On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (l,S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures

Temperatures in Pigs During 3 T MRI Temperatures, Heart Rates, and Breathing Rates of Pigs During RF Power Deposition in a 3 T (128 MHz) Body Coil

Exposure to radiofrequency (RF) power deposition during magnetic resonance imaging (MRI) induces elevated body-tissue temperatures and may cause changes in heart and breathing rates, disturbing thermoregulation. Eleven temperature sensors were placed in muscle tissue and one sensor in the rectum (measured in 10 cm depth) of 20 free-breathing anesthetized pigs to verify temperature curves during RF exposure. Tissue temperatures and heart and breathing rates were measured before, during, and after RF exposure. Pigs were placed into a 60-cm diameter whole-body resonator of a 3 T MRI system. Nineteen anesthetized pigs were divided into four RF exposure groups: sham (0 W/kg), low-exposure (2.7 W/kg, mean exposure time 56 min), moderate-exposure (4.8 W/kg, mean exposure time 31 min), and high-exposure (4.4 W/kg, mean exposure time 61 min). One pig was exposed to a whole-body specific absorption rate (wbSAR) of 11.4 W/kg (extreme-exposure). Hotspot temperatures, measured by sensor 2, increased by mean 5.0 ± 0.9°C, min 3.9; max 6.3 (low), 7.0 ± 2.3°C, min 4.6; max 9.9 (moderate), and 9.2 ± 4.4°C, min 6.1, max 17.9 (high) compared with 0.3 ± 0.3°C in the sham-exposure group (min 0.1, max 0.6). Four time-temperature curves were identified: sinusoidal, parabolic, plateau, and linear. These curve shapes did not correlate with RF intensity, rectal temperature, breathing rate, or heart rate. In all pigs, rectal temperatures increased (2.1 ± 0.9°C) during and even after RF exposure, while hotspot temperatures decreased after exposure. When rectal temperature increased by 1°C, hotspot temperature increased up to 42.8°C within 37 min (low-exposure) or up to 43.8°C within 24 min (high-exposure). Global wbSAR did not correlate with maximum hotspot. Bioelectromagnetics. 2021;42:37–50

Circulating proteins as predictors of cardiovascular mortality in endstage renal disease

Introduction: Proteomic profiling of end-stage renal disease (ESRD) patients could lead to improved risk prediction and novel insights into cardiovascular disease mechanisms. Plasma levels of 92 cardiovascular disease-associated proteins were assessed by proximity extension assay (Proseek Multiplex CVD-1, Olink Bioscience, Uppsala, Sweden) in a discovery cohort of dialysis patients, the Mapping of Inflammatory Markers in Chronic Kidney disease cohort [MIMICK; n = 183, 55% women, mean age 63 years, 46 cardiovascular deaths during follow-up (mean 43 months)]. Significant results were replicated in the incident and prevalent hemodialysis arm of the Salford Kidney Study [SKS dialysis study, n = 186, 73% women, mean age 62 years, 45 cardiovascular deaths during follow-up (mean 12 months)], and in the CKD5-LD-RTxcohort with assessments of coronary artery calcium (CAC)-score by cardiac computed tomography (n = 89, 37% women, mean age 46 years). Results: In age and sex-adjusted Cox regression in MIMICK, 11 plasma proteins were nominally associated with cardiovascular mortality (in order of significance: Kidney injury molecule-1 (KIM-1), Matrix metalloproteinase-7, Tumour necrosis factor receptor 2, Interleukin-6, Matrix metalloproteinase-1, Brain-natriuretic peptide, ST2 protein, Hepatocyte growth factor, TNF-related apoptosis inducing ligand receptor-2, Spondin-1, and Fibroblast growth factor 25). Only plasma KIM-1 was associated with cardiovascular mortality after correction for multiple testing, but also after adjustment for dialysis vintage, cardiovascular risk factors and inflammation (hazard ratio) per standard deviation (SD) increase 1.84, 95% CI 1.26–2.69, p = 0.002. Addition of KIM-1, or nine of the most informative proteins to an established risk-score (modified AROii CVM-score) improved discrimination of cardiovascular mortality risk from C = 0.777 to C = 0.799 and C = 0.823, respectively. In the SKS dialysis study, KIM-1 predicted cardiovascular mortality in age and sex adjusted models (hazard ratio per SD increase 1.45, 95% CI 1.03–2.05, p = 0.034) and higher KIM-1 was associated with higher CACscores in the CKD5-LD-RTx-cohort. Conclusions Our proteomics approach identified plasma KIM-1 as a risk marker for cardiovascular mortality and coronary artery calcification in three independent ESRD-cohorts. The improved risk prediction for cardiovascular mortality by plasma proteomics merit further studies.Swedish Research CouncilSwedish Heart–Lung foundationEuropean Union Horizon 2020 (Grant number 634869)Dalarna UniversityUppsala UniversitySwedish Medical Research CouncilNjurfondenEuropean Union’s Horizon 2020 research and innovation programme, Marie Sklodowska-Curie Grant Agreement no. 722609Publishe

