Complex Systems Summer School 2012

Cities are the main sources of innovation and hence of novel solutions to technological, social and biological issues, from climate change to growing populations. Statistically, the more people in a city, the more innovation in the city, as measured by patent production or by economic output (Bettencourt et al., PNAS 104(17) 2007). The conjectured mechanism for these increasing returns is that in more dense cities, people interact with more people—and more diverse people in terms of occupations and skills—and these interactions across boundaries leads to innovation and invention. Here we determine how diversity of occupations and their integration in US cities correlates with measures of innovation, measured by patents and gross metropolitan product (GMP). We find that occupation diversity does not significantly explain whether a city under- or over-innovates for a city of its size. A measure of occupational integration is proposed, but the correlation is also found to be weak with cities’ success. This suggests that more fine-scale data on interactions among people of different disciplines—or the culture, laws and peculiarities of cities—is required to better assess the under- or over-performance of innovation of cities.LINK

Antiviral resistance in influenza is rampant and has the possibility of causing major morbidity and mortality. Previous models have identified treatment regimes to minimize total infections and keep resistance low. However, the bulk of these studies have ignored stochasticity and heterogeneous contact structures. Here we develop a network model of influenza transmission with treatment and resistance, and present both standard mean-field approximations as well as simulated dynamics. We find differences in the final epidemic sizes for identical transmission parameters (bistability) leading to different optimal treatment timing depending on the number initially infected. We also find, contrary to previous results, that treatment targeted by number of contacts per individual (node degree) gives rise to more resistance at lower levels of treatment than non-targeted treatment. Finally we highlight important differences between the two methods of analysis (mean-field versus stochastic simulations), and show where traditional mean-field approximations fail. Our results have important implications not only for the timing and distribution of influenza chemotherapy, but also for mathematical epidemiological modeling in general. Antiviral resistance in influenza may carry large consequences for pandemic mitigation efforts, and models ignoring contact heterogeneity and stochasticity may provide misleading policy recommendations.LINK

While disease propagation is a main focus of network science, its coevolution with treatment has yet to be studied in this framework. We present a mean-field and stochastic analysis of an epidemic model with antiviral administration and resistance development. We show how this model maps to a coevolutive competition between site and bond percolation featuring hysteresis and both second- and first-order phase transitions. The latter, whose existence on networks is a long-standing question, imply that a microscopic change in infection rate can lead to macroscopic jumps in expected epidemic size.LINK

The large-scale use of antivirals during influenza pandemics poses a significant selection pressure for drug-resistant pathogens to emerge and spread in a population. This requires treatment strategies to minimize total infections as well as the emergence of resistance. Here we propose a mathematical model in which individuals infected with wild-type influenza, if treated, can develop de novo resistance and further spread the resistant pathogen. Our main purpose is to explore the impact of two important factors influencing treatment effectiveness: i) the relative transmissibility of the drug-resistant strain to wild-type, and ii) the frequency of de novo resistance. For the endemic scenario, we find a condition between these two parameters that indicates whether treatment regimes will be most beneficial at intermediate or more extreme values (e.g., the fraction of infected that are treated). Moreover, we present analytical expressions for effective treatment regimes and provide evidence of its applicability across a range of modeling scenarios: endemic behavior with deterministic homogeneous mixing, and single-epidemic behavior with deterministic homogeneous mixing and stochastic heterogeneous mixing. Therefore, our results provide insights for the control of drug-resistance in influenza across time scales.LINK

The purpose of this paper is to explore the evolutionary dynamics of literary genre: the development of the 19th Century British novel is used as a motivating case study. The author constructs an agent-based model in NetLogo consisting of two interacting levels: (I) A genetic algorithm in which cultural forms (e.g., works of literature, pieces of music, etc.) are represented as binary feature strings. Cultural forms evolve across generations via asexual and sexual reproduction. Genres are represented as hierarchical clusters of similar feature strings. (II) Cultural forms are subjected to the selection pressure of consumer preferences. Preferences are heterogeneous: each consumer’s tastes are represented by an ideal point in feature space. Preferences are configured in landscapes that vary in their levels of structure, entropy, and diversity. Landscapes are dynamic and may change due to (1) exogenous demographic shifts (e.g., population growth, generational turnover) or (2) endogenous feedback effects (e.g., preference co-evolution, conformity / anti-conformity effects).LINK

