Network Farthest-Point Diagrams

Consider the continuum of points along the edges of a network, i.e., an undirected graph with positive edge weights. We measure distance between these points in terms of the shortest path distance along the network, known as the network distance. Within this metric space, we study farthest points. We introduce network farthest-point diagrams, which capture how the farthest points---and the distance to them---change as we traverse the network. We preprocess a network G such that, when given a query point q on G, we can quickly determine the farthest point(s) from q in G as well as the farthest distance from q in G. Furthermore, we introduce a data structure supporting queries for the parts of the network that are farther away from q than some threshold R > 0, where R is part of the query. We also introduce the minimum eccentricity feed-link problem defined as follows. Given a network G with geometric edge weights and a point p that is not on G, connect p to a point q on G with a straight line segment pq, called a feed-link, such that the largest network distance from p to any point in the resulting network is minimized. We solve the minimum eccentricity feed-link problem using eccentricity diagrams. In addition, we provide a data structure for the query version, where the network G is fixed and a query consists of the point p.Comment: A preliminary version of this work was presented at the 24th Canadian Conference on Computational Geometr

Application of Geographic Information Systems

The importance of Geographic Information Systems (GIS) can hardly be overemphasized in today’s academic and professional arena. More professionals and academics have been using GIS than ever – urban & regional planners, civil engineers, geographers, spatial economists, sociologists, environmental scientists, criminal justice professionals, political scientists, and alike. As such, it is extremely important to understand the theories and applications of GIS in our teaching, professional work, and research. “The Application of Geographic Information Systems” presents research findings that explain GIS’s applications in different subfields of social sciences. With several case studies conducted in different parts of the world, the book blends together the theories of GIS and their practical implementations in different conditions. It deals with GIS’s application in the broad spectrum of geospatial analysis and modeling, water resources analysis, land use analysis, infrastructure network analysis like transportation and water distribution network, and such. The book is expected to be a useful source of knowledge to the users of GIS who envision its applications in their teaching and research. This easy-to-understand book is surely not the end in itself but a little contribution to toward our understanding of the rich and wonderful subject of GIS

Search Problems in Mission Planning and Navigation of Autonomous Aircraft

An architecture for the control of an autonomous aircraft is presented. The architecture is a hierarchical system representing an anthropomorphic breakdown of the control problem into planner, navigator, and pilot systems. The planner system determines high level global plans from overall mission objectives. This abstract mission planning is investigated by focusing on the Traveling Salesman Problem with variations on local and global constraints. Tree search techniques are applied including the breadth first, depth first, and best first algorithms. The minimum-column and row entries for the Traveling Salesman Problem cost matrix provides a powerful heuristic to guide these search techniques. Mission planning subgoals are directed from the planner to the navigator for planning routes in mountainous terrain with threats. Terrain/threat information is abstracted into a graph of possible paths for which graph searches are performed. It is shown that paths can be well represented by a search graph based on the Voronoi diagram of points representing the vertices of mountain boundaries. A comparison of Dijkstra's dynamic programming algorithm and the A* graph search algorithm from artificial intelligence/operations research is performed for several navigation path planning examples. These examples illustrate paths that minimize a combination of distance and exposure to threats. Finally, the pilot system synthesizes the flight trajectory by creating the control commands to fly the aircraft

