Project+Milestone

Results: Thus far, my research has been forming around two spheres: ecology and urban growth. I am also looking at how mathematics can be used to describe relationships between humans and environment.

How do people think and define "cities"? How is that changing now?

Baltimore study: http://www.beslter.org/

Urban metabolism: http://en.wikipedia.org/wiki/Urban_metabolism

http://www.thenatureofcities.com/2013/09/27/building-cities-that-think-like-planets/

http://urbaneco.washington.edu/wp/ http://urbdp.be.washington.edu/people/faculty/departmental/profiles/alberti.html http://urbaneco.washington.edu/wp/team-2/marina-alberti/ http://urbaneco.washington.edu/wp/urban-resilience/

 Luis Bettencourt; The Kind of Problem a City Is 2013-03-00, Sfi Working Paper:. //The Kind of Problem a City Is // (n.d.): n. pag. //Sante Fe Institute //. Web.


 * "Abstract: ** The title of this essay is taken verbatim from the challenge posed by Jane Jacobs in her influential book the Death and Life of Great American Cities (1). My main objective is to answer Jane Jacob’s question with the benefit of over 50 years of research since its publication and especially from the perspective of new insights from the emerging science of cities as complex systems. I show that we have made significant progress over the last decade and that a science of cities, recognizable across the full spectrum of urban disciplines, from physics and biology to social psychology and sociology is starting to emerge. Here, I show that cities are not only complex adaptive systems, a point already clear for several traditions of urbanism, but demonstrate also that they are a particular and unique type of system, a new organizational invention that can combine and amplify the cognitive abilities of humans and generate open-­‐ended socioeconomic development. "

 Bettencourt, Luis M.A., Jose Lobo, Dirk Helbing, Christian Kuhnert, and Geoffrey B. West. "Growth, Innovation, Scaling, and the pace of Life in Cities." //Growth, Innovation, Scaling, and the pace of Life in Cities //. Proceedings of the National Academy of Sciences of the United States of America, n.d. Web. 02 Mar. 2015.

"Abstract: Humanity has just crossed a major landmark in its history with the majority of people now living in cities. Cities have long been known to be society's predominant engine of innovation and wealth creation, yet they are also its main source of crime, pollution, and disease. The inexorable trend toward urbanization worldwide presents an urgent challenge for developing a predictive, quantitative theory of urban organization and sustainable development. Here we present empirical evidence indicating that the processes relating urbanization to economic development and knowledge creation are very general, being shared by all cities belonging to the same urban system and sustained across different nations and times. Many diverse properties of cities from patent production and personal income to electrical cable length are shown to be power law functions of population size with scaling exponents, β, that fall into distinct universality classes. Quantities reflecting wealth creation and innovation have β ≈1.2 >1 (increasing returns), whereas those accounting for infrastructure display β ≈0.8 <1 (economies of scale). We predict that the pace of social life in the city increases with population size, in quantitative agreement with data, and we discuss how cities are similar to, and differ from, biological organisms, for which β<1. Finally, we explore possible consequences of these scaling relations by deriving growth equations, which quantify the dramatic difference between growth fueled by innovation versus that driven by economies of scale. This difference suggests that, as population grows, major innovation cycles must be generated at a continually accelerating rate to sustain growth and avoid stagnation or collapse." Ying, XU. //The Making of Mathematical Models for Ecological Cities //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;"> (2014): n. pag. Web. [|http://eds.a.ebscohost.com/eds/pdfviewer/pdfviewer?sid=4256d41c-f920-4665-8c29- 3386519cf8d4%40sessionmgr4001&vid=1&hid=4210] <span style="background-color: #ffffff; color: #333333; display: block; font-family: Arial,sans-serif; font-size: 14px; text-align: justify; vertical-align: baseline;">This article explains the mathematical inputs in creating an ecological model. Despite using Chinese cities as a model, this a perfect description of the modern way to formulate ecological models. Also it breaks down the function sets of a city and includes how to qualify them into largely three divisions: social, natural, and economic systems. Uses series.


