Shutter Plot: A Visual Display Of Summary Statistics Over A Scatter Plot,
2020
DePauw University
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.
Energy Spectrum Of Linear Internal Wave Field In The Vicinity Of Continental Slope,
2020
The University of Texas Rio Grande Valley
Energy Spectrum Of Linear Internal Wave Field In The Vicinity Of Continental Slope, Ranis N. Ibragimov, Austin Biondi, Nathan Arndt, Maria Castillo, Guang Lin, Vesselin Vatchev, Sheng Zhang
School of Mathematical & Statistical Sciences Faculty Publications
The purpose of the research was to investigate two-dimensional modeling of efficiency of mixing, resulting from the reflection of a linear internal wave field (IWF) off a continental slope. Efficiency of deep ocean mixing was associated with the energy balance of the radiating IWF into an interior of the ocean in the vicinity of a sloping bottom topography. Since waves are generated not only at the fundamental frequency but also at all of its harmonics ωn = nω less than buoyancy frequency N and greater than Coriolis frequency f, our analysis includes, in general, an infinite number of …
Learning To Leverage Obstacles, Resources, And Strategies In Math Classes With Multilingual Learners,
2020
The University of Texas Rio Grande Valley
Learning To Leverage Obstacles, Resources, And Strategies In Math Classes With Multilingual Learners, Aaron T. Wilson, Hyung Won Kim, Mayra Ortiz Galarza, Josef A. Sifuentes
School of Mathematical & Statistical Sciences Faculty Publications
Mathematics teachers must be ready for diverse classrooms, where students who are multilingual learners (MLs) bring new dimensions to the teaching and learning. While MLs face obstacles to learning particular to their linguistic and cultural background, they also bring resources and strengths to bear that can be applied to teaching and learning. We have developed a Challenge-Based Instructional activity to help teachers leverage their experiences of teaching math to ML students, to better understand the obstacles and resources, and to select more effective pedagogical strategies particular to this context. This paper reports the benefits teachers gain in implementing this activity.
Unveiling The Molecular Mechanism Of Sars-Cov-2 Main Protease Inhibition From 137 Crystal Structures Using Algebraic Topology And Deep Learning,
2020
University of Kentucky
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 …
Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density,
2020
National University of Uzbekistan
Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density, Maftuha Sayfullayeva
Acta of Turin Polytechnic University in Tashkent
В работе установлены критические и двойные критические случаи, обусловленные представлением двойного нелинейного параболического уравнения с переменной плотностью с поглощением в "радиально-симметричной" форме.Такое представление исходного уравнения дало возможность легко построить решения типа Зельдовоч-Баренбатт-Паттл для критических случаев в виде функций сравнения.
Isomorphism Of Trees And Isometry Of Ultrametric Spaces,
2020
Institute of Applied Mathematics and Mechanics of NASU of Ukraine
Isomorphism Of Trees And Isometry Of Ultrametric Spaces, Oleksiy Dovgoshey
Theory & Applications of Graphs
We study the conditions under which the isometry of spaces with metrics generated by weights given on the edges of finite trees is equivalent to the isomorphism of these trees. Similar questions are studied for ultrametric spaces generated by labelings given on the vertices of trees. The obtained results generalized some facts previously known for phylogenetic trees and for Gurvich---Vyalyi monotone trees.
Some Topics Involving Derived Categories Over Noetherian Formal Schemes.,
2020
Indian Statistical Institute
Some Topics Involving Derived Categories Over Noetherian Formal Schemes., Saurabh Singh Dr.
Doctoral Theses
There are two parts to this thesis and both the parts involve working with derived categories over noetherian formal schemes. Beyond this there is no overlap between them and we discuss them separately.The first part concerns Grothendieck duality on noetherian formal schemes.Grothendieck duality is a vast generalisation of Serreduality in algebraic geometry. The main statements in this theory are expressed in the language of derived categories. We begin with an important special case.Let f : X → Y be a proper map of noetherian schemes which is smooth of relative dimension n. For any G ∈ D+ qc(Y ) (where …
Multiple Positive Solutions To The Fractional Kirchhoff Problem With Critical Indefinite Nonlinearities,
2020
The University of Texas Rio Grande Valley
Multiple Positive Solutions To The Fractional Kirchhoff Problem With Critical Indefinite Nonlinearities, Jie Yang, Haibo Chen, Zhaosheng Feng
School of Mathematical & Statistical Sciences Faculty Publications
This article concerns the existence and multiplicity of positive solutions to the fractional Kirchhoff equation with critical indefinite nonlinearities by applying the Nehari manifold approach and fibering maps.
Qualitative Features Of A Nonlinear, Nonlocal, Agent-Based Pde Model With Applications To Homelessness,
2020
The University of Texas Rio Grande Valley
Qualitative Features Of A Nonlinear, Nonlocal, Agent-Based Pde Model With Applications To Homelessness, Michael R. Lindstrom, Andrea L. Bertozzi
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we develop a continuum model for the movement of agents on a lattice, taking into account location desirability, local and far-range migration, and localized entry and exit rates. Specifically, our motivation is to qualitatively describe the homeless population in Los Angeles. The model takes the form of a fully nonlinear, nonlocal, non-degenerate parabolic partial differential equation. We derive the model and prove useful properties of smooth solutions, including uniqueness and L2 -stability under certain hypotheses. We also illustrate numerical solutions to the model and find that a simple model can be qualitatively similar in behavior to observed …
Topological And H^Q Equivalence Of Cyclic N-Gonal Actions On Riemann Surfaces - Part Ii,
2020
Rose-Hulman Institute of Technology
Topological And H^Q Equivalence Of Cyclic N-Gonal Actions On Riemann Surfaces - Part Ii, Sean A. Broughton
Mathematical Sciences Technical Reports (MSTR)
We consider conformal actions of the finite group G on a closed Riemann surface S, as well as algebraic actions of G on smooth, complete, algebraic curves over an arbitrary, algebraically closed field. There are several notions of equivalence of actions, the most studied of which is topological equivalence, because of its close relationship to the branch locus of moduli space. A second important equivalence relation is that induced by representation of G on spaces of holomorphic q-differentials. The notion of topological equivalence does not work well in positive characteristic. We shall discuss an alternative to topological equivalence, …
Weather Derivatives And The Market Price Of Risk,
2020
University of Mary Washington, Fredericksburg, Virginia USA
Weather Derivatives And The Market Price Of Risk, Julius Esunge, James J. Njong
Journal of Stochastic Analysis
No abstract provided.
