An analysis of mixed integer linear sets based on lattice point free convex sets

Split cuts are cutting planes for mixed integer programs whose validity is derived from maximal lattice point free polyhedra of the form $S:=\{x : \pi_0 \leq \pi^T x \leq \pi_0+1 \}$ called split sets. The set obtained by adding all split cuts is called the split closure, and the split closure is known to be a polyhedron. A split set $S$ has max-facet-width equal to one in the sense that $\max\{\pi^T x : x \in S \}-\min\{\pi^T x : x \in S \} \leq 1$. In this paper we consider using general lattice point free rational polyhedra to derive valid cuts for mixed integer linear sets. We say that lattice point free polyhedra with max-facet-width equal to $w$ have width size $w$. A split cut of width size $w$ is then a valid inequality whose validity follows from a lattice point free rational polyhedron of width size $w$. The $w$-th split closure is the set obtained by adding all valid inequalities of width size at most $w$. Our main result is a sufficient condition for the addition of a family of rational inequalities to result in a polyhedral relaxation. We then show that a corollary is that the $w$-th split closure is a polyhedron. Given this result, a natural question is which width size $w^*$ is required to design a finite cutting plane proof for the validity of an inequality. Specifically, for this value $w^*$, a finite cutting plane proof exists that uses lattice point free rational polyhedra of width size at most $w^*$, but no finite cutting plane proof that only uses lattice point free rational polyhedra of width size smaller than $w^*$. We characterize $w^*$ based on the faces of the linear relaxation

Uncertainties in life cycle greenhouse gas emissions from U.S. beef cattle

Beef cattle feedlots are estimated to contribute 26% of U.S. agricultural greenhouse gas (GHG) emissions, and future climate change policy could target reducing these emissions. Life cycle assessment (LCA) of GHG emissions from U.S. grain-fed beef cattle was conducted based on industry statistics and previous studies to identify the main sources of uncertainty in these estimations. Uncertainty associated with GHG emissions from indirect land use change, pasture soil emissions (e.g. soil carbon sequestration), enteric fermentation from cattle on pasture, and methane emissions from feedlot manure, respectively, contributed the most variability to life cycle GHG emissions from beef production. Feeding of coproducts from ethanol production was estimated to reduce life cycle emissions by 1.7%, but could increase emissions by 0.6–2.0% with higher feeding rates. Monte Carlo simulation found a range of life cycle emissions from 2.52 to 9.58 kg CO2 per kg live weight (5th and 95th percentiles), with a calculated average of 8.14, which is between recent estimates. Current methods used by the U.S. Environmental Protection Agency (EPA) associated with beef production in feedlots were found to account for only 3–20% of life cycle GHG emissions. Includes Supplementary Information/Appendix A

Influence of pH, competing ions, and salinity on the sorption of strontium and cobalt onto biogenic hydroxyapatite

Anthropogenic radionuclides contaminate a range of environments as a result of nuclear activities, for example, leakage from waste storage tanks/ponds (e.g. Hanford, USA or Sellafield sites, UK) or as a result of large scale nuclear accidents (e.g. Chernobyl, Ukraine or Fukushima, Japan). One of the most widely applied remediation techniques for contaminated waters is the use of sorbent materials (e.g. zeolites and apatites). However, a key problem at nuclear contaminated sites is the remediation of radionuclides from complex chemical environments. In this study, biogenic hydroxyapatite (BHAP) produced by Serratia sp. bacteria was investigated for its potential to remediate surrogate radionuclides (Sr2+ and Co2+) from environmentally relevant waters by varying pH, salinity and the type and concentration of cations present. The sorption capacity of the BHAP for both Sr2+ and Co2+ was higher than for a synthetically produced hydroxyapatite (HAP) in the solutions tested. BHAP also compared favorably against a natural zeolite (as used in industrial decontamination) for Sr 2+ and Co 2+ uptake from saline waters. Results confirm that hydroxyapatite minerals of high surface area and amorphous calcium phosphate content, typical for biogenic sources, are suitable restoration or reactive barrier materials for the remediation of complex contaminated environments or wastewaters

Latent variable modeling to develop a robust proxy for sensitive behaviors: application to latrine use behavior and its association with sanitation access in a middle-income country

Abstract Background Globally, diarrhea is a leading cause of child morbidity and mortality. Although latrines are integral for reducing enteric pathogen transmission, several studies have shown no evidence that latrine ownership improved child health. There are a number of explanations for these results. One explanation is that latrine access does not equate to latrine use. Latrine use, however, is difficult to accurately ascertain, as defecation behavior is often stigmatized. To address this measurement issue, we measure latrine use as a latent variable, indicated by a suite of psychosocial variables. Methods We administered a survey of 16 defecation-related psychosocial questions to 251 individuals living in rural Ecuador. We applied latent class analysis (LCA) to these data to model the probability of latrine use as a latent variable. To account for uncertainty in predicted latent class membership, we used a pseudo-class approach to impute five different probabilities of latrine use for each respondent. Via regression modeling, we tested the association between household sanitation and each imputed latrine use variable. Results The optimal model presented strong evidence of two latent classes (entropy = 0.86): consistent users (78%) and inconsistent users (22%), predicted by 5 of our 16 psychosocial variables. There was no evidence of an association between the probability of latrine use, predicted from the LCA, and household access to basic sanitation (OR = 1.1, 95% CI = 0.6–2.1). This suggests that home access to a sanitation facility may not ensure the use of the facility for every family member at all times. Conclusion Effective implementation and evaluation of sanitation programs requires accurate measurement of latrine use. Psychosocial variables, such as norms, perceptions, and attitudes may provide robust proxy-measures. Future longitudinal studies will help to strengthen the use of these surrogate measures, as many of these factors may be subject to secular trends. Additionally, subgroup analyses will elucidate how our  proxy indicators of latrine defecation vary by individual-level characteristics.https://deepblue.lib.umich.edu/bitstream/2027.42/147344/1/12889_2018_Article_6373.pd

