Mathematics Faculty PublicationsCopyright (c) 2021 Ateneo de Manila University All rights reserved.
https://archium.ateneo.edu/mathematics-faculty-pubs
Recent documents in Mathematics Faculty Publicationsen-usThu, 29 Apr 2021 02:51:32 PDT3600The N-integral
https://archium.ateneo.edu/mathematics-faculty-pubs/150
https://archium.ateneo.edu/mathematics-faculty-pubs/150Wed, 28 Apr 2021 00:14:19 PDT
In this paper, we introduced a Henstock-type integral named $N$-integral of a real valued function $f$ on a closed and bounded interval $[a,b]$. The $N$-integrable functions lie entirely between Riemann integrable functions and Henstock integrable functions. It was shown that for a Henstock integrable function $f$ on $[a,b]$ the following are equivalent: \begin{enumerate} \item[$(1)$] The function $f$ is $N$-integrable; \item[$(2)$] There exists a null set $S$ for which given $\epsilon >0$ there exists a gauge $\delta$ such that for any $\delta$-fine partial division $D=\{(\xi,[u,v])\}$ of $[a,b]$ we have \[(\phi_S(D)\cap \Gamma_{\epsilon})\sum |f(v)-f(u)||v-u|<\epsilon\] where $\phi_S(D)=\{(\xi,[u,v])\in D:\xi \notin S\}$ and \[\Gamma_{\epsilon}=\{(\xi,[u,v]): |f(v)-f(u)|\geq \epsilon\}\] \end{enumerate} and \begin{enumerate} \item[$(3)$] The function $f$ is continuous almost everywhere. \end{enumerate} A characterization of continuous almost everywhere functions was also given.
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Abraham P. Racca et al.Sigma Coloring and Edge Deletions
https://archium.ateneo.edu/mathematics-faculty-pubs/149
https://archium.ateneo.edu/mathematics-faculty-pubs/149Mon, 15 Feb 2021 22:53:06 PST
A vertex coloring c : V(G) → N of a non-trivial graph G is called a sigma coloring if σ(u) is not equal to σ(v) for any pair of adjacent vertices u and v. Here, σ(x) denotes the sum of the colors assigned to vertices adjacent to x. The sigma chromatic number of G, denoted by σ(G), is defined as the fewest number of colors needed to construct a sigma coloring of G. In this paper, we consider the sigma chromatic number of graphs obtained by deleting one or more of its edges. In particular, we study the difference σ(G)−σ(G−e) in general as well as in restricted scenarios; here, G−e is the graph obtained by deleting an edge e from G. Furthermore, we study the sigma chromatic number of graphs obtained via multiple edge deletions in complete graphs by considering the complements of paths and cycles.
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Agnes Garciano et al.Development of a mobile ten frames app for Philippine K-12 schools
https://archium.ateneo.edu/mathematics-faculty-pubs/148
https://archium.ateneo.edu/mathematics-faculty-pubs/148Sun, 14 Feb 2021 23:13:03 PST
This paper reports on the Quick Images app, whose design framework is informed by research on ten-structured thinking and gamification principles. Inclusivity was also a major consideration, especially in the context of a developing country. Thus, the app was made freely available and required only moderate system requirements. Pilot studies revealed that the app has the potential to promote children’s ability to see two-digit numbers in relation to tens and ones, which is a major goal of elementary school mathematics. Collaborations with the Philippine Department of Education to ensure the app’s sustained use are also discussed.
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Debbie Marie Versoza et al.Deploying System Dynamics Models for Disease Surveillance in the Philippines
https://archium.ateneo.edu/mathematics-faculty-pubs/147
https://archium.ateneo.edu/mathematics-faculty-pubs/147Sun, 14 Feb 2021 22:55:55 PST
Disease surveillance is vital for monitoring outbreaks and designing timely public health interventions. However, especially in developing contexts, disease surveillance efforts are constrained by challenges of data scarcity. In this work, we discuss the deployment of system dynamics simulation models to aid in local disease surveillance programs in the Philippines. More specifically, we propose that (a) available time series records of disease incidence can be used to initialize simulation models with high accuracy and interpretability, and (b) virtual experiments can be used to test various what-if scenarios in designing potential interventions. Experiments with three years of data on dengue fever in the Western Visayas region illustrate our proposed framework as deployed on the FASSSTER platform. We conclude by outlining challenges and potential directions for future work.
