Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, 2018 Utah State University

#### Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

*All Graduate Plan B and other Reports*

Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms ...

Color Space Standardization And Image Analysis For High-Throughput Phenotyping Of Sorghum Bicolor, 2018 Department of Mathematics, Illinois State University

#### Color Space Standardization And Image Analysis For High-Throughput Phenotyping Of Sorghum Bicolor, Alexandria A. Pokorny

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Transformations On Double Occurrence Words Motivated By Dna Rearrangement, 2018 University of South Florida

#### Transformations On Double Occurrence Words Motivated By Dna Rearrangement, Daniel Cruz, Margherita Maria Ferrari, Lukas Nabergall, Natasa Jonoska, Masahico Saito

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Semi-Tensor Product Representations Of Boolean Networks, 2018 Illinois State University

#### Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, 2018 Illinois State University

#### The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Combinatorial Geometry Of Threshold-Linear Networks, 2018 Illinois State University

#### Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Topological Detection Of The Dimension Of The Stimuli Space, 2018 Illinois State University

#### Topological Detection Of The Dimension Of The Stimuli Space, Aliaksandra Yarosh

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, 2018 Illinois State University

#### Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Otto Holder's Formal Christening Of The Quotient Group Concept, 2018 Colorado State University-Pueblo

#### Otto Holder's Formal Christening Of The Quotient Group Concept, Janet Heine Barnett

*Abstract Algebra*

No abstract provided.

Microstructure Design Using Graphs, 2018 Iowa State University

#### Microstructure Design Using Graphs, Pengfei Du, Adrian Zebrowski, Jaroslaw Zola, Baskar Ganapathysubramanian, Olga Wodo

*Mechanical Engineering Publications*

Thin films with tailored microstructures are an emerging class of materials with applications such as battery electrodes, organic electronics, and biosensors. Such thin film devices typically exhibit a multi-phase microstructure that is confined, and show large anisotropy. Current approaches to microstructure design focus on optimizing bulk properties, by tuning features that are statistically averaged over a representative volume. Here, we report a tool for morphogenesis posed as a graph-based optimization problem that evolves microstructures recognizing confinement and anisotropy constraints. We illustrate the approach by designing optimized morphologies for photovoltaic applications, and evolve an initial morphology into an optimized morphology exhibiting ...

Equivalent Constructions Of Cartan Pairs, 2018 University of New Mexico

#### Equivalent Constructions Of Cartan Pairs, Phung Thanh Tran

*Math Theses*

Feldman and Moore [4] introduce Cartan subalgebra of the von Neumann algebra M on a separable Hilbert space H from the natural subalgebra of M(R, sigma), the twisted algebra of matrices over the relation R on a Borel space (X, B, muy). They show that if M has a Cartan subalgebra A, then M is isomorphic to M(R, sigma) where A is the twisted algebra onto the diagonal subalgebra L^inf (X, muy). The relation R is unique to isomorphism and the orbit of the two-cohomology class on R in the torus T, which is the automorphism group ...

Stranded Cellular Automaton And Weaving Products, 2018 Rose-Hulman Institute of Technology

#### Stranded Cellular Automaton And Weaving Products, Hao Yang

*Mathematical Sciences Technical Reports (MSTR)*

In order to analyze weaving products mathematically and find out valid weaving products, it is natural to relate them to Cellular Automaton. They are both generated based on specific rules and some initial conditions. Holden and Holden have created a Stranded Cellular Automaton that can represent common weaving and braiding products. Based on their previous findings, we were able to construct a Java program and analyze various aspects of the automaton they created. This paper will discuss the complexity of the Stranded Cellular Automaton, how to determine whether a weaving product holds together or not based on the automaton and ...

Tutte-Equivalent Matroids, 2018 California State University - San Bernardino

#### Tutte-Equivalent Matroids, Maria Margarita Rocha

*Electronic Theses, Projects, and Dissertations*

We begin by introducing matroids in the context of finite collections of vectors from a vector space over a specified field, where the notion of independence is linear independence. Then we will introduce the concept of a matroid invariant. Specifically, we will look at the Tutte polynomial, which is a well-defined two-variable invariant that can be used to determine differences and similarities between a collection of given matroids. The Tutte polynomial can tell us certain properties of a given matroid (such as the number of bases, independent sets, etc.) without the need to manually solve for them. Although the Tutte ...

Elementary Set Theory, 2018 University of North Dakota

#### Elementary Set Theory, Richard P. Millspaugh

*Open Educational Resources*

This text is appropriate for a course that introduces undergraduates to proofs. The material includes elementary symbolic logic, logical arguments, basic set theory, functions and relations, the real number system, and an introduction to cardinality. The text is intended to be readable for sophomore and better freshmen majoring in mathematics.

