Min-Max Theorems for Packing and Covering Odd (u,v)(u,v)-trails

We investigate the problem of packing and covering odd $(u,v)$-trails in a graph. A $(u,v)$-trail is a $(u,v)$-walk that is allowed to have repeated vertices but no repeated edges. We call a trail odd if the number of edges in the trail is odd. Let $\nu(u,v)$ denote the maximum number of edge-disjoint odd $(u,v)$-trails, and $\tau(u,v)$ denote the minimum size of an edge-set that intersects every odd $(u,v)$-trail. We prove that $\tau(u,v)\leq 2\nu(u,v)+1$. Our result is tight---there are examples showing that $\tau(u,v)=2\nu(u,v)+1$---and substantially improves upon the bound of $8$ obtained in [Churchley et al 2016] for $\tau(u,v)/\nu(u,v)$. Our proof also yields a polynomial-time algorithm for finding a cover and a collection of trails satisfying the above bounds. Our proof is simple and has two main ingredients. We show that (loosely speaking) the problem can be reduced to the problem of packing and covering odd $(uv,uv)$-trails losing a factor of 2 (either in the number of trails found, or the size of the cover). Complementing this, we show that the odd-$(uv,uv)$-trail packing and covering problems can be tackled by exploiting a powerful min-max result of [Chudnovsky et al 2006] for packing vertex-disjoint nonzero $A$-paths in group-labeled graphs

Assessing Regulatory Impact Analyses: The Failure of Agencies to Comply With Executive Order 12,866

None.Environment, Health and Safety, Regulatory Reform

Assessing the Quality of Regulatory Impact Analyses

This study provides the most comprehensive evaluation of the quality of recent economic analyses that agencies conduct before finalizing major regulations. We construct a new dataset that includes analyses of forty-eight major health, safety, and environmental regulations from mid-1996 to mid-1999. This dataset provides detailed information on a variety of issues, including an agency's treatment of benefits, costs, net benefits, discounting, and uncertainty. We use this dataset to assess the quality of recent economic analyses and to determine the extent to which they are consistent with President Clinton's Executive Order 12866 and the benefit-cost guidelines issued by the Office of Management and Budget (OMB). We find that economic analyses prepared by regulatory agencies typically do not provide enough information to make decisions that will maximize the efficiency or effectiveness of a rule. Agencies quantified net benefits for only 29 percent of the rules. Agencies failed to discuss alternatives in 27 percent of the rules and quantified costs and benefits of alternatives in only 31 percent of the rules. Our findings strongly suggest that agencies generally failed to comply with the executive order and adhere to the OMB guidelines. We offer specific suggestions for improving the quality of analysis and the transparency of the regulatory process, including writing clear executive summaries, making analyses available on the Internet, providing more careful consideration of alternatives to a regulation, and estimating net benefits of a regulation when data on costs and benefits are provided.

Aerostructural Optimization of the D8 Wing with Varying Cruise Mach Numbers

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143079/1/6.2017-4436.pd

Generalized Interpolation Material Point Approach to High Melting Explosive with Cavities Under Shock

Criterion for contacting is critically important for the Generalized Interpolation Material Point(GIMP) method. We present an improved criterion by adding a switching function. With the method dynamical response of high melting explosive(HMX) with cavities under shock is investigated. The physical model used in the present work is an elastic-to-plastic and thermal-dynamical model with Mie-Gr\"uneissen equation of state. We mainly concern the influence of various parameters, including the impacting velocity $v$, cavity size $R$, etc, to the dynamical and thermodynamical behaviors of the material. For the colliding of two bodies with a cavity in each, a secondary impacting is observed. Correspondingly, the separation distance $D$ of the two bodies has a maximum value $D_{\max}$ in between the initial and second impacts. When the initial impacting velocity $v$ is not large enough, the cavity collapses in a nearly symmetric fashion, the maximum separation distance $D_{\max}$ increases with $v$. When the initial shock wave is strong enough to collapse the cavity asymmetrically along the shock direction, the variation of $D_{\max}$ with $v$ does not show monotonic behavior. Our numerical results show clear indication that the existence of cavities in explosive helps the creation of ``hot spots''.Comment: Figs.2,4,7,11 in JPG format; Accepted for publication in J. Phys. D: Applied Physic

Modeling Boundary Layer Ingestion Using a Coupled Aeropropulsive Analysis

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143109/1/1.C034601.pd

The Association of Early Dietary Supplementation with Vitamin E with the Incidence of Ulcerative Dermatitis in Mice on a C57BL/6 Background

The purpose of this study was to ascertain if prophylactic ingestion of a diet rich in vitamin E would prevent  or impede the development of ulcerative dermatitis in mice on a C57BL/6 background. Mice were fed after  weaning a standard mouse diet, vitamin E (99 IU/kg), or a mouse diet fortified with vitamin E (3000 IU/  kg). Cases of ulcerative dermatitis were recorded by individuals (i.e. aware of) the diet assignment. The  incidence of ulcerative dermatitis in a retrospective cohort of mice on standard diet was compared with the  group on the diet fortified with vitamin E. Age was associated with ulcerative dermatitis in standard diet  and vitamin E fortified diet groups, r = 0.43, p-value < 0.0001 and r = 0.18, p-value < 0.02, respectively.  The average age of incidence for ulcerative dermatitis in the mice fed the standard diet was 89 weeks and  for the mice fed the vitamin E diet it was 41 weeks. The unadjusted odds ratio comparing the incidence of  ulcerative dermatitis between the two diet groups was 4.6 with a 95% confidence interval of (2.44, 8.58),  x2 p-value < 0.0001. Therefore, there was an association between the diets and ulcerative dermatitis, with  the mice on the vitamin E fortified diet having almost five times the odds of having ulcerative dermatitis  compared with mice on the standard diet. Incidence of ulcerative dermatitis was not influenced by sex or  genotype. Our study results show that a diet fortified in vitamin E initiated at weaning does not prevent or  impede the development of ulcerative dermatitis in mice on a C57BL/6 background and on the contrary  accelerate development when administered to young mice.

Principles And Practices Fostering Inclusive Excellence: Lessons From The Howard Hughes Medical Institute’s Capstone Institutions

Best-practices pedagogy in science, technology, engineering, and mathematics (STEM) aims for inclusive excellence that fosters student persistence. This paper describes principles of inclusivity across 11 primarily undergraduate institutions designated as Capstone Awardees in Howard Hughes Medical Institute’s (HHMI) 2012 competition. The Capstones represent a range of institutional missions, student profiles, and geographical locations. Each successfully directed activities toward persistence of STEM students, especially those from traditionally underrepresented groups, through a set of common elements: mentoring programs to build community; research experiences to strengthen scientific skill/identity; attention to quantitative skills; and outreach/bridge programs to broaden the student pool. This paper grounds these program elements in learning theory, emphasizing their essential principles with examples of how they were implemented within institutional contexts. We also describe common assessment approaches that in many cases informed programming and created traction for stakeholder buy-in. The lessons learned from our shared experiences in pursuit of inclusive excellence, including the resources housed on our companion website, can inform others’ efforts to increase access to and persistence in STEM in higher education