Specifications-Based Grading Reduces Anxiety For Students Of Ordinary Differential Equations,
2020
Wentworth Institute of Technology
Specifications-Based Grading Reduces Anxiety For Students Of Ordinary Differential Equations, Mel Henriksen, Jakob Kotas, Mami Wentworth
CODEE Journal
Specifications-based grading (SBG) is an assessment scheme in which student grades are based on demonstrated understanding of known specifications which are tied to course learning outcomes. Typically with SBG, students are given multiple opportunities to demonstrate such understanding. In undergraduate-level introductory ordinary differential equations courses at two institutions, SBG has been found to markedly decrease students’ self-reported anxiety related to the course as compared to traditionally graded courses.
Tridiagonal And Pentadiagonal Doubly Stochastic Matrices,
2020
Shandong Normal University - China; Nova Southeastern University
Tridiagonal And Pentadiagonal Doubly Stochastic Matrices, Lei Cao, Darian Mclaren, Sarah Plosker
Mathematics Faculty Articles
We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix A is completely positive and provide examples including how one can change the initial conditions or deal with block matrices, which expands the range of matrices to which our decomposition can be applied. Our decomposition leads us to a number of related results, allowing us to prove that for tridiagonal doubly stochastic matrices, positive semidefiniteness is equivalent to complete positivity (rather than merely being implied by complete positivity). We then consider symmetric pentadiagonal matrices, proving some analogous results, and providing two different decompositions sufficient for complete …
Simulating Phase Transitions And Control Measures For Network Epidemics Caused By Infections With Presymptomatic, Asymptomatic, And Symptomatic Stages,
2020
University of Kentucky
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 …
Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder,
2020
University of Pittsburgh
Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya
Department of Mathematics Faculty Scholarship and Creative Works
We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the …
Effectiveness Of Virtual Manipulative Teaching Method In Enhancing Year Four Pupils’ Understanding Of Fractions,
2020
Universiti Malaya
Effectiveness Of Virtual Manipulative Teaching Method In Enhancing Year Four Pupils’ Understanding Of Fractions, Kavitha Karbal Singh
Student Works (2020-2029)
Fractions are common numerical representations in mathematics. However, they seem to be a complicated mathematical concept to master, particularly among school pupils. Pupils have a hard time studying fraction due to insufficient understanding of the concept. An effective teaching method is therefore essential for the teaching and learning of this particular component. The purpose of this study is to determine the effectiveness of the virtual manipulative teaching method in improving the understanding of fraction among Primary Year Four pupils. Essentially a quasi-experimental research, the method used was a non-equivalent, control group pretest-posttest approach. A total of 80 pupils from a …
Exchangeably Weighted Bootstraps Of Martingale Difference Arrays Under The Uniformly Integrable Entropy,
2020
Alliance Sorbonne Universités, Université de Technologie de Compiègne, L.M.A.C., Compiègne, France
Exchangeably Weighted Bootstraps Of Martingale Difference Arrays Under The Uniformly Integrable Entropy, Salim Bouzebda, Nikolaos Limnios
Journal of Stochastic Analysis
No abstract provided.
Active Nonlocal Metasurfaces,
2020
Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY
Active Nonlocal Metasurfaces, Stephanie C. Malek, Adam C. Overvig, Sajan Shrestha, Nanfang Yu
Advanced Science Research Center
Actively tunable and reconfigurable wavefront shaping by optical metasurfaces poses a significant technical challenge often requiring unconventional materials engineering and nanofabrication. Most wavefront-shaping metasurfaces can be considered “local” in that their operation depends on the responses of individual meta-units. In contrast, “nonlocal” metasurfaces function based on the modes supported by many adjacent meta-units, resulting in sharp spectral features but typically no spatial control of the outgoing wavefront. Recently, nonlocal metasurfaces based on quasi-bound states in the continuum have been shown to produce designer wavefronts only across the narrow bandwidth of the supported Fano resonance. Here, we leverage the enhanced light-matter …
On An Asset Model Of Hobson-Rogers Type,
2020
4F Astro-Math Building, National Taiwan University, Taipei 10617, Taiwan
On An Asset Model Of Hobson-Rogers Type, Narn-Rueih Shieh
Journal of Stochastic Analysis
No abstract provided.
Rosenzweig, Equality, And Assignment,
2020
The University of Texas at El Paso
Rosenzweig, Equality, And Assignment, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In his seminal book "The Star of Redemption", the renowned philosopher Franz Rosenzweig illustrated his ideas by the intuitive difference between mathematical statements A=B and B=A. Of course, from the purely mathematical viewpoint, these two statements are always equivalent, so to a person trained in mathematics -- even in simple school mathematics -- this illustration is puzzling. What we show is that from the viewpoint of common folks, there is indeed a subtle difference between how people understand these two equalities. To us, the understanding of this difference helped us better understand Rosenzweig's ideas. But we believe that this difference …
