.
[7] Feng, J., Brown, D., Impact of temporal variation and the balance between excitation and inhibition on the output of the perfect integrate-and-fire model[J]. Biol. Cybern., 1998b, 78: 369-376.
[8] Bernander O, Koch C, Usher M, The effects of synchronized inputs at the single neuron level[J]. Neural Comput., 1994, 6: 622-641.
[9] Feng J, Brown D, Coeffcient or variation greater than 0.5 how and when?[J]. Biol Cybern., 1999a, 80: 291-297.
[10] Brown D, Feng J, Is there a problem matching model and real CV(ISI)[J]. Neurocomputing., 1999, 26-7: 117-122.
[11] Cope, D. K.,and Tuckwell, H. C. Firing rates of neurons with random excitation and inhibion[J]. J. Theor. Biol., 1979, 80: 1-14.
[12] Yingchun Deng, Enrico Rossoni, Jianfeng Feng, Dynamics of moment neuronal networks I:Foundations[J]. Europe Phys lett., (in press).
[13] Zohary,E.,Shadlen,M.N.,and Newsome,W.T. Correlated neuronal discharge rate and its implications for psychophysical performance[J].Nature,1994,370:140-143.
[14] Stevens,C.F.,and Zador,A.M. Input synchrony and the irregular firing of cortical neurons [J].Nat.Neurosci., 1998,1:210-217.
[15] Salinas E. and Sejnowski T.J.,Correlated neuronal activity and the flow of neural information[J].Nat Rev Neurosci,2001,2:539-550.
[16] Feng J,Computational neuroscience -A comprehensive approach[M].ChapmanHall:CRC Press,2003.
[17] Salinas E. and Sejnowski T.J.,Impact of correlated synaptic input on output fir- ing rate and variability in simple neuronal models[J]. J.Neurosci.,2000,20(16):6193- 6209.
[18] Deng Y C,Ding M,Feng,J, Synchronization in stochastic coupled systems[J].J.Phys A: Math and Gen.,1999, 11:91-101.
[19] Tuckwell H C, Stochastic processes in the neuroscience[M].SIAM: Philadel-phia, 1989.
[20] Cox P.R.,and Lewis P.A.W. The statistical analysis of series of events[M].Latimer Trend & Co.Ltd Whitstable,1966.
[21] Hunter J.J. Renewal theory in two dimensions:Basic results.[J].Adv.Appl.Probab., 1974,6:376-391.
[22] Hunter J.J. Renewal theory in two dimensions:asymptotic results[J]. Adv. Appl. Pr obab.,1974,6: 546-562.
[23] Gawne TJ,Richmond BJ ,How independent are the messages carried by adjacent inferior temporal cortical neurons?[J].J Neurosci.,1993, 13:2758-2772.
[24] Abbott L.F., Varela J.A.,Sen K. and Nelson S.B. Synaptic depression and cor- tical gain control[J].Science.,1997,275:220-223.
[25] Yingchun Deng, Peter Williams, Feng Liu and Jianfeng Feng, Neuronal discrimination capacity [J]. J. Phys. A: Math. Gen., 2003, 36: 1-20.
[26] Decharms RC, Merxenich MM. Primary cortical representation of sounds by the coordination of action potential timing[J]. Nature., 1995, 381: 610-613.
[27] Dan Yet al., Coding of visual information by precisely correlated spikes in the lateral geniculate nucleus[J]. Nat Neurosci., 1998, 1: 501-507.
[28] Engel AK et al., Why does the cortex oscillate? [J]. Curt Biol., 1992, 2: 332-334.
[29] Leng G. et al., Responses of magnocellular neurons to osmotic stimulation involves coactivation of excitatory and inhibitory input: an experimental and theoretical analysis[J]. J Neurosci., 2001, 21: 6967-6977.
[30] Knight B. W. Dynamics of encoding in a population of neurons[J]. J. Gen. Physiol., 1972, 59: 734-766.
[31] Sompolinsky H., Yoon H., Kang K. J., Population coding in neuronal systems with correlated noise. [J]. Phy. Rev. E., 2001, 64(5)no.051904.
[32] Treves A. Mean-field analysis of neuronal spike dynamics[J]. Network., 1993, 4: 259-284.
[33] Nirenberg S, Latham PE, Decoding neuronal spike trains: How important are correlation?[J]. P Natl Acad Sci USA., 2003, 100: 7348-7353.
[34] Strong SP, Koberle R, Entropy and information in neural spike trains[J]. Phys Rev lett., 1998, 80: 197-200.
[35] Amit D. J.and Brunel N, Dynamics of a recurrent network of spiking neurons before and following learning[J]. Network: Computation in Neural Systems., 1997, 8: 373-404.
[36] Abbott L F, Dayan P, The effect of correlated activity on the accuracy of a population code[J]. Neural Comput., 1999, 11: 91-101.
[37] 茆诗松,王静龙,濮晓龙.高等数理统计[M].北京;高等教育出版社,1998.
[38] Ping Zhang,Jianfeng Feng,Ideal observer of single neuron activity [J]. Neurocomputing., 2002, 44-46:243-247.
[39] Feng J,Brown D,and Li G.Synchronization due to common pulsed input in steins model[J].Phys.Rev.E., 2000, 61:2987-2995.
[40] Feng,J.F.Is the integrate-and-fire model good enough?-a review.[J].Neural Net- works., 2001, 14:955-975.
[41] Aldous D, Probability approxmation via the poisson clumping heuristic[M]. Berlin:Springer,1989.