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

Organizational Structure at different scales

This project is funded by the NSF [link] with Chris Kempes, Geoffrey West, and Sidney Redner, Vicky Chuqiao Yang at Santa Fe Institute.

Complex organizational structures range from the very small (such as cells) to the very large (such as a system of government), and maintaining these structures requires a lot of energy and resources. Consider, for example, the part of the US legal system that is devoted to handling lawsuits and resolving conflicts. The structure of the legal system includes the law itself, the attorneys, judges, and all the other people involved in bringing a lawsuit forward and ensuring that it is resolved. As a result, US companies spend a lot of funds on litigation alone. In US colleges, administrative spending is comparable with instructional spending and has been cited as a key factor in the increasing tuition of US universities. The continuing growth of these kinds of costs is a major challenge, but they aren't understood very well. When these costs are studied, they are often viewed as hidden or unintended expenses that are unique to the systems in which they are found. The research supported by this grant develops a unified theoretical framework for studying regulatory mechanisms across different kinds of systems, from single cells to entire societies. The research improves society by suggesting ways to make the organization of institutions, such as companies, universities and governments, more efficient.

Regulatory functions and mechanisms are a necessary, essential, and ubiquitous feature across all biological, social, and mechanical systems. Bacteria have regulatory genes, companies have managers, and car engines have engine control units. Indeed, the challenge for all complex adaptive systems that aim to survive in multi-faceted and competitive environments is to optimally manage internal functions and interactions. The presence of regulatory mechanisms in complex systems is therefore a universal rule of life, and network structures emerge under the rule of life. This grant develops a unified science of regulatory functions and their associated emergent structures to answer questions such as: What causes an increase in regulatory costs? Can we predict the amount of regulatory costs an organism or organization needs, based on its size, function, and complexity? Is it necessary to grow the administrative or regulatory functions of a system to ensure the continued functioning of the system, or is it an unnecessary burden? This research develops scientific measurements to determine the appropriate or optimal size and network structure of bureaucracy for a system to perform its tasks. The research takes place in two steps: 1) gathering and organizing datasets that span biological and social systems; and 2) using these datasets to develop a theory for regulatory structures across a wide range of systems. The theory will start from a mathematical framework that describes cost as a function of the size and complexity of a system and integrate this theory with new results and models of the functional diversity of organizations and their structures.

1. 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.

  - Media Coverage: [the Economist] [MIT Technology Review] [Nature Physics], [SpringerOpen blog]
  - combinatorial inventions [link]
  - innovation as an outcome of collective behaviors [link].
  - novelty profile and invention's future impact [link]
  - [identify the technological pathway]
  - [quantifying the stream of technological innovation]
  - automating the labor force of U.S. metropolitan areas: which skills secure your job? [link], [COVER]
  - toward understanding the impact of artificial intelligence on labor PNAS 116 (14) 6531-6539 [link] [Forbes].

2. 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.

  - Media Coverage:
    [Science of Cities], [Forbes][WalletHub][The Economist] [Scientific American]
    [Phys.org], [News and Tribune] [Physics.org] [ArsTechnica]
    [MIT Technology Review][New Scientist] [ Kellogg Insight ]
  - scaling and universality in urban economic diversification [link]
  - universal trajectory of urban economy [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]
  - urban morphology, and centrality [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? [link], [COVER] [data visualization]
  - toward understanding the impact of artificial intelligence on labor PNAS 116 (14) 6531-6539 [link] [Forbes].

3. 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. .

  - 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].
  - analysing Physics text books (Griffith, Hewitt, and Knight), and Oxford dictionary to see how concepts (terminologies) appear in reading stream [link].
  - analysing Mongolians political cognition change [link]
  - studying language evolution in the age of Big Data [link]