Renier Mendoza

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• Dr.rer.nat.
• Associate Professor at University of the Philippines System

Optical character recognition (OCR) is a state-of-the-art technology that allows automated detection and recognition of text from scanned documents and other images. While OCR has highly developed in popular writing systems like Roman, Brahmic, and Han scripts, there is presently a lack of technological integration for Baybayin scripts − a precolon...

In May 2022, monkeypox started to spread in non-endemic countries. To investigate contact tracing and self-reporting of the primary case in the local community, a stochastic model is developed. An algorithm based on Gillespie's stochastic chemical kinetics is used to quantify the number of infections, contacts, and duration from the arrival of the...

Electrical impedance tomography (EIT) is an imaging technique that reconstructs the conductivity distribution in the interior of an object using electrical measurements from the electrodes that are attached around the boundary. The Complete Electrode Model (CEM) accurately incorporates the electrode size, shape, and effective contact impedance into...

The Lambert W function is defined by W(a)eW(a)−a=0. One of the many applications of the Lambert W function is in solving delay differential equations (DDEs). In 2003, Asl and Ulsoy provided a solution of some DDEs in terms of the Lambert W functions Asl et al. (2003)[1]. However, the solutions are limited to differential equations with delay in the...

Precise and accurate estimation of cosmological parameters is crucial for understanding the Universe's dynamics and addressing cosmological tensions. In this methods paper, we explore bio-inspired metaheuristic algorithms, including the Improved Multi-Operator Differential Evolution scheme and the Philippine Eagle Optimization Algorithm (PEOA), alo...

The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by the standard model of particle physics and a cold...

Due to the relatively low severity and fatality rates of the omicron variant of COVID-19, strict non-pharmaceutical interventions (NPIs) with high economic costs may not be necessary. We develop a mathematical model of the COVID-19 outbreak in Korea that considers NPIs, variants, medical capacity, and economic costs. Using optimal control theory, w...

Trend analysis plays an important role in infectious disease control. An analysis of the underlying trend in the number of cases or the mortality of a particular disease allows one to characterize its growth. Trend analysis may also be used to evaluate the effectiveness of an intervention to control the spread of an infectious disease. However, tre...

p>This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Metaheuristic algorithms for constrained optimiza- tion problems have become popular because of their ease of use and capability to obtain global solutions. However, these populatio...

p>This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Metaheuristic algorithms for constrained optimiza- tion problems have become popular because of their ease of use and capability to obtain global solutions. However, these populatio...

In response to the coronavirus disease 2019 (COVID-19) pandemic, the allocation of vaccines has become a crucial undertaking, particularly in the Philippines. The efficient distribution of vaccines across different regions remains vital. In this study, we present an approach to determine the optimal allocation of COVID-19 vaccines in the Philippine...

COVID-19 has affected millions of people worldwide, causing illness and death, and disrupting daily life while imposing a significant social and economic burden. Vaccination is an important control measure that significantly reduces mortality if properly and efficiently distributed. In this work, an age-structured model of COVID-19 transmission, in...

Background: More than half of the population in Korea had a prior COVID-19 infection. In 2022, most nonpharmaceutical interventions, except mask-wearing indoors, had been lifted. And in 2023, the indoor mask mandates were eased. Methods: We developed an age-structured compartmental model that distinguishes vaccination history, prior infection, a...

Due to the relatively low severity and fatality rates of the omicron variant of COVID-19, strict non-pharmaceutical interventions (NPIs) with high economic costs may not be necessary. We develop a mathematical model of the COVID-19 outbreak in Korea that considers NPIs, variants, medical capacity, and economic costs. Using optimal control theory, w...

As the COVID-19 situation changes because of emerging variants and updated vaccines, an elaborate mathematical model is essential in crafting proactive and effective control strategies. We propose a COVID-19 mathematical model considering variants, booster shots, waning, and antiviral drugs. We quantify the effects of social distancing in the Repub...

Background It was found that more than half of the population in Korea had a prior COVID-19 infection. In 2022, most nonpharmaceutical interventions, except mask-wearing indoors, had been lifted. Discussions about easing the indoor mask mandate are ongoing. Methods We developed an age-structured compartmental model that distinguishes vaccination hi...

We develop a mathematical model considering behavioral changes and underreporting to describe the first major COVID-19 wave in Metro Manila, Philippines. Key parameters are fitted to the cumulative cases in the capital from March to September 2020. A bi-objective optimization problem is formulated that allows for the easing of restrictions at an ea...

In this work, we present an approach to determine the optimal location of coronavirus disease 2019 (COVID-19) vaccination sites at the municipal level. We assume that each municipality is subdivided into smaller administrative units, which we refer to as barangays. The proposed method solves a minimization problem arising from a facility location p...

Without vaccines and medicine, non-pharmaceutical interventions (NPIs) such as social distancing, have been the main strategy in controlling the spread of COVID-19. Strict social distancing policies may lead to heavy economic losses, while relaxed social distancing policies can threaten public health systems. We formulate optimization problems that...

Data smoothing is a method that involves finding a sequence of values that exhibits the trend of a given set of data. This technique has useful applications in dealing with time series data with underlying fluctuations or seasonality and is commonly carried out by solving a minimization problem with a discrete solution that takes into account data...

Background: In May 2022, monkeypox started to spread in non-endemic countries. After the number of confirmed cases reached more than 16,000 in July, the World Health Organization declared the highest alert over the outbreak. Methods: To investigate the effects of contact tracing and self-reporting of primary cases in the local community, a stochas...

Without vaccines and medicine, non-pharmaceutical interventions (NPIs) such as social distancing, have been the main strategy in controlling the spread of COVID-19. Strict social distancing policies may lead to heavy economic losses, while relaxed social distancing policies can threaten public health systems. We formulate an optimization problem th...

Background: The most recent variant of concern, omicron (B.1.1.529), has caused numerous cases worldwide including the Republic of Korea due to its fast transmission and reduced vaccine effectiveness. Methods: A mathematical model considering age-structure, vaccine, antiviral drugs, and influx of the omicron variant was developed. We estimated t...

The Matlab package bvpsuite 2.0 is a numerical collocation code for the approximation of solutions of a broad range of boundary value problems in ordinary differential equations. In this article, its newly implemented pathfollowing module with automated step-length control is presented. Two versions using the pseudo-arclength continuation method, a...

Coronavirus disease 2019 (COVID-19) is an infectious disease caused by severe acute respiratory syndrome coronavirus 2. Millions of people have fallen sick, and some have died due to this affliction that has spread across the globe. The current pandemic has disrupted normal day-to-day human life, causing a profound social and economic burden. Vacci...

Background: The most recent variant of concern, Omicron (B.1.1.529), has caused numerous cases worldwide including the Republic of Korea due to its fast transmission and reduced vaccine effectiveness. Methods: A mathematical model considering age-structure, vaccine, antiviral treatment, and influx of the Omicron variant was developed. We estimated...

Introduction At the start of the pandemic, the Philippine capital Metro Manila was placed under a strict lockdown termed Enhanced Community Quarantine (ECQ). When ECQ was eased to General Community Quarantine (GCQ) after three months, healthcare systems were soon faced with a surge of COVID-19 cases, putting most facilities at high or critical risk...

Gradient-based algorithms rely on the derivative of functions to find suitable direction vectors. Their disadvantage is that they may get stuck at saddle points or local minimizers. This paper explores how a modified n-dimensional golden section search can be combined with Nesterov's accelerated gradient descent to escape saddle points or possibly...

Schistosomiasis is a neglected tropical disease endemic in the Philippines, affecting 28 provinces in 12 regions. This parasitic disease is caused by Schistosoma japonicum , a zoonotic parasite that infects other mammalian hosts aside from humans. In this study, a mathematical model is developed to describe the transmission of schistosomiasis in Ag...

We propose the Philippine Eagle Optimization Algorithm (PEOA), which is a meta-heuristic and population-based search algorithm inspired by the territorial hunting behavior of the Philippine Eagle. From an initial random population of eagles in a given search space, the best eagle is selected and undergoes a local food search using the interior poin...

We propose a COVID-19 mathematical model that considers Omicron and previous variants, booster shots, waning, breakthrough infections, and antiviral therapy. We quantify the effects of social distancing (SD) in the Republic of Korea by estimating the reduction in transmission µ induced by government policies from February 26, 2021 to January 16, 20...

Baybayin is a Tagalog-language writing system primarily used in the northern Philippines during the pre-Hispanic period. In 2018, the House of Representatives approved House Bill 1022 or the "National Writing System Act," which declares the Baybayin script as the Philippines' national writing system. Thus, documents, signages, books, etc. may soon...

We propose the Philippine Eagle Optimization Algorithm (PEOA), which is a meta-heuristic and population-based search algorithm inspired by the territorial hunting behavior of the Philippine Eagle. From an initial random population of eagles in a given search space, the best eagle is selected and undergoes a local food search using the interior poin...

We propose an approach in solving a parameter estimation problem in delay differential equations (DDE). By taking the interpolation of the data set, the problem is posed as a minimization problem using the L2–norm. We use a heuristic algorithm called Genetic Algorithm with multi-parent crossover to numerically solve the optimization problem. We con...

Tsunamis are destructive natural disasters that can cause severe damage to property and the loss of many lives. To mitigate the damage and casualties, tsunami warning systems are implemented in coastal areas, especially in locations with high seismic activity. This study presents a method to identify the placement of near-shore detection sensors by...

Neutral delay differential equations (NDDEs) are differential equations containing time lags not only in the states but also in the state derivatives. NDDEs have applications in modeling physical and biological systems. An NDDE model may consist of several parameters, some of which can be determined using available data. Various numerical technique...

