Renyi entropy of highly entangled spin chains

Entanglement is one of the most intriguing features of quantum theory and a main resource in quantum information science. Ground states of quantum many-body systems with local interactions typically obey an "area law" meaning the entanglement entropy proportional to the boundary length. It is exceptional when the system is gapless, and the area law had been believed to be violated by at most a logarithm for over two decades. Recent discovery of Motzkin and Fredkin spin chain models is striking, since these models provide significant violation of the entanglement beyond the belief, growing as a square root of the volume in spite of local interactions. Although importance of intensive study of the models is undoubted to reveal novel features of quantum entanglement, it is still far from their complete understanding. In this article, we first analytically compute the Renyi entropy of the Motzkin and Fredkin models by careful treatment of asymptotic analysis. The Renyi entropy is an important quantity, since the whole spectrum of an entangled subsystem is reconstructed once the Renyi entropy is known as a function of its parameter. We find non-analytic behavior of the Renyi entropy with respect to the parameter, which is a novel phase transition never seen in any other spin chain studied so far. Interestingly, similar behavior is seen in the Renyi entropy of Rokhsar-Kivelson states in two-dimensions.Comment: 14+22 pages, 8 figures; (v2) references added, (v3) version to be published in International Journal of Modern Physics

Ordered Rings and Fields

We introduce ordered rings and fields following Artin-Schreier’s approach using positive cones. We show that such orderings coincide with total order relations and give examples of ordered (and non ordered) rings and fields. In particular we show that polynomial rings can be ordered in (at least) two different ways [8, 5, 4, 9]. This is the continuation of the development of algebraic hierarchy in Mizar [2, 3].Schwarzweller Christoph - Institute of Informatics, University of Gdansk, Gdansk, PolandGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191-198, 2015.Adam Grabowski, Artur Korniłowicz, and Christoph Schwarzweller. On algebraic hierarchies in mathematical repository of Mizar. In M. Ganzha, L. Maciaszek, and M. Paprzycki, editors, Proceedings of the 2016 Federated Conference on Computer Science and Information Systems (FedCSIS), volume 8 of Annals of Computer Science and Information Systems, pages 363-371, 2016.Nathan Jacobson. Lecture Notes in Abstract Algebra, III. Theory of Fields and Galois Theory. Springer-Verlag, 1964.Manfred Knebusch and Claus Scheiderer. Einf¨uhrung in die reelle Algebra. Vieweg-Verlag, 1989.Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990.Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.Alexander Prestel. Lectures on Formally Real Fields. Springer-Verlag, 1984.Knut Radbruch. Geordnete K¨orper. Lecture Notes, University of Kaiserslautern, Germany, 1991.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990

Pattern Recognition and Clustering of Transient Pressure Signals for Burst Location

