Torsion-Adding and Asymptotic Winding Number for Periodic Window Sequences

In parameter space of nonlinear dynamical systems, windows of periodic states are aligned following routes of period-adding configuring periodic window sequences. In state space of driven nonlinear oscillators, we determine the torsion associated with the periodic states and identify regions of uniform torsion in the window sequences. Moreover, we find that the measured of torsion differs by a constant between successive windows in periodic window sequences. We call this phenomenon as torsion-adding. Finally, combining the torsion and the period adding rules, we deduce a general rule to obtain the asymptotic winding number in the accumulation limit of such periodic window sequences

Non-invasive brain stimulation techniques for chronic pain

Copyright © 2014 The Cochrane Collaboration.Various devices are available that can electrically stimulate the brain without the need for surgery or any invasive treatment in order to manage chronic pain. There are four main treatment types: repetitive transcranial magnetic stimulation (rTMS) in which the brain is stimulated by a coil applied to the scalp, cranial electrotherapy stimulation (CES) in which electrodes are clipped to the ears or applied to the scalp, transcranial direct current stimulation (tDCS) and reduced impedance non-invasive cortical electrostimulation (RINCE) in which electrodes are applied to the scalp. These have been used to try to reduce pain by aiming to alter the activity of the brain, but the efficacy of these treatments is uncertain. This review update included 56 studies: 30 of rTMS, 11 of CES, 14 of tDCS and one of RINCE. We judged only three studies as having a low risk of bias. Low or very low-quality evidence suggests that low-frequency rTMS and rTMS applied to pre-frontal areas of the brain are not effective but that a single dose of high-frequency stimulation of the motor cortex area of the brain provides short-term pain relief. This effect appears to be small and may be exaggerated by a number of sources of bias. Studies that gave a course of multiple treatments of rTMS produced conflicting results with no overall effect seen when we pooled the results of these studies. Most studies of rTMS are small and there is substantial variation between studies in terms of the treatment methods used. Low-quality evidence does not suggest that CES or tDCS are effective treatments for chronic pain. A single small study of RINCE provided very low-quality evidence of a short-term effect on pain. For all forms of stimulation the evidence is not conclusive and uncertainty remains. The reporting of side effects varied across the studies. Of the studies that clearly reported side effects, short-lived and minor side effects such as headache, nausea and skin irritation were usually reported both after real and sham stimulation. There were two reports of seizure following real rTMS. While the broad conclusions for rTMS and CES have not changed substantially, the addition of this new evidence and the application of the GRADE system has modified some of our interpretation. Previous readers should re-read this update. More studies of rigorous design and adequate size are required to evaluate accurately all forms of non-invasive brain stimulation for the treatment of chronic pain

Characterization in bi-parameter space of a non-ideal oscillator

The authors thank scientific agencies CAPES, CNPq (112952/2015-1), and FAPESP (2011/ 19269-11). M. S. Baptista also thanks EPSRC (EP/I03 2606/1).Peer reviewedPostprin

Noether symmetry for non-minimally coupled fermion fields

A cosmological model where a fermion field is non-minimally coupled with the gravitational field is studied. By applying Noether symmetry the possible functions for the potential density of the fermion field and for the coupling are determined. Cosmological solutions are found showing that the non-minimally coupled fermion field behaves as an inflaton describing an accelerated inflationary scenario, whereas the minimally coupled fermion field describes a decelerated period being identified as dark matter.Comment: Revised version accepted for publication in Classical and Quantum Gravit

Reducing the parameter space for Unparticle-inspired models using white dwarf masses

Based on astrophysical constraints derived from Chandrasekhar's mass limit for white-dwarfs, we study the effects of the model on the parameters of unparticle-inspired gravity, on scales $\Lambda_U > 1 \; TeV$ and $d_U \approx 1$.Comment: 4 pp., 4 Fig., to appear in PR