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

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

On an Algorithmic Algebra over Simple-Named Complex-Valued Nominative Data

This paper continues formalization in the Mizar system [2, 1] of basic notions of the composition-nominative approach to program semantics [14] which was started in [8, 12, 10].The composition-nominative approach studies mathematical models of computer programs and data on various levels of abstraction and generality and provides tools for reasoning about their properties. In particular, data in computer systems are modeled as nominative data [15]. Besides formalization of semantics of programs, certain elements of the composition-nominative approach were applied to abstract systems in a mathematical systems theory [4, 6, 7, 5, 3].In the paper we give a formal definition of the notions of a binominative function over given sets of names and values (i.e. a partial function which maps simple-named complex-valued nominative data to such data) and a nominative predicate (a partial predicate on simple-named complex-valued nominative data). The sets of such binominative functions and nominative predicates form the carrier of the generalized Glushkov algorithmic algebra for simple-named complex-valued nominative data [15]. This algebra can be used to formalize algorithms which operate on various data structures (such as multidimensional arrays, lists, etc.) and reason about their properties.In particular, we formalize the operations of this algebra which require a specification of a data domain and which include the existential quantifier, the assignment composition, the composition of superposition into a predicate, the composition of superposition into a binominative function, the name checking predicate. The details on formalization of nominative data and the operations of the algorithmic algebra over them are described in [11, 13, 9].Ievgen Ivanov - Taras Shevchenko National University, Kyiv, UkraineArtur Korniłowicz - Institute of Informatics, University of Białystok, PolandMykola Nikitchenko - Taras Shevchenko National University, Kyiv, UkraineGrzegorz 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.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.Ievgen Ivanov. On the underapproximation of reach sets of abstract continuous-time systems. In Erika Ábrahám and Sergiy Bogomolov, editors, Proceedings 3rd International Workshop on Symbolic and Numerical Methods for Reachability Analysis, SNR@ETAPS 2017, Uppsala, Sweden, 22nd April 2017, volume 247 of EPTCS, pages 46–51, 2017. doi:10.4204/EPTCS.247.4.Ievgen Ivanov. On representations of abstract systems with partial inputs and outputs. In T. V. Gopal, Manindra Agrawal, Angsheng Li, and S. Barry Cooper, editors, Theory and Applications of Models of Computation – 11th Annual Conference, TAMC 2014, Chennai, India, April 11–13, 2014. Proceedings, volume 8402 of Lecture Notes in Computer Science, pages 104–123. Springer, 2014. ISBN 978-3-319-06088-0. doi:10.1007/978-3-319-06089-7_8.Ievgen Ivanov. On local characterization of global timed bisimulation for abstract continuous-time systems. In Ichiro Hasuo, editor, Coalgebraic Methods in Computer Science – 13th IFIP WG 1.3 International Workshop, CMCS 2016, Colocated with ETAPS 2016, Eindhoven, The Netherlands, April 2–3, 2016, Revised Selected Papers, volume 9608 of Lecture Notes in Computer Science, pages 216–234. Springer, 2016. ISBN 978-3-319-40369-4. doi:10.1007/978-3-319-40370-0_13.Ievgen Ivanov, Mykola Nikitchenko, and Uri Abraham. On a decidable formal theory for abstract continuous-time dynamical systems. 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, pages 78–99. Springer International Publishing, 2014. ISBN 978-3-319-13206-8. doi:10.1007/978-3-319-13206-8_4.Ievgen Ivanov, Mykola Nikitchenko, and Uri Abraham. Event-based proof of the mutual exclusion property of Peterson’s algorithm. Formalized Mathematics, 23(4):325–331, 2015. doi:10.1515/forma-2015-0026.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 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 Korniłowicz, Ievgen Ivanov, and Mykola Nikitchenko. Kleene algebra of partial predicates. Formalized Mathematics, 26(1):11–20, 2018. doi:10.2478/forma-2018-0002.Artur Korniłowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the nominative algorithmic algebra in Mizar. In Jerzy Świątek, Leszek Borzemski, and Zofia Wilimowska, editors, Information Systems Architecture and Technology: Proceedings of 38th International Conference on Information Systems Architecture and Technology – ISAT 2017: Part II, pages 176–186. Springer International Publishing, 2018. ISBN 978-3-319-67229-8. doi:10.1007/978-3-319-67229-8_16.Nikolaj S. Nikitchenko. A composition nominative approach to program semantics. Technical Report IT-TR 1998-020, Department of Information Technology, Technical University of Denmark, 1998.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_6.26214915

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. Progress in materials science, 54(3), 397-425. https://doi.org/10.1016/j.pmatsci.2008.06.004George, D., Allena, R., Remond, Y. (2017). Mechanobiological stimuli for bone remodeling: mechanical energy, cell nutriments and mobility. Computer Methods in Biomechanics and Biomedical Engineering, 20(sup1), S91-S92, https://doi.org/10.1080/10255842.2017.1382876Guastaldi, F., Martini, A., Rocha, E., Hochuli-Vieira, E., Guastaldi, A. (2019). Ti-15Mo Alloy Decreases the Stress Concentration in Mandibular Angle Fracture Internal Fixation Hardware. Journal of Maxillofacial and Oral Surgery, 19, 314-320. https://doi.org/10.1007/s12663-019-01251-8Hayes, J., Richards, R. (2010). The use of titanium and stainless steel in fracture fixation. Expert review of medical devices, 7(6), 843-853. https://doi.org/10.1586/erd.10.53Heimbach, B., Grassie, K., Shaw, M.T., Olson, J.R., Wei, M. (2017). Effect of hydroxyapatite concentration on highmodulus composite for biodegradable bone-fixation devices. Journal of Biomedical Materials Research Part B: Applied Biomaterials, 105(7), 1963-1971. https://doi.org/10.1002/jbm.b.33713Jahagirdar, R., Scammell, B.E. (2009). Principles of fracture healing and disorders of bone union. Surgery (Oxford), 27(2), 63-69. https://doi.org/10.1016/j.mpsur.2008.12.011Kanno, T., Sukegawa, S., Furuki, Y., Nariai, Y., Sekine, J. (2018). Overview of innovative advances in bioresorbable plate systems for oral and maxillofacial surgery. Japanese Dental Science Review, 54(3), 127-138. https://doi.org/10.1016/j.jdsr.2018.03.003Kim, H.J., Chang, S.H., Jung, H.J. (2012). The simulation of tissue differentiation at a fracture gap using a mechanoregulation theory dealing with deviatoric strains in the presence of a composite bone plate. Composites Part B: Engineering, 43(3), 978-987. https://doi.org/10.1016/j.compositesb.2011.09.011Klein, K.F., Hu, J., Reed, M.P., Hoff, C.N., Rupp, J.D. (2015). 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. Injury, 50(11), 1895-1900. https://doi.org/10.1016/j.injury.2019.08.024Liu, B., Zhang, S., Zhang, J., Xu, Z., Chen, Y., Liu, S., Yang, L. (2019). A personalized preoperative modeling system for internal fixation plates in long bone fracture surgery-A straightforward way from CT images to plate model. The International Journal of Medical Robotics and Computer Assisted Surgery, 15(5), e2029. https://doi.org/10.1002/rcs.2029McClellan, R.T. (2013). The variable angle hip fracture nail relative to the Gamma 3: A finite element analysis illustrating the same stiffness and fatigue characteristics. Advances in orthopedics, 2013. https://doi.org/10.1155/2013/143801Murr, L.E. (2016). Frontiers of 3D printing/additive manufacturing: from human organs to aircraft fabrication. Journal of Materials Science & Technology, 32(10), 987-995. https://doi.org/10.1016/j.jmst.2016.08.011Narayanan, G., Vernekar, V.N., Kuyinu, E.L., Laurencin, C.T. (2016). Poly (lactic acid)-based biomaterials for orthopaedic regenerative engineering. Advanced drug delivery reviews, 107, 247-276. https://doi.org/10.1016/j.addr.2016.04.015Nurettin, D., Burak, B. (2018). Feasibility of carbon-fiber-reinforced polymer fixation plates for treatment of atrophic mandibular fracture: A finite element method. Journal of Cranio-Maxillofacial Surgery, 46(12), 2182-2189. https://doi.org/10.1016/j.jcms.2018.09.030Parthasarathy, J. (2015). 14 Additive Manufacturing of Medical Devices. Additive Manufacturing: Innovations, Advances, and Applications, 369.Ridzwan, M., Shuib, S., Hassan, A., Shokri, A., Ibrahim, M. (2006). Optimization in implant topology to reduce stress shielding problem. Journal of Applied Sciences, 6(13), 2768-2773. https://doi.org/10.3923/jas.2006.2768.2773Sariali, E., Mouttet, A., Pasquier, G., Durante, E. (2009). Three-dimensional hip anatomy in osteoarthritis: analysis of the femoral offset. 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). Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A review. Biomaterials, 83, 127-141. https://doi.org/10.1016/j.biomaterials.2016.01.012Wu, C., Zheng, K., Fang, J., Steven, G.P., Li, Q. (2020). Time-dependent topology optimization of bone plates considering bone remodeling. Computer Methods in Applied Mechanics and Engineering, 359, 112702. https://doi.org/10.1016/j.cma.2019.112702Wu, K.J., Li, S.H., Yeh, K.T., Chen, H., Lee, R.P., Yu, T.C., Wang, J.H. (2019). The risk factors of nonunion after intramedullary nailing fixation of femur shaft fracture in middle age patients. Medicine, 98(29). https://doi.org/10.1097/MD.0000000000016559Wu, X., Wang, Z., Li, H., Li, Y., Wang, H., Tian, W. (2019). Biomechanical evaluation of osteoporotic fracture: Metal fixation versus absorbable fixation in Sawbones models. Injury, 50(7), 1272-1276. https://doi.org/10.1016/j.injury.2019.05.023Zhao, X., Niinomi, M., Nakai, M., Hieda, J., Ishimoto, T., Nakano, T. (2012). Optimization of Cr content of metastable β-type Ti-Cr alloys with changeable Young's modulus for spinal fixation applications. Acta biomaterialia, 8(6), 2392-2400. https://doi.org/10.1016/j.actbio.2012.02.01

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). Universality probability of a prefix-free machine. Philosophical transactions of the Royal Society A [Mathematical, Physical and Engineering Sciences] (Phil Trans A), Theme Issue ‘The foundations of computation, physics and mentality: The Turing legacy’ compiled and edited by Barry Cooper and Samson Abramsky, 370, pp 3488–3511.Chaitin, G. J. (1966). On the length of programs for computing finite sequences. Journal of the Association for Computing Machinery, 13, 547–569.Chaitin, G. J. (1975). A theory of program size formally identical to information theory. Journal of the ACM (JACM), 22(3), 329–340.Dowe, D. L. (2008, September). Foreword re C. S. Wallace. Computer Journal, 51(5):523–560, Christopher Stewart WALLACE (1933–2004) memorial special issue.Dowe, D. L. (2011). MML, hybrid Bayesian network graphical models, statistical consistency, invariance and uniqueness. In: P. S. Bandyopadhyay, M. R. Forster (Eds), Handbook of the philosophy of science—Volume 7: Philosophy of statistics (pp. 901–982). Amsterdam: Elsevier.Dowe, D. L. & Hajek, A. R. (1997a). A computational extension to the turing test. Technical report #97/322, Dept Computer Science, Monash University, Melbourne, Australia, 9 pp, http://www.csse.monash.edu.au/publications/1997/tr-cs97-322-abs.html .Dowe, D. L. & Hajek, A. R. (1997b, September). A computational extension to the Turing Test. in Proceedings of the 4th conference of the Australasian Cognitive Science Society, University of Newcastle, NSW, Australia, 9 pp.Dowe, D. L. & Hajek, A. R. (1998, February). A non-behavioural, computational extension to the Turing Test. In: International conference on computational intelligence and multimedia applications (ICCIMA’98), Gippsland, Australia, pp 101–106.Dowe, D. L., Hernández-Orallo, J. (2012). IQ tests are not for machines, yet. Intelligence, 40(2), 77–81.Gallistel, C. R., Fairhurst, S., & Balsam, P. (2004). The learning curve: Implications of a quantitative analysis. In Proceedings of the National Academy of Sciences of the United States of America, 101(36), 13124–13131.Gardner, M. (1970). Mathematical games: The fantastic combinations of John Conway’s new solitaire game “life”. Scientific American, 223(4), 120–123.Goertzel, B. & Bugaj, S. V. (2009). AGI preschool: A framework for evaluating early-stage human-like AGIs. In Proceedings of the second international conference on artificial general intelligence (AGI-09), pp 31–36.Hernández-Orallo, J. (2000a). Beyond the Turing Test. Journal of Logic, Language & Information, 9(4), 447–466.Hernández-Orallo, J. (2000b). On the computational measurement of