Mixed integer programming in production planning with backlogging and setup carryover : modeling and algorithms

This paper proposes a mixed integer programming formulation for modeling the capacitated multi-level lot sizing problem with both backlogging and setup carryover. Based on the model formulation, a progressive time-oriented decomposition heuristic framework is then proposed, where improvement and construction heuristics are effectively combined, therefore efficiently avoiding the weaknesses associated with the one-time decisions made by other classical time-oriented decomposition algorithms. Computational results show that the proposed optimization framework provides competitive solutions within a reasonable time

A Cauchy-Dirac delta function

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201

Simulation of cell-substrate traction force dynamics in response to soluble factors

Finite element (FE) simulations of contractile responses of vascular muscular thin films (vMTFs) and endothelial cells resting on an array of micro-posts under stimulation of soluble factors were conducted in comparison with experimental measurements reported in literature. Two types of constitutive models were employed in the simulations, i.e. smooth muscle cell type and non-smooth muscle cell type. The time histories of the effects of soluble factors were obtained via calibration against experimental measurements of contractile responses of tissues or cells. The numerical results for vMTFs with micropatterned tissues suggest that the radius of curvature of vMTFs under stimulation of soluble factors is sensitive to width of the micropatterned tissue, i.e. the radius of curvature increases as the tissue width decreases. However, as the tissue response is essentially isometric, the time history of the maximum principal stress of the micropatterned tissues is not sensitive to tissue width. Good agreement has been achieved for predictions of the vasoconstrictor endothelin-1 (ET-1) induced contraction stress between the FE numerical simulation and the experiment based approach of Alford, et al. (2011) for the vMTFs with 40, 60, 80 and 100 μm width patterns. This may suggest the contraction stress is weakly sensitive to the tissue width for these patterns. However, for 20 μm width tissue patterning, the numerical simulation result for contraction stress is less than the average value of experimental measurements, which may suggest the thinner and more elongated spindle-like cells within the 20 μm width tissue patterning have higher contractile output. The constitutive model for non-smooth muscle cells was used to simulate the contractile response of the endothelial cells. The substrate was treated as an effective continuum. For agonists such as Lysophosphatidic acid (LPA) and vascular endothelial growth factor (VEGF), the deformation of the cell diminishes from edge to centre and the central part of the cell is essentially under isometric state. Numerical studies demonstrated the scenarios that cell polarity can be triggered via manipulation of the effective stiffness and Possion’s ratio of the substrate

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

Voluntary organizations and society–military relations in contemporary Russia

The 2014 crisis in Ukraine has refocused attention on Russia as a European security actor. Despite showing renewed military capability, compared to the post-Soviet period, Russian society–military relations have remained the same. This relationship (between society and the security organs) provides the key context for assessing security. Analysis of everyday militarization and the role of voluntary organizations (such as DOSAAF [Dobrovol'noe obshchestvo sodeistviya armii, aviatsii i flotu] and Nashi [Molodezhnoe demokraticheskoe antifashistskoe dvizheni]) in supporting the military can provide an important insight into Russian behaviour as a security actor. These organizations generate a pro-military outlook and at the same time provide training and activities, thus contributing to military effectiveness by developing the competency of young people prior to military service as well as increasing public knowledge of military affairs. However, strong support for the military, a lack of independent information, and an absence of a shared vision on how society–military relations should be developed and also represent political challenges in terms of everyday militarization. This dynamic is important for understanding both Russia's security posture and wider security implications for Europe