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Targeted Image Segmentation Using Graph Methods
Published in Olivier Lézoray, Leo Grady, Image Processing and Analysis with Graphs, 2012
The optimization of fractional values of p was considered in [36, 9], in which this algorithm was termed P-brush and optimized using iterative reweighted least squares. Additionally, it was shown in [36, 9] that the optimal solutions are strongly continuous as p varies smoothly. Consequently, a choice of q finite and p = 1.5 would yield an algorithm which was a hybrid of graph cuts and random walker. It was shown in [18, 36, 9] that if q is finite, lower values of p create solutions with increased shrinking bias, while higher values of p create solutions with increased sensitivity to the locations of user-defined seeds. Furthermore, it was shown that the metrication artifacts are removed for p = 2 (due to the connection with the Laplace equation [9]), but are present for the p = 1 and p = ∞ solutions.
Structure of networks
Published in Karthik Raman, An Introduction to Computational Systems Biology, 2021
A random walk on a graph involves taking a series of random steps, visiting one node after another, traversing the corresponding connecting edges. Starting at a given node in a graph, a random walker will explore all outgoing edges with equal probability. Some interesting centrality measures have been defined based on random walks, such as “random walk betweenness centrality” [16] or “random walk closeness centrality”. As a random walker explores a graph, the (stationary) probability of visiting different nodes is proportional to their accessibility (or importance). For instance, a highly connected node is much more likely to be visited than a node with few edges.
Fractal Kinetics
Published in Mihai V. Putz, New Frontiers in Nanochemistry, 2020
Francesc Mas, Laura Pitulice, Sergio Madurga, Josep Lluís Garcés, Eudald Vilaseca, Adriana Isvoran
In terms of statistical mechanics, it is useful to define the fracton as a random walker that diffuses over a fractal environment (Alexander & Orbach, 1982; Avnir, 1989), which has a spectral dimension, ds, related to the probability of the random walker to come back to its initial position, and it is related to the fractal dimension of the random walk as follows: ()ds=2dfdω
Priority analysis of port investment along the 21st-Century Maritime Silk Road region: the case of Southeast Asia
Published in Maritime Policy & Management, 2022
Jianfeng Zheng, Lingxiao Yang, Wei Li, Xiaowen Fu, Daqing Li
Given a simple network , the random walk method can be described by using a Markov chain, which determines the sequence of nodes visited by each random walker. For any random walker , this process can be described by a Markov transition matrix , where its component represents the probability that random walker staying at node will move to node in the next time step. Different from the previous random walk methods (Tong, Faloutsos, and Pan 2008; Liu and Lü 2010; Lü and Zhou 2011; Mantrach et al. 2011; Masuda, Porter, and Lambiotte 2017; Song et al. 2019; Curado 2020), we generate an OD pair for each random walker, according to the port attraction evaluation index. The details will be shown in the procedure of our random walk method. We further consider that each random walker staying at the current node will move to one of its neighbor nodes with a probability proportional to the shortest distance between the neighbor node and the destination node. Let denote the destination port of random walker . If , we have , otherwise is defined as follows: