Shiela Coloma
Talk: Leveraging Extended Persistence to Enrich Features for Machine Learning in Predicting Neurological Outcomes of Coma Patients After Cardiac Arrest
Abstract: Examining electroencephalogram (EEG) recordings is significant for assessing the neurological recovery of coma patients post-cardiac arrest. However, manual interpretation of EEGs is time-consuming, susceptible to bias, and may lead to self-fulfilling prophecies which influences the decision making regarding early withdrawal of life-sustaining therapies. To address these challenges, Zheng et al. developed a multiscale Deep Neural Network (DNN) to enhance prognostication by leveraging data-driven EEG representations. Despite its advancements, this approach lacks interpretability and relies on basic demographic information which limits the understanding of predictions. Integrating extended persistence in machine learning offers a solution. While ordinary persistence evaluates the lifespan of connected components in abstract representations of simplicial models, extended persistence overcomes limitations by capturing persisting topological features across sublevel sets and looking at superlevel sets. By incorporating PersLay—a neural network layer tailored for handling extended persistence diagrams—into DNN architectures, complex EEG patterns can be efficiently captured and transformed into feature vectors, potentially improving predictive accuracy and interpretability.
Jaskine Baricaua
Talk: On the Solution of Inverse Kinematics Problem of 7R/P Manipulator
Abstract: The goal of this study is to solve the inverse kinematics problem for 7R/P chain. To do this, we used the methodology used in the paper of Husty. In particular, we will divide the kinematic equation of the 7R/P chain into the left 4R/P and right 3R/P chain. Utilizing the methodology introduced by Pfurner in solving the simplified chains of 6R serial manipulators and upon obtaining the transformations via DH-convention, we fix the first and last, first and second, third and last joints of the manipulators to derive the simplified chains. Using the algebra of dual quaternions, we derive its Study parameter which will be used later on in the computations of hyperplanes in the 7-dimensional projective space. Multiplication of dual quaternions is done in MATLAB symbolically which treats dual quaternions as 8-tuples.
William Ceasar A. Laureta
Talk: Notions of optimal cycle representatives in persistent homology: how do we describe the shape of topological holes in a dataset?
Persistent homology is a fast-growing subfield of Topological Data Analysis that is concerned with the detection, identification, and characterization of topological features from a dataset at various scales. This is done by recording the connected components, holes, voids, and other n-dimensional counterparts formed and eliminated at different scale parameters. Recent advancements in the field have explored the inverse route: from topological holes obtained via persistent homology, we want to find the best-suited hole representing a topological feature called the optimal cycle representative. However, this localization problem poses many difficulties. One of the major challenges in determining optimal cycle representatives is the non-uniqueness of the notion of optimality. In this talk, we take a quick review of computational topology and have an overview of the various linear programming problems describing the notions of optimality of cycle representatives, namely, minimizing 1 and 2-simplices, length, and area enclosed by the cycle, subject to some appropriate constraints. We also discuss its applications, limitations, and possible extensions.
Rocila P. Bendillo
Talk: Stability and Hopf Bifurcation of a Delayed Solow Model with Variable Carrying Capacity and Two Time-Delay
In this work, a nonlinear delayed model of mutual interaction between economic growth and active population is considered. This study focuses on the dynamics of the proposed generalized model with two time-delay and variable carrying capacity. The first time-delay is the delay in the production function, while the second time-delay is the delay in the recruitment process. The main goal of this study is to determine how both time delays affects the economic growth.
Our results include existence, uniqueness, positivity, and boundedness of the equilibrium solution of the said model. We also considered four cases to investigate the local stability of the equilibrium solution and derive its conditions. The first case is when both time delays are zero; second case is when the first time-delay is zero while the second time-delay is positive; the third case is when the first time-delay is positive while the second time-delay is zero; and for the fourth case, both time delays are positive.
Results show that for the local stability of the system in the first case, the ratio of reproduction rate to the labor's share should always be greater than the depreciation rate and the impact of the current capital stock on the system should be controlled to ensure stability. Moreover, in the second case, population growth relative to the labor's share should be moderate relation to the depreciation rate. It also acknowledges that both capital and labor contribute and are essential factors to the production process. Finally, we performed numerical simulations to illustrate the theoretical results.