intelligence factors. In A. Meystel (Ed), Performance metrics for intelligent systems workshop (pp 1–8). Gaithersburg, MD: National Institute of Standards and Technology.Hernández-Orallo, J. (2010). On evaluating agent performance in a fixed period of time. In M. Hutter et al. (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). Measuring cognitive abilities of machines, humans and non-human animals in a unified way: towards universal psychometrics. Technical report 2012/267, Faculty of Information Technology, Clayton School of I.T., Monash University, Australia.Hernández-Orallo, J., Insa, J., Dowe, D. L., & Hibbard, B. (2012b). Turing tests with Turing machines. In A. Voronkov (Ed.), The Alan Turing centenary conference, Turing-100, Manchester, volume 10 of EPiC Series, pp 140–156.Hernández-Orallo, J., & Minaya-Collado, N. (1998). A formal definition of intelligence based on an intensional variant of Kolmogorov complexity. In Proceedings of the international symposium of engineering of intelligent systems (EIS’98) (pp 146–163). Switzerland: ICSC Press.Herrmann, E., Call, J., Hernández-Lloreda, M. V., Hare, B., & Tomasello, M. (2007). Humans have evolved specialized skills of social cognition: The cultural intelligence hypothesis. Science, 317(5843), 1360–1366.Herrmann, E., Hernández-Lloreda, M. V., Call, J., Hare, B., & Tomasello, M. (2010). The structure of individual differences in the cognitive abilities of children and chimpanzees. Psychological Science, 21(1), 102–110.Horn, J. L., & Cattell, R. B. (1966). Refinement and test of the theory of fluid and crystallized general intelligences. Journal of educational psychology, 57(5), 253.Hutter, M. (2005). Universal artificial intelligence: Sequential decisions based on algorithmic probability. New York: Springer.Insa-Cabrera, J., Dowe, D. L., España, S., Hernández-Lloreda, M. V., & Hernández-Orallo, J. (2011a). Comparing humans and AI agents. In AGI: 4th conference on artificial general intelligence—Lecture Notes in Artificial Intelligence (LNAI), volume 6830, pp 122–132. Springer, New York.Insa-Cabrera, J., Dowe, D. L., & Hernández-Orallo, J. (2011b). Evaluating a reinforcement learning algorithm with a general intelligence test. In CAEPIA—Lecture Notes in Artificial Intelligence (LNAI), volume 7023, pages 1–11. Springer, New York.Kearns, M. & Singh, S. (2002). Near-optimal reinforcement learning in polynomial time. Machine Learning, 49(2), 209–232.Kolmogorov, A. N. (1965). Three approaches to the quantitative definition of information. Problems of Information Transmission, 1, 4–7.Legg, S. (2008, June). Machine super intelligence. Department of Informatics, University of Lugano.Legg, S. & Hutter, M. (2007). Universal intelligence: A definition of machine intelligence. Minds and Machines, 17(4), 391–444.Legg, S., & Veness, J. (2012). An approximation of the universal intelligence measure. In Proceedings of Solomonoff 85th memorial conference. New York: Springer.Levin, L. A. (1973). Universal sequential search problems. Problems of Information Transmission, 9(3), 265–266.Li, M., Vitányi, P. (2008). An introduction to Kolmogorov complexity and its applications (3rd ed). New York: Springer.Little, V. L., & Bailey, K. G. (1972). Potential intelligence or intelligence test potential? A question of empirical validity. Journal of Consulting and Clinical Psychology, 39(1), 168.Mahoney, M. V. (1999). Text compression as a test for artificial intelligence. In Proceedings of the national conference on artificial intelligence, AAAI (pp. 486–502). New Jersey: Wiley.Mahrer, A. R. (1958). Potential intelligence: A learning theory approach to description and clinical implication. The Journal of General Psychology, 59(1), 59–71.Oppy, G., & Dowe, D. L. (2011). The Turing Test. In E. N. Zalta (Ed.), Stanford encyclopedia of philosophy. Stanford University. http://plato.stanford.edu/entries/turing-test/ .Orseau, L. & Ring, M. (2011). Self-modification and mortality in artificial agents. In AGI: 4th conference on artificial general intelligence—Lecture Notes in Artificial Intelligence (LNAI), volume 6830, pages 1–10. Springer, New York.Ring, M. & Orseau, L. (2011). Delusion, survival, and intelligent agents. In AGI: 4th conference on artificial general intelligence—Lecture Notes in Artificial Intelligence (LNAI), volume 6830, pp. 11–20. Springer, New York.Schaeffer, J., Burch, N., Bjornsson, Y., Kishimoto, A., Muller, M., Lake, R., et al. (2007). Checkers is solved. Science, 317(5844), 1518.Solomonoff, R. J. (1962). Training sequences for mechanized induction. In M. Yovits, G. Jacobi, & G. Goldsteins (Eds.), Self-Organizing Systems, 7, 425–434.Solomonoff, R. J. (1964). A formal theory of inductive inference. Information and Control, 7(1–22), 224–254.Solomonoff, R. J. (1967). Inductive inference research: Status, Spring 1967. RTB 154, Rockford Research, Inc., 140 1/2 Mt. Auburn St., Cambridge, Mass. 02138, July 1967.Solomonoff, R. J. (1978). Complexity-based induction systems: comparisons and convergence theorems. IEEE Transactions on Information Theory, 24(4), 422–432.Solomonoff, R. J. (1984). Perfect training sequences and the costs of corruption—A progress report on induction inference research. Oxbridge research.Solomonoff, R. J. (1985). The time scale of artificial intelligence: Reflections on social effects. Human Systems Management, 5, 149–153.Sutton, R. S., & Barto, A. G. (1998). Reinforcement learning: An introduction. Cambridge: The MIT press.Thorp, T. R., & Mahrer, A. R. (1959). Predicting potential intelligence. Journal of Clinical Psychology, 15(3), 286–288.Turing, A. M. (1950). Computing machinery and intelligence. Mind, 59, 433–460.Veness, J., Ng, K. S., Hutter, M., & Silver, D. (2011). A Monte Carlo AIXI approximation. Journal of Artificial Intelligence Research, JAIR, 40, 95–142.Wallace, C. S. (2005). Statistical and inductive inference by minimum message length. New York: Springer.Wallace, C. S., & Boulton, D. M. (1968). An information measure for classification. Computer Journal, 11, 185–194.Wallace, C. S., & Dowe, D. L. (1999a). Minimum message length and Kolmogorov complexity. Computer Journal 42(4), 270–283.Wallace, C. S., & Dowe, D. L. (1999b). Refinements of MDL and MML coding. Computer Journal, 42(4), 330–337.Woergoetter, F., & Porr, B. (2008). Reinforcement learning. Scholarpedia, 3(3), 1448.Zvonkin, A. K., & Levin, L. A. (1970). The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms. Russian Mathematical Surveys, 25, 83–124

