Digital Commons Network^™

Maximum Spatial Perturbation Consistency For Unpaired Image-To-Image Translation, Yanwu Xu, Shaoan Xie, Wenhao Wu, Kun Zhang, Mingming Gong, Kayhan Batmanghelich

Machine Learning Faculty Publications

Unpaired image-to-image translation (I2I) is an ill-posed problem, as an infinite number of translation functions can map the source domain distribution to the target distribution. Therefore, much effort has been put into designing suitable constraints, e.g., cycle consistency (CycleGAN), geometry consistency (GCGAN), and contrastive learning-based constraints (CUTGAN), that help better pose the problem. However, these well-known constraints have limitations: (1) they are either too restrictive or too weak for specific I2I tasks; (2) these methods result in content distortion when there is a significant spatial variation between the source and target domains. This paper proposes a universal regularization technique called …

Review Of The History Of Mathematics: A Source-Based Approach (Vol. 2), Part I, Erik R. Tou

Euleriana

Review of The History of Mathematics: A Source-Based Approach (Vol. 2), Part I, by June Barrow-Green, Jeremy Gray, and Robin Wilson. MAA Press, 2022, 330 + xiv pages.

Influence Of Specimen Geometry And Anisotropy On Dynamic Modulus Of Asphalt Mixes In South Carolina, Srinivasan Nagarajan

All Dissertations

The objective of this study was to characterize the variability of dynamic modulus of asphalt mixes in South Carolina on the basis of geometry and anisotropy. High priority mixes Surface Type B, and C; Intermediate Type B and C and Base Type A from three different days of production were collected from seven different contractors each having a different aggregate source and the dynamic modulus was measured using the Asphalt Mixture Performance Tester (AMPT) at temperatures of 40, 70, 100 and 130℉ (4.4, 21.1, 37.8, and 54.4℃) and at frequencies of 25, 10, 5, 1, 0.5, and 0.1 Hz. One-way …

Geometric Analysis Of Insect Wing Vein Network, Jacob White, Ying Hu, Sangjin Ryu, Seunghee Kim, Haipeng Zhang

Department of Mechanical and Materials Engineering: Faculty Publications

An insect wing consists of a thin membrane supported by a system of veins, and flow of blood through the system of veins is critical for maintaining healthy insect wings. Better understanding of the insect wing vein circulation requires to know how the efficiency of blood flow in an insect wing relates to the geometric shape of the vein. Our investigation of the wing vein network of a dragonfly Anax junius follows the idea of Murray’s law, which is established in the study of efficiency of the vein network and the geometric shape of the vein. Instead of using the …

Equidistant Sets In Spaces Of Bounded Curvature, Logan Scott Fox

Dissertations and Theses

Given a metric space (X,d), and two nonempty subsets A,B ⊆ X, we study the properties of the set of points of equal distance to A and B, which we call the equidistant set E(A,B). In general, the structure of the equidistant set is quite unpredictable, so we look for conditions on the ambient space, as well as the given subsets, which lead to some regularity of the properties of the equidistant set. At a minimum, we will always require that X is path connected (so that E( …

Nature, Growth & Design: Architectural Investigations Into The Role Of Space-Making, Tate Baker

Bachelor of Architecture Theses - 5th Year

Nature and natural spaces have an inherent logic to them. Related to this logic is the inherent and characteristic ability of nature to create a sense of belonging. The purpose of this thesis is to explore the inherent logic found in nature in order to better understand the process of space-making, and to co-opt these natural principles in order to create a design intervention that mimics the natural experience.

Impact Of Stability And Control On Vehicle Geometry And Performance: A Design Study On Traditional Hypersonic Vehicles Vs Controlled Configured Hypersonic Vehicles, Juan Camilo Buritica Yate

2022 Spring Honors Capstone Projects

Hypersonic vehicles have been in development for over 60 years, yet a control-configure-vehicle has yet to be designed to understand the possible improvements over statically stable configurations. This paper studies the effect of stability and control on aircraft geometry and performance by comparing traditional vehicles versus control configured vehicles (CCV) that operate at subsonic and supersonic speeds and extrapolates this analysis to predict these effects on hypersonic vehicles. Data related to geometry, aerodynamic performance, and stability from various vehicles were collected and used to find trends by comparing aircraft design parameters to stability criteria. The results showed that by decreasing …

Sangaku In Multiple Geometries: Examining Japanese Temple Geometry Beyond Euclid, Nathan Hartmann

