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Articles 1 - 25 of 25
Full-Text Articles in Physical Sciences and Mathematics
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
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.
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.
Shutter Plot: A Visual Display Of Summary Statistics Over A Scatter Plot, Mamunur Rashid, Jyotirmoy Sarkar
Shutter Plot: A Visual Display Of Summary Statistics Over A Scatter Plot, Mamunur Rashid, Jyotirmoy Sarkar
Mathematics Faculty Publications
While a dot plot of one variable is naturally extended to a scatter plot of two variables, how should a box plot of one variable be extended to two variables? We propose a shutter plot that depicts the means and the standard deviations of both variables, the two regression lines and the coefficients of correlation and determination over a scatter plot. By showing all relevant summary statistics simultaneously, a shutter plot captures all aspects of a linear relationship, including flagging potential outliers, and helps the readers make good decisions.
Quasilinearization Applied To Boundary Value Problems At Resonance For Riemann-Liouville Fractional Differential Equations, Paul W. Eloe, Jaganmohan Jonnalagadda
Quasilinearization Applied To Boundary Value Problems At Resonance For Riemann-Liouville Fractional Differential Equations, Paul W. Eloe, Jaganmohan Jonnalagadda
Mathematics Faculty Publications
The quasilinearization method is applied to a boundary value problem at resonance for a Riemann-Liouville fractional differential equation. Under suitable hypotheses, the method of upper and lower solutions is employed to establish uniqueness of solutions. A shift method, coupled with the method of upper and lower solutions, is applied to establish existence of solutions. The quasilinearization algorithm is then applied to obtain sequences of lower and upper solutions that converge monotonically and quadratically to the unique solution of the boundary value problem at resonance.
A Data Analytic Framework For Physical Fatigue Management Using Wearable Sensors, Zahra Sedighi Maman, Ying-Ju Chen, Amir Baghdadi, Seamus Lombardo, Lora A. Cavuoto, Fadel M. Megahed
A Data Analytic Framework For Physical Fatigue Management Using Wearable Sensors, Zahra Sedighi Maman, Ying-Ju Chen, Amir Baghdadi, Seamus Lombardo, Lora A. Cavuoto, Fadel M. Megahed
Mathematics Faculty Publications
The use of expert systems in optimizing and transforming human performance has been limited in practice due to the lack of understanding of how an individual's performance deteriorates with fatigue accumulation, which can vary based on both the worker and the workplace conditions. As a first step toward realizing the human-centered approach to artificial intelligence and expert systems, this paper lays the foundation for a data analytic approach to managing fatigue in physically-demanding workplaces. The proposed framework capitalizes on continuously collected human performance data from wearable sensor technologies, and is centered around four distinct phases of fatigue: (a) detection, where …
A Two-Stage Machine Learning Framework To Predict Heart Transplantation Survival Probabilities Over Time With A Monotonic Probability Constraint, Hamidreza Ahady Dolatsaraa, Ying-Ju (Tessa) Chen, Christy Evans, Ashish Gupta, Fadel M. Megahed
A Two-Stage Machine Learning Framework To Predict Heart Transplantation Survival Probabilities Over Time With A Monotonic Probability Constraint, Hamidreza Ahady Dolatsaraa, Ying-Ju (Tessa) Chen, Christy Evans, Ashish Gupta, Fadel M. Megahed
Mathematics Faculty Publications
The overarching goal of this paper is to develop a modeling framework that can be used to obtain personalized, data-driven and monotonically constrained probability curves. This research is motivated by the important problem of improving the predictions for organ transplantation outcomes, which can inform updates made to organ allocation protocols, post-transplantation care pathways, and clinical resource utilization. In pursuit of our overarching goal and motivating problem, we propose a novel two-stage machine learning-based framework for obtaining monotonic probabilities over time. The first stage uses the standard approach of using independent machine learning models to predict transplantation outcomes for each time-period …
Unveiling The Molecular Mechanism Of Sars-Cov-2 Main Protease Inhibition From 137 Crystal Structures Using Algebraic Topology And Deep Learning, Duc Duy Nguyen, Kaifu Gao, Jiahui Chen, Rui Wang, Guo-Wei Wei
Unveiling The Molecular Mechanism Of Sars-Cov-2 Main Protease Inhibition From 137 Crystal Structures Using Algebraic Topology And Deep Learning, Duc Duy Nguyen, Kaifu Gao, Jiahui Chen, Rui Wang, Guo-Wei Wei
Mathematics Faculty Publications
Currently, there is neither effective antiviral drugs nor vaccine for coronavirus disease 2019 (COVID-19) caused by acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Due to its high conservativeness and low similarity with human genes, SARS-CoV-2 main protease (Mpro) is one of the most favorable drug targets. However, the current understanding of the molecular mechanism of Mpro inhibition is limited by the lack of reliable binding affinity ranking and prediction of existing structures of Mpro-inhibitor complexes. This work integrates mathematics (i.e., algebraic topology) and deep learning (MathDL) to provide a reliable ranking of the binding …
Simulating Phase Transitions And Control Measures For Network Epidemics Caused By Infections With Presymptomatic, Asymptomatic, And Symptomatic Stages, Benjamin Braun, Başak Taraktaş, Brian Beckage, Jane Molofsky
Simulating Phase Transitions And Control Measures For Network Epidemics Caused By Infections With Presymptomatic, Asymptomatic, And Symptomatic Stages, Benjamin Braun, Başak Taraktaş, Brian Beckage, Jane Molofsky
Mathematics Faculty Publications
We investigate phase transitions associated with three control methods for epidemics on small world networks. Motivated by the behavior of SARS-CoV-2, we construct a theoretical SIR model of a virus that exhibits presymptomatic, asymptomatic, and symptomatic stages in two possible pathways. Using agent-based simulations on small world networks, we observe phase transitions for epidemic spread related to: 1) Global social distancing with a fixed probability of adherence. 2) Individually initiated social isolation when a threshold number of contacts are infected. 3) Viral shedding rate. The primary driver of total number of infections is the viral shedding rate, with probability of …
Infinite Sets Of Solutions And Almost Solutions Of The Equation N∙M = Reversal(N∙M) Ii, Viorel Nitica, Cem Ekinci
Infinite Sets Of Solutions And Almost Solutions Of The Equation N∙M = Reversal(N∙M) Ii, Viorel Nitica, Cem Ekinci
Mathematics Faculty Publications
Motivated by their intrinsic interest and by applications to the study of numeric palindromes and other sequences of integers, we discover a method for producing infinite sets of solutions and almost solutions of the equation N M reversal N M ⋅= ⋅ ( ) , our results are valid in a general numeration base b > 2 .