Multiple particle tracking in PEPT using Voronoi tessellations

An algorithm is presented which makes use of three-dimensional Voronoi tessellations to track up to 20 tracers using a PET scanner. The lines of response generated by the PET scanner are discretized into sets of equidistant points, and these are used as the input seeds to the Voronoi tessellation. For each line of response, the point with the smallest Voronoi region is located; this point is assumed to be the origin of the corresponding line of response. Once these origin points have been determined, any outliers are removed, and the remaining points are clustered using the DBSCAN algorithm. The centroid of each cluster is classified as a tracer location. Once the tracer locations are determined for each time frame in the experimental data set, a custom multiple target tracking algorithm is used to associate identical tracers from frame to frame. Since there are no physical properties to distinguish the tracers from one another, the tracking algorithm uses velocity and position to extrapolate the locations of existing tracers and match the next frame's tracers to the trajectories. A series of experiments were conducted in order to test the robustness, accuracy and computational performance of the algorithm. A measure of robustness is the chance of track loss, which occurs when the algorithm fails to match a tracer location with its trajectory, and the track is terminated. The chance of track loss increases with the number of tracers; the acceleration of the tracers; the time interval between successive frames; and the proximity of tracers to each other. In the case of two tracers colliding, the two tracks merge for a short period of time, before separating and become distinguishable again. Track loss also occurs when a tracer leaves the field of view of the scanner; on return it is treated as a new object. The accuracy of location of the algorithm was found to be slightly affected by tracer velocity, but is much more dependent on the distance between consecutive points on a line of response, and the number of lines of response used per time frame. A single tracer was located to within 1.26mm. This was compared to the widely accepted Birmingham algorithm, which located the same tracer to within 0.92mm. Precisions of between 1.5 and 2.0mm were easily achieved for multiple tracers. The memory usage and processing time of the algorithm are dependent on the number of tracers used in the experiment. It was found that the processing time per frame for 20 tracers was about 15s, and the memory usage was 400MB. Because of the high processing times, the algorithm as is is not feasible for practical use. However, the location phase of the algorithm is massively parallel, so the code can be adapted to significantly increase the efficiency

Modeling Of Socio-economic Factors And Adverse Events In An Active War Theater By Using A Cellular Automata Simulation Approach

Department of Defense (DoD) implemented Human Social Cultural and Behavior (HSCB) program to meet the need to develop capability to understand, predict and shape human behavior among different cultures by developing a knowledge base, building models, and creating training capacity. This capability will allow decision makers to subordinate kinetic operations and promote non-kinetic operations to govern economic programs better in order to initiate efforts and development to address the grievances among the displeased by adverse events. These non-kinetic operations include rebuilding indigenous institutions’ bottom-up economic activity and constructing necessary infrastructure since the success in non-kinetic operations depends on understanding and using social and cultural landscape. This study aims to support decision makers by building a computational model to understand economic factors and their effect on adverse events. In this dissertation, the analysis demonstrates that the use of cellular automata has several significant contributions to support decision makers allocating development funds to stabilize regions with higher adverse event risks, and to better understand the complex socio-economic interactions with adverse events. Thus, this analysis was performed on a set of spatial data representing factors from social and economic data. In studying behavior using cellular automata, cells in the same neighborhood synchronously interact with each other to determine their next states, and small changes in iteration may yield to complex formations of adverse event risk after several iterations of time. The modeling methodology of cellular automata for social and economic analysis in this research was designed in two major implementation levels as follows: macro and micro-level. In the macro-level, the modeling framework integrates iv population, social, and economic sub-systems. The macro-level allows the model to use regionalized representations, while the micro-level analyses help to understand why the events have occurred. Macro-level subsystems support cellular automata rules to generate accurate predictions. Prediction capability of cellular automata is used to model the micro-level interactions between individual actors, which are represented by adverse events. The results of this dissertation demonstrate that cellular automata model is capable of evaluating socio-economic influences that result in changes in adverse events and identify location, time and impact of these events. Secondly, this research indicates that the socioeconomic influences have different levels of impact on adverse events, defined by the number of people killed, wounded or hijacked. Thirdly, this research shows that the socio-economic, influences and adverse events that occurred in a given district have impacts on adverse events that occur in neighboring districts. The cellular automata modeling approach can be used to enhance the capability to understand and use human, social and behavioral factors by generating what-if scenarios to determine the impact of different infrastructure development projects to predict adverse events. Lastly, adverse events that could occur in upcoming years can be predicted to allow decision makers to deter these events or plan accordingly if these events do occur

The Facility Location Problem

The purpose of this study was to analyze the location of an emergency facility location within a town based on given information from the village and to use the results to determine the optimal location for an emergency facility. A model of the problem was developed using a spreadsheet and computer program to record and analyze the optimal response time based on different locations of emergency facilities. Assumptions were made to create situations easily computed through spreadsheet and computer programs. Once calculated, information was used to create a framework of demand density across a gridded map. Once the computer program was updated to use the large amount of data, results were obtained. Based on data and modeling, the current location of emergency facility was not located in the most opportune locations and another location was deemed better suited for serving the community

