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The level-set method is a prominent approach to modelling the evolution of a fire over time based on a characterised rate of spread. It however does not provide a direct means for assimilating new data and quantifying uncertainty. Fire…
Hot-spot-based policing programs aim to deter crime through increased proactive patrols at high-crime locations. While most hot spot programs target easily identified chronic hot spots, we introduce models for predicting temporary hot spots…
Nowadays, traffic management has become a challenge for urban areas, which are covering larger geographic spaces and facing the generation of different kinds of traffic data. This article presents a robust traffic estimation framework for…
It is well known that time dependent Hamilton-Jacobi-Isaacs partial differential equations (HJ PDE), play an important role in analyzing continuous dynamic games and control theory problems. An important tool for such problems when they…
Potential violent criminals will often need to go through a sequence of preparatory steps before they can execute their plans. During this escalation process police have the opportunity to evaluate the threat posed by such people through…
This paper presents a novel learning-based approach for online estimation of maximal safe sets for local trajectory planning in unknown static environments. The neural representation of a set is used as the terminal set constraint for a…
Hamilton-Jacobi (HJ) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. However, the provided safety assurances are often predicated on the assumption that once deployed, the system or its environment…
The built environment has been postulated to have an impact on neighborhood crime rates, however, measures of the built environment can be subjective and differ across studies leading to varying observations on its association with crime…
The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of…
We consider the problem of geographic profiling and offer an approach to choosing a suitable model for each offender. Based on the analysis of the examined dataset, we divide offenders into several types with similar behavior. According to…
Here we present a decomposition technique for a class of differential games. The technique consists in a decomposition of the target set which produces, for geometrical reasons, a decomposition in the dimensionality of the problem. Using…
In this paper, we propose a general hidden state random walk model to describe the movement of an animal that takes into account movement taxis with respect to features of the environment. A circular-linear process models the direction and…
Although ground robotic autonomy has gained widespread usage in structured and controlled environments, autonomy in unknown and off-road terrain remains a difficult problem. Extreme, off-road, and unstructured environments such as…
Real-world autonomous vehicles often operate in a priori unknown environments. Since most of these systems are safety-critical, it is important to ensure they operate safely in the face of environment uncertainty, such as unseen obstacles.…
This paper focuses on finding spatial and temporal criminal hotspots. It analyses two different real-world crimes datasets for Denver, CO and Los Angeles, CA and provides a comparison between the two datasets through a statistical analysis…
Our work is motivated by environmental monitoring tasks, where finding the global maxima (i.e., hotspot) of a spatially varying field is crucial. We investigate the problem of identifying the hotspot for fields that can be sensed using an…
Fast and Safe Tracking (FaSTrack) is a modular framework that provides safety guarantees while planning and executing trajectories in real time via value functions of Hamilton-Jacobi (HJ) reachability. These value functions are computed…
Self-exciting point processes are widely used to model the contagious effects of crime events living within continuous geographic space, using their occurrence time and locations. However, in urban environments, most events are naturally…
We present a method to capture groupings of similar calls and determine their relative spatial distribution from a collection of crime record narratives. We first obtain a topic distribution for each narrative, and then propose a nearest…
Intense wildfires impact nature, humans, and society, causing catastrophic damage to property and the ecosystem, as well as the loss of life. Forecasting wildfire front propagation is essential in order to support fire fighting efforts and…