A robust a posteriori estimator for the residual-free bubbles method applied to advection-diffusion problems

We develop the a posteriori error analysis for the RFB method, applied to the linear advection-diffusion problem: the numerical error, measured in suitable norms, is estimated in terms of the numerical residual. The robustness is investiged, in the sense that we prove uniform equivalence between a norm of the numerical residual and a particular norm of the error

Somatic modulation of tinnitus: a review and some open questions

Tinnitus modulation by movements of the temporomandibular joint, head and neck musculoskeletal structures and the eye, can be found in one to two thirds of tinnitus sufferers; unfortunately this condition is often overlooked by otolaryngologists. Although somatic modulation has been initially hypothesized as a fundamental characteristic of tinnitus, there is increasing evidence of a tight connection with disorders of non-auditory regions. The structure that mostly modulates tinnitus is the temporomandibular joint, which mainly causes an increase in tinnitus loudness, followed by head and neck movements that may result in an increase or decrease of loudness and eye movements (gaze-evoked tinnitus). Besides loudness, somatic movements can also modulate tinnitus pitch and localization. Somatosensory tinnitus is a relatively new nding that leaves several open questions: are there individual predisposing factors to somatic modulation? How strong is the association between the capability to somatically modulate tinnitus and an underlying non-auditory disorder? Changes that occur after somatic maneuvers are only transitory? Why patients that have concomitant hyperacusis also have higher chances of tinnitus modulation? Further basic science and clinical research is required to address these and many other questions about somatosensory tinnitus

Local measurements of nonlocal observables and the relativistic reduction process

In this paper we reconsider the constraints which are imposed by relativistic requirements to any model of dynamical reduction. We review the debate on the subject and we call attention on the fundamental contributions by Aharonov and Albert. Having done this we present a new formulation, which is much simpler and more apt for our analysis, of the proposal put forward by these authors to perform measurements of nonlocal observables by means of local interactions and detections. We take into account recently proposed relativistic models of dynamical reduction and we show that, in spite of some mathematical difficulties related to the appearence of divergences, they represent a perfectly appropriate conceptual framework which meets all necessary requirements for a relativistic account of wave packet reduction. Subtle questions like the appropriate way to deal with counterfactual reasoning in a relativistic and nonlocal context are also analyzed in detail