## 3 Discussion  
In this section, the power spectrum generated by the synchronized closed-loop sequences of Markov-chain-correlated firing neurons will be confronted with typical features observed in EEG and MEG measurements. As discussed in Section 2, the sequences of electric and magnetic impulses received by the sensors on the scalp at every cycle correspond to \(N\) groups of \(N_{i}\) syncronized impulses generated by the firing of a single neuron in each loop. The average time interval \(u\) between subsequent neuron firings along the loop multiplied by \(N\) yields the loop duration, while its reciprocal yields the lowest frequency component of the mixed power spectrum. In principle \(N_{i}\) could be estimated by considering the intensity of either the elementary electric or the magnetic impulses, which are almost simultaneously produced by a single firing neuron in each sequence. More accurate estimates are obtained by using the magnetic component of the impulse, which is not attenuated by the cerebral matter and the scalp, contrarily to the electrical components of the signal [25; 26; 27]. The magnetic and electric field components \(\vec{B}\) and \(\vec{E}\) generated by the firing of a single neuron obey the Maxwell equation \(\mathbf{\
abla}\times\vec{B}=\mu_{0}\vec{J}+\epsilon_{0}\mu_{0}\ \delta\vec{E}/\delta t\), with \(\vec{J}\) and \(\mu_{0}\epsilon_{0}\ \delta\vec{E}/\delta t\), respectively, the conduction and displacement current density. The conduction charges in the axon move at speeds ranging between 0.5 ms\({}^{-1}\) and 5.0 ms\({}^{-1}\), i.e., much faster than the charges moving in the outer regions. Therefore, the electric field in the axon is partly screened by the conductive cerebral matter. The magnetic field generated by the conduction charge inside the axon can be estimated using the relationship valid for metallic conductors:  
\[\vec{B}(t)=\frac{\mu_{0}}{4\pi}I(t)\ \Delta\ell\ \frac{\vec{u}_{A}\ \times\ \vec{u}_{D}}{r_{s}^{2}}\,\]  
with \(I(t)\) the current intensity; \(r_{s}\) the distance between the midpoint of the axon and the point where \(\vec{B}(t)\) is measured; and \(\Delta\ell\) the length of the axon, which, for neurons connected in the same area of the brain, ranges between 50 \(\upmu\)m and 200 \(\upmu\)m. The unit vector \(\vec{u}_{A}\) and \(\vec{u}_{D}\) indicate, respectively, the directions of \(\Delta\ell\) and \(r_{s}\). The amplitude of the magnetic field \(\vec{B}(t)\) is:  
\[B(t)=\frac{\mu_{0}}{4\pi}\ I(t)\ \Delta\ell\ \frac{\sin\theta}{r_{s}^{2}}\quad, \tag{18}\]  
where \(\theta\) is the angle between \(\vec{u}_{A}\) and \(\vec{u}_{D}\). \(I(t)\) can be estimated by considering the charge transferred by the firing process to nearby neurons. When the neuron receives positive inputs from its dendrites over a short time interval, its resting membrane potential increases from about \(-75\) mV to a critical value of about \(-45\) mV. At this point, a positive charge \(Q\) enters the soma from the ionic channels making the membrane potential slightly positive. This process lasts about 1 ms. During a subsequent time interval of approximately the same duration (1 ms), the excess positive charge \(Q\) is ejected through the axon, restoring the membrane potential to the resting value (\(-75\) mV) after a small over-shut. As a good approximation, the ejection of this charge corresponds to a variation in the membrane potential of about 100 mV. By approximating the soma as a sphere of radius \(R\) with uniform inner charge density \(\rho\), the electric field can be written as \(E(r)=\rho\frac{4}{3}\pi r^{3}/4\pi\epsilon_{0}r^{2}=\rho r/3\epsilon_{0}\) at \(r\leq R\) with \(r\) the distance from the center of the sphere. The membrane potential \(V_{m}\) is:  
\[V_{m}=\int_{0}^{R}E(r)dr=\frac{\rho}{3\epsilon_{0}}\int_{0}^{R}rdr=\frac{\rho }{6\epsilon_{0}}R^{2}=\frac{Q}{8\pi\epsilon_{0}R} \tag{19}\]  
where \(Q=\rho\frac{4}{3}\pi R^{3}\) is the total charge within the sphere.