Approximately counting semismooth integers

An integer $n$ is $(y,z)$-semismooth if $n=pm$ where $m$ is an integer with all prime divisors $\le y$ and $p$ is 1 or a prime $\le z$. arge quantities of semismooth integers are utilized in modern integer factoring algorithms, such as the number field sieve, that incorporate the so-called large prime variant. Thus, it is useful for factoring practitioners to be able to estimate the value of $\Psi(x,y,z)$, the number of $(y,z)$-semismooth integers up to $x$, so that they can better set algorithm parameters and minimize running times, which could be weeks or months on a cluster supercomputer. In this paper, we explore several algorithms to approximate $\Psi(x,y,z)$ using a generalization of Buchstab's identity with numeric integration.Comment: To appear in ISSAC 2013, Boston M

Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance

The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the empirical measure obtained from $n$ independent samples from $\mu$ approaches $\mu$ in the Wasserstein distance of any order. We prove sharp asymptotic and finite-sample results for this rate of convergence for general measures on general compact metric spaces. Our finite-sample results show the existence of multi-scale behavior, where measures can exhibit radically different rates of convergence as $n$ grows

Teacher and Coach Implementation of Writers Workshop in America\u27s Choice Schools, 2001 and 2002

In this report, we follow a line of inquiry that we began in a 2002 Consortium for Policy Research in Education (CPRE) report titled Implementation of the America’s Choice Literacy Workshops. Herein, we examine the implementation of the writers workshop component of America’s Choice, which we consider the core instructional reform of the first year of implementation of the America’s Choice comprehensive school reform design. By conducting structured observations in a random sample of elementary and middle school classrooms in America’s Choice schools across the United States, and applying a rubric that assesses the fidelity of teachers’ implementation of writers workshop, we have produced a measure of implementation of a central component of the design. While our measure of implementation has limitations, it does reveal the degree of teachers’ implementation of the structures of the literacy component of America’s Choice and provides insight into the depth of teachers’ understanding of the larger concepts of the design. In our study, we focus on three particular questions. First, what is the extent of implementation of writers workshop in elementary and middle schools at the end of their first year of America’s Choice? Second, did 2002 teachers achieve higher levels of implementation in their first implementation year than 2001 teachers in their first year of implementation and, if so, could these differences be attributed to improvements in the America’s Choice design? Finally, what is the relationship between the fidelity of literacy coaches’ implementation of writers workshop and teachers’ implementation of writers workshop within the same schools? Through these questions, we seek to document the progress of America’s Choice and point out areas where further refinements might be warranted

Bone Loss During Spaceflight: Available Models and Counter-Measures

There is ongoing concern for human health during spaceflights. Of particular interest is the uncoupling of bone remodeling and its resultant effect on calcium metabolism and bone loss. The calculated average loss of bone mineral density (BMD) is approximately 1-1.5% per month of spaceflight. The effect of decreased BMD on associated fractures in astronauts is not known. Currently on the International Space Station (ISS), bone loss is managed through dietary supplements and modifications and resistance exercise regimen. As the duration of space flights increases, a review of the current methods available for the prevention of bone loss is warranted. The goal of this project is to review and summarize recent studies that have focused on maintaining BMD during exposure to microgravity. Interventions were divided into physical (Table 1), nutritional (Table 2), or pharmacologic (Table 3) categories. Physical modalities included resistance exercise, low level vibration, and low intensity pulsed ultrasound. Nutritional interventions included altering protein, salt, and fat intake; and vitamin D supplementation. Pharmacologic interventions included the use of bisphosphonates and beta blockers. Studies reported outcomes based on bone density determined by DXA bone scan, micro-architecture of histology and microCT, and serum and urine markers of bone turnover. The ground analog models utilized to approximate osseous physiology in microgravity included human patients previously paralyzed or subjects confined to bedrest. Ground analog animal models include paralysis, immobilization and ovariectomies. As a result of the extensive research performed there is a multi-modality approach available for the management of BMD during spaceflight that includes resistance training, nutrition and dietary supplements. However, there is a paucity of literature describing a formalized tiered protocol to guide investigators through the progression from animal models to human patient ground analogs to experiments on the ISS. With regards to testing, further evaluation to determine the association between non-invasive tests and fracture during and after spaceflight needs to be performed

A Randomized Sublinear Time Parallel GCD Algorithm for the EREW PRAM

We present a randomized parallel algorithm that computes the greatest common divisor of two integers of n bits in length with probability 1-o(1) that takes O(n loglog n / log n) expected time using n^{6+\epsilon} processors on the EREW PRAM parallel model of computation. We believe this to be the first randomized sublinear time algorithm on the EREW PRAM for this problem

Understanding An Interprofessional Team Through The Lens Of The Intentional Relationship Model (IRM)

Research poster describing the following process: The Intentional Relationship Model (IRM) is designed to explain the therapist\u27s roles and demands in both establishing and maintaining a therapeutic relationship with a patient. While based in occupational therapy, this model has wide implications on being applied in many contexts, including an interdisciplinary team. While based in occupational therapy, this model has wide implications for the application to health care interdisciplinary teams. The objective for our team was to analyze our own interactions with Alex and identify how our ability to use different modes of the IRM and mode-shift made an impact on our care both individually and as a collective.https://dune.une.edu/cecespring2020/1015/thumbnail.jp