How do children learn abstract concepts such as animal vs. artifact? Previous research has suggested that such concepts can partly be derived using cues from the language children hear around them. Following this suggestion, we propose a model where we represent the children's developing lexicon as an evolving network. The nodes of this network are based on vocabulary knowledge as reported by parents, and the edges between pairs of nodes are based on the probability of their co-occurrence in a corpus of child-directed speech. We found that several abstract categories can be identified as the dense regions in such networks. In addition, our simulations suggest that these categories develop simultaneously, rather than sequentially, thanks to the children's word learning trajectory which favors the exploration of the global conceptual space.

Films made from random nanowire arrays are an attractive choice for electronics requiring flexible transparent conductive films. However, thus far there has been no unified theory for predicting their electrical conductivity. In particular, the effects of orientation distribution on network conductivity remain poorly understood. We present a simplified analytical model for random nanowire network electrical conductivity that is the first to accurately capture the effects of arbitrary nanowire orientation distributions on conductivity. Our model is an upper bound and converges to the true conductivity as nanowire density grows. The model replaces Monte Carlo sampling with an asymptotically faster computation and in practice can be computed much more quickly than standard computational models. The success of our approximation provides novel theoretical insight into how nanowire orientation affects electrical conductivity, illuminating directions for future research.