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Foundations of semialgebraic gene-environment networks

  • * Corresponding author: Erik Kropat

    * Corresponding author: Erik Kropat 
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  • Gene-environment network studies rely on data originating from different disciplines such as chemistry, biology, psychology or social sciences. Sophisticated regulatory models are required for a deeper investigation of the unknown and hidden functional relationships between genetic and environmental factors. At the same time, various kinds of uncertainty can arise and interfere with the system's evolution. The aim of this study is to go beyond traditional stochastic approaches and to propose a novel framework of semialgebraic gene-environment networks. Foundation is laid for future research, methodology and application. This approach is a natural extension of interconnected systems based on stochastic, polyhedral, ellipsoidal or fuzzy (linguistic) uncertainty. It allows for a reconstruction of the underlying network from uncertain (semialgebraic) data sets and for a prediction of the uncertain futures states of the system. In addition, aspects of network pruning for large regulatory systems in genome-wide studies are discussed leading to mixed-integer programming (MIP) and continuous programming.

    Mathematics Subject Classification: Primary:90C35, 93A30, 92D10, 14P10;Secondary:62J02.


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  • Figure 1.  Gene-environment networks: Interactions between genes (red), environmental factors and genes (green) and between environmental factors (blue).

    Figure 2.  Gene-environment networks with cluster partition: Interactions between genetic clusters (red), environmental clusters and genetic clusters (green) and between environmental clusters (blue).

    Figure 3.  Gene-environment network under semialgebraic uncertainty: Interactions between genetic clusters and/or environmental clusters as well as the corresponding semialgebraic uncertainty sets.

    Figure 4.  Comparison of measurements and predictions. The computation of the parameter vector $\theta \in \Theta$ depends on $K$ direct comparisons of the intersection between semialgebraic measurements and predictions

