Martin B. Short's research while affiliated with Georgia Institute of Technology and other places

Publications (55)

Article
We develop a fully Bayesian tracking algorithm with the purpose of providing classification prediction results that are unbiased when applied uniformly to individuals with differing sensitive variable values, e.g., of different races, sexes, etc. Here, we consider bias in the form of group-level differences in false prediction rates between the dif...
Article
Full-text available
Dynamic estimation of the reproduction number of COVID-19 is important for assessing the impact of public health measures on virus transmission. State and local decisions about whether to relax or strengthen mitigation measures are being made in part based on whether the reproduction number, Rt , falls below the self-sustaining value of 1. Employin...
Article
Full-text available
Predicting the evolution of viral processes on networks is an important problem with applications arising in biology, the social sciences, and the study of the Internet. In existing works, mean-field analysis based upon degree distribution is used for the prediction of viral spreading across networks of different types. However, it has been shown t...
Preprint
Full-text available
We develop a fully Bayesian, logistic tracking algorithm with the purpose of providing classification results that are unbiased when applied uniformly to individuals with differing sensitive variable values. Here, we consider bias in the form of differences in false prediction rates between the different sensitive variable groups. Given that the me...
Preprint
We develop a fully Bayesian, logistic tracking algorithm with the purpose of providing classification results that are unbiased when applied uniformly to individuals with differing sensitive variable values. Here, we consider bias in the form of differences in false prediction rates between the different sensitive variable groups. Given that the me...
Article
Full-text available
Significance 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 remain a challenge. Here, we present and detail three regional-scale models for forecasting and assessing the course of the pandemic. This work is...
Preprint
Full-text available
Dynamic estimation of the reproduction number of COVID-19 is important for assessing the impact of public health measures on virus transmission. State and local decisions about whether to relax or strengthen mitigation measures are being made in part based on whether the reproduction number, R, falls below the self-sustaining value of 1. Using bran...
Article
Full-text available
Governments have implemented social distancing measures to address the ongoing COVID-19 pandemic. The measures include instructions that individuals maintain social distance when in public, school closures, limitations on gatherings and business operations, and instructions to remain at home. Social distancing may have an impact on the volume and d...
Preprint
Full-text available
We present three data driven model-types for COVID-19 with a minimal number of parameters to provide insights into the spread of the disease that may be used for developing policy responses. The first is exponential growth, widely studied in analysis of early-time data. The second is a self-exciting branching process model which includes a delay in...
Preprint
Full-text available
Governments have implemented social distancing measures to address the ongoing COVID-19 pandemic. The measures include instructions that individuals maintain a distance from one another when in public, limitations on gatherings and the operation of businesses, and instructions to remain at home. Social distancing may have a critical impact on the v...
Preprint
Full-text available
We analyze changes in the reproduction number, R, of COVID-19 in response to public health interventions. Our results indicate that public health measures undertaken in China reduced R from 1.5 in January to 0.4 in mid-March 2020. They also suggest, however, the limitations of isolation, quarantine, and large-scale attempts to limit travel. While t...
Article
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Residential burglary is a social problem in every major urban area. As such, progress has been to develop quantitative, informative and applicable models for this type of crime: (1) the Deterministic-time-step (DTS) model [Short, D’Orsogna, Pasour, Tita, Brantingham, Bertozzi & Chayes (2008) Math. Models Methods Appl. Sci.18 , 1249–1267], a pioneer...
Article
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Objectives The law of crime concentration states that half of the cumulative crime in a city will occur within approximately 4% of the city’s geography. The law is demonstrated by counting the number of incidents in each of N spatial areas (street segments or grid cells) and then computing a parameter based on the counts, such as a point estimate o...
Article
The primary focus is a sequential data assimilation method for count data modelled by an inhomogeneous Poisson process. In particular, a quadratic approximation technique similar to the extended Kalman filter is applied to develop a sub-optimal, discrete-time, filtering algorithm, called the extended Poisson–Kalman filter (ExPKF), where only the me...
Chapter
Transience of spatio-temporal clusters of residential burglary is well documented in empirical observations, and could be due to finite size effects anecdotally. However a theoretical understanding has been lacking. The existing agent-based statistical models of criminal behavior for residential burglary assume deterministic-time steps for arrivals...
Article
We model and analyze the dynamics of religious group membership and size. A group is distinguished by its strictness, which determines how much time group members are expected to spend contributing to the group. Individuals differ in their rate of return for time spent outside of their religious group. We construct a utility function that individua...