Models of complex networks have various properties which can be measured in real networks (WWW, social networks, biological networks), e.g. degree distribution, modularity, hierarchy, assortativity etc. Determining how robust these models are could have important implications for real-world network stability, but this direction of research has seen only some progress. For example, it was shown that scale-free networks are much more topologically robust to random errors than random networks, but more susceptible to targeted attacks. Various characteristics of complex networks might influence their robustness to failure. It is our goal to investigate how properties like degree distribution and clustering coefficient in growing network models effect how robust those networks are to failures. We generated continuous topological space of growing network models with parameters to tune degree distribution (from exponential to scale-free) and clustering (from none to high). Then we attacked the network by removing vertices chosen both randomly and selectively targeting highly connected vertices (hubs). To determine how robust these networks to random errors and targeted attacks, we investigated the size and diameter of networks’ giant connected component after attacks. We also investigated correlations between degree and clustering and the assortativity of the network under repeated errors and regrowth. We found that clustering tends to make our model more susceptible to both targeted attacks and random errors. We also found that under repeated small random errors and regrowth, correlations between node degree and clustering coefficients are reduced, and the disassortativity of the network becomes reduced.LINK

Political prediction markets such as INTRADE, in which people trade stocks based on their belief about the outcome of the election or political event, offer a unique opportunity to use market behavior to predict the outcome of political events. This paper provides a two-fold contribution to the literature. First, we analyze 457 political prediction markets contracts in terms of the accuracy of their predictions at various time intervals and high-level categorizations. Second, we attempt to forecast the outcome of political prediction markets using a standard feedforward/backpropagation neural network trained on the time history of contract prices. We find that we can out perform the market predictions by between 1% - 4% percent during times earlier than half-way to contract expiry. This suggests the market is not the most efficient aggregation of the likelihood of a future political event at these short times. Sanith Wijesinghe contributed substantially to this project.LINK

The field of autonomous robotics endeavors to engineer systems capable of transforming sensory inputs into motors outputs toward the achievement of goals. Ideally, the system would form novel motor behaviors appropriate to its environment of operation while concurrently learning the conditions of satisfaction for goals set by the roboticist. Unfortunately, the space of sensory inputs and motor outputs is often vast, posing a ghastly combinatorial selection problem, and goals are often overly restrictive or vague. For example, imagine a roboticist builds a system with visual, tactile, and proprioceptive sensors as well as sufficient actuators to control is limbs. Perhaps she wishes for it to approach red objects within the environment. Does the robot know how to produce coordinated movements? Does it know how to approach an object? For that matter, how does it know what an ”object” is? and what is meant by ”red”? In this paper we focus upon the use of chaos control as a means for generating coordinated movements in robotic systems. In particular, we examine the work of Steingrube et al. 2010, wherein chaos control of a single neural control circuit was used to produce multiple motor outputs conditional upon a variety of sensory inputs. We simulate some of their results and critique their autonomous system according to the amount of information programmed into it a priori. We then show how a recent advance in computer science, self-localizing and mapping (SLAM)systems, may vastly increase the memory systems of autonomous robots in general, and those utilizing chaos control in particular. We propose a generalization of SLAM that, when coupled with principles from optimal control theory, could greatly expand the functionality and independence of autonomous systems. We conclude by articulating some outstanding questions in the field while arguing that engineering systems with the ability to answer the kinds of questions enumerated above is as much a phenomenological and conceptual problem as it is a technical one.LINK

Many open problems in biology, as in the physical sciences, display nonlinear and ‘chaotic’ dynamics, which, to the extent possible, cannot be reasonably understood. Moreover, mathematical models which aim to predict/estimate unknown aspects of a biological system cannot provide more information about the set of biologically meaningful (e.g., ‘hidden’) states of the system than could be understood by the designer of the model ab initio. Here, the case is made for the utilization of such models to shift from a ‘predictive’ to a ‘questioning’ nature, and a simple natural-logarithm variation of the logistic polynomial map is presented that can invoke questions about protein trafficking in eukaryotic cells.LINK