Isomorphism Theorem on Vector Spaces over a Ring

SummaryIn this article, we formalize in the Mizar system [1, 4] some properties of vector spaces over a ring. We formally prove the first isomorphism theorem of vector spaces over a ring. We also formalize the product space of vector spaces. ℤ-modules are useful for lattice problems such as LLL (Lenstra, Lenstra and Lovász) [5] base reduction algorithm and cryptographic systems [6, 2].Futa Yuichi - Tokyo University of Technology, Tokyo, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.Wolfgang Ebeling. Lattices and Codes. Advanced Lectures in Mathematics. Springer Fachmedien Wiesbaden, 2013.Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Submodule of free ℤ-module. Formalized Mathematics, 21(4):273–282, 2013. doi:10.2478/forma-2013-0029.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.A. K. Lenstra, H. W. Lenstra Jr., and L. Lovász. Factoring polynomials with rational coefficients. Mathematische Annalen, 261(4):515–534, 1982. doi:10.1007/BF01457454.Daniele Micciancio and Shafi Goldwasser. Complexity of lattice problems: a cryptographic perspective. The International Series in Engineering and Computer Science, 2002.Yasunari Shidama. Differentiable functions on normed linear spaces. Formalized Mathematics, 20(1):31–40, 2012. doi:10.2478/v10037-012-0005-1.25317117

Recognize Geometry Shapes through Computer Learning in Early Math Skills

One form of early mathematical recognition is to introduce the concept of geometric shapes. Geometry is an important scientific discipline for present and future life by developing various ways that fit 21st century skills. This study aims to overcome the problem of early mathematical recognition of early childhood on geometry, especially how to recognize geometric forms based on computer learning. A total of 24 children aged 4-5 years in kindergarten has to carrying out 2 research cycles with a total of 5 meetings. Treatment activities in each learning cycle include mentioning, grouping and imitating geometric shapes. There were only 7 children who were able to recognize the geometric shapes in the pre-research cycle (29.2%). An increase in the number of children who are able to do activities well in each research cycle includes: 1) The activities mentioned in the first cycle and 75% in the second cycle; 2) Classifying activities in the first cycle were 37.5% and 75% in the second cycle; 3) Imitation activities in the first cycle 54.2% and 79.2% in the second cycle. The results of data acquisition show that computer learning application can improve the ability to recognize geometric shapes, this is because computer learning provides software that has activities to recognize geometric shapes with the animation and visuals displayed. Keywords: Early Childhood Computer Learning, Geometry Forms, Early Math Skills Reference Alia, T., & Irwansyah. (2018). Pendampingan Orang Tua pada Anak Usia Dini dalam Penggunaan Teknologi Digital. A Journal of Language, Literature, Culture and Education, 14(1), 65– 78. https://doi.org/10.19166/pji.v14i1.639 Ameliola, S., & Nugraha, H. D. (2013). 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Design and simulation of a resorbable bone fixation plate made by additive manufacturing for femoral mid-SHAFT fractures

