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

Predicting erythropoietin resistance in hemodialysis patients with type 2 diabetes

<p>Background: Resistance to ESAs (erythropoietin stimulating agents) is highly prevalent in hemodialysis patients with diabetes and associated with an increased mortality. The aim of this study was to identify predictors for ESA resistance and to develop a prediction model for the risk stratification in these patients.</p> <p>Methods: A post-hoc analysis was conducted of the 4D study, including 1015 patients with type 2 diabetes undergoing hemodialysis. Determinants of ESA resistance were identified by univariate logistic regression analyses. Subsequently, multivariate models were performed with stepwise inclusion of significant predictors from clinical parameters, routine laboratory and specific biomarkers.</p> <p>Results: In the model restricted to clinical parameters, male sex, shorter dialysis vintage, lower BMI, history of CHF, use of ACE-inhibitors and a higher heart rate were identified as independent predictors of ESA resistance. In regard to routine laboratory markers, lower albumin, lower iron saturation, higher creatinine and higher potassium levels were independently associated with ESA resistance. With respect to specific biomarkers, higher ADMA and CRP levels as well as lower Osteocalcin levels were predictors of ESA resistance.</p> <p>Conclusions: Easily obtainable clinical parameters and routine laboratory parameters can predict ESA resistance in diabetic hemodialysis patients with good discrimination. Specific biomarkers did not meaningfully further improve the risk prediction of ESA resistance. Routinely assessed data can be used in clinical practice to stratify patients according to the risk of ESA resistance, which may help to assign appropriate treatment strategies.</p&gt

Why 'scaffolding' is the wrong metaphor : the cognitive usefulness of mathematical representations.

The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least (and plausibly for others), scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts.Peer reviewe

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

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

Novel glucose-lowering drugs and the risk of acute kidney injury in routine care: the Stockholm CREAtinine Measurements (SCREAM) project

Introduction Little is known about the comparative effects of sodium glucose cotransporter-2 inhibitors (SGLT2i), glucagon-like peptide-1 receptor agonists (GLP1-RA), or dipeptidyl peptidase-4 inhibitors (DPP-4i) on the risk of acute kidney injury (AKI) in routine care, which may differ from the controlled setting of trials.Methods Observational study comparing risks of AKI among new users of SGLT2i, GLP1-RA or DPP-4i in the region of Stockholm, Sweden, during 2008-2018. AKI was defined by ICD-10 codes and creatinine-based KDIGO criteria. We used inverse probability of treatment weighting (IPTW) to adjust for 60 potential confounders, weighted Kaplan-Meier curves and Cox regression to estimate hazard ratios and absolute risks.Results We included 17,407 participants who newly initiated DPP-4i (N = 10,605), GLP1-RA (N = 4448) or SGLT2i (N = 2354). Mean age was 63 years (39% women) and median (IQR) eGFR was 89 (73-100) ml/min/1.73 m(2). During a median follow-up of 2.5 years, 1411 participants experienced AKI. SGLT2i users had the lowest incidence rate of AKI, 18.3 [CI 95% 14.1-23.4] per 1000 person years, followed by GLP1-RA (22.5; 19.9-25.3) and DPP-4i (26.6; 25-28.2). The weighted 3-year absolute risk for AKI was 5.79% [3.63-8.52] in the SGLT2i group, compared with 7.03% [5.69-8.69] and 7.00% [6.43-7.58] in the GLP1-RA and DPP-4i groups, respectively. The adjusted hazard ratio was 0.73 [CI 95% 0.45-1.16] for SGLT2i vs. DPP-4i, and 0.98 [CI 95% 0.82-1.18] for GLP1-RA vs. DPP-4i.Conclusion This study of routine care patients initiating novel glucose-lowering drugs showed similar occurrence of AKI between therapies, and suggests lower risk for SGLT2i.Clinical epidemiolog

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

The Cold Peace: Russo-Western Relations as a Mimetic Cold War

In 1989–1991 the geo-ideological contestation between two blocs was swept away, together with the ideology of civil war and its concomitant Cold War played out on the larger stage. Paradoxically, while the domestic sources of Cold War confrontation have been transcended, its external manifestations remain in the form of a ‘legacy’ geopolitical contest between the dominant hegemonic power (the United States) and a number of potential rising great powers, of which Russia is one. The post-revolutionary era is thus one of a ‘cold peace’. A cold peace is a mimetic cold war. In other words, while a cold war accepts the logic of conflict in the international system and between certain protagonists in particular, a cold peace reproduces the behavioural patterns of a cold war but suppresses acceptance of the logic of behaviour. A cold peace is accompanied by a singular stress on notions of victimhood for some and undigested and bitter victory for others. The perceived victim status of one set of actors provides the seedbed for renewed conflict, while the ‘victory’ of the others cannot be consolidated in some sort of relatively unchallenged post-conflict order. The ‘universalism’ of the victors is now challenged by Russia's neo-revisionist policy, including not so much the defence of Westphalian notions of sovereignty but the espousal of an international system with room for multiple systems (the Schmittean pluriverse)

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