Summary The Earth’s rotation exhibits periodic variations as a result of gravitational torques exerted by the Sun and the Moon and of angular momentum exchange of the solid Earth with the Earth’s atmosphere and hydrosphere. Here we aim at determining the complementary effect of the deep interior on variations in the Length-of-Day (LOD) and focus on the influence of topography at the core-mantle boundary (CMB). For this purpose, we have developed an analytical approach for solving the Navier-Stokes equation for global rotational motions and inertial waves, based on and extending the approach of Wu & Wahr (1997). An advantage of the analytical approach is that it allows to identify the frequencies and topographic spherical harmonics degrees and orders where resonance can happen, as well as to quantify the total amplifications in the tidal effects on LOD variations. Although the resonances are found to be sometimes quite near tidal frequencies, we show that they are not sufficiently close to induce significant perturbations in LOD variations, except for two of the tides, the fortnightly and monthly tides Mf and Mm. Our results go beyond the findings of Wu & Wahr (1997), extending them to a much wider range of degrees and orders of topographic coefficients. We show that there is an amplification in Mf and Mm induced by the degree 18-order 10 and by the degree 7-order 1 of the topography, respectively. Our approach is generic in the sense that it can be applied to other orientation changes of the Earth, as well as to other planets.

The evaluation of early school-aged children's handwritten symbols is a challenging problem. The teaching of handwriting is still an essential skill in effective written communication. There is a need for an automatic quality evaluation of handwritten symbols in order to assess the progress of children ability to write nice letters or other symbols. In our case, the letters are positioned in a well defined two-dimensional space, similar to the special notebooks children use in school when learning how to write. For this study, a Wacom system composed of a tablet and a digital pen is used for collecting the data that will be sent to the analysis and evaluation module. While the school-aged child writes a character, the pen transmits the (x,y) coordinates and the time t. Next, a normalization is needed in order to keep the same distance between neighboring pixels. Several approaches are investigated (e.g. normalization with/without interpolation). The coordinates sequence is transformed in a sequence of angles measured relatively to the X axis for each written character. They encode the changing directions during pen movement. An algorithm is used in order to detect if the overall shape of the written symbol is correct. Several parameters that characterise the written character are investigated (e.g. ,,centre of mass", height over width ratio, alignment errors etc.). Their correlation with subjective scores is verified. Several metrics are proposed based on spatial and temporal measurements. Next, the handwritten quality using the legibility, form size and alignment of the letters or digits is investigated. It is shown that a rough discrimination between proficient and non-proficient handwriting can be obtained by considering the size and space parameters. Our simulations have revealed the importance of good handwritten reference samples. The goal is to develop a calligraphic handwritting learning system designed for first grade or pre-school childrens. Further research is needed in order to address other aspects of an intelligent tutor.

The share of wind power in fuel mixes worldwide has increased considerably.The main ingredient when deriving wind power predictions are wind speed data; the closer to the wind farms, the better they forecast the power supply. The current paper proposes a hybrid model for predicting wind speeds at convenient locations. It is then applied to Southern California power price area. We build random fields with time series of gridded historical forecasts and actual wind speed observations. We estimate with ordinary kriging the spatial variability of the temporal parameters and derive predictions. The advantages of this work are twofold: (1) an accurate daily wind speed forecast at any location in the area and (2) a general method applicable to other markets.