Getting Over It, 2021 University of Richmond

#### Getting Over It, Thomas Kade, Kevorc Ibrahimian, Max Simpson

*Arts & Sciences Student Symposium*

The research extended a 2D motion planning system to three dimensional environments. The updated system is now able to plan the motion for robots over 3D terrains modeled by polyhedrons.

The School Mathematics Study Group: Lessons In Mathematics Education, 2021 University of Richmond

#### The School Mathematics Study Group: Lessons In Mathematics Education, Madeline Polhill

*Arts & Sciences Student Symposium*

This work argues that the "new math" project called the School Mathematics Study Group offers a valuable case study for mathematics educators seeking to venture into the future better informed about both the successes and failures of previous projects. Understanding this project requires recognizing that the School Mathematics Study Group was wholly a product of the forces—personal, educational, mathematical, and political—that shaped it. Admittedly, some of the SMSG's shortcomings resulted from its members' lack of understanding of the changes needed in mathematics education. Still, the majority of the SMSG's public vilification resulted through no fault of ...

Determination Of The Traits In Leguminous Crops Under Saline Condition, 2021 Gulistan state University

#### Determination Of The Traits In Leguminous Crops Under Saline Condition, Tojiddin Kuliev, Karomat Ismailova

*Karakalpak Scientific Journal*

In this study, the variability and determination of genetic traits for winter legume crop varieties the Vostok-55 (*Pisum arvense** *L) and Mirzachul-1 (*Vicia villoza Roth** *L) were investigated under moderate saline soil condition. Results show that the weight of the bean was marked as variable and highly deterministic, and the height of the plants was the most stable. The selection of plants based on these traits is the most effective way of salinity. Both variety the forage pea Vostok-55 and vetch Mirzachul-1 is highly recommended as a sideration and forage crop in saline lands.

Compact Representations Of Uncertainty In Clustering, 2021 University of Massachusetts Amherst

#### Compact Representations Of Uncertainty In Clustering, Craig Stuart Greenberg

*Doctoral Dissertations*

Flat clustering and hierarchical clustering are two fundamental tasks, often used to discover meaningful structures in data, such as subtypes of cancer, phylogenetic relationships, taxonomies of concepts, and cascades of particle decays in particle physics. When multiple clusterings of the data are possible, it is useful to represent uncertainty in clustering through various probabilistic quantities, such as the distribution over partitions or tree structures, and the marginal probabilities of subpartitions or subtrees.

Many compact representations exist for structured prediction problems, enabling the efficient computation of probability distributions, e.g., a trellis structure and corresponding Forward-Backward algorithm for Markov models that ...

Stitching Dedekind Cuts To Construct The Real Numbers, 2021 Saint Edwards University

#### Stitching Dedekind Cuts To Construct The Real Numbers, Michael P. Saclolo

*Analysis*

No abstract provided.

Examining Middle School Students' Methods Of Justification, 2021 Undergraduate

#### Examining Middle School Students' Methods Of Justification, Leslie Reyes- Hernandez

*Mathematics*

Researching students’ thinking is imperative to improving the education system throughout the world. From extensive research, it is noted that students are unaccustomed and struggle with providing valid mathematical justifications (e.g. Inglis & Alcock 2012). The National Council of Teachers of Mathematics (NCTM, 2000) and Common Core State Standards of Mathematics (CCSSM, 2010) suggest that students should have several opportunities to construct mathematical arguments across all grade levels. To take a closer look at this educational phenomenon, we prompt fifth to eighth-grade students with nine mathematical tasks. Within our research, we focus on tasks based on number properties, algebraic thinking ...

Squigonometry, 2021 Undergraduate

#### Squigonometry, Andrew Hatfield, Riley Klette, Christopher Moore, Beth Warden

*Mathematics*

Trigonometry is the study of circular functions - functions defined on the unit circle where distances are measured with respect to the Euclidean norm. In our research, we develop a parallel theory of trigonometric and inverse trigonometric functions for the p-norm. This is called squigonometry because the resulting functions are defined on a squircle. This approach leads to new transcendental periods, formulas, and identities. It also extends to exponential, hyperbolic, and logarithmic functions in the p-norm.