[EN] A large volume of the water produced for public supply is lost in the systems between sources and consumers. An important-in many cases the greatest-fraction of these losses are physical losses, mainly related to leaks and bursts in pipes and in consumer connections. Fast detection and location of bursts plays an important role in the design of operation strategies for water loss control, since this helps reduce the volume lost from the instant the event occurs until its effective repair (run time). The transient pressure signals caused by bursts contain important information about their location and magnitude, and stamp on any of these events a specific "hydraulic signature". The present work proposes and evaluates three methods to disaggregate transient signals, which are used afterwards to train artificial neural networks (ANNs) to identify burst locations and calculate the leaked flow. In addition, a clustering process is also used to group similar signals, and then train specific ANNs for each group, thus improving both the computational efficiency and the location accuracy. The proposed methods are applied to two real distribution networks, and the results show good accuracy in burst location and characterization.Manzi, D.; Brentan, BM.; Meirelles, G.; Izquierdo Sebastián, J.; Luvizotto Jr., E. (2019). Pattern Recognition and Clustering of Transient Pressure Signals for Burst Location. Water. 11(11):1-13. https://doi.org/10.3390/w11112279S1131111Creaco, E., & Walski, T. (2017). Economic Analysis of Pressure Control for Leakage and Pipe Burst Reduction. Journal of Water Resources Planning and Management, 143(12), 04017074. doi:10.1061/(asce)wr.1943-5452.0000846Campisano, A., Creaco, E., & Modica, C. (2010). RTC of Valves for Leakage Reduction in Water Supply Networks. Journal of Water Resources Planning and Management, 136(1), 138-141. doi:10.1061/(asce)0733-9496(2010)136:1(138)Campisano, A., Modica, C., Reitano, S., Ugarelli, R., & Bagherian, S. (2016). Field-Oriented Methodology for Real-Time Pressure Control to Reduce Leakage in Water Distribution Networks. Journal of Water Resources Planning and Management, 142(12), 04016057. doi:10.1061/(asce)wr.1943-5452.0000697Vítkovský, J. P., Simpson, A. R., & Lambert, M. F. (2000). Leak Detection and Calibration Using Transients and Genetic Algorithms. Journal of Water Resources Planning and Management, 126(4), 262-265. doi:10.1061/(asce)0733-9496(2000)126:4(262)Pérez, R., Puig, V., Pascual, J., Quevedo, J., Landeros, E., & Peralta, A. (2011). Methodology for leakage isolation using pressure sensitivity analysis in water distribution networks. Control Engineering Practice, 19(10), 1157-1167. doi:10.1016/j.conengprac.2011.06.004Jung, D., & Kim, J. (2017). Robust Meter Network for Water Distribution Pipe Burst Detection. Water, 9(11), 820. doi:10.3390/w9110820Colombo, A. F., Lee, P., & Karney, B. W. (2009). A selective literature review of transient-based leak detection methods. Journal of Hydro-environment Research, 2(4), 212-227. doi:10.1016/j.jher.2009.02.003Choi, D., Kim, S.-W., Choi, M.