Learning from Neighbors about a Changing State

Agents learn about a changing state using private signals and past actions of neighbors in a network. We characterize equilibrium learning and social influence in this setting. We then examine when agents can aggregate information well, responding quickly to recent changes. A key sufficient condition for good aggregation is that each individual's neighbors have sufficiently different types of private information. In contrast, when signals are homogeneous, aggregation is suboptimal on any network. We also examine behavioral versions of the model, and show that achieving good aggregation requires a sophisticated understanding of correlations in neighbors' actions. The model provides a Bayesian foundation for a tractable learning dynamic in networks, closely related to the DeGroot model, and offers new tools for counterfactual and welfare analyses.Comment: minor revision tweaking exposition relative to v5 - which added new Section 3.2.2, new Theorem 2, new Section 7.1, many local revision

Rational points on twisted K3 surfaces and derived equivalences

Using a construction of Hassett--V\'arilly-Alvarado, we produce derived equivalent twisted K3 surfaces over $\mathbb{Q}$, $\mathbb{Q}_2$, and $\mathbb{R}$, where one has a rational point and the other does not. This answers negatively a question recently raised by Hassett and Tschinkel.Comment: To appear in the proceedings volume for the AIM conference "Brauer groups and obstruction problems: moduli spaces and arithmetic

Virus dynamics with behavioral responses

First author draf

Process modeling using stacked neural networks

Typically neural network modelers in chemical engineering focus on identifying and using a single hopefully optimal neural network model. Using a single optimal model implicitly assumes that one neural network model can extract all the information available in a given data set and that the other candidate models are redundant. In general, there is no assurance that any individual model has extracted all relevant information from the data set. In this work, the stacked neural network approach is introduced. Stacked neural networks (SNNs) allow multiple neural networks to be selected and used to model a given process. The idea is that improved predictions can be obtained using multiple networks, instead of simply selecting a single hopefully optimal network as is usually done. A methodology for stacking neural networks for plant process modeling has been developed. This method is inspired by the technique of stacked generalization proposed by Wolpert (1992). The feasibility of the stacked neural network approach is first demonstrated using linear combinations. A general technique known as the information theoretic stacking algorithm is then developed and evaluated. The ITS algorithm is able to identify and combine informative neural network models regardless of how their outputs related to the process output. The power of the ITS algorithm is demonstrated through three examples including application to a dynamic process modeling problem. Results obtained demonstrate that the SNNs developed using the ITS algorithm can achieve highly improved performance as compared to selecting and using a single hopefully optimal network or using SNNs based on a linear combination of neural networks

Virus Dynamics with Behavioral Responses

Motivated by epidemics such as COVID-19, we study the spread of a contagious disease when behavior responds to the disease's prevalence. We extend the SIR epidemiological model to include endogenous meeting rates. Individuals benefit from economic activity, but activity involves interactions with potentially infected individuals. The main focus is a theoretical analysis of contagion dynamics and behavioral responses to changes in risk. We obtain a simple condition for when public-health interventions or changes in disease prevalence will paradoxically increase infection rates due to risk compensation. Behavioral responses are most likely to undermine public-health interventions near the peak of severe diseases