Abstract: A qualitative research study is presented herein with the purpose of identifying mathematics learning opportunities in students between 10 and 12 years old while playing a commercial version of a Tower Defense game. These learning opportunities are understood as mathematicisable moments of the game and involve the establishment of relationships between the game and mathematical problem solving. Based on the analysis of these mathematicisable moments, we conclude that the game can promote problem-solving processes and learning opportunities that can be associated with different mathematical contents that appears in mathematics curricula, thought it seems that teacher or new game elements might be needed to facilitate the processes.

Abstract: On September 8, 2001 around 2 h UT, the largest uranian moon, Titania, occulted Hipparcos star 106829 (alias SAO 164538, a V=7.2, K0 III star). This was the first-ever observed occultation by this satellite, a rare event as Titania subtends only 0.11 arcsec on the sky. The star's unusual brightness allowed many observers, both amateurs or professionals, to monitor this unique event, providing fifty-seven occultations chords over three continents, all reported here. Selecting the best 27 occultation chords, and assuming a circular limb, we derive Titania's radius: View the MathML source (1-σ error bar). This implies a density of View the MathML source using the value View the MathML source derived by Taylor [Taylor, D.B., 1998. Astron. Astrophys. 330, 362–374]. We do not detect any significant difference between equatorial and polar radii, in the limit View the MathML source, in agreement with Voyager limb image retrieval during the 1986 flyby. Titania's offset with respect to the DE405 + URA027 (based on GUST86 theory) ephemeris is derived: ΔαTcos(δT)=−108±13 mas and ΔδT=−62±7 mas (ICRF J2000.0 system). Most of this offset is attributable to a Uranus' barycentric offset with respect to DE405, that we estimate to be: View the MathML source and ΔδU=−85±25 mas at the moment of occultation. This offset is confirmed by another Titania stellar occultation observed on August 1st, 2003, which provides an offset of ΔαTcos(δT)=−127±20 mas and ΔδT=−97±13 mas for the satellite. The combined ingress and egress data do not show any significant hint for atmospheric refraction, allowing us to set surface pressure limits at the level of 10–20 nbar. More specifically, we find an upper limit of 13 nbar (1-σ level) at 70 K and 17 nbar at 80 K, for a putative isothermal CO2 atmosphere. We also provide an upper limit of 8 nbar for a possible CH4 atmosphere, and 22 nbar for pure N2, again at the 1-σ level. We finally constrain the stellar size using the time-resolved star disappearance and reappearance at ingress and egress. We find an angular diameter of 0.54±0.03 mas (corresponding to View the MathML source projected at Titania). With a distance of 170±25 parsecs, this corresponds to a radius of 9.8±0.2 solar radii for HIP 106829, typical of a K0 III giant.

Abstract: One of the major difficulties of handwriting symbol recognition is the high variability among symbols because of the different writer styles. In this paper, we introduce a robust approach for describing and recognizing hand-drawn symbols tolerant to these writer style differences. This method, which is invariant to scale and rotation, is based on the dynamic time warping (DTW) algorithm. The symbols are described by vector sequences, a variation of the DTW distance is used for computing the matching distance, and K-Nearest Neighbor is used to classify them. Our approach has been evaluated in two benchmarking scenarios consisting of hand-drawn symbols. Compared with state-of-the-art methods for symbol recognition, our method shows higher tolerance to the irregular deformations induced by hand-drawn strokes.

Abstract: The aim of writer identification is determining the writer of a piece of handwriting from a set of writers. In this paper, we present an architecture for writer identification in old handwritten music scores. Even though an important amount of music compositions contain handwritten text, the aim of our work is to use only music notation to determine the author. The main contribution is therefore the use of features extracted from graphical alphabets. Our proposal consists in combining the identification results of two different approaches, based on line and textural features. The steps of the ensemble architecture are the following. First of all, the music sheet is preprocessed for removing the staff lines. Then, music lines and texture images are generated for computing line features and textural features. Finally, the classification results are combined for identifying the writer. The proposed method has been tested on a database of old music scores from the seventeenth to nineteenth centuries, achieving a recognition rate of about 92% with 20 writers.

Abstract: Most document analysis applications rely on the extraction of shape descriptors, which may be grouped into different categories, each category having its own advantages and drawbacks (O.R. Terrades et al. in Proceedings of ICDAR’07, pp. 227–231, 2007). In order to improve the richness of their description, many authors choose to combine multiple descriptors. Yet, most of the authors who propose a new descriptor content themselves with comparing its performance to the performance of a set of single state-of-the-art descriptors in a specific applicative context (e.g. symbol recognition, symbol spotting...). This results in a proliferation of the shape descriptors proposed in the literature. In this article, we propose an innovative protocol, the originality of which is to be as independent of the final application as possible and which relies on new quantitative and qualitative measures. We introduce two types of measures: while the measures of the first type are intended to characterize the descriptive power (in terms of uniqueness, distinctiveness and robustness towards noise) of a descriptor, the second type of measures characterizes the complementarity between multiple descriptors. Characterizing upstream the complementarity of shape descriptors is an alternative to the usual approach where the descriptors to be combined are selected by trial and error, considering the performance characteristics of the overall system. To illustrate the contribution of this protocol, we performed experimental studies using a set of descriptors and a set of symbols which are widely used by the community namely ART and SC descriptors and the GREC 2003 database.