Existence of symmetric and asymmetric spikes for a crime hotspot model

Copyright @ 2014 Society for Industrial and Applied MathematicsWe study a crime hotspot model suggested by Short, Bertozzi, and Brantingham in [SIAM J. Appl. Dyn. Syst., 9 (2010), pp. 462--483]. The aim of this work is to establish rigorously the formation of hotspots in this model representing concentrations of criminal activity. More precisely, for the one-dimensional system, we rigorously prove the existence of steady states with multiple spikes of the following types: (i) multiple spikes of arbitrary number having the same amplitude (symmetric spikes), and (ii) multiple spikes having different amplitude for the case of one large and one small spike (asymmetric spikes). We use an approach based on Lyapunov--Schmidt reduction and extend it to the quasilinear crime hotspot model. Some novel results that allow us to carry out the Lyapunov--Schmidt reduction are (i) approximation of the quasilinear crime hotspot system on the large scale by the semilinear Schnakenberg model, and (ii) estimate of the spatial dependence of the second component on the small scale which is dominated by the quasilinear part of the system. The paper concludes with an extension to the anisotropic case

Steady State Solutions for a System of Partial Differential Equations Arising from Crime Modeling

I consider a model for the control of criminality in cities. The model was developed during my REU at UCLA. The model is a system of partial differential equations that simulates the behavior of criminals and where they may accumulate, hot spots. I have proved a prior bounds for the partial differential equations in both one-dimensional and higher dimensional case, which proves the attractiveness and density of criminals in the given area will not be unlimitedly high. In addition, I have found some local bifurcation points in the model

ON META-NETWORKS, DEEP LEARNING, TIME AND JIHADISM

Il terrorismo di stampo jihadista rappresenta una minaccia per la società e una sfida per gli scienziati interessati a comprenderne la complessità. Questa complessità richiede costantemente nuovi sviluppi in termini di ricerca sul terrorismo. Migliorare la conoscenza empirica rispetto a tale fenomeno può potenzialmente contribuire a sviluppare applicazioni concrete e, in ultima istanza, a prevenire danni all’uomo. In considerazione di tali aspetti, questa tesi presenta un nuovo quadro metodologico che integra scienza delle reti, modelli stocastici e apprendimento profondo per far luce sul terrorismo jihadista sia a livello esplicativo che predittivo. In particolare, questo lavoro compara e analizza le organizzazioni jihadiste più attive a livello mondiale (ovvero lo Stato Islamico, i Talebani, Al Qaeda, Boko Haram e Al Shabaab) per studiarne i pattern comportamentali e predirne le future azioni. Attraverso un impianto teorico che si poggia sulla concentrazione spaziale del crimine e sulle prospettive strategiche del comportamento terroristico, questa tesi persegue tre obiettivi collegati utilizzando altrettante tecniche ibride. In primo luogo, verrà esplorata la complessità operativa delle organizzazioni jihadiste attraverso l’analisi di matrici stocastiche di transizione e verrà presentato un nuovo coefficiente, denominato “Normalized Transition Similarity”, che misura la somiglianza fra paia di gruppi in termini di dinamiche operative. In secondo luogo, i processi stocastici di Hawkes aiuteranno a testare la presenza di meccanismi di dipendenza temporale all’interno delle più comuni sotto-sequenze strategiche di ciascun gruppo. Infine, il framework integrerà la meta-reti complesse e l’apprendimento profondo per classificare e prevedere i target a maggiore rischio di essere colpiti dalle organizzazioni jihadiste durante i loro futuri attacchi. Per quanto riguarda i risultati, le matrici stocastiche di transizione mostrano che i gruppi terroristici possiedono un ricco e complesso repertorio di combinazioni in termini di armi e obiettivi. Inoltre, i processi di Hawkes indicano la presenza di diffusa self-excitability nelle sequenze di eventi. Infine, i modelli predittivi che sfruttano la flessibilità delle serie temporali derivanti da grafi dinamici e le reti neurali Long Short-Term Memory forniscono risultati promettenti rispetto ai target più a rischio. Nel complesso, questo lavoro ambisce a dimostrare come connessioni astratte e nascoste fra eventi possano essere fondamentali nel rivelare le meccaniche del comportamento jihadista e come processi memory-like (ovvero molteplici comportamenti ricorrenti, interconnessi e non randomici) possano risultare estremamente utili nel comprendere le modalità attraverso cui tali organizzazioni operano.Jihadist terrorism represents a global threat for societies and a challenge for scientists interested in understanding its complexity. This complexity continuously calls for developments in terrorism research. Enhancing the empirical knowledge on the phenomenon can potentially contribute to developing concrete real-world applications and, ultimately, to the prevention of societal damages. In light of these aspects, this work presents a novel methodological framework that integrates network science, mathematical modeling, and deep learning to shed light on jihadism, both at the explanatory and predictive levels. Specifically, this dissertation will compare and analyze the world's most active jihadist terrorist organizations (i.e. The Islamic State, the Taliban, Al Qaeda, Boko Haram, and Al Shabaab) to investigate their behavioral patterns and forecast their future actions. Building upon a theoretical framework that relies on the spatial concentration of terrorist violence and the strategic perspective of terrorist behavior, this dissertation will pursue three linked tasks, employing as many hybrid techniques. Firstly, explore the operational complexity of jihadist organizations using stochastic transition matrices and present Normalized Transition Similarity, a novel coefficient of pairwise similarity in terms of strategic behavior. Secondly, investigate the presence of time-dependent dynamics in attack sequences using Hawkes point processes. Thirdly, integrate complex meta-networks and deep learning to rank and forecast most probable future targets attacked by the jihadist groups. Concerning the results, stochastic transition matrices show that terrorist groups possess a complex repertoire of combinations in the use of weapons and targets. Furthermore, Hawkes models indicate the diffused presence of self-excitability in attack sequences. Finally, forecasting models that exploit the flexibility of graph-derived time series and Long Short-Term Memory networks provide promising results in terms of correct predictions of most likely terrorist targets. Overall, this research seeks to reveal how hidden abstract connections between events can be exploited to unveil jihadist mechanics and how memory-like processes (i.e. multiple non-random parallel and interconnected recurrent behaviors) might illuminate the way in which these groups act