  • [1] M. U. AkhmetM. KiraneM. A. Tleubergenova and G. Weber, Control and optimal response problems for quasilinear impulsive integrodifferential equations, European J. Oper. Res., 169 (2006), 1128-1147.  doi: 10.1016/j.ejor.2004.10.030.
    [2] B. Akteke-ÖztürkG.-W. Weber and G. Köksal, Optimization of generalized desirability functions under model uncertainty, Optimization, 66 (2017), 2157-2169.  doi: 10.1080/02331934.2017.1371167.
    [3] A. Arnau-Soler, et al., Genome-wide by environment interaction studies of depressive symptoms and psychosocial stress in UK Biobank and Generation Scotland, Translational Psychiatry, 9 (2019), 13 pp. doi: 10.1214/19-AOAS1291.
    [4] E. AyyildizV. Purutçuoglu and G. W. Weber, Loop-based conic multivariate adaptive regression splines is a novel method for advanced construction of complex biological networks, European J. Oper. Res., 270 (2018), 852-861.  doi: 10.1016/j.ejor.2017.12.011.
    [5] J. Bochnak, M. Coste and M.-F. Roy, Semi-algebraic Sets, A Series of Modern Surveys in Mathematics, 36, Springer Berlin Heidelberg, Berlin, Heidelberg, 1998, 23-58. doi: 10.1007/978-3-662-03718-8_3.
    [6] A. ÇevikG. WeberB. M. Eyüboglu and K. K. Oguz, The Alzheimer's disease neuroimaging initiative Voxel-MARS: A method for early detection of Alzheimer's disease by classification of structural brain MRI, Ann. Oper. Res., 258 (2017), 31-57.  doi: 10.1007/s10479-017-2405-7.
    [7] H. Delfs and M. Knebusch, Locally Semialgebraic Spaces, Lecture Notes in Mathematics, Vol. 1173, Springer-Verlag, Berlin, 1985. doi: 10.1007/BFb0074551.
    [8] R. Dobson and G. Giovannoni, Multiple sclerosis - A review, European Journal of Neurology, 26 (2019), 27-40.  doi: 10.1111/ene.13819.
    [9] X. Dong and Y. Yang, Network pruning via transformable architecture search, NeurIPS, 32 (2019), 760-771. 
    [10] A. EidI. Mhatre and J. R. Richardson, Gene-environment interactions in Alzheimer's disease: A potential path to precision medicine, Pharmacology & Therapeutics, 199 (2019), 173-187.  doi: 10.1016/j.pharmthera.2019.03.005.
    [11] S. Z. A. Gök and G.-W. Weber, On dominance core and stable sets for cooperative ellipsoidal games, Optimization, 62 (2013), 1297-1308.  doi: 10.1080/02331934.2013.793327.
    [12] A. GoliH. K. ZareR. Tavakkoli-Moghaddam and A. Sadegheih, Multiobjective fuzzy mathematical model for a financially constrained closed-loop supply chain with labor employment, Computational Intelligence, 36 (2020), 4-36.  doi: 10.1111/coin.12228.
    [13] A. Goli, H. Khademi Zare, R. Tavakkoli-Moghaddam and A. Sadeghieh, Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem case study: The dairy products industry, Computers and Industrial Engineering, 137 (2019), 106090. doi: 10.1016/j.cie.2019.106090.
    [14] G. KaraA. Özmen and G.-W. Weber, Stability advances in robust portfolio optimization under parallelepiped uncertainty, CEJOR Cent. Eur. J. Oper. Res., 27 (2019), 241-261.  doi: 10.1007/s10100-017-0508-5.
    [15] E. KropatA. ÖzmenG.-W. WeberS. Meyer-Nieberg and O. Defterli, Fuzzy prediction strategies for gene-environment networks- fuzzy regression analysis for two-modal regulatory systems, RAIRO-Oper. Res., 50 (2016), 413-435.  doi: 10.1051/ro/2015044.
    [16] E. Kropat and G.-W. Weber, Fuzzy target-environment networks and fuzzy-regression approaches, Numer. Algebra, Control Optim., 8 (2018), 135-155.  doi: 10.3934/naco.2018008.
    [17] E. Kropat, G.-W. Weber and C. Pedamallu, Regulatory networks under ellipsoidal uncertainty - data analysis and prediction by optimization theory and dynamical systems, in Data Mining: Foundations and Intelligent Paradigms Vol. 2, Intell. Syst. Ref. Libr., 24, Springer, Berlin, 2012, 27-56. doi: 10.1007/978-3-642-23241-1_3.
    [18] E. KropatG.-W. Weber and J.-J. Rückmann, Regression analysis for clusters in gene-environment networks based on ellipsoidal calculus and optimization, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 17 (2010), 639-657. 
    [19] E. KürümG.-W Weber and C. Iyigun, Early warning on stock market bubbles via methods of optimization, clustering and inverse problems, Ann. Oper. Res., 260 (2018), 293-320.  doi: 10.1007/s10479-017-2496-1.