 * "Abstract.** Ecological city, in a broad sense, is a new cultural notion based on mankind’s profound understanding of the relationship between human and nature, new-type social relationship in accord with ecological rules which coordinate society, economy and nature, and also a sustainable lifestyle. In a narrow sense, ecological city is a highly effective, harmonious and healthy environment where people gather. This passage will clarify the definition ecological city and comprehensively depict the systematic model and index system in current ecological cities. A new mathematical model, related theories and calculation as well as its significance are to be mentioned. "

<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">Shannon, C.E. //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">The Mathematical Theory of Communication //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;"> (1948): n. pag. //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">Cm.bell-labs.com //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">. Web. 01 Mar. 2015. []

This article from C.E. Shannon describes the mathematical process behind communication. This is probably the most off-topic article that I read, however it gives me further background into using mathematical functions to describe social relationships and activities.

<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">Bettencourt, L. M. A. "The Origins of Scaling in Cities." //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">Science //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;"> 340.6139 (2013): 1438-441. //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">Sante Fe Institute //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">. Web. 01 Mar. 2015.

"Cities are perhaps the ultimate expression of human sociality displaying at once humanity’s greatest achievements and some of its most difficult challenges. Despite the increasing importance of cities in human societies our ability to understand them scientifically, and manage them in practice, has remained unsatisfactorily limited. The greatest difficulties to any scientific approach to cities have resulted from their many interdependent facets, as social, economic, infrastructural and spatial complex systems, which exist in similar but changing forms over a huge range of scales. Here, I show how cities may evolve following a small set of basic principles that operate locally and can explain how cities change gradually from the bottom-up. As a result I obtain a theoretical framework that derives the general open-ended properties of cities through the optimization of a set of local conditions. This framework is used to predict, in a unified and quantitative way, the average social, spatial and infrastructural properties of cities as a set of scaling relations that apply to all urban systems, many of which have been observed in nations around the world. Finally, I compare and contrast the structure and dynamics of cities to those of other complex systems that share some analogous properties."

<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">Ancient Cities Grew Pretty Much like Modern Ones, Say Scientists." //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">The Christian Science Monitor //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">. The Christian Science Monitor, n.d. Web. 26 Feb. 2015. This Christian Science Monitor article is the first step in understanding growth of cities--their patterns, either physically or socially--and frames them in a historical context.

<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">Ortman, Scott G., Andrew H.F. Cabaniss, Jennie O. Sturm, and Luis M. A. Bettencourt. "The Pre-History of Urban Scaling." (n.d.): n. pag. //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">PLOS ONE: //<span style="background-color: #f2f2f2; font-family: 'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">. 12 Feb. 2014. Web. 01 Mar. 2015.

"Cities are increasingly the fundamental socio-economic units of human societies worldwide, but we still lack a unified characterization of urbanization that captures the social processes realized by cities across time and space. This is especially important for understanding the role of cities in the history of human civilization and for determining whether studies of ancient cities are relevant for contemporary science and policy. As a step in this direction, we develop a theory of settlement scaling in archaeology, deriving the relationship between population and settled area from a consideration of the interplay between social and infrastructural networks. We then test these models on settlement data from the Pre-Hispanic Basin of Mexico to show that this ancient settlement system displays spatial scaling properties analogous to those observed in modern cities. Our data derive from over 1,500 settlements occupied over two millennia and spanning four major cultural periods characterized by different levels of agricultural productivity, political centralization and market development. We show that, in agreement with theory, total settlement area increases with population size, on average, according to a scale invariant relation with an exponent in the range <span class="inline-formula" style="background-color: #ffffff; color: #333333; font-family: arial; vertical-align: middle;">. As a consequence, we are able to infer aggregate socio-economic properties of ancient societies from archaeological measures of settlement organization. Our findings, from an urban settlement system that evolved independently from its old-world counterparts, suggest that principles of settlement organization are very general and may apply to the entire range of human history." Abstract.