Rostum Paolo B. Alanas
Talk: Local Stability Analysis of a Patch-forming Plankton Model with Toxin Delay
The periodic nature of algal blooms has been documented in different parts of the world. Many phytoplankton species developed different defense mechanisms in the presence of high grazing pressures. In this presentation, we present a modified model of Chattopadhyay et al (2008) of a predator-prey model between patch-forming toxin-producing phytoplankton (TPP) and zooplankton species. We considered a non-monotonic predation response to capture the TPP group defense and a time delay parameter to account for the toxin liberation delay. The well-posedness of the model and the existence and local stability of equilibrium solutions will be discussed. The occurrence of a Hopf bifurcation was investigated using the time delay as our main parameter. Finally, we perform some numerical simulations to verify our theoretical results.
Saraleen Mae Manongsong, Ph.D.
Talk: Inverse Kinematics of Six-Joint Special Manipulators
Abstract: This work provides a solution to the inverse kinematics problem of special six-joint manipulators using the algebra of dual quaternions and techniques in algebraic geometry such as the Grobner basis and multi-dimension analysis of varieties in the seven-dimensional projective space. Unlike general six-joint manipulators, special manipulators have the property that the workspace of the left or the right 3-chain lies entirely in the Study quadric. It is found that desirable finite inverse kinematics solutions depend on the nature of the computed hyperplane pencils or fixed linear spaces that contain the workspaces of the 3-chains. Algorithms are provided to outline the procedure when the workspaces are contained in a pencil and a linear space in the quadric. To illustrate, we provide an example of a special manipulator and solve its inverse kinematics solutions.
Gilbert Peralta
Talk: Mathematical Analysis of Non-isothermal, Incompressible, Viscous Binary Fluid Flows with Measure-Valued Sources
Abstract: We present a system of nonlinear partial differential equations governing the dynamics of non-isothermal, viscous, and incompressible binary fluid flows on two-dimensional domains. In this talk, we will establish the existence and uniqueness of weak or very weak solutions for measure-valued sources. The essential tools employed in the analysis are the maximal parabolic regularity and semigroup theory for the linearized system, and a spectral Galerkin method for the nonlinear part with the solutions of the linearized dynamics as frozen coefficients. Differentiability properties of the operator that maps the sources and initial data to the solutions, and higher temporal-integrability of solutions, will be discussed.
4 December 2023, 08:30 AM via Zoom [Online] and UP Baguio KA 402
Steven Karl Gantala
Talk: On the Diophantine Equation x2 + y3 = qzp
Abstract: A Diophantine equation is an equation that is usually solved in the set of integers. It contains special cases that have been studied by numerous researchers. One of the forms is Axp + Byq = Czr where A, B, C are non-zero integers.
In particular, this study explored the existence of primitive non-zero integer solutions (x, y, z) for the Diophantine Equation x2 + y3 = qzp, where p and q are odd primes. Primitive integer solutions (x, y, z) were found depending on the assumed parities of the integers x and y. Whereas, no solutions were found when x, y and z are odd primes. The proofs were based on elementary number theory methods and backed up by computations using MATLAB codes.
For further studies, it is recommended that parametric solutions be formulated for the given Diophantine equation.
13 November 2023, 08:30 AM via Zoom [Online] and UP Baguio KA 402
Paul Samuel Ignacio, Ph.D.
Talk: Tracks, Trends, and Traps in Topological Data Analysis
Abstract: In this talk, I will provide a concise introduction to Topological Data Analysis (TDA), highlighting its historical
tracks and current trends while cautioning against potential traps and obstructions both in the development of the theory and applications
of TDA. We delve into the evolution of TDA techniques, showcase real-world applications, and highlight the integration with machine
learning. We end the lecture with some open problems and case studies appropriate for an introductory exploration on the theory and applications of TDA.
23 October 2023, 01:00 PM via Zoom [Online] and UP Baguio KA 301
Ryan De Quiña
Talk: Reconfiguration Problem on Dominating Sets
Abstract: In graph theory, a reconfiguration problem deals with the relationship among solutions to a given problem for a
specific graph. In particular, the reconfiguration of one solution into another occurs via a sequence of step transformations,
defined according to a predetermined rule, such that each step is an immediate solution to a problem. Meanwhile, a dominating set
is a subset of vertex set in a graph such that each vertex not in the dominating set is dominated by a vertex in the dominating set.