Factors Affecting Teacher Readiness for Online Learning (TROL) in Early Childhood Education: TISE and TPACK

This study aims to find empirical information about the effect of Technological Pedagogical Content Knowledge (TPACK), and Technology Integration Self Efficacy (TISE) on Teacher Readiness for Online Learning (TROL). This study uses a quantitative survey method with path analysis techniques. This study measures the readiness of kindergarten teachers in distance learning in Tanah Datar Regency, West Sumatra Province, Indonesia with a sampling technique using simple random sampling involving 105 teachers. Empirical findings reveal that; 1) there is a direct positive effect of Technology Integration Self Efficacy on Teacher Readiness for Online Learning; 2) there is a direct positive effect of PACK on Teacher Readiness for Online Learning; 3) there is a direct positive effect of Technology Integration Self Efficacy on TPACK. If want to improve teacher readiness for online learning, Technological Pedagogical Content Knowledge (TPACK) must be improved by paying attention to Technology Integration Self Efficacy (TISE). Keywords: TROL, TPACK, TISE, Early Childhood Education References: Abbitt, J. T. (2011). An Investigation of the Relationship between Self-Efficacy Beliefs about Technology Integration and Technological Pedagogical Content Knowledge (TPACK) among Preservice Teachers. Journal of Digital Learning in Teacher Education, 27(4), 134–143. Adedoyin, O. B., & Soykan, E. (2020). Covid-19 pandemic and online learning: The challenges and opportunities. Interactive Learning Environments, 1–13. https://doi.org/10.1080/10494820.2020.1813180 Adnan, M. (2020). Online learning amid the COVID-19 pandemic: Students perspectives. Journal of Pedagogical Sociology and Psychology, 1(2), 45–51. https://doi.org/10.33902/JPSP.2020261309 Alqurashi, E. (2016). Self-Efficacy in Online Learning Environments: A Literature Review. Contemporary Issues in Education Research (CIER), 9(1), 45–52. https://doi.org/10.19030/cier.v9i1.9549 Amir, H. (2016). Korelasi Pengaruh Faktor Efikasi Diri Dan Manajemen Diri Terhadap Motivasi Berprestasi Pada Mahasiswa Pendidikan Kimia Unversitas Bengkulu. Manajer Pendidikan, 10(4). Anderson, T. (2008). The theory and practice of online learning. Athabasca University Press. Anggraeni, N., Ridlo, S., & Setiati, N. (2018). The Relationship Between TISE and TPACK among Prospective Biology Teachers of UNNES. Journal of Biology Education, 7(3), 305–311. https://doi.org/10.15294/jbe.v7i3.26021 Ariani, D. N. (2015). Hubungan antara Technological Pedagogical Content Knowledge dengan Technology Integration Self Efficacy Guru Matematika di Sekolah Dasar. Muallimuna: Jurnal Madrasah Ibtidaiyah, 1(1), 79–91. Birisci, S., & Kul, E. (2019). Predictors of Technology Integration Self-Efficacy Beliefs of Preservice Teachers. Contemporary Educational Technology, 10(1). https://doi.org/10.30935/cet.512537 Bozkurt, A., Jung, I., Xiao, J., Vladimirschi, V., Schuwer, R., Egorov, G., Lambert, S. R., Al-freih, M., Pete, J., Olcott, D., Rodes, V., Aranciaga, I., Bali, M., Alvarez, A. V, Roberts, J., Pazurek, A., Raffaghelli, J. E., Panagiotou, N., Coëtlogon, P. De, … Paskevicius, M. (2020). UVicSPACE: Research & Learning Repository Navigating in a time of uncertainty and crisis. Asian Journal of Distance Education, 15(1), 1–126. Brinkley-Etzkorn, K. E. (2018). Learning to teach online: Measuring the influence of faculty development training on teaching effectiveness through a TPACK lens. The Internet and Higher Education, 38, 28–35. https://doi.org/10.1016/j.iheduc.2018.04.004 Butnaru, G. I., Niță, V., Anichiti, A., & Brînză, G. (2021). The effectiveness of online education during covid 19 pandemic—A comparative analysis between the perceptions of academic students and high school students from romania. Sustainability (Switzerland), 13(9). https://doi.org/10.3390/su13095311 Carliner, S. (2003). Modeling information for three-dimensional space: Lessons learned from museum exhibit design. Technical Communication, 50(4), 554–570. Cengiz, C. (2015). The development of TPACK, Technology Integrated Self-Efficacy and Instructional Technology Outcome Expectations of pre-service physical education teachers. Asia-Pacific Journal of Teacher Education, 43(5), 411–422. https://doi.org/10.1080/1359866X.2014.932332 Chou, P., & Ph, D. (2012). Effect of Students ’ Self -Directed Learning Abilities on Online Learning Outcomes: Two Exploratory Experiments in Electronic Engineering Department of Education. 2(6), 172–179. Crawford, J., Butler-Henderson, K., Rudolph, J., Malkawi, B., Burton, R., Glowatz, M., Magni, P. A., & Lam, S. (2020). COVID-19: 20 countries’ higher education intra-period digital pedagogy responses. Journal of Applied Learning & Teaching, 3(1). https://doi.org/10.37074/jalt.2020.3.1.7 Dolighan, T., & Owen, M. (2021). Teacher efficacy for online teaching during the COVID-19 pandemic. Brock Education Journal, 30(1), 95. https://doi.org/10.26522/brocked.v30i1.851 Dong, Y., Chai, C. S., Sang, G.-Y., Koh, J. H. L., & Tsai, C.-C. (2015). Exploring the Profiles and Interplays of Pre-service and In-service Teachers’ Technological Pedagogical Content Knowledge (TPACK) in China. International Forum of Educational Technology & Society, 18(1), 158–169. Donitsa-Schmidt, S., & Ramot, R. (2020). Opportunities and challenges: Teacher education in Israel in the Covid-19 pandemic. Journal of Education for Teaching, 46(4), 586–595. https://doi.org/10.1080/02607476.2020.1799708 Elas, N. I. B., Majid, F. B. A., & Narasuman, S. A. (2019). Development of Technological Pedagogical Content Knowledge (TPACK) For English Teachers: The Validity and Reliability. International Journal of Emerging Technologies in Learning (IJET), 14(20), 18. https://doi.org/10.3991/ijet.v14i20.11456 Ghozali, I. (2011). Aplikasi multivariate dengan program IBM SPSS 19. Badan Penerbit Universitas Diponegoro. Giles, R. M., & Kent, A. M. (2016). An Investigation of Preservice Teachers ’ Self-Efficacy for Teaching with Technology. 