A Method for Geodesic Distance on Subdivision of Trees With Arbitrary Orders and Their Applications

Ma, Fei; Wang, Ping; Luo, Xudong

doi:10.1109/tkde.2020.3014191

Cited by 15 publications

(7 citation statements)

References 43 publications

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“…More generally, determining structural parameters on networked models is useful to understand underlying structure on networks. As will see in the following, our tree network T t indeed shows some characteristics associated with both degree distribution and diameter that can not be found in some previous tree models [23]- [30].…”

Section: Two Significant Topological Parameterssupporting

confidence: 65%

“…Although they have scale-free feature, the powerlaw exponents fall into two distinct regions. As pointed out in our prior work [30], if one only inserts new vertices on existing edge of tree, the mean hitting time for the end tree can asymptotically reach to the theoretical upper bound in the large graph size limit. On the contrary, connecting new vertices to each vertex of tree directly at each time step leads to a tree whose mean hitting time gradually tends to the opposite direction, i.e., to the theoretical lower bound.…”

Section: Discussionmentioning

confidence: 72%

“…As known, there are various kinds of networked models proposed in the last years, such as Apollonian Networks [15], Pseudofractal scale-free web [16], Hierarchical networks [17] and flower graphs [18]. Tree network, as the simplest connected networked model, has widely studied in various disciplines [19]- [30]. For instance, the scale-free BA-tree is immediately obtained by setting the number m of edges originating from each newly added vertex in BA-model to 1 [5].…”

Section: Introductionmentioning

confidence: 99%

“…In [22], Gabel et al discussed growth tree networks and studied the associated structural parameters. In addition, some trees with deterministic structure have also been studied in detail, such as, deterministic uniform recursive tree [23], growing treelike networks [24], Fibonacci treelike models [25], Vicsek fractal [26]- [27] and T-graph [28]- [30]. In this paper, we will introduce a class of tree networks sharing interesting features as will be shown later.…”

Section: Introductionmentioning

confidence: 99%

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Scale-free tree network with an ultra-large diameter

Ma,

Wang

2021

Preprint

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Scale-free networks are prevalently observed in a great variety of complex systems, which triggers various researches relevant to networked models of such type. In this work, we propose a family of growth tree networks T t , which turn out to be scale-free, in an iterative manner. As opposed to most of published tree models with scale-free feature, our tree networks have the power-law exponent γ = 1 + ln 5/ ln 2 that is obviously larger than 3. At the same time, "small-world" property can not be found particularly because models T t have an ultra-large diameter D t , i.e., D t ∼ |T t | ln 3/ ln 5 where |T t | represents vertex number. In addition, we also study random walks on tree networks T t and derive exact solution to mean hitting time H t . The results suggest that analytic formula for quantity H t as a function of vertex number T t has a power-law form, i.e., H t ∼ |T t | 1+ln 3/ ln 5 , a characteristic that is rarely encountered in the realm of scale-free tree networks. Lastly, we execute extensive experimental simulations, and find that empirical analysis is in strong agreement with theoretical results.

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Section: Two Significant Topological Parameterssupporting

confidence: 65%

Section: Discussionmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scale-free tree network with an ultra-large diameter

Ma,

Wang

2021

Preprint

Self Cite

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“…The geodesic distance, the shortest path length, has proven to be a useful metric for a great variety of applications in computer vision, signal, and shape analysis. 48,49 Therefore, as shown in Figure 5, we align and compute the distance between the droplet and the pendulum motion for both the phase difference, dx, and the amplitude of signal difference, dy.…”

Section: ■ Modelingmentioning

confidence: 99%

Describing Droplet Motion on Surface-Textured Ratchet Tracks with an Inverted Double Pendulum Model

Naji

Kirici²,

Javili

et al. 2021

Langmuir

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We describe the motion of a droplet on a textured ratchet track using a nonlinear resonator model. A textured ratchet track is composed of a semicircular pillar array that induces a net surface tension local gradient on a droplet placed on it. When a vertical vibration is applied, hysteresis is overcome, and the droplet moves toward the local lower energy barrier; however, due to the repetitive structure of texture, it keeps moving until the end of the track. The droplet motion depends on the amplitude and frequency of the vertical oscillation, and this dependence is nonlinear. Therefore, finding a fully analytic solution to represent this motion is not trivial. Consequently, the droplet motion remains poorly understood. In this study, we elaborate on the utility of a double pendulum as a basis for modeling the droplet motion on surfaces inducing asymmetric force. Similar to the droplet motion, resonators, such as a double pendulum, are simple, yet nonlinear systems. Moreover, an inverted double pendulum motion has key characteristics such as the two-phase motion and the double peak motion, which are also observed in the droplet motion. We use various data-processing methods to highlight the similarity between these two systems both qualitatively and quantitatively. After establishing this comparison, we propose a model that utilizes an inverted double pendulum mounted on a moving cart to successfully simulate the motion of a droplet on a ratchet track. This methodology will lead to the development of an accurate droplet-motion modeling approach, and we believe that it will be useful to understand droplet dynamics more deeply.

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Understanding influence of fractal generative manner on structural properties of tree networks

Ma,

Wang

2024

Chaos, Solitons & Fractals

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A Method for Geodesic Distance on Subdivision of Trees With Arbitrary Orders and Their Applications

Cited by 15 publications

References 43 publications

Scale-free tree network with an ultra-large diameter

Scale-free tree network with an ultra-large diameter

Describing Droplet Motion on Surface-Textured Ratchet Tracks with an Inverted Double Pendulum Model

Understanding influence of fractal generative manner on structural properties of tree networks

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