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Numerical Analysis and Scientific Computing

The Numerical Analysis and Scientific Computing (NASC) Academic Group of the Institute of Mathematics is a dynamic research entity at the forefront of tackling complex problems in science and technology. The group focuses on developing and analyzing methods for numerically approximating solutions to complex mathematical problems. Moreover, it specializes on computational models, algorithms, and software tools for solving scientific issues, encompassing areas like numerical differential equations, parallel and high-performance computing, and data analysis. The research group fosters interdisciplinary collaboration, knowledge exchange, and the creation of innovative methods.

Areas of Research: Numerical analysis. Scientific computing and algorithms. Numerical differential equations. Numerical linear algebra. Variational analysis. Shape optimization. PDE-constrained optimization. Energy minimization. Optimal control. Inverse problems. Interface (geometric) evolution. Free boundary problems. Data science. Artificial Intelligence. Image processing and analysis.

  • Publications
    • Cabanilla, K. I., Mohammad, R. Z., & Lope, J. E. Neural Networks with ReLU Powers Need Less Depth. Journal on Neural Networks (under review ). Preprint available at SSRN 4457166.
    • Escosio, R. A., & Mendoza, R. A Modified Accelerated Gradient Descent Using an N-Dimensional Golden Section Search for Escaping Saddle Points. Mathematical Biosciences and Engineering (under review ). Preprint available at SSRN 4069780.
    • Lim, Y., Ko, Y., Mendoza, R., Mendoza, V. M. P., Lee, J., & Jung, E. Optimal Non-Pharmaceutical Interventions Considering Limited Healthcare System Capacity and Economic Costs in the Republic of Korea. Mathematical Modelling of Natural
      Phenomena (under review ). Preprint available at medRxiv, 2023-05.
    • Escosio, R., Cawiding, O., Hernandez, B., Mendoza, R., Mendoza, V., Mohammad, R., … & de los Reyes V, A. A Model-Based Strategy on COVID-19 Vaccine Roll-out in the Philippines. Journal of Theoretical Biology (under review). Preprint available at medRxiv, 2022-05.
    • Castillo, R.C.J., Mendoza, V.M., Lope, J.E, & Mendoza, R. Modeling infectious disease trend using Sobolev polynomials. Communication in Biomathematical Sciences (under review ).
    • Pino, R., Mendoza, V. M., Velasco, A.C., Enriquez E.A, & Mendoza, R. Optimal allocation of COVID-19 vaccines to the regions in the Philippines. Healthcare Analytics (under review ).
    • Ko, Y., Mendoza, V. M., Mendoza, R., Seo, Y., Lee, J., & Jung, E. (2023). Estimation of monkeypox spread in a nonendemic country considering contact tracing and self-reporting: A stochastic modeling study. Journal of Medical Virology, 95(1), e28232.
    • Ko, Y., Mendoza, V. M., Mendoza, R., Seo, Y., Lee, J., & Jung, E. (2023). Risk estimation of lifted mask mandates and emerging variants using mathematical model. Heliyon.
    • Lee, J., Mendoza, R., Mendoza, V. M. P., Lee, J., Seo, Y., & Jung, E. (2023). Modelling the effects of social distancing, antiviral therapy, and booster shots on mitigating Omicron spread. Scientific Reports, 13(1), 6914.
    • Auzinger, W., Burdeos, K. N., Fallahpour, M., Koch, O., Mendoza, R. G., & Weinmüller, E. B. (2022). A numerical continuation method for parameter-dependent boundary value problems using bvpsuite 2.0. Journal of Numerical Analysis Industrial & Applied Mathematics, 16.
    • Cabanilla, K. I., Enriquez, E. A. T., Velasco, A. C., Mendoza, V. M. P., & Mendoza, R. (2022). Optimal selection of COVID-19 vaccination sites in the Philippines at the municipal level. PeerJ, 10, e14151.
    • Castillo, R. C. J., & Mendoza, R. (2022). On smoothing of data using Sobolev polynomials. AIMS Mathematics, 7(10), 19202-19220.
    • Enriquez, E. A. T., Mendoza, R. G., & Velasco, A. C. T. (2022). Philippine eagle optimization algorithm. IEEE Access, 10, 29089-29120.
    • Ko, Y., Mendoza, V. M., Mendoza, R., Seo, Y., Lee, J., Lee, J., … & Jung, E. (2022). Multi-faceted analysis of COVID-19 epidemic in Korea considering omicron variant: mathematical modeling-based study. Journal of Korean medical science, 37(26).
    • Mendoza, V. M. P., Mendoza, R., Ko, Y., Lee, J., & Jung, E. (2022). Managing bed capacity and timing of interventions: a COVID-19 model considering behavior and underreporting. AIMS Mathematics, 8(1), 2201-2225.
    • Mendoza, V. M. P., Mendoza, R., Lee, J., & Jung, E. (2022). Adjusting non-pharmaceutical interventions based on hospital bed capacity using a multi-operator differential evolution. AIMS Mathematics, 7(11), 19922-19953.
    • Mohammad, R. Z., Murakawa, H., Svadlenka, K., & Togashi, H. (2022). A numerical algorithm for modeling cellular rearrangements in tissue morphogenesis. Communications Biology, 5(1), 239.
    • Pino, R. B., Mendoza, R. G., & Sambayan, R. R. (2022). Block-level Optical Character Recognition System for Automatic Transliterations of Baybayin Texts Using Support Vector Machine. Philippine Journal of Science, 151(1).
    • Caro, L. A. P., Mendoza, R., & Mendoza, V. M. P. (2021, November). Application of genetic algorithm with multi-parent crossover on an inverse problem in delay differential equations. In AIP Conference Proceedings (Vol. 2423, No. 1). AIP Publishing.
    • Darbas, M., Heleine, J., Mendoza, R., & Velasco, A. C. (2021). Sensitivity analysis of the complete electrode model for electrical impedance tomography. AIMS Mathematics, 6(7), 7333-7366.
    • Jamilla, C. U., Mendoza, R. G., & Mendoza, V. M. P. (2021). Parameter estimation in neutral delay differential equations using genetic algorithm with multi-parent crossover. IEEE Access, 9, 131348-131364.
    • Magdalena, I., La’lang, R., & Mendoza, R. (2021). Quantification of wave attenuation in mangroves in manila bay using nonlinear shallow water equations. Results in Applied Mathematics, 12, 100191.
    • Magdalena, I., La’lang, R., Mendoza, R., & Lope, J. E. (2021). Optimal placement of tsunami sensors with depth constraint. PeerJ Computer Science, 7, e685.
    • Pino, R., Mendoza, R., & Sambayan, R. (2021). A Baybayin word recognition system. PeerJ Computer Science, 7, e596.
    • Pino, R., Mendoza, R., & Sambayan, R. (2021). Optical character recognition system for Baybayin scripts using support vector machine. PeerJ Computer Science, 7, e360.
    • Salonga, P. K. N., Mendoza, V. M. P., Mendoza, R. G., & Belizario Jr, V. Y. (2021). A mathematical model of the dynamics of lymphatic filariasis in Caraga Region, the Philippines. Royal Society Open Science, 8(6), 201965.
    • Velasco, A. C., Darbas, M., & Mendoza, R. (2021). Numerical resolution of the electrical impedance tomography inverse problem with fixed inclusions. Computer Science, 16(3), 1063-1076.
    • Ferrolino, A. R., Lope, J. E. C., & Mendoza, R. G. (2020). Optimal location of sensors for early detection of tsunami waves. In Computational Science–ICCS 2020: 20th International Conference, Amsterdam, The Netherlands, June 3–5, 2020, Proceedings, Part II 20 (pp. 562-575). Springer International Publishing.
    • Ferrolino, A., Mendoza, R., Magdalena, I., & Lope, J. E. (2020). Application of particle swarm optimization in optimal placement of tsunami sensors. PeerJ Computer Science, 6, e333.
    • Jamilla, C. U., Mendoza, R. G., & Mendoza, V. M. P. (2020). Explicit solution of a Lotka-Sharpe-McKendrick system involving neutral delay differential equations using the r-Lambert W function. Mathematical Biosciences and Engineering, 17(5), 5686-5708.
    • Jamilla, C., Mendoza, R., & Mező, I. (2020). Solutions of neutral delay differential equations using a generalized Lambert W function. Applied Mathematics and Computation, 382, 125334.
    • Manejero, J. L., & Mendoza, R. (2020). Variational Approach to Data Graduation. Philippine Journal of Science, 149(2).
    • Mendoza, R., & Keeling, S. (2020). Existence of solution for a segmentation approach to the impedance tomography problem.
    • Velasco, A. C., Darbas, M., Mendoza, R., Bacon, M., & de Leon, J. C. (2020). Comparative study of heuristic algorithms for electrical impedance tomography. Philippine Journal of Science, 149(3), 747-772.
    • Recio, K. R. O., & Mendoza, R. G. (2019, March). A Three-Step Approach to Edge Detection of Texts. In 20 th European Conference on Mathematics for Industry (p. 414).
    • Riñon, J. B., Mendoza, R., & Mendoza, V. M. P. (2019, March). Parameter estimation of an S-system model using hybrid genetic algorithm with the aid of sensitivity analysis. In Proceedings of Philippines Computing Science Congress, Manila, Philippines (pp. 94-102).
    • Rivero, R., & David, G. (2019, June). Modeling structural breakpoints in volatility of Philippine Peso-US Dollar currency exchange rate. In Empowering Science and Mathematics for Global Competitiveness: Proceedings of the Science and Mathematics International Conference (SMIC 2018), November 2-4, 2018, Jakarta, Indonesia (p. 413). CRC Press.
    • Rivero, R., Onuma, Y., & Kato, T. (2019). Threshold Auto-Tuning Metric Learning. IEICE TRANSACTIONS on Information and Systems, 102(6), 1163-1170.
    • Salonga, P. K., Inaudito, J. M., & Mendoza, R. (2019, December). An unconstrained minimization technique using successive implementations of golden search algorithm. In AIP Conference Proceedings (Vol. 2192, No. 1). AIP Publishing.
    • Weinmüller, E., Burdeos, K., Fallahpour, M., & Mendoza, R. (2019). Path-following for parameter-dependent boundary value problems in singular ordinary differential equations.
    • Rivero, R., & Kato, T. (2018). Parametric models for mutual kernel matrix completion. IEICE TRANSACTIONS on Information and Systems, 101(12), 2976-2983.
    • Bargo, M. C. R. The Use of Projection Operators with the Parareal Algorithm to Solve the Heat and the KdVB Equation. Matimyás Matematika 40 (1-2), 41-55.