Mathematics Commons^™

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 (M^pro) is one of the most favorable drug targets. However, the current understanding of the molecular mechanism of M^pro inhibition is limited by the lack of reliable binding affinity ranking and prediction of existing structures of M^pro-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, 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, 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., 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, 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, 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, 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, Julius Esunge, James J. Njong

Journal of Stochastic Analysis

No abstract provided.

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, 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, 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, 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, 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, Salim Bouzebda, Nikolaos Limnios

Journal of Stochastic Analysis

No abstract provided.

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, Narn-Rueih Shieh

Journal of Stochastic Analysis

No abstract provided.

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 …

Meager Sets, Games And Singular Cardinals, Liljana Babinkostova, Marion Scheepers

Mathematics Faculty Publications and Presentations

We show that a statement concerning the existence of winning strategies of limited memory in an infinite two-person topological game is equivalent to a weak version of the Singular Cardinals Hypothesis.

A Fast And Accurate Algorithm For Spherical Harmonic Analysis On Healpix Grids With Applications To The Cosmic Microwave Background Radiation, Kathryn P. Drake, Grady B. Wright

Mathematics Faculty Publications and Presentations

The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) scheme is used extensively in astrophysics for data collection and analysis on the sphere. The scheme was originally designed for studying the Cosmic Microwave Background (CMB) radiation, which represents the first light to travel during the early stages of the universe's development and gives the strongest evidence for the Big Bang theory to date. Refined analysis of the CMB angular power spectrum can lead to revolutionary developments in understanding the nature of dark matter and dark energy. In this paper, we present a new method for performing spherical harmonic analysis for HEALPix data, …

Alternative Cichoń Diagrams And Forcing Axioms Compatible With Ch, Corey B. Switzer

Dissertations, Theses, and Capstone Projects

This dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cichoń diagram. First I show that for a wide variety of reduction concepts there is a Cichoń diagram for effective cardinal characteristics relativized to that reduction. As an application I investigate in detail the Cichoń diagram for degrees of constructibility relative to a fixed inner model of ZFC. Then I study generalizations of cardinal characteristics to the space of functions from Baire space to Baire space. …

Role Of Influence In Complex Networks, Nur Dean

Dissertations, Theses, and Capstone Projects

Game theory is a wide ranging research area; that has attracted researchers from various fields. Scientists have been using game theory to understand the evolution of cooperation in complex networks. However, there is limited research that considers the structure and connectivity patterns in networks, which create heterogeneity among nodes. For example, due to the complex ways most networks are formed, it is common to have some highly “social” nodes, while others are highly isolated. This heterogeneity is measured through metrics referred to as “centrality” of nodes. Thus, the more “social” nodes tend to also have higher centrality.

In this thesis, …

Growth Of Conjugacy Classes Of Reciprocal Words In Triangle Groups, Blanca T. Marmolejo

Dissertations, Theses, and Capstone Projects

In this thesis we obtain the growth rates for conjugacy classes of reciprocal words for triangle groups of the form G = Z2 ∗ H where H is finitely generated and does not contain an order 2 element. We explore cases where H is infinite cyclic and finite cyclic. The quotient O = H/G is an orbifold and contains a cone point of order 2, due to the first factor Z2 in the free product G. The reciprocal words in G correspond to geodesics on O which pass through the order 2 cone point on O. We use methods from …

Spectral Sequences For Almost Complex Manifolds, Qian Chen

Dissertations, Theses, and Capstone Projects

In recent work, two new cohomologies were introduced for almost complex manifolds: the so-called J-cohomology and N-cohomology [CKT17]. For the case of integrable (complex) structures, the former cohomology was already considered in [DGMS75], and the latter agrees with de Rham cohomology. In this dissertation, using ideas from [CW18], we introduce spectral sequences for these two cohomologies, showing the two cohomologies have natural bigradings. We show the spectral sequence for the J-cohomology converges at the second page whenever the almost complex structure is integrable, and explain how both fit in a natural diagram involving Bott-Chern cohomology and the Frolicher spectral sequence. …

Solar Power Forecasting Using Wavelet Transform And Machine Learning Approaches, Abdullah Nor Azliana

Student Works (2020-2029)

Generation of photovoltaic (PV) power is intermittent in nature and integration of PV system into the grid system causes an imbalanced power production and power demand. One of the efforts to reduce this problem is to forecast the generation of solar power in the PV system. Solar power forecasting requires the collection of solar power and meteorological data. Hence, this work collected solar power data and various meteorological data (global radiation, tilted radiation, temperature surrounding, humidity surrounding, PV module/ PV panel temperature and wind speed) from Universiti Teknikal Malaysia Melaka (UTeM). A pre-processing process is carried out to ensure that …

Tile Based Self-Assembly Of The Rook's Graph, Ernesto Gonzalez

Electronic Theses, Projects, and Dissertations

The properties of DNA make it a useful tool for designing self-assembling nanostructures. Branched junction molecules provide the molecular building blocks for creating target complexes. We model the underlying structure of a DNA complex with a graph and we use tools from linear algebra to optimize the self-assembling process. Some standard classes of graphs have been studied in the context of DNA self-assembly, but there are many open questions about other families of graphs. In this work, we study the rook's graph and its related design strategies.

Solving Parametric Radical Equations With Depth 2 Rigorously Using The Restriction Set Method, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

We review the history and previous literature on radical equations and present the rigorous solution theory for radical equations of depth 2, continuing a previous study of radical equations of depth 1. Radical equations of depth 2 are equations where the unknown variable appears under at least one square root and where two steps are needed to eliminate all radicals appearing in the equation. We state and prove theorems for all three equation forms with depth 2 that give the solution set of all real-valued solutions. The theorems are shown via the restriction set method that uses inequality restrictions to …

Tilings By Hexagonal Prisms And Embeddings Into Primitive Cubic Networks, Mikhail M. Bouniaev, Nikolay Dolbilin, Mikhail I. Shtogrin

School of Mathematical & Statistical Sciences Faculty Publications

All possible combinatorial embeddings into primitive cubic networks of arbitrary tilings of 3D space by pairwise congruent and parallel regular hexagonal prisms are discussed and classified.

Length Neutrosophic Subalgebras Of Bck/Bci-Algebras, Florentin Smarandache, Young Bae Jun, Madad Khan, Seok-Zun Song

Branch Mathematics and Statistics Faculty and Staff Publications

the notion of (i, j, k)-length neutrosophic subalgebras in BCK/BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided.

Plithogenic Cubic Sets, Florentin Smarandache, S.P. Priyadharshini, F. Nirmala Irudayam

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, using the concepts of cubic set and plithogenic set, the ideas of plithogenic fuzzy cubic set, plithogenic intuitionistic fuzzy cubic set, plithogenic neutrosophic cubic set are introduced and its corresponding internal and external cubic sets are discussed with examples.

A Novel Approach For Assessing The Reliability Of Data Contained In A Single Valued Neutrosophic Number And Its Application In Multiple Criteria Decision Making, Florentin Smarandache, Dragisa Stanujkic, Darjan Karabasevic, Gabrijela Popovic

Branch Mathematics and Statistics Faculty and Staff Publications

Multiple criteria decision making is one of the many areas where neutrosophic sets have been applied to solve various problems so far.