A commentary on Freudenthal’s didactic phenomenology of the mathematical structures associated with the notion of measurement

This paper discusses Freudenthal\u27s didactical phenomenology for the mathematical structures related to measurement. Freudenthal starts with the set G of all objects having the attribute of weight, an attribute that is to be measured. He proposes two operations, the first one among the measurements themselves, called “addition . Addition is interpreted in terms of the mental actions associated with measurement and, in the case of weights, it consists on the process of placing weights on one of the two dishes of a balance in order to balance them with a predetermined gauge, its fractions or multiples thereof, which are placed on the other. Their total weight is obtained by comparison with a predetermined gauge. The second operation, between weights and positive integers, allow weights to be amplified (by adding as many times as desired their weight measure). A related operation to amplification is that of contraction (by dividing the weight into as many equal parts as desired.) Freudenthal then extends his definitions in order to assign a meaning to the multiplication of a measure by, first, any positive rational number, and, second, by completeness, to any real number. Freudenthal\u27s didactical phenomenology is based on the historical phenomenology of measurement, fractions, decimals and percentages. It is a central tenet of Realistic Mathematics Education (RME) that didactical phenomenologies of mathematical structures constitute proposals from which to make cognitively advantageous teaching sequences for the relevant mathematical structures. We discuss how Freudenthal\u27s phenomenology of the mathematical structures for measurement gets translated into the mathematical models associated with the rational numbers. Finally, we make reference to a paradigmatic teaching unit which incorporates coherently Freudenthal\u27s didactical phenomenology

A semiotic reflection on the didactics of the Chain rule

According to (Fried, 2008), there is an intrinsic tension in trying to apply the history of mathematics to its didactics. Besides the widespread feeling that the introduction of didactic elements taken from the history of mathematics can detract the pedagogy of mathematics from the attainment of important goals, (Fried, 2008, p. 193) describes a pair of specific pitfalls that can arise in implementing such historical applications in mathematics education. The description in (Fried, 2008), is presented in the parlance of Sausserian Semiotics and identifies two semiotic “deformations” that arise when one fails to observe that the pairing between signs and meanings in a given synchronic “cross-section” associated with the development of mathematics need not hold for another synchronic cross section at a different time. In this exposition, an example related to an application of the history of the chain rule to the didactics of calculus is presented. Our example illustrates the semiotic deformations alluded by (Fried, 2008), and points out a possible explanation of how this may lead to unrealistic pedagogical expectations for student performance. Finally, an argument is presented for the creation of a framework for a historical heuristics for mathematics education, possibly beyond the bounds of semiotics

Teaching Calculus with Infinitesimals: New Perspectives

The present research corroborates K. Sullivan\u27s initial results as stated in her epoch making study about the effectiveness of teaching elementary calculus using Robinson\u27s non standard approach. Our research added to her results related to the teaching of the elementary integral, with similar positive results. In this essay we propose a definition of the notion of cognitive advantage mentioned by Sullivan in expressing the dramatic differences in understanding of students of non standard calculus as opposed to those of its standard counterpart. Our proposal is based on ideas of Kitcher and Kuhn and allows us to better understand the didactics of Calculus. Formally K. Sullivan\u27s claim of an observed advantage when referring to the improved understanding of non standard calculus students (as opposed to the standard approach of Weierstrass) is a consequence to the accepted fact that mathematical truths remain the same when changes of paradigms ensue, a situation markedly different from that science. While mathematical truths remain, mathematical justifications (proofs) change dramatically and increase in complexity