In this talk, we review the reconfiguration problem on dominating sets. In particular, we give emphasis to the problem arising from
the graph called reconfiguration graph which is formed by the solutions of the dominating set of a graph according to a predetermined
rule. Motivated by this reconfiguration on dominating sets, we introduce the reconfiguration on fair dominating sets, another variation
of dominating set studied by Y. Caro, et.al. (2012). Moreover, we present some of our preliminary results on fair dominating set of paths,
cycles and full binary trees which will be helpful in the study of reconfiguration on fair dominating sets.
Kleo Jude Amarles
Talk: Redundant Parallel Manipulators
Abstract: Parallel manipulators are manipulators that utilize several serial chains to support a single platform.
In most studies, they have an equal number of actuators and degrees of freedom, but there are some practices that use more
actuators than required. These are known as redundant parallel manipulators. In this talk, we will show that kinematic redundancy
can be used for solving the direct kinematics problem and kinematic singularity. Some applications will also be discussed.
09 October 2023, 09:00 AM via Zoom [Online]
Noemi Ann De Guzman
Talk: Modeling the Dynamics of Ducks for the Control of Golden Apple Snail (Pomacea Canaliculata) in Rice Paddies
Abstract: Golden apple snail (Pomacea Canaliculata) infestations were a major problem for farmers.
Major areas of the Philippines were affected by the dilemma, particularly Northern Luzon and Western Visayas,
which were both regarded as the country’s rice growing regions. The use of biological control, such as an integrated
rice-duck farming system, has the ability to deal with these infestation concerns. In rice-duck farming, ducks are employed
to control weeds and golden apple snail. Rice is grown along with the ducks in an irrigated paddy. In this presentation,
we discuss the dynamics of a four-species predator-prey food web model, that is, golden apple snails and ducks preying on
rice plants and weeds. The mathematical model is a system of four ordinary differential equations.
02 October 2023, 02:00 PM via Zoom [Online] and UP Baguio KA 402
Loren Gavila
Talk: SARIMA Model in Forecasting Electricity Consumption and Regression Analysis of Electricity Rates
Abstract: In this talk, we present an effective seasonal autoregressive integrated moving average (SARIMA) model for
forecasting the electricity consumption of the whole service area of Benguet Electric Cooperative (BENECO). The SARIMA model
is built upon several time series analysis models, namely the autoregressive (AR), moving average (MA), and ARIMA models.
In generating the model, the Box and Jenkins methodology was implemented. We discuss the descriptive statistics of our historical data,
the stationarity analysis, its autocorrelation function and partial autocorrelation function plots, the model identification and
estimation process, and the error analysis of the competing models. After the generation of the best forecasting model, we also
perform a regression analysis with the electricity rates of different customer types. We describe the linear relationship between
the amount of consumption and the rates set by BENECO for its consumers. This study not only aids BENECO's operational management
in delivering better-quality services to its customers, but also allows consumers to understand the correlation between their
electricity usage and costs.
Andrei Domogo, Ph.D.
Talk: Modeling The Heart and Circulation
Abstract: Important physiological mechanisms in the circulatory system have been simulated and understood using
mathematical models. In this talk, we look at the plan of the circulation and then present models of blood flow and mechanisms
for their control. We discuss how an algebraic model is able to capture the steady-state behavior of the circulatory system and
provide insights on understanding its physiology. We end the talk with possible areas of study in Cardiovascular modeling.
25 September 2023, 09:00 AM via Zoom [Online] and UP Baguio KA 402
Gerald Navida
Talk: Fractional Order Model of HIV-TB Co-infection
Abstract: In this talk, we present a novel fractional order model for HIV-TB co-infection in the presence of
exogenous reinfection and recurrent TB. This model has been introduced by Tanvi, Aggarwal & Raj (2021) using Caputo fractional
order derivative. The main goal of incorporating fractional order to the model is to include the memory effect of both diseases.
First, we discuss the proof of the existence and uniqueness of solutions as well as positivity of solutions and the invariant region.
Moreover, we employ the next-generation matrix approach to determine the basic reproduction numbers. Lastly, we analyze the local
stability of the disease-free and endemic equilibrium points using established results regarding fractional order derivatives.
18 September 2023, 01:00 PM via Zoom [Online] and UP Baguio KA 402
Junius Wilhelm Bueno
Talk: Introduction to Navier-Stokes Equation
Abstract: Navier-Stokes Equation (NSE) combines the principles of conservation of mass, conservation of momentum,
and conservation of energy to describe fluid flow. One of the millennium prize problem asks if a solution to the 3-dimensional
NSE exists and if it is unique. In this presentation, we introduce the function spaces related to the study and derive the NSE
mathematically and its different forms. The notion of weak solutions to 2-dimensional NSE will also be discussed.
