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Bent Hamiltonian Paths in Toroidal Grid Graphs and Applications to the Snake Cube Puzzle
No full textThe snake cube puzzle is a popular toy that can be represented by an encoding of a Hamiltonian path in a grid graph. We computationally determine all possible solvable puzzle configurations and counts of solutions of each configuration up to symmetry, finding agreement with prior analysis. This allows us to introduce a measure of the difficulty of a particular snake cube puzzle, revealing that the commonly sold puzzle configuration has maximal difficulty. Then we extend the work to other topological spaces by considering various toroidal grid graphs and determine all encodings and unique solutions. It is known that there do not exist bent Hamiltonian paths in 3x3x3 grid graphs; we prove that there cannot exist a bent Hamiltonian path in a 3x3x3 toroidal grid graph with one or two pairs of faces identified, however, there is such a path when three pairs of faces are identified. Finally, we discuss the minimum number of non-bent portions of a Hamiltonian path/cycle in an nxnxn (toroidal) grid graph more generally
How many crossing changes does it take to get to a homotopy trivial link?
No full textAn intensely studied problem in knot theory is to determine the unlinking number of a link; that is, the number of crossing changes needed to transform a link into the unlink. We ask a related question: How many crossing changes are needed to turn a link into a homotopy trivial link? A link is called homotopy trivial if it can be transformed into the trivial link by allowing components to pass through themselves but not each other. We determine this homotopy trivializing number for all 4-component links up to link homotopy. In particular, we provide a table where one can read off the homotopy trivializing number of a link given its linking data (pairwise linking number and higher order Milnor invariants). Moreover, we give upper and lower bounds on the homotopy trivializing number for links with an arbitrary number of components, showing that the difference between the homotopy trivializing number and the sum of the pairwise linking numbers is bounded by quadratics on the number of components
Running From the Headlines: Evaluating Levels of News Consumption Attitudes Across Generations
No full textAbstract The primary goal of this research is to answer the question What behavioral trends exist across various generations and other demographics when it comes to how people consume and interact with news coverage? With newspapers and other traditional mediums for news consumption being largely phased out of our increasingly digital society, it is important for communicators and journalists to have a comprehensive understanding of how to best reach members of their desired audience. I have studied the data collected and analyzed what trends are apparent in the survey\u27s sample size, which can hopefully be applied to the larger population. To measure outcomes and conclusions, I have identified various percentages and correlations between the consistent demographics and their answers. I hypothesize that younger groups of people will tend to be less engaged with longer forms of news content but will be heavily reliant on shorter-form content for only a few specific topics when compared to older demographics. I also believe that the rates of consumption for political news will decrease as a result of polarization and sensationalism in the media
Synthesis and Evaluation of Amidoximes as Potential Pharmaceuticals Against Antimicrobial-Resistant Bacteria
No full textThe rise of antimicrobial-resistant bacteria in the healthcare industry has led to devastating effects in recent years, ranging from increased risks associated with hospital treatment to longer illness duration, which may eventually lead to increased death rates (Naghavi, Mohsen et al, 2024). To combat this ongoing challenge, this project aims to synthesize amidoximes, which are organic derivatives of carboxylic acids with an oxime and an amino acid group. Amidoximes have been utilized in various clinical applications, including antituberculosis medication, hypotensives, antiarrhythmics, antibacterials, and antifungals (J. Chil et al., 2011). -- The focus of this project was to test their antibacterial properties and their susceptibility to bioisosterism, which is a useful feature in producing effective drugs. In exploring the antibacterial effects of amidoximes, this could lead to further discoveries on their potential usage in pharmaceuticals and their efficacy in treating selected strains of bacteria that have been known to be prevalent in healthcare settings- Pseudomonas aeruginosa, Staphylococcus aureus, and Escherichia coli. From the research, it was discovered that the amidoxime derived from the nitrile 3.4 dihydroxybenzonitrile was the most effective against Pseudomonas aeruginosa and Staphylococcus aureus, while none of the amidoximes synthesized were effective against Escherichia coli. This proved to be a significant result as Pseudomonas aeruginosa and Staphylococcus aureus are known to form biofilms which are difficult to treat, they have also been included in poor outcomes seen by cystic fibrosis patients as they affect lung function among other diseases . (Orazi et.al 2019
Little Cards, Big Impact: No-Prep Activities for ELT in Literacy, Oracy, Assessment and AI
No full textEugenia Nitowski removing human skeleton from tomb 16
No full text#651https://digitalcommons.andrews.edu/hiap-photos/3171/thumbnail.jp
John Wood placing a string for a strip
No full text#808https://digitalcommons.andrews.edu/hiap-photos/3163/thumbnail.jp
