×

From ecology to finance (and back?): a review on entropy-based null models for the analysis of bipartite networks. (English) Zbl 1419.91482

Summary: Bipartite networks provide an insightful representation of many systems, ranging from mutualistic networks of species interactions to investment networks in finance. The analyses of their topological structures have revealed the ubiquitous presence of properties which seem to characterize many – apparently different – systems. Nestedness, for example, has been observed in biological plant-pollinator as well as in country-product exportation networks. Due to the interdisciplinary character of complex networks, tools developed in one field, for example ecology, can greatly enrich other areas of research, such as economy and finance, and vice versa. With this in mind, we briefly review several entropy-based bipartite null models that have been recently proposed and discuss their application to real-world systems. The focus on these models is motivated by the fact that they show three very desirable features: analytical character, general applicability, and versatility. In this respect, entropy-based methods have been proven to perform satisfactorily both in providing benchmarks for testing evidence-based null hypotheses and in reconstructing unknown network configurations from partial information. Furthermore, entropy-based models have been successfully employed to analyze ecological as well as economic systems. As an example, the application of entropy-based null models has detected early-warning signals, both in economic and financial systems, of the 2007–2008 world crisis. Moreover, they have revealed a statistically-significant export specialization phenomenon of country export baskets in international trade, a result that seems to reconcile Ricardo’s hypothesis in classical economics with recent findings on the (empirical) diversification industrial production at the national level. Finally, these null models have shown that the information contained in the nestedness is already accounted for by the degree sequence of the corresponding graphs.

MSC:

91B60 Trade models
05C80 Random graphs (graph-theoretic aspects)
05C90 Applications of graph theory
91B82 Statistical methods; economic indices and measures
91G99 Actuarial science and mathematical finance
92C42 Systems biology, networks
62P20 Applications of statistics to economics
62P05 Applications of statistics to actuarial sciences and financial mathematics
91G10 Portfolio theory
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Allen, F.; Gale, D., Financial contagion, J. Polit. Econ., 108, 1-33, (2000) · doi:10.1086/262109
[2] Allesina, Stefano; Tang, Si, Stability criteria for complex ecosystems, Nature, 483, 205-208, (2012) · doi:10.1038/nature10832
[3] Almeida-Neto, M.; Guimarães, P.; Guimarães, PR; Loyola, RD; Ulrich, W., A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement, Oikos, 117, 1227-1239, (2008) · doi:10.1111/j.0030-1299.2008.16644.x
[4] Alon, Uri, Network motifs: theory and experimental approaches, Nature Reviews Genetics, 8, 450-461, (2007) · doi:10.1038/nrg2102
[5] Angelini, O.; Cristelli, M.; Zaccaria, A.; Pietronero, L., The complex dynamics of products and its asymptotic properties, PLoS ONE, 12, 1-20, (2017) · doi:10.1371/journal.pone.0177360
[6] Annunziata, MA; Petri, A.; Pontuale, G.; Zaccaria, A., How log-normal is your country? An analysis of the statistical distribution of the exported volumes of products, Eur. Phys. J. Spec. Top., 1995, 1985-1995, (2016) · doi:10.1140/epjst/e2015-50320-7