    [20] A. Mardani, D. Kannan, R. E. Hooker, S. Ozkul, M. Alrasheedi and E. B. Tirkolaee, Evaluation of green and sustainable supply chain management using structural equation modelling: A systematic review of the state of the art literature and recommendations for future research, Journal of Cleaner Production, 249 (2020), 119383. doi: 10.1016/j.jclepro.2019.119383.
    [21] K. McAllister, et al., Current challenges and new opportunities for gene-environment interaction studies of complex diseases, American Journal of Epidemiology, 186 (2017), 753-761.  doi: 10.1093/aje/kwx227.
    [22] M. C. Mills and C. Rahal, A scientometric review of genome-wide association studies, Communications Biology, 2 (2019), 11 pp. doi: 10.1038/s42003-018-0261-x.
    [23] R. J. Musci, J. L. Augustinavicius and H. Volk, Gene-environment interactions in psychiatry: Recent evidence and clinical implications, Current Psychiatry Reports, 21 (2019), 81 pp. doi: 10.1007/s11920-019-1065-5.
    [24] Ö. N. Onak, Y. S. Dogrusoz and G. Weber, Robustness of reduced order nonparametric model for inverse ECG solution against modeling and measurement noise, in Computing in Cardiology, CinC 2018, Maastricht, The Netherlands, September 23-26, 2018, 2018, 1-4.
    [25] A. ÖzmenE. Kropat and G.-W. Weber, Spline regression models for complex multi-modal regulatory networks, Optim. Methods Softw., 29 (2014), 515-534.  doi: 10.1080/10556788.2013.821611.
    [26] A. ÖzmenE. Kropat and G.-W. Weber, Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty, Optimization, 66 (2017), 2135-2155.  doi: 10.1080/02331934.2016.1209672.
    [27] A. ÖzmenG.-W. Weber and E. Kropat, Robustification of conic generalized partial linear models under polyhedral uncertainty, International IFNA-ANS Scientific Journal "Problems of Nonlinear Analysis in Engineering Systems", 38 (2012), 104-113. 
    [28] S. Özöǧür-Akyüz and G.-W. Weber, On numerical optimization theory of infinite kernel learning, J. Global Optim., 48 (2010), 215-239.  doi: 10.1007/s10898-009-9488-x.
    [29] S. Özögür-Akyüz and G.-W. Weber, Infinite kernel learning via infinite and semi-infinite programming, Optim. Methods Softw., 25 (2010), 937-970.  doi: 10.1080/10556780903483349.
    [30] T. PaksoyE. Özceylan and G.-W. Weber, Profit oriented supply chain network optimization, CEJOR Cent. Eur. J. Oper. Res., 21 (2013), 455-478.  doi: 10.1007/s10100-012-0240-0.
    [31] J. RogersT. Renoir and A. J. Hannan, Gene-environment interactions informing therapeutic approaches to cognitive and affective disorders, Neuropharmacology, 145 (2019), 37-48.  doi: 10.1016/j.neuropharm.2017.12.038.
    [32] S. K. RoyG. Maity and G.-W Weber, Multi-objective two-stage grey transportation problem using utility function with goals, CEJOR Cent. Eur. J. Oper. Res., 25 (2017), 417-439.  doi: 10.1007/s10100-016-0464-5.
    [33] E. Savku and G. -W Weber, A stochastic maximum principle for a Markov regime-switching jump-diffusion model with delay and an application to finance, J. Optim. Theory Appl., 179 (2018), 696-721.  doi: 10.1007/s10957-017-1159-3.
    [34] A. J. Schork, et al., A genome-wide association study of shared risk across psychiatric disorders implicates gene regulation during fetal neurodevelopment, Nature Neuroscience, 22 (2019), 353-361.  doi: 10.1038/s41593-018-0320-0.
    [35] A. Shapiro, D. Dentcheva and A. Ruszczyński, Lectures on Stochastic Programming: Modeling and Theory, Second Edition, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2014. doi: 10.1137/1.9781611973433.
    [36] O. Stein, Bi-Level Strategies in Semi-Infinite Programming, Nonconvex Optimization and its Applications, 71, Kluwer Academic Publishers, Boston, MA, 2003. doi: 10.1007/978-1-4419-9164-5.
    [37] P. TaylanG.-W. Weber and E. Kropat, Approximation of stochastic differential equations by additive models using splines and conic programming, International Journal of Computing Anticipatory Systems, 21 (2008), 341-352. 
    [38] E. B. Tirkolaee, A. Goli and G.-W. Weber, Multi-objective Aggregate Production Planning Model Considering Overtime and Outsourcing Options Under Fuzzy Seasonal Demand, Springer, Cham, 2019, 81-96.
    [39] E. B. TirkolaeeS. HadianG.-W. Weber and I. Mahdavi, A robust green traffic-based routing problem for perishable products distribution, Computational Intelligence, 36 (2020), 80-101.  doi: 10.1111/coin.12240.
