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Articles 1 - 13 of 13
Full-Text Articles in Physical Sciences and Mathematics
Sigma Coloring And Edge Deletions, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino
Sigma Coloring And Edge Deletions, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino
Mathematics Faculty Publications
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) …
Development Of A Mobile Ten Frames App For Philippine K-12 Schools, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Mark L. Loyola
Development Of A Mobile Ten Frames App For Philippine K-12 Schools, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Mark L. Loyola
Mathematics Faculty Publications
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.
Concerning A Decision-Diagram-Based Solution To The Generalized Directed Rural Postman Problem, Renzo Roel P. Tan, Jun Kawahara, Kazushi Ikeda, Agnes Garciano, Kyle Stephen S. See
Concerning A Decision-Diagram-Based Solution To The Generalized Directed Rural Postman Problem, Renzo Roel P. Tan, Jun Kawahara, Kazushi Ikeda, Agnes Garciano, Kyle Stephen S. See
Mathematics Faculty Publications
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 …
Approximation And Computational Complexity Of Some Hammock Variations Of The Poset Cover Problem, Ivy Ordanel, Proceso L. Fernandez Jr, Richelle Ann B. Juayong, Henry N. Adorna
Approximation And Computational Complexity Of Some Hammock Variations Of The Poset Cover Problem, Ivy Ordanel, Proceso L. Fernandez Jr, Richelle Ann B. Juayong, Henry N. Adorna
Department of Information Systems & Computer Science Faculty Publications
The Hammock(⏟𝟐, 𝟐 , … , 𝟐 / 𝒌 )-Poset Cover Problem is a variation of the Poset Cover Problem with the same input – set {𝑳𝟏, 𝑳𝟐, … , 𝑳𝒎} of linear orders over the set {𝟏, 𝟐, … ,𝒏}, but the solution is restricted to a set of simple hammock(𝟐⏟, 𝟐 , … , 𝟐 / 𝒌 ) posets. The problem is NP-Hard when 𝒌 ≥ 𝟑 but is in 𝑷 when 𝒌 = 𝟏. The computational complexity of the problem when 𝒌 = 𝟐 is not yet known. In this paper, …
Underwater Gesture Recognition Using Classical Computer Vision And Deep Learning Techniques, Mygel Andrei M. Martija, Jakov Ivan S. Dumbrique, Prospero C. Naval Jr.
Underwater Gesture Recognition Using Classical Computer Vision And Deep Learning Techniques, Mygel Andrei M. Martija, Jakov Ivan S. Dumbrique, Prospero C. Naval Jr.
Mathematics Faculty Publications
Underwater Gesture Recognition is a challenging task since conditions which are normally not an issue in gesture recognition on land must be considered. Such issues include low visibility, low contrast, and unequal spectral propagation. In this work, we explore the underwater gesture recognition problem by taking on the recently released Cognitive Autonomous Diving Buddy Underwater Gestures dataset. The contributions of this paper are as follows: (1) Use traditional computer vision techniques along with classical machine learning to perform gesture recognition on the CADDY dataset; (2) Apply deep learning using a convolutional neural network to solve the same problem; (3) Perform …
Geometric Realizations Of Abstract Regular Polyhedra With Automorphism Group H3, Mark L. Loyola, Jonn Angel L. Aranas
Geometric Realizations Of Abstract Regular Polyhedra With Automorphism Group H3, Mark L. Loyola, Jonn Angel L. Aranas
Mathematics Faculty Publications
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.
The Sigma Chromatic Number Of The Sierpinski Gasket Graphs And The Hanoi Graphs, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino
The Sigma Chromatic Number Of The Sierpinski Gasket Graphs And The Hanoi Graphs, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino
Mathematics Faculty Publications
A vertex coloring c : V(G) → of a non-trivial connected graph G is called a sigma coloring if σ(u) ≠ 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 determine the sigma chromatic numbers of the …
The N-Integral, Abraham P. Racca, Emmanuel A. Cabral
The N-Integral, Abraham P. Racca, Emmanuel A. Cabral
Mathematics Faculty Publications
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.
Twin Chromatic Indices Of Some Graphs With Maximum Degree 3, Jayson D. Tolentino, Reginaldo M. Marcelo, Mark Anthony C. Tolentino
Twin Chromatic Indices Of Some Graphs With Maximum Degree 3, 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 k and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in 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 . In this paper, we determine the …
Sigma Chromatic Number Of Graph Coronas Involving Complete Graphs, Agnes Garciano, Maria Czarina T. Lagura, Reginaldo M. Marcelo
Sigma Chromatic Number Of Graph Coronas Involving Complete Graphs, Agnes Garciano, Maria Czarina T. Lagura, Reginaldo M. Marcelo
Mathematics Faculty Publications
Let c : V(G) → be a coloring of the vertices in a graph G. For a vertex u in G, the color sum of u, denoted by σ(u), is the sum of the colors of the neighbors of u. The coloring c is called a sigma coloring of G if σ(u) ≠ σ(v) whenever u and v are adjacent vertices in G. The minimum number of colors that can be used in a sigma coloring of G is called the sigma chromatic …
Designing Mobile Apps To Promote Numeracy And Statistical Reasoning, Ma. Louise Antonette N. De Las Peñas, Mark L. Loyola, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Versoza
Designing Mobile Apps To Promote Numeracy And Statistical Reasoning, Ma. Louise Antonette N. De Las Peñas, Mark L. Loyola, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Versoza
Mathematics Faculty Publications
Developing countries typically do not perform well in international benchmarks of mathematics achievement. This may be partially explained by students’ immersion in classrooms characterized by superficial strategies or rote-learning methods. This paper reports on the design of mobile applications (apps) developed by the authors as part of an ongoing project funded by a national government agency and intended to promote structural thinking and statistical reasoning. It describes the general features of the apps, as well as the pedagogical principles upon which the apps’ designs were anchored on. These principles are grounded on research and established practices on number sense and …
On The Set Chromatic Number Of The Join And Comb Product Of Graphs, Bryan Ceasar L. Felipe, Agnes Garciano, Mark Anthony C. Tolentino
On The Set Chromatic Number Of The Join And Comb Product Of Graphs, Bryan Ceasar L. Felipe, Agnes Garciano, Mark Anthony C. Tolentino
Mathematics Faculty Publications
A vertex coloring c : V(G) → of a non-trivial connected graph G is called a set coloring if NC(u) ≠ NC(v) for any pair of adjacent vertices u and v. Here, NC(x) denotes the set of colors assigned to vertices adjacent to x. The set chromatic number of G, denoted by χs (G), is defined as the fewest number of colors needed to construct a set coloring of G. In this paper, we study the set chromatic number in relation to two graph operations: …
On Eigenvalue Bounds For The Finite-State Birth-Death Process Intensity Matrix, R.R.P Tan, K Ikeda, Len Patrick Dominic M. Garces
On Eigenvalue Bounds For The Finite-State Birth-Death Process Intensity Matrix, R.R.P Tan, K Ikeda, Len Patrick Dominic M. Garces
Mathematics Faculty Publications
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 …