[7] Arinaminpathy, N.; Kapadia, S.; May, RM, Size and complexity in model financial systems, PNAS, 109, 18338-18343, (2012) · doi:10.1073/pnas.1213767109
[8] Atmar, W.; Patterson, BD, The measure of order and disorder in the distribution of species in fragmented habitat, Oecologia, 96, 373-382, (1993) · doi:10.1007/BF00317508
[9] Azaele, S., Suweis, S., Grilli, J., Volkov, I., Banavar, J.R., Maritan, A.: Statistical mechanics of ecological systems: neutral theory and beyond. Rev. Mod. Phys. (2016). https://doi.org/10.1103/RevModPhys.88.035003
[10] Baiser, B.; Elhesha, R.; Kahveci, T., Motifs in the assembly of food web networks, Oikos, 125, 480-491, (2016) · doi:10.1111/oik.02532
[11] Balassa, B., Trade liberalization and ’revealed’ comparative advantage, Manch. Sch. Econ. Soc. Stud., 33, 99-123, (1965) · doi:10.1111/j.1467-9957.1965.tb00050.x
[12] Barigozzi, M., Fagiolo, G., Garlaschelli, D.: Multinetwork of international trade: a commodity-specific analysis. Phys. Rev. E 81(4), 046,104 (2010). https://doi.org/10.1103/PhysRevE.81.046104
[13] Bastolla, U.; Fortuna, Ma; Pascual-García, A.; Ferrera, A.; Luque, B.; Bascompte, J., The architecture of mutualistic networks minimizes competition and increases biodiversity, Nature, 458, 1018-1020, (2009) · doi:10.1038/nature07950
[14] Battiston, S.; Farmer, JD; Flache, A.; Garlaschelli, D.; Haldane, A.; Heesterbeek, H.; Hommes, C.; Jaeger, C.; May, RM; Scheffer, M., Complexity theory and financial regulation, Science, 351, 818-819, (2016) · doi:10.1126/science.aad0299
[15] Battiston, S.; Puliga, M.; Kaushik, R.; Tasca, P.; Caldarelli, G., DebtRank: too central to Fail? Financial networks, the FED and systemic risk, Sci. Rep., 2, 1-6, (2012) · doi:10.1038/srep00541
[16] Bonanno, G.; Caldarelli, G.; Lillo, F.; Mantegna, RN, Topology of correlation based minimal spanning trees in real and model markets, Phys. Rev. E, 046130, 17-20, (2003) · doi:10.1103/PhysRevE.68.046130
[17] Bonanno, G.; Caldarelli, G.; Lillo, F.; Micciché, S.; Vandewalle, N.; Mantegna, RN, Networks of equities in financial markets, Eur. Phys. J. B, 38, 363-371, (2004) · doi:10.1140/epjb/e2004-00129-6
[18] Borge-Holthoefer, J.; Baños, RA; Gracia-lázaro, C.; Moreno, Y., Emergence of consensus as a modular-to-nested transition in communication dynamics, Sci. Rep., 7, 1-9, (2017) · doi:10.1038/srep41673
[19] Brunnermeier, Markus K., Deciphering the Liquidity and Credit Crunch 2007-2008, Journal of Economic Perspectives, 23, 77-100, (2009) · doi:10.1257/jep.23.1.77
[20] Caccioli, Fabio; Shrestha, Munik; Moore, Cristopher; Farmer, J. Doyne, Stability analysis of financial contagion due to overlapping portfolios, Journal of Banking & Finance, 46, 233-245, (2014) · doi:10.1016/j.jbankfin.2014.05.021
[21] Cadot, Olivier; Carrère, Céline; Strauss-Kahn, Vanessa, Export Diversification: What’s behind the Hump?, Review of Economics and Statistics, 93, 590-605, (2011) · doi:10.1162/REST_a_00078
[22] Caldarelli, G.; Cristelli, M.; Gabrielli, A.; Pietronero, L.; Scala, A.; Tacchella, A., A network analysis of countries’ export flows: firm grounds for the building blocks of the economy, PLoS ONE, 7, 1-17, (2012) · doi:10.1371/journal.pone.0047278
[23] Cane, JH; Minckley, RL; Kervin, LJ; Roulston, TH; Williams, NM, Complex responses within a desert bee guild (Hymenoptera: Apiformes) to urban habitat fragmentation, Ecol. Appl., 16, 632-644, (2006) · doi:10.1890/1051-0761(2006)016[0632:CRWADB]2.0.CO;2
[24] Cerina, F.; Riccaboni, M., World input-output network world input-output network, PLoS ONE, 10, 1-21, (2014) · doi:10.1371/journal.pone.0134025
[25] Chan-Lau, J.A., Espinosa, M., Giesecke, K., Solé, J.A.: Assessing the systemic implications of financial linkages. IMF Glob. Financ. Stab. Rep. 2, 1-38 (2009). https://ssrn.com/abstract=1417920
[26] Chung, Fan; Lu, Linyuan, Connected Components in Random Graphs with Given Expected Degree Sequences, Annals of Combinatorics, 6, 125-145, (2002) · Zbl 1009.05124 · doi:10.1007/PL00012580
[27] Connor, E.F., Simberloff, D.: The assembly of species communities: chance or competition? Ecology 60(6), 1132 (1979). https://doi.org/10.2307/1936961 · doi:10.2307/1936961
[28] Cont, R.; Wagalath, L., Fire sales forensics: measuring endogenous risk, Math. Financ., 26, 835-866, (2016) · Zbl 1348.91291 · doi:10.1111/mafi.12071
[29] Cristelli, M.; Gabrielli, A.; Tacchella, A.; Caldarelli, G.; Pietronero, L., Measuring the intangibles: a metrics for the economic complexity of countries and products, PLoS ONE, 8, e70726, (2013) · Zbl 1327.91053 · doi:10.1371/journal.pone.0070726
[30] Cristelli, M.; Tacchella, A.; Pietronero, L., The heterogeneous dynamics of economic complexity, PLoS ONE, 10, 1-15, (2015) · doi:10.1371/journal.pone.0117174
[31] Di Gangi, D., Lillo, F., Pirino, D.: Assessing systemic risk due to fire sales spillover through maximum entropy network reconstruction. SSRN Electron. J. (2015). https://doi.org/10.2139/ssrn.2639178. https://ssrn.com/abstract=2639178 · Zbl 1402.91842
[32] Diamond, J.M.: Assembly of Species Communities. Belknap Press, Cambridge, MA (1975). https://doi.org/10.2307/1936961 · doi:10.2307/1936961
[33] Diamond, JM; Gilpin, ME, Examination of the null model of connor and simberloff for species co-occurrences on Islands, Oecologia, 52, 64-74, (1982) · doi:10.1007/BF00349013
[34] Donnelly, R.; Marzluff, JM, Importance of reserve size and landscape context to urban bird conservation, Conserv. Biol., 18, 733-745, (2004) · doi:10.1111/j.1523-1739.2004.00032.x
[35] Dormann, CF; Fründ, J.; Bluthgen, N.; Gruber, B., Indices, graphs and null models: analysing bipartite ecological networks, Open Ecol. J., 2, 7-24, (2009) · doi:10.2174/1874213000902010007
[36] Dueñas, M.; Fagiolo, G., Modeling the International-Trade Network: a gravity approach, J. Econ. Interact. Coord., 8, 155-178, (2013) · doi:10.1007/s11403-013-0108-y
[37] Eisenberg, L.; Noe, TH, Systemic risk in financial systems, Manag. Sci., 47, 236-249, (2001) · Zbl 1232.91688 · doi:10.1287/mnsc.47.2.236.9835
[38] Elton, C.S.: Animal Ecology. Sidgwick and Jackson, London (1927)
[39] Erdos, P.; Rényi, A., On random graphs I, Publ. Math. Debr., 6, 290-297, (1959) · Zbl 0092.15705
[40] Fagiolo, G., Reyes, J., Schiavo, S.: World-trade web: topological properties, dynamics, and evolution. Phys. Rev. E (2009). https://doi.org/10.1103/PhysRevE.79.036115
[41] Fahrig, L.: Relative effects of habitat loss and fragmentation on population extinction. J. Wildl. Manag. 61(3), 603-610 (1997). https://doi.org/10.2307/3802168 · doi:10.2307/3802168
[42] Fortunato, Santo, Community detection in graphs, Physics Reports, 486, 75-174, (2010) · doi:10.1016/j.physrep.2009.11.002
[43] Furceri, D.; Mourougane, A., The effect of financial crises on potential output: new empirical evidence from OECD countries, J. Macroecono., 34, 822-832, (2012) · doi:10.1016/j.jmacro.2012.05.010
[44] Glasserman, Paul; Young, H. Peyton, Contagion in Financial Networks, Journal of Economic Literature, 54, 779-831, (2016) · doi:10.1257/jel.20151228