System Identification for the design of behavioral controllers in crowd evacuations

Behavioral modification using active instructions is a promising interventional method to optimize crowd evacuations. However, existing research efforts have been more focused on eliciting general principles of optimal behavior than providing explicit mechanisms to dynamically induce the desired behaviors, which could be claimed as a significant knowledge gap in crowd evacuation optimization. In particular, we propose using dynamic distancekeeping instructions to regulate pedestrian flows and improve safety and evacuation time. We investigate the viability of using Model Predictive Control (MPC) techniques to develop a behavioral controller that obtains the optimal distance-keeping instructions to modulate the pedestrian density at bottlenecks. System Identification is proposed as a general methodology to model crowd dynamics and build prediction models. Thus, for a testbed evacuation scenario and input?output data generated from designed microscopic simulations, we estimate a linear AutoRegressive eXogenous model (ARX), which is used as the prediction model in the MPC controller. A microscopic simulation framework is used to validate the proposal that embeds the designed MPC controller, tuned and refined in closed-loop using the ARX model as the Plant model. As a significant contribution, the proposed combination of MPC control and System Identification to model crowd dynamics appears ideally suited to develop realistic and practical control systems for controlling crowd motion. The flexibility of MPC control technology to impose constraints on control variables and include different disturbance models in the prediction model has confirmed its suitability in the design of behavioral controllers in crowd evacuations. We found that an adequate selection of output disturbance models in the predictor is critical in the type of responses given by the controller. Interestingly, it is expected that this proposal can be extended to different evacuation scenarios, control variables, control systems, and multiple-input multiple-output control structures.Ministerio de Economía y Competitivida

Safe, Remote-Access Swarm Robotics Research on the Robotarium

This paper describes the development of the Robotarium -- a remotely accessible, multi-robot research facility. The impetus behind the Robotarium is that multi-robot testbeds constitute an integral and essential part of the multi-agent research cycle, yet they are expensive, complex, and time-consuming to develop, operate, and maintain. These resource constraints, in turn, limit access for large groups of researchers and students, which is what the Robotarium is remedying by providing users with remote access to a state-of-the-art multi-robot test facility. This paper details the design and operation of the Robotarium as well as connects these to the particular considerations one must take when making complex hardware remotely accessible. In particular, safety must be built in already at the design phase without overly constraining which coordinated control programs the users can upload and execute, which calls for minimally invasive safety routines with provable performance guarantees.Comment: 13 pages, 7 figures, 3 code samples, 72 reference

Geospatial Tessellation in the Agent-In-Cell Model: A Framework for Agent-Based Modeling of Pandemic

Agent-based simulation is a versatile and potent computational modeling technique employed to analyze intricate systems and phenomena spanning diverse fields. However, due to their computational intensity, agent-based models become more resource-demanding when geographic considerations are introduced. This study delves into diverse strategies for crafting a series of Agent-Based Models, named "agent-in-the-cell," which emulate a city. These models, incorporating geographical attributes of the city and employing real-world open-source mobility data from Safegraph's publicly available dataset, simulate the dynamics of COVID spread under varying scenarios. The "agent-in-the-cell" concept designates that our representative agents, called meta-agents, are linked to specific home cells in the city's tessellation. We scrutinize tessellations of the mobility map with varying complexities and experiment with the agent density, ranging from matching the actual population to reducing the number of (meta-) agents for computational efficiency. Our findings demonstrate that tessellations constructed according to the Voronoi Diagram of specific location types on the street network better preserve dynamics compared to Census Block Group tessellations and better than Euclidean-based tessellations. Furthermore, the Voronoi Diagram tessellation and also a hybrid -- Voronoi Diagram - and Census Block Group - based -- tessellation require fewer meta-agents to adequately approximate full-scale dynamics. Our analysis spans a range of city sizes in the United States, encompassing small (Santa Fe, NM), medium (Seattle, WA), and large (Chicago, IL) urban areas. This examination also provides valuable insights into the effects of agent count reduction, varying sensitivity metrics, and the influence of city-specific factors