Modelling the dynamics of the students academic performance in the German region of North Rhine- Westphalia: an epidemiological approach with uncertainty

This is an author's accepted manuscript of an article published in "International Journal of Computer Mathematics"; Volume 91, Issue 2, 2014; copyright Taylor & Francis; available online at: http://dx.doi.org/10.1080/00207160.2013.813937Student academic underachievement is a concern of paramount importance in Europe, where around 15% of the students in the last high school courses do not achieve the minimum knowledge academic requirement. In this paper, we propose a model based on a system of differential equations to study the dynamics of the students academic performance in the German region of North Rhine-Westphalia. This approach is supported by the idea that both, good and bad study habits, are a mixture of personal decisions and influence of classmates. This model allows us to forecast the student academic performance by means of confidence intervals over the next few years.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness grant MTM2009-08587 and Universitat Politecnica de Valencia grant PAID06-11-2070.Cortés, J.; Ehrhardt, M.; Sánchez Sánchez, A.; Santonja, F.; Villanueva Micó, RJ. (2014). Modelling the dynamics of the students academic performance in the German region of North Rhine- Westphalia: an epidemiological approach with uncertainty. International Journal of Computer Mathematics. 91(2):241-251. https://doi.org/10.1080/00207160.2013.813937S241251912Akaike, H. (1969). Fitting autoregressive models for prediction. Annals of the Institute of Statistical Mathematics, 21(1), 243-247. doi:10.1007/bf02532251Brockwell, P. J., & Davis, R. A. (1996). Introduction to Time Series and Forecasting. Springer Texts in Statistics. doi:10.1007/978-1-4757-2526-1Dogan, G. (2007). Bootstrapping for confidence interval estimation and hypothesis testing for parameters of system dynamics models. System Dynamics Review, 23(4), 415-436. doi:10.1002/sdr.362Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 7(1), 1-26. doi:10.1214/aos/1176344552LJUNG, G. M., & BOX, G. E. P. (1979). The likelihood function of stationary autoregressive-moving average models. Biometrika, 66(2), 265-270. doi:10.1093/biomet/66.2.265Martcheva, M., & Castillo-Chavez, C. (2003). Diseases with chronic stage in a population with varying size. Mathematical Biosciences, 182(1), 1-25. doi:10.1016/s0025-5564(02)00184-0J.D. Murray,Mathematical Biology, Springer, New York, 2002.Nelder, J. A., & Mead, R. (1965). A Simplex Method for Function Minimization. The Computer Journal, 7(4), 308-313. doi:10.1093/comjnl/7.4.308Yazici, B., & Yolacan, S. (2007). A comparison of various tests of normality. Journal of Statistical Computation and Simulation, 77(2), 175-183. doi:10.1080/10629360600678310M.Á.M. Zabal, P.F. Berrocal, C. Coll, and M. de los Ángeles Melero Zabal,La Interacción Social en Contextos Educativos[Social interaction in educational contexts], Psicología/Siglo XXI de España Editores Series, Siglo XXI de España, 1995

Discovery of Malicious Attacks to Improve Mobile Collaborative Learning (MCL)

Mobile collaborative learning (MCL) is highly acknowledged and focusing paradigm in eductional institutions and several organizations across the world. It exhibits intellectual synergy of various combined minds to handle the problem and stimulate the social activity of mutual understanding. To improve and foster the baseline of MCL, several supporting architectures, frameworks including number of the mobile applications have been introduced. Limited research was reported that particularly focuses to enhance the security of those pardigms and provide secure MCL to users. The paper handles the issue of rogue DHCP server that affects and disrupts the network resources during the MCL. The rogue DHCP is unauthorized server that releases the incorrect IP address to users and sniffs the traffic illegally. The contribution specially provides the privacy to users and enhances the security aspects of mobile supported collaborative framework (MSCF). The paper introduces multi-frame signature-cum anomaly-based intrusion detection systems (MSAIDS) supported with novel algorithms through addition of new rules in IDS and mathematcal model. The major target of contribution is to detect the malicious attacks and blocks the illegal activities of rogue DHCP server. This innovative security mechanism reinforces the confidence of users, protects network from illicit intervention and restore the privacy of users. Finally, the paper validates the idea through simulation and compares the findings with other existing techniques.Comment: 20 pages and 11 figures; International Journal of Computer Networks and Communications (IJCNC) July 2012, Volume 4. Number

On the use of stabilization techniques in the Cartesian grid finite element method framework for iterative solvers

