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A logic-based framework leveraging neural networks for studying the evolution of neurological disorders. (English) Zbl 1472.68187

Summary: Deductive formalisms have been strongly developed in recent years; among them, answer set programming (ASP) gained some momentum and has been lately fruitfully employed in many real-world scenarios. Nonetheless, in spite of a large number of success stories in relevant application areas, and even in industrial contexts, deductive reasoning cannot be considered the ultimate, comprehensive solution to artificial intelligence; indeed, in several contexts, other approaches result to be more useful. Typical bioinformatics tasks, for instance classification, are currently carried out mostly by machine learning (ML)-based solutions.
In this paper, we focus on the relatively new problem of analyzing the evolution of neurological disorders. In this context, ML approaches already demonstrated to be a viable solution for classification tasks; here, we show how ASP can play a relevant role in the brain evolution simulation task. In particular, we propose a general and extensible framework to support physicians

MSC:

68T27 Logic in artificial intelligence
68N17 Logic programming
92-08 Computational methods for problems pertaining to biology
92-10 Mathematical modeling or simulation for problems pertaining to biology
92B20 Neural networks for/in biological studies, artificial life and related topics
92C20 Neural biology
92C50 Medical applications (general)
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[1] Adrian, W. T., Alviano, M., Calimeri, F., Cuteri, B., Dodaro, C., Faber, W., Fuscà, D., Leone, N., Manna, M., Perri, S., Ricca, F., Veltri, P. and Zangari, J.2018. The ASP system DLV: advancements and applications. KI 32, 2-3, 177-179.
[2] Alviano, M., Amendola, G., Dodaro, C., Leone, N., Maratea, M. and Ricca, F.2019. Evaluation of disjunctive programs in WASP. In Logic Programming and Nonmonotonic Reasoning - 15th International Conference, LPNMR 2019, Philadelphia, PA, USA, June 3-7, 2019, Proceedings, Balduccini, M., Lierler, Y., and Woltran, S., Eds. Lecture Notes in Computer Science, vol. 11481. Springer, 241-255. · Zbl 07115978
[3] Arias, J., Carro, M., Salazar, E., Marple, K. and Gupta, G.2018. Constraint answer set programming without grounding. TPLP 18, 3-4, 337-354. · Zbl 1451.68063
[4] Balduccini, M. and Lierler, Y.2017. Constraint answer set solver EZCSP and why integration schemas matter. TPLP 17, 4, 462-515. · Zbl 1379.68038
[5] Baral, C.2003. Knowledge Representation, Reasoning, and Declarative Problem Solving. Cambridge University Press, New York, NY, USA. · Zbl 1056.68139
[6] Bargmann, C. and Marder, E.2013. From the connectome to brain function. Nature Methods 10, 483.
[7] Barrett, C., Fontaine, P. and Tinelli, C.2016. The Satisfiability Modulo Theories Library (SMT-LIB). URL: www.SMT-LIB.org
[8] Barrett, C. W., Deters, M., De Moura, L. M., Oliveras, A. and Stump, A.2013. 6 years of SMT-COMP. J. Autom. Reasoning 50, 3, 243-277.
[9] Barrett, C. W. and Tinelli, C.2018. Satisfiability modulo theories. In Handbook of Model Checking, Clarke, E. M., Henzinger, T. A., Veith, H. and Bloem, R., Eds. Springer, 305-343. · Zbl 1392.68379
[10] Baselice, S., Bonatti, P. A. and Gelfond, M.2005. Towards an integration of answer set and constraint solving. In Logic Programming, 21st International Conference, ICLP 2005, Sitges, Spain, October 2-5, 2005, Proceedings, Gabbrielli, M. and Gupta, G., Eds. Lecture Notes in Computer Science, vol. 3668. Springer, 52-66. · Zbl 1165.68481
[11] Beck, H., Dao-Tran, M., Eiter, T. and Fink, M.2015. LARS: A logic-based framework for analyzing reasoning over streams. In AAAI. AAAI Press, 1431-1438.
[12] Brooks, D. R., Erdem, E., Erdogan, S. T., Minett, J. W. and Ringe, D.2007. Inferring phylogenetic trees using answer set programming. J. Autom. Reasoning 39, 4, 471-511. · Zbl 1132.68676
[13] Calimeri, F., Cauteruccio, F., Marzullo, A., Stamile, C. and Terracina, G.2018. Mixing logic programming and neural networks to support neurological disorders analysis. In RuleML+RR. Lecture Notes in Computer Science, vol. 11092. Springer, 33-47.
