Information spreading on metapopulation networks with heterogeneous contacting

2021 ◽  
Author(s):  
Yanyi Nie ◽  
Liming Pan ◽  
Tao Lin ◽  
Wei Wang
Keyword(s):  
Normal Distribution ◽  
Exponential Distribution ◽  
Power Law ◽  
Social Systems ◽  
Real Data ◽  
Power Law Distribution ◽  
Specific Distribution ◽  
Mean And Variance ◽  
Information Spreading ◽  
Individual Contact

Extensive real-data reveals that individuals exhibit heterogeneous contacting frequency in social systems. We propose a mathematical model to investigate the effects of heterogeneous contacting for information spreading in metapopulation networks. In the proposed model, we assume the number of contacting (NOC) distribution follows a specific distribution, including the normal, exponential, and power-law distributions. We utilize the Markov chain method to study the information spreading dynamics and find that mean and variance display no significant effect on the outbreak threshold for all the considered distributions. Under the same values of NOC distribution’s mean and variance, the information prevalence is largest when the distribution of NOC follows the normal distribution and second-largest for the exponential distribution, the smallest for the power-law distribution. When the distribution of NOC obeys the normal distribution, experimental results show that the information prevalence will decrease with individual contact ability heterogeneity. We observe similar phenomena when the distribution of NOC follows a power-law and exponential distribution. Furthermore, a larger mean of individual contact capacity distribution will result in higher information prevalence.

Web Usage Mining in Search Engines

Web Mining ◽  
2011 ◽  
pp. 307-321 ◽  
Author(s):  
Ricardo Baeza-Yates
Keyword(s):  
User Interface ◽  
Search Engine ◽  
Power Law ◽  
Search Engines ◽  
Real Data ◽  
Web Usage Mining ◽  
Power Law Distribution ◽  
Main Ideas ◽  
Answer Ranking ◽  
Navigation Information

Search engine logs not only keep navigation information, but also the queries made by their users. In particular, queries to a search engine follow a power-law distribution, which is far from uniform. Queries and related clicks can be used to improve the search engine itself in different aspects: user interface, index performance, and answer ranking. In this chapter we present some of the main ideas proposed in query mining and we show a few examples based on real data from a search engine focused on the Chilean Web.

scholarly journals Regression to the tail: Why the Olympics blow up

2020 ◽  
pp. 0308518X2095872
Author(s):  
Bent Flyvbjerg ◽  
Alexander Budzier ◽  
Daniel Lunn
Keyword(s):  
Power Law ◽  
Blow Up ◽  
Extreme Event ◽  
Good Practice ◽  
Cost Overrun ◽  
Power Law Distribution ◽  
Tight Coupling ◽  
Mean And Variance ◽  
Generative Mechanism ◽  
The Cost

The Olympic Games are the largest, highest-profile, and most expensive megaevent hosted by cities and nations. Average sports-related costs of hosting are $12.0 billion. Non-sports-related costs are typically several times that. Every Olympics since 1960 has run over budget, at an average of 172 percent in real terms, the highest overrun on record for any type of megaproject. The paper tests theoretical statistical distributions against empirical data for the costs of the Games, in order to explain the cost risks faced by host cities and nations. It is documented, for the first time, that cost and cost overrun for the Games follow a power-law distribution. Olympic costs are subject to infinite mean and variance, with dire consequences for predictability and planning. We name this phenomenon "regression to the tail": it is only a matter of time until a new extreme event occurs, with an overrun larger than the largest so far, and thus more disruptive and less plannable. The generative mechanism for the Olympic power law is identified as strong convexity prompted by six causal drivers: irreversibility, fixed deadlines, the Blank Check Syndrome, tight coupling, long planning horizons, and an Eternal Beginner Syndrome. The power law explains why the Games are so difficult to plan and manage successfully, and why cities and nations should think twice before hosting. Based on the power law, two heuristics are identified for better decision making on hosting. Finally, the paper develops measures for good practice in planning and managing the Games, including how to mitigate the extreme risks of the Olympic power law.

scholarly journals Probability Density Functions for Prediction Using Normal and Exponential Distribution