Juancho Collera, Ph.D.
Talk: Delay Differential Equations and the El Niño Southern Oscillation
Abstract: In this talk, we revisit the delayed action oscillator (DAO), introduced by Suarez and Schopf in 1988,
which models the sea-surface temperature (SST) anomalies on a region in the central equatorial Pacific. The DAO model is a
simple scalar delay differential equation (DDE) and yet is able to capture the periodic behavior of the El Niño Southern Oscillation
(ENSO). This talk serves both as an introduction and an invitation to DDEs targeted to senior undergraduate and beginning graduate
students. By the way, 2023 is an El Niño year.
20 March 2023, 01:00 PM via Zoom [Online]
Jhunas Paul Viernes
Talk: Deterministic and Stochastic SVITR Transmission Model of Covid-19
Abstract:
In this talk, we adopt the Susceptible-Vaccinated-Infected-Treated-Recovered (SVITR) model formulated
by Tesfaye and Santana to describe the transmission dynamics of COVID-19. For the qualitative analysis
of the model, we discuss the positivity of solutions, invariant region, equilibrium points, local
stability of equilibrium points, and sensitivity. The normalized sensitivity index formula was used to
determine each parameter's effect on the model's basic reproduction number. Furthermore, we extend
the SVITR deterministic model to a stochastic model by introducing Brownian motion. Lastly, we present
numerical simulations of the deterministic and stochastic models.
27 February 2023, 09:00 AM via Zoom [Online] and UP Baguio KA 402
Rostum Paolo Alanas
Talk: Effect of Time Delay on the Dynamics of a Patch-forming Toxin-producing Phytoplankton-Zooplankton Model
Abstract: The idea of a patch-forming plankton model was first introduced by Chattopadhyay et al. in 2008. We introduce a
time delay in their model, representing the toxin liberation delay of the toxin-producing phytoplankton to defend against grazing
zooplankton. We ensure the existence, uniqueness, positivity, and boundedness of solutions. We provide conditions for the existence
of equilibrium solutions and perform local stability analysis. We perform bifurcation analysis using the time delay for toxin liberation
as a Hopf bifurcation parameter. Lastly, numerical simulation via MatLab and the DDE BIFTOOL was conducted to verify the theoretical
findings and provide new information.
05 January 2023, 03:00 PM via Zoom [Online]
Renz Jimwel Mina
Talk: Non-π-Congruent Numbers
Abstract: The Congruent Number Theorem is a problem in Number Theory which aims to determine which
natural numbers occur as an area of a right triangle with rational sides. It can be solved by determining
the rank of an elliptic curve defined over the field of rationals. An extension to the problem is the
θ-Congruent Number Problem on triangles that have an angle θ not necessarily π/2.
This extension can also be addressed using the concepts of elliptic curve. In this presentation, we prove results of
M. Fujiwara on natural numbers that are non-π-congruent.
21 October 2022, 01:00 PM via Zoom [Online]
Noemi Ann De Guzman
Talk: Modeling the Dynamics of Ducks for the Control of Golden Apple Snail (Pomacea canaliculata) in Rice Paddies
Abstract: In rice-duck farming, ducks are employed to control weeds, and golden apple snail
(Pomacea canaliculata), an invasive species in rice farms. Rice is grown along with the ducks in an irrigated paddy.
In this talk, we model the dynamics of ducks, apple snails, and weeds. The model is a system of four first-order differential
equations with fourteen parameters.
19 September 2022, 10:00 AM via Zoom [Online]
Rocila Bendillo
Talk: On Delayed Model with Variable Carrying Capacity and Two Time-Delay
Abstract: In this talk, a nonlinear delayed model of mutual interaction between economic growth and active population
is considered. The main goal of this study is to introduce time-delays and determine how it affects economic growth.
The first delay is the delay in the production function, while the second delay is the delay in the recruitment process.
Jhunas Paul Viernes
Talk: Introduction to Numerical Methods for SDE and some Applications
Abstract: Stochastic Differential Equations (SDEs) are essential in modeling different phenomena.
In this talk, we discuss the different numerical methods for SDEs, namely, Euler-Maruyama, Milstein, and Runge-Kutta methods.
