Find, Process, and Share: An Optimal Control in the Vidale-Wolfe Marketing Model

The Vidale-Wolfe marketing model is a first-order, linear, non-homogeneous ordinary differential equation (ODE) where the forcing term is proportional to advertising expenditure. With an initial response in sales as the initial condition, the solution of the initial value problem is straightforward for a first undergraduate ODE course. The model serves as an excellent example of many relevant topics for those students whose interests lie in economics, finance, or marketing. Its inclusion in the curriculum is particularly rewarding at an institution without a physics program. The model is not new, but it was novel to us when a group of students chose it for an exploratory project that we designed in order to help students acquire the ability to interpret and communicate mathematical results. In addition to describing the project in this work, we discuss the Vidale-Wolfe model and show how it can lead one to use Green\u27s theorem in a real situation

Inequality of Educational Opportunity in East and West Germany: Convergence or Continued Differences?

Diversity in education systems, and broader political and economic conditions, are commonly credited with international variation in inequality of educational opportunity (IEO). Comparing East and West Germany before reunification allows us to investigate whether vastly different political, economic, and educational systems led to differences in IEO. Postreunification, East Germany adopted the West’s systems and experienced an economic recession. IEO had been smaller in East Germany than in West Germany but was on an upward trajectory before reunification. After 1990, IEO in East Germany converged to the West German level as a result of decreased IEO in the west and increasing levels in the east. Postreunification convergence suggests that differences in political context and education policy are crucial for IEO

Sustainable Sourcing and Expansion for Frita Batidos

Frita Batidos (Frita) is a small Cuban fusion restaurant in Ann Arbor that has strong values woven within its core business. The owner, Eve Aronoff, focuses heavily on the community, developing strong relationships with her employees, customers, and purveyors. She also focuses on implementing Slow Food movement tenets by creating food from scratch using seasonal ingredients, and sourcing from farms with humane practices focused on animal treatment. Given Eve’s sustainability focus, the difficulty of implementing these practices at scale, and her ideas around entering new markets, she turned to the School of Natural Resources and Environment (SNRE) Master’s Project team for assistance. The main goals of the project included: (1) create a priority list and resource base for sourcing, especially animal products; (2) assess the feasibility of composting in Ann Arbor and develop a methodology for implementation in new locations; and (3) assess the viability of operating Frita Batidos restaurants in new markets and create a methodology for assessing future locations under consideration. These goals guided the 18-month Master’s Project and led to corresponding recommendations. The priority list and resource base for sourcing are included in Appendix B, with taste and relationships with suppliers having the highest importance, then humanely raised, local, and organic following. Composting was deemed infeasible in the Ann Arbor location, but requirements for the layout of new locations and composting providers were determined, as described in the compost recommendation section. Lastly, within the next few years, the neighborhoods of Midtown and Downtown in Detroit were considered to be most appropriate for a second Frita location. Resources for analyzing priority neighborhoods into which Frita can expand and a methodology for assessing new cities and neighborhoods can be found in Appendix LMaster of ScienceNatural Resources and EnvironmentUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/117624/1/[MP] Frita Batidos Final Paper.pd

Generalizability and Validation of PROMIS Scores to Predict Surgical Success in Foot and Ankle Patients: A Tale of Two Academic Centers

Introduction/Purpose: Patient-reported outcomes are advancing clinical care by improving patient satisfaction and engagement. A recent publication reported preoperative PROMIS scores to be highly predictive in selecting patients who would and would not benefit from foot and ankle (F/A) surgery. Although this publication used the data from 5 fellowship trained foot and ankle surgeons at one institution, the generalizability to other patient populations and geographic areas is unknown. This validation study assesses the pre-operative PROMIS physical function (PF) and pain interference (PI) t-scores as a predictor of post-operative success from a separate geographic area

Complications and clinical outcome of hepatic artery embolisation in patients with hereditary haemorrhagic telangiectasia

BACKGROUND: Hepatic artery embolisation (HAE) in patients with hereditary haemorrhagic telangiectasia (HHT) is controversial because of the associated complications and unproven long-term benefit. We present our results in 20 such patients over a time span of 17 years. METHODS: Staged HAE was performed using polyvinyl alcohol (PVA) particles and coils. Complications, clinical symptoms and cardiac output were assessed before and after therapy as well as at the end of follow-up (median 92 months, range 26–208 months). RESULTS: Two patients died within 30 days following HAE (10 %). Four further deaths resulted from causes unrelated to HAE. Ischaemic cholangitis, cholecystitis and focal hepatic necrosis with biliary sepsis necessitated re-intervention in four patients. In all but one patient, clinical symptoms resolved with mean cardiac output falling from 11.84 ± 3.22 l/min pre-treatment to 8.13 ± 2.67 l/min at the end of follow-up (P < 0.001). One patient required liver transplantation for de novo symptoms of portal hypertension 4 years after primary symptoms had been cured by HAE. CONCLUSION: The 30-day mortality of HAE in patients with HHT is 10 %. The rate of complications requiring re-intervention is 20 %. Clinical response at long-term follow-up is satisfactory. KEY POINTS: • Hepatic artery embolisation (HAE) in hereditary haemorrhagic telangiectasia (HHT) provides long-term benefit. • Mortalities of HAE and liver transplantation in HHT patients are comparable. • In HHT, complications of HAE are lower than those of liver transplantation. • Complications of HAE can be further reduced by refinement of technique. • Complications include ischaemic cholangitis, hepatic necrosis, biliary sepsis and death