Preprint
Full-text available
Objectives. The law of crime concentration states that a large percentage of crime falls within a small area of a city. The law is demonstrated by counting the number of incidents in each of N spatial areas (street segments or grid cells) and then computing a statistic based on the counts, such as a point estimate on the Lorenz curve or the Gini in...
Article
Full-text available
A number of models – such as the Hawkes process and log Gaussian Cox process – have been used to understand how crime rates evolve in time and/or space. Within the context of these models and actual crime data, parameters are often estimated using maximum likelihood estimation (MLE) on batch data, but this approach has several limitations such as l...
Article
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We model radicalization in a society consisting of two competing religious, ethnic or political groups. Each of the 'sects' is divided into moderate and radical factions, with intra-group transitions occurring either spontaneously or through indoctrination. We also include the possibility of one group violently attacking the other. The intra-group...
Article
In this paper, we develop two efficient numerical methods for a multiscale kinetic equation in the context of crowd dynamics with emotional contagion [A. Bertozzi, J. Rosado, M. Short and L. Wang, Contagion shocks in one dimension, J. Stat. Phys. 158 (2014) 647-664]. In the continuum limit, the mesoscopic kinetic equation produces a natural Euleria...
Article
We propose various self-exciting point process models for the times when e-mails are sent between individuals in a social network. Using an EM-type approach, we fit these models to an e-mail network dataset from West Point Military Academy and the Enron e-mail dataset. We argue that the self-exciting models adequately capture major temporal cluster...
Article
We examine the game theoretic properties of a model of crime first introduced by Short et al. (2010 Phys. Rev. E 82 , 066114) as the SBD Adversarial Game. We identify the rationalizable strategies and one-shot equilibria under multiple equilibrium refinements. We further show that SBD's main result about the effectiveness of defecting-punishers (“I...
Article
Full-text available
The concentration of police resources in stable crime hotspots has proven effective in reducing crime, but the extent to which police can disrupt dynamically changing crime hotspots is unknown. Police must be able to anticipate the future location of dynamic hotspots to disrupt them. Here we report results of two randomized controlled trials of nea...
Conference Paper
Full-text available
There are a growing number of automated decision aids based on game-theoretic algorithms in daily use by security agencies to assist in allocating or scheduling their limited security resources. These applications of game theory, based on the " security games " paradigm, are leading to fundamental research challenges: one major challenge is modelin...
Article
Full-text available
In this paper, we explore some of the various issues that may occur in attempting to fit a dynamical systems (either agent- or continuum-based) model of urban crime to data on just the attack times and locations. We show how one may carry out a regression analysis for the model described by Short et al. (2008, Math. Mod. Meth. Appl. Sci. ) by using...
Article
We consider an agent-based model of emotional contagion coupled with motion in one dimension that has recently been studied in the computer science community. The model involves movement with a speed proportional to a “fear” variable that undergoes a temporal consensus averaging based on distance to other agents. We study the effect of Riemann init...
Conference Paper
Full-text available
There are a growing number of automated decision aids based on game-theoretic algorithms in daily use by security agencies to assist in allocating or scheduling their limited security resources. These applications of game theory, based on the " security games " paradigm, are leading to fundamental research challenges: one major challenge is modelin...
Conference Paper
Full-text available
This paper introduces a new game-theoretic framework and algorithms for addressing opportunistic crime. The Stackelberg Security Game (SSG), which models highly strategic and resourceful adversaries, has become an important computational framework within multiagent systems. Unfortunately, SSG is ill-suited as a framework for handling opportunistic...
Article
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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 part...
Article
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We introduce a point process model for inter-gang violence driven by retaliation a core feature of gang behavior and multi-party inhibition. Here, a coupled system of state-dependent jump stochastic differential equations is used to model the conditional intensities of the directed network of gang rivalries. The system admits an exact simulation st...
Article
Full-text available
In urban transportation networks, crime diffuses as criminals travel through the networks and look for illicit opportunities. It is important to first model this diffusion in order to recommend actions or patrol policies to control the diffusion of such crime. Previously, game theory has been used for such patrol policy recommendations, but these a...
Article
A mathematical model based on well-documented features of criminal behavior illuminates why crime hot spots form, and it can direct police to the most efficient use of their resources.
