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Although mixed use is an emerging strategy that has been widely accepted in urban planning for promoting neighbourhood vibrancy, there is no consensus on how to quantitatively measure the mix and the effects of mixed use on neighbourhood vibrancy. Shannon entropy, the most commonly used diversity measurement in assessing mixed use, has been found to be inadequate in measuring the multifaceted, multidimensional characteristics of mixed use. And lack of data also makes it difficult to find the relationship between mixed use and neighbourhood vibrancy. However, the recent availability of new sources including mobile phone data and Point of Interest (POI) data have made it possible to develop new indices of mixed use and neighbourhood vibrancy to analyse their relationships. Taking advantage of these emerging new data sources, this study used the numbers of mobile phone users in a 24-hour period as a proxy of neighbourhood vibrancy and used POIs from a navigation database to develop a series of mixed-use indicators that can better reflect the multifaceted, multidimensional characteristics of mixed-use neighbourhoods. The Hill numbers, a unified form of diversity measurement used in ecological literature that includes richness, entropy, and the Simpson index, are used to measure the degrees of mixed use. Using such fine-grained data sets and the Hill numbers allowed us to obtain better insights into the relationship between mixed use and neighbourhood vibrancy. Four models varying in POI measurements that reflect different dimensions of mixed use were presented. The results showed that either POI density or entropy can explain approximately 1% of neighbourhood vibrancy, while POI richness contributes significantly in improving neighbourhood vibrancy. The results also revealed that the entropy has limitations as a measure for representing mixed use and demonstrated the necessity of adopting a set of more appropriate measurements for mixed use. Increasing the number of POIs has limited power to improve neighbourhood vibrancy compared with encouraging the mixing of complementary POIs. These exploratory findings may be useful for adjusting mixeduse assessments and to help guide urban planning and neighbourhood design.ARTICLE HISTORY

We report the observation of two signatures of a pressure-induced topological quantum phase transition in the polar semiconductor BiTeI using x-ray powder diffraction and infrared spectroscopy. The x-ray data confirm that BiTeI remains in its ambient-pressure structure up to 8 GPa. The lattice parameter ratio c/a shows a minimum between 2.0-2.9 GPa, indicating an enhanced c-axis bonding through p(z) band crossing as expected during the transition. Over the same pressure range, the infrared spectra reveal a maximum in the optical spectral weight of the charge carriers, reflecting the closing and reopening of the semiconducting band gap. Both of these features are characteristics of a topological quantum phase transition and are consistent with a recent theoretical proposal.