Abstract. On account of the complexity and uncertainty in cyberspace competition, cyber ecosystem is brought forth to meet the requirements of cyberspace security and complex adaptive system. Herein, a novel **information** **diffusion** **model** is presented with the change of notes based on Susceptible-Escaped-Infected-Removed-Quarantined-Susceptible (SEIQRS). In detail, the process and mechanism of nodes increasing and decreasing are considered upon traditional epidemic and **information** **diffusion** **model**, and the system dynamics equations are derived. Via the criterion of Routh-Hurwitz stability, the stability conditions are further investigated, as well as the corresponding requirements. Theoretical research and simulations demonstrate that in an open cyber ecosystem the proposed **information** **diffusion** **model** can be well controlled by modulating the number of nodes in the case of node increasing and decreasing.

With the rapid development of Internet and smart mobile terminal, **information** can be diffused and spread by online social network quickly. There are some special characters in social network, such as small world, scale free, high levels of clustering. SIR-based **Information** **diffusion** models are proposed and improved by multi-discipline researchers. Network topology structure plays an important role in **information** **diffusion** and spreading process. Different centrality measure algorithms are summarized in this paper. High centrality degree nodes generally are high influential nodes in social networks. While the relationship between network topology and **information** **diffusion** dynamics should be researched in detail. Pagerank value computing for SinaWeibo users is done by Hadoop cloud technique to meet the requirement of high scale social network computing. Some new problem and challenge are proposed in the paper, such as **information** **diffusion** **model**, big data and mining algorithm in social network, **information** security and privacy protection problem. We think that **information** **diffusion** involves multi-discipline interaction, many problems and challenges exist in the research aspect. Researchers from different aspects can contribute to the research aspect.

Due to similar patterns in the spread of epidemics and social contagion processes, most research adopts the same theoretical principles for epidemics in describing the **information** diffusion.Recent many researchers study models of **information** **diffusion** based on epidemic diseases. **Information** dissemination epidemic models have been developed for different network topologies, e.g., social networks [1]and multiple social networks [2]. Goffman and Newill[3] developed the analogy between the adoption of scientific **information** and the spread of infectious disease.The independent cascade **model** (ICM)[4] , which is widely adopted in describing the **information** **diffusion** on online social networks, is a special case of the SIR **model** reflecting the network structure of the population. The first study on **information** **diffusion** modeling using epidemic models has been made using the study on the spread of scientific ideas. Liu and Zhang [5] proposed a dynamic susceptible infected recovered (SIR) **model** considering dynamic rewiring network in which people can break links and reconnect to their second-order friends. Wang et al. [6] proposed the emotion-based SIS **model** for and showed that it outperforms SIS **model** in describing **information** **diffusion** with Twitter data.The real world networks is full of randomness and stochasticity, using stochastic models can gain more real benefits. Since the parameters in the deterministic models are constant, they have some limitations when we describe the systems. Consequently, Some researchers have paid their attention to the stochastic **Information** **Diffusion** **model** [7,9].

Abstract. The paper explore an **information** **diffusion** models with random perturbation in social network. First, we show the models exit the unique global positive solution. By the construction of the Lyapunov function, we give the positive solution is stochastically asymptotically stable in the large around disease-free equilibrium, i.e. the conditions of the **information** **diffusion** will die out, investigate the stochastic asymptotic behavior of the positive solution around endemic equilibrium of the deterministic models, obtain the stochastic asymptotic stability condition, i.e. the conditions of the **information** **diffusion** will be persistent in social networks.

and the fans can repost or ignore w . If a node had ignored the message, he may choose to repost the message again because many of his neighbors had forwarded w . Moreover, Weibo was a time-sensitive media. As time goes by, users will lose interest in messages whose spreading would gradually decline. According to the propagation mechanism of Weibo, this paper proposed a new **information** **diffusion** **model** which defined four node states: susceptible, contacted, infected and refractory. Susceptible nodes(S) are the users who had not seen the message, and contacted nodes(C) had seen the message but had not decided whether repost or ignore. The nodes reposted message are defined as infected (I), while the nodes who ignored are called refractory(R). The contacted is temporary state and the other status are final states. The **diffusion** rules in UA-SCIR as follows:

Bangham plot for MTZ adsorption by the PA/HA nanocomposite was shown in Fig. 2e. The non- linearity of the plot indicates that pore **diffusion** of MTZ is not the only rate-controlling step of the adsorption process, since there is a previous transport of the adsorbate from the aqueous phase through the boundary layer of the adsorbent. This is in concordance to the results shown by Weber and Morris plot, intra-particle **diffusion** **model**, which was employed to explore whether the adsorption

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Abstract. The analytical solutions of the fractional **diffusion** equations in one and two-dimensional spaces have been proposed. The analytical solution of the Cattaneo-Hristov **diffusion** **model** with the particular boundary conditions has been suggested. In general, the numerical methods have been used to solve the fractional **diffusion** equations and the Cattaneo-Hristov **diffusion** **model**. The Laplace and the Fourier sine transforms have been used to get the analytical solutions. The analytical solutions of the classical **diffusion** equations and the Cattaneo-Hristov **diffusion** **model** obtained when the order of the fractional derivative converges to 1 have been recalled. The graphical representations of the analytical solutions of the fractional **diffusion** equations and the Cattaneo-Hristov **diffusion** **model** have been provided.

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An implication of the present approach is that not all ties that could be added to a net- work are beneficial for **information** **diffusion**. Although the virtue of rewiring or adding random ties has been widely demonstrated (Newman 2000; Kleinberg 2002; Valente and Davis 1999; Pastor-Satorras and Vespignani 2001; Newman 2002; López-Pintado 2008), this article demonstrates that the presumption of full-capacity ties and perfect opportu- nity to transmit which underlies earlier approaches is necessary for random ties to be beneficial. By accounting for limited opportunities and varying capacity, the findings here help qualify these results. The findings presented here are consistent with those revealing that network modularity can improve **information** dissemination via social reinforce- ment (Centola 2010; Nematzadeh et al. 2014). The results here suggest that modularity is helpful for another reason: insofar as modularity is indicative of strong ties within the communities and weak ties across them, the presence of too many weak ties spanning communities can inhibit **information** spread within the communities as well.

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Following the pioneering work of Feng et al. [16] on modeling schistosomiasis, we establish and analyzed a schistosomiasis **model** with **diffusion** effect and saturated incidence function, in which two groups of human share the water contaminated by schistosomiasis and migrate each other. we derived the basic reproduction number R 0 and proved that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 , and the unique endemic equilibrium is locally asymptotically stable for R 0 is larger than 1 and near 1. Our results indicate that the **diffusion** rates and the infection rates play an important role in the determination of the permanence and extinction of schistosomiasis. The **diffusion** from the mild endemic village to severe endemic village is benefit to control schistosomiasis transmission.

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Jason J. Jung is a corresponding author of this paper. He is an associate professor in Yeungnam University, Korea, since September 2007. He was a postdoctoral researcher in INRIA Rhˆone-Alpes, France in 2006, and a visiting scientist in Fraunhofer Institute (FIRST) in Berlin, Germany in 2004. He received the B.Eng. in Computer Science and Mechanical Engineering from Inha University in 1999. He received M.S. and Ph.D. de- grees in Computer and **Information** Engineering from Inha University in 2002 and 2005, respectively. His research topics are knowledge engineering on social networks by using machine learning, semantic Web mining, and ambient intelligence.

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communities, cultures, events, critical incidences) are selected because they are “**information** rich” and illuminative, that is, they offer useful manifestations of the phenomenon of interest; sampling, then, is aimed at insight about the phenomenon, not empirical

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Furthermore to leading order, the second and higher moments of the change in allele frequency are the same as for the neutral case (i.e., when R and M are equivalent, dropping all terms in- volving eÞ: Consequently, we derive the second moment for the change in allele frequency using the **diffusion** limit ðN/NÞ when selection is absent (Appendix C and File S1), which allows us to determine the variance effective population size for this **model**. We also conﬁrmed that the third moment goes to zero in the **diffusion** limit for the Moran **model**, justifying the use of a **diffusion** approximation (Karlin and Taylor 1981, p. 165).

