circuit of the membrane in dynamic stateFigure 3.12. Other equivalent circuit of the membrane in dynamic state. The arro...Figure 3.13. Rule for the variation of the activation coefficient, n, leading to...Figure 3.14. Coefficients nss, mss and hss, extracted from expressions [3.24]. T...Figure 3.15. Time constants τn τm and τh, extracted from expressions [3.24]. The...Figure 3.16. Membrane potential, Vm(t), in response to a current impulse of 3.5 ...Figure 3.17. Activation coefficients, n(t), m(t) and h(t), in response to a curr...Figure 3.18. Sodium, GNa(t), and potassium, GK(t), conductances in response to a...Figure 3.19. Sodium, potassium and leakage currents in response to a current imp...Figure 3.20. Membrane potential in response to a current pulse of 6 μA/cm2 appli...Figure 3.21. Coefficient h as a function of n in the event of a spike. The red d...Figure 3.22. Nullclines of n (blue line) and of Vm Iex=0 (red dotted line) and I...Figure 3.23. Nullclines of n and Vm (Iex=6μA/cm2) and Vm(t), n(t) cycles resulti...Figure 3.24. Isoclines n and Vm for different values of excitation current, Iex....Figure 3.25. Action potentials of the ML model for two excitation current values...Figure 3.26. Equivalent circuit of a non-myelinated axonFigure 3.27. Axon represented by an RC line. For a color version of the figure, ...Figure 3.28. Axon represented by an active line. Conductances GNa and GK are gov...Figure 3.29. Generation of a spike at the soma-axon junction (red disc). Propaga...Figure 3.30. Equivalent circuit of a myelinated axon. For a color version of the...Figure 3.31. Shape of Excitation current, Iex(t), in red, and associated respons...3.32. Excitatory postsynaptic potentials in red, inhibitory in green. For a colo...Figure 3.33. Mathematical models of EPSPs given by expressions [3.50a, b, c]. Fo...Figure 3.34. EPSP of an excitatory synapse for different synaptic weight values....Figure 3.35. Principle of STDP, according to Bi and Poo. w is the synaptic weigh...4 Chapter 4Figure 4.1. Signal-flow graph of the perceptron. Coefficients wi are the synapti...Figure 4.2. Signal-flow graph of the multilayer perceptron or feedforward networ...Figure 4.3. Principle of a convolutional networkFigure 4.4. Signal-flow graph of a hidden-layer recurrent neural network. The re...Figure 4.5. Graph of an “Elman”-type recurrent network. For a color version of t...Figure 4.6. Graph of a “Hopfield”-type recurrent network, for which the intercon...Figure 4.7. Principle of reservoir computing. The black arrows represent fixed-w...Figure 4.8. Modeling of the Pavlov experiment with three neurons (N1 “food”, N2 ...Figure 4.9. Current control by ion channel in a biological membrane and by a tra...Figure 4.10. Two “current-mirror” circuits enabling the relationship between I1 ...Figure 4.11. Diagram of a DPI composed of a differential pair and two current mi...Figure 4.12. Diagram of a DPI neuron. The yellow block models the leakage conduc...Figure 4.13. Circuit diagram, transfer function Vout(Vin) and voltage gain Gv of...Figure 4.14. Transfer function, Vout(Vin), of a subthreshold inverter (Vdd=200 m...Figure 4.15. Reduction of the effective subthreshold slope of a transistor throu...Figure 4.16. Electrical circuit of an axon-hillock artificial neuronFigure 4.17. Signal-flow graph of the amplifier (a), ideal transfer function (b)...Figure 4.18. Time variation of potentials Vin and Vout in the case of the simpli...Figure 4.19. Time variation of potentials Vin and Vout, obtained by SPICE simula...Figure 4.20. Block diagram of the electronic circuit simulating the ML modelFigure 4.21. Complete schematic diagram of the eight-transistor electronic circu...Figure 4.22. Simplified diagram of the ML neuron comprising only six transistors...Figure 4.23. Temporal variation in membrane potential and sodium and potassium c...Figure 4.24. Comparison between a very complete biomimetic neuron model (top) an...Figure 4.25. Dendritic tree of post-neuron, j. Vmi (or Vmk, respectively) repres...Figure 4.26. Definition of the memristance or fourth element based on state vari...Figure 4.27. V(t)–I(t) curves when I = I0sin(ωt), for a resistance, R, an induct...Figure 4.28. Architecture for the electronic implementation of the STDP. The two...Figure 4.29. Principle of implementation of the STDP. (a) Scenario where tpre < ...Figure 4.30. Circuit enabling highlighting of the stochastic resonance. Transcon...Figure 4.31. Response of the neuron as a function of noise power. The membrane p...Figure 4.32. Simulation of a cortical column by a reservoir-computing architectu...Figure 4.33. General architecture of the TrueNorth chip (a) and detailed archite...
Guide
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