In this paper, we investigate the wave attenuation by mangroves using modified 2D Nonlinear Shallow Water Equations. Numerically, we solve the model using a staggered finite volume method that is free from damping error. Further, several benchmark tests are performed to show the robustness of our numerical model. Then, we implement our numerical mo...

Despite being one of the first countries to implement mass drug administration (MDA) for elimination of lymphatic filariasis (LF) in 2001 after a pilot study in 2000, the Philippines is yet to eliminate the disease as a public health problem with 6 out of the 46 endemic provinces still implementing MDA for LF as of 2018. In this work, we propose a...

In this work, we present an approach to determine the optimal location of coronavirus disease (COVID-19) vaccination sites at the municipal level. We assume that each municipality or town is subdivided into smaller administrative units, which we refer to as villages or barangays. The proposed method solves a minimization problem arising from a faci...

Baybayin is a pre-Hispanic Philippine writing system used in Luzon island. With the effort in reintroducing the script, in 2018, the Committee on Basic Education and Culture of the Philippine Congress approved House Bill 1022 or the ”National Writing System Act,” which declares the Baybayin script as the Philippines’ national writing system. Since...

Electrical Impedance Tomography or EIT is an imaging technique that reconstructs the conductivity distribution in the interior of an object using electric currents. In this paper, we study the continuum model for EIT in a domain where the geometric inclusions are fixed and only the conductivity values inside these inclusions are unknown. We show an...

In 2018, the Philippine Congress signed House Bill 1022 declaring the Baybayin script as the Philippines’ national writing system. In this regard, it is highly probable that the Baybayin and Latin scripts would appear in a single document. In this work, we propose a system that discriminates the characters of both scripts. The proposed system consi...

Rapid detection and early warning systems demonstrate crucial significance in tsunami risk reduction measures. So far, several tsunami observation networks have been deployed in tsunamigenic regions to issue effective local response. However, guidance on where to station these sensors are limited. In this article, we address the problem of determin...

Based on electrical measurements from electrodes placed around the boundary of a body, Electrical Impedance Tomography (EIT) is an imaging procedure that recovers the spatial distribution of the conductivities in the interior of a body. Recent studies have shown promising results in reconstructing EIT images using heuristic algorithms. This work pr...

In electrical impedance tomography (EIT), image reconstruction of the conductivity distribution of a body can be calculated using measured voltages at the boundary. This is done by solving an inverse problem for an elliptic partial differential equation (PDE). In this work, we present some sensitivity results arising from the solution of the PDE. W...

Structured population models, which account for the state of individuals given features such as age, gender, and size, are widely used in the fields of ecology and biology. In this paper, we consider an age-structured population model describing the population of adults and juveniles. The model consists of a system of ordinary and neutral delay dif...

The Fitzhugh-Nagumo equations is a system of first-order nonlinear ordinary differential equations based on the researches of Fitzhugh and Nagumo et al. This reduced model captures the simplistic essence of neuronal spiking dependent on two variables, the membrane potential and the recovery variable. From a collection of data points, three paramet...

Tsunami early detection systems are of great importance as they provide time to prepare for a tsunami and mitigate its impact. In this paper, we propose a method to determine the optimal location of a given number of sensors to report a tsunami as early as possible. The rainfall optimization algorithm, a population-based algorithm, was used to solv...

The Whittaker-Henderson graduation is a data smoothing method commonly used in actuarial science for mortality table computation. This method is a finite-dimensional minimization problem, which aims to give a smooth approximation of the crude data. Our goal is to treat the Whittaker-Henderson method as a minimization problem in a Sobolev space. We...

In this paper, we propose a new technique in solving the minimum of a function defined on a ball centered at x⁰ with radius ρ¯ using successive implementations of Golden Search algorithm. We show numerically that our proposed method can effectively approximate the minimum of a function even if it is nonsmooth or discontinuous. We also introduce par...

A biochemical system is a biological system consisting of a collection of chemical compounds interacting with each other. One way to model and analyze a biochemical system is by using S-systems, which are coupled ordinary differential equations based on power-law formalism. In this paper, we do a parameter estimation on an S-system model called HS9...

We proposed a three-step image segmentation approach to determine the edges of images containing old texts. In general, texts from old books and articles tend to be very noisy. Thus, we first employed a suitable denoising method to obtain a smooth approximation 𝑰𝒔 of a given image 𝑰 ̃. Then, the fuzzy edge map 𝑬 ̃ was obtained using the gradient of...

In electrical impedance tomography, image reconstruction of the conductivity distribution σ in a body Ω is estimated using measured voltages at the boundary ∂ Ω . This is done by solving an inverse problem associated with a generalized Laplacian equation. We approach this problem by using a multi-phase segmentation method. We partition σ into 2 pha...

In Electrical Impedance Tomography (EIT), different current patterns are injected to the unknown object through the electrodes attached at the boundary ∂ Ω of Ω. The corresponding voltages V are then measured on its boundary surface. Based on these measured voltages, the image reconstruction of the conductivity distribution σ is done by solving an...