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We applied the MCMC algorithm to previously published iSCAT SPT data [51], where CTxB coated AuNPs were introduced to a DOPC lipid bilayer containing 0.03% GM1 lipids. Confinement events were detected, which displayed two distinct spatial localisa- tions: a Gaussian-like localisation and a ring-like confinement. The authors proposed that the CTxB attached to the AuNP (by streptavidin) binds multiple GM1 on the upper membrane leaflet; these GM1 interact with GM1 in the lower leaflet. A bind- ing (confinement) event corresponds to an interaction with a lower leaflet GM1 that is immobilised to the glass surface; no binding events were observed for GM1 in **model** membranes on mica surfaces. Rocking of the AuNP around the binding site then pro- duces a Gaussian confinement localisation. Non-Gaussian confinement distributions are explained by a second CTxB on the nanoparticle transiently binding to another, pos- sibly diffusing GM1. These multiple-bound particles yield trajectories centered around an immobilized central CTxB that resembles a ring-like structure at the nanoscale. We investigated these confinement events in greater detail using our hidden Markov **model**. The dataset includes 71 trajectories of 20nm AuNP/CTxB/GM1 diffusing in a **model** membrane on a glass substrate, and 18 trajectories of 40nm AuNP/CTxB/GM1 diffusing in a **model** membrane on a mica substrate. To determine if subsampling is necessary (to increase the signal to noise ratio), we performed an MSD analysis indicating that a subsampling of 10 is appropriate, (Appendix B.1, [62]). This analysis in fact revealed a dynamic error in the localisation efficiency at the 50 kHz sampling rate, that results in apparent superdiffusive behaviour at short times, [51]. Subsampling down to 5 kHz removes this problem. We also removed trajectory artifacts due to multiple AuNPs in the focal area (Appendix B.1).

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The conclusion we draw from our studies is that the kernel method works eﬀec- tively for testing of diﬀusion models and is capable of modeling dependence induced by a diﬀusion **model**. It is clear from the studies of Pritsker (1998) and this paper that a proper implementation is vitally important. After all, the kernel method is just an instrument for constructing nonparametric curve estimates. For a complex task of testing a diﬀusion **model**, it will not work automatically by itself and requires other procedures to make it work. However, what is working is the idea of comparing the kernel estimate of a characteristic curve and the corresponding **model**-implied curve of a diﬀusion **model**. This is the main idea of A¨ıt-Sahalia (1996). The role of the kernel method is in translating the idea into some raw discrepancy measure. Anything beyond it, for instance, the test statistic formulation and the choice of the critical value should be the responsibilities of the other procedures.

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In this paper, we particularly investigate methods to identify groups of content con- tributions with a similar sphere of influence. This aims at discovering potential indirect influences between users. Moreover, it helps to identify groups of people with simi- lar access to **information** while the groups may lack a direct relationship. Non-negative matrix factorisation is employed to reduce the possibly large and complex **diffusion** net- work to its basic underlying structure, facilitating an easier interpretation. Groups of contributions with similar positions in **information** cascades reveal who has similar infor- mation at similar points in time. A possible application is the identification of potential **information** biases by investigating which groups are reached or not reached by certain **information** pathways. Furthermore, this abstraction allows to observe **diffusion** pro- cesses on a group-level and to infer roles of users and contributions. Such roles can, for example, be forerunner posts that are taken up quickly by many others or latecomers which denote posts that are usually leaves of **diffusion** chains and take up **information** with high latency.

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served only in the case of non-restricted **diffusion**, while in many systems where sig- nificant deviations occur from this linear form, the data may be interpreted as the ef- fects of restricted **diffusion** [13] [17] [22] [24]. For a molecule moving in an isotropic and homogeneous medium (in the absence of chemical exchange), the measured diffu- sion coefficient is independent of the experimental **diffusion** time, Δ. However, for a molecule diffusing within a restricted geometry, the displacement along the direction of the applied field gradient will be a function of Δ, D , and the size and shape of the re- striction geometry [16] [20] [22]. As Δ becomes larger, a fraction of the molecules will be affected by the boundary of the sphere and the measured **diffusion** coefficient ( D app )