2021 ◽  
pp. 40-52
Author(s):  
Kunio Takezawa
Keyword(s):  
Probability Density Function ◽  
Normal Distribution ◽  
Probability Density ◽  
Density Function ◽  
Exponential Distribution ◽  
Predictive Ability ◽  
Probability Density Functions ◽  
Density Functions ◽  
Specific Distribution ◽  
Using Data

When data are found to be realizations of a specific distribution, constructing the probability density function based on this distribution may not lead to the best prediction result. In this study, numerical simulations are conducted using data that follow a normal distribution, and we examine whether probability density functions that have shapes different from that of the normal distribution can yield larger log-likelihoods than the normal distribution in the light of future data. The results indicate that fitting realizations of the normal distribution to a different probability density function produces better results from the perspective of predictive ability. Similarly, a set of simulations using the exponential distribution shows that better predictions are obtained when the corresponding realizations are fitted to a probability density function that is slightly different from the exponential distribution. These observations demonstrate that when the form of the probability density function that generates the data is known, the use of another form of the probability density function may achieve more desirable results from the standpoint of prediction.

Mining Information Spreading Based on Users' Retweet Behavior in Twitter

2013 ◽  
Vol 380-384 ◽  
pp. 2866-2870 ◽  
Author(s):  
Rong Ze Xia ◽  
Yan Jia ◽  
Wang Qun Lin ◽  
Hu Li
Keyword(s):  
Social Networks ◽  
Power Law ◽  
Power Law Distribution ◽  
Spreading Process ◽  
Spreading Model ◽  
The World ◽  
Information Spread ◽  
Information Spreading

Twitter is one of the largest social networks in the world. People could share contents on it. When we interact with each other, the information spreads. And its users retweet behavior that makes information spread so fast. So there comes an important question: Whats about users retweet behavior? Could we simulate information spreading in twitter by retweeting behavior? We crawl twitter and mine information spreading based on users retweet behavior in it. Through our dateset, we verify the power-law distribution of the retweet-width and retweet-depth. At the same time, we study the correlation between retweet-width and retweet-depth. Finally, we propose an information spreading model to simulate the information spreading process in twitter and get a good result.

scholarly journals ENTROPY-GROWTH-BASED MODEL OF EMOTIONALLY CHARGED ONLINE DIALOGUES

2013 ◽  
Vol 16 (04n05) ◽  
pp. 1350026 ◽  
Author(s):  
JULIAN SIENKIEWICZ ◽  
MARCIN SKOWRON ◽  
GEORGIOS PALTOGLOU ◽  
JANUSZ A. HOŁYST
Keyword(s):  
Probability Distribution ◽  
Numerical Simulations ◽  
Power Law ◽  
Driving Force ◽  
Real Data ◽  
Massive Data ◽  
Power Law Distribution ◽  
Internet Relay Chat ◽  
Entropy Growth ◽  
Good Agreement

We analyze emotionally annotated massive data from Internet relay chat (IRC) as well as from BBC forum website and model the dialogues between chat participants by assuming that the driving force for the discussion is the entropy growth of emotional probability distribution. This process is claimed to be responsible for a power-law distribution of the discussion lengths observed in the dialogues. We perform numerical simulations based on the noticed phenomenon obtaining a good agreement with the real data. Finally, we propose a method to artificially prolong the duration of the discussion that relies on the entropy of emotional probability distribution.

scholarly journals Transient and slim versus recurrent and fat: Random walks and the trees they grow

2019 ◽  
Vol 56 (3) ◽  
pp. 769-786
Author(s):  
Giulio Iacobelli ◽  
Daniel R. Figueiredo ◽  
Giovanni Neglia
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Exponential Distribution ◽  
Power Law ◽  
Random Network ◽  
Power Law Distribution ◽  
Current Position ◽  
Network Growth ◽  
Model Driven ◽  
Bounded Below