Math 215: Introduction To Statistics, 2021 City University of New York (CUNY)

#### Math 215: Introduction To Statistics, Cuny School Of Professional Studies

*Open Educational Resources*

Introduces the basic principles of statistics and probability, with an emphasis on understanding the underlying concepts, real-world applications, and the underlying story that the numbers tell. Uses Microsoft Excel’s statistical functions to analyze data. Provides an introduction to probability, descriptive statistics, hypothesis testing, and inferential statistics.

Math 102: Mathematics In Contemporary Society, 2021 City University of New York (CUNY)

#### Math 102: Mathematics In Contemporary Society, Cuny School Of Professional Studies

*Open Educational Resources*

Designed to provide students with an understanding of the mathematical ideas and methods found in the social sciences, the arts, and business, this course covers the fundamentals of statistics, scatter plots, graphics in the media, problem-solving strategies, dimensional analysis, and mathematical modeling. Students can expect to explore real world applications.

Evaluation Of Broadcast Steam Application With Mustard Seed Meal In Fruiting Strawberry, 2021 University of California, Davis

#### Evaluation Of Broadcast Steam Application With Mustard Seed Meal In Fruiting Strawberry, Dong Sub Kim, Steven Kim, Steven A. Fennimore

*Mathematics and Statistics Faculty Publications and Presentations*

Soil disinfestation with steam has potential to partially replace fumigants such as methyl bromide, chloropicrin, and 1,3-dichloropropene because it is effective, safer to apply, and has less negative impact on the environment. Here, we compared the efficacy of steam and steam + mustard seed meal (MSM) to chloropicrin on soil disinfection, plant growth, and fruit yield in a strawberry (*Fragaria* ×*ananassa*) fruiting field. The MSM was applied at 3368 kg·ha−1 before the steam application. Steam was injected into a 3-m-wide reverse tiller that was set to till 30 to 40 cm deep. Soil temperatures at depths of 10 ...

Functional Singular Spectrum Analysis: Nonparametric Decomposition And Forecasting Approaches For Functional Time Series, 2021 Marquette University

#### Functional Singular Spectrum Analysis: Nonparametric Decomposition And Forecasting Approaches For Functional Time Series, Jordan Christopher Trinka

*Dissertations (1934 -)*

In this dissertation, we develop nonparametric decomposition methods and the subsequent forecasting techniques for functional, time-dependent data known as functional time series (FTS). We use ideas from functional data analysis (FDA) and singular spectrum analysis (SSA) to introduce the nonparametric decomposition method known as functional SSA (FSSA) and its associated forecasting techniques. We also extend these developed methodologies into multivariate FSSA (MFSSA) over different dimensional domains and its subsequent forecasting routines so that we may perform nonparametric decomposition and prediction of multivariate FTS (MFTS). The FSSA algorithm may be viewed as a signal extraction technique and we find that the ...

Mathematical Modeling In Finance, 2021 Grand Valley State University

#### Mathematical Modeling In Finance, Owen Sweeney

*Honors Projects*

Financial tools play an integral role in the day-to-day lives of individuals and businesses. Many of these tools use predefined formulas to calculate items such as loan payments, interest and capital structure components. These tools do not usually provide the flexibility needed when new parameters are introduced. By utilizing mathematical modeling, these standard formulas can be derived and even improved to provide the needed flexibility.

A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, 2021 Old Dominion University

#### A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Gamage, Yan Peng

*College of Sciences Posters*

Interface problems have many applications in fluid dynamics, molecular biology, electromagnetism, material science, heat distribution in engines, and hyperthermia treatment of cancer. Mathematically, interface problems commonly lead to partial differential equations (PDE) whose in- put data are discontinuous or singular across the interfaces in the solution domain. Many standard numerical methods designed for smooth solutions poorly work for interface problems as solutions of the interface problems are mostly non-smoothness or discontinuous. Moving interface problems depends on the accuracy of the gradient of the solution at the interface. Therefore, it became essential to derive a method for interface problems that gives ...

Math 120 Precalculus Review, 2021 CUNY York College

#### Math 120 Precalculus Review, York College Math 120 Students, Virginia L. Thompson

*Open Educational Resources*

No abstract provided.