[EN] Finite element method has been employed to establish the feasibility of a fixation plate made of PLA by additive manufacturing for femoral shaft fractures. For this purpose, Von Mises stress and the pressure contact between bones had been analysed. The proposed design has been compared with an actual titanium fixation plate as a point of reference.J. Ivorra-Martinez is funded with a Formación de Profesorado Universitario (FPU) grant from the Spanish Government (Ministerio de Ciencia, Innovación y Universidades), with reference FPU19/01759.Ivorra Martínez, J.; Sellés Cantó, MÁ.; Sánchez Caballero, S.; Boronat Vitoria, T. (2021). Design and simulation of a resorbable bone fixation plate made by additive manufacturing for femoral mid-SHAFT fractures. Journal of Applied Research in Technology & Engineering. 2(1):11-16. https://doi.org/10.4995/jarte.2021.14712OJS111621Alizadeh-Osgouei, M., Li, Y., Wen, C. (2019). A comprehensive review of biodegradable synthetic polymerceramic composites and their manufacture for biomedical applications. Bioactive materials, 4(1), 22-36. https://doi.org/10.1016/j.bioactmat.2018.11.003Arabnejad, S., Johnston, B., Tanzer, M., Pasini, D. (2017). Fully porous 3D printed titanium femoral stem toreduce stress-shielding following total hip arthroplasty. Journal of Orthopaedic Research, 35(8), 1774-1783.https://doi.org/10.1002/jor.23445Elkins, J., Marsh, J.L., Lujan, T., Peindl, R., Kellam, J., Anderson, D D., & Lack, W. (2016). Motion predicts clinical callus formation: construct-specific finite element analysis of supracondylar femoral fractures. The Journal of bone and joint surgery. American volume, 98(4), 276. https://doi.org/10.2106/JBJS.O.00684Geetha, M., Singh, A.K., Asokamani, R., Gogia, A.K. (2009). Ti based biomaterials, the ultimate choice for orthopaedic implants-a review. 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Development and validation of statistical models of femur geometry for use with parametric finite element models. Annals of biomedical engineering, 43(10), 2503-2514. https://doi.org/10.1007/s10439-015-1307-6Li, J., Li, Z., Ye, L., Zhao, X., Coates, P., Caton-Rose, F. (2017). Structure and biocompatibility improvement mechanism of highly oriented poly (lactic acid) produced by solid die drawing. European Polymer Journal, 97, 68-76. https://doi.org/10.1016/j.eurpolymj.2017.09.038Li, J., Qin, L., Yang, K., Ma, Z., Wang, Y., Cheng, L., Zhao, D. (2020). Materials evolution of bone plates for internal fixation of bone fractures: A review. Journal of Materials Science & Technology, 36, 190-208. https://doi.org/10.1016/j.jmst.2019.07.024Li, J., Yin, P., Zhang, L., Chen, H., Tang, P. (2019). Medial anatomical buttress plate in treating displaced femoral neck fracture a finite element analysis. 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The Journal of arthroplasty, 24(6), 990-997. https://doi.org/10.1016/j.arth.2008.04.031Singh, D., Singh, R., Boparai, K.S. (2018). Development and surface improvement of FDM pattern based investment casting of biomedical implants: A state of art review. Journal of Manufacturing Processes, 31, 80-95. https://doi.org/10.1016/j.jmapro.2017.10.026Spiridon, I., Tanase, C.E. (2018). Design, characterization and preliminary biological evaluation of new lignin-PLA biocomposites. International journal of biological macromolecules, 114, 855-863. https://doi.org/10.1016/j.ijbiomac.2018.03.140Tang, G., Liu, S.L., Wang, D.M., Wei, G.F., Wang, C.T. (2013). Finite element analysis in femoral fixation with TA3 titanium compressioll plate. In Advanced Materials Research, 647, 16-19. Trans Tech Publications Ltd. https://doi.org/10.4028/www.scientific.net/AMR.647.16Tymrak, B., Kreiger, M., Pearce, J.M. (2014). Mechanical properties of components fabricated with open-source 3-D printers under realistic environmental conditions. Materials & Design, 58, 242-246. https://doi.org/10.1016/j.matdes.2014.02.038Wang, A.Y., Peng, J., Sun, M.X., Sui, X., Wang, X., Tian, Y., Lu, S.B. (2006). Biomechanical comparison of different structural bone grafting in femoral heads' defects of weight-bearing region. Journal of Medical Biomechanics, 4.Wang, J., Ma, J.X., Lu, B., Bai, H.H., Wang, Y., Ma, X.L. (2020). Comparative finite element analysis of three implants fixing stable and unstable subtrochanteric femoral fractures: Proximal Femoral Nail Antirotation (PFNA), Proximal Femoral Locking Plate (PFLP), and Reverse Less Invasive Stabilization System (LISS). Orthopaedics & Traumatology: Surgery & Research, 106(1), 95-101. https://doi.org/10.1016/j.otsr.2019.04.027Wang, X., Xu, S., Zhou, S., Xu, W., Leary, M., Choong, P., Xie, Y.M. (2016). 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A B2B Architecture and Protocol for Researchers Cooperation