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Joshua Uyheng et al.Hindsight-Combined and Hindsight-Prioritized Experience Replay
https://archium.ateneo.edu/mathematics-faculty-pubs/146
https://archium.ateneo.edu/mathematics-faculty-pubs/146Mon, 08 Feb 2021 23:23:53 PST
Reinforcement learning has proved to be of great utility; execution, however, may be costly due to sampling inefficiency. An efficient method for training is experience replay, which recalls past experiences. Several experience replay techniques, namely, combined experience replay, hindsight experience replay, and prioritized experience replay, have been crafted while their relative merits are unclear. In the study, one proposes hybrid algorithms – hindsight-combined and hindsight-prioritized experience replay – and evaluates their performance against published baselines. Experimental results demonstrate the superior performance of hindsight-combined experience replay on an OpenAI Gym benchmark. Further, insight into the nonconvergence of hindsightprioritized experience replay is presented towards the improvement of the approach.
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Renzo Roel P. Tan et al.Concerning a Decision-Diagram-Based Solution to the Generalized Directed Rural Postman Problem
https://archium.ateneo.edu/mathematics-faculty-pubs/145
https://archium.ateneo.edu/mathematics-faculty-pubs/145Mon, 08 Feb 2021 22:41:04 PST
Decision-diagram-based solutions for discrete optimization have been persistently studied. Among these is the use of the zero-suppressed binary decision diagram, a compact graph-based representation for a specified family of sets. Such a diagram may work out combinatorial problems by efficient enumeration. In brief, an extension to the frontierbased search approach for zero-suppressed binary decision diagram construction is proposed. The modification allows for the inclusion of a class-determined constraint in formulation. Variations of the generalized directed rural postman problem, proven to be nondeterministic polynomial-time hard, are solved on some rapid transit systems as illustration. Lastly, results are juxtaposed against standard integer programming in establishing the relative superiority of the new technique.
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Renzo Roel P. Tan et al.Optimal strategies for mitigating the HIV/AIDS epidemic in the Philippines
https://archium.ateneo.edu/mathematics-faculty-pubs/144
https://archium.ateneo.edu/mathematics-faculty-pubs/144Wed, 03 Feb 2021 00:00:12 PST
The human immunodeficiency virus (HIV) impairs a person's immune system against many infections and some types of cancer, leading to acquired immunodeficiency syndrome (AIDS), which is characterized by severe illnesses. The number of HIV infections in the Philippines has increased, more than doubled, within the last decade. This alarming HIV crisis in the country requires urgent actions. In this study, a mathematical model is developed to describe the disease transmission in the Philippines. Disease‐free and endemic equilibria are obtained, stability analysis is performed, and the basic reproduction number is computed. Sensitivity analyses and subset selection are performed to identify influential parameters and to determine an identifiable parameter set given measurements, respectively. Available data on the number of asymptomatic aware infectious, those who are in the AIDS stage, and those under treatment are utilized to estimate key epidemiological parameters such as transmission, treatment, and screening rates. Uncertainty of these parameter estimates is quantified through bootstrapping method. Furthermore, intervention strategies are investigated in the framework of optimal control theory. Control measures include precaution, HIV screening, antiretroviral treatment, and pre‐exposure prophylaxis (PrEP) treatment. These various control efforts are compared with regard to cost efficiency and effectiveness in reducing the number of infected individuals. Given limited available control measures, the PrEP‐only scenario is shown to be the most cost‐effective, followed by other scenarios that combine PrEP with other controls.
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Carlo Delfin S. Estadilla et al.Geometric realizations of abstract regular polyhedra with automorphism group H3
https://archium.ateneo.edu/mathematics-faculty-pubs/143
https://archium.ateneo.edu/mathematics-faculty-pubs/143Sun, 10 Jan 2021 23:11:26 PST
A geometric realization of an abstract polyhedron P is a mapping that sends an i-face to an open set of dimension i. This work adapts a method based on Wythoff construction to generate a full rank realization of an abstract regular polyhedron from its automorphism group Gamma. The method entails finding a real orthogonal representation of Gamma of degree 3 and applying its image to suitably chosen (not necessarily connected) open sets in space. To demonstrate the use of the method, it is applied to the abstract polyhedra whose automorphism groups are isomorphic to the non-crystallographic Coxeter group H3.
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Mark L. Loyola et al.Tilings with Congruent Edge Coronae
https://archium.ateneo.edu/mathematics-faculty-pubs/142
https://archium.ateneo.edu/mathematics-faculty-pubs/142Sun, 10 Jan 2021 22:14:21 PST
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.
