Math and the Mouse: Explorations of Mathematics and Science in Walt Disney World

Math and the Mouse is an intensive, collaborative, project-driven, study away course that runs during the three-week May Experience term at Furman University and has many of the attributes of a course-based undergraduate research experience in mathematics. We take twelve students to Orlando, Florida to study the behind-the-scenes mathematics employed to make Walt Disney World operate efficiently. Students learn techniques of mathematical modeling (mostly resource allocation, logistics, and scheduling models), statistical analysis (mostly probability, clustering, data collection, and hypothesis testing), and ow management (queuing theory and some beginning ow dynamics) in an applied setting. Through planned course modules, collaborative activities, conversations with guest speakers, and three group projects, one of which is of the students\u27 choosing, this academic experience provides an engaged learning experience that shows how material from eleven academic courses comes together in connection with real-world applications

Cold collisions of OH and Rb. I: the free collision

We have calculated elastic and state-resolved inelastic cross sections for cold and ultracold collisions in the Rb($^1 S$) + OH($^2 \Pi_{3/2}$) system, including fine-structure and hyperfine effects. We have developed a new set of five potential energy surfaces for Rb-OH($^2 \Pi$) from high-level {\em ab initio} electronic structure calculations, which exhibit conical intersections between covalent and ion-pair states. The surfaces are transformed to a quasidiabatic representation. The collision problem is expanded in a set of channels suitable for handling the system in the presence of electric and/or magnetic fields, although we consider the zero-field limit in this work. Because of the large number of scattering channels involved, we propose and make use of suitable approximations. To account for the hyperfine structure of both collision partners in the short-range region we develop a frame-transformation procedure which includes most of the hyperfine Hamiltonian. Scattering cross sections on the order of $10^{-13}$ cm$^2$ are predicted for temperatures typical of Stark decelerators. We also conclude that spin orientation of the partners is completely disrupted during the collision. Implications for both sympathetic cooling of OH molecules in an environment of ultracold Rb atoms and experimental observability of the collisions are discussed.Comment: 20 pages, 16 figure

Enteric Neural Cells From Hirschsprung Disease Patients Form Ganglia in Autologous Aneuronal Colon

Background & Aims: Hirschsprung disease (HSCR) is caused by failure of cells derived from the neural crest (NC) to colonize the distal bowel in early embryogenesis, resulting in absence of the enteric nervous system (ENS) and failure of intestinal transit postnatally. Treatment is by distal bowel resection, but neural cell replacement may be an alternative. We tested whether aneuronal (aganglionic) colon tissue from patients may be colonized by autologous ENS-derived cells. Methods: Cells were obtained and cryopreserved from 31 HSCR patients from the proximal resection margin of colon, and ENS cells were isolated using flow cytometry for the NC marker p75 (nine patients). Aneuronal colon tissue was obtained from the distal resection margin (23 patients). ENS cells were assessed for NC markers immunohistologically and by quantitative reverse-transcription polymerase chain reaction, and mitosis was detected by ethynyl-2\u27-deoxyuridine labeling. The ability of human HSCR postnatal ENS-derived cells to colonize the embryonic intestine was demonstrated by organ coculture with avian embryo gut, and the ability of human postnatal HSCR aneuronal colon muscle to support ENS formation was tested by organ coculture with embryonic mouse ENS cells. Finally, the ability of HSCR patient ENS cells to colonize autologous aneuronal colon muscle tissue was assessed. Results: ENS-derived p75-sorted cells from patients expressed multiple NC progenitor and differentiation markers and proliferated in culture under conditions simulating Wnt signaling. In organ culture, patient ENS cells migrated appropriately in aneural quail embryo gut, and mouse embryo ENS cells rapidly spread, differentiated, and extended axons in patient aneuronal colon muscle tissue. Postnatal ENS cells derived from HSCR patients colonized autologous aneuronal colon tissue in cocultures, proliferating and differentiating as neurons and glia. Conclusions: NC-lineage cells can be obtained from HSCR patient colon and can form ENS-like structures in aneuronal colonic muscle from the same patient

Treatment of fecal impaction in children using combined polyethylene glycol and sodium picosulphate

Background and Aim: Polyethylene glycol (PEG) is the gold standard for fecal disimpaction in constipation. A regimen of PEG combined with the stimulant laxative sodium picosulphate (SPS) produced fecal disimpaction in chronically constipated children in the community, but it is unknown if it is effective for more severe constipation. To determine the stool output and effect of a combined PEG and SPS regimen on fecaloma in children with severe constipation and impaction. Methods: Children with symptoms for a duration of >= 2 years, a palpable fecaloma, and enlarged rectum on X-ray (rectal: pelvic ratio > 0.6) were recruited from a tertiary hospital. Daily diaries recorded laxative dose, stool frequency, volume, and consistency (Bristol stool scale, BSS). Abdominal X-rays were taken on day 1 and day 8, and stool loading was assessed using the Leech score. Laxative doses were based on the child's age. The dose of PEG with electrolytes taken was 2-8 sachets (14.7 g/sachet) on days 1-2, reducing to 2-6 sachets on day 3. The SPS dose was 15-20 drops on days 2-3. Results: Eighty-nine children (4-18 years) produced a large volume of soft stool (median/inter-quartile-range: 2.2/1.6-3.1 L) over 7 days. Stool volume on X-rays decreased significantly in the colon (P <0.001). Fecalomas resolved in 40 of 89 children, while 49 needed a second high dose. Rectal: pelvic ratios did not change. Conclusions: A combined high dose of PEG and SPS on days 1 and 2 was effective in removing the fecaloma in half of the children. Administering high doses for a longer period should be tested to provide outpatient disimpaction for severe fecalomas. Rectums remained flaccid after emptying