Tensile properties of the transverse carpal ligament and carpal tunnel complex

A new sophisticated method that uses video analysis techniques together with a Maillon Rapide Delta to determine the tensile properties of the transverse carpal ligament–carpal tunnel complex has been developed. Six embalmed cadaveric specimens amputated at the mid-forearm and aged (mean (SD)): 82 (6.29) years were tested. The six hands were from three males (four hands) and one female (two hands). Using trigonometry and geometry the elongation and strain of the transverse carpal ligament and carpal arch were calculated. The cross-sectional area of the transverse carpal ligament was determined. Tensile properties of the transverse carpal ligament–carpal tunnel complex and Load–Displacement data were also obtained. Descriptive statistics, one-way ANOVA together with a post-hoc analysis (Tukey) and t-tests were incorporated. A transverse carpal ligament–carpal tunnel complex novel testing method has been developed. The results suggest that there were no significant differences between the original transverse carpal ligament width and transverse carpal ligament at peak elongation (P= 0.108). There were significant differences between the original carpal arch width and carpal arch width at peak elongation (P=0.002). The transverse carpal ligament failed either at the mid-substance or at their bony attachments. At maximum deformation the peak load and maximum transverse carpal ligament displacements ranged from 285.74 N to 1369.66 N and 7.09 mm to 18.55 mm respectively. The transverse carpal ligament cross-sectional area mean (SD) was 27.21 (3.41)mm2. Using this method the results provide useful biomechanical information and data about the tensile properties of the transverse carpal ligament–carpal tunnel complex

New distances to RAVE stars

Probability density functions are determined from new stellar parameters for the distance moduli of stars for which the RAdial Velocity Experiment (RAVE) has obtained spectra with S/N>=10. Single-Gaussian fits to the pdf in distance modulus suffice for roughly half the stars, with most of the other half having satisfactory two-Gaussian representations. As expected, early-type stars rarely require more than one Gaussian. The expectation value of distance is larger than the distance implied by the expectation of distance modulus; the latter is itself larger than the distance implied by the expectation value of the parallax. Our parallaxes of Hipparcos stars agree well with the values measured by Hipparcos, so the expectation of parallax is the most reliable distance indicator. The latter are improved by taking extinction into account. The effective temperature absolute-magnitude diagram of our stars is significantly improved when these pdfs are used to make the diagram. We use the method of kinematic corrections devised by Schoenrich, Binney & Asplund to check for systematic errors for general stars and confirm that the most reliable distance indicator is the expectation of parallax. For cool dwarfs and low-gravity giants tends to be larger than the true distance by up to 30 percent. The most satisfactory distances are for dwarfs hotter than 5500 K. We compare our distances to stars in 13 open clusters with cluster distances from the literature and find excellent agreement for the dwarfs and indications that we are over-estimating distances to giants, especially in young clusters.Comment: 20 pages accepted by MNRAS. Minor changes to the submitted versio

Total and Parity-Projected Level Densities of Iron-Region Nuclei in the Auxiliary Fields Monte Carlo Shell Model

We use the auxiliary-fields Monte Carlo method for the shell model in the complete $(pf+0g_{9/2})$-shell to calculate level densities. We introduce parity projection techniques which enable us to calculate the parity dependence of the level density. Results are presented for $^{56}$Fe, where the calculated total level density is found to be in remarkable agreement with the experimental level density. The parity-projected densities are well described by a backshifted Bethe formula, but with significant dependence of the single-particle level-density and backshift parameters on parity. We compare our exact results with those of the thermal Hartree-Fock approximation.Comment: 14 pages, 3 Postscript figures included, RevTe

Atomic motion in tilted optical lattices

This paper presents a formalism describing the dynamics of a quantum particle in a one-dimensional, time-dependent, tilted lattice. The formalism uses the Wannier-Stark states, which are localized in each site of the lattice, and provides a simple framework allowing fully-analytical developments. Analytic solutions describing the particle motion are explicit derived, and the resulting dynamics is studied.Comment: 6 pages, 2 figs, submitted to EPJD, Springer Verlag styl

Isospin Dependence of the Spin-Orbit Force and Effective Nuclear Potentials,

The isospin dependence of the spin-orbit potential is investigated for an effective Skyrme-like energy functional suitable for density dependent Hartree-Fock calculations. The magnitude of the isospin dependence is obtained from a fit to experimental data on finite spherical nuclei. It is found to be close to that of relativistic Hartree models. Consequently, the anomalous kink in the isotope shifts of Pb nuclei is well reproduced.Comment: Revised, 11 pages (Revtex) and 2 figures available upon request, Preprint MPA-833, Physical Review Letters (in press)