'Fair' Partitions of Polygons - an Introduction

We address the question: Given a positive integer $N$, can any 2D convex polygonal region be partitioned into $N$ convex pieces such that all pieces have the same area and same perimeter? The answer to this question is easily `yes' for $N$=2. We prove the answer to be `yes' for $N$=4 and also discuss higher powers of 2.Comment: 7 pages. 1 figure. This version (v6) is mostly a formal reworking of the main proof in v2 which was uploaded in December 200

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

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

Reversible linkage of two distinct small molecule inhibitors of myc generates a dimeric inhibitor with improved potency that is active in myc over-expressing cancer cell lines

We describe the successful application of a novel approach for generating dimeric Myc inhibitors by modifying and reversibly linking two previously described small molecules.We synthesized two directed libraries of monomers, each comprised of a ligand, a connector, and a bioorthogonal linker element, to identify the optimal dimer configuration required to inhibit Myc. We identified combinations of monomers, termed self-assembling dimeric inhibitors, which displayed synergistic inhibition of Myc-dependent cell growth. We confirmed that these dimeric inhibitors directly bind to Myc blocking its interaction with Max and affect transcription of MYC dependent genes. Control combinations that are unable to form a dimer do not show any synergistic effects in these assays. Collectively, these data validate our new approach to generate more potent and selective inhibitors of Myc by self-assembly from smaller, lower affinity components. This approach provides an opportunity for developing novel therapeutics against Myc and other challenging protein:protein interaction (PPI) target classes. © 2015 Wanner et al

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

Cell wall components and pectin esterification levels as markers of proliferation and differentiation events during pollen development and pollen embryogenesis in Capsicum annuum L.

Plant cell walls and their polymers are regulated during plant development, but the specific roles of their molecular components are still unclear, as well as the functional meaning of wall changes in different cell types and processes. In this work the in situ analysis of the distribution of different cell wall components was performed during two developmental programmes, gametophytic pollen development, which is a differentiation process, and stress-induced pollen embryogenesis, which involves proliferation followed by differentiation processes. The changes in cell wall polymers were compared with a system of plant cell proliferation and differentiation, the root apical meristem. The analysis was also carried out during the first stages of zygotic embryogenesis. Specific antibodies recognizing the major cell wall polymers, xyloglucan (XG) and the rhamnogalacturonan II (RGII) pectin domain, and antibodies against high- and low-methyl-esterified pectins were used for both dot-blot and immunolocalization with light and electron microscopy. The results showed differences in the distribution pattern of these molecular complexes, as well as in the proportion of esterified and non-esterified pectins in the two pollen developmental pathways. Highly esterified pectins were characteristics of proliferation, whereas high levels of the non-esterified pectins, XG and RGII were abundant in walls of differentiating cells. Distribution patterns similar to those of pollen embryos were found in zygotic embryos. The wall changes reported are characteristic of proliferation and differentiation events as markers of these processes that take place during pollen development and embryogenesis