1(1), 32–40. https://doi.org/10.20849/aes.v1i1.19 Gil-flores, J., & Rodríguez-santero, J. (2017). Computers in Human Behavior Factors that explain the use of ICT in secondary-education classrooms: The role of teacher characteristics and school infrastructure. Computers in Human Behavior, 68, 441–449. https://doi.org/10.1016/j.chb.2016.11.057 Habibi, A., Yusop, F. D., & Razak, R. A. (2019). The role of TPACK in affecting pre-service language teachers’ ICT integration during teaching practices: Indonesian context. Education and Information Technologies. https://doi.org/10.1007/s10639-019-10040-2 Harris, J. B., & Hofer, M. J. (2011). Technological Pedagogical Content Knowledge (TPACK) in Action. Journal of Research on Technology in Education, 43(3), 211–229. https://doi.org/10.1080/15391523.2011.10782570 Hatlevik, I. K. R., & Hatlevik, O. E. (2018). Examining the relationship between teachers’ ICT self-efficacy for educational purposes, collegial collaboration, lack of facilitation and the use of ICT in teaching practice. Frontiers in Psychology, 9(JUN), 1–8. https://doi.org/10.3389/fpsyg.2018.00935 Hung, M. L. (2016). Teacher readiness for online learning: Scale development and teacher perceptions. Computers and Education, 94, 120–133. https://doi.org/10.1016/j.compedu.2015.11.012 Hung, M. L., Chou, C., Chen, C. H., & Own, Z. Y. (2010). Learner readiness for online learning: Scale development and student perceptions. Computers and Education, 55(3), 1080–1090. https://doi.org/10.1016/j.compedu.2010.05.004 Juanda, A., Shidiq, A. S., & Nasrudin, D. (2021). Teacher Learning Management: Investigating Biology Teachers’ TPACK to Conduct Learning During the Covid-19 Outbreak. Jurnal Pendidikan IPA Indonesia, 10(1), 48–59. https://doi.org/10.15294/jpii.v10i1.26499 Karatas, M. A.-K. (2020). COVID - 19 Pandemisinin Toplum Psikolojisine Etkileri ve Eğitime Yansımaları. Journal of Turkish Studies, Volume 15(Volume 15 Issue 4), 1–13. https://doi.org/10.7827/TurkishStudies.44336 Kaymak, Z. D., & Horzum, M. B. (2013). Relationship between online learning readiness and structure and interaction of online learning students. Kuram ve Uygulamada Egitim Bilimleri, 13(3), 1792–1797. https://doi.org/10.12738/estp.2013.3.1580 Keser, H., Karaoğlan Yılmaz, F. G., & Yılmaz, R. (2015). TPACK Competencies and Technology Integration Self-Efficacy Perceptions of Pre-Service Teachers. Elementary Education Online, 14(4), 1193–1207. https://doi.org/10.17051/io.2015.65067 Kim, J. (2020). Learning and Teaching Online During Covid-19: Experiences of Student Teachers in an Early Childhood Education Practicum. International Journal of Early Childhood, 52(2), 145–158. https://doi.org/10.1007/s13158-020-00272-6 Koehler, M. J., Mishra, P., & Cain, W. (2013). What is Technological Pedagogical Content Knowledge (TPACK)? Journal of Education, 193(3), 13–19. https://doi.org/10.1177/002205741319300303 Lee, Y., & Lee, J. (2014). Enhancing pre-service teachers’ self-efficacy beliefs for technology integration through lesson planning practice. Computers and Education, 73, 121–128. https://doi.org/10.1016/j.compedu.2014.01.001 Mallillin, L. L. D., Mendoza, L. C., Mallillin, J. B., Felix, R. C., & Lipayon, I. C. (2020). Implementation and Readiness of Online Learning Pedagogy: A Transition To Covid 19 Pandemic. European Journal of Open Education and E-Learning Studies, 5(2), 71–90. https://doi.org/10.46827/ejoe.v5i2.3321 Mishra, P. (2019). Considering Contextual Knowledge: The TPACK Diagram Gets an Upgrade. Journal of Digital Learning in Teacher Education, 35(2), 76–78. https://doi.org/10.1080/21532974.2019.1588611 Moorhouse, B. L. (2020). Adaptations to a face-to-face initial teacher education course ‘forced’ online due to the COVID-19 pandemic. Journal of Education for Teaching, 46(4), 609–611. https://doi.org/10.1080/02607476.2020.1755205 Mulyadi, D., Wijayatingsih, T. D., Budiastuti, R. E., Ifadah, M., & Aimah, S. (2020). Technological Pedagogical and Content Knowledge of ESP Teachers in Blended Learning Format. International Journal of Emerging Technologies in Learning (IJET), 15(06), 124. https://doi.org/10.3991/ijet.v15i06.11490 Murtaza, G., Mahmood, K., & Fatima, N. (2021). Readiness for Online Learning during COVID-19 pandemic: A survey of Pakistani LIS students The Journal of Academic Librarianship Readiness for Online Learning during COVID-19 pandemic: A survey of Pakistani LIS students. The Journal of Academic Librarianship, 47(3), 102346. https://doi.org/10.1016/j.acalib.2021.102346 Mustika, M., & Sapriya. (2019). Kesiapan Guru IPS dalam E-learning Berdasarkan: Survei melalui Pendekatan TPACK. 32–35. https://doi.org/10.1145/3306500.3306566 Niess, M. L. (2011). Investigating TPACK: Knowledge Growth in Teaching with Technology. Journal of Educational Computing Research, 44(3), 299–317. https://doi.org/10.2190/EC.44.3.c Oketch, & Otchieng, H. (2013). University of Nairobi, H. A. (2013). E-Learning Readiness Assessment Model in Kenyas’ Higher Education Institutions: A Case Study of University of Nairobi by: Oketch, Hada Achieng a Research Project Submitted in Partial Fulfillment of the Requirement of M. October. Pamuk, S., Ergun, M., Cakir, R., Yilmaz, H. B., & Ayas, C. (2015). Exploring relationships among TPACK components and development of the TPACK instrument. Education and Information Technologies, 20(2), 241–263. https://doi.org/10.1007/s10639-013-9278-4 Paraskeva, F., Bouta, H., & Papagianni, A. (2008). Individual characteristics and computer self-efficacy in secondary education teachers to integrate technology in educational practice. Computers and Education, 50(3), 1084–1091. https://doi.org/10.1016/j.compedu.2006.10.006 Putro, S. T., Widyastuti, M., & Hastuti, H. (2020). Problematika Pembelajaran di Era Pandemi COVID-19 Stud Kasus: Indonesia, Filipina, Nigeria, Ethiopia, Finlandia, dan Jerman. Geomedia Majalah Ilmiah Dan Informasi Kegeografian, 18(2), 50–64. Qudsiya, R., Widiyaningrum, P., & Setiati, N. (2018). The Relationship Between TISE and TPACK among Prospective Biology Teachers of UNNES. Journal of Biology Education, 7(3), 305–311. https://doi.org/10.15294/jbe.v7i3.26021 Reflianto, & Syamsuar. (2018). Pendidikan dan Tantangan Pembelajaran Berbasis Teknologi Informasi di Era Revolusi Industri 4.0. Jurnal Ilmiah Teknologi Pendidikan, 6(2), 1–13. Reski, A., & Sari, K. (2020). Analisis Kemampuan TPACK Guru Fisika Se-Distrik Merauke. Jurnla Kreatif Online, 8(1), 1–8. Ruggiero, D., & Mong, C. J. (2015). The teacher technology integration experience: Practice and reflection in the classroom. Journal of Information Technology Education, 14. Santika, V., Indriayu, M., & Sangka, K. B. (2021). Profil TPACK Guru Ekonomi di Indonesia sebagai Pendekatan Integrasi TIK selama Pembelajaran Jarak Jauh pada Masa Pandemi Covid-19. Duconomics Sci-Meet (Education & Economics Science Meet), 1, 356–369. https://doi.org/10.37010/duconomics.v1.5470 Semiz, K., & Ince, M. L. (2012). Pre-service physical education teachers’ technological pedagogical content knowledge, technology integration self-efficacy and instructional technology outcome expectations. Australasian Journal of Educational Technology, 28(7). https://doi.org/10.14742/ajet.800 Senthilkumar, Sivapragasam, & Senthamaraikannan. (2014). Role of ICT in Teaching Biology. International Journal of Research, 1(9), 780–788. Setiaji, B., & Dinata, P. A. C. (2020). Analisis kesiapan mahasiswa jurusan pendidikan fisika menggunakan e-learning dalam situasi pandemi Covid-19 Analysis of e-learning readiness on physics education students during Covid-19 pandemic. 