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Ma. Louise Antonette N. De Las Peñas et al.Ethnomathematics for capacity building in mathematics education
https://archium.ateneo.edu/mathematics-faculty-pubs/141
https://archium.ateneo.edu/mathematics-faculty-pubs/141Mon, 21 Sep 2020 00:31:36 PDT
The Mathematics Framework for Philippine Basic Education (MATHTED and SEI, in press), a document that aims to guide the development of curricular contents in mathematics, identifies cultural-rootedness as one of the cognitive values that mathematics education in the Philippines must inculcate. Cultural-rootedness is defined as ?appreciating the cultural value of mathematics and its origins in many cultures, its rich history and how it has grown and continues to evolve?. Ethnomathematics, described as the ?mathematics which is practiced among identifiable cultural groups, such as national tribal societies, labor groups, children of a certain age bracket, professional classes and so on? (D?Ambrosio, 1997, p.16), has rich potentials in increasing a country?s capacity to provide better mathematics education to its people. It is a vehicle for developing the value of cultural-rootedness thus recognizing and valuing the significant mathematical knowledge within the Philippines and how this mathematics has and continues to play a significant role in building capacity within the Philippines and its people. This paper provides examples of ?latent? mathematics that are found in various cultural groups in the Philippines. With these examples, the paper argues for changes in Philippine mathematics education to recognize and include Ethnomathematics encouraging teachers and communities to actively seek ways to include the non-traditional, non-Western mathematics in their teaching of mathematics in schools. These would include the different ways of counting, measuring, patterning, navigating, constructing, creating shapes, computing and other mathematical skills of various cultural groups. By this, Filipino students will learn to both appreciate the many cultures in the country and develop ways to include these cultures into the mainstream Philippine culture, thereby supporting the inclusion of all as being more comprehensively truly a part of the Philippines. The Mathematics Framework for Philippine Basic Education (MATHTED and SEI, in press), a document that aims to guide the development of curricular contents in mathematics, identifies cultural-rootedness as one of the cognitive values that mathematics education in the Philippines must inculcate. Cultural-rootedness is defined as ?appreciating the cultural value of mathematics and its origins in many cultures, its rich history and how it has grown and continues to evolve?. Ethnomathematics, described as the ?mathematics which is practiced among identifiable cultural groups, such as national tribal societies, labor groups, children of a certain age bracket, professional classes and so on? (D?Ambrosio, 1997, p.16), has rich potentials in increasing a country?s capacity to provide better mathematics education to its people. It is a vehicle for developing the value of cultural-rootedness thus recognizing and valuing the significant mathematical knowledge within the Philippines and how this mathematics has and continues to play a significant role in building capacity within the Philippines and its people. This paper provides examples of ?latent? mathematics that are found in various cultural groups in the Philippines. With these examples, the paper argues for changes in Philippine mathematics education to recognize and include Ethnomathematics encouraging teachers and communities to actively seek ways to include the non-traditional, non-Western mathematics in their teaching of mathematics in schools. These would include the different ways of counting, measuring, patterning, navigating, constructing, creating shapes, computing and other mathematical skills of various cultural groups. By this, Filipino students will learn to both appreciate the many cultures in the country and develop ways to include these cultures into the mainstream Philippine culture, thereby supporting the inclusion of all as being more comprehensively truly a part of the Philippines.
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Catherine P. Vistro-YuGutt Products and Representations of Lie Groups
https://archium.ateneo.edu/mathematics-faculty-pubs/140
https://archium.ateneo.edu/mathematics-faculty-pubs/140Thu, 17 Sep 2020 01:13:06 PDTJob A. NableLinear Operators that Preserve the Edgesum of a Graph
https://archium.ateneo.edu/mathematics-faculty-pubs/139
https://archium.ateneo.edu/mathematics-faculty-pubs/139Thu, 17 Sep 2020 01:04:41 PDTIan June L. Garces et al.Characterizing Convergence Conditions for the Mα-Integral
https://archium.ateneo.edu/mathematics-faculty-pubs/138
https://archium.ateneo.edu/mathematics-faculty-pubs/138Fri, 11 Sep 2020 00:33:30 PDT
Park, Ryu, and Lee recently defined a Henstock-type integral, which lies entirely between the McShane and the Henstock integrals. This paper presents two characterizing convergence conditions for this integral, and derives other known convergence theorems as corollaries.
