I work on a variety of topics at the interface between mathemtaical methods and socio-economic systems. Below is a brief summary of three areas of ongoing research.

Science of Cities

Cities are now home to the majority of the world’s population and built environments are now centers of population growth and energy consumption. The unprecedented pace of urbanization presents both significant challenges and opportunities, including poverty alleviation, sustainable development, and adaption to climate change. How we manage urbanization, by transforming social, economic, and physical structure of the area, will have a huge impact on developing countries, and indirectly on developed countries over the a long term. In order to design, build and manage cities in ways that address these issues, we need both a scientific and an engineering understanding of cities to provide theoretical predictions and practical solutions. Not surprisingly, much research effort is now devoted to understanding the drivers and dynamics of urbanization, and to designing and managing “smart” cities using sensor technologies. A collaboration with Geoffrey B. West, Luis Bettencourt, Marcus Hamilton, Jose Lobo, and Deborah Strumsky

  - scaling and universality in urban economic diversification [link]
  - the ecology and energetics of hunter-gatherer [link]
  - what is urban scaling [link]
  - delineating urban area: spatial definition of cities [link]
  - urban division of labor and diversity [link]
  - urban crime [link]
  - urban transportation network optimisation [link]
  - are cities greener? project page: [link]
  - what is science of cities
  - automating the labor force of U.S. metropolitan areas: which skills secure your job?

Pathway of innovation

Technological progress plays a key role in economic growth and development. Solutions for many of humanity’s most pressing challenges—sustainable growth, poverty reduction, and climate change—demand significant additions to society's technological toolkit. The process of technological change is derived from, and governed by, accumulation of knowledge. It is therefore essential to understand how knowledge is created, shared, utilized and accumulated. Some of these processes—inventive activities—leave a footprint whose dynamics we can study in detail. Here, we propose to develop a formal methodology based on a systematic, comparative analysis of empirical data (large-scale U.S. Patent data spanning 220 years) for constructing a detailed space of technological change in the form of multilayer networks. Our aim is to illuminate potential innovation pathways both visually and mathematically. The project consists of data mining, statistical analysis, mathematical modeling, and theory development, and draws on, and further develops, techniques and concepts from distinct academic disciplines. The outcome of the project will enable us to trace dynamics of knowledge accumulation. A collaboration with Daniel Kim, Doyne Farmer, Jose Lobo, Deborah Strumsky, Francois Lafond, Daniel Burkhardt Cerigo, Ioannis Psorakis

  - combinatorial inventions [link]
  - novelty profile and invention's future impact [link]
  - [identify the technological pathway]
  - [quantifying the stream of technological innovation]

Lexical Semantic Shift [link]

How universal is human conceptual structure? The way concepts are organized in the human brain may reflect distinct features of cultural, historical, and environmental background in addition to properties universal to human cognition. Semantics, or meaning expressed through language, provides direct access to the underlying conceptual structure, but meaning is notoriously difficult to measure, let alone parameterize. Using cross-linguistic dictionaries, we provide here an empirical measure of semantic proximity between concepts and analyze the structure of a network derived from it. Across languages carefully selected from a phylogenetically and geographically stratified sample of genera, translations of words re- veal cases where a particular language uses a single polysemous word to express concepts represented by distinct words in another. We use the frequency of polysemy linking two concepts as a measure of their semantic proximity, and represent the pattern of such linkages by a weighted network. This network is highly uneven and fragmented: certain concepts are far more prone to polysemy than others, and there emerge naturally interpretable clusters that are loosely connected to each other. Furthermore, the networks of different language groups exhibit consistent structures, largely independent of geography, environment, and literacy. We therefore conclude the conceptual structure connecting basic vocabulary studied is primarily due to universal features of human cognition and language use. A collaboration with Tanmoy bhattacharya, Eric Smith, Cris Moore, John F. Wilkins, William Croft, Logan Sutton, and Ian Maddieson.

  - the project page [link]: interactive webpage with linguistic dataset [link]
  - on the universal structure of human lexical semantics [link]
  - media coverage: [Phys.org], [Santa Fe Institute news], [Mathematical Institute news, University of Oxford], [ PNAS highlights], [QUARTZ video clip], [Nature], [과학동아], and [National Geography Blog].
  - [studying language evolution in the age of Big Data]