Article
The effects of personal relationships and shared ideologies on levels of crime and the formation of criminal coalitions are studied within the context of an adversarial, evolutionary game first introduced in Short et al. (Phys. Rev. E 82:066114, 2010). Here, we interpret these relationships as connections on a graph of N players. These connections...
Article
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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 a...
Article
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We consider an optimal control problem based on the evolutionary game theory model introduced by Short et al. (Short, M. B., Brantingham, P. J. & D'Orsogna, M. R. (2010) Cooperation and punishment in an adversarial game: How defectors pave the way to a peaceful society. Phys. Rev. E 82(6), 066114.1–066114.7) to study societal attitudes in relation...
Article
Full-text available
In urban transportation networks, crime diffuses as criminals travel through the networks and look for illicit opportunities. It is important to first model this diffusion in order to recommend actions or patrol policies to control the diffusion of such crime. Previously, game theory has been used for such patrol policy recommendations, but these a...
Article
Laboratory testbeds are an important part of the design of cooperative control algorithms. Sensor noise, communication delays, dropped packets, and network connectivity issues can all affect algorithm performance in different ways, and although these sources of error can be included in simulations, the degree of their effects is often not known unt...
Article
Full-text available
Within any type of system, the actors in the system inevitably compete over resources. With competition comes the possibility of conflict. To minimize such effects, actors often will partition the system into geographic territories. It is against the larger ecological backdrop of competition and conflict that we examine territory formation among ur...
Article
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This paper describes the third generation of an economical cooperative control testbed, last described in (Le-ung et al., 2007). The new testbed vehicles are improved with powerful on-board computing, upgraded and expanded on-board sensing, and enhanced wireless communication, while maintaining economic feasibility and scale. The new hardware allow...
Article
We consider the problem of estimating the probability density of the \anchor point" (residence, place of work, etc.) of a criminal of- fender given a set of observed spatial locations of crimes committed by the oender. Starting from kinetic models of criminal behavior, we de- rive the probability density of anchor points using the Fokker-Planck equ...
Article
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We discuss a mathematical framework based on a self-exciting point process aimed at analyzing temporal patterns in the series of interaction events between agents in a social network. We then develop a reconstruction model that allows one to predict the unknown participants in a portion of those events. Finally, we apply our results to the Los Ange...
Article
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Abstract Highly clustered event sequences are observed in certain types of crime data, such as burglary and gang violence, due to crime specic patterns of criminal behavior. Similar clustering patterns are observed by seismologists, as earthquakes are well known to increase the risk of subsequent earthquakes, or aftershocks, nearby the location of...
Article
Full-text available
The evolution of human cooperation has been the subject of much research, especially within the framework of evolutionary public goods games, where several mechanisms have been proposed to account for persistent cooperation. Yet, in addressing this issue, little attention has been given to games of a more adversarial nature, in which defecting play...
Article
Full-text available
The mechanisms driving the nucleation, spread, and dissipation of crime hotspots are poorly understood. As a consequence, the ability of law enforcement agencies to use mapped crime patterns to design crime prevention strategies is severely hampered. We also lack robust expectations about how different policing interventions should impact crime. He...
Article
Full-text available
We present a weakly nonlinear analysis of our recently developed model for the formation of crime patterns. Using a perturbative approach, we nd amplitude equations that govern the development of crime \hotspot" patterns in our system in both the 1D and 2D cases. In addition to the supercritical spots already shown to exist in our previous work, we...
Conference Paper
This paper presents a multiscale searching and target-locating algorithm for a group of agents moving in a swarm and sensing potential targets. The aim of the algorithm is to use these agents to efficiently search for and locate targets with a finite sensing radius in some bounded area. We present an algorithm that both controls agent movement and...
Article
Full-text available
We develop a mathematical framework aimed at analyzing repeat and near-repeat effects in crime data. Parsing burglary data from Long Beach, CA according to different counting methods, we determine the probability distribution functions for the time interval τ between repeat offenses. We then compare these observed distributions to theoretically der...
Article
Full-text available
This paper presents a searching and target- locating algorithm for a group of agents moving in a swarm and sensing potential targets. The aim of the algorithm is to use these agents to efficiently search for and locate targets with a finite sensing radius in some bounded area. We present an algorithm that both controls agent movement and analyzes s...
Article
Full-text available
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 varia...
Article
Full-text available
We develop a mathematical framework aimed at analyzing repeat and near-repeat eects in crime data. Parsing data according to dierent counting methods, we determine the probability distribution functions for the time interval ¿ between repeat oenses. One of the main focuses of this paper is the fact that, even under the assumption that crimes are ra...

