2013 IEEE International Conference on Emerging Trends in Computing, Communication and Nanotechnology (ICECCN 2013)

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Classification of Different Neuron Behavior by Designing Spiking Neuron Model Ankit Kumar M.Tech Scholar Mathematics Department IIT Delhi

Sachin Kansal Research Scholar Mechanical Department IIT Delhi

[email protected]

[email protected]

Dr.M.Hanmandlu Professor Electrical Engineering Department IIT Delhi [email protected]

In

Int.

J.

Bifurc. Chaos,

vol.10 we have introduced concept of Neural excitability, Abstract— We have presented a simple two equation model which produces the rich behavior of biological neurons, including tonic spiking, tonic bursting, mixed mode firing, spike frequency adaptation, resonator, integrator etc. Our model is capable of producing 19 different kinds of dynamics of real biological neuron. We have illustrated the richness and complexity of spiking behavior of individual neuron in response to simple pulses of dc current. Index Terms— Neuron, Spike, Spike neuron model, Neuroncomputational features.

A

I. INTRODUCTION

spiking, and bursting [1],

Parker, G. E., & Sochacki,[2]

introduces Picard-Maclaurin theorem for initial value PDE’s. Izhikevich,E.M. [3] proposed resonate-and-fire neurons model[4]. Later Izhikevich,E.M. [4] proposes simple model of spiking neurons, Richard Naud [5] proposes firing patterns in the adaptive exponential integrate-and –fire model The paper is organized as follows. Section II briefly describes the proposed model. Section III depicts the details of Neuro-

ll organisms live in a dynamic environment and to be

computation features equation. Section IV demonstrates

able to interact with it intelligently, some have evolved a

results. Section V states conclusion. Finally, in the Section VI

special organ: the brain. This complex organ can deal with a large quantity of streams of input-information in a highly efficient manner. Looking more closely at the brain, we see that it consists of a large number of nerve-cells, more specifically called neurons. These neurons form connections with each other to compose a network, hence the name neural network. The study of artificial neural networks, a sub-field of AI, tries to model these biological neurons and by forming networks with these model-neurons wants to achieve the same processing-qualities as the brain. The models we will study are called the Spiking Neuron models, which are recently gaining

states future work II. PROPOSED MODEL A. Model Description In the previous chapter we learned various models of spiking neuron. Most of the spiking models except Izhikevich and Hodgkin-Huxley models were not capable of producing all computational features exhibited by real biological neuron [5]. So here we are presenting a simple two equation model which is capable of producing all computational features of a real biological neuron. Our model is inspired by Izhikevich model.

much interest in the field of artificial neural networks.

978-1-4673-5036-5/13/$31.00 © 2013 IEEE

26 ………

(1.1)

D. Phasic Bursting Some neurons are phasic bursters, as shown in Fig. 3(d). Such

du/dt = a(bv-u) ………………

(1.2)

E. Mixed Model (Bursting Then Spiking)

With the spike resting conditions then

If

neurons transmit a burst at the beginning of the stimulation. Some neuron fire a phasic burst at the beginning of stimulation

(1.3)

Where u and v are dimensionless variables. a, b, c, d are also dimensionless parameters and t denotes time. The variable v is the membrane potential of the neuron and u is a membrane

and then switches to the tonic spiking mode. F. Spike Frequency Adaptation Some neurons fire tonic spikes with decreasing frequency, as shown in Fig. 3(f).

recovery variable which tells the activation of K+ ionic currents and inactivation of Na+ ionic currents, and it gives negative feedback to v. When the spike reaches its peak (+3 mV), the membrane voltage and the recovery variable are reset by the (1.3). Variable ‘I’ represents synaptic currents or injected dc-currents. The part

e^ (v^2) -10v –u +I is

obtained by fitting the spike initiation dynamics of a neuron so that the membrane potential v has mV scale and the time t has ms scale. Different choices of the parameters give different intrinsic firing patterns, including those obtained from known types of neocortical neurons. III. NEURO-COMPUTATIONAL FEATURES EQUATION

G. Class 1 Excitability Some neurons fire at low (above threshold) current and spike frequency is proportional to current.These neurons can encode the strength of the input into their firing rate, as shown in Fig. 3(g). H. Class 2 Excitability Some neurons cannot fire low-frequency spike trains. That means, they are either quiescent or fire a train of spikes with a certain relatively large frequency, as shown in Fig. 3(h).. I. Spike Latency Most cortical neurons fire spikes with a delay. This delay

We have generated 19 of the most prominent features of

depends on the strength of the input signal. For a relatively

biological spiking neurons. The goal of this section is to

weak input, spike latency, can be quite large, as shown in Fig.

demonstrate the richness and complexity of spiking behavior of

3(i).

individual neurons in response to simple pulses of dc current. A. Tonic Spiking

J. Frequency Preference and Resonance

Most neurons are excitable, that means they are quiescent but

Some neurons fire spikes only when inputs resonate with

can fire spikes when stimulated..

subthreshold oscillation frequency.We stimulate such a neuron

B. Phasic Spiking

with two doubles (pairs of spikes) having different interspike

A neuron may fire only a single spike when the input is on, as

frequencies, as shown in fig 3(j).

in Fig. 1(b), and remain quiescent afterwards. K. Integration and Coincidence Detection C. Tonic Bursting

Neurons without oscillatory potentials perform as integrators.

