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

Solid-phase XRN1 reactions for RNA cleavage: application in single-molecule sequencing

Modifications in RNA are numerous (∼170) and in higher numbers compared to DNA (∼5) making the ability to sequence an RNA molecule to identify these modifications highly tenuous using next generation sequencing (NGS). The ability to immobilize an exoribonuclease enzyme, such as XRN1, to a solid support while maintaining its activity and capability to cleave both the canonical and modified ribonucleotides from an intact RNA molecule can be a viable approach for single-molecule RNA sequencing. In this study, we report an enzymatic reactor consisting of covalently attached XRN1 to a solid support as the groundwork for a novel RNA exosequencing technique. The covalent attachment of XRN1 to a plastic solid support was achieved using EDC/NHS coupling chemistry. Studies showed that the solid-phase digestion efficiency of model RNAs was 87.6 ± 2.8%, while the XRN1 solution-phase digestion for the same model was 78.3 ± 4.4%. The ability of immobilized XRN1 to digest methylated RNA containing m6A and m5C ribonucleotides was also demonstrated. The processivity and clipping rate of immobilized XRN1 secured using single-molecule fluorescence measurements of a single RNA transcript demonstrated a clipping rate of 26 ± 5 nt s−1 and a processivity of >10.5 kb at 25°C

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

Corrigendum to ‘Dietary aflatoxin B1 (AFB1) reduces growth performance, impacting growth axis, metabolism, and tissue integrity in juvenile gilthead sea bream (Sparus aurata)’. Aquaculture, volume 533, 25 February 2021, 736189

The authors regret the errors in a few table references within the text. Specifically, it should reads as follows within the following subsections/ page: 3.2. Blood analysis (page 5)info:eu-repo/semantics/publishedVersio

Prediction of blood-based biomarkers and subsequent design of bisulfite PCR-LDR-qPCR assay for breast cancer detection

This work is licensed under a Creative Commons Attribution 4.0 International License.Background Interrogation of site-specific CpG methylation in circulating tumor DNAs (ctDNAs) has been employed in a number of studies for early detection of breast cancer (BrCa). In many of these studies, the markers were identified based on known biology of BrCa progression, and interrogated using methyl-specific PCR (MSP), a technique involving bisulfite conversion, PCR, and qPCR. Methods In this report, we are demonstrating the development of a novel assay (Multiplex Bisulfite PCR-LDR-qPCR) which can potentially offer improvements to MSP, by integrating additional steps such as ligase detection reaction (LDR), methylated CpG target enrichment, carryover protection (use of uracil DNA glycosylase), and minimization of primer-dimer formation (use of ribose primers and RNAseH2). The assay is designed to for breast cancer-specific CpG markers identified through integrated analyses of publicly available genome-wide methylation datasets for 31 types of primary tumors (including BrCa), as well as matching normal tissues, and peripheral blood. Results Our results indicate that the PCR-LDR-qPCR assay is capable of detecting ~ 30 methylated copies of each of 3 BrCa-specific CpG markers, when mixed with excess amount unmethylated CpG markers (~ 3000 copies each), which is a reasonable approximation of BrCa ctDNA overwhelmed with peripheral blood cell-free DNA (cfDNA) when isolated from patient plasma. The bioinformatically-identified CpG markers are located in promoter regions of NR5A2 and PRKCB, and a non-coding region of chromosome 1 (upstream of EFNA3). Additional bioinformatic analyses would reveal that these methylation markers are independent of patient race and age, and positively associated with signaling pathways associated with BrCa progression (such as those related to retinoid nuclear receptor, PTEN, p53, pRB, and p27). Conclusion This report demonstrates the potential utilization of bisulfite PCR-LDR-qPCR assay, along with bioinformatically-driven biomarker discovery, in blood-based BrCa detection

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

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