Citations

... Numerous efforts have been made to test the decision-making capabilities of individuals based on having prior information. Bayesian tracking algorithms can be used for effective methods in reducing bias and improving performance by limiting misclassifications (Short and Mohler, 2022). The importance of Bayes-revised probabilities on decision makers could pose a problem to some that want to take ownership of their decision process, but in the case of the individual that prefers the assistance, Bayesian classification can bridge the gap (Goodwin et al., 2018). ...
... 2 importations (Perkins et al., 2020;MIDAS Network, 2021) (Fig. 1A). This estimate is within the range of other estimates for R(t) that include the state of Indiana (Fernández-Villaverde and Jones, 2020; Mohler et al., 2021). Driven by a calibrated estimate that the proportion of people sheltering in place rose in early March and peaked at a median of 32.1 % (95 % CrI: 28.8-66.9 ...
... The primary goal of utilizing the two distinct modeling approaches is to connect the testing rate to the unlock process since contact tracing can not be implemented in ODE based epidemic models. Earlier studies discuss the limitations of ODE based models and agent-based models 32 , but studies connecting both modeling approaches especially in the context of the COVID19 epidemics to understand the relation between testing rate and unlock measures are not reported in the literature. Here, feeding the country specific epidemic parameters from the ODE model into the agent-based model, we derive country specific optimal testing rates through contact tracing. ...
... Many studies have examined crime in the context of the COVID-19 pandemic [2,[4][5][6][7][8][9][10][11][12][13][14]. Campedelli et al. [6] assessed the impact of quarantine policies on crime using a Bayesian time series and found that crimes, such as robbery, burglary, assault, and battery, decreased significantly under quarantine policies. ...
... They also allow for estimation of the probability of extinction at early stages of an epidemic. These models have been used for various social interactions including spread of Ebola [13], retaliatory gang crimes [34], and Reported cumulative deaths/million [6] using a non-parametric branching process [25]. Current estimates as of April 1, 2020 of the reproduction number in New York, California, and Indiana (confirmed cases used instead of mortality for Indiana). ...
... In [29] it is suggested, for example, that there is a tradeoff between the concentration of crime in space [52] and the stability of the associated hotspots. In general, at fine spatiotemporal scales crime is much more concentrated, but hotspots also frequently shift from place to place (see also [51]). At coarse spatiotemporal scales, crime is more diffuse, but the resulting hotspots also rarely move around. ...
... Several models are used to overcome the heterogeneous effect are negative binomial model [4] , Penalized Conway-Maxwell-Poisson regression [5] , multilevel Zero-Inflated Generalized Poisson regression [6] , generalized Poisson with time varying population sizes [7] , fitting N-mixture models [8] , and generalized Poisson integer-valued GARCH model [9] . While the methods used to analyze count data from several previous studies are bell distribution [10] , Bayesian additive regression [11] , approximate filtering of conditional intensity process [12] , gamma block effect [13] , Bayesian forecasting [14] ...
... Following the seminal work (see reference [18]) on the mathematics of agent-based models for residential burglary, many works have been done on mathematical crime modeling and prediction, see e.g. references [1], [3], [7], [9], [12], [13], [14], [15], [16], [18], [19] and [20], and the references cited therein, and in [18]. ...
... We then fit Poisson regressions on yearly shooting incident counts per block group, disaggregated by race/ethnicity, with indicator variables for pre-pandemic shooting decile and time period (2016-2019 vs. 2020-2021). In the second approach, we measure inequality in the distribution of shootings using a Poisson-Gamma estimate of the spatial gini index of shootings in census block groups that corrects for small sample size (Mohler et al., 2019). We compare the gini index disaggregated by race/ethnicity in the pre/post pandemic time periods. ...
... We point out that here we consider specifically a case in which each location may have its own background intensity i , but that all locations share the same and parameters. While certainly Eq. 18 generally causes nonstationary intensities at each location, it is also true (Da Fonseca and Zaatour 2014;Santitissadeekorn et al. 2018) that the steady-state expected intensity for the Hawkes process is given by i ∕(1 − ) , while the steady-state variance of the intensity is given by a chosen , and where the background rates i are Gamma distributed with shape k = 0.82 and rate = 1∕7.28 for N = 1000 locations; these parameters are identical to those used in "Simulation Study" section. ...