An increase in fractal dimension is shown to occur in filtered chaotic signals. The dependence of the Lyapunov dimension on the filter parameters is used to predict the behavior of the information dimension which is directly evaluated for two experimental systems: the NMR laser and Rayleigh-Benard convection. Good quantitative agreement with the theoretical predictions is found. The understanding of the role of filtering not only clarifies aspects relevant in the calculation of fractal dimensions, but also yields an indirect but precise way to evaluate Lyapunov exponents.PACS numbers: 05.45.+b, 47.20.Tg, Experimental chaotic signals are more and more frequently characterized by the evaluation of the fractal dimension of the underlying strange attractor, reconstructed in a suitable embedding space. In order to increase the signal-to-noise ratio, the experimental data are often filtered, with use of either analog or digital techniques. Moreover, the finite instrumental bandwidth of the measuring apparatus may produce similar effects. Here we show that filtering processes introduce additional Lyapunov exponents and may cause an increase of the fractal dimension D(q). The results of direct evaluations of the information dimension for two sets of experimental data are also presented. The increase of D(q) with decreasing filter-bandwidth 77 confirms quantitatively the theoretical predictions. A precise estimate of the Lyapunov exponents is also obtained. Consider a physical system modeled by evolution equations of the form u(f)=F(u), where xx(t) is the state vector in phase space. The nonlinear differentiate function F(u) determines the time behavior of u(/). In the case of an experimental system, a single component x(t) of uG) is usually measured, and its values are recorded as a scalar time series {x(t)\. We concentrate, for simplicity, on an ideal linear low-pass filter, whose action can be described by our adding to the original differential model the further equation(1) where z(t) is the output of the filter and 77 the cutoff frequency. Since z(t) is coupled to the system through x(r), a faithful description of the dynamics can be obtained by the reconstruction of the attractor in an Edimensional "embedding" space through points Zi = {z(ti),z(ti+te), . . . ,z(ti + (E-\)At)}, At being a suitably chosen sampling time. If we indicate with X\ > X2 > • • • > A,£ the Lyapunov exponents of the original system, the Lyapunov dimension Z)L of the unfiltered attractor is given by Z>L "./ + £&*/1 X/ + i I, where j is the largest index for which the sum over k is nonnegative. x If the filter is present, a new Lyapunov exponent Xj = -77 should be taken into account, while the others remain unaffected, as a result of the form of Eq.(1). As a consequence, the dimension D^ remains unchanged as long as 77 > | A. y -+11 • To discuss what happens when the latter inequality is no longer satisfied, we assume, for simplicity, that only three Lyapunov exponents (one of which is equal to 0) determine the information dimension of the unfil...

Long-term results (average follow-up, 9.3 years) obtained in 1000 consecutive patients suffering from cryptogenetic (“essential”) trigeminal neuralgia treated with percutaneous thermorhizotomy are analyzed. Pain relief was obtained in 95% of the treated patients. Permanent morbidity was as follows: masseter weakness in 105 patients; oculomotor palsies in 5 patients; weakening of the corneal reflex in 197 patients, 6 of whom requested an ocular operation for keratitis; and painful dysesthesia in 52 patients, 15 of whom developed a painful anesthesia syndrome. There was a recurrence rate of 18.1%, and a correlation between postoperative sensory deficit and the cure rate was found. These results are discussed and compared to the results obtained with different techniques.

A consensus has yet to emerge whether deep brain stimulation (DBS) for treatment-refractory obsessive-compulsive disorder (OCD) can be considered an established therapy. In 2014, the World Society for Stereotactic and Functional Neurosurgery (WSSFN) published consensus guidelines stating that a therapy becomes established when “at least two blinded randomized controlled clinical trials from two different groups of researchers are published, both reporting an acceptable risk-benefit ratio, at least comparable with other existing therapies. The clinical trials should be on the same brain area for the same psychiatric indication.” The authors have now compiled the available evidence to make a clear statement on whether DBS for OCD is established therapy. Two blinded randomized controlled trials have been published, one with level I evidence (Yale-Brown Obsessive Compulsive Scale (Y-BOCS) score improved 37% during stimulation on), the other with level II evidence (25% improvement). A clinical cohort study (N = 70) showed 40% Y-BOCS score improvement during DBS, and a prospective international multi-center study 42% improvement (N = 30). The WSSFN states that electrical stimulation for otherwise treatment refractory OCD using a multipolar electrode implanted in the ventral anterior capsule region (including bed nucleus of stria terminalis and nucleus accumbens) remains investigational. It represents an emerging, but not yet established therapy. A multidisciplinary team involving psychiatrists and neurosurgeons is a prerequisite for such therapy, and the future of surgical treatment of psychiatric patients remains in the realm of the psychiatrist.

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The trigemino-facial reflex was studied in 7 patients affected by Huntington’s chorea and in 10 patients affected by Parkinson’s disease. The results show a different behavior of the habituation phenomenon in the two groups of patients: it is enhanced in the choreic and abolished in the parkinsonian patients. The main changes concern the time course of the second phase (the first inhibitory phase) of the reflex excitability cycle, in fact, the inhibitory phase appears very pronounced and prolonged in huntingtonian patients and reduced or abolished in parkinsonian patients.Some pathophysiological mechanisms involved in the control of the trigemino-facial reflex excitability are discussed with particular regard to the role of the hemispheric structures.