Scalings of first-return time for random walks on generalized and weighted transfractal networks

2019 ◽  
Vol 33 (26) ◽  
pp. 1950306
Author(s):  
Qin Liu ◽  
Weigang Sun ◽  
Suyu Liu
Keyword(s):  
Random Walks ◽  
Large Scale ◽  
Probability Generating Function ◽  
Return Time ◽  
Network Size ◽  
Large Network ◽  
Large Scale Network ◽  
Scale Network ◽  
The Mean ◽  
First Return Time

The first-return time (FRT) is an effective measurement of random walks. Presently, it has attracted considerable attention with a focus on its scalings with regard to network size. In this paper, we propose a family of generalized and weighted transfractal networks and obtain the scalings of the FRT for a prescribed initial hub node. By employing the self-similarity of our networks, we calculate the first and second moments of FRT by the probability generating function and obtain the scalings of the mean and variance of FRT with regard to network size. For a large network, the mean FRT scales with the network size at the sublinear rate. Further, the efficiency of random walks relates strongly with the weight factor. The smaller the weight, the better the efficiency bears. Finally, we show that the variance of FRT decreases with more number of initial nodes, implying that our method is more effective for large-scale network size and the estimation of the mean FRT is more reliable.

scholarly journals Neural Differentiation Dynamics Controlled by Multiple Feedback Loops in a Comprehensive Molecular Interaction Network

Processes ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 166
Author(s):  
Tsuyoshi Iwasaki ◽  
Ryo Takiguchi ◽  
Takumi Hiraiwa ◽  
Takahiro G. Yamada ◽  
Kazuto Yamazaki ◽  
...  
Keyword(s):  
Regulatory Network ◽  
Neural Differentiation ◽  
Large Scale ◽  
Model Simulation ◽  
Interaction Network ◽  
Feedback Loops ◽  
Characteristic Change ◽  
Large Network ◽  
Large Scale Network ◽  
Scale Network

Mathematical model simulation is a useful method for understanding the complex behavior of a living system. The construction of mathematical models using comprehensive information is one of the techniques of model construction. Such a comprehensive knowledge-based network tends to become a large-scale network. As a result, the variation of analyses is limited to a particular kind of analysis because of the size and complexity of the model. To analyze a large-scale regulatory network of neural differentiation, we propose a contractive method that preserves the dynamic behavior of a large network. The method consists of the following two steps: comprehensive network building and network reduction. The reduction phase can extract network loop structures from a large-scale regulatory network, and the subnetworks were combined to preserve the dynamics of the original large-scale network. We confirmed that the extracted loop combination reproduced the known dynamics of HES1 and ASCL1 before and after differentiation, including oscillation and equilibrium of their concentrations. The model also reproduced the effects of the overexpression and knockdown of the Id2 gene. Our model suggests that the characteristic change in HES1 and ASCL1 expression in the large-scale regulatory network is controlled by a combination of four feedback loops, including a large loop, which has not been focused on. The model extracted by our method has the potential to reveal the critical mechanisms of neural differentiation. The method is applicable to other biological events.

scholarly journals Large-Scale Network Plan Optimization Using Improved Particle Swarm Optimization Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Houxian Zhang ◽  
Zhaolan Yang
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Algorithm ◽  
Large Scale ◽  
Particle Swarm Optimization Algorithm ◽  
Particle Swarm ◽  
Large Network ◽  
Swarm Optimization ◽  
Improved Particle Swarm Optimization ◽  
Large Scale Network ◽  
Scale Network

No relevant reports have been reported on the optimization of a large-scale network plan with more than 200 works due to the complexity of the problem and the huge amount of computation. In this paper, an improved particle swarm optimization algorithm via optimization of initial particle swarm (OIPSO) is first explained by the stochastic processes theory. Then two optimization examples are solved using this method which are the optimization of resource-leveling with fixed duration and the optimization of resources constraints with shortest project duration in a large network plan with 223 works. Through these two examples, under the same number of iterations, it is proven that the improved algorithm (OIPSO) can accelerate the optimization speed and improve the optimization effect of particle swarm optimization (PSO).

scholarly journals A Hierarchical and Abstraction-Based Blockchain Model

2019 ◽  
Vol 9 (11) ◽  
pp. 2343 ◽  
Author(s):  
Swagatika Sahoo ◽  
Akshay M. Fajge ◽  
Raju Halder ◽  
Agostino Cortesi
Keyword(s):  
Large Scale ◽  
Abstract Interpretation ◽  
Organizational Structures ◽  
Network Size ◽  
Small Scale ◽  
Time Interval ◽  
Huge Number ◽  
Large Scale Network ◽  
Regular Time ◽  
Scale Network

In the nine years since its launch, amid intense research, scalability is always a serious concern in blockchain, especially in case of large-scale network generating huge number of transaction-records. In this paper, we propose a hierarchical blockchain model characterized by: (1) each level maintains multiple local blockchain networks, (2) each local blockchain records local transactional activities, and (3) partial views (tunable w.r.t. precision) of different subsets of local blockchain-records are maintained in the blockchains at next level of the hierarchy. To meet this objective, we apply abstractions on a set of transaction-records in a regular time interval by following the Abstract Interpretation framework, which provides a tunable precision in various abstract domain and guarantees the soundness of the system. While this model suitably fits to the real-worlds organizational structures, the proposal is powerful enough to scale when large number of nodes participate in a network resulting into an enormous growth of the network-size and the number of transaction-records. We discuss experimental results on a small-scale network with three sub networks at lower-level and by abstracting the transaction-records in the abstract domain of intervals. The results are encouraging and clearly indicate the effectiveness of this approach to control exponential growth of blockchain size w.r.t. the total number of participants in the network.

SCALING PROPERTIES OF FIRST RETURN TIME ON WEIGHTED TRANSFRACTALS (1,3)-FLOWERS

Fractals ◽  
2018 ◽  
Vol 26 (06) ◽  
pp. 1850095 ◽  
Author(s):  
MEIFENG DAI ◽  
HUIJIA CHI ◽  
XIANBIN WU ◽  
YUE ZONG ◽  
WENJING FENG ◽  
...  
Keyword(s):  
Complex Networks ◽  
Real Life ◽  
Probability Generating Function ◽  
Return Time ◽  
Exact Probability ◽  
Scaling Properties ◽  
Mean And Variance ◽  
The Mean ◽  
First Return Time ◽  
The Impact

Complex networks are omnipresent in science and in our real life, and have been the focus of intense interest. It is vital to research the impact of their characters on the dynamic progress occurring on complex networks for weight-dependent walk. In this paper, we first consider the weight-dependent walk on one kind of transfractal (or fractal) which is named the weighted transfractal [Formula: see text]-flowers. And we pay attention to the first return time (FRT). We mainly calculate the mean and variance of FRT for a prescribed hub (i.e. the most concerned nodes) in virtue of exact probability generating function and its properties. Then, we obtain the mean and the secondary moment of the first return time. Finally, using the relationship among the variance, mean and the secondary moment, we obtain the variance of FRT and the scaling properties of the mean and variance of FRT on weighted transfractals [Formula: see text]-flowers.

Large-Scale Network Analysis for Online Social Brand Advertising

MIS Quarterly ◽  
2016 ◽  
Vol 40 (4) ◽  
pp. 849-868 ◽  
Author(s):  
Kunpeng Zhang ◽  
◽  
Siddhartha Bhattacharyya ◽  
Sudha Ram ◽  
◽  
...  
Keyword(s):  
Network Analysis ◽  
Large Scale ◽  
Large Scale Network ◽  
Brand Advertising ◽  
Scale Network
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