Enhanced Koszulity In Galois Cohomology, 2019 The University of Western Ontario

#### Enhanced Koszulity In Galois Cohomology, Marina Palaisti

*Electronic Thesis and Dissertation Repository*

Despite their central role in Galois theory, absolute Galois groups remain rather mysterious; and one of the main problems of modern Galois theory is to characterize which profinite groups are realizable as absolute Galois groups over a prescribed field. Obtaining detailed knowledge of Galois cohomology is an important step to answering this problem. In our work we study various forms of enhanced Koszulity for quadratic algebras. Each has its own importance, but the common ground is that they all imply Koszulity. Applying this to Galois cohomology, we prove that, in all known cases of finitely generated pro-$p$-groups, Galois ...

Prediction Of Stress Increase At Ultimate In Unbonded Tendons Using Sparse Principal Component Analysis, 2019 Utah State University

#### Prediction Of Stress Increase At Ultimate In Unbonded Tendons Using Sparse Principal Component Analysis, Eric Mckinney, Minwoo Chang, Marc Maguire, Yan Sun

*Mathematics and Statistics Faculty Publications*

While internal and external unbonded tendons are widely utilized in concrete structures, an analytical solution for the increase in unbonded tendon stress at ultimate strength, Δ𝑓𝑝𝑠, is challenging due to the lack of bond between strand and concrete. Moreover, most analysis methods do not provide high correlation due to the limited available test data. The aim of this paper is to use advanced statistical techniques to develop a solution to the unbonded strand stress increase problem, which phenomenological models by themselves have done poorly. In this paper, Principal Component Analysis (PCA), and Sparse Principal Component Analysis (SPCA) are employed on ...

Predicting Time To Dementia Using A Quantitative Template Of Disease Progression, 2019 National Institutes of Health

#### Predicting Time To Dementia Using A Quantitative Template Of Disease Progression, Murat Bilgel, Bruno Jedynak

*Bruno Jedynak*

*Introduction*: Characterization of longitudinal trajectories of biomarkers implicated in sporadic Alzheimer's disease (AD) in decades prior to clinical diagnosis is important for disease prevention and monitoring.

*Methods*: We used a multivariate Bayesian model to temporally align 1369 AD Neuroimaging Initiative participants based on the similarity of their longitudinal biomarker measures and estimated a quantitative template of the temporal evolution cerebrospinal fluid (CSF) Aβ_{1-42}, p-tau_{181p}, and t-tau, hippocampal volume, brain glucose metabolism, and cognitive measurements. We computed biomarker trajectories as a function of time to AD dementia, and predicted AD dementia onset age in a disjoint sample.

*Results ...*

Pascal's Triangle Modulo N And Its Applications To Efficient Computation Of Binomial Coefficients, 2019 University of Nebraska - Lincoln

#### Pascal's Triangle Modulo N And Its Applications To Efficient Computation Of Binomial Coefficients, Zachary Warneke

*Honors Theses, University of Nebraska-Lincoln*

In this thesis, Pascal's Triangle modulo *n* will be explored for *n* prime and *n* a prime power. Using the results from the case when *n* is prime, a novel proof of Lucas' Theorem is given. Additionally, using both the results from the exploration of Pascal's Triangle here, as well as previous results, an efficient algorithm for computation of binomial coefficients modulo *n* (*a* choose *b* mod *n*) is described, and its time complexity is analyzed and compared to naive methods. In particular, the efficient algorithm runs in *O*(*n* log(*a*)) time (as opposed to the naive ...

Drones And “Ghost Guns”: Unregulated Legal Space, 2019 Utah State University

#### Drones And “Ghost Guns”: Unregulated Legal Space, Tori Bodine

*Research on Capitol Hill*

Law enforcement agencies are fighting a two - pronged battle when it comes to emerging technologies: keeping up with new ways criminals are using technology and developing effective ways to combat these innovations, while balancing these challenges against preserving the individual liberties of law - abiding citizens. This conflict is especially apparent with regard to criminal use of commercial drones and the developing fringe market surrounding homemade untraceable firearms (“ghost guns”).

The Duals Of *-Operator Frames For End*A(H), 2019 Nova Southeastern University

#### The Duals Of *-Operator Frames For End*A(H), Abdelkrim Bourouihiya, M. Rossafi, H. Labrigui, A. Touri

*Abdelkrim Bourouihiya*

Frames play significant role in signal and image processing, which leads to many applications in differents fields. In this paper we define the dual of ∗-operator frames and we show their propreties obtained in Hilbert *A*-modules and we establish some results.

