Counting elliptic curves of bounded Faltings height

We give an asymptotic formula for the number of elliptic curves over $\mathbb{Q}$ with bounded Faltings height. Silverman has shown that the Faltings height for elliptic curves over number fields can be expressed in terms of modular functions and the minimal discriminant of the elliptic curve. We use this to recast the problem as one of counting lattice points in a particular region in $\mathbb{R}^2$.Comment: 12 pages, 2 figures, 1 table. To be published in Acta Arithmetic

A Universal Approach to Vertex Algebras

We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.Comment: To appear in the Journal of Algebr

The Female Overactive Bladder in our Beverage-Centered Society: An Evolutionary Perspective

Abstract Over recent decades, chronic disease has trended upwards, associated with the mismatch between our modern nutritional environment and our paleolithic genome. The beverage industry has exploded in sync with chronic conditions, including bladder symptomatology. This dissertation uses the logic and paradigm of evolutionary medicine to examine the modern beverage culture as a cause of the current high overactive bladder prevalence rates (17-31%, age dependent). A natural experiment exemplar concludes the dissertation with proof of concept that societal-wide influences to hyper-hydrate by drinking beyond thirst influences non-pathological changes to bladder state. The study is a secondary analysis with main outcome measure as void frequency. In this natural experiment, the preventative treatment group is considered to be 40 women who at 8 months postpartum are not breastfeeding and hence not receiving same degree of societal messaging to hyper-hydrate, as compared to 52 breastfeeding women . The preventative treatment group (non-breastfeeding women) show significantly lower daily beverage intake (62.6 oz) than the breastfeeding group (77.6 oz), p = 0.01. Results show a strong trend towards a significantly lower average number of daily voids in the preventative treatment group who have less societal messaging compared to the control group with high societal messaging (6.3 voids/day versus 7.2 voids/day respectively), p = .04. This natural experiment provides first evidence-based proof of concept for the argument that in terms of evolutionary perspective, the new (50 years) cultural milieu of the beverage driven society may be driving the contemporaneous increase in bladder symptoms, and that its prevalence may lessen without conscious individual effort if societal messages to hyper-hydrate (drink beyond thirst) decrease. The dissertation concludes with recommendation for more research to test the theoretical construct that non-pathological but bothersome and costly symptoms of overactive bladder occur when our evolutionarily designed bladder is exposed to the modern beverage driven society.PHDNursingUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144080/1/redfish_1.pd

Virtual Biology: Teaching Histology in the Age of Facebook

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154528/1/fsb2027002001.pd

Listening to Graduates: An Evaluation of a U.S. Catholic High School Religious Education Program

Recent research indicates that membership in the Catholic Church is steadily declining. Simultaneously, the rise of the religiously unaffiliated continues to grow. This phenomenon is a spiritual and cultural crisis within the Church. Studies demonstrate an inverse relationship between age and disaffiliation as younger generations are more reflective of identifying with no religious affiliation. Recognizing a growing generational gap and the need to better understand the lives of young people, Pope Francis is urging the faithful to become a “listening Church.” Situated as an important meeting point for many young people, Catholic schools are an important proximal zone for faith formation. Specifically, Catholic high schools require four years of religious education designed to provide a holistic foundation through three inter-related domains: cognitive, affective, and behavioral. The purpose of this study was to investigate the impact of a U.S. Catholic high school religious education program upon recent graduates and their subsequent religious affiliation. In aggregate, 106 survey responses were collected from graduates of one Catholic high school spanning the previous one to three years. Twenty-three of the graduates surveyed participated in one of four different focus groups assigned by their current religious affiliation: Catholic, Former Catholic, Non-Catholic Christian, and No Religious Affiliation. Key findings revealed that an open invitation, the promotion of questions, teacher relationships with students, and experiential learning opportunities were viewed as essential elements of quality religious instruction. The educational outcomes from this study promote cultivating student questions, tailoring educational experiences for different learners, inviting students to discern their own beliefs, and providing real-life learning activities as methods for improved practice

A Neuroeducation Approach to Writing Instruction with Kindergarteners: A Case Study

American elementary schools are seeing the lowest literacy rates to date across grade-levels. As this literacy rate has dropped across our nation, reading and writing standards have simultaneously increased in difficulty through Common Core State Standards. Kindergarten writing standards have drastically changed in the last decade in our American schools, yet many of our youngest learners are not reaching the new standards. Most commonly seen in our nation’s schools is a psycholinguistic approach to reading and writing instruction. Through this instruction, students are being left behind. The purpose of this case study was to explore an alternation method to writing instruction in a kindergarten classroom; this approach was founded by neuroeducation-based methods influenced by Arwood’s neuroeducation model. This study examined the extent to which six kindergarten students made advancements in their language function level and characteristics during an eight-week period of time at the beginning of their kindergarten academic year. The participants were assessed through four language samples; one oral and one written language sample at the beginning of the study and one oral and one written language sample after six weeks of neuroeducation-based writing instruction. The researcher found that the participants all remained at the same language function level of pre-language level; however improvements were made in language function characteristics. The results of this study suggest that neuroeducation-based writing instruction may provide educators with a new method to instruct writing in early elementary classrooms

Duplications in nomenclature

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62822/1/389539a0.pd