-A., & Geem, Z. (2016). Adaptive Kalman Filter Based on Adjustable Sampling Interval in Burst Detection for Water Distribution System. Water, 8(4), 142. doi:10.3390/w8040142Christodoulou, S. E., Kourti, E., & Agathokleous, A. (2016). Waterloss Detection in Water Distribution Networks using Wavelet Change-Point Detection. Water Resources Management, 31(3), 979-994. doi:10.1007/s11269-016-1558-5Guo, X., Yang, K., & Guo, Y. (2012). Leak detection in pipelines by exclusively frequency domain method. Science China Technological Sciences, 55(3), 743-752. doi:10.1007/s11431-011-4707-3Holloway, M. B., & Hanif Chaudhry, M. (1985). Stability and accuracy of waterhammer analysis. Advances in Water Resources, 8(3), 121-128. doi:10.1016/0309-1708(85)90052-1Sanz, G., Pérez, R., Kapelan, Z., & Savic, D. (2016). Leak Detection and Localization through Demand Components Calibration. Journal of Water Resources Planning and Management, 142(2), 04015057. doi:10.1061/(asce)wr.1943-5452.0000592Zhang, Q., Wu, Z. Y., Zhao, M., Qi, J., Huang, Y., & Zhao, H. (2016). Leakage Zone Identification in Large-Scale Water Distribution Systems Using Multiclass Support Vector Machines. Journal of Water Resources Planning and Management, 142(11), 04016042. doi:10.1061/(asce)wr.1943-5452.0000661Mounce, S. R., & Machell, J. (2006). Burst detection using hydraulic data from water distribution systems with artificial neural networks. Urban Water Journal, 3(1), 21-31. doi:10.1080/15730620600578538Covas, D., Ramos, H., & de Almeida, A. B. (2005). Standing Wave Difference Method for Leak Detection in Pipeline Systems. Journal of Hydraulic Engineering, 131(12), 1106-1116. doi:10.1061/(asce)0733-9429(2005)131:12(1106)Liggett, J. A., & Chen, L. (1994). Inverse Transient Analysis in Pipe Networks. Journal of Hydraulic Engineering, 120(8), 934-955. doi:10.1061/(asce)0733-9429(1994)120:8(934)Caputo, A. C., & Pelagagge, P. M. (2002). An inverse approach for piping networks monitoring. Journal of Loss Prevention in the Process Industries, 15(6), 497-505. doi:10.1016/s0950-4230(02)00036-0Van Zyl, J. E. (2014). Theoretical Modeling of Pressure and Leakage in Water Distribution Systems. Procedia Engineering, 89, 273-277. doi:10.1016/j.proeng.2014.11.187Izquierdo, J., & Iglesias, P. . (2004). Mathematical modelling of hydraulic transients in complex systems. Mathematical and Computer Modelling, 39(4-5), 529-540. doi:10.1016/s0895-7177(04)90524-9Lin, J., Keogh, E., Wei, L., & Lonardi, S. (2007). Experiencing SAX: a novel symbolic representation of time series. Data Mining and Knowledge Discovery, 15(2), 107-144. doi:10.1007/s10618-007-0064-zNavarrete-López, C., Herrera, M., Brentan, B., Luvizotto, E., & Izquierdo, J. (2019). Enhanced Water Demand Analysis via Symbolic Approximation within an Epidemiology-Based Forecasting Framework. Water, 11(2), 246. doi:10.3390/w11020246Meirelles, G., Manzi, D., Brentan, B., Goulart, T., & Luvizotto, E. (2017). Calibration Model for Water Distribution Network Using Pressures Estimated by Artificial Neural Networks. Water Resources Management, 31(13), 4339-4351. doi:10.1007/s11269-017-1750-2Adamowski, J., & Chan, H. F. (2011). A wavelet neural network conjunction model for groundwater level forecasting. Journal of Hydrology, 407(1-4), 28-40. doi:10.1016/j.jhydrol.2011.06.013Brentan, B., Meirelles, G., Luvizotto, E., & Izquierdo, J. (2018). Hybrid SOM+ k -Means clustering to improve planning, operation and management in water distribution systems. Environmental Modelling & Software, 106, 77-88. doi:10.1016/j.envsoft.2018.02.013Calinski, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics - Theory and Methods, 3(1), 1-27. doi:10.1080/0361092740882710