6(1), 59–70. Siagian, H. S., Ritonga, T., & Lubis, R. (2021). Analisis Kesiapan Belajar Daring Siswa Kelas Vii Pada Masa Pandemi Covid-19 Di Desa Simpang. JURNAL MathEdu (Mathematic Education Journal), 4(2), 194–201. Sintawati, M., & Indriani, F. (2019). Pentingnya Technological Pedagogical Content Knowledge (TPACK) Guru di Era Revolusi Industri 4.0. Seminar Nasional Pagelaran Pendidikan Dasar Nasional (PPDN), 1(1), 417–422. Sojanah, J., Suwatno, Kodri, & Machmud, A. (2021). Factors affecting teachers’ technological pedagogical and content knowledge (A survey on economics teacher knowledge). Cakrawala Pendidikan, 40(1), 1–16. https://doi.org/10.21831/cp.v40i1.31035 Subhan, M. (2020). Analisis Penerapan Technological Pedagogical Content Knowledge Pada Proses Pembelajaran Kurikulum 2013 di Kelas V. International Journal of Technology Vocational Education and Training, 1(2), 174–179. Sum, T. A., & Taran, E. G. M. (2020). Kompetensi Pedagogik Guru PAUD dalam Perencanaan dan Pelaksanaan Pembelajaran. Jurnal Obsesi : Jurnal Pendidikan Anak Usia Dini, 4(2), 543. https://doi.org/10.31004/obsesi.v4i2.287 Suryawati, E., Firdaus, L. N., & Yosua, H. (2014). Analisis keterampilan technological pedagogical content knowledge (TPCK) guru biologi SMA negeri kota Pekanbaru. Jurnal Biogenesis, 11(1), 67-72. Suyamto, J., Masykuri, M., & Sarwanto, S. (2020). Analisis Kemampuan Tpack (Technolgical, Pedagogical, and Content, Knowledge) Guru Biologi Sma Dalam Menyusun Perangkat Pembelajaran Materi Sistem Peredaran Darah. INKUIRI: Jurnal Pendidikan IPA, 9(1), 46. https://doi.org/10.20961/inkuiri.v9i1.41381 Tiara, D. R., & Pratiwi, E. (2020). Pentingnya Mengukur Kesiapan Guru Sebagai Dasar Pembelajaran Daring. Jurnal Golden Age, 04(2), 362–368. Trionanda, S. (2021). Analisis kesiapan dan pelaksanaan pembelajaran matematika jarak jauh berdasarkan profil TPACK di SD Katolik Tanjungpinang tahun ajaran 2020 / 2021. In Prosiding Seminar Nasional Matematika Dan Pendidikan Matematika, 6, 69–76. Tsai, C.-C., & Chai, C. S. (2012). The ‘third’-order barrier for technology-integration instruction: Implications for teacher education. Australasian Journal of Educational Technology, 28(6). https://doi.org/10.14742/ajet.810 Wahyuni, F. T. (2019). Hubungan Antara Technological Pedagogical Content Knowledge (Tpack) Dengan Technology Integration Self Efficacy (Tise) Guru Matematika Di Madrasah Ibtidaiyah. Jurnal Pendidikan Matematika (Kudus), 2(2), 109–122. https://doi.org/10.21043/jpm.v2i2.6358 Wang, L., Ertmer, P. A., & Newby, T. J. (2014). Journal of Research on Technology in Education Increasing Preservice Teachers’ Self-Efficacy Beliefs for Technology Integration. Journal of Research on Technology in Education, 36(3), 37–41. https://doi.org/10.1080/15391523.2004.10782414 Warden, C. A., Yi-Shun, W., Stanworth, J. O., & Chen, J. F. (2020). Millennials’ technology readiness and self-efficacy in online classes. Innovations in Education and Teaching International, 00(00), 1–11. https://doi.org/10.1080/14703297.2020.1798269 Widarjono, A. (2015). Analisis Multivariat Terapan edisi kedua. UPP STIM YKPN. Wiresti, R. D. (2021). Analisis Dampak Work from Home pada Anak Usia Dini di Masa Pandemi Covid-19. Jurnal Obsesi: Jurnal Pendidikan Anak Usia Dini, 5(1), 641653. https://doi.org/10.31004/obsesi.v5i1.563 Yildiz Durak, H. (2019). Modeling of relations between K-12 teachers’ TPACK levels and their technology integration self-efficacy, technology literacy levels, attitudes toward technology and usage objectives of social networks. Interactive Learning Environments, 1–27. https://doi.org/10.1080/10494820.2019.1619591 Yudha, F., Aziz, A., & Tohir, M. (2021). Pendampingan Siswa Terdampak Covid-19 Melalui Media Animasi Sebagai Inovasi Pembelajaran Online. JMM (Jurnal Masyarakat Mandiri), 5(3), 964–978. Yurdugül, H., & Demir, Ö. (2017). An investigation of Pre-service Teachers’ Readiness for E-learning at Undergraduate Level Teacher Training Programs: The Case of Hacettepe University. The Case of Hacettepe University. &nbsp

General Theory and Tools for Proving Algorithms in Nominative Data Systems

In this paper we introduce some new definitions for sequences of operations and extract general theorems about properties of iterative algorithms encoded in nominative data language [20] in the Mizar system [3], [1] in order to simplify the process of proving algorithms in the future. This paper continues verification of algorithms [10], [13], [12], [14] written in terms of simple-named complex-valued nominative data [6], [8], [18], [11], [15], [16]. 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 postconditions [17], [19], [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.Adrian Jaszczak. Partial correctness of a power algorithm. Formalized Mathematics, 27 (2):189–195, 2019. doi:10.2478/forma-2019-0018.Adrian Jaszczak and Artur Korniłowicz. Partial correctness of a factorial algorithm. Formalized Mathematics, 27(2):181–187, 2019. doi:10.2478/forma-2019-0017.Artur Korniłowicz. Partial correctness of a Fibonacci algorithm. Formalized Mathematics, 28(2):187–196, 2020. doi:10.2478/forma-2020-0016.Artur Korniłowicz, 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 Korniłowicz, 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_6.28426927

Automatic classification of human facial features based on their appearance

