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Academic literature on the topic 'Forward Reachable Sets'

Author: Grafiati
Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Forward Reachable Sets"

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ARMBRUSTER, BENJAMIN, LI WANG, and MARTINA MORRIS. "Forward reachable sets: Analytically derived properties of connected components for dynamic networks." Network Science 5, no. 3 (June 29, 2017): 328–54. http://dx.doi.org/10.1017/nws.2017.10.

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AbstractFormal analysis of the emergent structural properties of dynamic networks is largely uncharted territory. We focus here on the properties of forward reachable sets (FRS) as a function of the underlying degree distribution and edge duration. FRS are defined as the set of nodes that can be reached from an initial seed via a path of temporally ordered edges; a natural extension of connected component measures to dynamic networks. Working in a stochastic framework, we derive closed-form expressions for the mean and variance of the exponential growth rate of the FRS for temporal networks with both edge and node dynamics. For networks with node dynamics, we calculate thresholds for the growth of the FRS. The effects of finite population size are explored via simulation and approximation. We examine how these properties vary by edge duration and different cross-sectional degree distributions that characterize a range of scientifically interesting normative outcomes (Poisson and Bernoulli). The size of the forward reachable set gives an upper bound for the epidemic size in disease transmission network models, relating this work to epidemic modeling (Ferguson, 2000; Eames, 2004).
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Jones, Morgan, and Matthew M. Peet. "Using SOS and Sublevel Set Volume Minimization for Estimation of Forward Reachable Sets." IFAC-PapersOnLine 52, no. 16 (2019): 484–89. http://dx.doi.org/10.1016/j.ifacol.2019.12.008.

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Sun, Gengxin, and Chih-Cheng Chen. "Influence Maximization Algorithm Based on Reverse Reachable Set." Mathematical Problems in Engineering 2021 (July 27, 2021): 1–12. http://dx.doi.org/10.1155/2021/5535843.

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Most of the existing influence maximization algorithms are not suitable for large-scale social networks due to their high time complexity or limited influence propagation range. Therefore, a D-RIS (dynamic-reverse reachable set) influence maximization algorithm is proposed based on the independent cascade model and combined with the reverse reachable set sampling. Under the premise that the influence propagation function satisfies monotonicity and submodularity, the D-RIS algorithm uses an automatic debugging method to determine the critical value of the number of reverse reachable sets, which not only obtains a better influence propagation range but also greatly reduces the time complexity. The experimental results on the two real datasets of Slashdot and Epinions show that D-RIS algorithm is close to the CELF (cost-effective lazy-forward) algorithm and higher than RIS algorithm, HighDegree algorithm, LIR algorithm, and pBmH (population-based metaheuristics) algorithm in influence propagation range. At the same time, it is significantly better than the CELF algorithm and RIS algorithm in running time, which indicates that D-RIS algorithm is more suitable for large-scale social network.
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Edelkamp, Stefan, Peter Kissmann, and Martha Rohte. "Symbolic and Explicit Search Hybrid through Perfect Hash Functions — A Case Study in Connect Four." Proceedings of the International Conference on Automated Planning and Scheduling 24 (May 10, 2014): 101–10. http://dx.doi.org/10.1609/icaps.v24i1.13637.

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This work combines recent advances in AI planning under memory limitation, namely bitvector and symbolic search. Bitvector search assumes a bijective mapping between state and memory addresses, while symbolic search compactly represents state sets. The memory requirements vary with the structure of the problem to be solved. The integration of the two algorithms into one hybrid algorithm for strongly solving general games initiates a BDD-based solving algorithm, which consists of a forward computation of the reachable state set, possibly followed by a layered backward retrograde analysis. If the main memory becomes exhausted, it switches to explicit-state two-bit retrograde search. We use the classical game of Connect Four as a case study, and solve some instances of the problem space-efficiently with the proposed hybrid search algorithm.
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Zhang, Ke, Liwen Huang, Yixiong He, Liang Zhang, Weiguo Huang, Cheng Xie, and Guozhu Hao. "Collision Avoidance Method for Autonomous Ships Based on Modified Velocity Obstacle and Collision Risk Index." Journal of Advanced Transportation 2022 (October 8, 2022): 1–22. http://dx.doi.org/10.1155/2022/1534815.