AbstractThe no restart random walk (NRRW) is a random network growth model driven by a random walk that builds the graph while moving on it, adding and connecting a new leaf node to the current position of the walker every s steps. We show a fundamental dichotomy in NRRW with respect to the parity of s: for ${s}=1$ we prove that the random walk is transient and non-leaf nodes have degrees bounded above by an exponential distribution; for s even we prove that the random walk is recurrent and non-leaf nodes have degrees bounded below by a power law distribution. These theoretical findings highlight and confirm the diverse and rich behaviour of NRRW observed empirically.

scholarly journals POWER-LAW DISTRIBUTIONS BASED ON EXPONENTIAL DISTRIBUTIONS: LATENT SCALING, SPURIOUS ZIPF'S LAW, AND FRACTAL RABBITS

Fractals ◽  
2015 ◽  
Vol 23 (02) ◽  
pp. 1550009 ◽  
Author(s):  
YANGUANG CHEN
Keyword(s):  
Exponential Distribution ◽  
Power Law ◽  
Power Laws ◽  
Power Exponent ◽  
Power Law Distribution ◽  
Exponential Distributions ◽  
Real Power ◽  
The Real ◽  
Dimension Space ◽  
Power Law Distributions

The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. This paper is devoted to exploring the relationships between exponential laws and power laws from the angle of view of urban geography. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through a semi-moving average process of an exponential distribution. For the distributions defined in a one-dimension space (e.g. Zipf's law), the power exponent is 1; while for those defined in a two-dimension space (e.g. Clark's law), the power exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distributions. Third, it is the real power-law distributions that can be related with fractal dimension. This study discloses an inherent link between simplicity and complexity. In practice, maybe the result presented in this paper can be employed to distinguish the real power laws from spurious power laws (e.g. the fake Zipf distribution).

scholarly journals Effect of Hub Radius on Rotational Stability of Functionally Graded Timoshenko Beams

2019 ◽  
Vol 9 (1) ◽  
pp. 4246-4251
Keyword(s):  
Exponential Distribution ◽  
Power Law ◽  
Functionally Graded ◽  
Rotational Stability ◽  
Timoshenko Beams ◽  
Power Law Distribution ◽  
Exponential Law ◽  
Radius Parameter ◽  
Graded Material ◽  
The Stability

This work is concerned to examine the rotational stability of functionally graded cantilever Timoshenko beams. Power law with various indices as well as exponential law were used to find out the effect of hub radius parameter on the stability of both functionally graded ordinary (FGO) beam. Floquet’s theory was used to establish the stability boundaries. The governing equation of motion was followed by Hamilton’s principle and solved by Finite element method. Dependence of Bulk modulus on thickness of beam was studied using both power law and exponential distribution. The influence of hub radius parameter was found to be enhancing the stability of FGO beams. It has further been confirmed that the effect of hub radius with exponential distribution of constituent phases renders better stability compared to power law distribution of the phases in the functionally graded material(FGM).

Exploring the Effect of Power Law Social Popularity on Language Evolution

2014 ◽  
Vol 20 (3) ◽  
pp. 385-408 ◽  
Author(s):  
Tao Gong ◽  
Lan Shuai
Keyword(s):  
Power Law ◽  
Artificial Life ◽  
Large Scale ◽  
Language Evolution ◽  
Social Systems ◽  
Power Laws ◽  
Power Law Distribution ◽  
Cross Model ◽  
Linguistic Conventions ◽  
Social Optimality

We evaluate the effect of a power-law-distributed social popularity on the origin and change of language, based on three artificial life models meticulously tracing the evolution of linguistic conventions including lexical items, categories, and simple syntax. A cross-model analysis reveals an optimal social popularity, in which the λ value of the power law distribution is around 1.0. Under this scaling, linguistic conventions can efficiently emerge and widely diffuse among individuals, thus maintaining a useful level of mutual understandability even in a big population. From an evolutionary perspective, we regard this social optimality as a tradeoff among social scaling, mutual understandability, and population growth. Empirical evidence confirms that such optimal power laws exist in many large-scale social systems that are constructed primarily via language-related interactions. This study contributes to the empirical explorations and theoretical discussions of the evolutionary relations between ubiquitous power laws in social systems and relevant individual behaviors.

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