Regression on fixed-rank positive semidefinite matrices: A Riemannian approach

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixedrank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks. © 2011 Gilles Meyer, Silvere Bonnabel and Rodolphe Sepulchre.

Magnetophonon resonance in graphite: High-field Raman measurements and electron-phonon coupling contributions

We perform Raman scattering experiments on natural graphite in magnetic fields up to 45 T, observing a series of peaks due to interband electronic excitations over a much broader magnetic field range than previously reported. We also explore electron-phonon coupling in graphite via magnetophonon resonances. The Raman G peak shifts and splits as a function of magnetic field, due to the magnetically tuned coupling of the E 2g optical phonons with the K- and H-point inter-Landau-level excitations. The analysis of the observed anticrossing behavior allows us to determine the electron-phonon coupling for both K- and H-point carriers. In the highest field range (>35 T) the G peak narrows due to suppression of electron-phonon interaction. © 2012 American Physical Society.

Observations on some German contributions to engineering design in memory of professor Wolfgang Beitz

This paper, written in memory of Professor Wolfgang Beitz, discusses some of the influences of the work undertaken in Germany on systematic engineering design. It highlights differences between the language regions, and gives examples of design research and design education linked to Konstruktionslehre - the standard text on systematic engineering design for which Professor Beitz was most widely recognised outside Germany. The paper finishes with a plea for a greater exchange of ideas.