Sequential Therapy in Metastatic Renal Cell Carcinoma

The treatment of metastatic renal cell carcinoma (mRCC) has changed dramatically in the past decade. As the number of available agents, and related volume of research, has grown, it is increasingly complex to know how to optimally treat patients. The authors are practicing medical oncologists at the US Oncology Network, the largest community-based network of oncology providers in the country, and represent the leadership of the Network's Genitourinary Research Committee. We outline our thought process in approaching sequential therapy of mRCC and the use of real-world data to inform our approach. We also highlight the evolving literature that will impact practicing oncologists in the near future

Formation and dynamics of van der Waals molecules in buffer-gas traps

We show that weakly bound He-containing van der Waals molecules can be produced and magnetically trapped in buffer-gas cooling experiments, and provide a general model for the formation and dynamics of these molecules. Our analysis shows that, at typical experimental parameters, thermodynamics favors the formation of van der Waals complexes composed of a helium atom bound to most open-shell atoms and molecules, and that complex formation occurs quickly enough to ensure chemical equilibrium. For molecular pairs composed of a He atom and an S-state atom, the molecular spin is stable during formation, dissociation, and collisions, and thus these molecules can be magnetically trapped. Collisional spin relaxations are too slow to affect trap lifetimes. However, helium-3-containing complexes can change spin due to adiabatic crossings between trapped and untrapped Zeeman states, mediated by the anisotropic hyperfine interaction, causing trap loss. We provide a detailed model for Ag3He molecules, using ab initio calculation of Ag-He interaction potentials and spin interactions, quantum scattering theory, and direct Monte Carlo simulations to describe formation and spin relaxation in this system. The calculated rate of spin-change agrees quantitatively with experimental observations, providing indirect evidence for molecular formation in buffer-gas-cooled magnetic traps.Comment: 20 pages, 13 figure

Ancient Lowland Maya neighborhoods: Average Nearest Neighbor analysis and kernel density models, environments, and urban scale

Many humans live in large, complex political centers, composed of multi-scalar communities including neighborhoods and districts. Both today and in the past, neighborhoods form a fundamental part of cities and are defined by their spatial, architectural, and material elements. Neighborhoods existed in ancient centers of various scales, and multiple methods have been employed to identify ancient neighborhoods in archaeological contexts. However, the use of different methods for neighborhood identification within the same spatiotemporal setting results in challenges for comparisons within and between ancient societies. Here, we focus on using a single method—combining Average Nearest Neighbor (ANN) and Kernel Density (KD) analyses of household groups—to identify potential neighborhoods based on clusters of households at 23 ancient centers across the Maya Lowlands. While a one-size-fits all model does not work for neighborhood identification everywhere, the ANN/KD method provides quantifiable data on the clustering of ancient households, which can be linked to environmental zones and urban scale. We found that centers in river valleys exhibited greater household clustering compared to centers in upland and escarpment environments. Settlement patterns on flat plains were more dispersed, with little discrete spatial clustering of households. Furthermore, we categorized the ancient Maya centers into discrete urban scales, finding that larger centers had greater variation in household spacing compared to medium-sized and smaller centers. Many larger political centers possess heterogeneity in household clustering between their civic-ceremonial cores, immediate hinterlands, and far peripheries. Smaller centers exhibit greater household clustering compared to larger ones. This paper quantitatively assesses household clustering among nearly two dozen centers across the Maya Lowlands, linking environment and urban scale to settlement patterns. The findings are applicable to ancient societies and modern cities alike; understanding how humans form multi-scalar social groupings, such as neighborhoods, is fundamental to human experience and social organization

Ancient Lowland Maya neighborhoods: Average Nearest Neighbor analysis and kernel density models, environments, and urban scale

Many humans live in large, complex political centers, composed of multi-scalar communities including neighborhoods and districts. Both today and in the past, neighborhoods form a fundamental part of cities and are defined by their spatial, architectural, and material elements. Neighborhoods existed in ancient centers of various scales, and multiple methods have been employed to identify ancient neighborhoods in archaeological contexts. However, the use of different methods for neighborhood identification within the same spatiotemporal setting results in challenges for comparisons within and between ancient societies. Here, we focus on using a single method—combining Average Nearest Neighbor (ANN) and Kernel Density (KD) analyses of household groups—to identify potential neighborhoods based on clusters of households at 23 ancient centers across the Maya Lowlands. While a one-size-fits all model does not work for neighborhood identification everywhere, the ANN/KD method provides quantifiable data on the clustering of ancient households, which can be linked to environmental zones and urban scale. We found that centers in river valleys exhibited greater household clustering compared to centers in upland and escarpment environments. Settlement patterns on flat plains were more dispersed, with little discrete spatial clustering of households. Furthermore, we categorized the ancient Maya centers into discrete urban scales, finding that larger centers had greater variation in household spacing compared to medium-sized and smaller centers. Many larger political centers possess heterogeneity in household clustering between their civic-ceremonial cores, immediate hinterlands, and far peripheries. Smaller centers exhibit greater household clustering compared to larger ones. This paper quantitatively assesses household clustering among nearly two dozen centers across the Maya Lowlands, linking environment and urban scale to settlement patterns. The findings are applicable to ancient societies and modern cities alike; understanding how humans form multi-scalar social groupings, such as neighborhoods, is fundamental to human experience and social organization