Modeling the Global Citation Network using the Scalable Agent-based Simulator for Citation Analysis with Recency-emphasized Sampling (SASCA-ReS)

Supplementary Material For Modeling the Global Citation Network using the Scalable Agent-based Simulator for Citation Analysis with Recency-emphasized Sampling (SASCA-ReS) Minhyuk Park1, Haotian Yi1, Tandy Warnow1, George Chacko1,2* 1*Siebel School of Computing and Data Science, University of Illinois Urbana-Champaign, 201 N. Goodwin Ave, Urbana, 21801, IL, USA. 2Grainger College of Engineering, University of Illinois Urbana-Champaign, 1308 W Green St, Urbana, 61801, IL, USA. *Corresponding author(s). E-mail(s): chack[email protected]; Contributing authors: [email protected];[email protected]; warno[email protected]; Contents S1 Additional details for SASCA-ReS 3 S1.1 Description of PyABM ........................... 3 S1.2 Description of SASCA-ReS ........................ 4 S2 Figures 7 S3 Tables 8 S4 Computing a SASCA-ReS network with 218 million nodes 10 S5 Additional Details for Materials and Methods 11 List of Figures S1 Impurity-based feature importances for abm14 ............. 7 1 List of Tables S1 In-degree statistics and average local clustering coefficients for agents in abm14 variants .............................. 8 S2 Disruption in mavericks .......................... 9 2 S1 Additional details for SASCA-ReS The SASCA-ReS algorithm is an extension of agent-based modeling code developed by us to simulate the growth of citation networks. The major releases in this development path are v3 (PyABM) [1] written in Python, v5 (SASCA and SASCA-S) [2], written in C++, and v6 (SASCA-ReS) [3], written in C++. SASCA-ReS differs from SASCA-s and PyABM in several respects, some of which are about computational performance and others about the model. Here we discuss the difference in terms of the model. Since the details of the PyABM model are available [1], we provide first a description of PyABM and then specify how SASCA-ReS differs from it. S1.1 Description of PyABM The PyABM model can be described as. having 5 basic steps, as provided in the paper on PyABM [1]: 1. The network begins with a seed network with nodes and directed edges. Each year, a batch of new agents is created, defined by the rate of agent birth (typically 3% to 10%, a parameter given to the simulator). 2. To generate a new agent, a node is selected from the network at random and designated as a “generator”; this generator then spawns the new agent, and the new agent cites the generator. The new agent is also assigned a fitness value drawn from a power-law distribution which does not change over time. 3. The newly created agent is assigned an integer-valued quota of references it can make to other nodes, where the quota is drawn from a distribution derived from real-world citation data. One of these citations is to its generator, and for a subset of the new agents (typically 12% of all new agents), an additional citation is made to another a node from its own year. The remainder of the citations are made to other nodes in the network. 4. For each agent, the selection of which citations to make depends on the target nodes properties, namely: fitness, current in degree, and year of publication, as well as the agent’s own relative preference for these properties, which we refer to as its “phenotype”. The agent also has a parameter, which we will refer to here as αP (where “P” refers to PyABM), that determines the fraction of its references that will come from the 1-hop neighborhood of its generator. Each node in the network is a potential recipient of a citation, and hence is scored according to the agent’s phenotype. Then, given the number of citations the agent should make to nodes one edge from its generator, the agent selects the nodes to cite based on a weighted sampling function using the A-res algorithm presented in [4], and the same process is used for selecting nodes to cite that are further than one edge from the generator. 5. Once an agent exhausts its quota of references, it does not make any more citations and can only receive citations from other agents. Some comments are relevant. Note that the agent’s phenotype determines the relative importance of fitness, in-degree (which determines the preferential attachment score), year of publication, and whether a node is in the 1-hop neighborhood of its generator 3 (i.e., all the nodes of distance exactly one edge from the generator). For example, when fitness and preferential attachment are equally weighted, then the assigned fitness of a node drives the early period of citation accumulation, and gradually decreases as the node accumulates in-degree. The process ensures that nodes with higher scores are more likely to be selected while maintaining stochasticity. S1.2 Description of SASCA-ReS The model for SASCA-ReS is nearly identical to PyABM. Steps 1–3 and 5 are the same as for PyABM, which means that every node is spawned by a randomly selected generator, which it cites; every node has a fitness value; and a small subset of the new nodes in each year will cite nodes within the same year. There are however substantial changes to Step 4, which determines the remaining citations an agent will make in order to fill its quota. As with PyABM, the distance to the generator impacts this decision, and we define the 2-hop neighborhood of the generator to be all those nodes of distance 1 or 2 to the generator, and hence the 1-hop neighborhood is the set of nodes of distance exactly 1 from the generator; thus, the 2-hop neighborhood contains the 1-hop neighborhood. To define how SASCA-ReS decides what other node to cite, we use the following parameters: •q (quota): the allotted quota of citations to be made (out-degree) •IF (idiosyncratic fraction): the fraction of the quota that is allotted to idiosyncratic citations (default IF = 5%) •α: the fraction of the number of citations made within the 2-hop neighborhood of the generator that are made to citations in the 1-hop neighborhood (no default) •SY: the fraction of agents in a given year that make citations to other agents from the same year (default SY = 12%) •B: the maximum number of nodes that each agent scores within the 1-hop and 2-hop neighborhoods of the generator node (default B= 10,000) We now describe how SASCA-ReS uses these parameters. One important aspect of the changes in Step 4 is that SASCA-ReS only scores at most Bnode in the 1-hop neighborhood and Bnodes in the 2-hop neighborhood; an agent may cite a node that is not in the 2-hop neighborhood, but if so then such citations are made randomly and do not require scoring the node (furthermore, we call such citations “idiosyncratic”). The number of idiosyncratic citations it will make is ⌊q×IF ⌋, and so can be 0 if q < IF −1. The citations going to the 2-hop neighborhood is divided into those going into the 1-hop and those going to nodes of distance 2 from the generator node, with α defining the fraction of the total that go to the 1-hop. proportion going to the 1-hop. Thus, when α= 0, all these citations go to the 1-hop neighborhood, and when α= 1, then all these citations go to nodes at distance 2 from the generator. There is also one more very important difference, which has to do with how SASCAReS ensures a better fit to the recency distribution: it bins all the nodes at distance 1 from the generator (N1) as well as the nodes that are at distance 2 from the generator (N2), by year of publication into a small number of bins. The first ten bins are for the first ten years, as follows. Assuming the agent is created in year y, then papers in N1 that were published in the previous year are in Bin1, papers in the year before (i.e., 4 year y−2) are in Bin2, and so forth, producing bins Bin1, Bin2, . . . , Bin10. After this, the next eight bins are for five years at a time (i.e., Bin11 has years 11−15, Bin12 has years 16 −20, etc.). Finally, all publications (nodes) that are 51 years or older at the time of the agent’s creation are in the final bin. Note that the nodes in the final bin are also not scored, just like idosyncratic citations, and instead selected randomly for citations. The same binning is done for the nodes in N2, producing bins Bin′ 1, Bin′ 2, etc. Each agent then determines the integer count of how many citations to make within each bin based on a computed “recency table” from a real-world network, which reflects the preference to cite publications from recent years more than papers many years ago. We first process N1and then process N2. Each bin is processed in turn, starting with Bin1and then processing Bin2, etc., for N1, and a similar sequence for N2. This protocol may succeed in achieving the quota for the agent. However, if the number of nodes in a given bin is not large enough to achieve the target number of citations from that bin, then the process may not meet the quota entirely. In this case, we perform a post-processing step to make additional citations, as follows. For a given bin that was insufficient in size to meet its quota, we check the bins already processed (i.e., bins with lower index), one by one, to see if any nodes were left un-cited by the agent. If so, we can make a. citation to any such nodes. We repeat this until we meet the quota. If this is still insufficient, we then move on to the higher indexed bins. Finally, if the 2-hop neighborhood is too small to cover the quota, then we perform additional idiosyncratic citations, which do not involve scoring. Note that because of this binning property, the phenotype for each agent no longer considers recency in calculating the score of a target node, and instead only considers the relative importance of preferential attachment and fitness. This relative importance is specified by assigning weights between 0 and 1 for these two properties that sum to 1, with the obvious interpretation that whichever has a higher weight will contribute more to the score. For example, if the weight for preferential attachment is 1 and the weight for fitness is 0, then fitness is not considered at all in computing the weight of any target node, but if both are weighted 0.5 then they both contribute equally to the weight. We now summarize this discussion and provide some details for how nodes are selected to be cited. Recall that the parameters we use specify a fraction of the new agents in a single year will perform a single same-year citation; this is done at the beginning of each year of the simulation. For a new agent with a given integer-valued quota qand generator node x, the steps for fulfilling the quota is as follows. 1. Make ⌊IF ×q⌋idiosyncratic citations and decrement qby this value. 2. Cite the generator node xand decrement q. 3. If the agent was selected to make a same-year citation, then select a random other agent from the same year that was not selected for same-year citations and cite it; then decrement q. 4. Obtain N1and N2, where Niis the set of nodes that are distance ifrom the generator node x. 5. Let q1:= ⌊αq⌋and let q2:= q−q1 5 6. Randomly select min{|N1|,10000}nodes from N1and score them according to the agent’s phenotype. Cite q1nodes from the selected set based on their scores for all bins except last. Cite randomly from the last bin. 7. Randomly select min{|N2|,10000}nodes from N2and score them according to the agent’s phenotype. Cite q2nodes from the selected set based on their scores for all bins except last. Cite randomly from the last bin. 8. Make additional idiosyncratic citations if needed to satisfy quota. The “no-α” variant Recall that parameter αdetermines the proportion of citations that should go to N1 out of the 2-hop neighborhood, with higher αvalues leading to more citations from N1. We also allow for a “no-α” variant, which has the consequence that instead of partitioning the 2-hop neighborhood into N1and N2, we just sample from the 2-hop neighborhood, which is N1∪N2. As with the default way of running SASCA-ReS, we partition Ninto bins based on year of publication, and scoring and selection of nodes to cite follows the same structure. 6 S2 Figures 0.0 0.2 0.4 0.6 0 20 40 60 80 Simulation Year Feature Fitness Out Degree PA Weight Pub Year Feature Importance Fig. S1 Impurity-based feature importances for abm14 Here we show the impurity-based feature importances of random forest regressors trained on abm14 datasets at different years of the simulation. Each random forest regressor consisted of 100 decision trees and predicts the final citation received by an agent using four features: fitness, out degree, preferential attachment weight, and publication year. 7 S3 Tables abm14 variants alcc min 25th median 75th max ra 0.0839 0 5 12 24 260404 ra noalpha 0.0239 0 3 7 14 329261 alpha0.05 0.0212 0 3 7 15 302766 alpha0.95 0.1498 0 8 20 39 417066 pa0.05 0.0824 0 5 12 26 342999 pa0.95 0.0883 0 4 11 22 443169 alpha0.00 0.0054 0 3 7 14 338176 alpha0.20 0.0530 0 4 9 18 244258 alpha0.40 0.0807 0 4 11 23 341497 alpha0.60 0.1052 0 6 14 28 311606 alpha0.80 0.1296 0 7 17 34 372994 alpha1.00 0.1605 0 8 21 42 437329 Table S1 In degree statistics and average local clustering coefficient (alcc) for agents in different simulated networks with 14 million nodes. The networks are variants of the abm14 network produced by varying whether αand preferential attachment weight are randomized or static. For each network we display statistics for its in degree distribution and alcc. Note that high αsettings increase in degree and alcc of agent nodes. 8 condition maverick type avg n i avg n j avg n k 1 od249 f1 maximizer 92984.67 67828.67 262947.00 2 od249 f1 randomnik 30.67 32.00 3269.33 3 od249 f1 minimizer 2.33 10.00 2023.67 4 od249 f1 control 8.33 22.00 10355.33 5 od249 f10 maximizer 99286.67 80901.33 285889.00 6 od249 f10 randomnik 380.67 92.67 3208.67 7 od249 f10 minimizer 395.00 88.67 2013.00 8 od249 f10 control 971.00 567.33 15230.00 9 od249 f100 maximizer 136190.00 123351.33 251704.33 10 od249 f100 randomnik 9418.00 291.00 3527.67 11 od249 f100 minimizer 5916.33 207.33 1963.33 12 od249 f100 control 10927.33 944.33 6683.00 13 od249 f1000 maximizer 155252.67 114938.33 230361.67 14 od249 f1000 randomnik 12805.33 330.33 2884.00 15 od249 f1000 minimizer 10475.00 262.33 1941.67 16 od249 f1000 control 18705.33 6958.67 42342.67 17 od10 f1 maximizer 118.33 42.33 6566.67 18 od10 f1 randomnik 2.33 0.67 180.00 19 od10 f1 minimizer 2.33 0.67 110.67 20 od10 f1 control 2.67 0.33 167.33 21 od10 f10 maximizer 2123.00 380.33 21042.00 22 od10 f10 randomnik 18.67 3.00 106.00 23 od10 f10 minimizer 15.00 3.00 76.67 24 od10 f10 control 147.33 119.33 5671.00 25 od10 f100 maximizer 29772.33 921.33 8540.00 26 od10 f100 randomnik 1576.00 16.67 239.33 27 od10 f100 minimizer 575.33 12.00 77.67 28 od10 f100 control 6774.67 335.33 5716.33 29 od10 f1000 maximizer 63427.00 1069.33 10041.00 30 od10 f1000 randomnik 845.00 11.00 134.67 31 od10 f1000 minimizer 444.00 9.67 85.67 32 od10 f1000 control 13624.33 472.67 4918.00 Table S2 Disruption in mavericks Disruption was computed using the formula in [5], which has the terms ni,nj, and nk. Each maverick experiment has nine mavericks (three of each type) and is characterized by a fixed out-degree for the mavericks (indicated by “od” followed by the fixed outdegree) and a fixed fitness value (indicated by “f” followed by the fitness value). The average of the three replicates is shown in the table. 9