Mathematics of Planet Earth

Workshop Announcement

In 1900 only 13% of the world’s population lived in cities but by 2050 that number will have risen to 70%. Rapidly growing urban environments present new and evolving challenges: growing needs for energy and water, impacts on greenhouse gases, public health, safety, and security. As city expansion continues apace, mathematical scientists can play a key role in shaping sustainable living environments.

The Role of Data in “Smart Cities” points out: “With recent advances in technology, we can infuse our existing infrastructures with new intelligence,…digitizing and connecting… [to] sense, analyze and integrate data, and respond intelligently to the needs of their jurisdictions. In short, we can revitalize them so they can become smarter and more efficient.” The amount of data available to help us run our cities better is increasing dramatically, and we will investigate ways to use data to make smarter, more livable cities. More and more, we are in need of modern “smart” technologies that use data to understand the patterns driving human behavior, causes of the state of the environment, and ways to optimize our choices. For instance, we will investigate smart systems to reduce congestion and pollution through traffic prediction and optimization, with real-time decision support, using examples from Singapore, New Jersey, and London, and innovative electric vehicle sharing systems using the example of Milan. We will also explore the use of modern algorithms for large data sets to design aids to health care allocation in emergency situations. Many cities (e.g., Chicago, Dublin, Albuquerque), have developed sophisticated ways of sharing information across agencies that keep citizens informed and provide municipal services more efficiently.

Among the problems we will investigate are: ways to provide information to citizens concerning services (e.g., info-mobility terminals); real-time rerouting of passengers on commuter trains and buses; and use of GIS to synthesize information. We will explore tools of operations research, data mining, social media, recommender systems, and clustering to help cities manage traffic and emergency services more efficiently, e.g. through merging heterogeneous information sources about traffic; models of markets of mobility credits for diversified mobility services (including bike sharing, car pooling, dial-a-ride, etc.); and dynamically reallocating mobility resources when there are traffic disruptions. Wireless sensor networks and sensor signal processing can aid in creating sustainable human environments (see e.g., http://smarten-itn/eu). One of the mathematical challenges is to understand how to handle “weak signals,” signals of low intensity, but containing critical information. Other challenges include designing sensor configurations so as to maximize user utility and design of real-time control systems.

Anthropogenic Biomes: A city can be viewed as a system of systems. Considering cities to be like complex, interconnected ecosystems can assist us in developing models for the interaction of humans and their environment. This idea is not new. In the 1970s Dantzig and Saaty developed the concept of an idealized future city with 500,000 inhabitants in an urban environment with five 100,000-person skyscrapers surrounded by green space. This concept gave rise to a wide variety of mathematical problems ranging from management of vertical traffic to the physics of delivering water to the top floors. A broader modern rendering of this concept is based on the ecological concept of a “biome” or ecosystem. Cities are an “anthropogenic biome” in which human intervention with natural ecosystems is large and significant. Sustainability of urban environments needs to take into account limits to growth; fairness in using and distributing resources; and environmental constraints. Designing “sustainable biomes” raises challenges that include: monitoring networks and early warning systems (for natural and others hazards); incenting best practices by users, consumers, and producers; improving paradigms for inclusion and ownership (of natural resources). Networks are a core feature of the human environment, from physical networks (electric grid, transportation systems) to social networks and supply chains. We need to add to models aimed at optimizing network usage models features to make them more sustainable, which is critical to designing robust, resilient, and sustainable biomes.

Security: Cities of the future need to be safe places, and mathematical perspectives can help. For example, we will explore the use of: algorithms for large data sets to gain understanding of crime patterns and aid in deployment of police forces; discrete event simulation to model evacuations from sport stadiums and other large gathering places; algorithms for inspection of people entering department stores, restaurants, or sporting events; mathematical models for improved access to healthcare.; and mathematical models showing the effect of security initiatives (traffic barriers, more police, video cameras, subway bag inspection) on economic activity. These questions raise challenges at the interface of data mining, economic modeling, decision analysis, and spatial statistics, and require new concepts in combinatorial optimization, models of sequential inspection processes, “layered defense”, and new clustering algorithms involving notions of scan statistics.