Acknowledgement: Electronic version of an article published as International Journal of Cooperative Information Systems, Volume 22, Issue 02, 2013, DOI: 10.1142/S021884301350010X © World Scientific Publishing Company http://www.worldscientific.com/Some works on the researchers cooperation's literature provide the key lines for building research networks and propose new protocols and standards for business to business (B2B) data exchange, but none of them explains how researchers should contact and the procedure to select the most appropriate partner of a research enterprise, institute or university. In this paper, we propose a B2B architecture and protocol between research entities, that uses ebXML protocol. The contacts for cooperation are established based on some defined parameters and an information retrieval system. We explain the information retrieval system, the researcher selection procedure, the XML-based protocol and the workflow of our proposal. We also show the information that has to be exchanged to contact other researchers. Several simulations demonstrate that our proposal is a feasible architecture and may be used to promote the research cooperation. The main purpose of this paper is to propose an efficient procedure for searching project partners.Lloret, J.; Tomás Gironés, J.; García Pineda, M.; Lacuesta Contreras, R. (2013). A B2B Architecture and Protocol for Researchers Cooperation. International Journal of Cooperative Information Systems. 22(2):1-27. doi:10.1142/S021884301350010XS127222B. Wellman and S. D. Berkowitz, Social Structures: A Network Approach (Cambridge University Press, Cambridge, 1988) pp. 19–61.Wasserman, S., & Faust, K. (1994). Social Network Analysis. doi:10.1017/cbo9780511815478Wellman, B., Salaff, J., Dimitrova, D., Garton, L., Gulia, M., & Haythornthwaite, C. (1996). Computer Networks as Social Networks: Collaborative Work, Telework, and Virtual Community. Annual Review of Sociology, 22(1), 213-238. doi:10.1146/annurev.soc.22.1.213Fulk, J., & Steinfield, C. (1990). Organizations and Communication Technology. doi:10.4135/9781483325385B. Wellman and M. Gulia, Networks in the Global Village (Westview Press, Boulder, CO, 1997) pp. 331–367.Marsden, P. V., & Campbell, K. E. (1984). Measuring Tie Strength. Social Forces, 63(2), 482-501. doi:10.1093/sf/63.2.482Wellman, B., & Wortley, S. (1990). Different Strokes from Different Folks: Community Ties and Social Support. American Journal of Sociology, 96(3), 558-588. doi:10.1086/229572Adamic, L., & Adar, E. (2005). How to search a social network. Social Networks, 27(3), 187-203. doi:10.1016/j.socnet.2005.01.007Ebel, H., Mielsch, L.-I., & Bornholdt, S. (2002). Scale-free topology of e-mail networks. Physical Review E, 66(3). doi:10.1103/physreve.66.035103Jung, J.-Y., Kim, H., & Kang, S.-H. (2006). Standards-based approaches to B2B workflow integration. Computers & Industrial Engineering, 51(2), 321-334. doi:10.1016/j.cie.2006.02.011Lloret, J., Palau, C., Boronat, F., & Tomas, J. (2008). Improving networks using group-based topologies. Computer Communications, 31(14), 3438-3450. doi:10.1016/j.comcom.2008.05.030Lloret, J., Garcia, M., Tomás, J., & Boronat, F. (2008). GBP-WAHSN: A Group-Based Protocol for Large Wireless Ad Hoc and Sensor Networks. Journal of Computer Science and Technology, 23(3), 461-480. doi:10.1007/s11390-008-9147-6Lloret, J., Garcia, M., Bri, D., & Diaz, J. R. (2009). Study and performance of a group-based Content Delivery Network. Journal of Network and Computer Applications, 32(5), 991-999. doi:10.1016/j.jnca.2009.03.008Lloret, J., Garcia, M., Tomas, J., & Sendra, S. (2010). A group-based architecture for grids. Telecommunication Systems, 46(2), 117-133. doi:10.1007/s11235-010-9279-1Lin, T.-C., & Huang, C.-C. (2010). Withholding effort in knowledge contribution: The role of social exchange and social cognitive on project teams. Information & Management, 47(3), 188-196. doi:10.1016/j.im.2010.02.001Maron, M. E., & Kuhns, J. L. (1960). On Relevance, Probabilistic Indexing and Information Retrieval. Journal of the ACM, 7(3), 216-244. doi:10.1145/321033.321035Tomás, J., Lloret, J., & Casacuberta, F. (2005). Phrase-Based Alignment Models for Statistical Machine Translation. Lecture Notes in Computer Science, 605-613. doi:10.1007/11492542_74Turel, O., & Zhang, Y. (Jenny). (2011). Should I e-collaborate with this group? A multilevel model of usage intentions. Information & Management, 48(1), 62-68. doi:10.1016/j.im.2010.12.004Okuda, T., Tanaka, E., & Kasai, T. (1976). A Method for the Correction of Garbled Words Based on the Levenshtein Metric. IEEE Transactions on Computers, C-25(2), 172-178. doi:10.1109/tc.1976.500923