Programmed Cell Death-Related Proteases in Plants

From an ancient Greek term related to the “leavening of bread” (en, in; zyme, leaven), an enzyme can be defined as a substance showing the properties of a catalyst that is produced as a result of cellular activity. Every proteinaceous enzyme that performs hydrolysis of peptide bonds is appropriately termed “protease” (peptidase). All of them share aspects of catalytic strategy, but with some variation. As a result, the proteases are grouped into six different catalytic families: serine, threonine, cysteine, aspartic, glutamic and metallopeptidases (http://merops.sanger.ac.uk/). The larger families (cysteine, serine, aspartic and metallopeptidases) have a wide range of distribution on living organism groups, and are also present in the “controversial” viruses. As a well‐represented family, the cysteine proteases play important roles in events such as signalling pathways, programmed cell death (PCD), nutrient mobilization, protein maturing, hormone synthesis and degradation. In the past two decades, an increased interest was driven to the study of the programmed cell death (PCD), mainly after the discovery of caspase‐related proteins and caspase‐like activities in organisms not metazoan. Caspases are cysteine proteases that cleave their substrate after aspartate residues and are part of signalling cascades of the apoptotic PCD process (also in inflammatory process), unique of metazoan. The caspase‐related proteins are named paracaspases and metacaspases. Paracaspases are found on metazoan and Dictyostelium, whereas the metacaspases are present on plants, fungi and groups of protozoan. On plants, PCD has features that are distinct from that of animals and is an important pathway on developmental events, defensive and stress response (biotic and abiotic). All these events have their own particularities, but the participation of proteases seems to be universal with those responsible for caspase‐like activities and metacaspases having an increasing number of reports that put them as important for plant PCD. In this chapter, we tackle important aspects of the proteases, in special that involved in plant PDC, as well as their specific regulators. Aspects of function, catalytic mechanisms and interaction with ligands will be on focus

Collaborative, Distributed Simulations of Agri-Food Supply Chains. Analysis on How Linking Theory and Practice by Using Multi-agent Structures

Simulations help to understand and predict the behaviour of complex phenomena’s, likewise distributed socio-technical systems or how stakeholders interacts in complex domains. Such domains are normally based on networked based interaction, where information, product and decision flows comes in to play, especially under the well-known supply chains structures. Although tools exist to simulate supply chains, they do not adequately support multiple stakeholders to collaboratively create and explore a variety of decision-making scenarios. Hence, in order to provide a preliminary understanding on how these interaction affects stakeholders decision-making, this research presents an study, analysis and proposal development of robust platform to collaboratively build and simulate communication among supply chain. Since realistic supply chain behaviours are complex, a multi-agent approach was selected in order to represent such complexities in a standardised manner. The platform provides agent behaviours for common agent patterns. It provides extension hotspots to implement more specific agent behaviour for expert users (that requires programming). Therefore, as key contribution, technical aspects of the platform are presented, and also the role of multi-level supply chain scenario simulation is discussed and analysed, especially under de context of digital supply chain transformation in the agri-food context. Finally, we discuss lessons learned from early tests with the reference implementation of the platform

Vitamin D protects against oxidative stress and inflammation in human retinal cells

Diabetic retinopathy is a vision-threatening microvascular complication of diabetes and is one of the leading causes of blindness. Oxidative stress and inflammation play a major role in its pathogenesis, and new therapies counteracting these contributors could be of great interest. In the current study, we investigated the role of vitamin D against oxidative stress and inflammation in human retinal pigment epithelium (RPE) and human retinal endothelial cell lines. We demonstrate that vitamin D effectively counteracts the oxidative stress induced by hydrogen peroxide (H2O2). In addition, the increased levels of proinflammatory proteins such as Interleukin (IL)-6, IL-8, Monocyte chemoattractant protein (MCP)-1, Interferon (IFN)-γ, and tumor necrosis factor (TNF)-α triggered by lipopolysaccharide (LPS) exposure were significantly decreased by vitamin D addition. Interestingly, the increased IL-18 only decreased by vitamin D addition in endothelial cells but not in RPE cells, suggesting a main antiangiogenic role under inflammatory conditions. Moreover, H2O2 and LPS induced the alteration and morphological damage of tight junctions in adult retinal pigment epithelium (ARPE-19) cells that were restored under oxidative and inflammatory conditions by the addition of vitamin D to the media. In conclusion, our data suggest that vitamin D could protect the retina by enhancing antioxidant defense and through exhibiting anti-inflammatory properties