Then, implement these methods to observe the dynamics of some systems related to ecologies such as the Malthusian and logistic
growth, and predator-prey model. Likewise we present a Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) model of
COVID-19 taking into account random contacts of individuals. Lastly, we compare deterministic and stochastic models for the
above mentioned systems.
25 June 2022
Criselda Libatique
Talk: On Estimating Persistence and Extinction Using Single-Type Branching Process
Joseph Ludwin Marigmen
Talk: Introduction to SIJR Dengue Transmission Model in the Philippines
11 March 2022
Gilbert Peralta, Dr. rer. nat.
Talk: Optimal Borel Measure Controls for the Twodimensional Stationary Boussinesq System
06 December 2021
Yanka Lunor
Talk: Local Stability and Hopf Bifurcation Analysis in a Delayed Kaldor-Kalecki Model
08 November 2021
Christian Matthew Tandingan
Talk: Optimal Control of ODEs with State Suprema
18 October 2021
Geremae Tibule
Talk: Average Flow and Pumping Solutions of Valveless Flow Model in Rigid Pipes
20 September 2021
Maricar Balolong
Talk: Analysis of a Tuberculosis Epidemic Model with Nonlinear Incidence Rate and Two Time Delays
Jenelyn Dagongdong
Talk: On the Equilibrium Points, Boundedness. Stability and Numerical Sensivity of Nsuami-Witbooi HIV/AIDS Model
20 August 2021
Renz Jimwel Mina
Talk: Solving Diophantine Equations of the Form px+(p+a)y=z2
Jasper Constantino
Talk: Formula for the Frobenius Number in Three Variables
23 July 2021
Jan Martin Gonzales
Talk: Modelling an IVGTT Glucose-Insulin-Free Fatty Acids Dynamical System with Time Delays
Criselda Libatique
Talk: Some Preliminaries in Modeling Stochastic Differential Equations
25 June 2021
Jean Marc Dela Cruz
Talk: Numerical Continuation and Analysis in a Tumor/Immune Competitive System with Time Delay
Rostum Paolo Alanas
Talk: Dynamics of Prey-Predator Model with Strong Rocila P. BendilloAllee Effect in the Prey with Gestation Delay
17 May 2021
Rocila Bendillo
Talk: On Delayed HIV/AIDS Model with Vertical Transmission
Andhee Jacobe
Talk: An Investigation on a Stochastic Compartmental Model for HIV/AIDS Transimission
19 April 2021
Ryan De Quina
Talk: On the Packing Coloring Problem
Celestino Jerome Picar
Talk: Graph Labeling: The Local Super Antimagic
22 March 2021
Ranie Azote
Talk: Understanding Diophantine Equations
Flerida Regine Cruz
Talk: Local Stability and Hopf Bifurcation Analysis in a Delayed Kaldor-Kalecki Model
26 February 2021
Criselda Libatique
Talk: Deriving SDE Systems form ODE Systems
Richard Taclay
Talk: Exploring the Equation: 2px4+y4=z4Exploring the Equation: 2px4+y4=z4
18 January 2021
Saraleen Mae Manongsong, Ph.D.
Talk: Algebraic Geometry and Robot Kinematics
Shielden Grail Domilies
Talk: Determining Abatement Costs Using a Model on Carbon Cycle for Global Warming Mitigation Policies
20 November 2020
Ronnel John Garcia
Talk: Local Stability and Hopf Bifurcation of Coupled Neuron System with Leakage, Coupling, and Distributed Delays
Jay-Anne Bulauan
Talk: LUMAWIG beats Dionysus and Hera
Anna Clarice Yanday
Talk: On the Diophantine Equation pqx + (pq+1)y = z2
16 October 2020
Joyce Agbanlog
Talk: Ambrosio-Tortorelli Segmentation and Delaunay Triangulation of Images
John Rick Manzanares
Talk: A Topolgy Informed Random Forest Classifier for ECG Classification
Daniel Bezalel Garcia
Talk: Bayesian Hierarchical Models in Estimating the Relative Risk of HIV Prevalence in Baguio City
18 September 2020
Neil Montero
Talk: An SEIQVS Covid-19 Model with Partial Temporary Immunity
Jorem Jordan Cawagas
Talk: Symmetries of 2-fold Plain Weavings on Polyhedral Surfaces
Trisha Mae Marpuri
Talk: Delay-Coupled FitzHugh-Naguno Neuron Model City