"This is the peer reviewed version of the following article: Navarro-Jiménez, José Manuel, Enrique Nadal, Manuel Tur, José Martínez-Casas, and Juan José Ródenas. 2020. "On the Use of Stabilization Techniques in the Cartesian Grid Finite Element Method Framework for Iterative Solvers." International Journal for Numerical Methods in Engineering 121 (13). Wiley: 3004-20. doi:10.1002/nme.6344, which has been published in final form at https://doi.org/10.1002/nme.6344. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] Fictitious domain methods, like the Cartesian grid finite element method (cgFEM), are based on the use of unfitted meshes that must be intersected. This may yield to ill-conditioned systems of equations since the stiffness associated with a node could be small, thus poorly contributing to the energy of the problem. This issue complicates the use of iterative solvers for large problems. In this work, we present a new stabilization technique that, in the case of cgFEM, preserves the Cartesian structure of the mesh. The formulation consists in penalizing the free movement of those nodes by a smooth extension of the solution from the interior of the domain, through a postprocess of the solution via a displacement recovery technique. The numerical results show an improvement of the condition number and a decrease in the number of iterations of the iterative solver while preserving the problem accuracy.The authors wish to thank the Spanish "Ministerio de Economía y Competitividad," the "Generalitat Valenciana," and the "Universitat Politècnica de València" for their financial support received through the projects DPI2017-89816-R, Prometeo 2016/007 and the FPI2015 program, respectively.Navarro-Jiménez, J.; Nadal, E.; Tur Valiente, M.; Martínez Casas, J.; Ródenas, JJ. (2020). On the use of stabilization techniques in the Cartesian grid finite element method framework for iterative solvers. International Journal for Numerical Methods in Engineering. 121(13):3004-3020. https://doi.org/10.1002/nme.6344S3004302012113Burman, E., & Hansbo, P. (2010). Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method. Computer Methods in Applied Mechanics and Engineering, 199(41-44), 2680-2686. doi:10.1016/j.cma.2010.05.011Ruiz-Gironés, E., & Sarrate, J. (2010). Generation of structured hexahedral meshes in volumes with holes. Finite Elements in Analysis and Design, 46(10), 792-804. doi:10.1016/j.finel.2010.04.005Geuzaine, C., & Remacle, J.-F. (2009). Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering, 79(11), 1309-1331. doi:10.1002/nme.2579Parvizian, J., Düster, A., & Rank, E. (2007). Finite cell method. Computational Mechanics, 41(1), 121-133. doi:10.1007/s00466-007-0173-yDüster, A., Parvizian, J., Yang, Z., & Rank, E. (2008). The finite cell method for three-dimensional problems of solid mechanics. Computer Methods in Applied Mechanics and Engineering, 197(45-48), 3768-3782. doi:10.1016/j.cma.2008.02.036Nadal, E., Ródenas, J. J., Albelda, J., Tur, M., Tarancón, J. E., & Fuenmayor, F. J. (2013). Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization. Abstract and Applied Analysis, 2013, 1-19. doi:10.1155/2013/953786Nadal, E., Ródenas, J. J., Sánchez-Orgaz, E. M., López-Real, S., & Martí-Pellicer, J. (2014). Sobre la utilización de códigos de elementos finitos basados en mallados cartesianos en optimización estructural. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 30(3), 155-165. doi:10.1016/j.rimni.2013.04.009Giovannelli, L., Ródenas, J. J., Navarro-Jiménez, J. M., & Tur, M. (2017). Direct medical image-based Finite Element modelling for patient-specific simulation of future implants. Finite Elements in Analysis and Design, 136, 37-57. doi:10.1016/j.finel.2017.07.010Schillinger, D., & Ruess, M. (2014). The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models. Archives of Computational Methods in Engineering, 22(3), 391-455. doi:10.1007/s11831-014-9115-yBurman, E., Claus, S., Hansbo, P., Larson, M. G., & Massing, A. (2014). CutFEM: Discretizing geometry and partial differential equations. International Journal for Numerical Methods in Engineering, 104(7), 472-501. doi:10.1002/nme.4823Tur, M., Albelda, J., Marco, O., & Ródenas, J. J. (2015). Stabilized method of imposing Dirichlet boundary conditions using a recovered stress field. Computer Methods in Applied Mechanics and Engineering, 296, 352-375. doi:10.1016/j.cma.2015.08.001Tur, M., Albelda, J., Nadal, E., & Ródenas, J. J. (2014). Imposing Dirichlet boundary conditions in hierarchical Cartesian meshes by means of stabilized Lagrange multipliers. International Journal for Numerical Methods in Engineering, 98(6), 399-417. doi:10.1002/nme.4629De Prenter, F., Verhoosel, C. V., van Zwieten, G. J., & van Brummelen, E. H. (2017). Condition number analysis and preconditioning of the finite cell method. Computer Methods in Applied Mechanics and Engineering, 316, 297-327. doi:10.1016/j.cma.2016.07.006Berger-Vergiat, L., Waisman, H., Hiriyur, B., Tuminaro, R., & Keyes, D. (2011). Inexact