The power of any kind of network approach lies in the ability to simplify a complex system so that one can better understand its function as a whole. Sometimes it is beneficial, however, to include more information than in a simple graph of only nodes and links. Adding information about times of interactions can make predictions and mechanistic understanding more accurate. The drawback, however, is that there are not so many methods available, partly because temporal networks is a relatively young field, partly because it is more difficult to develop such methods compared to for static networks. In this colloquium, we review the methods to analyze and model temporal networks and processes taking place on them, focusing mainly on the last three years. This includes the spreading of infectious disease, opinions, rumors, in social networks; information packets in computer networks; various types of signaling in biology, and more. We also discuss future directions.

/pdf/modern-temporal-network-theory-a-colloquium-2artviu6zb.pdf

Modern temporal network theory: a colloquium

The power of any kind of network approach lies in the ability to simplify a complex system so that one can better understand its function as a whole. Sometimes it is beneficial, however, to include more information than in a simple graph of only nodes and links. Adding information about times of interactions can make predictions and mechanistic understanding more accurate. The drawback, however, is that there are not so many methods available, partly because temporal networks is a relatively young field, partly because it more difficult to develop such methods compared to for static networks. In this colloquium, we review the methods to analyze and model temporal networks and processes taking place on them, focusing mainly on the last three years. This includes the spreading of infectious disease, opinions, rumors, in social networks; information packets in computer networks; various types of signaling in biology, and more. We also discuss future directions.

Modern temporal network theory: A colloquium

The coronavirus disease 2019 (COVID-19) pandemic has placed epidemic modeling at the forefront of worldwide public policy making. Nonetheless, modeling and forecasting the spread of COVID-19 remains a challenge. Here, we detail three regional-scale models for forecasting and assessing the course of the pandemic. This work demonstrates the utility of parsimonious models for early-time data and provides an accessible framework for generating policy-relevant insights into its course. We show how these models can be connected to each other and to time series data for a particular region. Capable of measuring and forecasting the impacts of social distancing, these models highlight the dangers of relaxing nonpharmaceutical public health interventions in the absence of a vaccine or antiviral therapies.

/pdf/the-challenges-of-modeling-and-forecasting-the-spread-of-3pp2vhrpx7.pdf

The challenges of modeling and forecasting the spread of COVID-19.

https://flore.unifi.it/bitstream/2158/1087565/1/2015%20PhLifeRev.pdf

Statistical physics of crime: a review.

Information diffusion in online social networks is affected by the underlying network topology, but it also has the power to change it. Online users are constantly creating new links when exposed to new information sources, and in turn these links are alternating the way information spreads. However, these two highly intertwined stochastic processes, information diffusion and network evolution, have been predominantly studied separately, ignoring their co-evolutionary dynamics

We propose a temporal point process model, Coevolve, for such joint dynamics, allowing the intensity of one process to be modulated by that of the other. This model allows us to efficiently simulate interleaved diffusion and network events, and generate traces obeying common diffusion and network patterns observed in real-world networks such as Twitter. Furthermore, we also develop a convex optimization framework to learn the parameters of the model from historical diffusion and network evolution traces. We experimented with both synthetic data and data gathered from Twitter, and show that our model provides a good fit to the data as well as more accurate predictions than alternatives.

/pdf/coevolve-a-joint-point-process-model-for-information-176tmer3is.pdf

COEVOLVE: a joint point process model for information diffusion and network evolution

Electronic communications, as well as other categories of interactions within social networks, exhibit bursts of activity localised in time We adopt a self-exciting Hawkes process model for this behaviour First we investigate parameter estimation of such processes and find that, in the parameter regime we encounter, the choice of triggering function is not as important as getting the correct parameters once a choice is made Then we present a relaxed maximum likelihood method for filling in missing data in records of communications in social networks Our optimisation algorithm adapts a recent curvilinear search method to handle inequality constraints and a non-vanishing derivative Finally we demonstrate the method using a data set composed of email records from a social network based at the United States Military Academy The method performs differently on this data and data from simulations, but the performance degrades only slightly as more information is removed The ability to fill in large blocks of missing social network data has implications for security, surveillance, and privacy

/pdf/point-process-models-of-social-network-interactions-4vj7q0wfnk.pdf

Point-process models of social network interactions: Parameter estimation and missing data recovery

Hotspots of crime localized in space and time are well documented. Previous mathematical models of urban crime have exhibited these hotspots but considered a static or otherwise suboptimal police response to them. We introduce a program of police response to hotspots of crime in which the police adapt dynamically to changing crime patterns. In particular, they choose their deployment to solve an optimal control problem at every time. This gives rise to a free boundary problem for the police deployment's spatial support. We present an efficient algorithm for solving this problem numerically and show that police presence can prompt surprising interactions among adjacent hotspots.

/pdf/cops-on-the-dots-in-a-mathematical-model-of-urban-crime-and-39osr03wda.pdf

Joseph R. Zipkin

Papers

Point-process models of social network interactions: Parameter estimation and missing data recovery

Cops on the dots in a mathematical model of urban crime and police response