Heterogeneous Boolean Networks With Two Totalistic Rules, 2019 University of Nebraska at Omaha

#### Heterogeneous Boolean Networks With Two Totalistic Rules, Katherine Toh

*Student Research and Creative Activity Fair*

Boolean Networks are being used to analyze models in biology, economics, social sciences, and many other areas. These models simplify the reality by assuming that each element in the network can take on only two possible values, such as ON and OFF. The node evolution is governed by its interaction with other nodes in its neighborhood, which is described mathematically by a Boolean function or rule. For simplicity reasons, many models assume that all nodes follow the same Boolean rule. However, real networks often use more than one Boolean rule and therefore are heterogeneous networks. Heterogeneous networks have not yet ...

Fourier Series Expansion Methods For The Heat And Wave Equations In Two And Three Dimensions On Spherical Domains, 2019 University of Nebraska at Omaha

#### Fourier Series Expansion Methods For The Heat And Wave Equations In Two And Three Dimensions On Spherical Domains, Matthew Eller

*Student Research and Creative Activity Fair*

**Description**: The Fourier series expansion method is an invaluable approach to solving partial differential equations, including the heat and wave equations. For homogeneous heat and wave equations, the solution can readily be found through separation of variables and then expansion of the solution in terms of the eigenfunctions. Solutions to inhomogeneous heat and wave equations through Fourier series expansion methods were not readily available in the literature for two- and three-dimensional cases. In my previous paper, I developed an approach for solving inhomogeneous heat and wave equations on cubic domains using Fourier series expansion methods. I shall extend my general ...

Forensics Analysis For Bone Pair Matching Using Bipartite Graphs In Commingled Remains, 2019 University of Nebraska at Omaha

#### Forensics Analysis For Bone Pair Matching Using Bipartite Graphs In Commingled Remains, Ryan Ernst

*Student Research and Creative Activity Fair*

Identification of missing prisoners of war is a complex and time consuming task. There are many missing soldiers whose remains have yet to be returned to their families and loved ones. This nation has a solemn obligation to its soldiers and their families who have made the ultimate sacrifice for their country. There are currently over 82,000 unidentified prisoners of war which are identified at a rate of 100+ per year. At this rate it would take 300+ years to complete the identification process. Previously, anthropologists used excel spreadsheets to sort through skeletal data. This project aims to streamline ...

Experience Of A Noyce-Student Learning Assistant In An Inquiry-Based Learning Class, 2019 University of Nebraska at Omaha

#### Experience Of A Noyce-Student Learning Assistant In An Inquiry-Based Learning Class, Melissa Riley

*Student Research and Creative Activity Fair*

This presentation refers to an undergraduate course called introduction to abstract mathematics at the University of Nebraska at Omaha. During the academic year 2017-2018, undergraduate, mathematics student Melissa Riley was a Noyce-student learning assistant for the Inquiry Based Learning (IBL) section of the course. She assisted the faculty-in-charge with all aspects of the course. These included: materials preparation, class organization, teamwork, class leading, presentations, and tutoring. This presentation shall address some examples of how the IBL approach can be used in this type of class including: the structure of the course, the activities and tasks performed by the students, learning ...

Large Scale Dynamical Model Of Macrophage/Hiv Interactions, 2019 University of Nebraska at Omaha

#### Large Scale Dynamical Model Of Macrophage/Hiv Interactions, Sean T. Bresnahan, Matthew M. Froid

*Student Research and Creative Activity Fair*

Properties emerge from the dynamics of large-scale molecular networks that are not discernible at the individual gene or protein level. Mathematical models - such as probabilistic Boolean networks - of molecular systems offer a deeper insight into how these emergent properties arise. Here, we introduce a non-linear, deterministic Boolean model of protein, gene, and chemical interactions in human macrophage cells during HIV infection. Our model is composed of 713 nodes with 1583 interactions between nodes and is responsive to 38 different inputs including signaling molecules, bacteria, viruses, and HIV viral particles. Additionally, the model accurately simulates the dynamics of over 50 different ...

Dense Geometry Of Music And Visual Arts: Vanishing Points, Continuous Tonnetz, And Theremin Performance, 2019 Independent researcher, Palermo, Italy

#### Dense Geometry Of Music And Visual Arts: Vanishing Points, Continuous Tonnetz, And Theremin Performance, Maria Mannone, Irene Iaccarino, Rosanna Iembo

*The STEAM Journal*

The dualism between continuous and discrete is relevant in music theory as well as in performance practice of musical instruments. Geometry has been used since longtime to represent relationships between notes and chords in tonal system. Moreover, in the field of mathematics itself, it has been shown that the continuity of real numbers can arise from geometrical observations and reasoning. Here, we consider a geometrical approach to generalize representations used in music theory introducing continuous pitch. Such a theoretical framework can be applied to instrument playing where continuous pitch can be naturally performed. Geometry and visual representations of concepts of ...