Honors College Theses

When the country of Japan was closed from the rest of the world from 1603 until
1867 during the Edo period, the field of mathematics developed in a different way
from how it developed in the rest of the world. One way we see this development
is through the sangaku, the thousands of geometric problems hung in various Shinto and Buddhist temples throughout the country. Written on wooden tablets by people from numerous walks of life, all these problems hold true within Euclidean geometry. During the 1800s, while Japan was still closed, non-Euclidean geometries began to develop across the …

Release Of Large Water Droplets, Jeffrey N. Fonnesbeck

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Water is familiar to all human beings and water droplets are an integral part of our daily lives. From irrigation sprinklers to waterfalls we can observe the formation of water droplets. For most, the droplets are so common and mundane that no thought is given to how the droplets form. Scientists have spent many decades detailing the processes that lead to droplet formation. Current theories and experiments agree quite well for specific cases such as pendant drop formation and jet breakup, but in regards to large volumes of free falling liquid there is very little experimental work to confirm the …

How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli

The Review: A Journal of Undergraduate Student Research

The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …

Math Basics Afterschool Club, Lexi Soukup, Meg Williams

Honors Expanded Learning Clubs

This is a compilation of Lexi Soukup and Meg Williams’ work as Club Leaders in an Afterschool Club run through the University of Nebraska- Lincoln and YMCA Afterschool Programs titled Math Basics. Our club is an interactive, hands-on math exploration where students are challenged to change their perspective of math, and it is meant to occur once weekly. During this club, we try to challenge their current views of math and expand their knowledge on math concepts they learn in class through activities and games. This is meant to make math FUN! Our compilation of lesson plans are sure to …

Transformnet: Self-Supervised Representation Learning Through Predicting Geometric Transformations, Hashim Sayed, Muhammad Ali

Student Publications

Deep neural networks need a big amount of training data, while in the real world there is a scarcity of data available for training purposes. To resolve this issue unsupervised methods are used for training with limited data. In this report, we describe the unsupervised semantic feature learning approach for recognition of the geometric transformation applied to the input data. The basic concept of our approach is that if someone is unaware of the objects in the images, he/she would not be able to quantitatively predict the geometric transformation that was applied to them. This self supervised scheme is based …

Making Upper-Level Math Accessible To A Younger Audience, Allyson Roller

WWU Honors College Senior Projects

Symmetry is all around us. It appears on fabrics and on the buildings that surround us. Believe it or not, there is actually quite a bit of math that goes into generating these patterns, which are known as the seven frieze patterns. In my work, I explain how each unique pattern is generated using different types of symmetries. I also created a PDF of a children’s book about frieze patterns to ensure that people of all ages have the opportunity to learn about seemingly complex patterns.

The Plight Of Western Rivers, W. Howard Brandenburg

Natural Resources Journal

My oil paintings weave a narrative about the human species. I am interested in the space where our proliferation infringes upon ecosystem function. I am fascinated in what makes our species so successful and what that success means for the balance of nature. My paintings often target concepts around environmental transformations attributed to human activities and economies. Visual art provides me the latitude and freedom to explore and communicate these concepts, using a visual language which conveys disparate perspectives; universally and individualistically.

This duality is what I strive for in my work; producing an image that not only speaks a …

Cache Code Math Mathematics Lesson Plans: Geometry, Jody Clarke-Midura, Jessica Shumway, Kimberly Beck, Umar Shehzad, Mimi Recker

Instructional resources

This document is comprised of a set of six 5^th grade mathematics lesson plans. The lessons are intended to be implemented in conjunction with the computer lab activities “Jump Using My Blocks and Variables,” “Guess the Triangle,” and “Guess the Quadrilateral.” Geometry concepts (classifying triangles and quadrilaterals) are paired with computer coding concepts of conditionals and variables.

Counting The Moduli Space Of Pentagons On Finite Projective Planes, Maxwell Hosler

Senior Independent Study Theses

Finite projective planes are finite incidence structures which generalize the concept of the real projective plane. In this paper, we consider structures of points embedded in these planes. In particular, we investigate pentagons in general position, meaning no three vertices are colinear. We are interested in properties of these pentagons that are preserved by collineation of the plane, and so can be conceived as properties of the equivalence class of polygons up to collineation as a whole. Amongst these are the symmetries of a pentagon and the periodicity of the pentagon under the pentagram map, and a generalization of …

The Reciprocal Of The Butterfly Theorem, Ion Patrascu, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.