On potential cognitive abilities in the machine kingdom

The final publication is available at Springer via http://dx.doi.org/10.1007/s11023-012-9299-6Animals, including humans, are usually judged on what they could become, rather than what they are. Many physical and cognitive abilities in the ‘animal kingdom’ are only acquired (to a given degree) when the subject reaches a certain stage of development, which can be accelerated or spoilt depending on how the environment, training or education is. The term ‘potential ability’ usually refers to how quick and likely the process of attaining the ability is. In principle, things should not be different for the ‘machine kingdom’. While machines can be characterised by a set of cognitive abilities, and measuring them is already a big challenge, known as ‘universal psychometrics’, a more informative, and yet more challenging, goal would be to also determine the potential cognitive abilities of a machine. In this paper we investigate the notion of potential cognitive ability for machines, focussing especially on universality and intelligence. We consider several machine characterisations (non-interactive and interactive) and give definitions for each case, considering permanent and temporal potentials. From these definitions, we analyse the relation between some potential abilities, we bring out the dependency on the environment distribution and we suggest some ideas about how potential abilities can be measured. Finally, we also analyse the potential of environments at different levels and briefly discuss whether machines should be designed to be intelligent or potentially intelligent.We thank the anonymous reviewers for their comments, which have helped to significantly improve this paper. This work was supported by the MEC-MINECO projects CONSOLIDER-INGENIO CSD2007-00022 and TIN 2010-21062-C02-02, GVA project PROMETEO/2008/051, the COST - European Cooperation in the field of Scientific and Technical Research IC0801 AT. Finally, we thank three pioneers ahead of their time(s). We thank Ray Solomonoff (1926-2009) and Chris Wallace (1933-2004) for all that they taught us, directly and indirectly. And, in his centenary year, we thank Alan Turing (1912-1954), with whom it perhaps all began.Hernández-Orallo, J.; Dowe, DL. (2013). On potential cognitive abilities in the machine kingdom. Minds and Machines. 23(2):179-210. https://doi.org/10.1007/s11023-012-9299-6S179210232Amari, S., Fujita, N., Shinomoto, S. (1992). Four types of learning curves. Neural Computation 4(4), 605–618.Aristotle (Translation, Introduction, and Commentary by Ross, W.D.) (1924). Aristotle’s Metaphysics. Oxford: Clarendon Press.Barmpalias, G. & Dowe, D. L. (2012). 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(Eds.), Proceedings of 3rd international conference on artificial general intelligence (pp. 25–30). New York: Atlantis Press.Hernández-Orallo, J., & Dowe, D. L. (2010). Measuring universal intelligence: Towards an anytime intelligence test. Artificial Intelligence, 174(18), 1508–1539.Hernández-Orallo, J. & Dowe, D. L. (2011, April). Mammals, machines and mind games. Who’s the smartest?. The conversation, http://theconversation.edu.au/mammals-machines-and-mind-games-whos-the-smartest-566 .Hernández-Orallo J., Dowe D. L., España-Cubillo S., Hernández-Lloreda M. V., & Insa-Cabrera J. (2011). On more realistic environment distributions for defining, evaluating and developing intelligence. In: J. Schmidhuber, K. R. Thórisson, & M. Looks (Eds.), Artificial general intelligence 2011, volume 6830, LNAI series, pp. 82–91. New York: Springer.Hernández-Orallo, J., Dowe, D. L., & Hernández-Lloreda, M. V. (2012a, March). 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Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm