12 resultados para Mathematical Programs

em Duke University


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This study explored the factors associated with state-level allocations to tobacco-control programs. The primary research question was whether public sentiment regarding tobacco control was a significant factor in the states' 2001 budget decisions. In addition to public opinion, several additional political and economic measures were considered. Significant associations were found between our outcome, state-level tobacco-control funding per capita, and key variables of interest including public opinion, amount of tobacco settlement received, the party affiliation of the governor, the state's smoking rate, excise tax revenue received, and whether the state was a major producer of tobacco. The findings from this study supported our hypothesis that states with citizens who favor more restrictive indoor air policies allocate more to tobacco control. Effective public education to change public opinion and the cultural norms surrounding smoking may affect political decisions and, in turn, increase funding for crucial public health programs.

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Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

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BACKGROUND: Serotonin is a neurotransmitter that has been linked to a wide variety of behaviors including feeding and body-weight regulation, social hierarchies, aggression and suicidality, obsessive compulsive disorder, alcoholism, anxiety, and affective disorders. Full understanding of serotonergic systems in the central nervous system involves genomics, neurochemistry, electrophysiology, and behavior. Though associations have been found between functions at these different levels, in most cases the causal mechanisms are unknown. The scientific issues are daunting but important for human health because of the use of selective serotonin reuptake inhibitors and other pharmacological agents to treat disorders in the serotonergic signaling system. METHODS: We construct a mathematical model of serotonin synthesis, release, and reuptake in a single serotonergic neuron terminal. The model includes the effects of autoreceptors, the transport of tryptophan into the terminal, and the metabolism of serotonin, as well as the dependence of release on the firing rate. The model is based on real physiology determined experimentally and is compared to experimental data. RESULTS: We compare the variations in serotonin and dopamine synthesis due to meals and find that dopamine synthesis is insensitive to the availability of tyrosine but serotonin synthesis is sensitive to the availability of tryptophan. We conduct in silico experiments on the clearance of extracellular serotonin, normally and in the presence of fluoxetine, and compare to experimental data. We study the effects of various polymorphisms in the genes for the serotonin transporter and for tryptophan hydroxylase on synthesis, release, and reuptake. We find that, because of the homeostatic feedback mechanisms of the autoreceptors, the polymorphisms have smaller effects than one expects. We compute the expected steady concentrations of serotonin transporter knockout mice and compare to experimental data. Finally, we study how the properties of the the serotonin transporter and the autoreceptors give rise to the time courses of extracellular serotonin in various projection regions after a dose of fluoxetine. CONCLUSIONS: Serotonergic systems must respond robustly to important biological signals, while at the same time maintaining homeostasis in the face of normal biological fluctuations in inputs, expression levels, and firing rates. This is accomplished through the cooperative effect of many different homeostatic mechanisms including special properties of the serotonin transporters and the serotonin autoreceptors. Many difficult questions remain in order to fully understand how serotonin biochemistry affects serotonin electrophysiology and vice versa, and how both are changed in the presence of selective serotonin reuptake inhibitors. Mathematical models are useful tools for investigating some of these questions.

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We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a "penalty" that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values. © 2010 INFORMS.

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PURPOSE: To develop a mathematical model that can predict refractive changes after Descemet stripping endothelial keratoplasty (DSEK). METHODS: A mathematical formula based on the Gullstrand eye model was generated to estimate the change in refractive power of the eye after DSEK. This model was applied to four DSEK cases retrospectively, to compare measured and predicted refractive changes after DSEK. RESULTS: The refractive change after DSEK is determined by calculating the difference in the power of the eye before and after DSEK surgery. The power of the eye post-DSEK surgery can be calculated with modified Gullstrand eye model equations that incorporate the change in the posterior radius of curvature and change in the distance between the principal planes of the cornea and lens after DSEK. Analysis of this model suggests that the ratio of central to peripheral graft thickness (CP ratio) and central thickness can have significant effect on refractive change where smaller CP ratios and larger graft thicknesses result in larger hyperopic shifts. This model was applied to four patients, and the average predicted hyperopic shift in the overall power of the eye was calculated to be 0.83 D. This change reflected in a mean of 93% (range, 75%-110%) of patients' measured refractive shifts. CONCLUSIONS: This simplified DSEK mathematical model can be used as a first step for estimating the hyperopic shift after DSEK. Further studies are necessary to refine the validity of this model.

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The health of clergy is important, and clergy may find health programming tailored to them more effective. Little is known about existing clergy health programs. We contacted Protestant denominational headquarters and searched academic databases and the Internet. We identified 56 clergy health programs and categorized them into prevention and personal enrichment; counseling; marriage and family enrichment; peer support; congregational health; congregational effectiveness; denominational enrichment; insurance/strategic pension plans; and referral-based programs. Only 13 of the programs engaged in outcomes evaluation. Using the Socioecological Framework, we found that many programs support individual-level and institutional-level changes, but few programs support congregational-level changes. Outcome evaluation strategies and a central repository for information on clergy health programs are needed. © 2011 Springer Science+Business Media, LLC.