Partial Correctness of a Power Algorithm

This work continues a formal verification of algorithms written in terms of simple-named complex-valued nominative data [6],[8],[15],[11],[12],[13]. In this paper we present a formalization in the Mizar system [3],[1] of the partial correctness of the algorithm: i := val.1 j := val.2 b := val.3 n := val.4 s := val.5 while (i n) i := i + j s := s * b return s computing the natural n power of given complex number b, where variables i, b, n, s are located as values of a V-valued Function, loc, as: loc/.1 = i, loc/.3 = b, loc/.4 = n and loc/.5 = s, and the constant 1 is located in the location loc/.2 = j (set V represents simple names of considered nominative data [17]).The validity of the algorithm is presented in terms of semantic Floyd-Hoare triples over such data [9]. Proofs of the correctness are based on an inference system for an extended Floyd-Hoare logic [2],[4] with partial pre- and post-conditions [14],[16],[7],[5].Institute of Informatics, University of Białystok, PolandGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.R.W. Floyd. Assigning meanings to programs. Mathematical aspects of computer science, 19(19–32), 1967.Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.C.A.R. Hoare. An axiomatic basis for computer programming. Commun. ACM, 12(10): 576–580, 1969.Ievgen Ivanov and Mykola Nikitchenko. On the sequence rule for the Floyd-Hoare logic with partial pre- and post-conditions. In Proceedings of the 14th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Volume II: Workshops, Kyiv, Ukraine, May 14–17, 2018, volume 2104 of CEUR Workshop Proceedings, pages 716–724, 2018.Ievgen Ivanov, Mykola Nikitchenko, Andrii Kryvolap, and Artur Korniłowicz. Simple-named complex-valued nominative data – definition and basic operations. Formalized Mathematics, 25(3):205–216, 2017. doi:10.1515/forma-2017-0020.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. Implementation of the composition-nominative approach to program formalization in Mizar. The Computer Science Journal of Moldova, 26(1):59–76, 2018.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. On an algorithmic algebra over simple-named complex-valued nominative data. Formalized Mathematics, 26(2):149–158, 2018. doi:10.2478/forma-2018-0012.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. An inference system of an extension of Floyd-Hoare logic for partial predicates. Formalized Mathematics, 26(2): 159–164, 2018. doi:10.2478/forma-2018-0013.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. Partial correctness of GCD algorithm. Formalized Mathematics, 26(2):165–173, 2018. doi:10.2478/forma-2018-0014.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. On algebras of algorithms and specifications over uninterpreted data. Formalized Mathematics, 26(2):141–147, 2018. doi:10.2478/forma-2018-0011.Artur Kornilowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the algebra of nominative data in Mizar. In Maria Ganzha, Leszek A. Maciaszek, and Marcin Paprzycki, editors, Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, FedCSIS 2017, Prague, Czech Republic, September 3–6, 2017., pages 237–244, 2017. ISBN 978-83-946253-7-5. doi:10.15439/2017F301.Artur Kornilowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the nominative algorithmic algebra in Mizar. In Leszek Borzemski, Jerzy Świątek, and Zofia Wilimowska, editors, Information Systems Architecture and Technology: Proceedings of 38th International Conference on Information Systems Architecture and Technology – ISAT 2017 – Part II, Szklarska Poręba, Poland, September 17–19, 2017, volume 656 of Advances in Intelligent Systems and Computing, pages 176–186. Springer, 2017. ISBN 978-3-319-67228-1. doi:10.1007/978-3-319-67229-8_16.Artur Korniłowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. An approach to formalization of an extension of Floyd-Hoare logic. In Vadim Ermolayev, Nick Bassiliades, Hans-Georg Fill, Vitaliy Yakovyna, Heinrich C. Mayr, Vyacheslav Kharchenko, Vladimir Peschanenko, Mariya Shyshkina, Mykola Nikitchenko, and Aleksander Spivakovsky, editors, Proceedings of the 13th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer, Kyiv, Ukraine, May 15–18, 2017, volume 1844 of CEUR Workshop Proceedings, pages 504–523. CEUR-WS.org, 2017.Artur Korniłowicz, Ievgen Ivanov, and Mykola Nikitchenko. Kleene algebra of partial predicates. Formalized Mathematics, 26(1):11–20, 2018. doi:10.2478/forma-2018-0002.Andrii Kryvolap, Mykola Nikitchenko, and Wolfgang Schreiner. Extending Floyd-Hoare logic for partial pre- and postconditions. In Vadim Ermolayev, Heinrich C. Mayr, Mykola Nikitchenko, Aleksander Spivakovsky, and Grygoriy Zholtkevych, editors, Information and Communication Technologies in Education, Research, and Industrial Applications: 9th International Conference, ICTERI 2013, Kherson, Ukraine, June 19–22, 2013, Revised Selected Papers, pages 355–378. Springer International Publishing, 2013. ISBN 978-3-319-03998-5. doi:10.1007/978-3-319-03998-5_18.Volodymyr G. Skobelev, Mykola Nikitchenko, and Ievgen Ivanov. On algebraic properties of nominative data and functions. In Vadim Ermolayev, Heinrich C. Mayr, Mykola Nikitchenko, Aleksander Spivakovsky, and Grygoriy Zholtkevych, editors, Information and Communication Technologies in Education, Research, and Industrial Applications – 10th International Conference, ICTERI 2014, Kherson, Ukraine, June 9–12, 2014, Revised Selected Papers, volume 469 of Communications in Computer and Information Science, pages 117–138. Springer, 2014. ISBN 978-3-319-13205-1. doi:10.1007/978-3-319-13206-8_6.27218919

Binder chemistry – Low-calcium alkali-activated materials

Early developments in the developments of low-calcium (including calcium-free) alkali-activated binders were led by the work of Davidovits in France, as noted in Chap. 2. These materials were initially envisaged as a fire-resistant replacement for organic polymeric materials, with identification of potential applications as a possible binder for concrete production following relatively soon afterwards [1]. However, developments in the area of concrete production soon led back to more calcium-rich systems, including the hybrid Pyrament binders, leaving work based on the use of low-calcium systems predominantly aimed at high-temperature applications and other scenarios where the ceramic-like nature of clay-derived alkali-activated pastes was beneficial. Early work in this area was conducted with an almost solely commercial focus, meaning that little scientific information was made available with the exception of a conference proceedings volume [2], several scattered publications in other conferences, and an initial journal publication [3]. Academic research into the alkaline activation of metakaolin to form a binder material led to initial publications in the early 1990s [4, 5], and the first description of the formation of a strong and durable binder by alkaline activation of fly ash was published by Wastiels et al. [6-8]. With ongoing developments in fly ash activation, which offers more favourable rheology than is observed in clay-based binders, interest in low-calcium AAM concrete production was reignited, and work since that time in industry and academia has led to the development of a number of different approaches to this problem. A review of the binder chemistry of low-calcium AAM binder systems published in 2007 [9] has since received more than 350 citations in the scientific literature, indicating the high current level of interest in understanding and utilisation of these types of gels

