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

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

A computational analysis of lower bounds for big bucket production planning problems

In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provide crucial insights on why these problems are hard to solve, and this is addressed by a thorough analysis in the paper. We conclude with computational results on a variety of widely used test sets, and a discussion of future research

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

Aggregation of Aqueous Kaolin Suspensions in the Presence of Cationic Polyelectrolytes, Anionic Polyelectrolytes and their Mixtures

The influence of anionic, cationic synthetic polyelectrolytes and their mixtures on the aggregation of kaolin hydrosuspension has been studied by means of spectrophotometry, electrophoresis and dynamic light scattering (DLS). An enhancement of the flocculating property of the cationic polyelectrolyte FO 4650 in accordance with its consumption increases from 0.77 mg/g to 7.7 mg/g has been found. At these conditions the relative size of floccules (R) increases from 1.0 to 13.0. The increase of the flocculating property accordingly to the increasing charge of anionic polyelectrolyte is observed in mixtures of cationic and anionic polyelectrolytes. The time dependences of R in presence of the weakly charged cationic polyelectrolyte mixtures reach a plateau region. This can be associated with the formation of electrostatic contacts between the solid surface and the polymer mixtures, as well as with stabilizing equilibrium conformation of macromolecules. It has been found that mixtures of oppositely charged polyelectrolytes lead to more efficient aggregation of particles than individual polyelectrolytes. This process is enhanced by the introduction primarily of the cationic polyelectrolyte and then the anionic one (R = 6‒10). Use of the preformulated mixtures of polymers leads to the marked increase in degree of particle aggregation (R = 12). The reason is an interaction of kaolin particles with inter-polymer complex formed by electrostatic attraction of oppositely charged polyelectrolytes

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

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

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

Frequency drift in MR spectroscopy at 3T

Purpose: Heating of gradient coils and passive shim components is a common cause of instability in the B0 field, especially when gradient intensive sequences are used. The aim of the study was to set a benchmark for typical drift encountered during MR spectroscopy (MRS) to assess the need for real-time field-frequency locking on MRI scanners by comparing field drift data from a large number of sites. Method: A standardized protocol was developed for 80 participating sites using 99 3T MR scanners from 3 major vendors. Phantom water signals were acquired before and after an EPI sequence. The protocol consisted of: minimal preparatory imaging; a short pre-fMRI PRESS; a ten-minute fMRI acquisition; and a long post-fMRI PRESS acquisition. Both pre- and post-fMRI PRESS were non-water suppressed. Real-time frequency stabilization/adjustment was switched off when appropriate. Sixty scanners repeated the protocol for a second dataset. In addition, a three-hour post-fMRI MRS acquisition was performed at one site to observe change of gradient temperature and drift rate. Spectral analysis was performed using MATLAB. Frequency drift in pre-fMRI PRESS data were compared with the first 5:20 minutes and the full 30:00 minutes of data after fMRI. Median (interquartile range) drifts were measured and showed in violin plot. Paired t-tests were performed to compare frequency drift pre- and post-fMRI. A simulated in vivo spectrum was generated using FID-A to visualize the effect of the observed frequency drifts. The simulated spectrum was convolved with the frequency trace for the most extreme cases. Impacts of frequency drifts on NAA and GABA were also simulated as a function of linear drift. Data from the repeated protocol were compared with the corresponding first dataset using Pearson\u27s and intraclass correlation coefficients (ICC). Results: Of the data collected from 99 scanners, 4 were excluded due to various reasons. Thus, data from 95 scanners were ultimately analyzed. For the first 5:20 min (64 transients), median (interquartile range) drift was 0.44 (1.29) Hz before fMRI and 0.83 (1.29) Hz after. This increased to 3.15 (4.02) Hz for the full 30 min (360 transients) run. Average drift rates were 0.29 Hz/min before fMRI and 0.43 Hz/min after. Paired t-tests indicated that drift increased after fMRI, as expected (p \u3c 0.05). Simulated spectra convolved with the frequency drift showed that the intensity of the NAA singlet was reduced by up to 26%, 44 % and 18% for GE, Philips and Siemens scanners after fMRI, respectively. ICCs indicated good agreement between datasets acquired on separate days. The single site long acquisition showed drift rate was reduced to 0.03 Hz/min approximately three hours after fMRI. Discussion: This study analyzed frequency drift data from 95 3T MRI scanners. Median levels of drift were relatively low (5-min average under 1 Hz), but the most extreme cases suffered from higher levels of drift. The extent of drift varied across scanners which both linear and nonlinear drifts were observed

Association between high-dose erythropoiesis-stimulating agents, inflammatory biomarkers, and soluble erythropoietin receptors

<p>Abstract</p> <p>Background</p> <p>High-dose erythropoiesis-stimulating agents (ESA) for anemia of chronic kidney disease (CKD) have been associated with adverse clinical outcomes and do not always improve erythropoiesis. We hypothesized that high-dose ESA requirement would be associated with elevated inflammatory biomarkers, decreased adipokines, and increased circulating, endogenous soluble erythropoietin receptors (sEpoR).</p> <p>Methods</p> <p>A cross-sectional cohort of anemic 32 CKD participants receiving ESA were enrolled at a single center and cytokine profiles, adipokines, and sEpoR were compared between participants stratified by ESA dose requirement (usual-dose darbepoetin-α (< 1 μg/kg/week) and high-dose (≥1 μg/kg/week)).</p> <p>Results</p> <p>Baseline characteristics were similar between groups; however, hemoglobin was lower among participants on high-dose (1.4 μg/kg/week) vs usual-dose (0.5 μg/kg/week) ESA.</p> <p>In adjusted analyses, high-dose ESA was associated with an increased odds for elevations in c-reactive protein and interleukin-6 (p < 0.05 for both). There was no correlation between high-dose ESA and adipokines. Higher ESA dose correlated with higher levels of sEpoR (r_s= 0.39, p = 0.03). In adjusted analyses, higher ESA dose (per μcg/kg/week) was associated with a 53% greater odds of sEpoR being above the median (p < 0.05).</p> <p>Conclusion</p> <p>High-dose ESA requirement among anemic CKD participants was associated with elevated inflammatory biomarkers and higher levels of circulating sEpoR, an inhibitor of erythropoiesis. Further research confirming these findings is warranted.</p> <p>Trial registration</p> <p>Clinicaltrials.gov <a href="http://www.clinicaltrials.gov/ct2/show/NCT00526747">NCT00526747</a></p