[EN] Classification or typology systems used to categorize different human body parts have existed for many years. Nevertheless, there are very few taxonomies of facial features. Ergonomics, forensic anthropology, crime prevention or new human-machine interaction systems and online activities, like e-commerce, e-learning, games, dating or social networks, are fields in which classifications of facial features are useful, for example, to create digital interlocutors that optimize the interactions between human and machines. However, classifying isolated facial features is difficult for human observers. Previous works reported low inter-observer and intra-observer agreement in the evaluation of facial features. This work presents a computer-based procedure to automatically classify facial features based on their global appearance. This procedure deals with the difficulties associated with classifying features using judgements from human observers, and facilitates the development of taxonomies of facial features. Taxonomies obtained through this procedure are presented for eyes, mouths and noses.Fuentes-Hurtado, F.; Diego-Mas, JA.; Naranjo Ornedo, V.; Alcañiz Raya, ML. (2019). Automatic classification of human facial features based on their appearance. PLoS ONE. 14(1):1-20. https://doi.org/10.1371/journal.pone.0211314S120141Damasio, A. R. (1985). Prosopagnosia. Trends in Neurosciences, 8, 132-135. doi:10.1016/0166-2236(85)90051-7Bruce, V., & Young, A. (1986). Understanding face recognition. British Journal of Psychology, 77(3), 305-327. doi:10.1111/j.2044-8295.1986.tb02199.xTodorov, A. (2011). Evaluating Faces on Social Dimensions. Social Neuroscience, 54-76. doi:10.1093/acprof:oso/9780195316872.003.0004Little, A. C., Burriss, R. P., Jones, B. C., & Roberts, S. C. (2007). Facial appearance affects voting decisions. Evolution and Human Behavior, 28(1), 18-27. doi:10.1016/j.evolhumbehav.2006.09.002Porter, J. P., & Olson, K. L. (2001). Anthropometric Facial Analysis of the African American Woman. Archives of Facial Plastic Surgery, 3(3), 191-197. doi:10.1001/archfaci.3.3.191Gündüz Arslan, S., Genç, C., Odabaş, B., & Devecioğlu Kama, J. (2007). Comparison of Facial Proportions and Anthropometric Norms Among Turkish Young Adults With Different Face Types. Aesthetic Plastic Surgery, 32(2), 234-242. doi:10.1007/s00266-007-9049-yFerring, V., & Pancherz, H. (2008). Divine proportions in the growing face. American Journal of Orthodontics and Dentofacial Orthopedics, 134(4), 472-479. doi:10.1016/j.ajodo.2007.03.027Mane, D. R., Kale, A. D., Bhai, M. B., & Hallikerimath, S. (2010). Anthropometric and anthroposcopic analysis of different shapes of faces in group of Indian population: A pilot study. Journal of Forensic and Legal Medicine, 17(8), 421-425. doi:10.1016/j.jflm.2010.09.001Ritz-Timme, S., Gabriel, P., Tutkuviene, J., Poppa, P., Obertová, Z., Gibelli, D., … Cattaneo, C. (2011). Metric and morphological assessment of facial features: A study on three European populations. Forensic Science International, 207(1-3), 239.e1-239.e8. doi:10.1016/j.forsciint.2011.01.035Ritz-Timme, S., Gabriel, P., Obertovà, Z., Boguslawski, M., Mayer, F., Drabik, A., … Cattaneo, C. (2010). A new atlas for the evaluation of facial features: advantages, limits, and applicability. International Journal of Legal Medicine, 125(2), 301-306. doi:10.1007/s00414-010-0446-4Kong, S. G., Heo, J., Abidi, B. R., Paik, J., & Abidi, M. A. (2005). Recent advances in visual and infrared face recognition—a review. Computer Vision and Image Understanding, 97(1), 103-135. doi:10.1016/j.cviu.2004.04.001Tavares, G., Mourão, A., & Magalhães, J. (2016). Crowdsourcing facial expressions for affective-interaction. Computer Vision and Image Understanding, 147, 102-113. doi:10.1016/j.cviu.2016.02.001Buckingham, G., DeBruine, L. M., Little, A. C., Welling, L. L. M., Conway, C. A., Tiddeman, B. P., & Jones, B. C. (2006). Visual adaptation to masculine and feminine faces influences generalized preferences and perceptions of trustworthiness. Evolution and Human Behavior, 27(5), 381-389. doi:10.1016/j.evolhumbehav.2006.03.001Boberg M, Piippo P, Ollila E. Designing Avatars. DIMEA ‘08 Proc 3rd Int Conf Digit Interact Media Entertain Arts. ACM; 2008; 232–239. doi: https://doi.org/10.1145/1413634.1413679Rojas Q., M., Masip, D., Todorov, A., & Vitria, J. (2011). Automatic Prediction of Facial Trait Judgments: Appearance vs. Structural Models. PLoS ONE, 6(8), e23323. doi:10.1371/journal.pone.0023323Laurentini, A., & Bottino, A. (2014). Computer analysis of face beauty: A survey. Computer Vision and Image Understanding, 125, 184-199. doi:10.1016/j.cviu.2014.04.006Alemany S, Gonzalez J, Nacher B, Soriano C, Arnaiz C, Heras H. Anthropometric survey of the Spanish female population aimed at the apparel industry. Proceedings of the 2010 Intl Conference on 3D Body scanning Technologies. 2010. pp. 307–315.Vinué, G., Epifanio, I., & Alemany, S. (2015). Archetypoids: A new approach to define representative archetypal data. Computational Statistics & Data Analysis, 87, 102-115. doi:10.1016/j.csda.2015.01.018Jee, S., & Yun, M. H. (2016). An anthropometric survey of Korean hand and hand shape types. International Journal of Industrial Ergonomics, 53, 10-18. doi:10.1016/j.ergon.2015.10.004Kim, N.-S., & Do, W.-H. (2014). Classification of Elderly Women’s Foot Type. Journal of the Korean Society of Clothing and Textiles, 38(3), 305-320. doi:10.5850/jksct.2014.38.3.305Sarakon P, Charoenpong T, Charoensiriwath S. Face shape classification from 3D human data by using SVM. The 7th 2014 Biomedical Engineering International Conference. IEEE; 2014. pp. 1–5. doi: https://doi.org/10.1109/BMEiCON.2014.7017382PRESTON, T. A., & SINGH, M. (1972). Redintegrated Somatotyping. Ergonomics, 15(6), 693-700. doi:10.1080/00140137208924469Lin, Y.-L., & Lee, K.-L. (1999). Investigation of anthropometry basis grouping technique for subject classification. Ergonomics, 42(10), 1311-1316. doi:10.1080/001401399184965Malousaris, G. G., Bergeles, N. K., Barzouka, K. G., Bayios, I. A., Nassis, G. P., & Koskolou, M. D. (2008). Somatotype, size and body composition of competitive female volleyball players. Journal of Science and Medicine in Sport, 11(3), 337-344. doi:10.1016/j.jsams.2006.11.008Carvalho, P. V. R., dos Santos, I. L., Gomes, J. O., Borges, M. R. S., & Guerlain, S. (2008). Human factors approach for evaluation and redesign of human–system interfaces of a nuclear power plant simulator. Displays, 29(3), 273-284. doi:10.1016/j.displa.2007.08.010Fabri M, Moore D. The use of emotionally expressive avatars in Collaborative Virtual Environments. AISB’05 Convention:Proceedings of the Joint Symposium on Virtual Social Agents: Social Presence Cues for Virtual Humanoids Empathic Interaction with Synthetic Characters Mind Minding Agents. 