[14] Calimeri, F., Cozza, S. and Ianni, G.2007. External sources of knowledge and value invention in logic programming. Ann. Math. Artif. Intell. 50,3-4, 333-361. · Zbl 1125.68026
[15] Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Ricca, F. and Schaub, T.2012. ASP-Core-2: Input language format.
[16] Calimeri, F., Fink, M., Germano, S., Humenberger, A., Ianni, G., Redl, C., Stepanova, D., Tucci, A. and Wimmer, A.2016. Angry-hex: An artificial player for angry birds based on declarative knowledge bases. IEEE Trans. Comput. Intellig. and AI in Games 8,2, 128-139.
[17] Calimeri, F., Fuscà, D., Germano, S., Perri, S., and Zangari, J.2019. Fostering the use of declarative formalisms for real-world applications: The embasp framework. New Generation Comput. 37, 1, 29-65.
[18] Calimeri, F., Fuscà, D., Perri, S. and Zangari, J.2017a. External computations and interoperability in the new DLV grounder. In AI*IA 2017 Advances in Artificial Intelligence - XVIth International Conference of the Italian Association for Artificial Intelligence, Bari, Italy, November 14-17, 2017, Proceedings,Esposito, F., Basili, R., Ferilli, S. and Lisi, F. A., Eds. Lecture Notes in Computer Science, vol. 10640. Springer, 172-185.
[19] Calimeri, F., Fuscà, D., Perri, S. and Zangari, J.2017b. I-DLV: the new intelligent grounder of DLV. Intelligenza Artificiale 11, 1, 5-20.
[20] Calimeri, F., Ianni, G., Krennwallner, T. and Ricca, F.2012. The answer set programming competition. AI Magazine 33, 4, 114-118.
[21] Calimeri, F., Marzullo, A., Stamile, C. and Terracina, G.2018. Graph based neural networks for automatic classification of multiple sclerosis clinical courses. In 26th European Symposium on Artificial Neural Networks, ESANN 2018, Bruges, Belgium, April 25-27, 2018.
[22] Calimeri, F. and Ricca, F.2013. On the application of the answer set programming system DLV in industry: a report from the field. Book Reviews 2013, 03, 1-16.
[23] Cauteruccio, F., Lo Giudice, P., Terracina, G., Ursino, D., Mammone, N. and Morabito, F.2019. A new network-based approach to investigating neurological disorders. International Journal of Data Mining, Modelling and Management 11, 315-349.
[24] Chabierski, P., Russo, A., Law, M. and Broda, K.2017. Machine comprehension of text using combinatory categorial grammar and answer set programs. In COMMONSENSE. CEUR Workshop Proceedings, vol. 2052. CEUR-WS.org.
[25] Cok, D. R., Stump, A. and Weber, T.2015. The 2013 evaluation of SMT-COMP and SMT-LIB. J. Autom. Reasoning 55, 1, 61-90. · Zbl 1356.68185
[26] Dodaro, C. and Ricca, F.2018. The external interface for extending WASP. Theory and Practice of Logic Programming [online] 1-24. doi: doi:10.1017/S1471068418000558.
[27] Duun-Henriksen, J., Madsen, R., Remvig, L., Thomsen, C., Sorensen, H. and Kjaer, T.2012. Automatic detection of childhood absence epilepsy seizures: toward a monitoring device. Pediatric Neurology 46, 5, 287-292.
[28] Eiter, T., Fink, M., Ianni, G., Krennwallner, T., Redl, C. and Schüller, P.2016. A model building framework for answer set programming with external computations. TPLP 16, 4, 418-464. · Zbl 1379.68058
[29] Eiter, T., Germano, S., Ianni, G., Kaminski, T., Redl, C., Schüller, P. and Weinzierl, A.2018. The DLVHEX system. KI - Künstliche Intelligenz 32, 2-3, 187-189.
[30] Eiter, T., Germano, S., Ianni, G., Kaminski, T., Redl, C., Schüller, P. and Weinzierl, A.2018. The DLVHEX system. KI 32, 2-3, 187-189.
[31] Eiter, T., Redl, C. and Schüller, P.2016. Problem solving using the HEX family. In Computational Models of Rationality, Essays Dedicated to Gabriele Kern-Isberner on the Occasion of her 60th Birthday, Beierle, C., Brewka, G., and Thimm, M., Eds. College Publications, 150-174.
[32] Erdem, E., Gelfond, M. and Leone, N.2016. Applications of answer set programming. AI Magazine 37, 3, 53-68.
[33] Faber, W., Leone, N. and Pfeifer, G.2004. Recursive aggregates in disjunctive logic programs: Semantics and complexity. In Proceedings of the 9th European Conference on Artificial Intelligence (JELIA 2004), Alferes, J. J. and Leite, J., Eds. Lecture Notes on Artificial Intelligence (LNAI), vol. 3229. Springer Verlag, 200-212. · Zbl 1111.68380
[34] Febbraro, O., Leone, N., Grasso, G. and Ricca, F.2012. JASP: A framework for integrating answer set programming with Java. In Principles of Knowledge Representation and Reasoning: Proceedings of the Thirteenth International Conference, KR 2012, Rome, Italy, June 10-14, 2012,Brewka, G., Eiter, T., and Mcilraith, S. A., Eds. AAAI Press.
[35] Febbraro, O., Reale, K. and Ricca, F.2011. Aspide: Integrated development environment for answer set programming. In Logic Programming and Nonmonotonic Reasoning - 11th International Conference, LPNMR 2011, Vancouver, Canada, May 16-19, 2011. Proceedings. Lecture Notes in Computer Science, vol. 6645, 317-330.
[36] Fuscà, D., Calimeri, F., Zangari, J. and Perri, S.2017. I-DLV+MS: preliminary report on an automatic ASP solver selector. In RCRA@AI*IA. CEUR Workshop Proceedings, vol. 2011. CEUR-WS.org, 26-32.
[37] Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T.2014. Clingo = ASP + control: Preliminary report. In Technical Communications of the Thirtieth International Conference on Logic Programming (ICLP’14), Leuschel, M. and Schrijvers, T., Eds. Vol. arXiv:1405.3694v1. Theory and Practice of Logic Programming, Online Supplement. · Zbl 07107408
[38] Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T.2019. Multi-shot ASP solving with clingo. TPLP 19, 1, 27-82. · Zbl 07107408
[39] Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T., Schneider, M. T. and Ziller, S.2011. A portfolio solver for answer set programming: Preliminary report. In LPNMR. LNCS, vol. 6645. Springer, 352-357.
[40] Gebser, M., Leone, N., Maratea, M., Perri, S., Ricca, F. and Schaub, T.2018. Evaluation techniques and systems for answer set programming: a survey. In Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI 2018, July 13-19, 2018, Stockholm, Sweden., J. Lang, Ed. ijcai.org, 5450-5456.
[41] Gebser, M., Maratea, M. and Ricca, F.2016. What’s hot in the answer set programming competition. In Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, February 12-17, 2016, Phoenix, Arizona, USA., Schuurmans, D. and Wellman, M. P., Eds. AAAI Press, 4327-4329.
[42] Gebser, M., Maratea, M. and Ricca, F.2017. The sixth answer set programming competition. Journal of Artificial Intelligence Research 60, 41-95. · Zbl 1418.68030
[43] Gebser, M., Maratea, M. and Ricca, F.2019. The seventh answer set programming competition: Design and results. CoRR abs/1904.09134. · Zbl 1418.68029
[44] Gebser, M., Schaub, T., Thiele, S. and Veber, P.2011. Detecting inconsistencies in large biological networks with answer set programming. Theory and Practice of Logic Programming 11, 2-3, 323-360. · Zbl 1220.68036
[45] Gelfond, M.2010. Knowledge representation language p-log - A short introduction. In Datalog, De Moor, O., Gottlob, G., Furche, T., and Sellers, A., Eds. LNCS, vol. 6702. Springer, 369-383.
[46] Gelfond, M. and Leone, N.2002. Logic Programming and Knowledge Representation – the A-Prolog perspective. Artificial Intelligence 138, 1-2, 3-38. · Zbl 0995.68022
[47] Gelfond, M. and Lifschitz, V.1991.Classical Negation in Logic Programs and Disjunctive Databases. New Gen. Comput. 9, 365-385. · Zbl 0735.68012
[48] Goodfellow, I. J., Bengio, Y. and Courville, A. C.2016. Deep Learning. Adaptive Computation and Machine Learning. MIT Press. · Zbl 1373.68009
[49] Haykin, S.1998. Neural Networks: A Comprehensive Foundation, 2nd ed. Prentice Hall PTR, Upper Saddle River, NJ, USA. · Zbl 0934.68076
[50] Hornero, R., Abásolo, D., Escudero, J. and Gómez, C.2009. Nonlinear analysis of electroencephalogram and magnetoencephalogram recordings in patients with Alzheimer’s disease. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 367, 1887, 317-336. · Zbl 1221.94016
[51] Hu, Z., Ma, X., Liu, Z., Hovy, E. H. and Xing, E. P.2016. Harnessing deep neural networks with logic rules. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, ACL 2016, August 7-12, 2016, Berlin, Germany, Volume 1: Long Papers.
[52] Ion-Margineanu, A., Kocevar, G., Stamile, C., Sima, D. M., Durand-Dubief, F., Huffel, S. V. and Sappey-Marinier, D.2017. A comparison of machine learning approaches for classifying multiple sclerosis courses using MRSI and brain segmentations. In ICANN (2). LNCS, vol. 10614. Springer, 643-651.
[53] Jenkinson, M., Beckmann, C. F., Behrens, T. E. J., Woolrich, M. W. and Smith, S. M.2012. FSL. NeuroImage62, 2, 782-790.
[54] Jeong, J.2004. EEG dynamics in patients with Alzheimer’s disease. Clinical Neurophysiology 115, 7, 1490-1505.
[55] Kaminski, R., Schaub, T. and Wanko, P.2017. A tutorial on hybrid answer set solving with clingo. In Reasoning Web. Semantic Interoperability on the Web - 13th International Summer School 2017, London, UK, July 7-11, 2017, Tutorial Lectures, Ianni, G., Lembo, D., Bertossi, L. E., Faber, W., Glimm, B., Gottlob, G. and Staab, S., Eds. Lecture Notes in Computer Science, vol. 10370. Springer, 167-203.
[56] Kawahara, J., Brown, C. J., Miller, S. P., Booth, B. G., Chau, V., Grunau, R. E., Zwicker, J. G. and Hamarneh, G.2017. Brainnetcnn: Convolutional neural networks for brain networks; towards predicting neurodevelopment. NeuroImage 146, 1038-1049.
[57] Kingma, D. P. and Ba, J.2014. Adam: A method for stochastic optimization. CoRR abs/1412.6980.
[58] Kocevar, G., Stamile, C., Hannoun, S., Cotton, F., Vukusic, S., Durand-Dubief, F. and Sappey-Marinier, D.2016. Graph theory-based brain connectivity for automatic classification of multiple sclerosis clinical courses. Frontiers in Neuroscience 10, 478.
[59] Kouvaros, P. and Lomuscio, A.2018. Formal verification of CNN-based perception systems. CoRR abs/1811.11373. · Zbl 1351.68294
[60] Law, M., Russo, A. and Broda, K.2015. Learning weak constraints in answer set programming. TPLP 15, 4-5, 511-525. · Zbl 1379.68073
[61] Law, M., Russo, A. and Broda, K.2016. Iterative learning of answer set programs from context dependent examples. TPLP 16, 5-6, 834-848. · Zbl 1379.68074
[62] Lenka, A., Naduthota, R., Jha, M., R, R. P., Prajapati, A., Jhunjhunwala, K., Saini, J., Yadav, R., Bharath, R. and Pal, P.2015. Freezing of gait in parkinsons disease is associated with altered functional brain connectivity. Parkinsonism & Related Disorders24, 100-106.
[63] Leofante, F., Narodytska, N., Pulina, L. and Tacchella, A.2018. Automated verification of neural networks: Advances, challenges and perspectives. CoRR abs/1805.09938.
[64] Leone, N. and Ricca, F.2015. Answer set programming: A tour from the basics to advanced development tools and industrial applications. In Web Reasoning and Rule Systems - 9th International Conference, RR 2015, Berlin, Germany, August 4-5, 2015, Proceedings. Lecture Notes in Computer Science (LNCS). Springer Verlag, 308-326.
[65] Lierler, Y. and Susman, B.2017. On relation between constraint answer set programming and satisfiability modulo theories. TPLP 17, 4, 559-590. · Zbl 1379.68285
[66] Lifschitz, V.1999. Answer Set Planning. In Proceedings of the 16th International Conference on Logic Programming (ICLP’99), Schreye, D. D., Ed. The, Mit Press, Cruces, Las, New Mexico, Usa, 23-37.
[67] Lonc, Z. and Truszczyński, M.2006. Computing minimal models, stable models and answer sets. TPLP 6, 4, 395-449. · Zbl 1110.68022
[68] Lublin, F. D., Reingold, S. C., Cohen, J. A., Cutter, G. R., Sørensen, P. S., Thompson, A. J., Wolinsky, J. S., Balcer, L. J., Banwell, B., Barkhof, F., Bebo, B. J., Calabresi, P. A., Clanet, M., Comi, G., Fox, R. J., Freedman, M. S., Goodman, A. D., Inglese, M., Kappos, L., Kieseier, B. C., Lincoln, J. A., Lubetzki, C., Miller, A. E., Montalban, X., O’Connor, P. W., Petkau, J., Pozzilli, C., Rudick, R. A., Sormani, M. P., Stüve, O., Waubant, E. and Polman, C. H.2014. Defining the clinical course of multiple sclerosis: the 2013 revisions. Neurology 83, 3, 278-286.
[69] Manna, M., Ricca, F. and Terracina, G.2015. Taming primary key violations to query large inconsistent data via ASP. Theory and Practice of Logic Programming (TPLP). Cambridge University Press, UK. 15 (4-5), 696-710. · Zbl 1379.68114
[70] Maratea, M., Pulina, L. and Ricca, F.2014. A multi-engine approach to answer-set programming. Theory and Practice of Logic Programming 14, 6, 841-868.
[71] Marek, V. W. and Truszczyński, M.1999. Stable Models and an Alternative Logic Programming Paradigm. In The Logic Programming Paradigm - A 25-Year Perspective, Apt, K. R., Marek, V. W., Truszczyński, M. and Warren, D. S., Eds. Springer Verlag, 375-398. · Zbl 0979.68524
[72] Mcdonald, W. I., Compston, A., Edan, G., Goodkin, D., Hartung, H.-P., Lublin, F. D., Mcfarland, H. F., Paty, D. W., Polman, C. H., Reingold, S. C., Sandberg-Wollheim, M., Sibley, W., Thompson, A., Van Den Noort, S., Weinshenker, B. Y. and Wolinsky, J. S.2001. Recommended diagnostic criteria for multiple sclerosis: guidelines from the international panel on the diagnosis of multiple sclerosis. Annals of Neurology: Official Journal of the American Neurological Association and the Child Neurology Society 50, 1, 121-127.
[73] Mellarkod, V. S., Gelfond, M. and Zhang, Y.2008. Integrating answer set programming and constraint logic programming. Ann. Math. Artif. Intell. 53,1-4, 251-287. · Zbl 1165.68504
[74] Newman, M. E. J.2002. Assortative mixing in networks. Physical Review Letters89, 208701.
[75] Nickles, M. and Mileo, A.2014. Web stream reasoning using probabilistic answer set programming. In RR. LNCS, vol. 8741. Springer, 197-205.
[76] Niemelä, I.1999. Logic programming with stable model semantics as constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 3-4, 241-273. · Zbl 0940.68018
[77] Petersen, R.2004. Mild cognitive impairment as a diagnostic entity. Journal of Internal Medicine 256, 3, 183-194.
[78] Przymusinski, T. C.1991. Stable semantics for disjunctive programs. New Generation Computing 9, 401-424. · Zbl 0796.68053
[79] Pulina, L. and Tacchella, A.2010. An abstraction-refinement approach to verification of artificial neural networks. In Computer Aided Verification, Touili, T., Cook, B. and Jackson, P., Eds. Springer, Berlin, Heidelberg, 243-257.
[80] Qiu, J., Tang, J., Ma, H., Dong, Y., Wang, K. and Tang, J.2018. Deepinf: Social influence prediction with deep learning. In Proc. of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 2110-2119. ACM. New York, NY, USA.
[81] Rath, J. and Redl, C.2017. Integrating answer set programming with object-oriented languages. In Practical Aspects of Declarative Languages - 19th International Symposium, PADL 2017, Paris, France, January 16-17, 2017, Proceedings,Lierler, Y. and Taha, W., Eds. Lecture Notes in Computer Science, vol. 10137. Springer, 50-67.
[82] Redl, C.2016.The dlvhex system for knowledge representation: recent advances (system description). TPLP 16, 5-6, 866-883. · Zbl 1379.68304
[83] Ricca, F.2003. A Java wrapper for DLV. In Answer Set Programming, Advances in Theory and Implementation, Proceedings of the 2nd Intl. ASP’03 Workshop, Messina, Italy, September 26-28, 2003, Vos, M. D. and Provetti, A., Eds. CEUR Workshop Proceedings, vol. 78. CEUR-WS.org.
