Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Gene and protein expression of glucose transporter 1 and glucose transporter 3 in human laryngeal cancer—the relationship with regulatory hypoxia-inducible factor-1α expression, tumor invasiveness, and patient prognosis

Increased glucose uptake mediated by glucose transporters and reliance on glycolysis are common features of malignant cells. Hypoxia-inducible factor-1α supports the adaptation of hypoxic cells by inducing genes related to glucose metabolism. The contribution of glucose transporter (GLUT) and hypoxia-inducible factor-1α (HIF-1α) activity to tumor behavior and their prognostic value in head and neck cancers remains unclear. The aim of this study was to examine the predictive value of GLUT1, GLUT3, and HIF-1α messenger RNA (mRNA)/protein expression as markers of tumor aggressiveness and prognosis in laryngeal cancer. The level of hypoxia/metabolic marker genes was determined in 106 squamous cell laryngeal cancer (SCC) and 73 noncancerous matched mucosa (NCM) controls using quantitative realtime PCR. The related protein levels were analyzed by Western blot. Positive expression of SLC2A1, SLC2A3, and HIF-1α genes was noted in 83.9, 82.1, and 71.7 % of SCC specimens and in 34.4, 59.4, and 62.5 % of laryngeal cancer samples. Higher levels of mRNA/protein for GLUT1 and HIF-1α were noted in SCC compared to NCM (p<0.05). SLC2A1 was found to have a positive relationship with grade, tumor front grading (TFG) score, and depth and mode of invasion (p<0.05). SLC2A3 was related to grade and invasion type (p<0.05). There were also relationships of HIF-1α with pTNM, TFG scale, invasion depth and mode, tumor recurrences, and overall survival (p<0.05). In addition, more advanced tumors were found to be more likely to demonstrate positive expression of these proteins. In conclusion, the hypoxia/metabolic markers studied could be used as molecular markers of tumor invasiveness in laryngeal cancer.This work was supported, in part, by the statutory fund of the Department of Cytobiochemistry, University of Łódź, Poland (506/811), and by grant fromtheNational Science Council, Poland (N403 043 32/2326)

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

7. Biological Effectiveness of 12 C and 20 Ne Ions with Very High LET

Knowledge of radiobiological effects of heavy ions at the cellular and molecular level is of fundamental importance in the field of radiation therapy (for example C ions) and space radiation biology (for example Ne ions). One of the issues that require deeper investigations is a determination of RBE values for a wide range of LET, for all relevant doses, for many cell types and various kinds of radiations During recent years, the biological effectiveness of heavy ions has been widely investigated with the aim to identify physical characteristics relevant to biological actions. These investigations are pertinent to the use of heavy ions in radiosurgery and radiotherapy. What has not been investigated so thoroughly is the biological effectiveness of heavy ions at low energies and very high LET values. The LET, which is equal to the stopping power of heavy particles, increases sharply at the end of the particle&apos;s path, forming a so-called Bragg peak. The shape of the Bragg peak depends on the particle type. Because overlying beams with different energies and components of primary and secondary particles are used in radiotherapy, the knowledge of RBE values of very high LET radiation need to be well characterized. An experimental set-up designed for such investigations was constructed at the isochronic cyclotron in Heavy Ion Laboratory. A more detailed description of the set-up can be found in Ref. CHO-K1 cells have been used as a suitable biological system for our studies. The cell line is characterized by genetic stability, the ability to form colonies, a relatively rapid growth rate with a cell cycle of 12-14 hours. For exposure to ions the cells were seeded in specially designed Petri dishes, which were filled with medium, sealed by a parafilm cover and placed in a vertical sample holder mounted in an x-y-z table that was connected to a special stepping motor. The irradiated sample moved under the beam according to a planned route. Movement was initiated when the number of counts detected by the 20 o particle detector reached the preset value. When all fields have been exposed the sample holder returned to the start position. Stored information enabled to evaluate the beam stability and intensity. The whole set-up was surveyed by a digital camera. The total time of exposure per dish was between 1-5 min. depending on the dose and beam intensity. The dose rates were changed from 0.05 Gy/min. to 1 Gy/min depending on the dose. Cell survival was estimated according to standard procedure

Relationship Between Anti-DFS70 Autoantibodies and Oxidative Stress

Background: The anti-DFS70 autoantibodies are one of the most commonly and widely described agent of unknown clinical significance, frequently detected in healthy individuals. It is not known whether the DFS70 autoantibodies are protective or pathogenic. One of the factors suspected of inducing the formation of anti-DFS70 antibodies is increased oxidative stress. We evaluated the coexistence of anti-DFS70 antibodies with selected markers of oxidative stress and investigated whether these antibodies could be considered as indirect markers of oxidative stress. Methods: The intensity of oxidative stress was measured in all samples via indices of free-radical damage to lipids and proteins such as total oxidant status (TOS), concentrations of lipid hydroperoxides (LPH), lipofuscin (LPS), and malondialdehyde (MDA). The parameters of the non-enzymatic antioxidant system, such as total antioxidant status (TAS) and uric acid concentration (UA), were also measured, as well as the activity of superoxide dismutase (SOD). Based on TOS and TAS values, the oxidative stress index (OSI) was calculated. All samples were also tested with indirect immunofluorescence assay (IFA) and 357 samples were selected for direct monospecific anti DFS70 enzyme-linked immunosorbent assay (ELISA) testing. Results: The anti-DFS70 antibodies were confirmed by ELISA test in 21.29% of samples. Compared with anti-DFS70 negative samples we observed 23% lower concentration of LPH (P =.038) and 11% lower concentration of UA (P =.005). TOS was 20% lower (P =.014). The activity of SOD was up to 5% higher (P =.037). The Pearson correlation showed weak negative correlation for LPH, UA, and TOS and a weak positive correlation for SOD activity. Conclusion: In samples positive for the anti-DFS70 antibody a decreased level of oxidative stress was observed, especially in the case of samples with a high antibody titer. Anti-DFS70 antibodies can be considered as an indirect marker of reduced oxidative stress or a marker indicating the recent intensification of antioxidant processes

Cyanobacteria and cyanotoxins in Polish freshwater bodies.