    [40] E. B. TirkolaeeI. MahdaviM. M. Seyyed Esfahani and G.-W. Weber, A hybrid augmented ant colony optimization for the multi-trip capacitated arc routing problem under fuzzy demands for urban solid waste management, Waste Management and Research, 38 (2020), 156-172.  doi: 10.1177/0734242X19865782.
    [41] E. B. Tirkolaee, I. Mahdavi, M. M. Seyyed Esfahani and G.-W. Weber, A novel hybrid method using fuzzy decision making and multi-objective programming for sustainable-reliable supplier selection in two-echelon supply chain design, Journal of Cleaner Production, 250 (2020), 119517. doi: 10.1016/j.jclepro.2019.119517.
    [42] E. B. TirkolaeeI. MahdaviM. M. Seyyed Esfahani and G.-W. Weber, A robust green location-allocation-inventory problem to design an urban waste management system under uncertainty, Waste Management, 102 (2020), 340-350.  doi: 10.1016/j.wasman.2019.10.038.
    [43] E. B. TirkolaeeJ. MahmoodkhaniM. R. Bourani and R. Tavakkoli-Moghaddam, A self-learning particle swarm optimization for robust multi-echelon capacitated location-allocation-inventory problem, Journal of Advanced Manufacturing Systems, 18 (2019), 677-694.  doi: 10.1142/S0219686719500355.
    [44] R. Uher, The implications of gene-environment interactions in depression: Will cause inform cure?, Molecular Psychiatry, 13 (2008), 1070-1078.  doi: 10.1038/mp.2008.92.
    [45] S. Van der Auwera, et al., Genome-wide gene-environment interaction in depression: A systematic evaluation of candidate genes, American Journal of Medical Genetics Part B: Neuropsychiatric Genetics, 177 (2018), 40-49.  doi: 10.1002/ajmg.b.32593.
    [46] A. VasinP. Kartunova and G.-W Weber, Models for capacity and electricity market design, CEJOR Cent. Eur. J. Oper. Res., 21 (2013), 651-661.  doi: 10.1007/s10100-012-0259-2.
    [47] M. VidalM. Cusick and A.-L. Barabási, Interactome networks and human disease, Cell, 144 (2011), 986-998.  doi: 10.1016/j.cell.2011.02.016.
    [48] G.-W. Weber, Charakterisierung struktureller stabilität in der nichtlinearen optimierung, Aachener Beiträge zur Mathematik, 5, Augustinus publishing house (now: Mainz publishing house), Aachen, 1992.
    [49] G.-W. Weber, Generalized Semi-infinite Optimization and Related Topics, Research and Exposition in Mathematics, 29, Heldermann Verlag, Lemgo, 2003.
    [50] G.-W. WeberS. Alparslan-Gök and N. Dikmen, Environmental and life sciences: Gene-environment networks optimization, games and control - a survey on recent achievements, Journal of Organisational Transformation & Social Change, 5 (2008), 197-233.  doi: 10.1386/jots.5.3.197_1.
    [51] G.-W. WeberS. Z. Alparslan-Gök and B. Söyler, A new mathematical approach in environmental and life sciences: Gene-environment networks and their dynamics, Environmental Modeling & Assessment, 14 (2009), 267-288.  doi: 10.1007/s10666-007-9137-z.
    [52] G.-W. Weber, R. Branzei and S. Alparslan-Gök, On cooperative ellipsoidal games, in 24th Mini EURO Conference-On Continuous Optimization and Information-Based Technologies in the Financial Sector, MEC EurOPT, 2010, 369-372.
    [53] G.-W. WeberE. KropatB. Akteke-Öztürk and Z.-K. Görgülü, A survey on OR and mathematical methods applied on gene-environment networks, CEJOR Cent. Eur. J. Oper. Res., 17 (2009), 315-341.  doi: 10.1007/s10100-009-0092-4.
    [54] G.-W. WeberE. KropatA. Tezel and S. Belen, Optimization applied on regulatory and eco-finance networks - survey and new developments, Pac. J. Optim., 6 (2010), 319-340. 
    [55] G.-W. WeberS. Özögür-Akyüz and E. Kropat, A review on data mining and continuous optimization applications in computational biology and medicine, Birth Defects Research Part C: Embryo Today: Reviews, 87 (2009), 165-181.  doi: 10.1002/bdrc.20151.
    [56] G.-W. Weber and A. Tezel, On generalized semi-infinite optimization of genetic networks, TOP, 15 (2007), 65-77.  doi: 10.1007/s11750-007-0003-6.
    [57] A. YildizbasiA. CalikT. PaksoyR. Farahani and G.-W. Weber, Multi-level optimization of an automotive closed-loop supply chain network with interactive fuzzy programming approaches, Technological and Economic Development of Economy, 24 (2018), 1004-1028.  doi: 10.3846/20294913.2016.1253044.
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