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The assumption I made here, that temporal averaging is the result of only one accu- mulator being active during the compounds and fed with half the rate for each of the stimuli, is plausible and can accommodate the main features of the data. However, given the evidence from mixed FIs it seems animals are capable of keeping multiple timers running in parallel, without averaging their rates. Also, if averaging of rates always happened during compounds, then the explanation provided by RWDDM for the left shift in the response curve in the compound peak procedure would not hold. I suggest one possible way of interpreting these three phenomena based on a failure of representation selection caused by the ambiguity of the signal. In mixed FIs there is one single CS that signals two rewards at very different times. There is not much ambiguity in how to interpret the signal, so the subject keeps two timers running in parallel. In the case of compounds formed by individual CSs that signal reward at the same time, as in the compound peak procedure, there is also not much ambiguity. There’s very little difference between the time memories evoked by the CSs, so choosing only one, the faster one, leaves no ambiguity as to which CS is signalling reward. In the case of compounds formed by individual CSs of different modalities that signal reward at different times, the ambiguity might be such that cannot be resolved easily. The **information** from each CS may then be only partially retrieved and added into one representation, resulting in temporal averaging.

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The Keele University Research Ethics Panel approved the study, which was therefore performed in accordance with the ethical standards laid down in the 1964 Declaration of Helsinki. A total of 100 adult drinkers were recruited. However, not all partici- pants were analysed due to a number of a priori exclusion crite- ria. First, some participants only turned up for one session, so those with incomplete data were obviously excluded (n=22). Participants who had positive blood alcohol levels (tested via a breath test) on the day of testing for either the hangover or control day were excluded (n=20), as were participants for whom there was missing blood alcohol level (BAL) **information** (n=12). Some participants were removed as they did not confirm that they had never been diagnosed with a drink or drug problem (n=4), or they did not provide **information** on drink history (n=1). Participants who declared they had not had a drink the night before the hangover condition and participants who declared they did have a drink the night before the control condition were excluded (n=2). Participants with a body mass index (BMI) score over 30 were also excluded (n=2), to prevent atypical metabolic effects influencing the data. Participants who scored below 80%

The work most closely related to ours is the empirical study of **information** **diffusion** and network evolution (Gross and Blasius, 2008; Singer et al., 2012; Weng et al., 2013; Antoniades and Dovrolis, 2015; Myers and Leskovec, 2014). Among them, (Weng et al., 2013) was the first to show experimental evidence that **information** **diffusion** influences network evolution in microblogging sites both at system-wide and individual levels. In particular, they studied Yahoo! Meme, a social micro-blogging site similar to Twitter, which was active between 2009 and 2012, and showed that the likelihood that a user u starts following a user s increases with the number of messages from s seen by u. Antoniades and Dovrolis (2015) investigated the temporal and statistical characteristics of retweet-driven connections within the Twitter network and then identified the number of retweets as a key factor to infer such connections, in agreement with (Weng et al., 2013). Besides link prediction, they argue about which potential network motifs TRF events can lead to in the network structure. Myers and Leskovec (2014) showed that the Twitter network can be characterized by steady rates of change, interrupted by sudden bursts of new connections, triggered by retweet cascades. They also developed a method to predict which retweets are more likely to trigger these bursts. Finally, Tran et al. (2015) utilized multivariate Hawkes process to establish a connection between temporal properties of activities and the structure of the network. In contrast to our work they studied the static properties, e.g., community structure and inferred the latent clusters using the observed activities.

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We propose a **model**-free approach of estimating macro-level **diffusion** without any assumptions on social interactions [87, 88, 89, 90], which not only provides benefits of studying nonlinear dynamics of complex systems but also gives an abstract view of cross-population **diffusion**. We define a stochastic process at a system level and the systems’ signals transmitted to other systems at a population level, which can be applicable to a variety of real-world scenarios. This conceptual framework enables us to estimate macro-level **information** transfer across heterogeneous social systems in terms of the strength and directionality of influence. To the best of our knowledge, this is the first attempt to apply this macro-level **model**-free approach to social media and academic publications. Estimation results can be comparable with the outcomes from the **model**-driven approach, which provides opportunities to enhance the per- formance of both approaches. When estimating **information** transfer from a source to a destination system, the effects of time-delay and memory (the length of adop- tion histories) are all considered. That is, behavioral characteristics of different social systems can be obtained, which helps to better understand the context of **diffusion**. By applying this approach to our target application domains, we provide different ways of understanding topic-related **diffusion** across heterogeneous social networks. 1.4.4 Part IV – Comparison of Approaches

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