[45] Galeano, J.; Fernandez, M.; Hidalgo, C., ipartite networks provide new insights on international trade markets, Am. Inst. Math. Sci., 7, 399-413, (2012) · Zbl 1268.91107
[46] Garlaschelli, D., Loffredo, M.I.: Fitness-dependent topological properties of the world trade web. Phys. Rev. Lett. 93, 188,701, (2004). https://doi.org/10.1103/PhysRevLett.93.188701
[47] Garlaschelli, D.; Loffredo, MI, Maximum likelihood: extracting unbiased information from complex networks, Phys. Rev. E, 78, 1-5, (2008) · doi:10.1103/PhysRevE.78.015101
[48] Gilpin, ME; Diamond, JM, Factors contributing to non-randomness in species Co-occurrences on Islands, Oecologia, 52, 75-84, (1982) · doi:10.1007/BF00349014
[49] Greenwood, R.; Landier, A.; Thesmar, D., Vulnerable banks, J. Financ. Econ., 115, 471-485, (2015) · doi:10.1016/j.jfineco.2014.11.006
[50] Gualdi, S.; Cimini, G.; Primicerio, K.; Clemente, R.; Challet, D., Statistically validated network of portfolio overlaps and systemic risk, Sci. Rep., 6, 39,467, (2016) · doi:10.1038/srep39467
[51] Guimerà, R., Sales-Pardo, M., Amaral, L.A.N.: Module identification in bipartite and directed networks. Phys. Rev. E 76, 036,102 (2007). https://doi.org/10.1103/PhysRevE.76.036102
[52] Harte, J.: Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics. Oxford University Press, Oxford (2011) · Zbl 1321.92007 · doi:10.1093/acprof:oso/9780199593415.001.0001
[53] Hausmann, Ricardo; Hidalgo, César A., The network structure of economic output, Journal of Economic Growth, 16, 309-342, (2011) · doi:10.1007/s10887-011-9071-4
[54] Hidalgo, C. A.; Hausmann, R., The building blocks of economic complexity, Proceedings of the National Academy of Sciences, 106, 10570-10575, (2009) · doi:10.1073/pnas.0900943106
[55] Hidalgo, C. A.; Klinger, B.; Barabasi, A.-L.; Hausmann, R., The Product Space Conditions the Development of Nations, Science, 317, 482-487, (2007) · doi:10.1126/science.1144581
[56] Hong, Y., On computing the distribution function for the poisson binomial distribution, Comput. Stat. Data Anal., 59, 41-51, (2013) · Zbl 1400.62036 · doi:10.1016/j.csda.2012.10.006
[57] James, Alex; Pitchford, Jonathan W.; Plank, Michael J., Disentangling nestedness from models of ecological complexity, Nature, 487, 227-230, (2012) · doi:10.1038/nature11214
[58] Jaynes, E. T., Information Theory and Statistical Mechanics, Physical Review, 106, 620-630, (1957) · Zbl 0084.43701 · doi:10.1103/PhysRev.106.620
[59] Krause, A.; Giansante, S., Interbank lending and the spread of bank failures: a network model of systemic risk, J. Econ. Behav. Org., 83, 583-608, (2012) · doi:10.1016/j.jebo.2012.05.015
[60] Levy-Carciente, S.; Kenett, DY; Avakian, A.; Stanley, HE; Havlin, S., Dynamical macroprudential stress testing using network theory, J. Bank. Financ., 59, 164-181, (2015) · doi:10.1016/j.jbankfin.2015.05.008
[61] Lintner, J., The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Rev. Econ. Stat., 47, 13-37, (1965) · doi:10.2307/1924119
[62] Mastrandrea, R., Squartini, T., Fagiolo, G., Garlaschelli, D.: Enhanced reconstruction of weighted networks from strengths and degrees. New J. Phys. (2014). https://doi.org/10.1088/1367-2630/16/4/043022 · doi:10.1088/1367-2630/16/4/043022
[63] McGill, Brian J.; Etienne, Rampal S.; Gray, John S.; Alonso, David; Anderson, Marti J.; Benecha, Habtamu Kassa; Dornelas, Maria; Enquist, Brian J.; Green, Jessica L.; He, Fangliang; Hurlbert, Allen H.; Magurran, Anne E.; Marquet, Pablo A.; Maurer, Brian A.; Ostling, Annette; Soykan, Candan U.; Ugland, Karl I.; White, Ethan P., Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework, Ecology Letters, 10, 995-1015, (2007) · doi:10.1111/j.1461-0248.2007.01094.x