Some neurons fire periodic bursts of spikes when stimulated, as

These neurons prefer high-frequency input. If the frequency is

in Fig. 3(c).Chattering neurons in cat neocortex are examples

higher neurons are more likely to fire, as shown in Fig. 3(k).

of this type of behavior.

27 L. Rebound Spike When a neuron is released from an inhibitory input, it can fire a

in the thalamo-cortical system and it plays an important role in sleep rhythms.

post-inhibitory (rebound) spike, as shown in Fig. 3(l). IV. RESULTS. M. Rebound Burst Some neurons may fire post-inhibitory bursts, as shown in Fig.

The input current and the neuronal response are plotted in Fig. 1(a). While the input is on, the neuron keeps on firing a train of spikes.

3(m). Such bursts contribute to the sleep oscillations in the thalamo-cortical system. N. Threshold Variability A common delusion in the artificial neural network society is the belief that spiking neurons have a fixed voltage threshold. O. Bistability of Resting and Spiking States Some neurons may switch between resting and tonic spiking (or bursting) states. An excitatory or inhibitory pulse can switch between the modes, as shown in Fig. 3(o).

Fig 1(a) Tonic Spiking

P. Depolarizing After-Potentials Some neurons may experience a period of superexcitability after a spike, instead of a refractory period, as shown in fig 3(p). Q. Accommodation Neurons are really very sensitive to brief coincident inputs. These neurons may not fire in response to a strong but slowly increasing input, as shown in Fig. 3(q).

Fig 1(b) Phasic Spiking

R. Inhibition-Induced Spiking A bizarre feature of thalamo-cortical neurons: These neurons are quiescent when there is no input, but fire when inhibitory input or an injected current is supplied, as shown in Fig. 3(r). The injected current activates the h-current and deinactivates calcium T-current, therefore leading to tonic spiking. S. Inhibition-Induced Bursting A thalamo-cortical neuron can fire tonic bursts of spikes in response to a prolonged hyper polarization, as shown in Fig. 3(s). Such bursting takes place during spindle wave oscillations

Fig 1(c) Tonic Bursting

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Fig 1(d) Phasic Bursting

Fig 1(e) Mixed Mode

Fig 1(f) Spike Frequency Adaption

Fig 1(g) Class 1 Excitable

Fig 1(h) Class 2 Excitable

Fig 1(i) Spike Latency

29 Fig 1(j) Resonator

Fig 1(o) Bistability Fig 1(k) Integrator

Fig 1(p) Depolarizing after-potential Fig 1(l) Rebound Spike

Fig 1(q) Accomodation Fig 1(m) Rebound Burst

Fig 1(r) Inhibition-induced spiking Fig 1(n) Threshold Variability

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Ankit Kumar Born in Moradabad (10 August 1986). Persuing M.Tech (Computer Application) from Indian Institute Of Technology Delhi India. Working in the field of mathematics, machine learning, and soft computing.

Fig 1(s) Inhibition-induced bursting

V. CONCLUSION Some of these 19 properties are mutually exclusive so no model should exhibit all these properties simultaneously. For example, at the same time, a neuron cannot be an integrator and a resonator. However, there are models that can easily be tuned to produce each such neuro-computational property. For example, all of the neuronal responses in Fig. 3 were produced using a simple spiking model having four easily tunable parameters. VI. FUTURE After the simulation work and designing the spiking neuron model we can move to spiking neural network. Using spiking neuron model we can design spiking neural network architecture for solving any real world problem. REFERENCES [1]. “Neural excitability, spiking, and bursting,” Int. J. Bifurc. Chaos, vol. 10, pp. 1171–1266, 2000. [2]. Parker, G. E., & Sochacki, J. S. (2000). A Picard-Maclaurin theorem for initial value PDE’s. Abstract and Applied Analysis, 5(1), 47–63. [3]. Izhikevich, E. M. (2001). Resonate-and-fire neurons. Neural networks, 14(6–7), 883–894, July–September. [4]. Izhikevich, E.M. (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks, 14(6), 1569–1572. [5]. Izhikevich, E. M. (2004). Which model to use for cortical spiking neurons? IEEE Transactions on Neural Networks, 15(5), 1063–1070, September.

Sachin Kansal Born in Aligarh (02 December 1987). Persued M.Tech (Robotics) from Indian Institute of Information Technology Allahabad (Uttar Pradesh) India. Worked in the field of robotics, image processing, machine learning, and soft computing. Currently he is doing Phd from IIT Delhi in Mechanical Engineering Department. India.