Physical wavelets and their sources: real physics in complex spacetime

Angular spectral framework to test full corrections of paraxial solutions

Different correction methods for paraxial solutions have been used when such solutions extend out of the paraxial regime. The authors have used correction methods guided by either their experience or some educated hypothesis pertinent to the particular problem that they were tackling. This article provides a framework so as to classify full wave correction schemes. Thus, for a given solution of the paraxial wave equation, we can select the best correction scheme of those available. Some common correction methods are considered and evaluated under the proposed scope. Another remarkable contribution is obtained by giving the necessary conditions that two solutions of the Helmholtz equation must accomplish to accept a common solution of the parabolic wave equation as a paraxial approximation of both solutions.

Multi-point accelerometric detection and principal component analysis of heart sounds

Heart sounds are a fundamental physiological variable that provide a unique insight into cardiac semiotics. However a deterministic and unambiguous association between noises in cardiac dynamics is far from being accomplished yet due to many and different overlapping events which contribute to the acoustic emission. The current computer-based capacities in terms of signal detection and processing allow one to move from the standard cardiac auscultation, even in its improved forms like electronic stethoscopes or hi-tech phonocardiography, to the extraction of information on the cardiac activity previously unexplored. In this report, we present a new equipment for the detection of heart sounds, based on a set of accelerometric sensors placed in contact with the chest skin on the precordial area, and are able to measure simultaneously the vibration induced on the chest surface by the heart's mechanical activity. By utilizing advanced algorithms for the data treatment, such as wavelet decomposition and principal component analysis, we are able to condense the spatially extended acoustic information and to provide a synthetical representation of the heart activity. We applied our approach to 30 adults, mixed per gender, age and healthiness, and correlated our results with standard echocardiographic examinations. We obtained a 93% concordance rate with echocardiography between healthy and unhealthy hearts, including minor abnormalities such as mitral valve prolapse.