Design for Inspiration: Children, personal connections and educational technology

The project is working towards building an understanding of the personal interests and experiences of children with the aim of designing appropriate, usable and, most importantly, inspirational educational technology. kidprobe, an adaptation of the technology probe concept, has been used as a lightweight method of gaining contextual information about children's interactions with 'fun' technology. kidprobe has produced design inspiration which focuses primarily on the social and emotional connections children made. The use of kidprobe has generated some important ideas for improving the use of probes with children. It is an important first step in understanding how to effectively adapt probing techniques to inspire the design of technology for children.

Statistical mechanics of low-density parity check error-correcting codes over Galois fields

A variation of low-density parity check (LDPC) error-correcting codes defined over Galois fields (GF(q)) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of C non-zero elements per column. We examine the dependence of the code performance on the value of q, for finite and infinite C values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different q-dependence in the cases of C = 2 and C ≥ 3; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.

Lobe connections and lobe crowding are associated with growth rate in the lichen Xanthoparmelia conspersa

The association between lobe connections and the degree of lobe crowding and radial growth was studied in thalli of the foliose lichen Xanthoparmelia conspersa. In 35 thalli, 15% of the lobes were not physically connected to either of their neighbours before the lobes merged into the centre of the thallus. Twenty-five percent of the lobes were connected in pairs and 29% in groups of three. Approximately 5% of the lobes were interconnected in larger groups of six or more. The mean number of lobes per group in a thallus was positively correlated with thallus diameter and with the degree of lobe growth variation but was unrelated to annual radial growth rate (RGR). The degree of crowding of the lobes in a thallus was defined as a 'crowding index', viz., the product of lobe density and mean lobe width. Crowding index increased rapidly with size in smaller thalli but changed less with size in larger thalli. Crowding index was positively correlated with RGR but was unrelated to lobe growth variation. Lobes removed from large thalli and glued in various configurations to simulate different degrees of crowding did not demonstrate an association between lobe crowding and RGR over one year. These results suggest that the pattern of lobe connectivity of a thallus is associated with lobe growth variation in X. conspersa. The degree of lobe crowding is associated with the increase in RGR with thallus size in smaller thalli and by restricting lobe width, could also be a factor associated with the more constant growth of larger thalli.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.