[64] Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.: Network motifs: simple building blocks of complex networks. Sci. Rep. 298(October), 11-14 (2002). www.sciencemag.org/cgi/content/full/298/5594/824/DC1 · doi:10.1126/science.298.5594.824
[65] Molloy, M., Reed, B.: The critical phase for random graphs with a given degree sequence. Random Struct. Algorithms. 6, 161-179 (1995). https://doi.org/10.1017/S096354830700867X · Zbl 0823.05050
[66] Mossin, J., Equilibrium in a capital asset market, Econometrica, 34, 768-783, (1966) · doi:10.2307/1910098
[67] Munoz, MA; Jonhson, S.; Dominquez-Garcia, V., Factors determining nestedness in complex networks, PLoS ONE, 8, e74025, (2013) · doi:10.1371/journal.pone.0074025
[68] Newman, M.E.J.: Scientific collaboration networks. ii. shortest paths, weighted networks, and centrality. Phys. Rev. E 64, 016,132 (2001). https://doi.org/10.1103/PhysRevE.64.016132
[69] Newman, MEJ; Girvan, M., Finding and evaluating community structure in networks, Phys. Rev. E, 69, 026,113, (2004) · doi:10.1103/PhysRevE.69.026113
[70] O’Neill, J.: Who You Calling a BRIC? Bloomberg, New York (2013). https://www.bloomberg.com/view/articles/2013-11-12/who-you-calling-a-bric-. Accessed 05 Sep, 2017
[71] Park, J.; Newman, MEJ, Statistical mechanics of networks, Phys. Rev. E, 70, 66,117, (2004) · doi:10.1103/PhysRevE.70.066117
[72] Payrató Borrás, C., Hernández, L., Moreno, Y.: Breaking the spell of nestedness. ArXiv e-prints (2017). arXiv:1711.03134
[73] Pilosof, S.; Porter, MA; Pascual, M.; Kéfi, S., The multilayer nature of ecological networks, Nat. Ecol. Evol., 1, 1-9, (2017) · doi:10.1038/s41559-017-0101
[74] Pugliese, E., Cimini, G., Patelli, A., Zaccaria, A., Pietronero, L., Gabrielli, A.: Unfolding the innovation system for the development of countries: co-evolution of Science, Technology and Production. ArXiv e-prints (2017). arXiv:1707.05146
[75] Pugliese, E., Zaccaria, A., Pietronero, L.: On the convergence of the Fitness-Complexity Algorithm. ArXiv e-prints (2014). arXiv:1410.0249
[76] Pugliese, E.; Zaccaria, A.; Pietronero, L., On the convergence of the Fitness-Complexity Algorithm, Eur. Phys. J. Spec. Top., 225, 1893-1911, (2016) · doi:10.1140/epjst/e2015-50118-1
[77] Ricardo, D.: On the Principles of Political Economy, and Taxation. John Murray, London (1817)
[78] Roberts, A.; Stone, L., Island-sharing by archipelago species, Oecologia, 83, 560-567, (1990) · doi:10.1007/BF00317210
[79] Saavedra, S., Reed-Tsochas, F., Uzzi, B.: Common Organizing Mechanisms in Ecological and Socio-economic Networks. ArXiv e-prints (2011) arXiv:1110.0376
[80] Saracco, F., Di Clemente, R., Gabrielli, A., Squartini, T.: Randomizing bipartite networks: the case of the World Trade Web. Sci. Rep. 5, 10,595 (2015). http://www.nature.com/articles/srep10595
[81] Saracco, F., Di Clemente, R., Gabrielli, A., Squartini, T.: Detecting early signs of the 2007-2008 crisis in the world trade. Sci. Rep. 6, 30,286 (2016). https://doi.org/10.1038/srep30286
[82] Saracco, F.; Straka, MJ; Clemente, R.; Gabrielli, A.; Caldarelli, G.; Squartini, T., Inferring monopartite projections of bipartite networks: an entropy-based approach, New J. Phys., 19, 053,022, (2016) · doi:10.1088/1367-2630/aa6b38
[83] Serrano, M.A., Boguñá, M.: Topology of the world trade web. Phys. Rev. E 68, 015,101 (2003). https://doi.org/10.1103/PhysRevE.68.015101
