Maria R. D'Orsogna

A STATISTICAL MODEL OF CRIMINAL BEHAVIOR

Motivated by empirical observations of spatio-temporal clusters of crime across a wide variety of urban settings, we present a model to study the emergence, dynamics, and steady-state properties of crime hotspots. We focus on a two-dimensional lattice model for residential burglary, where each site is characterized by a dynamic attractiveness variable, and where each criminal is represented as a random walker. The dynamics of criminals and of the attractiveness field are coupled to each other via specific biasing and feedback mechanisms. Depending on parameter choices, we observe and describe several regimes of aggregation, including hotspots of high criminal activity. On the basis of the discrete system, we also derive a continuum model; the two are in good quantitative agreement for large system sizes. By means of a linear stability analysis we are able to determine the parameter values that will lead to the creation of stable hotspots. We discuss our model and results in the context of established crim...

Multi-Vehicle Flocking: Scalability of Cooperative Control Algorithms using Pairwise Potentials

In this paper, we study cooperative control algorithms using pairwise interactions, for the purpose of controlling flocks of unmanned vehicles. An important issue is the role the potential plays in the stability and possible collapse of the group as agent number increases. We model a set of interacting Dubins vehicles with fixed turning angle and speed. We perform simulations for a large number of agents and we show experimental realizations of the model on a testbed with a small number of vehicles. In both cases, critical thresholds exist between coherent, stable, and scalable flocking and dispersed or collapsing motion of the group.

Fluctuation-facilitated charge migration along DNA.

We propose a model Hamiltonian for charge transfer along the DNA double helix with temperature-driven fluctuations in the base pair positions acting as the rate limiting factor for charge transfer between neighboring base pairs. We compare the predictions of the model with the recent work of Barton and Zewail on the unusual two-stage charge transfer of DNA.

Statistical physics of crime: a review.

Containing the spread of crime in urban societies remains a major challenge. Empirical evidence suggests that, if left unchecked, crimes may be recurrent and proliferate. On the other hand, eradicating a culture of crime may be difficult, especially under extreme social circumstances that impair the creation of a shared sense of social responsibility. Although our understanding of the mechanisms that drive the emergence and diffusion of crime is still incomplete, recent research highlights applied mathematics and methods of statistical physics as valuable theoretical resources that may help us better understand criminal activity. We review different approaches aimed at modeling and improving our understanding of crime, focusing on the nucleation of crime hotspots using partial differential equations, self-exciting point process and agent-based modeling, adversarial evolutionary games, and the network science behind the formation of gangs and large-scale organized crime. We emphasize that statistical physics of crime can relevantly inform the design of successful crime prevention strategies, as well as improve the accuracy of expectations about how different policing interventions should impact malicious human activity that deviates from social norms. We also outline possible directions for future research, related to the effects of social and coevolving networks and to the hierarchical growth of criminal structures due to self-organization.

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 aggregations structure and reveal transiently traveling clumps of gregarious insects. Our predictions of aggregation and mass gregarization suggest several possible future biological experiments.

First passage times in homogeneous nucleation and self-assembly

Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present a thorough analysis of the general problem of stochastic self-assembly of a fixed number of identical particles in a finite volume. We derive the backward Kolmogorov equation (BKE) for the cluster probability distribution. From the BKE, we study the distribution of times it takes for a single maximal cluster to be completed, starting from any initial particle configuration. In the limits of slow and fast self-assembly, we develop analytical approaches to calculate the mean cluster formation time and to estimate the first assembly time distribution. We find, both analytically and numerically, that faster detachment can lead to a shorter mean time to first completion of a maximum-sized cluster. This unexpected effect arises from a redistribution of trajectory weights such that upon increasing the detachment rate, paths that take a shorter time to complete a cluster become more likely.

Diffusion-Dependent Mechanisms of Receptor Engagement and Viral Entry

Enveloped viruses attach to host cells by binding to receptors on the cell surface. For many viruses, entry occurs via membrane fusion after a sufficient number of receptors have engaged ligand proteins on the virion. Under conditions where the cell surface receptor densities are low, recruitment of receptors may be limited by diffusion rather than by receptor-ligand interactions. We present a receptor-binding model that includes the effects of receptor availability at the viral binding site. The receptor binding and unbinding kinetics are coupled to receptor diffusion across the cell membrane. We find numerical solutions to our model and analyze the viral entry probabilities and the mean times to entry as functions of receptor concentration, receptor diffusivity, receptor binding stoichiometry, receptor detachment rates, and virus degradation/detachment rates. We also show how entry probabilities and times differ when receptors bind randomly or sequentially to the binding sites on the viral glycoprotein spikes. Our results provide general insight into the biophysical transport mechanisms that may arise in viral attachment and entry.

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.

Interparticle gap distributions on one-dimensional lattices

We analyse the successive binding of two species of particles on a one-dimensional discrete lattice, where the second variety is deposited only after complete adsorption of the first. We consider the two extreme cases of a perfectly irreversible initial deposition, with non-sliding particles, and that of a fully equilibrated one. For the latter we construct the exact gap distribution from the Tonks gas partition function. This distribution is contrasted with that obtained from the random sequential adsorption process. We discuss implications for the kinetics of adsorption of the second species, as well as experimental relevance of our results.

Recidivism and Rehabilitation of Criminal Offenders: A Carrot and Stick Evolutionary Game

Motivated by recent efforts by the criminal justice system to treat and rehabilitate nonviolent offenders rather than focusing solely on their punishment, we introduce an evolutionary game theoretic model to study the effects of “carrot and stick” intervention programs on criminal recidivism. We use stochastic simulations to study the evolution of a population where individuals may commit crimes depending on their past history, surrounding environment and, in the case of recidivists, on any counseling, educational or training programs available to them after being punished for their previous crimes. These sociological factors are embodied by effective parameters that determine the decision making probabilities. Players may decide to permanently reform or continue engaging in criminal activity, eventually reaching a state where they are considered incorrigible. Depending on parameter choices, the outcome of the game is a society with a majority of virtuous, rehabilitated citizens or incorrigibles. Since total resources may be limited, we constrain the combined punishment and rehabilitation costs per crime to be fixed, so that increasing one effort will necessarily decrease the other. We find that the most successful strategy in reducing crime is to optimally allocate resources so that after being punished, criminals experience impactful intervention programs, especially during the first stages of their return to society. Excessively harsh or lenient punishments are less effective. We also develop a system of coupled ordinary differential equations with memory effects to give a qualitative description of our simulated societal dynamics. We discuss our findings and sociological implications.