Physical Sciences and Mathematics Commons^™

On Twin Edge Colorings In M-Ary Trees, Jayson D. Tolentino, Reginaldo M. Marcelo, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Let k ≥ 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from ℤ_k and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in ℤ_k) of the colors of the edges incident with v. The smallest integer k for which G has a twin k-edge coloring is the twin chromatic index of G and is denoted by χ′_t(G …

Sigma Chromatic Numbers Of The Middle Graph Of Some Families Of Graphs, Jay-R Manamtam, Agnes Garciano, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Let G be a nontrivial connected graph and let c : V (G) → be a vertex coloring of G, where adjacent vertices may have the same color. For a vertex υ of G, the color sum σ(υ) of υ is the sum of the colors of the vertices adjacent to υ. The coloring c is said to be a sigma coloring of G if σ(u) ≠ σ(υ) whenever u and υ are adjacent vertices in G. The minimum number of colors that can be …

Development Of An App And Videos To Support The Fraction Learning Trajectory From Grades 1-7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Juan Carlo F. Mallari, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Lack of procedural fluency in fractions impedes access to advanced mathematical courses and limits opportunities for entry into STEM-related fields. This paper describes the design and pedagogical basis of the Moving Fractions app and supplementary fraction videos for promoting fraction learning. Moving Fractions utilizes game-design factors to draw students through a trajectory of fraction learning from part-whole comparisons to a more robust understanding of the measurement concept of fractions. The supplementary video immerses students in a broad range of fraction representations. The app and video are intended to form a fraction learning package for distribution in Philippine schools. Future work …

Entropy Analysis Of Boolean Network Reduction According To The Determinative Power Of Nodes, Matthew J. Pelz, Mihaela T. Velcsov

Mathematics Faculty Publications

Boolean networks are utilized to model systems in a variety of disciplines. The complexity of the systems under exploration often necessitates the construction of model networks with large numbers of nodes and unwieldy state spaces. A recently developed, entropy-based method for measuring the determinative power of each node offers a new method for identifying the most relevant nodes to include in subnetworks that may facilitate analysis of the parent network. We develop a determinative-power-based reduction algorithm and deploy it on 36 network types constructed through various combinations of settings with regards to the connectivity, topology, and functionality of networks. We …

Growth-Profile Configuration For Specific Deformations Of Tubular Organs: A Study Of Growth-Induced Thinning And Dilation Of The Human Cervix, Kun Gou, Seungik Baek, Marvin M.F. Lutnesky, Hai-Chao Han

Mathematics Faculty Publications

Growth is a significant factor that results in deformations of tubular organs, and particular deformations associated with growth enable tubular organs to perform certain physiological functions. Configuring growth profiles that achieve particular deformation patterns is critical for analyzing potential pathological conditions and for developing corresponding clinical treatments for tubular organ dysfunctions. However, deformation-targeted growth is rarely studied. In this article, the human cervix during pregnancy is studied as an example to show how cervical thinning and dilation are generated by growth. An advanced hyperelasticity theory called morphoelasticity is employed to model the deformations, and a growth tensor is used to …

Understanding Covid-19 Dynamics And The Effects Of Interventions In The Philippines: A Mathematical Modelling Study, Jamie M. Caldwell, Elvira P. De Lara-Tuprio, Timothy Robin Y. Teng, Ma. Regina Justina E. Estuar, Raymond Francis R. Sarmiento, Milinda Abayawardana B. Eng, Robert Neil F. Leong, Richard T. Gray, James G. Wood, Linh-Vi Le, Emma S. Mcbryde, Romain Ragonnet, James M. Trauer

Mathematics Faculty Publications

Background

COVID-19 initially caused less severe outbreaks in many low- and middle-income countries (LMIC) compared with many high-income countries; possibly because of differing demographics; socioeconomics; surveillance; and policy responses. Here; we investigate the role of multiple factors on COVID-19 dynamics in the Philippines; a LMIC that has had a relatively severe COVID-19 outbreak.

