Pattern avoidance in forests of binary shrubs

We investigate pattern avoidance in permutations satisfying some additional restrictions. These are naturally considered in terms of avoiding patterns in linear extensions of certain forest-like partially ordered sets, which we call binary shrub forests. In this context, we enumerate forests avoiding patterns of length three. In four of the five non-equivalent cases, we present explicit enumerations by exhibiting bijections with certain lattice paths bounded above by the line y = lx, for some l in Q+, one of these being the celebrated Duchon’s club paths with l = 2/3. In the remaining case, we use the machinery of analytic combinatorics to determine the minimal polynomial of its generating function, and deduce its growth rate

Improving Mental Health Screening with Predictive and Generative Modeling of Text Messages

Screening for mental illnesses is vital, but traditional screening questionnaires are susceptible to conscious and unconscious bias. In my dissertation, I explore the mental illness screening capabilities of retrospectively harvested text messages. Leveraging lexical category features derived from the text message content of crowd-sourced participants, I trained traditional machine learning models and evaluated their ability to screen for depression and suicidal ideation. For sent texts, I discovered the most recent weeks of texts were more predictive than greater temporal quantities like the last year of texts. I further constructed lexicons with less formal language to improve the depression screening models. For received texts, I identified the 25 percent most prolific contacts as the subset with the messages most predictive of depression. To mitigate privacy concerns, I also explore depression screening potential of text reply latencies and time series of communications. I then collect a new dataset with a larger quantity of call and text logs labeled with depression and anxiety screening scores. Deep learning was more effective at screening for lower score cutoffs while machine learning was more effective at screening for higher score cutoffs. Lastly, I explore the depression screening potential of generated text content. I identify and adopt nine different conditional approaches for sequence generation. I then conduct a comparative evaluation of their ability to generate text messages from depressed and not depressed participants. The transformer-based classifiers proved better able to screen for depression with texts generated by the unconditioned models than the conditioned models, revealing future research opportunities

Math 380: Research Methods in Mathematics

Color poster with text, images, and graphs.Math 380: Research Methods was developed for Fall semester of 2015 by Dr. Dandrielle Lewis, Dr. Carolyn Otto, and three undergraduate mentors. The main premise of this course is to instruct future mathematicians on the art and procedures of mathematics research. This course prepares students for student/faculty research collaboration at UWEC, readies them for the rigors of graduate study in mathematics, and equips students with skills that will aid in careers in academia or industry. The class was divided into three units: proof methods, presentation formats and practice, and a final research project. A prominent part of research is the ability to communicate effectively, not only when giving a research presentation, but when working with colleagues. Therefore, throughout the class students were challenged to develop their written and oral communication skills.University of Wisconsin--Eau Claire Office of Research and Sponsored Program

Pattern avoidance in forests of binary shrubs

We investigate pattern avoidance in permutations satisfying some additional restrictions. These are naturally considered in terms of avoiding patterns in linear extensions of certain forest-like partially ordered sets, which we call binary shrub forests. In this context, we enumerate forests avoiding patterns of length three. In four of the five non-equivalent cases, we present explicit enumerations by exhibiting bijections with certain lattice paths bounded above by the line $y=\ell x$, for some $\ell\in\mathbb{Q}^+$, one of these being the celebrated Duchon's club paths with $\ell=2/3$. In the remaining case, we use the machinery of analytic combinatorics to determine the minimal polynomial of its generating function, and deduce its growth rate

AI Chatbots in Education: A Comparative Analysis at Bryant University

Artificial Intelligence (AI) has been making significant strides in various sectors, and education is no exception. AI chatbots, in particular, have been gaining popularity for their potential to enhance teaching, learning, research, and administrative tasks. A recent survey conducted at Bryant University reveals an interesting trend: while students and faculty are increasingly adopting AI chatbots, staff members seem to lag behind. This guest blog post delves into the possible reasons behind this disparity using the 77 faculty, 111 staff, and 224 student responses collected between November 2023 and February 2024. A full survey report will be published on the Bryant University website at a later date. Bryant University is participating in Ithaka S+R’s cohort project, Making AI Generative for Higher Education

Pattern avoidance in forests of binary shrubs

We investigate pattern avoidance in permutations satisfying some additionalrestrictions. These are naturally considered in terms of avoiding patterns inlinear extensions of certain forest-like partially ordered sets, which we callbinary shrub forests. In this context, we enumerate forests avoiding patternsof length three. In four of the five non-equivalent cases, we present explicitenumerations by exhibiting bijections with certain lattice paths bounded aboveby the line $y=\ell x$, for some $\ell\in\mathbb{Q}^+$, one of these being thecelebrated Duchon's club paths with $\ell=2/3$. In the remaining case, we usethe machinery of analytic combinatorics to determine the minimal polynomial ofits generating function, and deduce its growth rate