The Philosophical Foundations Of Plen: A Protocol-Theoretic Logic Of Epistemic Norms, 2018 The Graduate Center, City University of New York

#### The Philosophical Foundations Of Plen: A Protocol-Theoretic Logic Of Epistemic Norms, Ralph E. Jenkins

*All Dissertations, Theses, and Capstone Projects*

In this dissertation, I defend the protocol-theoretic account of epistemic norms. The protocol-theoretic account amounts to three theses: (i) There are norms of epistemic rationality that are procedural; epistemic rationality is at least partially defined by rules that restrict the possible ways in which epistemic actions and processes can be sequenced, combined, or chosen among under varying conditions. (ii) Epistemic rationality is ineliminably defined by procedural norms; procedural restrictions provide an irreducible unifying structure for even apparently non-procedural prescriptions and normative expressions, and they are practically indispensable in our cognitive lives. (iii) These procedural epistemic norms are best analyzed in ...

Galois Groups Of Differential Equations And Representing Algebraic Sets, 2018 The Graduate Center, City University of New York

#### Galois Groups Of Differential Equations And Representing Algebraic Sets, Eli Amzallag

*All Dissertations, Theses, and Capstone Projects*

The algebraic framework for capturing properties of solution sets of differential equations was formally introduced by Ritt and Kolchin. As a parallel to the classical Galois groups of polynomial equations, they devised the notion of a differential Galois group for a linear differential equation. Just as solvability of a polynomial equation by radicals is linked to the equation’s Galois group, so too is the ability to express the solution to a linear differential equation in "closed form" linked to the equation’s differential Galois group. It is thus useful even outside of mathematics to be able to compute and ...

Studying The Space Of Almost Complex Structures On A Manifold Using De Rham Homotopy Theory, 2018 The Graduate Center, City University of New York

#### Studying The Space Of Almost Complex Structures On A Manifold Using De Rham Homotopy Theory, Bora Ferlengez

*All Dissertations, Theses, and Capstone Projects*

In his seminal paper *Infinitesimal Computations in Topology*, Sullivan constructs algebraic models for spaces and then computes various invariants using them. In this thesis, we use those ideas to obtain a finiteness result for such an invariant (the de Rham homotopy type) for each connected component of the space of cross-sections of certain fibrations. We then apply this result to differential geometry and prove a finiteness theorem of the de Rham homotopy type for each connected component of the space of almost complex structures on a manifold. As a special case, we discuss the space of almost complex structures on ...

Identification Of Biologically Essential Nodes Via Determinative Power In Logical Models Of Cellular Processes, 2018 University of Nebraska at Omaha

#### Identification Of Biologically Essential Nodes Via Determinative Power In Logical Models Of Cellular Processes, Trevor Pentzien, Bhanwar L. Puniya, Tomáš Helikar, Mihaela T. Matache

*Mathematics Faculty Publications*

A variety of biological networks can bemodeled as logical or Boolean networks. However, a simplification of the reality to binary states of the nodes does not ease the difficulty of analyzing the dynamics of large, complex networks, such as signal transduction networks, due to the exponential dependence of the state space on the number of nodes. This paper considers a recently introduced method for finding a fairly small subnetwork, representing a collection of nodes that determine the states of most other nodes with a reasonable level of entropy. The subnetwork contains the most determinative nodes that yield the highest information ...

Yelp’S Review Filtering Algorithm, 2018 Southern Methodist University

#### Yelp’S Review Filtering Algorithm, Yao Yao, Ivelin Angelov, Jack Rasmus-Vorrath, Mooyoung Lee, Daniel W. Engels

*SMU Data Science Review*

In this paper, we present an analysis of features influencing Yelp's proprietary review filtering algorithm. Classifying or misclassifying reviews as *recommended* or *non-recommended* affects average ratings, consumer decisions, and ultimately, business revenue. Our analysis involves systematically sampling and scraping Yelp restaurant reviews. Features are extracted from review metadata and engineered from metrics and scores generated using text classifiers and sentiment analysis. The coefficients of a multivariate logistic regression model were interpreted as quantifications of the relative importance of features in classifying reviews as recommended or non-recommended. The model classified review recommendations with an accuracy of 78%. We found that ...

High Performance Sparse Multivariate Polynomials: Fundamental Data Structures And Algorithms, 2018 The University of Western Ontario

#### High Performance Sparse Multivariate Polynomials: Fundamental Data Structures And Algorithms, Alex Brandt

*Electronic Thesis and Dissertation Repository*

Polynomials may be represented sparsely in an effort to conserve memory usage and provide a succinct and natural representation. Moreover, polynomials which are themselves sparse – have very few non-zero terms – will have wasted memory and computation time if represented, and operated on, densely. This waste is exacerbated as the number of variables increases. We provide practical implementations of sparse multivariate data structures focused on data locality and cache complexity. We look to develop high-performance algorithms and implementations of fundamental polynomial operations, using these sparse data structures, such as arithmetic (addition, subtraction, multiplication, and division) and interpolation. We revisit a sparse ...