six papers on modelling single neuron and SVM are available

[Dr J. Feng]

Dear All,

Five papers on modelling single neuron
and one on SVM (see below for abstracts)
are available on my home-page

http://www.cogs.susx.ac.uk/users/jianfeng


the best

Jianfeng


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Titles:

[54] Feng J. (2001)  Is the integrate-and-fire model good enough? --a review
     Neural Networks (in press)

[53] Feng J.,  Brown D., Wei G., and Tirozzi  B. (2001)    Detectable And
     Undetectable  Input Signals For The Integrate-and-fire  Model?
     J. Phys. A.   vol. 34, 1637-1648

[52] Feng J.,  and, Zhang P. (2001)   The Behaviour of Integrate-and-fire
     and Hodgkin-Huxley Models With  Correlated Inputs
     Phys. Rev. E.  (in press).

[51] Feng J.,  Li, G.B.,  Brown D.,  and Buxton H. (2001)   Balance
     between four types  of synaptic input for  the integrate-and-fire  model
     J. Theor. Biol.  vol. 203, 61-79

[50] Feng J.,  and, Li  G. (2001)   Neuronal models with current inputs
     J. Phys. A.  vol. 34, 1649-1664


[55] Feng J., and Williams P. M. (2001)   The generalization
      error of the symmetric and scaled  Support Vector Machines
     IEEE T. Neural Networks (in press).





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Abstracts:


[54] Feng J. (2001)  Is the integrate-and-fire model good enough? --a
     review Neural Networks(in press)


We review some recent results on the behaviour of the integrate-and-fire
(IF) model, the FitzHugh-Nagumo (FHN) model, a simplified version of the
FHN (IF-FHN) model [11] and the Hodgkin-Huxley (HH) model with correlated
inputs. The effect of inhibitory inputs on the model behaviour is also
taken into account. Here inputs exclusively take the form of diffusion
approximation and correlated inputs mean correlated  synaptic inputs
(Section 2 and 3). It is found that the IF and HH models respond to
correlated inputs in totally opposite ways, but the IF-FHN model shows the
similar behaviour as the HH model. Increasing inhibitory input to single
neuronal model, such as the FHN model and the HH model, can sometimes
increase their firing rates, which we termed as inhibition-boosted firing
(IBF). Using the IF model and IF-FHN model, we theoretically explore how
and when the IBF can happen. The computational complexity of the IF-FHN
model is very similar to the conventional IF model, but the former
captures some interesting and essential features of biophysical models and
could serve as a better model for spiking neuron computation.



[53] Feng J.,  Brown D., Wei G., and Tirozzi  B. (2001)    Detectable And
Undetectable  Input Signals For The Integrate-and-fire Model?      J.
Phys. A.   vol. 34, 1637-1648


We consider the integrate-and-fire model with non-stationary, stochastic
inputs and address the following issue: what are the conditions on the
input currents that make the input signal undetectable? A novel
theoretical approach to tackle the problem for the model with
non-stationary inputs is introduced. When the noise strength is independent
of the deterministic component of the synaptic  input, an expression for
the critical input signal is given. If the input signal is weaker than the
critical input signal, the neuron ultimately stops firing, i.e. is not
able to detect the input signal; otherwise it fires with probability one.
Similar results are established for Poisson type inputs where the strength
of the noise is proportional to the deterministic component of the
synaptic input.




[52] Feng J.,  and, Zhang P. (2001)   The Behaviour of Integrate-and-fire
and Hodgkin-Huxley Models With  Correlated Inputs  Phys. Rev. E.  (in
press).

We assess, both numerically and theoretically, how positively correlated
Poisson inputs affect the output of the integrate-and-fire and
Hodgkin-Huxley models. For the integrate-and-fire model the variability of
efferent spike trains is an increasing function of input correlation, and
of the ratio between inhibitory and excitatory inputs. Interestingly for
the Hodgkin-Huxley model the variability of efferent spike trains is a
decreasing function of input correlations, and for fixed input correlation
it is almost independent of the ratio between inhibitory and excitatory
inputs. In terms of the  signal to noise ratio of efferent spike trains the
IF model works better in an environment of asynchronous inputs, but the
Hodgkin-Huxley model has an advantage for more synchronous (correlated )
inputs. In conclusion the integrate-and-fire and HH models respond to
correlated inputs in totally opposite ways.





[51] Feng J.,  Li, G.B.,  Brown D.,  and Buxton H. (2001)   Balance
between four types  of synaptic input for  the integrate-and-fire model
J. Theor. Biol.  vol. 203, 61-79

We consider the integrate-and-fire model with AMPA, NMDA, GABA_A and
GABA_B synaptic inputs, wit model parameters based upon experimental
data. An analytical approach is presented to determine when a post-synaptic
balance between excitation and inhibition can be achieved. Secondly we
compare the model behaviour subject to these four types of input, with its
behaviour  subjected to conventional point process inputs. We conclude
that point processes are not a good approximation, even away from exact
presynaptic balance. Thirdly, numerical simulations are  presented which
demonstrate that we can treat NMDA and GABA_B as DC currents. Finally we
conclude that a balanced input is plausible neither presynaptically not
postsynaptically for the model and parameters we employed.






[50] Feng J.,  and, Li  G. (2001)   Neuronal models with current inputs
J. Phys. A.  vol. 34, 1649-1664

For the integrate-and-fire model and the HH model, we consider how current
inputs including alpha-wave and square-wave affect their outputs.
Firstly
the usual approximation is employed to approximate the models with current
inputs which  reveals the
difference between instantaneous and
non-instantaneous (current) inputs. When the rising time of alpha-wave
inputs is long or the ratio between the inhibitory and excitatory inputs is
close to one, the usual approximation fails to approximate the alpha-wave
inputs in the integrate-and-fire model. For the Hodgkin-Huxley model, the
usual approximation in general gives an unsatisfying approximation. A
novel approach based upon a superposition of 'coloured' and 'white' noise
is then proposed to replace the usual approximation. Numerical results
show
that the novel approach substantially improves the approximation within
widely physiologically reasonable regions  of the  rising rime of alpha-wave
inputs.






[55] Feng J., and Williams P. M. (2001)    The generalization
      error of the symmetric and scaled  Support Vector Machines
     IEEE T. Neural Networks (in press).

It is generally believed that the support vector machine (SVM) optimises
the generalisation error and output performs other learning machines. We
show analytically, by concrete examples in the one dimensional case, that
the support vector machine does improve the mean and standard deviation of
the generalisation error by a constant factor, compared to the worst
learning machine. Our approach is in terms of extreme value theory and
both the  mean and variance of the generalisation error are calculated
exactly for all cases considered. We propose a new version of the SVM
(scaled SVM) which can further reduce the mean of the generalisation error
 of the  SVM.