The Fundamental Limit Theorem Of Countable Markov Chains, 2021 Liberty University

#### The Fundamental Limit Theorem Of Countable Markov Chains, Nathanael Gentry

*Senior Honors Theses*

In 1906, the Russian probabilist A.A. Markov proved that the independence of a sequence of random variables is not a necessary condition for a law of large numbers to exist on that sequence. Markov's sequences -- today known as Markov chains -- touch several deep results in dynamical systems theory and have found wide application in bibliometrics, linguistics, artificial intelligence, and statistical mechanics. After developing the appropriate background, we prove a modern formulation of the law of large numbers (fundamental theorem) for simple countable Markov chains and develop an elementary notion of ergodicity. Then, we apply these chain convergence results ...

A University Forest Fire: Examining The Spread Of The Coronavirus Through College Social Networks Using A Modified Forest Fire Probabilistic Model, 2021 University of Rhode Island

#### A University Forest Fire: Examining The Spread Of The Coronavirus Through College Social Networks Using A Modified Forest Fire Probabilistic Model, Raechel Griffin

*Senior Honors Projects*

No abstract provided.

Free Semigroupoid Algebras From Categories Of Paths, 2021 University of Nebraska-Lincoln

#### Free Semigroupoid Algebras From Categories Of Paths, Juliana Bukoski

*Dissertations, Theses, and Student Research Papers in Mathematics*

Given a directed graph *G*, we can define a Hilbert space *H _{G}* with basis indexed by the path space of the graph, then represent the vertices of the graph as projections on

*H*and the edges of the graph as partial isometries on

_{G}*H*. The weak operator topology closed algebra generated by these projections and partial isometries is called the free semigroupoid algebra for

_{G}*G*. Kribs and Power showed that these algebras are reflexive, and that they are semisimple if and only if each path in the graph lies on a cycle. We extend the free semigroupoid ...

Gauge-Invariant Uniqueness And Reductions Of Ordered Groups, 2021 University of Nebraska-Lincoln

#### Gauge-Invariant Uniqueness And Reductions Of Ordered Groups, Robert Huben

*Dissertations, Theses, and Student Research Papers in Mathematics*

A reduction φ of an ordered group (G,P) to another ordered group is an order homomorphism which maps each interval [1, p] bijectively onto [1, φ(p)]. We show that if (G,P) is weakly quasi-lattice ordered and reduces to an amenable ordered group, then there is a gauge-invariant uniqueness theorem for P -graph algebras. We also consider the class of ordered groups which reduce to an amenable ordered group, and show this class contains all amenable ordered groups and is closed under direct products, free products, and hereditary subgroups.

Adviser: Mark Brittenham and David Pitts

Mathematical Modeling Of The Candida Albicans Yeast To Hyphal Transition Reveals Novel Control Strategies, 2021 Pennsylvania State University

#### Mathematical Modeling Of The Candida Albicans Yeast To Hyphal Transition Reveals Novel Control Strategies, David J. Wooten, Jorge Gómez Tejeda Zañudo, David Murrugarra, Austin M. Perry, Anna Dongari-Bagtzoglou, Reinhard Laubenbacher, Clarissa J. Nobile, Réka Albert

*Mathematics Faculty Publications*

*Candida albicans*, an opportunistic fungal pathogen, is a significant cause of human infections, particularly in immunocompromised individuals. Phenotypic plasticity between two morphological phenotypes, yeast and hyphae, is a key mechanism by which *C*. *albicans* can thrive in many microenvironments and cause disease in the host. Understanding the decision points and key driver genes controlling this important transition and how these genes respond to different environmental signals is critical to understanding how *C*. *albicans* causes infections in the host. Here we build and analyze a Boolean dynamical model of the *C*. *albicans* yeast to hyphal transition, integrating multiple environmental factors and ...

Entropic Dynamics Of Networks, 2021 Department of Physics, University at Albany, State University of New York

#### Entropic Dynamics Of Networks, Felipe Xavier Costa, Pedro Pessoa

*Northeast Journal of Complex Systems (NEJCS)*

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into account the natural information geometry of probability distributions. We apply this framework to the Gibbs distribution of random graphs obtained with constraints on the node connectivity. The information geometry for this graph ensemble is calculated and the dynamical process is obtained as a diffusion equation. We compare the steady state of this dynamics to degree distributions found on real-world networks.