The current methods used by forensic experts to analyse blood spatter neglects the influence of gravitation and drag on the trajectory of the droplet. This research attempts to suggest a more accurate method to determine the trajectory of a blood droplet using multi-target tracking. The multi-target tracking problem can be rewritten as a linear programming problem and solved by means of optimization and numerical methods. A literature survey is presented on relevant articles on blood spatter analysis and multi-target tracking. In contrast to a more advanced approach that assumes a background in probability, mathematical modelling and forensic science, this dissertation aims to give a comprehensive mathematical exposition of particle tracking. The tracking of multi-targets, through multi-target tracking, is investigated. The dynamic programming methods to solve the multi-target tracking are coded in the MATLAB programming language. Results are obtained for different scenarios and option inputs. Research strategies include studying documents, articles, journal entries and books. / MSc (Applied Mathematics), North-West University, Potchefstroom Campus, 2014

The current methods used by forensic experts to analyse blood spatter neglects the influence of gravitation and drag on the trajectory of the droplet. This research attempts to suggest a more accurate method to determine the trajectory of a blood droplet using multi-target tracking. The multi-target tracking problem can be rewritten as a linear programming problem and solved by means of optimization and numerical methods. A literature survey is presented on relevant articles on blood spatter analysis and multi-target tracking. In contrast to a more advanced approach that assumes a background in probability, mathematical modelling and forensic science, this dissertation aims to give a comprehensive mathematical exposition of particle tracking. The tracking of multi-targets, through multi-target tracking, is investigated. The dynamic programming methods to solve the multi-target tracking are coded in the MATLAB programming language. Results are obtained for different scenarios and option inputs. Research strategies include studying documents, articles, journal entries and books. / MSc (Applied Mathematics), North-West University, Potchefstroom Campus, 2014

Finding the shortest paths in a graph has been studied for a long time, and there are many main memory based algorithms dealing with this problem. Among these, Dijkstra's shortest path algorithm is one of the most commonly used efficient algorithms to the non-negative graphs. Even more efficient algorithms have been developed recently for graphs with particular properties such as the weights of edges fall into a range of integer. All of the mentioned algorithms require the graph totally reside in the main memory. Howevery, for very large graphs, such as the digital maps managed by Geographic Information Systems (GIS), the requirement cannot be satisfied in most cases, so the algorithms mentioned above are not appropriate. My objective in this thesis is to design and evaluate the performance of external memory (disk-based) shortest path algorithms and data structures to solve the shortest path problem in very large digital maps. In particular the following questions are studied:What have other researchers done on the shortest path queries in very large digital maps?What could be improved on the previous works? How efficient are our new shortest paths algorithms on the digital maps, and what factors affect the efficiency? What can be done based on the algorithm? In this thesis, we give a disk-based Dijkstra's-like algorithm to answer shortest path queries based on pre-processing information. Experiments based on our Java implementation are given to show what factors affect the running time of our algorithms.

Distributed-system observation is foundational to understanding and controlling distributed computations. Existing tools for distributed-system observation are constrained in the size of computation that they can observe by three fundamental problems. They lack scalable information collection, scalable data-structures for storing and querying the information collected, and scalable information-abstraction schemes. This dissertation addresses the second of these problems. Two core problems were identified in providing a scalable data structure. First, in spite of the existence of several distributed-system-observation tools, the requirements of such a structure were not well-defined. Rather, current tools appear to be built on the basis of events as the core data structure. Events were assigned logical timestamps, typically Fidge/Mattern, as needed to capture causality. Algorithms then took advantage of additional properties of these timestamps that are not explicit in the formal semantics. This dissertation defines the data-structure interface precisely, and goes some way toward reworking algorithms in terms of that interface. The second problem is providing an efficient, scalable implementation for the defined data structure. The key issue in solving this is to provide a scalable precedence-test operation. Current tools use the Fidge/Mattern timestamp for this. While this provides a constant-time test, it requires space per event equal to the number of processes. As the number of processes increases, the space consumption becomes sufficient to affect the precedence-test time because of caching effects. It also becomes problematic when the timestamps need to be copied between processes or written to a file. Worse, existing theory suggested that the space-consumption requirement of Fidge/Mattern timestamps was optimal. In this dissertation we present two alternate timestamp algorithms that require substantially less space than does the Fidge/Mattern algorithm.

