Some results on a class of functional optimization problems

We first describe a general class of optimization problems that describe many natu- ral, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances of these problems in statistical physics, facility allocation, and machine learning. A dynamic description and statement of a partial inverse problem follow. When attempting to optimize the state of a system governed by the generalized equipartitioning princi- ple, it is vital to understand the nature of the governing probability distribution. We show that optimiziation for the incorrect probability distribution can have catas- trophic results, e.g., infinite expected cost, and describe a method for continuous Bayesian update of the posterior predictive distribution when it is stationary. We also introduce and prove convergence properties of a time-dependent nonparametric kernel density estimate (KDE) for use in predicting distributions over paths. Finally, we extend the theory to the case of networks, in which an event probability density is defined over nodes and edges and a system resource is to be partitioning among the nodes and edges as well. We close by giving an example of the theory’s application by considering a model of risk propagation on a power grid

Essays on modeling and analysis of dynamic sociotechnical systems

A sociotechnical system is a collection of humans and algorithms that interact under the partial supervision of a decentralized controller. These systems often display in- tricate dynamics and can be characterized by their unique emergent behavior. In this work, we describe, analyze, and model aspects of three distinct classes of sociotech- nical systems: financial markets, social media platforms, and elections. Though our work is diverse in subject matter content, it is unified though the study of evolution- and adaptation-driven change in social systems and the development of methods used to infer this change. We first analyze evolutionary financial market microstructure dynamics in the context of an agent-based model (ABM). The ABM’s matching engine implements a frequent batch auction, a recently-developed type of price-discovery mechanism. We subject simple agents to evolutionary pressure using a variety of selection mech- anisms, demonstrating that quantile-based selection mechanisms are associated with lower market-wide volatility. We then evolve deep neural networks in the ABM and demonstrate that elite individuals are profitable in backtesting on real foreign ex- change data, even though their fitness had never been evaluated on any real financial data during evolution. We then turn to the extraction of multi-timescale functional signals from large panels of timeseries generated by sociotechnical systems. We introduce the discrete shocklet transform (DST) and associated similarity search algorithm, the shocklet transform and ranking (STAR) algorithm, to accomplish this task. We empirically demonstrate the STAR algorithm’s invariance to quantitative functional parameteri- zation and provide use case examples. The STAR algorithm compares favorably with Twitter’s anomaly detection algorithm on a feature extraction task. We close by using STAR to automatically construct a narrative timeline of societally-significant events using a panel of Twitter word usage timeseries. Finally, we model strategic interactions between the foreign intelligence service (Red team) of a country that is attempting to interfere with an election occurring in another country, and the domestic intelligence service of the country in which the election is taking place (Blue team). We derive subgame-perfect Nash equilibrium strategies for both Red and Blue and demonstrate the emergence of arms race inter- ference dynamics when either player has “all-or-nothing” attitudes about the result of the interference episode. We then confront our model with data from the 2016 U.S. presidential election contest, in which Russian military intelligence interfered. We demonstrate that our model captures the qualitative dynamics of this interference for most of the time under stud

Noncooperative dynamics in election interference

Foreign power interference in domestic elections is an existential threat to societies. Manifested through myriad methods from war to words, such interference is a timely example of strategic interaction between economic and political agents. We model this interaction between rational game players as a continuous-time differential game, constructing an analytical model of this competition with a variety of payoff structures. All-or-nothing attitudes by only one player regarding the outcome of the game lead to an arms race in which both countries spend increasing amounts on interference and counterinterference operations. We then confront our model with data pertaining to the Russian interference in the 2016 United States presidential election contest. We introduce and estimate a Bayesian structural time-series model of election polls and social media posts by Russian Twitter troll accounts. Our analytical model, while purposefully abstract and simple, adequately captures many temporal characteristics of the election and social media activity. We close with a discussion of our model\u27s shortcomings and suggestions for future research

Continuum rich-get-richer processes: Mean field analysis with an application to firm size

Classical rich-get-richer models have found much success in being able to broadly reproduce the statistics and dynamics of diverse real complex systems. These rich-get-richer models are based on classical urn models and unfold step by step in discrete time. Here, we consider a natural variation acting on a temporal continuum in the form of a partial differential equation (PDE). We first show that the continuum version of Simon\u27s canonical preferential attachment model exhibits an identical size distribution. In relaxing Simon\u27s assumption of a linear growth mechanism, we consider the case of an arbitrary growth kernel and find the general solution to the resultant PDE. We then extend the PDE to multiple spatial dimensions, again determining the general solution. We then relax the zero-diffusion assumption and find an envelope of solutions to the general model in the presence of small fluctuations. Finally, we apply the model to size and wealth distributions of firms. We obtain power-law scaling for both to be concordant with simulations as well as observational data, providing a parsimonious theoretical explanation for these phenomena

The sociospatial factors of death: Analyzing effects of geospatially-distributed variables in a Bayesian mortality model for Hong Kong

Human mortality is in part a function of multiple socioeconomic factors that differ both spatially and temporally. Adjusting for other covariates, the human lifespan is positively associated with household wealth. However, the extent to which mortality in a geographical region is a function of socioeconomic factors in both that region and its neighbors is unclear. There is also little information on the temporal components of this relationship. Using the districts of Hong Kong over multiple census years as a case study, we demonstrate that there are differences in how wealth indicator variables are associated with longevity in (a) areas that are affluent but neighbored by socially deprived districts versus (b) wealthy areas surrounded by similarly wealthy districts. We also show that the inclusion of spatially-distributed variables reduces uncertainty in mortality rate predictions in each census year when compared with a baseline model. Our results suggest that geographic mortality models should incorporate nonlocal information (e.g., spatial neighbors) to lower the variance of their mortality estimates, and point to a more in-depth analysis of sociospatial spillover effects on mortality rates.Comment: 26 pages (15 main, 11 appendix), 22 figures (6 main, 11 appendix), 2 table

The shocklet transform: a decomposition method for the identification of local, mechanism-driven dynamics in sociotechnical time series

We introduce a qualitative, shape-based, timescale-independent time-domain transform used to extract local dynamics from sociotechnical time series—termed the Discrete Shocklet Transform (DST)—and an associated similarity search routine, the Shocklet Transform And Ranking (STAR) algorithm, that indicates time windows during which panels of time series display qualitatively-similar anomalous behavior. After distinguishing our algorithms from other methods used in anomaly detection and time series similarity search, such as the matrix profile, seasonal-hybrid ESD, and discrete wavelet transform-based procedures, we demonstrate the DST’s ability to identify mechanism-driven dynamics at a wide range of timescales and its relative insensitivity to functional parameterization. As an application, we analyze a sociotechnical data source (usage frequencies for a subset of words on Twitter) and highlight our algorithms’ utility by using them to extract both a typology of mechanistic local dynamics and a data-driven narrative of socially-important events as perceived by English-language Twitter