Χρήστης:Gkastel/draft

${\displaystyle \tau _{fast}{\frac {dV_{fast}}{dt}}=\sum _{i}w_{i}E_{i}\delta (t-t_{i}^{syn})-V_{fast}}$

${\displaystyle dspike:V_{fast}+V_{BAP}>V_{dspike,thresh}+V_{dspike,refractory}}$

${\displaystyle soma:V_{soma}>V_{thresh,soma}(1-a_{CREB})-V_{soma,refractory}}$

${\displaystyle \tau _{dspike}{\frac {dV_{dspike}}{dt}}=(E_{dspike}-V_{fast}-V_{BAP})\sum _{i}\delta (t-t_{i}^{dspike})-V_{dspike}}$

${\displaystyle V_{soma}=\sum _{j}(V_{fast,i}+B_{i}V_{dspike,i})-R_{adapt}I_{adapt}}$

${\displaystyle \tau _{adapt}{\frac {dI_{adapt}}{dt}}=I_{adapt,0}\sum _{i}\delta (t-t_{i}^{soma})-I_{adapt}}$

${\displaystyle \tau _{BAP}{\frac {dV_{BAP}}{dt}}=E_{BAP}\sum _{i}\delta (t-t_{i}^{soma})-V_{BAP}}$

${\displaystyle \tau _{Ca}{\frac {dCa}{dt}}=a_{Ca}sigmoid(V_{fast}+V_{dspike}+V_{BAP})\sum _{i}\delta (t-t_{i}^{syn})-Ca}$

${\displaystyle ETag=\int _{0}^{t}(ETag_{max}-ETag)CDP(Ca(t))_{+}+(ETag-ETag_{min})CDP(Ca(t))_{-}}$

${\displaystyle PRPs(t)=\sum _{i}{\frac {t-t_{i}}{\tau _{1}}}e^{1-{\frac {t-t_{i}}{\tau _{2}}}}}$

${\displaystyle \tau _{W_{early}}{\frac {dW_{early}}{dt}}=ETag(t)(W_{max}-(W_{late}+W_{early}))-W_{early}}$

${\displaystyle \tau _{a_{CREB}}{\frac {da_{CREB}}{dt}}=\sum _{i}a_{CREB,0}\delta (t-t_{i}^{CREB})-a_{CREB}}$

${\displaystyle W_{early}\rightarrow _{\tau _{W_{late}}}^{proteins}\rightarrow W_{late}}$

${\displaystyle w(t)=W_{early}(t)+W_{late}(t)}$

${\displaystyle \tau _{B_{tag}}{\frac {dB_{tag}}{dt}}=B_{tag,0}\sum _{i}\delta (t-t_{i}^{dspike})-B_{tag}}$

${\displaystyle {\frac {dB_{j}}{dt}}={\frac {1}{\tau _{B_{j}}}}B_{tag,j}(B_{max}-B_{j})+{\frac {1}{\tau _{B_{H}}}}B(1-{\frac {\sum _{j}B_{j}}{N}})}$

${\displaystyle {\frac {dW_{j}}{dt}}={\frac {1}{\tau _{W_{H}}}}B(1-{\frac {\sum _{j}W_{j}}{N_{syn}}})}$