Distributed-system observation is foundational to understanding and controlling distributed computations. Existing tools for distributed-system observation are constrained in the size of computation that they can observe by three fundamental problems. They lack scalable information collection, scalable data-structures for storing and querying the information collected, and scalable information-abstraction schemes. This dissertation addresses the second of these problems. Two core problems were identified in providing a scalable data structure. First, in spite of the existence of several distributed-system-observation tools, the requirements of such a structure were not well-defined. Rather, current tools appear to be built on the basis of events as the core data structure. Events were assigned logical timestamps, typically Fidge/Mattern, as needed to capture causality. Algorithms then took advantage of additional properties of these timestamps that are not explicit in the formal semantics. This dissertation defines the data-structure interface precisely, and goes some way toward reworking algorithms in terms of that interface. The second problem is providing an efficient, scalable implementation for the defined data structure. The key issue in solving this is to provide a scalable precedence-test operation. Current tools use the Fidge/Mattern timestamp for this. While this provides a constant-time test, it requires space per event equal to the number of processes. As the number of processes increases, the space consumption becomes sufficient to affect the precedence-test time because of caching effects. It also becomes problematic when the timestamps need to be copied between processes or written to a file. Worse, existing theory suggested that the space-consumption requirement of Fidge/Mattern timestamps was optimal. In this dissertation we present two alternate timestamp algorithms that require substantially less space than does the Fidge/Mattern algorithm.

Finding the shortest paths in a graph has been studied for a long time, and there are many main memory based algorithms dealing with this problem. Among these, Dijkstra's shortest path algorithm is one of the most commonly used efficient algorithms to the non-negative graphs. Even more efficient algorithms have been developed recently for graphs with particular properties such as the weights of edges fall into a range of integer. All of the mentioned algorithms require the graph totally reside in the main memory. Howevery, for very large graphs, such as the digital maps managed by Geographic Information Systems (GIS), the requirement cannot be satisfied in most cases, so the algorithms mentioned above are not appropriate. My objective in this thesis is to design and evaluate the performance of external memory (disk-based) shortest path algorithms and data structures to solve the shortest path problem in very large digital maps. In particular the following questions are studied:What have other researchers done on the shortest path queries in very large digital maps?What could be improved on the previous works? How efficient are our new shortest paths algorithms on the digital maps, and what factors affect the efficiency? What can be done based on the algorithm? In this thesis, we give a disk-based Dijkstra's-like algorithm to answer shortest path queries based on pre-processing information. Experiments based on our Java implementation are given to show what factors affect the running time of our algorithms.

In a peer-to-peer shared ride system, transportation clients with traffic demand negotiate with transportation hosts offering shared ride services for ad-hoc ridesharing in a continuously changing environment, using wireless geosensor networks. Due to the distinctive characteristic of this system—a complex and non-deterministic transportation network, and a local peer-to-peer communication strategy—clients will always have limited transportation knowledge, both from a spatial and a temporal perspective. Clients hear only from nearby hosts, and they do not know the future availability of current or new hosts. Clients can plan optimal trips prior to departure according to their current knowledge, but it is unlikely that these trips will be final optimal trip due to continuously changing traffic conditions. Therefore, it is necessary to evaluate the trip quality in this dynamic environment in order to assess different communication and wayfinding strategies. (For complete abstract open document)

Disasters (e.g. earthquakes) and emergencies (e.g. fire) threaten the safety of occupants in the buildings and cause injuries and mortalities. These harmful effects are even more dangerous when secondary hazards (e.g. post-earthquake fires) emerge and it is commonly observed that the disasters/emergencies trigger secondary hazards.An effective indoor emergency guidance and navigation approach for occupants and first responders can decrease the number of injuries and mortalities during building emergencies by improving the evacuation process and response operations. For this reason, this research will propose a model-based guidance and vulnerability assessment approach for facilities that are under the threat of multi-hazard emergencies. The approach can be used to guide occupants from the facility affected by disasters/emergencies to safer zones and to direct the first responders by supplying them necessary building related information such as identified vulnerable locations in the indoor environments. An integrated utilization of Building Information Modeling tools, sensors, shortest path algorithms, and vulnerability assessment algorithms is proposed for the system in this research. The research steps of this thesis include (1) determination of requirements of an indoor navigation during emergency response and disaster management,(2) review, comparison, and evaluation of shortest path algorithms from an emergency response and disaster management point of view, (3) proposing a vulnerability assessment approach, and (4) proposing a real-time indoor emergency guidance and navigation system framework for buildings under the threat of multi-hazard emergencies. The findings of the research can be used in future studies on emergency response and disaster management domains.