Methods

We applied an age-structured compartmental model that incorporated time-varying mobility; testing; and personal protective behaviors (through a “Minimum Health Standards” policy; MHS) to represent the first wave of the Philippines COVID-19 epidemic nationally and for three highly affected regions (Calabarzon; Central Visayas; and the National Capital …

Awegnn: Auto-Parametrized Weighted Element-Specific Graph Neural Networks For Molecules., Timothy Szocinski, Duc Duy Nguyen, Guo-Wei Wei

Mathematics Faculty Publications

While automated feature extraction has had tremendous success in many deep learning algorithms for image analysis and natural language processing, it does not work well for data involving complex internal structures, such as molecules. Data representations via advanced mathematics, including algebraic topology, differential geometry, and graph theory, have demonstrated superiority in a variety of biomolecular applications, however, their performance is often dependent on manual parametrization. This work introduces the auto-parametrized weighted element-specific graph neural network, dubbed AweGNN, to overcome the obstacle of this tedious parametrization process while also being a suitable technique for automated feature extraction on these internally complex …

Dpp: Deep Predictor For Price Movement From Candlestick Charts, Chih-Chieh Hung, Ying-Ju (Tessa) Chen

Mathematics Faculty Publications

Forecasting the stock market prices is complicated and challenging since the price movement is affected by many factors such as releasing market news about earnings and profits, international and domestic economic situation, political events, monetary policy, major abrupt affairs, etc. In this work, a novel framework: deep predictor for price movement (DPP) using candlestick charts in the stock historical data is proposed. This framework comprises three steps: 1. decomposing a given candlestick chart into sub-charts; 2. using CNN-autoencoder to acquire the best representation of sub-charts; 3. applying RNN to predict the price movements from a collection of sub-chart representations. An …

Algebraic Graph-Assisted Bidirectional Transformers For Molecular Property Prediction, Dong Chen, Kaifu Gao, Duc Duy Nguyen, Xin Chen, Yi Jiang, Guo-Wei Wei, Feng Pan

Mathematics Faculty Publications

The ability of molecular property prediction is of great significance to drug discovery, human health, and environmental protection. Despite considerable efforts, quantitative prediction of various molecular properties remains a challenge. Although some machine learning models, such as bidirectional encoder from transformer, can incorporate massive unlabeled molecular data into molecular representations via a self-supervised learning strategy, it neglects three-dimensional (3D) stereochemical information. Algebraic graph, specifically, element-specific multiscale weighted colored algebraic graph, embeds complementary 3D molecular information into graph invariants. We propose an algebraic graph-assisted bidirectional transformer (AGBT) framework by fusing representations generated by algebraic graph and bidirectional transformer, as well as …

A Single-Scale Fractal Feature For Classification Of Color Images: A Virus Case Study, Walker Arce, James E. Pierce, Mihaela T. Velcsov

Mathematics Faculty Publications

Current methods of fractal analysis rely on capturing approximations of an images’ fractal dimension by distributing iteratively smaller boxes over the image, counting the set of box and fractal, and using linear regression estimators to estimate the slope of the set count line. To minimize the estimation error in those methods, our aim in this study was to derive a generalized fractal feature that operates without iterative box sizes or any linear regression estimators. To do this, we adapted the Minkowski-Bouligand box counting dimension to a generalized form by fixing the box size to the smallest fundamental unit (the individual …

Mathematical Modeling Of The Candida Albicans Yeast To Hyphal Transition Reveals Novel Control Strategies, David J. Wooten, Jorge Gómez Tejeda Zañudo, David Murrugarra, Austin M. Perry, Anna Dongari-Bagtzoglou, Reinhard Laubenbacher, Clarissa J. Nobile, Réka Albert

Mathematics Faculty Publications

Candida albicans, an opportunistic fungal pathogen, is a significant cause of human infections, particularly in immunocompromised individuals. Phenotypic plasticity between two morphological phenotypes, yeast and hyphae, is a key mechanism by which C. albicans can thrive in many microenvironments and cause disease in the host. Understanding the decision points and key driver genes controlling this important transition and how these genes respond to different environmental signals is critical to understanding how C. albicans causes infections in the host. Here we build and analyze a Boolean dynamical model of the C. albicans yeast to hyphal transition, integrating …