Neutrophil Function in Elderly Patients Hospitalized with Community- Acquired Pneumonia

Background: Advanced age is associated with immunosenescence as well as increased risk for poor outcomes during episodes of community-acquired pneumonia (CAP). Data on neutrophil function in hospitalized elderly patients with CAP is lacking. In this study we compared neutrophil function in elderly and non-elderly hospitalized patients with CAP. Methods: Prospective study of healthy controls (HC) and patients hospitalized with CAP nonelderly (NE-CAP) and elderly (E-CAP). Blood samples were obtained on the day of hospitalization. The following neutrophil functional assays were performed: degranulation of secretory vesicles (CD35), degranulation of specific granules (CD66b), phagocytosis, and hydrogen peroxide (H2O2) production. The Mann-Whitney U-test was used to compare differences in neutrophil function. Results: A total of 12 HC, 28 NE-CAP, and 12 E-CAP were evaluated. There were no significant differences between NE-CAP and E-CAP patients in regard to CD35 expression (p=0.465), CD66b expression (p=0.601), phagocytosis (p=0.654), or H2O2 production (p=0.541) Conclusions: We failed to demonstrate any significant difference in neutrophil function in nonelderly versus elderly patients hospitalized with CAP in relation to membrane expression of CD35 and CD66b, phagocytosis, and respiratory burst. Abnormal neutrophil function is unlikely to be an important component of the immunosenescence described in elderly patients with CAP

A higher proportion of eicosapentaenoic acid (EPA) when combined with docosahexaenoic acid (DHA) in omega-3 dietary supplements provides higher antioxidant effects in human retinal cells

Retinal pigment epithelium (RPE) is a key regulator of retinal function and is directly related to the transport, delivery, and metabolism of long-chain n-3 polyunsaturated fatty acids (n3-PUFA), in the retina. Due to their functions and location, RPE cells are constantly exposed to oxidative stress. Eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) have shown to have antioxidant effects by different mechanisms. For this reason, we designed an in vitro study to compare 10 formulations of DHA and EPA supplements from different origins and combined in different proportions, evaluating their effect on cell viability, cell proliferation, reactive oxygen species production, and cell migration using ARPE-19 cells. Furthermore, we assessed their ability to rescue RPE cells from the oxidative conditions seen in diabetic retinopathy. Our results showed that the different formulations of n3-PUFAs have a beneficial effect on cell viability and proliferation and are able to restore oxidative induced RPE damage. We observed that the n3-PUFA provided different results alone or combined in the same supplement. When combined, the best results were obtained in formulations that included a higher proportion of EPA than DHA. Moreover, n3-PUFA in the form of ethyl-esters had a worse performance when compared with triglycerides or phospholipid based formulations

First Human Isolate of Hantavirus (Andes virus) in the Americas

We isolated Andes virus (formal name: Andes virus [ANDV], a species in the genus Hantavirus), from serum of an asymptomatic 10-year-old Chilean boy who died 6 days later of hantavirus pulmonary syndrome (HPS). The serum was obtained 12 days after his grandmother died from HPS and 2 days before he became febrile. No hantavirus immunoglobulin (Ig) G or IgM antibodies were detected in the serum sample. After three blind passages, ANDV antigens were detected in Vero E6 cells by immunofluorescence assay and enzyme-linked immunosorbent assay, and ANDV RNA was detected by reverse transcription-polymerase chain reaction. A fragment of the virus genome showed 96.2% nucleotide identity with that of prototype ANDV. To our knowledge, this is the first isolation of any agent of hemorrhagic fever with renal syndrome from a human and the first such isolation of hantavirus before symptoms of that syndrome or HPS began