Validation and Generalizability of Preoperative PROMIS Scores to Predict Postoperative Success in Foot and Ankle Patients

Background: A recent publication reported preoperative Patient-Reported Outcomes Measurement Instrumentation System (PROMIS) scores to be highly predictive in identifying patients who would and would not benefit from foot and ankle surgery. Their applicability to other patient populations is unknown. The aim of this study was to assess the validation and generalizability of previously published preoperative PROMIS physical function (PF) and pain interference (PI) threshold t scores as predictors of postoperative clinically meaningful improvement in foot and ankle patients from a geographically unique patient population. Methods: Prospective PROMIS PF and PI scores of consecutive patient visits to a tertiary foot and ankle clinic were obtained between January 2014 and November 2016. Patients undergoing elective foot and ankle surgery were identified and PROMIS values obtained at initial and follow-up visits (average, 7.9 months). Analysis of variance was used to assess differences in PROMIS scores before and after surgery. The distributive method was used to estimate a minimal clinically important difference (MCID). Receiver operating characteristic curve analysis was used to determine thresholds for achieving and failing to achieve MCID. To assess the validity and generalizability of these threshold values, they were compared with previously published threshold values for accuracy using likelihood ratios and pre- and posttest probabilities, and the percentages of patients identified as achieving and failing to achieve MCID were evaluated using χ2 analysis. Results: There were significant improvements in PF (P \u3c .001) and PI (P \u3c .001) after surgery. The area under the curve for PF (0.77) was significant (P \u3c .01), and the thresholds for achieving MCID and not achieving MCID were similar to those in the prior study. A significant proportion of patients (88.9%) identified as not likely to achieve MCID failed to achieve MCID (P = .03). A significant proportion of patients (84.2%) identified as likely to achieve MCID did achieve MCID (P \u3c .01). The area under the curve for PROMIS PI was not significant. Conclusions: PROMIS PF threshold scores from published data were successful in classifying patients from a different patient and geographic population who would improve with surgery. If functional improvement is the goal, these thresholds could be used to help identify patients who will benefit from surgery and, most important, those who will not, adding value to foot and ankle health care. Level of evidence: Level II, Prospective Comparative Stud

Multivesicular exocytosis in rat pancreatic beta cells

AIMS/HYPOTHESIS: To establish the occurrence, modulation and functional significance of compound exocytosis in insulin-secreting beta cells. METHODS: Exocytosis was monitored in rat beta cells by electrophysiological, biochemical and optical methods. The functional assays were complemented by three-dimensional reconstruction of confocal imaging, transmission and block face scanning electron microscopy to obtain ultrastructural evidence of compound exocytosis. RESULTS: Compound exocytosis contributed marginally (&lt;5% of events) to exocytosis elicited by glucose/membrane depolarisation alone. However, in beta cells stimulated by a combination of glucose and the muscarinic agonist carbachol, 15-20% of the release events were due to multivesicular exocytosis, but the frequency of exocytosis was not affected. The optical measurements suggest that carbachol should stimulate insulin secretion by ∼40%, similar to the observed enhancement of glucose-induced insulin secretion. The effects of carbachol were mimicked by elevating [Ca(2+)](i) from 0.2 to 2 μmol/l Ca(2+). Two-photon sulforhodamine imaging revealed exocytotic events about fivefold larger than single vesicles and that these structures, once formed, could persist for tens of seconds. Cells exposed to carbachol for 30 s contained long (1-2 μm) serpentine-like membrane structures adjacent to the plasma membrane. Three-dimensional electron microscopy confirmed the existence of fused multigranular aggregates within the beta cell, the frequency of which increased about fourfold in response to stimulation with carbachol. CONCLUSIONS/INTERPRETATION: Although contributing marginally to glucose-induced insulin secretion, compound exocytosis becomes quantitatively significant under conditions associated with global elevation of cytoplasmic calcium. These findings suggest that compound exocytosis is a major contributor to the augmentation of glucose-induced insulin secretion by muscarinic receptor activation

Munc 18-1 Protein Molecules Move between Membrane Molecular Depots Distinct from Vesicle Docking Sites

Four evolutionarily conserved proteins are required for mammalian regulated exocytosis: three SNARE proteins, syntaxin, SNAP-25, and synaptobrevin, and the SM protein, Munc18-1. Here, using single-molecule imaging, we measured the spatial distribution of large cohorts of single Munc18-1 molecules correlated with the positions of single secretory vesicles in a functionally rescued Munc18-1-null cellular model. Munc18-1 molecules were nonrandomly distributed across the plasma membrane in a manner not directed by mode of interaction with syntaxin1, with a small mean number of molecules observed to reside under membrane resident vesicles. Surprisingly, we found that the majority of vesicles in fully secretion-competent cells had no Munc18-1 associated within distances relevant to plasma membrane-vesicle SNARE interactions. Live cell imaging of Munc18-1 molecule dynamics revealed that the density of Munc18-1 molecules at the plasma membrane anticorrelated with molecular speed, with single Munc18-1 molecules displaying directed motion between membrane hotspots enriched in syntaxin1a. Our findings demonstrate that Munc18-1 molecules move between membrane depots distinct from vesicle morphological docking sites