Low dimensional manifold embedding for scattering coefficients of intrapartum fetale heart rate variability.

Intrapartum fetal surveillance for early detection of fetal acidosis in clinical practice focuses on reducing neonatal morbidity via early detection. It is the subject of on going research studies attempting notably to improve detection performance by reducing false positive rate. In that context, the present contribution tailors to fetal heart rate variability analysis a graph-based dimensionality reduction procedure performed on scattering coefficients. Applied to a high quality and well-documented database constituted by obstetricians from a French academic hospital, the low dimensional embedding enables to distinguish between the temporal dynamics of healthy and acidotic fetuses, as well as to achieve satisfactory detection performance detection compared to those obtained by the clinical-benchmark FIGO criteria.

Geometric diffusions as a tool for harmonic analysis and structure definition of data: multiscale methods.

In the companion article, a framework for structural multiscale geometric organization of subsets of R(n) and of graphs was introduced. Here, diffusion semigroups are used to generate multiscale analyses in order to organize and represent complex structures. We emphasize the multiscale nature of these problems and build scaling functions of Markov matrices (describing local transitions) that lead to macroscopic descriptions at different scales. The process of iterating or diffusing the Markov matrix is seen as a generalization of some aspects of the Newtonian paradigm, in which local infinitesimal transitions of a system lead to global macroscopic descriptions by integration. This article deals with the construction of fast-order N algorithms for data representation and for homogenization of heterogeneous structures.

Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps.

We provide a framework for structural multiscale geometric organization of graphs and subsets of R(n). We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures. We show that appropriately selected eigenfunctions or scaling functions of Markov matrices, which describe local transitions, lead to macroscopic descriptions at different scales. The process of iterating or diffusing the Markov matrix is seen as a generalization of some aspects of the Newtonian paradigm, in which local infinitesimal transitions of a system lead to global macroscopic descriptions by integration. We provide a unified view of ideas from data analysis, machine learning, and numerical analysis.

Wavelets, adapted waveforms and de-noising.

This is a short summary of a talk given at the Frontier Science in EEG Symposium, Continuous Waveform Analysis, held on 9 October 1993 in New Orleans. We describe some new libraries of waveforms well-adapted to various numerical analysis and signal processing tasks. The main point is that by expanding a signal in a library of waveforms which are well-localized in both time and frequency, one can achieve both understanding of structure and efficiency in computation. We briefly cover the properties of the new "wavelet packet" and "localized trigonometric" libraries. The main focus will be applications of such libraries to the analysis of complicated transient signals: a feature extraction and data compression algorithm for speech signals which uses best-adapted time and frequency decompositions, and an adapted waveform analysis algorithm for removing fish noises from hydrophone recordings. These signals share many of the same properties as EEG traces, but with distinct features that are easier to characterize and detect.

Characterization of fourier transforms of hardy spaces.

Characterizations of Fourier transforms of boundary distributions of functions in H(p)(R) or H(p)(T), 0 < p

Maximal functions and h spaces defined by ergodic transformations.

Suppose an ergodic flow acts on a probability space enabling us to introduce the Ergodic Hilbert transform f of f in L(p)(), 1 <== p <== infinity. H(1) is the class of all functions of the form f + if in L(1)(). We show that H(1) can be characterized in terms of a class of maximal functions; moreover, the dual space of H(1) is identified with a space of functions of bounded mean oscillation defined in terms of the flow.

Distribution function inequalities for singular integrals.

This paper describes some distribution function inequalities between maximal functions and singular integral operators.