Thesis - Department of Electronic & Computer Engineering

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IFor example, let I 2= … = I Nand 1– I-------------- 2= δ 1, v 1( 0) = … = v N( 0) = 0 ,then we haveI 1τX ˙N() t = [ a – ( N – 1)b– 1]X N() t + I 1[ 1 + ( N – 1) ( 1 – δ 1)]τY ˙ N() t = [ a + b – 1 ]Y N() t + I 1δ 1.Further suppose a+ b = 1, it becomesτX ˙ N() t=– NbX N() t + I 1[ 1 + ( N – 1) ( 1 – δ 1)]τY ˙N() t = I 1δ 1tDefine y - and to be the solution toτ= y s δ 1 y=( N – 1)1 – -----------------δN 1-------------------------------- ( 1 – e .b– Nby )Hence the response timet s=y sτFor example, if we choosea = b = 0.5, then we get the WTA model:τv˙ i()t = – vi () t + I i + 0.5max( v i ()0 t , )–0.5 max( v j ()0 t , ).∑j≠iI 1Further fix the largest input I 1 = 1.0 and τ = 1ms. For δ 1 = 0.1 and N = 2 , theo-1.0retically, v 1 () t = ----------- = --------------- = 2.0 at steady state and t . These can1 – a 1 – 0.5s = 19ms14
e verified by computer simulation (Matlab Simulink) in Fig. 2.3. It shows the consistencybetween the simulation results and the predictions.2.5Neural activities V.S. time2The winnerNeural activities1.510.5The loser00 5 10 15 20 25 30Time (ms)Fig. 2.3 Two neuron WTA modelAlthough the closed-form solution is not available fort s, qualitatively, asδincreases, t sdecreases nearly inversely proportional to δ ; while t sis insensitive to thechange <strong>of</strong> N. This can be shown by computer simulations.For δ 1 = 0.1 , we calculate the response time for different network size N asshown in Fig. 2.4. It is shown that when N is larger than 50, the response time isvery insensitive to the change <strong>of</strong> N.t s15
Page 3 and 4: the system level. Our results show
Page 5: activities. The basin of attraction
Page 9 and 10: It is interesting to note that whic
Page 11 and 12: Although there is no saturation in
Page 13: • Response time of the system;As
Page 17 and 18: inhibition. Due to the fact that ea
Page 19 and 20: tion. Thus the power consumption is
Page 21 and 22: Let∆be the minimum time necessary
Page 23 and 24: The sender initiates the sequence b
Page 25 and 26: Here in Table 1 is the comparison o
Page 27 and 28: source cell will be broadcast on th
Page 29 and 30: At this point, it seems appropriate
Page 31 and 32: detected, all the potential spikes
Page 33 and 34: InitializationFor each timestep ε
Page 35 and 36: global inhibition BusActivity to fr
Page 37 and 38: Spikes from the winnerATpTTT n T n+
Page 39 and 40: the network will either work at WTA
Page 41 and 42: The computer simulation results for
Page 43 and 44: 5.5 Steady State AnalysisAs demonst
Page 45 and 46: all the losers. To ensure that all
Page 47 and 48: 10090θ=θ mThe necessary condition
Page 49 and 50: 100Necessary conditions to exhibit
Page 51 and 52: The response time is estimated in t
Page 53 and 54: 5.6.2 Further study on the non-arbi
Page 55 and 56: 100Response time V.S. equivalent ga
Page 57 and 58: cell will never collide with each o
Page 59 and 60: ps ( i) = ( 1 - ϕ i)δ( s)for s =
Page 61 and 62: These results show that the collisi
Page 63 and 64: 5.7.4 SummaryCompared with the Pois
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6. ConclusionsIn this thesis, a cla
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In this thesis, we consider only a
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v i() t≤I i----------- ( 1 - e1 -
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If a+ b - 1≥0, then τ---- d [ v
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If a+ b - 1 > 0, since v i() t > 0
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whereV ˙ i () t=max( v i ()0 t , )
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θ t s Nf f wp ct(%) p cl(%) p cw(%
Page 79 and 80:
10. “WTA networks with lateral ex
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Thesis - Department of Electronic & Computer Engineering

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