2005. pp. 88–94. doi:citeulike-article-id:790934Sukhija, P., Behal, S., & Singh, P. (2016). Face Recognition System Using Genetic Algorithm. Procedia Computer Science, 85, 410-417. doi:10.1016/j.procs.2016.05.183Trescak T, Bogdanovych A, Simoff S, Rodriguez I. Generating diverse ethnic groups with genetic algorithms. Proceedings of the 18th ACM symposium on Virtual reality software and technology—VRST ‘12. New York, New York, USA: ACM Press; 2012. p. 1. doi: https://doi.org/10.1145/2407336.2407338Vanezis, P., Lu, D., Cockburn, J., Gonzalez, A., McCombe, G., Trujillo, O., & Vanezis, M. (1996). Morphological Classification of Facial Features in Adult Caucasian Males Based on an Assessment of Photographs of 50 Subjects. Journal of Forensic Sciences, 41(5), 13998J. doi:10.1520/jfs13998jTamir, A. (2011). Numerical Survey of the Different Shapes of the Human Nose. Journal of Craniofacial Surgery, 22(3), 1104-1107. doi:10.1097/scs.0b013e3182108eb3Tamir, A. (2013). Numerical Survey of the Different Shapes of Human Chin. Journal of Craniofacial Surgery, 24(5), 1657-1659. doi:10.1097/scs.0b013e3182942b77Richler, J. J., Cheung, O. S., & Gauthier, I. (2011). Holistic Processing Predicts Face Recognition. Psychological Science, 22(4), 464-471. doi:10.1177/0956797611401753Taubert, J., Apthorp, D., Aagten-Murphy, D., & Alais, D. (2011). The role of holistic processing in face perception: Evidence from the face inversion effect. Vision Research, 51(11), 1273-1278. doi:10.1016/j.visres.2011.04.002Donnelly, N., & Davidoff, J. (1999). The Mental Representations of Faces and Houses: Issues Concerning Parts and Wholes. Visual Cognition, 6(3-4), 319-343. doi:10.1080/135062899395000Davidoff, J., & Donnelly, N. (1990). Object superiority: A comparison of complete and part probes. Acta Psychologica, 73(3), 225-243. doi:10.1016/0001-6918(90)90024-aTanaka, J. W., & Farah, M. J. (1993). Parts and Wholes in Face Recognition. The Quarterly Journal of Experimental Psychology Section A, 46(2), 225-245. doi:10.1080/14640749308401045Wang, R., Li, J., Fang, H., Tian, M., & Liu, J. (2012). Individual Differences in Holistic Processing Predict Face Recognition Ability. Psychological Science, 23(2), 169-177. doi:10.1177/0956797611420575Rhodes, G., Ewing, L., Hayward, W. G., Maurer, D., Mondloch, C. J., & Tanaka, J. W. (2009). Contact and other-race effects in configural and component processing of faces. British Journal of Psychology, 100(4), 717-728. doi:10.1348/000712608x396503Miller, G. A. (1994). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 101(2), 343-352. doi:10.1037/0033-295x.101.2.343Scharff, A., Palmer, J., & Moore, C. M. (2011). Evidence of fixed capacity in visual object categorization. Psychonomic Bulletin & Review, 18(4), 713-721. doi:10.3758/s13423-011-0101-1Meyers, E., & Wolf, L. (2007). Using Biologically Inspired Features for Face Processing. International Journal of Computer Vision, 76(1), 93-104. doi:10.1007/s11263-007-0058-8Cootes, T. F., Edwards, G. J., & Taylor, C. J. (2001). Active appearance models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(6), 681-685. doi:10.1109/34.927467Ahonen, T., Hadid, A., & Pietikainen, M. (2006). Face Description with Local Binary Patterns: Application to Face Recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28(12), 2037-2041. doi:10.1109/tpami.2006.244Belhumeur, P. N., Hespanha, J. P., & Kriegman, D. J. (1997). Eigenfaces vs. Fisherfaces: recognition using class specific linear projection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(7), 711-720. doi:10.1109/34.598228Turk, M., & Pentland, A. (1991). Eigenfaces for Recognition. Journal of Cognitive Neuroscience, 3(1), 71-86. doi:10.1162/jocn.1991.3.1.71Klare B, Jain AK. On a taxonomy of facial features. IEEE 4th International Conference on Biometrics: Theory, Applications and Systems, BTAS 2010. IEEE; 2010. pp. 1–8. doi: https://doi.org/10.1109/BTAS.2010.5634533Chihaoui, M., Elkefi, A., Bellil, W., & Ben Amar, C. (2016). A Survey of 2D Face Recognition Techniques. Computers, 5(4), 21. doi:10.3390/computers5040021Ma, D. S., Correll, J., & Wittenbrink, B. (2015). The Chicago face database: A free stimulus set of faces and norming data. Behavior Research Methods, 47(4), 1122-1135. doi:10.3758/s13428-014-0532-5Asthana A, Zafeiriou S, Cheng S, Pantic M. Incremental face alignment in the wild. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2014. pp. 1859–1866. doi: https://doi.org/10.1109/CVPR.2014.240Bag S, Barik S, Sen P, Sanyal G. A statistical nonparametric approach of face recognition: combination of eigenface & modified k-means clustering. Proceedings Second International Conference on Information Processing. 2008. p. 198.Doukas, C., & Maglogiannis, I. (2010). A Fast Mobile Face Recognition System for Android OS Based on Eigenfaces Decomposition. Artificial Intelligence Applications and Innovations, 295-302. doi:10.1007/978-3-642-16239-8_39Huang P, Huang Y, Wang W, Wang L. Deep embedding network for clustering. Proceedings—International Conference on Pattern Recognition. 2014. pp. 1532–1537. doi: https://doi.org/10.1109/ICPR.2014.272Dizaji KG, Herandi A, Deng C, Cai W, Huang H. Deep Clustering via Joint Convolutional Autoencoder Embedding and Relative Entropy Minimization. Proceedings of the IEEE International Conference on Computer Vision. 2017. doi: https://doi.org/10.1109/ICCV.2017.612Xie J, Girshick R, Farhadi A. Unsupervised deep embedding for clustering analysis [Internet]. Proceedings of the 33rd International Conference on International Conference on Machine Learning—Volume 48. JMLR.org; 2016. pp. 478–487. Available: https://dl.acm.org/citation.cfm?id=3045442Nousi, P., & Tefas, A. (2017). Discriminatively Trained Autoencoders for Fast and Accurate Face Recognition. Communications in Computer and Information Science, 205-215. doi:10.1007/978-3-319-65172-9_18Sirovich, L., & Kirby, M. (1987). Low-dimensional procedure for the characterization of human faces. Journal of the Optical Society of America A, 4(3), 519. doi:10.1364/josaa.4.00051