 ## Summary of the results of the Execution Phase 1

In this phase we have defined the deterministic model that will be used for calculating the iota indicator. The main principles have been discussed and the mathematical equations have been defined that will be used iteratively on the nodes of the citation network. Two tests have also been fixed which can be applied in case of the used initial conditions. The algorithm to be implemented has also been established. It was observed that, in order to be more efficient, before implementing the algorithm a topological sorting of the network is required. The first database has also been prepared based on citations from the Web of Sciences.

## Summary of the results of the Execution Phase 2

In this phase first we have implemented the deterministic model for calculating the iota indicator on two citation databases: Web of Science (WoS), and High Energy Physics (HEP). First, the databases have been prepared by topological sorting in order to perform an efficient calculation of the indicator values. The obtained values depend strongly on the year of publication which can be detected by a trend which favorizes the old articles. In order to eliminate this trend, analytical studies have been performed on Erdos-Rényi type networks. These studies resulted in the redefinition of the deterministic model. Similar methods have been successfully applied in case of WoS and HEP citation networks which resulted a time-normalized article indicator which is not sensible to the initial conditions.

The main objective in case of the probabilistic model is to estimate the precision of the indicator values, as well. In this model the indicator value is a random variable with unimodal distribution, and the master equations are written by convoluting the probability distribution functions. However, computig convolutions on very large networks are very costly. For our purpose it would be enough to estimate the standard deviation of the article indicator values ony. We have shown that in case of exponential distribution functions  these standard deviations can be efficiently calculated. Currently we are working on the implementation of this efficient algorithm.

## Summary of the results of the Execution Phase 2

In this phase we have developed the algorithms needed to evaluate the level of accuracy of the indicator value in case of the probabilistic model. According to the mathematical model developed in the previous phase, the direct calculation of the accuracy level involved significant computational resources making the process unfeasible. By using a recursive algorithm, however, the accuracy level may be approximated with arbitrary precision and convenient computational costs.

Moreover, a detailed study has been carried out regarding the comparison of iota values to impact factors in case of WoS citation network. The time evolution of the iota indicators have been studied, as well. The calculated indicators show good correlation with impact factors after a long time period since the publication date.

We have conducted a study on the cross-disciplinary normalization of the iota indicator. Is was shown that the indicator is normalized for different scientific domains and therefore, the normalization method should not be applied.

Finally, it was shown that the role of the initial values in the iota algorithm, which can be the impact factor of the journal, article ratings provided by readers or its combination, is important in the case of new articles. However, as time goes these initial values are diminuated and the iota value will be governed only by the citations received from other articles.

## Progress

Working Phase 1: Completed (Technical report delivered in December 2016)

• Act.1.1: Definition of the deterministic indicator calculation model.

Working Phase 2: Completed (Technical report delivered in November 2017)

• Act. 2.1. Algorithm implementation, indicator calculation on existing databases.
• Act. 2.2 Analytic and computer simulation study of the indicator convergence, and the effects of the initial conditions.
• Act. 2.3 Redefinition of the model in order to eliminate the dependence on initial conditions (return to Act. 1.1).
• Act. 2.4 Finding optimal time periods in order to interpolate between initial values and values obtained by article citation data.
• Act. 2.5 Analytical definition and development of the probabilistic article indicator model.
• Act. 2.6 Finding and implementation of some optimal algorithms for convoluting probability distributions.
• Act. 2.7 Study of probability distributions and their characteristics (expected value, variance etc.) convergence, and teir dependence on the initial form of the applied distributions.

Working Phase 2: Completed

• Act. 3.1. Comparison of the iota indicator with other existing scientometric indicators.
• Act. 3.2 Comparison of the results obtained for different scientific domains and application of normalization methods.
• Act. 3.3 Studying the methods by which peer review information provided by article rating can be used to improve the indicator.
• Act. 3.4 Investigating how to detect and reject attempts of indicator manipulation.
• Act. 3.5 Upload programs to server and solve the problem of parallel processing, prioritization and optimization of tasks.
• Act. 3.6 Continuous program verification and periodic submission of the updated database to the economic agent.

## Publications

• Lazar Zs-I, Papp I, Varga L, Jarai-Szabo F, Deritei D, Ercsey-Ravasz M, "Stochastic graph Voronoi tessellation reveals community structure", Physical Review E, vol. 95, 022306:1-13, 2017.
• X. Yin, B. Sedighi, M. Varga, M. Ercsey-Ravasz, Z. Toroczkai, X.S. Hu, "Efficient analog Circuits for Boolean Satisfiability", IEEE Transanctions on VLSI Systems, accepted and posted online, doi:10.1109/TVLSI.2017.2754192 (2017)
• Levente Varga; Dávid Deritei; Mária Ercsey-Ravasz, Razvan Florian, Zsolt I. Lázár, István Papp, Ferenc Járai-Szabó,  "Normalizing scientometric indicators of individual publications using local cluster detection methods on citation networks",   International Journal of Educational and Pedagogical Sciences, vol. 12, no. 9, (2018). ICCSIB 2018 : 20th International Conference on Cybermetrics, Scientometrics, Informetrics and Bibliometrics, Barcelona, Spain, October 29-30, 2018.
• X. Yin, B. Sedighi, M. Varga, M. Ercsey-Ravasz, Z. Toroczkai, X.S. Hu, "Efficient analog Circuits for Boolean Satisfiability", IEEE Transanctions on VLSI Systems, vol. 26, p. 155-167,  (2018)
• B. Molnar, F. Molnar, M. Varga, Z. Toroczkai, M Ercsey-Ravasz, Nature Communications, under evaluation 2018.
• Z.I. Lázár, D.J. Dijk, A.A. Lázár, Infraslow oscillations in human sleep spindle activity, Journal of Neuroscience Methods, under evaluation 2018
• Maria Ercsey-Ravasz, "A halozatkutatas viharos terhoditasa" ("The New Era of  Network Science"), Jozsef Attila Szabadegyetem,  Budapest, February 2018, invited talk