In this work, the authors examined the presence of cyanobacteria and cyanotoxins in 21 samples collected from fresh water bodies located in 5 provinces in Poland: Lublin (2), Podlasie (1), Pomerania (6), Warmia-Masuria (1) and Wielkopolska (11). In addition, to determine the general pattern of geographical distribution, frequency of cyanobacteria occurrence, and cyanotoxins production, the published data from 238 fresh water bodies in Poland were reviewed. On the basis of these collected results, we concluded that Planktothrix, Aphanizomenon, Microcystis and Dolichospermum were dominant. The general pattern in geographical distribution of the identified cyanobacterial genera was typical of other eutrophic waters in Europe. The production of cyanotoxins was revealed in 18 (86%) of the 21 samples analyzed in the present work and in 74 (75%) of the 98 total water bodies for which the presence of toxins had been examined. Among the 24 detected microcystin variants, [Asp3]MC-RR was most common. These results can be verified when more data from the less explored water bodies in the southern and eastern parts of Poland are available.The authors would like to acknowledge the European Cooperation in Science and Technology, COST Action ES 1105 "CYANOCOST- Cyanobacterial blooms and toxins in water resources: Occurrence, impacts and management" for adding value to this study through networking and knowledge sharing with European experts and researchers in the field.42435837

Teaching and Learning of Calculus

This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions

The sarcopenia and physical frailty in older people: multi-component treatment strategies (SPRINTT) project: description and feasibility of a nutrition intervention in community-dwelling older Europeans.

To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked DownloadBackground: The "Sarcopenia and Physical Frailty in Older People: Multicomponent Treatment Strategies" (SPRINTT) project sponsored a multi-center randomized controlled trial (RCT) with the objective to determine the effect of physical activity and nutrition intervention for prevention of mobility disability in community-dwelling frail older Europeans. We describe here the design and feasibility of the SPRINTT nutrition intervention, including techniques used by nutrition interventionists to identify those at risk of malnutrition and to carry out the nutrition intervention. Methods: SPRINTT RCT recruited older adults (≥ 70 years) from 11 European countries. Eligible participants (n = 1517) had functional limitations measured with Short Physical Performance Battery (SPPB score 3-9) and low muscle mass as determined by DXA scans, but were able to walk 400 m without assistance within 15 min. Participants were followed up for up to 3 years. The nutrition intervention was carried out mainly by individual nutrition counseling. Nutrition goals included achieving a daily protein intake of 1.0-1.2 g/kg body weight, energy intake of 25-30 kcal/kg of body weight/day, and serum vitamin D concentration ≥ 75 mmol/L. Survey on the method strategies and feasibility of the nutrition intervention was sent to all nutrition interventionists of the 16 SPRINTT study sites. Results: Nutrition interventionists from all study sites responded to the survey. All responders found that the SPRINTT nutrition intervention was feasible for the target population, and it was well received by the majority. The identification of participants at nutritional risk was accomplished by combining information from interviews, questionnaires, clinical and laboratory data. Although the nutrition intervention was mainly carried out using individual nutritional counselling, other assisting methods were used as appropriate. Conclusion: The SPRINTT nutrition intervention was feasible and able to adapt flexibly to varying needs of this heterogeneous population. The procedures adopted to identify older adults at risk of malnutrition and to design the appropriate intervention may serve as a model to deliver nutrition intervention for community-dwelling older people with mobility limitations. Keywords: Energy intake; Nutrition counselling; Nutrition intervention; Protein intake; SPRINTT.University of Helsinki including Helsinki University Central Hospital Innovative Medicine Initiative (IMI) Juho Vainio foundatio

Population genomics of the Viking world.

The maritime expansion of Scandinavian populations during the Viking Age (about AD 750-1050) was a far-flung transformation in world history1,2. Here we sequenced the genomes of 442 humans from archaeological sites across Europe and Greenland (to a median depth of about 1×) to understand the global influence of this expansion. We find the Viking period involved gene flow into Scandinavia from the south and east. We observe genetic structure within Scandinavia, with diversity hotspots in the south and restricted gene flow within Scandinavia. We find evidence for a major influx of Danish ancestry into England; a Swedish influx into the Baltic; and Norwegian influx into Ireland, Iceland and Greenland. Additionally, we see substantial ancestry from elsewhere in Europe entering Scandinavia during the Viking Age. Our ancient DNA analysis also revealed that a Viking expedition included close family members. By comparing with modern populations, we find that pigmentation-associated loci have undergone strong population differentiation during the past millennium, and trace positively selected loci-including the lactase-persistence allele of LCT and alleles of ANKA that are associated with the immune response-in detail. We conclude that the Viking diaspora was characterized by substantial transregional engagement: distinct populations influenced the genomic makeup of different regions of Europe, and Scandinavia experienced increased contact with the rest of the continent