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A novel real-time collision avoidance method for autonomous ships based on modified velocity obstacle (VO) algorithm and grey cloud model is proposed. A typical VO algorithm is used to judge whether there is a collision risk for ships in the potential collision area (PCA). Then, in order to quantify the collision risk of ships in different encounter situations within the PCA and trigger a prompt warning of danger of collision, this study sets up a novel collision risk assessment method based on asymmetric grey cloud model (AGC). It can effectively consider the randomness, ambiguity, and incompleteness of the information in the ship collision risk evaluation process. Moreover, reachable collision-free velocity sets under different encounter situations and optimal steering angle model are constructed. A real-time collision avoidance method based on modified VO algorithm and manoeuvring motion characteristics of vessels is put forward. In this model, various constraints are considered including the International Regulations for Preventing Collisions at Sea (COLREGs), ship manoeuvrability, and ordinary practice of seaman. Finally, several case studies are carried out to verify the performance and reliability of the collision avoidance model. The results show that the proposed method can not only effectively identify and quantify the collision risk in real-time but also offer proper collision-free solutions for autonomous ships.
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Fisher, Colby K., Ming Pan, and Eric F. Wood. "Spatiotemporal assimilation–interpolation of discharge records through inverse streamflow routing." Hydrology and Earth System Sciences 24, no. 1 (January 21, 2020): 293–305. http://dx.doi.org/10.5194/hess-24-293-2020.

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Abstract. Poorly monitored river flows in many regions of the world have been hindering our ability to accurately estimate global water budgets as well as the variability of the global water cycle. In situ gauging sites, as well as a number of satellite-based systems, make observations of river discharge throughout the globe; however, these observations are often sparse due to, for example, the sampling frequencies of sensors or a lack of reporting. Recently, efforts have been made to develop methods to integrate these discrete observations to gain a better understanding of the underlying processes. This paper presents an application of a fixed interval Kalman smoother-based model, called inverse streamflow routing (ISR), to generate spatially and temporally continuous river discharge fields from discrete observations. The method propagates the observed information across all reachable parts of the river network (up/downstream from gauging point) and all reachable times (before/after observation time) using a two-sweep procedure that first propagates information backward in time to the furthest upstream locations (inverse routing) and then propagates it forward in time to the furthest downstream locations (forward routing). The ISR methodology advances prediction of streamflow in ungauged basins by accounting for a physical representation of the river system that is not generally handled explicitly in more-commonly applied statistically based models. The key advantages of this approach are that it (1) maintains all the physical consistencies embodied by a diffusive wave routing model (flow confluence relationships on the river network and the resulting mass balance, wave velocity, and diffusivity), (2) updates the lateral influx (runoff) at the pixel level (furthest upstream) to guarantee exhaustive propagation of observed information, and (3) works both with a first guess of initial river discharge conditions from a routing model (assimilation) and without a first guess (pure interpolation of observations). Two sets of experiments are carried out under idealized conditions and under real-world conditions provided by United States Geological Survey (USGS) observations. Results show that the method can effectively reproduce the spatial and temporal dynamics of river discharge in each of the experiments presented. The performance is driven by the density of the gauge network as well as the quality of the data being assimilated. We find that when assimilating the actual USGS observations, the performance decreases relative to our idealized scenario; however, we are still able to produce an improved discharge product at each validation site. With further testing, as well as global application, ISR may prove to be a useful method for extending our current network of global river discharge observations.
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Trinh, H., Phan T. Nam, Pubudu N. Pathirana, and H. P. Le. "On backwards and forwards reachable sets bounding for perturbed time-delay systems." Applied Mathematics and Computation 269 (October 2015): 664–73. http://dx.doi.org/10.1016/j.amc.2015.07.116.

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Maclean, Craig, and James D. Biggs. "Path planning for simple wheeled robots: sub-Riemannian and elastic curves on SE(2)." Robotica 31, no. 8 (June 7, 2013): 1285–97. http://dx.doi.org/10.1017/s0263574713000519.

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SUMMARYThis paper presents a motion planning method for a simple wheeled robot in two cases: (i) where translational and rotational speeds are arbitrary, and (ii) where the robot is constrained to move forwards at unit speed. The motions are generated by formulating a constrained optimal control problem on the Special Euclidean group SE(2). An application of Pontryagin's maximum principle for arbitrary speeds yields an optimal Hamiltonian which is completely integrable in terms of Jacobi elliptic functions. In the unit speed case, the rotational velocity is described in terms of elliptic integrals, and the expression for the position is reduced to quadratures. Reachable sets are defined in the arbitrary speed case, and a numerical plot of the time-limited reachable sets is presented for the unit speed case. The resulting analytical functions for the position and orientation of the robot can be parametrically optimised to match prescribed target states within the reachable sets. The method is shown to be easily adapted to obstacle avoidance for static obstacles in a known environment.
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Guo, Qintian, Sibo Wang, Zhewei Wei, Wenqing Lin, and Jing Tang. "Influence Maximization Revisited: Efficient Sampling with Bound Tightened." ACM Transactions on Database Systems, May 19, 2022. http://dx.doi.org/10.1145/3533817.

