Uncovering the impact of delay phenomenon on random walks in a family of weighted m-triangulation networks

Uncovering the impact of special phenomena on dynamical processes in more distinct weighted network models is still needed. In this paper, we investigate the impact of delay phenomenon on random walk by introducing delayed random walk into a family of weighted m-triangulation networks. Specifically, we introduce delayed random walk into the networks. Then one and three traps are deployed, respectively, on the networks in two rounds of investigation. In both rounds of investigation, average trapping time (ATT) is applied to measure trapping efficiency and derived analytically by harnessing iteration rule of the networks. The analytical solutions of ATT obtained in both investigations show that ATT increases sub-linearity with the size of the network no matter what value the parameter [Formula: see text] manipulating delayed random walk takes. But [Formula: see text] can quantitatively change both its leading scaling and prefactor. So, introduction of delay phenomenon can control trapping efficiency quantitatively. Besides, parameters [Formula: see text] and [Formula: see text] governing networks’ evolution quantitatively impact both the prefactor and leading scaling of ATT simultaneously. In summary, this work may provide incremental insight into understanding the impact of observed phenomena on special trapping process and general random walks in complex systems.

An elementary approach to subdiffusion

We consider a basic one-dimensional model which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of a per-site trapping time. This models a discrete subordinated random walk, closely related to the continuous time random walks widely studied in the literature. The model we consider lends itself to a detailed elementary treatment, based on the study of recurrence relation for the time-[Formula: see text] dispersion of the process, making it possible to study deviations from normality due to finite time effects.

Dual-Task Gait Stability after Concussion and Subsequent Injury: An Exploratory Investigation

Persistent gait alterations can occur after concussion and may underlie future musculoskeletal injury risk. We compared dual-task gait stability measures among adolescents who did/did not sustain a subsequent injury post-concussion, and uninjured controls. Forty-seven athletes completed a dual-task gait evaluation. One year later, they reported sport-related injuries and sport participation volumes. There were three groups: concussion participants who sustained a sport-related injury (n = 8; age =15.4 ± 3.5 years; 63% female), concussion participants who did not sustain a sport-related injury (n = 24; 14.0 ± 2.6 years; 46% female), and controls (n = 15; 14.2 ± 1.9 years; 53% female). Using cross-recurrence quantification, we quantified dual-task gait stability using diagonal line length, trapping time, percent determinism, and laminarity. The three groups reported similar levels of sports participation (11.8 ± 5.8 vs. 8.6 ± 4.4 vs. 10.9 ± 4.3 hours/week; p = 0.37). The concussion/subsequent injury group walked slower (0.76 ± 0.14 vs. 0.65 ± 0.13 m/s; p = 0.008) and demonstrated higher diagonal line length (0.67 ± 0.08 vs. 0.58 ± 0.05; p = 0.02) and trapping time (5.3 ± 1.5 vs. 3.8 ± 0.6; p = 0.006) than uninjured controls. Dual-task diagonal line length (hazard ratio =1.95, 95% CI = 1.05–3.60), trapping time (hazard ratio = 1.66, 95% CI = 1.09–2.52), and walking speed (hazard ratio = 0.01, 95% CI = 0.00–0.51) were associated with subsequent injury. Dual-task gait stability measures can identify altered movement that persists despite clinical concussion recovery and is associated with future injury risk.

Delayed random walk on deterministic weighted scale-free small-world network with a deep trap

How to effectively control the trapping process in complex systems is of great importance in the study of trapping problem. Recently, the approach of delayed random walk has been introduced into several deterministic network models to steer trapping process. However, exploring delayed random walk on pseudo-fractal web with the co-evolution of topology and weight has remained out of reach. In this paper, we employ delayed random walk to guide trapping process on a salient deterministic weighted scale-free small-world network with the co-evolution of topology and weight. In greater detail, we first place a deep trap at one of initial nodes of the network. Then, a tunable parameter [Formula: see text] is introduced to modulate the transition probability of random walk and dominate the trapping process. Subsequently, trapping efficiency is used as readout of trapping process and average trapping time is employed to measure trapping efficiency. Finally, the closed form solution of average trapping time (ATT) is deduced analytically, which agrees with corresponding numerical solution. The analytical solution of ATT shows that the delayed parameter [Formula: see text] only modifies the prefactor of ATT, and keeps the leading scaling unchanged. In other words, ATT grows sublinearly with network size, whatever values [Formula: see text] takes. In summary, the work may serves as one piece of clues for modulating trapping process toward desired efficiency on more general deterministic networks.

Weighted trapping time of weighted directed treelike network

With the deepening of research on complex networks, many properties of complex networks are gradually studied, for example, the mean first-passage times, the average receive times and the trapping times. In this paper, we further study the average trapping time of the weighted directed treelike network constructed by an iterative way. Firstly, we introduce our model inspired by trade network, each edge [Formula: see text] in undirected network is replaced by two directed edges with weights [Formula: see text] and [Formula: see text]. Then, the trap located at central node, we calculate the weighted directed trapping time (WDTT) and the average weighted directed trapping time (AWDTT). Remarkably, the WDTT has different formulas for even generations and odd generations. Finally, we analyze different cases for weight factors of weighted directed treelike network.