An inverse dynamics model for the analysis, reconstruction and prediction of bipedal walking

Walking is a constrained movement which may best be observed during the double stance phase when both feet contact the floor. When analyzing a measured movement with an inverse dynamics model, a violation of these constrains will always occur due to measuring errors and deviations of the segments model from reality, leading to inconsistent results. Consistency is obtained by implementing the constraints into the model. This makes it possible to combine the inverse dynamics model with optimization techniques in order to predict walking patterns or to reconstruct non-measured rotations when only a part of the three-dimensional joint rotations is measured. In this paper the outlines of the extended inverse dynamics method are presented, the constraints which define walking are defined and the optimization procedure is described. The model is applied to analyze a normal walking pattern of which only the hip, knee and ankle flexions/extensions are measured. This input movement is reconstructed to a kinematically and dynamically consistent three-dimensional movement, and the joint forces (including the ground reaction forces) and joint moments of force, needed to bring about this movement are estimated

Observation of zero-point quantum fluctuations of a single-molecule magnet through the relaxation of its nuclear spin bath

A single-molecule magnet placed in a magnetic field perpendicular to its anisotropy axis can be truncated to an effective two-level system, with easily tunable energy splitting. The quantum coherence of the molecular spin is largely determined by the dynamics of the surrounding nuclear spin bath. Here we report the measurement of the nuclear spin--lattice relaxation in a single crystal of the single-molecule magnet Mn$_{12}$-ac, at $T \approx 30$ mK in perpendicular fields $B_{\perp}$ up to 9 T. Although the molecular spin is in its ground state, we observe an increase of the nuclear relaxation rates by several orders of magnitude up to the highest $B_{\perp}$. This unique finding is a consequence of the zero-point quantum fluctuations of the Mn$_{12}$-ac spin, which allow it to efficiently transfer energy from the excited nuclear spin bath to the lattice. Our experiment highlights the importance of quantum fluctuations in the interaction between an `effective two-level system' and its surrounding spin bath.Comment: 5 pages, 4 figure

Variable selection by searching for good subsets

Machine learning and statistical models are increasingly used in a prediction context and in the process of building these models the question of which variables to include often arises. Over the last 50 years a number of procedures have been proposed, especially in the statistical literature. In this paper a newvariable selection procedure is introduced for linear models. A subset of variables is defined here to be “good at margin λ” if it has two properties, namely (i) its associated criterion of fit will be improved in relative terms by less than λ if any variable is added to it, and (ii) its criterion of fit will deteriorate in relative terms by at least λ if any variable inside it, is dropped from it. Thus, such a subset contains all variables that are individually important and none that are unimportant at a given margin λ ≥ 0. This paper discusses calculation of such λ-good subsets. The “good” approach extends readily to generalised linear and many other models by using an appropriate criterion of performance. The approach is illustrated on an artificial data set and a number of real data sets

A framework for normal mean variance mixture innovations with application to GARCH modelling

GARCH models are useful to estimate the volatility of financial return series. Historically the innovation distribution of a GARCH model was assumed to be standard normal but recent research emphasizes the need for more general distributions allowing both asymmetry (skewness) and kurtosis in the innovation distribution to obtain better fitting models. A number of authors have proposed models which are special cases of the class of normal mean variance mixtures. We introduce a general framework within which this class of innovation distributions may be discussed. This entails writing the innovation term as a standardised combination of two variables, namely a normally distributed term and a mixing variable, each with its own interpretation. We list the existing models that fit into this framework and compare the corresponding innovation distributions, finding that they tend to be quite similar. This is confirmed by an empirical illustration which fits the models to the monthly excess returns series of the US stocks. The illustration finds further support for the ICAPM model of Merton, thus supporting recent results of Lanne and Saikonnen (2006)

Gesinsmoorde - Waar pas die kerk in?

Taking the final report of the HSRC’s exploratory study on family murder as a point of departure, the involvement of clergy and church regarding the phenomenon of family murder is discussed in this article. After highlighting some of the findings of the exploratory study, specific problematic aspects are addressed. The implications of the Christian message of hope to people in the situation of hopelessness, murder and suicide implicit in the phenomenon of family murder, are also evaluated. Likewise, the problematic relationship between the consequences of the gospel and the requirements for mental health is also touched upon. This relationship is looked at from the perspective of certain aspects of the empirical research done in this field. Furthermore, the possible supportive role of the church is stressed: this 'ecology of care’ and the church's message of hope ought to be functional in the situation of hopelessness accompanying family murder. In conclusion, certain preventative actions, in which the church may be instrumental, are pointed out