On The Sigma Value And Sigma Range Of The Join Of A Finite Number Of Even Cycles Of The Same Order, Marie Cris A. Bulay-Og, Agnes Garciano, Reginaldo M. Marcelo

Mathematics Faculty Publications

Let c be a vertex coloring of a simple; connected graph G that uses positive integers for colors. For a vertex v of G; the color sum of v is the sum of the colors of the neighbors of v. If no two adjacent vertices of G have the same color sum; then c is called a sigma coloring of G. The sigma chromatic number of G is the minimum number of colors required in a sigma coloring of G. Let max(c) be the largest color assigned to a vertex of G by a coloring c. The sigma value of …

The Set Chromatic Numbers Of The Middle Graph Of Graphs, Gerone Russel J. Eugenio, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino

Mathematics Faculty Publications

For a simple connected graph G; let c : V (G) → N be a vertex coloring of G; where adjacent vertices may be colored the same. The neighborhood color set of a vertex v; denoted by NC(v); is the set of colors of the neighbors of v. The coloring c is called a set coloring provided that NC(u) neq NC(v) for every pair of adjacent vertices u and v of G. The minimum number of colors needed for a set coloring of G is referred to as the set chromatic number of G and is denoted by χ_s(G). In …

On The Sigma Chromatic Number Of The Zero-Divisor Graphs Of The Ring Of Integers Modulo N, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino

Mathematics Faculty Publications

The zero-divisor graph of a commutative ring R with unity is the graph Γ(R) whose vertex set is the set of nonzero zero divisors of R; where two vertices are adjacent if and only if their product in R is zero. A vertex coloring c : V (G) → Bbb N of a non-trivial connected graph G is called a sigma coloring if σ(u) = σ(ν) for any pair of adjacent vertices u and v. Here; σ(χ) denotes the sum of the colors assigned to vertices adjacent to x. The sigma chromatic number of G; denoted by σ(G); is defined …

Tennis Anyone? Teaching Experimental Design By Designing And Executing A Tennis Ball Experiment, Laura Pyott

Mathematics Faculty Publications

Understanding the abstract principles of statistical experimental design can challenge undergraduate students, especially when learned in a lecture setting. This article presents a concrete and easily replicated example of experimental design principles in action through a hands-on learning activity for students enrolled in an experimental design course. The activity, conducted during five 50-min classes, requires the students to work as a team to design and execute a simple and safe factorial experiment and collect and analyze the data. During three in-class design meetings, the students design and plan all aspects of the experiment, including choosing the response variable and factors, …

Analytical And Numerical Convexity Results For Discrete Fractional Sequential Differences With Negative Lower Bound, Christopher S. Goodrich, Benjamin Lyons, Andrea Scapellato, Mihaela T. Velcsov

Mathematics Faculty Publications

We investigate relationships between the sign of the discrete fractional sequential difference (Δ^v _1+a-μ Δ^μ_af)(t) and the convexity of the function t→f(t). In particular, we consider the case in which the bound (Δ^v _1+a-μ Δ^μ_af)(t) ≥εf(a), for some ε > 0 and where f(a) < 0 is satisfied. Thus, we allow for the case in which the sequential difference may be negative, and we show that even though the fractional difference can be negative, the convexity of the function f can be implied by the above inequality nonetheless. This demonstrates a significant dissimilarity between the fractional and non-fractional cases. We use a combination of both hard analysis and numerical simulation.

Sars-Cov-2 And Rohingya Refugee Camp, Bangladesh: Uncertainty And How The Government Took Over The Situation, Md. Md. Kamrujjaman, Md. Shahriar Mahmud, Shakil Ahmed, Md. Omar Qayum, Mohammad Morshad Alam, Md. Nazmul Hassan, Md. Rafiul Islam, Kaniz Fatema Nipa, Ummugul Bulut

Mathematics Faculty Publications

Background: Bangladesh hosts more than 800,000 Rohingya refugees from Myanmar. The low health immunity, lifestyle, access to good healthcare services, and social-security cause this population to be at risk of far more direct effects of COVID-19 than the host population. Therefore, evidence-based forecasting of the COVID-19 burden is vital in this regard. In this study, we aimed to forecast the COVID-19 obligation among the Rohingya refugees of Bangladesh to keep up with the disease outbreak’s pace, health needs, and disaster preparedness. Methodology and Findings: To estimate the possible consequences of COVID-19 in the Rohingya camps of Bangladesh, we used a …

Visualizing Bivariate Data: What’S Your Point Of View?, Mamunur Rashid, Jyotirmoy Sarkar

Mathematics Faculty Publications

A scatter plot shows the relationship between two continuous variables x and y. If the relationship is linear or if the two variables have a bivariate normal distribution, then the least squares regression lines of y on x and x on y can predict one variable as a linear function of the other. These two regression lines suffice to identify the mean vector, the coefficient of determination, Pearson’s product moment correlation coefficient, and the ratio of the standard deviations (SD). So does a coverage ellipse! Additionally, we answer: In which direction must the points be projected to maximize (or minimize) …

Upward-Closed Hereditary Families In The Dominance Order, Michael D. Barrus, Jean A. Guillaume

Mathematics Faculty Publications

The majorization relation orders the degree sequences of simple graphs into posets called dominance orders. As shown by Ruch and Gutman (1979) and Merris (2002), the degree sequences of threshold and split graphs form upward-closed sets within the dominance orders they belong to, i.e., any degree sequence majorizing a split or threshold sequence must itself be split or threshold, respectively. Motivated by the fact that threshold graphs and split graphs have characterizations in terms of forbidden induced subgraphs, we define a class F of graphs to be dominance monotone if whenever no realization of e contains an element F as …

Optimal Tile-Based Dna Self-Assembly Designs For Lattice Graphs And Platonic Solids, Leyda Almodovar, Joanna Ellis-Monaghan, Amanda Harsy, Cory Johnson, Jessica Sorrells

Mathematics Faculty Publications

A design goal in self-assembly of DNA nanostructures is to find minimal sets of branched junction molecules that will self-assemble into targeted structures. This process can be modeled using techniques from graph theory. This paper is a collection of proofs for a set of DNA complexes which can be represented by specific graphs, namely Platonic solids, square lattice graphs, and triangular lattice graphs. This work supplements the results presented in https://arxiv.org/abs/2108.00035

Depicting Bivariate Relationship With A Gaussian Ellipse, Mamunur Rashid, Jyotirmoy Sarkar

Mathematics Faculty Publications

For data on two continuous variables, how should one depict the summary statistics (means, SDs, correlation coefficient, coefficient of determination, regression lines) so that their values can be read off easily from the depiction and potential outliers can be flagged also? We propose the Gaussian covariance ellipse as an answer that will benefit all users of statistics.

Analytical And Numerical Monotonicity Results For Discrete Fractional Sequential Differences With Negative Lower Bound, Christopher S. Goodrich, Benjamin Lyons, Mihaela T. Velcsov

Mathematics Faculty Publications

We investigate the relationship between the sign of the discrete fractional sequential difference(Δ^v_1+a-μ Δ_a^μf)(t) and the monotonicity of the function t→f(t). More precisely, we consider the special case in which this fractional difference can be negative and satisfies the lower bound (Δ^v_1+a-μ Δ_a^μf)(t) ≥ -εf(a), for some ε >0. We prove that even though the fractional difference can be negative, the monotonicity of the function f, nonetheless, is still implied by the above inequality. This demonstrates a significant dissimilarity between the fractional and non-fractional cases. Because of the challenges …

Global Dynamics Of Generalized Second-Order Beverton–Holt Equations Of Linear And Quadratic Type, Elliott J. Bertrand, Mustafa R. S. Kulenović

Mathematics Faculty Publications

We investigate second-order generalized Beverton–Holt difference equations ... In particular, we will investigate the local and global dynamics in the event f is a certain type of linear or quadratic polynomial, and we explore the existence problem of period-two solutions.