[84] Shleifer, A., Vishny, R.W.: Fire sales in finance and macroeconomics. Working Paper 16642, National Bureau of Economic Research (2010). https://doi.org/10.3386/w16642
[85] Shoval, Oren; Alon, Uri, SnapShot: Network Motifs, Cell, 143, 326-326.e1, (2010) · doi:10.1016/j.cell.2010.09.050
[86] Smith, A.: An Inquiry into the Nature and Causes of the Wealth of Nations. W. Strahan and T. Cadell, London (1776) · doi:10.1093/oseo/instance.00043218
[87] Squartini, T., Almog, A., Caldarelli, G., van Lelyveld, I., Garlaschelli, D., Cimini, G.: Enhanced capital-asset pricing model for the reconstruction of bipartite financial networks. Phys. Rev. E 96, 032,315 (2017). https://doi.org/10.1103/PhysRevE.96.032315
[88] Staniczenko, PPA; Kopp, JC; Allesina, S., The ghost of nestedness in ecological networks, Nat. Commun., 4, 1391-1396, (2013) · doi:10.1038/ncomms2422
[89] Stone, L.; Roberts, A., The checkerboard score and species distributions, Oecologia, 85, 74-79, (1990) · doi:10.1007/BF00317345
[90] Straka, MJ; Caldarelli, G.; Saracco, F., Grand canonical validation of the bipartite International Trade Network, Phys. Rev. E, 96, 1-12, (2017) · doi:10.1103/PhysRevE.96.022306
[91] Suweis, Samir; Simini, Filippo; Banavar, Jayanth R.; Maritan, Amos, Emergence of structural and dynamical properties of ecological mutualistic networks, Nature, 500, 449-452, (2013) · doi:10.1038/nature12438
[92] Tacchella, A.; Cristelli, M.; Caldarelli, G.; Gabrielli, A.; Pietronero, L., A new metrics for countries’ fitness and products’ complexity, Sci. Rep., 2, 1-4, (2012) · Zbl 1327.91053 · doi:10.1038/srep00723
[93] Thébault, Elisa, Identifying compartments in presence-absence matrices and bipartite networks: insights into modularity measures, Journal of Biogeography, 40, 759-768, (2012) · doi:10.1111/jbi.12015
[94] Thébault, E.; Fontaine, C., Stability of ecological communities and the architecture of mutualistic and trophic networks, Science, 329, 853-856, (2010) · doi:10.1126/science.1188321
[95] Toonders, J.: Data is the new oil of the digital economy. WIRED (2014). https://www.wired.com/insights/2014/07/data-new-oil-digital-economy/. Accessed 10 Sep, 2017
[96] Williams, Richard J., Simple MaxEnt models explain food web degree distributions, Theoretical Ecology, 3, 45-52, (2009) · doi:10.1007/s12080-009-0052-6
[97] Williams, Richard J., Biology, Methodology or Chance? The Degree Distributions of Bipartite Ecological Networks, PLoS ONE, 6, e17645, (2011) · doi:10.1371/journal.pone.0017645
[98] Wong, E.; Baur, B.; Quader, S.; Huang, CH, Biological network motif detection: principles and practice, Brief. Bioinform., 13, 202-215, (2012) · doi:10.1093/bib/bbr033
[99] World Economic Forum: Building Resilience in Supply Chains. Tech. Rep. January (2013). http://www3.weforum.org/docs/WEF_RRN_MO_BuildingResilienceSupplyChains_Report_2013.pdf
[100] World Trade Organization: Trade in goods and services has fluctuated significantly over the last 20 years. Tech. rep. (2015). https://www.wto.org/english/res_e/statis_e/its2015_e/its15_highlights_e.pdf
[101] Zaccaria, A.; Cristelli, M.; Tacchella, A.; Pietronero, L., How the taxonomy of products drives the economic development of countries, PLoS ONE, 9, 1-17, (2014) · doi:10.1371/journal.pone.0113770
[102] Zhou, T., Ren, J., Medo, M., Zhang, Y.C.: Bipartite network projection and personal recommendation. Phys. Rev. E (2007). https://doi.org/10.1103/PhysRevE.76.046115
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.