Parametric Natura Morta, 2019 Independent researcher, Palermo, Italy

#### Parametric Natura Morta, Maria C. Mannone

*The STEAM Journal*

Parametric equations can also be used to draw fruits, shells, and a cornucopia of a mathematical still life. Simple mathematics allows the creation of a variety of shapes and visual artworks, and it can also constitute a pedagogical tool for students.

Unfolding Humanity: Cross-Disciplinary Sculpture Design, 2019 University of San Diego

#### Unfolding Humanity: Cross-Disciplinary Sculpture Design, Gordon D. Hoople, Nate Parde, Quinn Pratt, Sydney Platt, Michael Sween, Ava Bellizzi, Viktoriya Alekseyeva, Alex Splide, Nicholas Cardoza, Christiana Salvosa, Eduardo Ortega, Elizabeth Sampson

*The STEAM Journal*

Unfolding Humanity is a 12 foot tall, 30 foot wide, 2 ton interactive metal sculpture that calls attention to the tension between technology and humanity. This sculpture was conceived, designed, and built by a large group (80+) of faculty, students, and community volunteers at the University of San Diego (USD). The piece is a dodecahedron whose pentagonal walls unfold under human power, an engineered design that alludes to Albrecht Dürer's 500-year-old unsolved math problem on unfolding polyhedra. When closed, the mirrored interior of the sculpture makes visitors feel as though they are at the center of the universe. The ...

Predicting Time To Dementia Using A Quantitative Template Of Disease Progression, 2019 National Institutes of Health

#### Predicting Time To Dementia Using A Quantitative Template Of Disease Progression, Murat Bilgel, Bruno Jedynak

*Portland Institute for Computational Science Publications*

*Introduction*: Characterization of longitudinal trajectories of biomarkers implicated in sporadic Alzheimer's disease (AD) in decades prior to clinical diagnosis is important for disease prevention and monitoring.

*Methods*: We used a multivariate Bayesian model to temporally align 1369 AD Neuroimaging Initiative participants based on the similarity of their longitudinal biomarker measures and estimated a quantitative template of the temporal evolution cerebrospinal fluid (CSF) Aβ_{1-42}, p-tau_{181p}, and t-tau, hippocampal volume, brain glucose metabolism, and cognitive measurements. We computed biomarker trajectories as a function of time to AD dementia, and predicted AD dementia onset age in a disjoint sample.

*Results ...*

How To Build A Human Brain: Evolution, Development, And Education, 2019 University of California, Los Angeles

#### How To Build A Human Brain: Evolution, Development, And Education, Aaron P. Blaisdell

*Journal of Evolution and Health*

No abstract provided.

Effective Questioning, 2019 Illinois Mathematics and Science Academy

#### Effective Questioning, Janice Krouse, Marti Shirley

*Faculty Publications & Research*

Three Major Findings

- Tasks are not created equal: they provide different opportunities for student learning and thinking.
- Tasks that encourage high level thinking and reasoning have the greatest student success. Student success is lowest where tasks are procedural.
- Tasks with high cognitive demand are the hardest to implement and often are transformed into less demanding tasks during instruction.

Context Is Critical: K-5th Grade Three-Act Math Tasks, 2019 Illinois Mathematics and Science Academy

#### Context Is Critical: K-5th Grade Three-Act Math Tasks, Lindsey Herlehy

*Publications & Research*

Mathematicians view mathematics within interesting and natural contexts. In this session, participants will engage and explore Three-Act Math Tasks; a story-telling pedagogical strategy that elicits student curiosity, collaboration, and questioning while redefining the term “real-world context” and the role that students play in the learning process. Resources will be provided

Forgotten Women In Adventism, 2019 Andrews University

#### Forgotten Women In Adventism, Caitlin Jankiewicz

*Lake Union Herald*

No abstract provided.

Arithmetic (Book Review), 2019 Dordt College

#### Arithmetic (Book Review), Calvin Jongsma

*Faculty Work Comprehensive List*

Reviewed Title: *Arithmetic* by Paul Lockhart. Cambridge, MA: Harvard University Press, 2017. 223 pp. ISBN: 9780674972230.