[84] Rubinov, M. and Sporns, O.2010. Complex network measures of brain connectivity: Uses and interpretations. NeuroImage 52, 3, 1059-1069.
[85] Schüller, P. and Weinzierl, A.2015. Answer set application programming: A case study on tetris. In Proceedings of the Technical Communications of the 31st International Conference on Logic Programming (ICLP 2015), Cork, Ireland, August 31 - September 4, 2015,Vos, M. D., Eiter, T., Lierler, Y. and Toni, F., Eds. CEUR Workshop Proceedings, vol. 1433. CEUR-WS.org.
[86] Shen, D. and Lierler, Y.2018. SMT-based constraint answer set solver EZSMT+ for non-tight programs. In Principles of Knowledge Representation and Reasoning: Proceedings of the Sixteenth International Conference, KR 2018, Tempe, Arizona, 30 October - 2 November 2018,Thielscher, M., Toni, F., and Wolter, F., Eds. AAAI Press, 67-71.
[87] Shovon, M. H. I., Nandagopal, N., Vijayalakshmi, R., Du, J. T. and Cocks, B.2017. Directed connectivity analysis of functional brain networks during cognitive activity using transfer entropy. Neural Processing Letters 45, 3, 807-824.
[88] Simonyan, K., Vedaldi, A., and Zisserman, A.2013. Deep inside convolutional networks: Visualising image classification models and saliency maps. CoRR abs/1312.6034.
[89] Stamile, C., Kocevar, G., Cotton, F., Hannoun, S., Durand-Dubief, F., Frindel, C., Rousseau, D. and Sappey-Marinier, D.2015. A longitudinal model for variations detection in white matter fiber-bundles. In 2015 International Conference on Systems, Signals and Image Processing (IWSSIP), 57-60.
[90] Stein, M., Simmons, A., Feinstein, J. and Paulus, M.2007. Increased amygdala and insula activation during emotion processing in anxiety-prone subjects. The American Journal of Psychiatry 164, 2, 318-327.
[91] Terracina, G., Leone, N., Lio, V. and Panetta, C.2008. Experimenting with recursive queries in database and logic programming systems. Theory and Practice of Logic Programming (TPLP) 8(2), 129-165. URL: http://arxiv.org/abs/0704.3157. · Zbl 1142.68338
[92] Thimm, M.2014. Tweety - A comprehensive collection of Java libraries for logical aspects of artificial intelligence and knowledge representation. In Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning (KR 2014).
[93] Tournier, J., Calamante, F. and Connelly, A.2012. Mrtrix: Diffusion tractography in crossing fiber regions. The International Journal of Imaging Systems and Technology 22, 1, 53-66.
[94] Towell, G. G. and Shavlik, J. W.1993. Extracting refined rules from knowledge-based neural networks. Machine Learning 13, 71-101.
[95] Vos, T., Allen, C., Arora, M., Barber, R., Bhutta, Z. and Brown, A.2016. Gbd 2015 disease and injury incidence and prevalence collaborators. global, regional, and national incidence, prevalence, and years lived with disability for 310 diseases and injuries, 1990-2015: A systematic analysis for the global burden of disease study 2015. Lancet 388, 10053, 1545-1602.
[96] Wieser, H., Schindler, K. and Zumsteg, D.2006. EEG in Creutzfeldt-Jakob disease. Clinical Neurophysiology 117, 5, 935-951.
[97] Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C. and Yu, P.2019. A comprehensive survey on graph neural networks. CoRR abs/1901.00596.
[98] Zhang, Q., Cao, R., Zhang, S., Edmonds, M., Wu, Y. N. and Zhu, S.2017. Interactively transferring CNN patterns for part localization. CoRR abs/1708.01783.
[99] Zhang, Q., Wu, Y. N. and Zhu, S.2018. Interpretable convolutional neural networks. In 2018 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2018, Salt Lake City, UT, USA, June 18-22, 2018. IEEE Computer Society, 8827-8836.
[100] Zhang, Q., Yang, Y., Wu, Y. N. and Zhu, S.2018. Interpreting CNNs via decision trees. CoRR abs/1802.00121.
[101] Zhang, Q. and Zhu, S.2018. Visual interpretability for deep learning: A survey. Frontiers of IT & EE 19, 1, 27-39.
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.