On the Hard Lefschetz property of stringy Hodge numbers

For projective varieties with a certain class of 'mild' isolated singularities and for projective threefolds with arbitrary Gorenstein canonical singularities, we show that the stringy Hodge numbers satisfy the Hard Lefschetz property. This result fits nicely with a 6-dimensional counterexample of Mustata and Payne for the Hard Lefschetz property for stringy Hodge numbers in general. We also give such an example, ours is a hypersurface singularity.Comment: 15 page

Jaarverslag 2009 KNPV Werkgroep Graanziekten

Jaarverslag 2009 van de KNPV Werkgroep Graanziekten. De excursie naar Rothamsted Research in Harpenden (UK) op 28 mei 2009 wordt beschreven

Stringy E-functions of hypersurfaces and of Brieskorn singularities

We show that for a hypersurface Batyrev's stringy E-function can be seen as a residue of the Hodge zeta function, a specialization of the motivic zeta function of Denef and Loeser. This is a nice application of inversion of adjunction. If an affine hypersurface is given by a polynomial that is non-degenerate with respect to its Newton polyhedron, then the motivic zeta function and thus the stringy E-function can be computed from this Newton polyhedron (by work of Artal, Cassou-Nogues, Luengo and Melle based on an algorithm of Denef and Hoornaert). We use this procedure to obtain an easy way to compute the contribution of a Brieskorn singularity to the stringy E-function. As a corollary, we prove that stringy Hodge numbers of varieties with a certain class of strictly canonical Brieskorn singularities are nonnegative. We conclude by computing an interesting 6-dimensional example. It shows that a result, implying nonnegativity of stringy Hodge numbers in lower dimensional cases, obtained in our previous paper, is not true in higher dimension.Comment: 21 page

Ambulatory estimation of foot movement during gait using inertial sensors

Human body movement analysis is commonly done in so-called 'gait laboratories’. In these laboratories, body movement is masured using optically based systems like Vicon, Optrotrak. The major drawback of these systems is the restriction to a laboratory environment. Therefore research is required to find ways for performing these measurements outside the gait laboratory. The estimation of foot movement is important, since balance is controlled by foot placement during gait. This study investigates whether it is possible to estimate foot movement, specifically foot placement, during gait under ambulatory conditions. The measurement system consisted of an orthopaedic sandal with two six degrees-of-freedom force/moment sensors beneath the heel and the forefoot. It should be noted that the force sensors were merely used for gait phase detection. The position and orientation of heel and forefoot were estimated using the accelerometers and gyroscopes of two miniature inertial sensors, rigidly attached to the force sensors [1,3]. In addition, errors in the walking direction were compensated for by using knowledge about the average walking direction. The proposed ambulatory measurement system was similar to the one used in a previous study [3]. In that study the position and orientation determination was restarted each step, while this study allows estimation of position and orientation during several steps including a change of direction. However, the accuracy should be investigated in more detail by an evaluation study. Moreover, the measurement system can be simplified by using a different gait phase detection system, for example by a gyroscope based detection system [2]. The financial support from the Dutch Ministry of Economic Affairs for the FreeMotion project is gratefully acknowledged. REFERENCES [1] H.J. Luinge and P.H. Veltink, “Measuring orientation of human body segments using miniature gyroscopes and accelerometers”, Med. Bio. Eng. Comp., Vol. 43, pp. 273-282, (2005). [2] I.P.I. Pappas, M.R. Popovic, M.R. Keller, V. Dietz and M. Morari, “A reliable gait phase detection system”, IEEE Trans. Neural Syst. Rehabil. Eng., Vol. 9, pp. 113-125, (2001). [3] H.M. Schepers, P.H. Veltink and H.F.J.M. Koopman, “Ambulatory assessment of ankle and foot dynamics”, IEEE Trans. Biomed. Eng., Submitted, (2006)

Center of mass movement estimation using an ambulatory measurement sytem

Center of Mass (CoM) displacement, an important variable to characterize human walking, was estimated in this study using an ambulatory measurement system. The ambulatory system was compared to an optical reference system. Root-mean-square differences between the magnitudes of the CoM appeared to be comparable to those described in literature