Thesis - Department of Electronic & Computer Engineering

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If 1 – a – b ≥ 0, τ---- d [ v ;dt i() t – v j() t ] > I i– I j> 0If 1 – a – b < 0, since – v i() t > 0 , ∴∃ε 1> 0, such that – v i() t ≥ ε 1.From Lemma 1, ∀ε > 0,∃T j < ∞,∀t > T j , v j () t < ----------- + ε , we obtain that1 – aI j∃ε 2 < ε 1 , ∃T j < ∞,∀t > T j , v j () t < -----------1 – a+ -------------------- a+b – 1I jε 2I jτ---- d [ v for all .dt i() t – v j() t ] > ( 1 – a – b)----------- + ( I1 – a i– I j) + ( ε 1– ε 2) t > T j( 1 – a)( a – 1)δSince b < ---------------- ⇒ 1 – a – b > ------------------- and I( 1 – δ)1 – δ j≤ I i( 1 – δ)τ d ( a – 1)δ---- [ vdt i () t – v j () t ] ------------------- Ii ( 1 – δ )>1 – δ-------------------- +1 – aI δ + ( ε – ε )i 1 2∴τ---- d [ vdt i () t – v j () t ] > ( ε 1 – ε 2 ) > 0To summarize, ∃ < ∞,∀t > T i, v i() t > v j() t .T i7.2 Proof for Properties of the Pulse Coupled WTAModelThe proposed pulse coupled model can be described asv i () ˙t=∑– v i () t + I i + as i () t – b s j () tj≠i74
whereV ˙ i () t=max( v i ()0 t , ), describing non-leaky integrator.s i() t = Aut [ ( – t ij– T p)–ut ( – t ij)], representing fixed width and fixed heightpulse.ut () is the step function, and { t ij} is the time sequence whenV i() t = θθ , = A⋅T p , then V i() t is reset to zero. The depicts below shows the waythe pulse is generated.Define the peak value and bottom values of the each neuron in steady state arev iand v i respectively. Let v˜i()t be the average of vi () t between two successive spikesas depicted in Figure 5.4.v˜i tT n + 1∫() = v( τ)dτ, where t ∈ ( T n , T n + 1 ] .T nLemma 1: ∀ε > 0,∀i1 … N T i∞ t T iv˜ I= , , , ∃ < , ∀ > , i()t < ----------- i+ ε1 – aProof:v i () ˙t=∑– v i () t + I i + as i () t – b s j () t < – v i () t + I i + as i () tj≠iConsider the steady state of the right hand side of the inequality,T p⎛ –-----⎞–----- ⎛v i = ( I i + aA) ⎜1 – e τ⎟ + v i e τ , v i = I i ⎜1 – e⎝ ⎠⎝T p( T – T p )–--------------------τ⎞⎟⎠+ v i e( T – T p )–--------------------τ75
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the system level. Our results show
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activities. The basin of attraction
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It is interesting to note that whic
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Although there is no saturation in
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• Response time of the system;As
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e verified by computer simulation (
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inhibition. Due to the fact that ea
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tion. Thus the power consumption is
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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
Page 65 and 66: 6. ConclusionsIn this thesis, a cla
Page 67 and 68: In this thesis, we consider only a
Page 69 and 70: v i() t≤I i----------- ( 1 - e1 -
Page 71 and 72: If a+ b - 1≥0, then τ---- d [ v
Page 73: If a+ b - 1 > 0, since v i() t > 0
Page 77 and 78: 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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