Unbiased copying models have been calibrated empirically against real data sets that represent easily copied variants, such as ancient pottery designs Bentley and Shennan, ; Crema et al. The time scales of these studies range from centuries to decades, months or days. In order to compare different models in explaining the data, models need to be generalized, through multiple parameters, to generate as many outcomes as possible, taking into account sampling and different possible biases in cultural transmission Kandler and Powell, The goal is to estimate probability distributions of those parameters to explain the set of posterior distributions.
To model the dynamics of Twitter cascades, we test several different models of context-biased learning. These models can be compared based on their ability to replicate the data while minimizing the number of model parameters. Once we have determined the best model, we then estimate a probabilistic range of each parameter values to best fit each data set. The goal is to compare parameter ranges between different data sets.
Kandler and Powell advocate the use of Approximate Bayesian Computation ABC , which can produce a probabilistic representation of parameter space that shows how likely the parameters are to explain the data. Using this approach on the Twitter data explored by Vosoughi et al. Moreover, as prior information on Twitter users is available, we can determine with precision the distribution of biases at the individual level in the population of Twitter users.
This opens the possibility of explaining how the observed differences Vosoughi et al. Here we consider a model of unbiased social learning, also known as the Neutral model. Consider a population of Twitter users in a fully-connected network. The number of modelled Twitter users, N , is kept constant, as we will assume the modelled time period days or weeks is short compared to any growth in number of users.
In this population, users either tweet something unique of their own or else re-tweet another message. In this basic unbiased copying model, a re-tweet is chosen from among N Twitter users , as opposed to choosing from the different Tweet messages themselves.
The number of different messages, k , observed by each user is typically much less than N. Next, we modify this unbiased model to introduce context-biases through three different forms of popularity bias. The first is a frequency bias, where the probability of a message being copied increases with frequency above the inherent frequency-dependent probability of the neutral model itself. The first context-biased model derives from a more general model of discrete choice with social interactions Brock and Durlauf, ; Bentley et al.
Another parameter, J , represents context-bias, specifically popularity bias here. While future models can explore this parameter, due to the computational cost to the ABC see Discussion section , here we simply assume the messages have no intrinsic utility, i.
This yields:. In this case the context-bias, Jp i is based upon the popularity, p i. Note that both context- and content-bias are, respectively, homogeneous for all agents.
We could, in a more advanced model, have heterogeneous distributions of J and U across all agents, but this becomes unwieldy, as the parameter space becomes too large to be explored by our current ABC algorithm. By contrast, under the neutral a. The other 1- C fraction of the population will re-tweet something else at random, per the Neutral model.
All the algorithmic description of the model are made available in the supplementary materials. Then to summarize the variables and parameters in these models, we have:. While they do not span the space of all possible models, even these four models require a rigorous means of discrimination when compared to the data.
In calibrating these models to Twitter cascade size, we use Approximate Bayesian Computation Kandler and Powell, The aim is to find the distribution of parameters of each model knowing data distribution, ie the posterior distributions of the model.
To do so one usually use Bayes equation:. Finding the likelihood of our models is not an easy task, however, as there is no direct way to do so. An indirect method approximates the likelihood by simulating the models and rejecting the parameter ranges that yield results to far from the data distribution Kandler and Powell, ABC requires a definition of a distance between model and the data, which allows approximation of the likelihood distribution of different model parameters.
Here we adapt an ABC version by Crema et al. In this simple version of ABC, called the rejection algorithm, a huge number of simulations are run and only the parameters of a small percentage of simulations yielding the lowest distance to the data are kept to draw the approximate posterior distributions. These stories were re- tweeted 4. For each different message in this dataset, Vosoughi et al.
Tweet cascades started by bots were not a significant factor in these data Vosoughi et al. Since Vosoughi et al. This reduces the dimension of the data set to one unique distribution, avoids the need to keep the full structure of each cascade and allows to directly compare our model to the data collected by Vosoughi et al.
Those CCDFs represent the percentage of respectively a cascades and b rumors that have reached a given number of re-tweets between and Figure 1a shows the distribution of cascade sizes when each cascade is taken separately, Fig.
To formally select between the different models we can use the posterior distributions of the different models given the data. The Bayes equation described by the Eq. Then we calculate how many simulations of each model are below this acceptance level. We note that the Top Threshold is by far the least likely model to explain the data.