Schwarz-algebraic multigrid preconditioners for crack problems modeled by extended finite element methods. International Journal for Numerical Methods in Engineering, 90(3), 311-328. doi:10.1002/nme.3318Menk, A., & Bordas, S. P. A. (2010). A robust preconditioning technique for the extended finite element method. International Journal for Numerical Methods in Engineering, 85(13), 1609-1632. doi:10.1002/nme.3032Dauge, M., Düster, A., & Rank, E. (2015). Theoretical and Numerical Investigation of the Finite Cell Method. Journal of Scientific Computing, 65(3), 1039-1064. doi:10.1007/s10915-015-9997-3Elfverson, D., Larson, M. G., & Larsson, K. (2018). CutIGA with basis function removal. Advanced Modeling and Simulation in Engineering Sciences, 5(1). doi:10.1186/s40323-018-0099-2Verhoosel, C. V., van Zwieten, G. J., van Rietbergen, B., & de Borst, R. (2015). Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone. Computer Methods in Applied Mechanics and Engineering, 284, 138-164. doi:10.1016/j.cma.2014.07.009Burman, E. (2010). Ghost penalty. Comptes Rendus Mathematique, 348(21-22), 1217-1220. doi:10.1016/j.crma.2010.10.006BadiaS VerdugoF MartínAF. The aggregated unfitted finite element method for elliptic problems;2017.Jomo, J. N., de Prenter, F., Elhaddad, M., D’Angella, D., Verhoosel, C. V., Kollmannsberger, S., … Rank, E. (2019). Robust and parallel scalable iterative solutions for large-scale finite cell analyses. Finite Elements in Analysis and Design, 163, 14-30. doi:10.1016/j.finel.2019.01.009Béchet, É., Moës, N., & Wohlmuth, B. (2008). A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method. International Journal for Numerical Methods in Engineering, 78(8), 931-954. doi:10.1002/nme.2515Hautefeuille, M., Annavarapu, C., & Dolbow, J. E. (2011). Robust imposition of Dirichlet boundary conditions on embedded surfaces. International Journal for Numerical Methods in Engineering, 90(1), 40-64. doi:10.1002/nme.3306Hansbo, P., Lovadina, C., Perugia, I., & Sangalli, G. (2005). A Lagrange multiplier method for the finite element solution of elliptic interface problems using non-matching meshes. Numerische Mathematik, 100(1), 91-115. doi:10.1007/s00211-005-0587-4Burman, E., & Hansbo, P. (2012). Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Applied Numerical Mathematics, 62(4), 328-341. doi:10.1016/j.apnum.2011.01.008Gerstenberger, A., & Wall, W. A. (2008). An eXtended Finite Element Method/Lagrange multiplier based approach for fluid–structure interaction. Computer Methods in Applied Mechanics and Engineering, 197(19-20), 1699-1714. doi:10.1016/j.cma.2007.07.002AxelssonO. Iterative solution methods;1994.Stenberg, R. (1995). On some techniques for approximating boundary conditions in the finite element method. Journal of Computational and Applied Mathematics, 63(1-3), 139-148. doi:10.1016/0377-0427(95)00057-7Zienkiewicz, O. C., & Zhu, J. Z. (1987). A simple error estimator and adaptive procedure for practical engineerng analysis. International Journal for Numerical Methods in Engineering, 24(2), 337-357. doi:10.1002/nme.1620240206Zienkiewicz, O. C., & Zhu, J. Z. (1992). The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique. International Journal for Numerical Methods in Engineering, 33(7), 1331-1364. doi:10.1002/nme.1620330702Blacker, T., & Belytschko, T. (1994). Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. International Journal for Numerical Methods in Engineering, 37(3), 517-536. doi:10.1002/nme.1620370309Díez, P., José Ródenas, J., & Zienkiewicz, O. C. (2007). Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error. International Journal for Numerical Methods in Engineering, 69(10), 2075-2098. doi:10.1002/nme.1837Xiao, Q. Z., & Karihaloo, B. L. (s. f.). Statically Admissible Stress Recovery using the Moving Least Squares Technique. Progress in Computational Structures Technology, 111-138. doi:10.4203/csets.11.5Ródenas, J. J., Tur, M., Fuenmayor, F. J., & Vercher, A. (2007). Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique. International Journal for Numerical Methods in Engineering, 70(6), 705-727. doi:10.1002/nme.1903Zhang, Z. (2001). Advances in Computational Mathematics, 15(1/4), 363-374. doi:10.1023/a:1014221409940González-Estrada, O. A., Nadal, E., Ródenas, J. J., Kerfriden, P., Bordas, S. P. A., & Fuenmayor, F. J. (2013). Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery. Computational Mechanics, 53(5), 957-976. doi:10.1007/s00466-013-0942-8Nadal, E., Díez, P., Ródenas, J. J., Tur, M., & Fuenmayor, F. J. (2015). A recovery-explicit error estimator in energy norm for linear elasticity. Computer Methods in Applied Mechanics and Engineering, 287, 172-190. doi:10.1016/j.cma.2015.01.013ZienkiewiczOC TaylorRL. The finite element method fifth edition volume 1: the basis.MA:Butterworth‐Heinemann;2000.Brenner, S. C., & Scott, L. R. (1994). The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics. doi:10.1007/978-1-4757-4338-