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We analyze technology adoption decisions of manufacturing plants in response to government-sponsored energy audits. Overall, plants adopt about half of the recommended energy-efficiency projects. Using fixed effects logit estimation, we find that adoption rates are higher for projects with shorter paybacks, lower costs, greater annual savings, higher energy prices, and greater energy conservation. Plants are 40% more responsive to initial costs than annual savings, suggesting that subsidies may be more effective at promoting energy-efficient technologies than energy price increases. Adoption decisions imply hurdle rates of 50-100%, which is consistent with the investment criteria small and medium-size firms state they use. © 2003 Elsevier B.V. All rights reserved.

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We analyze the cost-effectiveness of electric utility ratepayer-funded programs to promote demand-side management (DSM) and energy efficiency (EE) investments. We specify a model that relates electricity demand to previous EE DSM spending, energy prices, income, weather, and other demand factors. In contrast to previous studies, we allow EE DSM spending to have a potential longterm demand effect and explicitly address possible endogeneity in spending. We find that current period EE DSM expenditures reduce electricity demand and that this effect persists for a number of years. Our findings suggest that ratepayer funded DSM expenditures between 1992 and 2006 produced a central estimate of 0.9 percent savings in electricity consumption over that time period and a 1.8 percent savings over all years. These energy savings came at an expected average cost to utilities of roughly 5 cents per kWh saved when future savings are discounted at a 5 percent rate. Copyright © 2012 by the IAEE. All rights reserved.

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© 2015 Elsevier Inc.Links between emission trading programs are not immutable, as highlighted by New Jersey's exit from the Regional Greenhouse Gas Initiative in 2011. This raises the question of what to do with existing permits that are banked for future use-choices that have consequences for market behavior in advance of, or upon speculation about, delinking. We consider two delinking policies. One differentiates banked permits by origin, the other treats banked permits the same. We describe the price behavior and relative cost-effectiveness of each policy. Treating permits differently generally leads to higher costs, and may lead to price divergence, even with only speculation about delinking.

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Stimulated CD4(+) T lymphocytes can differentiate into effector T cell (Teff) or inducible regulatory T cell (Treg) subsets with specific immunological roles. We show that Teff and Treg require distinct metabolic programs to support these functions. Th1, Th2, and Th17 cells expressed high surface levels of the glucose transporter Glut1 and were highly glycolytic. Treg, in contrast, expressed low levels of Glut1 and had high lipid oxidation rates. Consistent with glycolysis and lipid oxidation promoting Teff and Treg, respectively, Teff were selectively increased in Glut1 transgenic mice and reliant on glucose metabolism, whereas Treg had activated AMP-activated protein kinase and were dependent on lipid oxidation. Importantly, AMP-activated protein kinase stimulation was sufficient to decrease Glut1 and increase Treg generation in an asthma model. These data demonstrate that CD4(+) T cell subsets require distinct metabolic programs that can be manipulated in vivo to control Treg and Teff development in inflammatory diseases.

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BACKGROUND: In the domain of academia, the scholarship of research may include, but not limited to, peer-reviewed publications, presentations, or grant submissions. Programmatic research productivity is one of many measures of academic program reputation and ranking. Another measure or tool for quantifying learning success among physical therapists education programs in the USA is 100 % three year pass rates of graduates on the standardized National Physical Therapy Examination (NPTE). In this study, we endeavored to determine if there was an association between research productivity through artifacts and 100 % three year pass rates on the NPTE. METHODS: This observational study involved using pre-approved database exploration representing all accredited programs in the USA who graduated physical therapists during 2009, 2010 and 2011. Descriptive variables captured included raw research productivity artifacts such as peer reviewed publications and books, number of professional presentations, number of scholarly submissions, total grant dollars, and numbers of grants submitted. Descriptive statistics and comparisons (using chi square and t-tests) among program characteristics and research artifacts were calculated. Univariate logistic regression analyses, with appropriate control variables were used to determine associations between research artifacts and 100 % pass rates. RESULTS: Number of scholarly artifacts submitted, faculty with grants, and grant proposals submitted were significantly higher in programs with 100 % three year pass rates. However, after controlling for program characteristics such as grade point average, diversity percentage of cohort, public/private institution, and number of faculty, there were no significant associations between scholarly artifacts and 100 % three year pass rates. CONCLUSIONS: Factors outside of research artifacts are likely better predictors for passing the NPTE.

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PURPOSE: This study aimed to compare selectivity characteristics among institution characteristics to determine differences by institutional funding source (public vs. private) or research activity level (research vs. non-research). METHODS: This study included information provided by the Commission on Accreditation in Physical Therapy Education (CAPTE) and the Federation of State Boards of Physical Therapy. Data were extracted from all students who graduated in 2011 from accredited physical therapy programs in the United States. The public and private designations of the institutions were extracted directly from the classifications from the 'CAPTE annual accreditation report,' and high and low research activity was determined based on Carnegie classifications. The institutions were classified into four groups: public/research intensive, public/non-research intensive, private/research intensive, and private/non-research intensive. Descriptive and comparison analyses with post hoc testing were performed to determine whether there were statistically significant differences among the four groups. RESULTS: Although there were statistically significant baseline grade point average differences among the four categorized groups, there were no significant differences in licensure pass rates or for any of the selectivity variables of interest. CONCLUSION: Selectivity characteristics did not differ by institutional funding source (public vs. private) or research activity level (research vs. non-research). This suggests that the concerns about reduced selectivity among physiotherapy programs, specifically the types that are experiencing the largest proliferation, appear less warranted.