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Given a social network G with n nodes and m edges, a positive integer k , and a cascade model \(\mathcal {C} \) , the influence maximization (IM) problem asks for k nodes in G such that the expected number of nodes influenced by the k nodes under cascade model \(\mathcal {C} \) is maximized. The state-of-the-art approximate solutions run in O ( k ( n + m )log n /ϵ 2 ) expected time while returning a (1 − 1/ e − ϵ) approximate solution with at least 1 − 1/ n probability. A key phase of these IM algorithms is the random reverse reachable (RR) set generation, and this phase significantly affects the efficiency and scalability of the state-of-the-art IM algorithms. In this paper, we present a study on this key phase and propose an efficient random RR set generation algorithm under IC model. With the new algorithm, we show that the expected running time of existing IM algorithms under IC model can be improved to O ( k · n log n /ϵ 2 ), when for any node v , the total weight of its incoming edges is no larger than a constant. For general IC model where the weights are skewed, we present a sampling algorithm SKIP. To the best of our knowledge, it is the first index-free algorithm that achieves the optimal time complexity of the sorted subset sampling problem. Moreover, existing approximate IM algorithms suffer from scalability issues in high influence networks where the size of random RR sets is usually quite large. We tackle this challenging issue by reducing the average size of random RR sets without sacrificing the approximation guarantee. The proposed solution is orders of magnitude faster than states of the art as shown in our experiment. Besides, we investigate the issues of forward propagation and derive its time complexity with our proposed subset sampling techniques. We also present a heuristic condition to indicate when the forward propagation approach should be utilized to estimate the expected influence of a given seed set.
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Köcher, Chris. "Reachability Problems on Reliable and Lossy Queue Automata." Theory of Computing Systems, June 19, 2021. http://dx.doi.org/10.1007/s00224-021-10031-2.

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AbstractWe study the reachability problem for queue automata and lossy queue automata. Concretely, we consider the set of queue contents which are forwards resp. backwards reachable from a given set of queue contents. Here, we prove the preservation of regularity if the queue automaton loops through some special sets of transformation sequences. This is a generalization of the results by Boigelot et al. and Abdulla et al. regarding queue automata looping through a single sequence of transformations. We also prove that our construction is possible in polynomial time.
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Dissertations / Theses on the topic "Forward Reachable Sets"

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Chung, Chern Ferng Mechanical &amp Manufacturing Engineering Faculty of Engineering UNSW. "Reachable sets analysis in the cooperative control of pursuer vehicles." 2008. http://handle.unsw.edu.au/1959.4/41525.

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This thesis is concerned with the Pursuit-and-Evasion (PE) problem where the pursuer aims to minimize the time to capture the evader while the evader tries to prevent capture. In the problem, the evader has two advantages: a higher manoeuvrability and that the pursuer is uncertain about the evader??s state. Cooperation among multiple pursuer vehicles can thus be used to overcome the evader??s advantages. The focus here is on the formulation and development of frameworks and algorithms for cooperation amongst pursuers, aiming at feasible implementation on real and autonomous vehicles. The thesis is split into Parts I and II. Part I considers the problem of capturing an evader of higher manoeuvrability in a deterministic PE game. The approach is the employment of Forward Reachable Set (FRS) analysis in the pursuers?? control. The analysis considers the coverage of the evader??s FRS, which is the set of reachable states at a future time, with the pursuer??s FRS and assumes that the chance of capturing the evader is dependent on the degree of the coverage. Using the union of multiple pursuers?? FRSs intuitively leads to more evader FRS coverage and this forms the mechanism of cooperation. A framework for cooperative control based on the FRS coverage, or FRS-based control, is proposed. Two control algorithms were developed within this framework. Part II additionally introduces the problem of evader state uncertainty due to noise and limited field-of-view of the pursuers?? sensors. A search-and-capture (SAC) problem is the result and a hybrid architecture, which includes multi-sensor estimation using the Particle Filter as well as FRS-based control, is proposed to accomplish the SAC task. The two control algorithms in Part I were tested in simulations against an optimal guidance algorithm. The results show that both algorithms yield a better performance in terms of time and miss distance. The results in Part II demonstrate the effectiveness of the hybrid architecture for the SAC task. The proposed frameworks and algorithms provide insights for the development of effective and more efficient control of pursuer vehicles and can be useful in the practical applications such as defence systems and civil law enforcement.
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Book chapters on the topic "Forward Reachable Sets"

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Bhattacharya, Somak, Samresh Malhotra, and S. K. Ghosh. "An Attack Graph Based Approach for Threat Identification of an Enterprise Network." In Cyber Security and Global Information Assurance, 23–47. IGI Global, 2009. http://dx.doi.org/10.4018/978-1-60566-326-5.ch002.

