Yingchun Deng

Training the integrate-and-fire model with the informax principle: I

In terms of the informax principle, and the input-output relationship of the integrate-and-fire (IF) model, IF neuron learning rules are developed. For supervised learning and with uniform weight of synapses (the theoretically tractable case), we show that the derived learning rule is stable and the stable state is unique. For unsupervised learning, within physiologically reasonable parameter regions, both long-term potentiation (LTP) and long-term depression (LTD) could happen when the inhibitory input is weak, but LTD cannot be observed when inhibitory input is strong enough. When both LTP and LTD occur, LTD is observable when the output of the postsynaptic neuron is faster than pre-synaptic inputs, otherwise LTP is observable, as observed in recent experiments. Learning rules of general cases are also studied and numerical examples show that the derived learning rule tends to equalize the contribution of different inputs to the output firing rates.

Synchronization in stochastic coupled systems: theoretical results

The stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in stochastic coupled dynamical systems (ordinary differential equations) is considered. A general approach is presented, based on the master stability function, Gershg¨ orin disc theory and the extreme value theory in statistics, to yield constraints on the distribution of coupling to ensure the stability of synchronized dynamics. Three types of different behaviour: global-stable, exponential-stable and power-stable, are found, depending on the nature of the distribution of the interactions between units. Systems with specific coupling schemes are used as examples to illustrate our general method.

Identifying transition rates of ionic channels of star-graph branch type

We consider how to determine all transition rates of an ionic channel when it can be conformationally described by a star-graph branch Markov chain with continuous time. It is found that all transition rates are uniquely determined by the distributions of their lifetime and death-time at the end state of each branch. An algorithm to exactly calculate all transition rates is developed. Numerical examples are included to demonstrate the application of our approach to data.

Spike-Rate Perceptrons

According to the diffusion approximation, we present a more biologically plausible so-called spike-rate perceptron based on IF model with renewal process inputs, which employs both first and second statistical representation, i.e. the means, variances and correlations of the synaptic input. We first identify the input-output relationship of the spike-rate model and apply an error minimization technique to train the model. We then show that it is possible to train these networks with a mathematically derived learning rule. We show through various examples that such perceptron, even a single neuron, is able to perform various complex non-linear tasks like the XOR problem. Here our perceptrons offer a significant advantage over classical models, in that they include both the mean and the variance of the input signal. Our ultimate purpose is to open up the possibility of carrying out a random computation in neuronal networks, by introducing second order statistics in computations.

Neuronal discrimination capacity

We explore neuronal mechanisms of discriminating between masked signals. It is found that when the correlation between input signals is zero, the output signals are separable if and only if input signals are separable. With positively (negatively) correlated signals, the output signals are separable (mixed) even when input signals are mixed (separable). Exact values of discrimination capacity are obtained for two most interesting cases: the exactly balanced inhibitory and excitatory input case and the uncorrelated input case. Interestingly, the discrimination capacity obtained in these cases is independent of model parameters, input distribution and is universal. Our results also suggest a functional role of inhibitory inputs and correlated inputs or, more generally, the large variability of efferent spike trains observed in in vivo experiments: the larger the variability of efferent spike trains, the easier it is to discriminate between masked input signals.

Second order spiking perceptrons

According to the diffusion approximation and usual approximation scheme, we present two more biologically plausible so called second order spiking perceptron (SOSP) and extended second order spiking perceptron (ESOSP) based on the integrate-and-fire model with renewal process inputs, which employ both first and second statistical representation, i.e., the means, variances and correlations of the synaptic input. We show through various examples that such perceptrons, even a single neuron, are able to perform various complex non-linear tasks like the XOR problem, which is impossible to be solved by traditional single-layer perceptrons. Here our perceptrons offer a significant advantage over classical models, in that they include the second order statistics in computations, specially in that the ESOSP considers the learning of variance in the training. Our ultimate purpose is to open up the possibility of carrying out a stochastic computation in neuronal networks.

Notice of Retraction Identifying kinetic constants of ion channel of hierarchical type

We have developed a totally different approach from Maximum likelihood widely employed to estimate the kinetic constants of single-ion channels of hierarchical mechanism. It is found that all kinetic constants are uniquely determined by the probability density functions of their lifetime and death-time of the middle states. An algorithm to calculate all kinetic constants is provided, which employs the intrinsic properties of the Markov process. Once we have them, all subsequent calculations are then automatic and exact.

Second Order Spiking Perceptron

According to the usual approximation scheme, we present a more biologically plausible so-called Second Order Spiking Perceptron with renewal process inputs, which employs both first and second statistics, i.e. the means, variances and correlations of the synaptic input. We show that such perceptron, even a single neuron, is able to perform complex non-linear tasks like the XOR problem, which is impossible to be solved by traditional single-layer perceptrons. Here such perceptron offers a significant advantage over classical models, in that it includes the second order statistics in computations, and that it introduces variance in the error representation. We are to open up the possibility of carrying out a random computation in neuronal networks.

Moment neuronal networks: stochastic computation in neuronal systems

Spike trains recorded in cortical neurons in vivo can be approximated by renewal processes, but are generally not Poisson. Besides, the spiking activity of neighboring neurons display small yet not negligible correlations. The Artificial Neuronal Network theory has traditionally neglected such observations, assuming that neurons could simply be described by their mean firing rate. Here we present a theoretical framework in which the dynamics of a system of neurons is specified in terms of higher-order moments of their spiking activity beyond the mean firing rate.