Asynchronous noise

Development of model based DBS techniques exploiting the methods of nonlinear dynamics and statistical physics was pioneered by P. A. Tass, who proposed a number of approaches. The main idea of these approaches is that suppression of the pathological rhythm should be achieved in such a way that (i) activity of individual units is not suppressed, but only their firing becomes asynchronous, and (ii) the stimulation should be minimized, e.g., it is desirable to switch it off as soon as the synchrony is suppressed (see [48, 49] and references therein). Following these ideas we suggested in our previous publications [40, 41] a delayed feedback suppression control scheme (Fig. 13.5), cf. delayed and non-delayed techniques for stabilization of lowdimensional systems [5, 22, 39] and for control of noise-induced motion [24]. In our approach it is assumed that the collective activity of many neurons is reflected in the local field potential (LFP) which can be registered by an extracellular microelectrode. Delayed and amplified LFP signal can be fed back into the systems via the second or same electrode (see [37] and references therein for a description of one electrode measurement -stimulation setup.) Numerical simulation as well as analytical analysis of the delayed feedback control demonstrate that it indeed can be exploited for suppression of the collective synchrony. 

Rose neurons (Eqs. (13.5)). The delayed feedback is switched on at ( = -5000. (b) The control. signal C = /(X(( — T) — X(t)) quickly decays to the noise level and the desired, asynchronous, state of the system is maintained with a minimal intervention. (c,d) Synchronous and asynchronoits bursting of two neurons in the absence and in the presence of the feedback, respectively. 

In the maps corresponding to the lipid (Figure 10.7) a clear difference can be seen between LDL and HDL. Whereas in LDL an autopeak is seen in the synchronous map at 1636 cm and a cross-peak 1736/1742 (-F), in HDL only noise is produced. As shown earlier, (Section 10.3), in LDL one peak is changing, but not only in intensity. Infrared studies of phospholipids have shown the presence of two bands corresponding to two different hydration states of the interface carbonyl. The asynchronous map would point to a change in the lipid core where different hydration states could be involved. In the case of HDL, no lipid transition was proposed, and the 2D-IR agrees with the absence of conformational changes in the lipid in the interval 20-40 °C. 

If the noise is completely random (i.e. asynchronous), then the last integrals in Eqs (28) and (29) are equal to zero provided that they are carried out over infinite time. If the integration is carried out over Nf periods of the sinusoidal perturbation, the equivalent filter selectively is given by (Gabrielli [1981])... 

The correlation technique is an averaging method and thus affords the same type of insensitivity to asynchronous system noise as phase-sensitive detection. 

Coloured noise, narrow band noise and periodic impulsive noise are usually modeled as background noise because they remain stationary from seconds to even hours. Periodic impulsive noise synchronous to the mains and asynchronous impulsive noise may cause bit or burst errors over the transmission, although they are time variant. A complete theoretical analysis on shown noises in Figure 2 can be found on [5, 6,11,12,13]. 

The control requirements for the previously described coloured noise, narrow band noise, periodic impnilsive noise and asynchronous impulsive noise, can be separately analyzed in two different scenarios. 

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