Growth and Containment of a Hierarchical Criminal Network

We model the hierarchical evolution of an organized criminal network via antagonistic recruitment and pursuit processes. Within the recruitment phase, a criminal kingpin enlists new members into the network, who in turn seek out other affiliates. New recruits are linked to established criminals according to a probability distribution that depends on the current network structure. At the same time, law enforcement agents attempt to dismantle the growing organization using pursuit strategies that initiate on the lower level nodes and that unfold as self-avoiding random walks. The global details of the organization are unknown to law enforcement, who must explore the hierarchy node by node. We halt the pursuit when certain local criteria of the network are uncovered, encoding if and when an arrest is made; the criminal network is assumed to be eradicated if the kingpin is arrested. We first analyze recruitment and study the large scale properties of the growing network; later we add pursuit and use numerical simulations to study the eradication probability in the case of three pursuit strategies, the time to first eradication and related costs. Within the context of this model, we find that eradication becomes increasingly costly as the network increases in size and that the optimal way of arresting the kingpin is to intervene at the early stages of network formation. We discuss our results in the context of dark network disruption and their implications on possible law enforcement strategies.Comment: 16 pages, 11 Figures; New title; Updated figures with color scheme better suited for colorblind readers and for gray scale printin

Exact steady-state velocity of ratchets driven by random sequential adsorption

We solve the problem of discrete translocation of a polymer through a pore, driven by the irreversible, random sequential adsorption of particles on one side of the pore. Although the kinetics of the wall motion and the deposition are coupled, we find the exact steady-state distribution for the gap between the wall and the nearest deposited particle. This result enables us to construct the mean translocation velocity demonstrating that translocation is faster when the adsorbing particles are smaller. Monte-Carlo simulations also show that smaller particles gives less dispersion in the ratcheted motion. We also define and compare the relative efficiencies of ratcheting by deposition of particles with different sizes and we describe an associated "zone-refinement" process.Comment: 11 pages, 4 figures New asymptotic result for low chaperone density added. Exact translocation velocity is proportional to (chaperone density)^(1/3

Criminal Defectors Lead to the Emergence of Cooperation in an Experimental, Adversarial Game

While the evolution of cooperation has been widely studied, little attention has been devoted to adversarial settings wherein one actor can directly harm another. Recent theoretical work addresses this issue, introducing an adversarial game in which the emergence of cooperation is heavily reliant on the presence of “Informants,” actors who defect at first-order by harming others, but who cooperate at second-order by punishing other defectors. We experimentally study this adversarial environment in the laboratory with human subjects to test whether Informants are indeed critical for the emergence of cooperation. We find in these experiments that, even more so than predicted by theory, Informants are crucial for the emergence and sustenance of a high cooperation state. A key lesson is that successfully reaching and maintaining a low defection society may require the cultivation of criminals who will also aid in the punishment of others

Continuum limit of self-driven particles with orientation interaction

We consider the discrete Couzin-Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools. In this article, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non conservative equation for the director of the mean velocity and is proved to be hyperbolic. The derivation is based on the introduction of a non-conventional concept of a collisional invariant of a collision operator

Impacts of California Proposition 47 on Crime in Santa Monica, CA

We examine crime patterns in Santa Monica, California before and after passage of Proposition 47, a 2014 initiative that reclassified some non-violent felonies to misdemeanors. We also study how the 2016 opening of four new light rail stations, and how more community-based policing starting in late 2018, impacted crime. A series of statistical analyses are performed on reclassified (larceny, fraud, possession of narcotics, forgery, receiving/possessing stolen property) and non-reclassified crimes by probing publicly available databases from 2006 to 2019. We compare data before and after passage of Proposition 47, city-wide and within eight neighborhoods. Similar analyses are conducted within a 450 meter radius of the new transit stations. Reports of monthly reclassified crimes increased city-wide by approximately 15% after enactment of Proposition 47, with a significant drop observed in late 2018. Downtown exhibited the largest overall surge. The reported incidence of larceny intensified throughout the city. Two new train stations, including Downtown, reported significant crime increases in their vicinity after service began. While the number of reported reclassified crimes increased after passage of Proposition 47, those not affected by the new law decreased or stayed constant, suggesting that Proposition 47 strongly impacted crime in Santa Monica. Reported crimes decreased in late 2018 concurrent with the adoption of new policing measures that enhanced outreach and patrolling. These findings may be relevant to law enforcement and policy-makers. Follow-up studies needed to confirm long-term trends may be affected by the COVID-19 pandemic that drastically changed societal conditions.Comment: 41 pages, 19 figure

Stochastic model of randomly end-linked polymer network micro-regions

Polymerization and formation of crosslinked polymer networks are important processes in manufacturing, materials fabrication, and in the case of hydrated polymer networks, synthesis of biomedical materials, drug delivery, and tissue engineering. While considerable research has been devoted to the modeling of polymer networks to determine averaged, mean-field, global properties, there are fewer studies that specifically examine the variance of the composition across "micro-regions" (composed of a large, but finite, number of polymer network strands) within the larger polymer network.Here, we mathematically model the stochastic formation of polymer networks comprised of linear homobifunctional network strands that undergo an end-linking gelation process. We introduce a master equation that describes the evolution of the probabilities of possible network micro-region configurations as a function of time and extent of reaction. We specifically focus on the dynamics of network formation and the statistical variability of the gel micro-regions, particularly at intermediate extents of reaction. We also consider possible annealing effects and study how cooperative binding between the two end-groups on a single network-strand affects network formation. Our results allow for a more detailed and thorough understanding of polymer network dynamics and variability of network properties.Comment: 16 pages, 9 figure

Locust Dynamics: Behavioral Phase Change and Swarming

Locusts exhibit two interconvertible behavioral phases, solitarious and gregarious. While solitarious individuals are repelled from other locusts, gregarious insects are attracted to conspecifics and can form large aggregations such as marching hopper bands. Numerous biological experiments at the individual level have shown how crowding biases conversion towards the gregarious form. To understand the formation of marching locust hopper bands, we study phase change at the collective level, and in a quantitative framework. Specifically, we construct a partial integrodifferential equation model incorporating the interplay between phase change and spatial movement at the individual level in order to predict the dynamics of hopper band formation at the population level. Stability analysis of our model reveals conditions for an outbreak, characterized by a large scale transition to the gregarious phase. A model reduction enables quantification of the temporal dynamics of each phase, of the proportion of the population that will eventually gregarize, and of the time scale for this to occur. Numerical simulations provide descriptions of the aggregation's structure and reveal transiently traveling clumps of gregarious insects. Our predictions of aggregation and mass gregarization suggest several possible future biological experiments.Comment: Main text plus figures and supporting information; to appear in PLOS Computational Biolog