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 …
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.
Boolean Network Topologies And The Determinative Power Of Nodes, Bronson W. Wacker, Mihaela T. Velcsov, Jim A. Rogers
Boolean Network Topologies And The Determinative Power Of Nodes, Bronson W. Wacker, Mihaela T. Velcsov, Jim A. Rogers
Mathematics Faculty Publications
Boolean networks have been used extensively for modeling networks whose node activity could be simplified to a binary outcome, such as on-off. Each node is influenced by the states of the other nodes via a logical Boolean function. The network is described by its topological properties which refer to the links between nodes, and its dynamical properties which refer to the way each node uses the information obtained from other nodes to update its state. This work explores the correlation between the information stored in the Boolean functions for each node in a property known as the determinative power and …
Approximate And Exact Merging Of Knapsack Constraints With Cover Inequalities, Fabio Vitor, Todd Easton
Approximate And Exact Merging Of Knapsack Constraints With Cover Inequalities, Fabio Vitor, Todd Easton
Mathematics Faculty Publications
This paper presents both approximate and exact merged knapsack cover inequalities, a class of cutting planes for knapsack and multiple knapsack integer programs. These inequalities combine the information from knapsack constraints and cover inequalities. Approximate merged knapsack cover inequalities can be generated through a O(n log n) algorithm, where n is the number of variables. This class of inequalities can be strengthened to an exact version with a pseudo-polynomial time algorithm. Computational experiments demonstrate an average improvement of approximately 8% in solution time and 5% in the number of ticks from CPLEX when approximate merged knapsack cover …
Free Subgroups With Torsion Quotients And Profinite Subgroups With Torus Quotients, Wayne Lewis, Peter Loth, Adolf Mader
Free Subgroups With Torsion Quotients And Profinite Subgroups With Torus Quotients, Wayne Lewis, Peter Loth, Adolf Mader
Mathematics Faculty Publications
Here “group” means abelian group. Compact connected groups contain δ-subgroups, that is, compact totally disconnected subgroups with torus quotients, which are essential ingredients in the important Resolution Theorem, a description of compact groups. Dually, full free subgroups of discrete torsion-free groups of finite rank are studied in order to obtain a comprehensive picture of the abundance of δ-subgroups of a protorus. Associated concepts are also considered.
Three Point Boundary Value Problems For Ordinary Differential Equations, Uniqueness Implies Existence, Paul W. Eloe, Johnny Henderson, Jeffrey T. Neugebauer
Three Point Boundary Value Problems For Ordinary Differential Equations, Uniqueness Implies Existence, Paul W. Eloe, Johnny Henderson, Jeffrey T. Neugebauer
Mathematics Faculty Publications
We consider a family of three point n − 2, 1, 1 conjugate boundary value problems for nth order nonlinear ordinary differential equations and obtain conditions in terms of uniqueness of solutions imply existence of solutions. A standard hypothesis that has proved effective in uniqueness implies existence type results is to assume uniqueness of solutions of a large family of n−point boundary value problems. Here, we replace that standard hypothesis with one in which we assume uniqueness of solutions of large families of two and three point boundary value problems. We then close the paper with verifiable conditions on the …
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 …
Stochastic Technique For Solutions Of Non-Linear Fin Equation Arising In Thermal Equilibrium Model, Iftikhar Ahmad, Hina Qureshi, Muhammad Bilal, Muhammad Usman
Stochastic Technique For Solutions Of Non-Linear Fin Equation Arising In Thermal Equilibrium Model, Iftikhar Ahmad, Hina Qureshi, Muhammad Bilal, Muhammad Usman
Mathematics Faculty Publications
In this study, a stochastic numerical technique is used to investigate the numerical solution of heat transfer temperature distribution system using feed forward artificial neural networks. Mathematical model of fin equation is formulated with the help of artificial neural networks. The effect of the heat on a rectangular fin with thermal conductivity and temperature de-pendent internal heat generation is calculated through neural networks optimization with optimizers like active set technique, interior point technique, pattern search, genetic algorithm and a hybrid approach of pattern search - interior point technique, genetic algorithm - active set technique, genetic algorithm - interior point technique, …
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 …