A C-complex is a union of Seifert surfaces for the components of a link which intersect each other in clasps. The clasp number of a link is the minimal number of clasps amongst all C-complexes it bounds It gives a measure of complexity and can be used to provide bounds on other useful characteristics of a link. This paper provides a new lower bound for the number of clasps of all C-complexes bounded by a given 3-component link improving results of Amundsen-Anderson-D.-Guyer. Furthermore, we construct links that achieve these bounds. In order to do so, we express the triple linking numbers as the area bounded by three curves, called word curves, and then perform the geometry and discrete optimization needed to minimize the length of these curves.
Some people call it a new “miracle drug.” Others are far more skeptical. However, one thing is certain: the surge in popularity of weight-loss drugs around the country is not going unnoticed. With obesity rates in the United States reaching over 40%, people are eager to find new ways to develop healthier lifestyles. Also known as Anti-Obesity Medications (AOMs), these drugs are still relatively new to the market and carry high, ongoing costs. Our research seeks to create an actuarial model to evaluate the financial impact of covering AOMs within employer-sponsored health plans. Current research on this subject is limited and studies that are available reflect conflicting results. We seek to create an accessible (Excel-based), functioning ROI model for AOM coverage that accounts for drug costs, expected utilization, weight-related risk reduction, and future medical cost offsets. We believe that the successful production of a dependable actuarial model could help employers make a more informed choice when it comes to the coverage of AOMs for their employees.
A C-complex is a union of Seifert surfaces for the components of a link which intersect each other in clasps. The clasp number of a link is the minimal number of clasps amongst all C-complexes bounded. It gives a measure of complexity and can be used to provide bounds on other useful characteristics of a link. This paper provides a new lower bound for the number of clasps of all C-complexes bounded by a given 3-component link improving results of Amundsen-Anderson-D.-Guyer. Furthermore, we construct links that achieve these bounds. In order to do so, we express the triple linking numbers as the area bounded by three curves, called word curves, and then perform the geometry and discrete optimization needed to minimize the length of these curves.
The Communities in a network are detected by investigating the corresponding graph and finding dense clusters of vertices. The decoding algorithm SASH determines the initial codeword of communities that would most likely result in specific clusters. SASH checks various candidate codewords at clustering types until the codeword with the smallest discrepancy from the observed dataset is located. Using the dataset Zachary’s Karate Club, errors within the algorithm that lead to a significantly lowered accuracy from expectations will be highlighted, as well as potential ways that could amend the issues to optimize performance.
This project investigates patterns in the decimal expansions of fractions of the form 𝑛/(3^𝑥), with particular focus on n/81. The central research question asks: which digits fail to appear in these repeating decimal representations, and can their absence be predicted using modular arithmetic? While repeating decimals are a familiar concept, the structural constraints governing their digit composition are less commonly examined.To explore this question, I analyzed decimal expansions in base 10 through the lens of modular arithmetic, examining how powers of 3 interact with powers of 10. By studying residue classes and cyclic behavior, I identified patterns that restrict which digits can occur in specific expansions. Preliminary results show that the structure of the multiplicative group modulo 3^𝑥 imposes predictable limitations on digit appearance. These findings provide a systematic method for forecasting digit absence in fractions with denominator 3^x, revealing deeper connections between modular arithmetic and decimal representation.