Development Of A Gamified Number Line App For Teaching Estimation And Number Sense In Grades 1 To 7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Fraction knowledge is known to be a gatekeeper to more advanced mathematical learning. On the basis of the literature on early number learning, a number line mobile application called Catch the Carrot was designed to develop students’ knowledge of whole number and fraction magnitude. This paper aims to describe the design of the Catch the Carrot app and discusses the rationale for using number lines as representational scaffolds for developing children’s understanding of numbers, particularly their estimation and number sense skills. The gamification features of the app, as well as strategies for integration in a classroom are also presented. This …

Tilings With Congruent Edge Coronae, Ma. Louise Antonette N. De Las Peñas, Mark D. Tomenes

Mathematics Faculty Publications

In this paper, we discuss properties of a normal tiling of the Euclidean plane with congruent edge coronae. We prove that the congruence of the first edge coronae is enough to say that the tiling is isotoxal.

Impact Of Vaccine Supplies And Delays On Optimal Control Of The Covid-19 Pandemic: Mapping Interventions For The Philippines, Carlo Delfin S. Estadilla, Joshua Uyheng, Elvira P. De Lara-Tuprio, Timothy Robin Y. Teng, Jay Michael R. Macalalag, Ma. Regina Justina E. Estuar

Mathematics Faculty Publications

Background

Around the world, controlling the COVID-19 pandemic requires national coordination of multiple intervention strategies. As vaccinations are globally introduced into the repertoire of available interventions, it is important to consider how changes in the local supply of vaccines, including delays in administration, may be addressed through existing policy levers. This study aims to identify the optimal level of interventions for COVID-19 from 2021 to 2022 in the Philippines, which as a developing country is particularly vulnerable to shifting assumptions around vaccine availability. Furthermore, we explore optimal strategies in scenarios featuring delays in vaccine administration, expansions of vaccine supply, and …

Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Maria Alva Q. Aberin, Mark Anthony C. Tolentino, Mark L. Loyola

Mathematics Faculty Publications

The problem of rote-based learning in mathematics is well documented. Mobile technology can provide a potential solution, especially when application (app) design is based on sound pedagogical principles and gamification elements. However, an inventory of available mobile apps for mathematics reveals that many of the available apps are guided by a behaviorist perspective that favors repetition over meaningful learning. This paper reports on the design of mobile mathematics apps that harness gamification techniques to promote higher-order thinking skills (HOTS) even in basic elementary school concepts such as number comparison, and addition and subtraction. The integration of these apps in the …

Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Maria Alva Q. Aberin, Mark Anthony C. Tolentino, Mark L. Loyola

Mathematics Faculty Publications

The problem of rote-based learning in mathematics is well documented. Mobile technology can provide a potential solution; especially when application (app) design is based on sound pedagogical principles and gamification elements. However; an inventory of available mobile apps for mathematics reveals that many of the available apps are guided by a behaviorist perspective that favors repetition over meaningful learning. This paper reports on the design of mobile mathematics apps that harness gamification techniques to promote higher-order thinking skills (HOTS) even in basic elementary school concepts such as number comparison; and addition and subtraction. The integration of these apps in the …

Designing Performance Tasks In Mathematics Using Technological Tools, Ma. Louise Antonette N. De Las Peñas, Debbie Marie Versoza, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino

Mathematics Faculty Publications

In the Philippines, the performance task is one of the major summative assessments in the K to 12 curriculum. This paper discusses how performance tasks may utilize mathematical apps within the context of blended learning. Guidelines on designing performance tasks; as well as the GRASPS framework; are discussed. Performance tasks that cut across various grade levels and strands of mathematics are presented. These involve divisibility (Numbers); integer and polynomial operations (Algebra); triangle centers (Geometry); and statistics (Statistics). The performance tasks described in this paper can provide an initial idea for the design of other summative assessments and contribute to the …

On Generating Functions In Additive Number Theory, Ii: Lower-Order Terms And Applications To Pdes, J. Brandes, Scott T. Parsell, C. Poulias, G. Shakan, R. C. Vaughn

Mathematics Faculty Publications

We obtain asymptotics for sums of the form

Sigma(p)(n=1) e(alpha(k) n(k) + alpha(1)n),

involving lower order main terms. As an application, we show that for almost all alpha(2) is an element of [0, 1) one has

sup(alpha 1 is an element of[0,1)) | Sigma(1 <= n <= P) e(alpha(1)(n(3) + n) + alpha(2)n(3))| << P3/4+epsilon,

and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrodinger and Airy equations.