The best models in Table 1 are the Unbiased and Top Alberto models. To calculate something comparable to AIC, we use the raw values from Table 1 divided by the total number of simulations. This would give us the approximated likelihood, L , for each model.
The ABC algorithm allows us not only to select between the models but also to look at the posterior distribution of the parameters that yield to simulations reproducing the data. The idea is then to explore the result of the Eq. As the Unbiased model is the most likely, we present only its posterior probability distributions in Fig.
Each panel of Fig. The grey curve represents the prior distributions for each parameters. There are fewer time steps required in modelling the true tweets compared to the false tweets. This is consistent with false tweet cascades persisting longer Vosoughi et al. Similar figures for the three context-dependent models are shown in the supplementary material. From those posterior distributions it is possible to determine the parameter range with the highest probability: the highest density region HDR Hyndman, — often also called the Highest Posterior Density Region HPD when they are calculated on posterior distributions, as it is the case here.
The resulting intervals and modes are given in the Tables 3 and 4. For the ABC, since we could not store the full results of all simulations, we saved only the parameters used together with the distance to the data.
Keeping this information for the 9 million simulations we ran for each model yielded about 1. Thus, to check the adequacy between the simulations selected through ABC and the observed distribution, we run a new set of simulations. For every model, we re-run 10, simulations, sampling the parameters from the selected posteriors distributions, for both the posteriors obtained with true as well as false messages.
This is also often called posterior predictive check Gelman and Hill, We present the results of the new simulations as distributions of cascade sizes. For a better visualization, we binned the cascades with similar size within logarithmic bins. The High Density Regions for all bins and models are represented in Figs 3 to 6.
The colored dots represent the data from Vosoughi et al. The raw data i. Posterior check of distributions of aggregated cascade sizes for the Unbiased neutral model versus data from true rumors at left in green and false rumors at right in red.
Each plot represents the percentage of rumors for which the accumulate number of RT falls within 18 bins of logarithmically growing size. The frequency of rumors within each bin is represented by a colored dot for data set, versus the mode and High Density Regions for the 10, posterior checks of the model. The curve at the bottom of each plot shows the percentage of simulations where zero rumors felt within the given bin.
Note Figs 4 — 6 use this same format. Posterior check of distributions of aggregated cascade sizes for the Conformist model, versus the data for true rumors in green on the left and false rumors red on the right. Plots were generated as described in the caption of Fig.
On the following image, you can see major definitions of LNL. If you want, you can also download image file to print, or you can share it with your friend via Facebook, Twitter, Pinterest, Google, etc. To see all meanings of LNL, please scroll down. The full list of definitions is shown in the table below in alphabetical order. This page illustrates how LNL is used in messaging and chat forums, in addition to social networking software like VK, Instagram, Whatsapp, and Snapchat.
From the table above, you can view all meanings of LNL: some are educational terms, the other are medical terms, and even computer terms. If you know of another definition of LNL, please contact us. The inter-country quality nodes ICQNs are a part of this drive.
The ICQNs serve as catalysts for the capitalization of innovative educational experiences in Africa and for the implementation of the lessons that each country or group of countries draws from these experiences in order to improve their programs.
Since the ICQN initiative is primarily driven by the countries concerned and involves several steps, the ministers identified the theme of literacy as a challenge common to several countries. After discussions with their peers, they initiated the various steps and procedures required to develop this ICQN.
Subsequently, at a meeting held in Lyon, the minister of education of Burkina Faso was designated by her peers to take over the leadership of the ICQN. A workshop was held in Ouagadougou in December with representatives of 13 countries to try to build a consensus on what the various parties involved could and should contribute to this process.
The workshop was also supposed to identify ways and means of providing non-formal education of good quality in Africa. One of the tangible outcomes achieved was a draft three-year program for the ICQN. To contribute to the achievement of inclusive, efficient development of literacy training and national languages as a catalyst for social, economic and cultural development in Africa.
The Windhoek conference of August on bilingual education and the use of mother tongues, as well as the regional conference in Ouagadougou on African languages and cultures in education, both recognized that the integration of African languages, multilingualism and cultural diversity into the education process were vital conditions for improving educational access, quality and efficiency in Africa. The Ouagadougou Conference of January also contributed to this process.
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