six papers available at my homepage

[Dr J. Feng]

Dear connectionists, 
 
You could find the following papers at address
 
  http://www.cus.cam.ac.uk/~jf218     
 
 
[46] Feng J., and Brown D.(2000) 
Integrate-and-fire models with nonlinear leakage       
Bulletin of Mathematical Biology (in press)

ABSTRACT

Can we express biophysical neuronal models as
integrate-and-fire models with leakage coefficients which are no
longer constant, as in the conventional leaky integrate-and-fire
(IF) model, but functions of membrane potential and other
biophysical variables? We illustrate the answer to this question
using the FitzHugh-Nagumo (FHN)  as an
example. Novel integrate-and-fire models, the IF-FHN 
model, which approximate to the FHN mode, is obtained.
The leakage coefficients derived in the IF-FHN  model
have non-monotonic relationships with membrane potential,
revealing at least in part the intrinsic mechanisms underlying
the model. The model correspondingly exhibits more complex
behaviour than the standard IF model. For example, in some
parameter regions, the IF-FHN model has a coefficient of variation
of output interspike interval which is independent of the number
of inhibitory inputs, being close to unity over the whole range,
comparable to the FHN model as we noted previously.

 
[45] Davison A., Feng J., Brown D.(2000) 
A reduced compartmental model of the mitral cell for use in network models
of the olfactory bulb 
 Brain Research Bulletin vol. 51,  393-399.

ABSTRACT

We have developed two-, three and four-compartment models of a mammalian
olfactory bulb mitral cell as a reduction of a complex 286-compartment
model. A minimum of three compartments, representing soma, secondary
dendrites and the glomerular tuft of the primary dendrite, is required to
adequately reproduce the behaviour of the full model over abroad range of
firing rates. Adding a fourth compartment to represent the shaft of the
primary dendrite gives a substantial improvement. The reduced models 
exhibit behaviours in common with the full model which were not used in
fitting the model parameters. The reduced modes run 75 or more times
faster
than the full model, making their use in large, realistic network models
of the olfactory bulb practical. 




 [44] Feng J., Brown D., and Li G. (2000) 
 Synchronization due to common pulsed input in Stein's model 
 Physics Review E   vol. 61, 2987-2995.

ABSTRACT

It is known that stimulus-evoked oscillatory synchronisation among
neurones
occurs in widely separated cortical regions.  In this paper
we provide a possible
mechanism to explain the phenomena.
When  a common, random input is presented, we
find that  a group of neurones-- of Stein's (integrate-and-fire) model
type
with or without reversal potentials--are capable of
quickly  synchronising their firing.
Interestingly the optimal average synchronisation time occurs when
the common input has a high CV (ISI) (greater than 0.5)
for this  model with or without reversal potentials.
The model with reversal potentials
 more quickly synchronises than that without
reversal potentials.





 
[43] Feng, J., and Tirozzi B. (2000) 
 Stochastic resonance tuned by correlations in neuronal models. 
 Phys. Rev. E. (in press, April)


ABSTRACT

The idea that neurons might use stochastic resonance (SR) to
take advantages of random signals  has
been extensively discussed in the literature. However, there are a few key
issues
which have not been clarified and thus  it is difficult to
assess that whether  SR in neuronal models
occurs inside plausible physiology parameter regions  or not.
We propose and show  that neurons  can adjust correlations between
synaptic
inputs, which  can  be measured in experiments and are  dynamical
variables, to exhibit  SR.  The benefit of such a mechanism over
the conventional SR is also discussed.



 
[42] Feng J., and Brown D.(2000). 
 Impact of correlated input on the output of the integrate-and-fire
 models  
 Neural Computation   vol. 12, 711-732.


ABSTRACT

For the integrate-and-fire model with or without  reversal potentials,
 we consider how correlated inputs affect the variability of cellular
output.  For both models the variability
of efferent spike trains measured by coefficient of variation  of
the interspike interval (abbreviated to CV in the remainder of
the paper)
 is a nondecreasing function of input correlation.
When the correlation coefficient is greater than 0.09,  the CV of
the integrate-and-fire model without reversal potentials is always
above 0.5, no matter how strong the inhibitory inputs. When the
correlation coefficient is greater than  0.05, CV  for the
integrate-and-fire model with reversal potentials is always above
0.5, independent of the strength of the inhibitory inputs. Under a
given condition on correlation coefficients we find that
correlated Poisson processes can be decomposed into independent
Poisson processes. We also develop a novel method to estimate the
distribution density of the first passage time of the
integrate-and-fire model.


 
 [41] Feng J., Georgii H.O., and Brown D. (2000) 
 Convergence to global minima for a class of diffusion processes 
 Physica A  vol. 276, 465-476.
 
ABSTRACT

We prove that there exists a gain function
$(\eta(t),\beta(t))_{t\ge 0}$ such that the solution of the  SDE
$dx_t=\eta(t)(-\mbox{ grad } U(x_t)dt +\beta(t)dB_t)$
'settles' down  on
 the set of  global minima of $U$. In particular the existence of
a gain function $(\eta(t))_{t\ge 0}$
 so that $y_t$  satisfying
$dy_t=\eta(t)(-\mbox{ grad } U(y_t)dt +dB_t)$
converges to the set of the global minima of $U$ is verified.
Then we apply the results to the  Robbins-Monro and the Kiefer-Wolfowitz
procedures
which are of particular interest in statistics and neural networks.




 
 with best regards
 
 
 Jianfeng Feng
 The Babraham Institute 
 Cambridge CB2 4AT
 UK