A Practical Procedure to Integrate the First 1:500 Urban Map of Valencia into a Tile-Based Geospatial Information System

[EN] The use of geographic data from early maps is a common approach to understanding urban geography as well as to study the evolution of cities over time. The specific goal of this paper is to provide a means for the integration of the first 1:500 urban map of the city of Valencia (Spain) on a tile-based geospatial system. We developed a workflow consisting of three stages: the digitization of the original 421 map sheets, the transformation to the European Terrestrial Reference System of 1989 (ETRS89), and the conversion to a tile-based file format, where the second stage is clearly the most mathematically involved. The second stage actually consists of two steps, one transformation from the pixel reference system to the 1929 local reference system followed by a second transformation from the 1929 local to the ETRS89 system. The last stage comprises a map reprojection to adapt to tile-based geospatial standards. The paper describes a pilot study of one map sheet and results showed that the affine and bilinear transformations performed well in both transformations with average residuals under 6 and 3 cm respectively. The online viewer developed in this study shows that the derived tile-based map conforms to common standards and lines up well with other raster and vector datasets.Villar-Cano, M.; Jiménez-Martínez, MJ.; Marqués-Mateu, Á. (2019). A Practical Procedure to Integrate the First 1:500 Urban Map of Valencia into a Tile-Based Geospatial Information System. ISPRS International Journal of Geo-Information. 8(9). https://doi.org/10.3390/ijgi809037837889Bitelli, G., & Gatta, G. (2011). Digital Processing and 3D Modelling of an 18th Century Scenographic Map of Bologna. Advances in Cartography and GIScience. Volume 2, 129-146. doi:10.1007/978-3-642-19214-2_9Brovelli, M. A., Minghini, M., Giori, G., & Beretta, M. (2012). Web Geoservices and Ancient Cadastral Maps: The Web C.A.R.T.E. Project. Transactions in GIS, 16(2), 125-142. doi:10.1111/j.1467-9671.2012.01311.xBitelli, G., Cremonini, S., & Gatta, G. (2014). Cartographic heritage: Toward unconventional methods for quantitative analysis of pre-geodetic maps. Journal of Cultural Heritage, 15(2), 183-195. doi:10.1016/j.culher.2013.04.003Cardesín Díaz, J. M., & Araujo, J. M. (2016). Historic Urbanization Process in Spain (1746–2013). Journal of Urban History, 43(1), 33-52. doi:10.1177/0096144215583481Villar-Cano, M., Marqués-Mateu, Á., & Jiménez-Martínez, M. J. (2019). Triangulation network of 1929–1944 of the first 1:500 urban map of València. Survey Review, 52(373), 317-329. doi:10.1080/00396265.2018.1564599Chen, W., & Hill, C. (2005). Evaluation Procedure for Coordinate Transformation. Journal of Surveying Engineering, 131(2), 43-49. doi:10.1061/(asce)0733-9453(2005)131:2(43)ISO 19157:2013: Geographic Information—Data Qualityhttps://www.iso.org/standard/32575.htmlASPRS Positional Accuracy Standards for Digital Geospatial Datahttps://www.asprs.org/news-resources/asprs-positional-accuracy-standards-for-digital-geospatial-dataEven-Tzur, G. (2018). Coordinate transformation with variable number of parameters. Survey Review, 52(370), 62-68. doi:10.1080/00396265.2018.1517477Yuanxi, Y., & Tianhe, X. (2002). Combined method of datum transformation between different coordinate systems. Geo-spatial Information Science, 5(4), 5-9. doi:10.1007/bf02826467Lehmann, R. (2014). Transformation model selection by multiple hypotheses testing. Journal of Geodesy, 88(12), 1117-1130. doi:10.1007/s00190-014-0747-

Neutrosophic Completion Technique for Incomplete Higher-Order AHP Comparison Matrices