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As networks continue to grow in size and complexity, automatic assessment of the security vulnerability becomes increasingly important. The typical means by which an attacker breaks into a network is through a series of exploits, where each exploit in the series satisfies the pre-condition for subsequent exploits and makes a causal relationship among them. Such a series of exploits constitutes an attack path where the set of all possible attack paths form an attack graph. Attack graphs reveal the threat by enumerating all possible sequences of exploits that can be followed to compromise a given critical resource. The contribution of this chapter is to identify the most probable attack path based on the attack surface measures of the individual hosts for a given network and also identify the minimum possible network securing options for a given attack graph in an automated fashion. The identified network securing options are exhaustive and the proposed approach aims at detecting cycles in forward reachable attack graphs. As a whole, the chapter deals with identification of probable attack path and risk mitigation which may facilitate in improving the overall security of an enterprise network.
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Conference papers on the topic "Forward Reachable Sets"

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Devonport, Alex, and Murat Arcak. "Data-driven estimation of forward reachable sets." In CPS-IoT Week '21: Cyber-Physical Systems and Internet of Things Week 2021. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3457335.3461707.

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El-Guindy, Ahmed, Dongkun Han, and Matthias Althoff. "Estimating the region of attraction via forward reachable sets." In 2017 American Control Conference (ACC). IEEE, 2017. http://dx.doi.org/10.23919/acc.2017.7963126.

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Shih, Jennifer C. "Predicting Stochastic Human Forward Reachable Sets Based on Learned Human Behavior." In 2019 American Control Conference (ACC). IEEE, 2019. http://dx.doi.org/10.23919/acc.2019.8814396.

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Ruan, Wenjie, Xiaowei Huang, and Marta Kwiatkowska. "Reachability Analysis of Deep Neural Networks with Provable Guarantees." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/368.

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Verifying correctness for deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-continuous function over its outputs computes the lower and upper bound on the function values. Because the network and the function are Lipschitz continuous, all values in the interval between the lower and upper bound are reachable. We show how to obtain the safety verification problem, the output range analysis problem and a robustness measure by instantiating the reachability problem. We present a novel algorithm based on adaptive nested optimisation to solve the reachability problem. The technique has been implemented and evaluated on a range of DNNs, demonstrating its efficiency, scalability and ability to handle a broader class of networks than state-of-the-art verification approaches.
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Kousik, Shreyas, Sean Vaskov, Matthew Johnson-Roberson, and Ram Vasudevan. "Safe Trajectory Synthesis for Autonomous Driving in Unforeseen Environments." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5361.

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Path planning for autonomous vehicles in arbitrary environments requires a guarantee of safety, but this can be impractical to ensure in real-time when the vehicle is described with a high-fidelity model. To address this problem, this paper develops a method to perform trajectory design by considering a low-fidelity model that accounts for model mismatch. The presented method begins by computing a conservative Forward Reachable Set (FRS) of a high-fidelity model’s trajectories produced when tracking trajectories of a low-fidelity model over a finite time horizon. At runtime, the vehicle intersects this FRS with obstacles in the environment to eliminate trajectories that can lead to a collision, then selects an optimal plan from the remaining safe set. By bounding the time for this set intersection and subsequent path selection, this paper proves a lower bound for the FRS time horizon and sensing horizon to guarantee safety. This method is demonstrated in simulation using a kinematic Dubin’s car as the low-fidelity model and a dynamic unicycle as the high-fidelity model.
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Tisdale, John, and J. Karl Hedrick. "A UAV Trajectory Planning Algorithm for Simultaneous Search and Track." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81100.

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This paper considers trajectories for an unmanned aerial vehicle (UAV) that must search an area while tracking a target. The UAV has a constrained turn rate and a constant velocity; it is assumed that there are certain areas of interest that have a higher search value than others. An algorithm is presented that seeks to maximize the value of the area searched while still maintaining the track. The problem is discretized in both time and the control; the motion of the UAV is constrained to the reachability graph, a subset of the forward reachable set. At each revisit, the target path is estimated for the next revisit. A heuristic method is used to determine the best UAV path, because the target path is not known a priori. Feasible paths are found by examining the terminating vertices of the reachability graph. A cooperative implementation, for a team of UAVs patrolling the same region, is developed. Simulation indicates the feasibility of the method for a real-time implementation. Trajectories for example scenarios are presented and discussed.
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