The cocked hat: formal statements and proofs of the theorems

Navigators have been taught for centuries to estimate the location of their craft on a map from three lines of position, for redundancy. The three lines typically form a triangle, called a cocked hat. How is the location of the craft related to the triangle? For more than 80 years navigators have also been taught that, if each line of position is equally likely to pass to the right and to the left of the true location, then the likelihood that the craft is in the triangle is exactly 1/4. This is stated in numerous reputable sources, but was never stated or proved in a mathematically formal and rigorous fashion. In this paper we prove that the likelihood is indeed 1/4 if we assume that the lines of position always intersect pairwise. We also show that the result does not hold under weaker (and more reasonable) assumptions, and we prove a generalisation to lines

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

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

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

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

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

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)