[EN] After the recent establishment of the Sustainable Development Goals and the Agenda 2030, the sustainable design of products in general and infrastructures in particular emerge as a challenging field for the development and application of multicriteria decision-making tools. Sustainability-related decision problems usually involve, by definition, a wide variety in number and nature of conflicting criteria, thus pushing the limits of conventional multicriteria decision-making tools practices. The greater the number of criteria and the more complex the relations existing between them in a decisional problem, the less accurate and certain are the judgments required by usual methods, such as the analytic hierarchy process (AHP). The present paper proposes a neutrosophic AHP completion methodology to reduce the number of judgments required to be emitted by the decision maker. This increases the consistency of their responses, while accounting for uncertainties associated to the fuzziness of human thinking. The method is applied to a sustainable-design problem, resulting in weight estimations that allow for a reduction of up to 22% of the conventionally required comparisons, with an average accuracy below 10% between estimates and the weights resulting from a conventionally completed AHP matrix, and a root mean standard error below 15%.The authors acknowledge the financial support of the Spanish Ministry of Economy and Business, along with FEDER funding (DIMALIFE Project: BIA2017-85098-R).Navarro, IJ.; Martí Albiñana, JV.; Yepes, V. (2021). Neutrosophic Completion Technique for Incomplete Higher-Order AHP Comparison Matrices. Mathematics. 9(5):1-19. https://doi.org/10.3390/math905049611995Worrell, E., Price, L., Martin, N., Hendriks, C., & Meida, L. O. (2001). CARBON DIOXIDE EMISSIONS FROM THE GLOBAL CEMENT INDUSTRY. Annual Review of Energy and the Environment, 26(1), 303-329. doi:10.1146/annurev.energy.26.1.303García, J., Yepes, V., & Martí, J. V. (2020). A Hybrid k-Means Cuckoo Search Algorithm Applied to the Counterfort Retaining Walls Problem. Mathematics, 8(4), 555. doi:10.3390/math8040555Penadés-Plà, V., García-Segura, T., & Yepes, V. (2020). Robust Design Optimization for Low-Cost Concrete Box-Girder Bridge. Mathematics, 8(3), 398. doi:10.3390/math8030398Kim, S., & Frangopol, D. M. (2017). Multi-objective probabilistic optimum monitoring planning considering fatigue damage detection, maintenance, reliability, service life and cost. Structural and Multidisciplinary Optimization, 57(1), 39-54. doi:10.1007/s00158-017-1849-3García-Segura, T., Yepes, V., & Frangopol, D. M. (2017). Multi-objective design of post-tensioned concrete road bridges using artificial neural networks. Structural and Multidisciplinary Optimization, 56(1), 139-150. doi:10.1007/s00158-017-1653-0Van den Heede, P., & De Belie, N. (2014). A service life based global warming potential for high-volume fly ash concrete exposed to carbonation. Construction and Building Materials, 55, 183-193. doi:10.1016/j.conbuildmat.2014.01.033García, J., Martí, J. V., & Yepes, V. (2020). The Buttressed Walls Problem: An Application of a Hybrid Clustering Particle Swarm Optimization Algorithm. Mathematics, 8(6), 862. doi:10.3390/math8060862García-Segura, T., Penadés-Plà, V., & Yepes, V. (2018). Sustainable bridge design by metamodel-assisted multi-objective optimization and decision-making under uncertainty. Journal of Cleaner Production, 202, 904-915. doi:10.1016/j.jclepro.2018.08.177Gursel, A. P., & Ostertag, C. (2016). Comparative life-cycle impact assessment of concrete manufacturing in Singapore. The International Journal of Life Cycle Assessment, 22(2), 237-255. doi:10.1007/s11367-016-1149-yPenadés-Plà, V., Martí, J. V., García-Segura, T., & Yepes, V. (2017). Life-Cycle Assessment: A Comparison between Two Optimal Post-Tensioned Concrete Box-Girder Road Bridges. Sustainability, 9(10), 1864. doi:10.3390/su9101864Navarro, I. J., Yepes, V., & Martí, J. V. (2018). Social life cycle assessment of concrete bridge decks exposed to aggressive environments. Environmental Impact Assessment Review, 72, 50-63. doi:10.1016/j.eiar.2018.05.003Sierra, L. A., Pellicer, E., & Yepes, V. (2017). Method for estimating the social sustainability of infrastructure projects. Environmental Impact Assessment Review, 65, 41-53. doi:10.1016/j.eiar.2017.02.004Navarro, I. J., Yepes, V., & Martí, J. V. (2019). Sustainability assessment of concrete bridge deck designs in coastal environments using neutrosophic criteria weights. 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