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Ian June L. Garces et al.Revisiting a Number-Theoretic Puzzle: The Census-Taker Problem
https://archium.ateneo.edu/mathematics-faculty-pubs/137
https://archium.ateneo.edu/mathematics-faculty-pubs/137Wed, 09 Sep 2020 00:27:53 PDT
The current work revisits the results of L.F. Meyers and R. See in [3], and presents the census-taker problem as a motivation to introduce the beautiful theory of numbers.
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Ian June L. Garces et al.On subgroups of hyperbolic tetrahedral Coxeter groups
https://archium.ateneo.edu/mathematics-faculty-pubs/136
https://archium.ateneo.edu/mathematics-faculty-pubs/136Wed, 09 Sep 2020 00:23:05 PDT
In this work we address the problem on the determination of the subgroup structure of crystallographic groups in hyperbolic space by deriving the low index subgroups of hyperbolic tetrahedral Coxeter groups and tetrahedral Kleinian groups. This paper continues the work giv en in [5, 6] on the subgroups of triangle groups.
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Ma. Louise Antonette N. De Las Peñas et al.Building a Student-Centered Organizational Culture
https://archium.ateneo.edu/mathematics-faculty-pubs/135
https://archium.ateneo.edu/mathematics-faculty-pubs/135Thu, 27 Aug 2020 23:03:18 PDT
The increasing demand for outcomes-based learning, changing demographics of students and advances in pedagogy and research in higher-education institutions have compelled educators to adopt practices aligned with the student-centered learning (SCL) approach. However, SCL is often understood unevenly and implemented inconsistently. This chapter focuses on how the Ateneo de Manila University, a Philippine university, has been working to build an organizational culture in order to strengthen and institutionalize SCL. Analysis of data from course syllabi, Annual Faculty Activity Reports, and course evaluations indicate that the Loyola Schools’ efforts to institutionalize SCL have been taking root in the curricula and in the classrooms. However, Loyola Schools faculty need to weaken knowledge boundaries and lessen control and regulation of knowledge production in order for the benefits of SCL to be fully experienced by the students.
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Catherine P. Vistro-Yu et al.On eigenvalue bounds for the finite-state birth-death process intensity matrix
https://archium.ateneo.edu/mathematics-faculty-pubs/134
https://archium.ateneo.edu/mathematics-faculty-pubs/134Thu, 13 Aug 2020 01:22:01 PDT
The paper sets forth a novel eigenvalue interlacing property across the finite-state birth-death process intensity matrix and two clearly identified submatrices as an extension of Cauchy’s interlace theorem for Hermitian matrix eigenvalues. A supplemental proof involving an examination of probabilities acquired from specific movements across states and a derivation of a form for the eigenpolynomial of the matrix through convolution and Laplace transform is then presented towards uncovering a similar characteristic for the general Markov chain transition rate matrix. Consequently, the proposition generates bounds for each eigenvalue of the original matrix, easing numerical computation. To conclude, the applicability of the property to some real square matrices upon transformation is explored.
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R.R.P Tan et al.s-Extremal Additive Codes over GF(4)
https://archium.ateneo.edu/mathematics-faculty-pubs/132
https://archium.ateneo.edu/mathematics-faculty-pubs/132Thu, 06 Aug 2020 22:21:46 PDT
Recently Bachoc and Gaborit introduced the notion of s-extremality for binary self-dual codes, generalizing Elkies' study on the highest possible minimum weight of the shadows of binary self-dual codes. In this paper, we introduce a concept of s-extremality for additive self-dual codes over F 4 , give a bound on the length of these codes with even distance d, classify them up to minimum distance d = 4, give possible lengths (only strongly conjectured for odd d) for which there exist s-extremal codes with 5 les d les 11, and give five s-extremal codes with d = 7 as well as four new s-extremal codes with d = 5. We also describe codes related to s-extremal codes
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Evangeline P. Bautista et al.A Framework for Coloring Symmetrical Patterns
https://archium.ateneo.edu/mathematics-faculty-pubs/131
https://archium.ateneo.edu/mathematics-faculty-pubs/131Wed, 29 Jul 2020 21:40:17 PDTMa. Louise Antonette N. De Las Peñas et al.On the Construction of Colored Plane Crystallographic Patterns
https://archium.ateneo.edu/mathematics-faculty-pubs/130
https://archium.ateneo.edu/mathematics-faculty-pubs/130Wed, 29 Jul 2020 21:27:04 PDT
In this paper, we present an approach to the construction of perfect and non-perfect colorings resulting from plane crystallographic groups. In particular, we consider colored patterns that arise with symmetry group normal in the symmetry group of the uncolored pattern.
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Ma. Louise Antonette N. De Las Peñas