Traditional shortest path algorithms can efficiently find the optimal paths in graphs using simple heuristics. However, formulating a simple heuristic is challenging under the road network setting since there are multiple factors to consider, such as road segment length, edge centrality, and speed limit. This study investigates how a neural network can learn to take these factors as inputs and yield a path given a pair of origin and destination. The research question is formulated as: Are neural networks applicable to real-time route planning tasks in a roadnetwork?. The proposed metric to evaluate the effectiveness of the neural network is arrival rate. The quality of generated paths is evaluated by time efficiency. The real-time performance of the model is also compared between pathfinding in dynamic and static graphs, using theabove metrics. A staggered approach is applied in progressing this investigation. The first step is to generate random graphs, which allows us to monitor the size and properties of the training graph without caring too many details in a road network. The next step is to determine, as a proof of concept, if a neural network can learn to traverse simple graphs with multiple strategies, given that road networks are in effect complex graphs. Finally, we scale up by including factors that might affect the pathfinding in real road networks. Overall, the training data is optimal paths in a graph generated by a shortest path algorithm. The model is then applied to new graphs to generate a path given a pair of origin and destination. The arrival rate and time efficiency are calculated and compared with that of the corresponding optimal path. Experimental results show that the effectiveness, i.e., arrival rate ofthe model is 90% and the path quality, i.e., time efficiency has a medianof 0.88 and a large variance. The experiment shows that the model has better performance in dynamic graphs than in static graphs. Overall, the answer to the research question is positive. However, there is still room to improve the effectiveness of the model and the paths generated by the model. This work shows that a neural network trained to make locally optimal choices can hardly give a globally optimal solution. We also show that our method, only making locally optimal choices, can adapt to dynamic graphs with little performance overhead. / Traditionella algoritmer för att hitta den kortaste vägen kan effektivt hitta de optimala vägarna i grafer med enkel heuristik. Att formulera en enkel heuristik är dock utmanande för vägnätverk eftersom det finns flera faktorer att överväga, såsom vägsegmentlängd, kantcentralitet och hastighetsbegränsningar. Denna studie undersöker hur ett neuralt nätverk kan lära sig att ta dessa faktorer som indata och finna en väg utifrån start- och slutpunkt. Forskningsfrågan är formulerad som: Är neuronnätverket tillämpliga på realtidsplaneringsuppgifter i ett vägnät?. Det föreslagna måttet för att utvärdera effektiviteten hos det neuronnätverket är ankomstgrad. Kvaliteten på genererade vägar utvärderas av tidseffektivitet. Prestandan hos modellen jämförs också mellan sökningen i dynamiska och statiska grafer, med hjälp av ovanstående mätvärden. Undersökningen bedrivs i flera steg. Det första steget är att generera slumpmässiga grafer, vilket gör det möjligt för oss att övervaka träningsdiagrammets storlek och egenskaper utan att ta hand om för många detaljer i ett vägnät. Nästa steg är att, som ett bevis på konceptet, undersöka om ett neuronnätverk kan lära sig att korsa enkla grafer med flera strategier, eftersom vägnätverk är i praktiken komplexa grafer. Slutligen skalas studien upp genom att inkludera faktorer som kan påverka sökningen i riktiga vägnät. Träningsdata utgörs av optimala vägar i en graf som genereras av en algoritm för att finna den kortaste vägen. Modellen appliceras sedan i nya grafer för att hitta en väg mellan start och slutpunkt. Ankomstgrad och tidseffektivitet beräknas och jämförs med den motsvarande optimala sökvägen. De experimentella resultaten visar att effektiviteten, dvs ankomstgraden av modellen är 90% och vägkvaliteten dvs tidseffektiviteten har en median på 0,88 och en stor varians. Experimentet visar att modellen har bättre prestanda i dynamiska grafer än i statiska grafer. Sammantaget är svaret på forskningsfrågan positivt. Det finns dock fortfarande utrymme att förbättra modellens effektivitet och de vägar som genereras av modellen. Detta arbete visar att ett neuronnätverk tränat för att göra lokalt optimala val knappast kan ge globalt optimal lösning. Vi visar också att vår metod, som bara gör lokalt optimala val, kan anpassa sig till dynamiska grafer med begränsad prestandaförlust.