An Introduction to Set Theory and Topology

These notes are an introduction to set theory and topology. They are the result of teaching a two-semester course sequence on these topics for many years at Washington University in St. Louis. Typically the students were advanced undergraduate mathematics majors, a few beginning graduate students in mathematics, and some graduate students from other areas that included economics and engineering. The usual background for the material is an introductory undergraduate analysis course, mostly because it provides a solid introduction to Euclidean space Rn and practice with rigorous arguments — in particular, about continuity. Strictly speaking, however, the material is mostly self-contained. Examples are taken now and then from analysis, but they are not logically necessary for the development of the material. The only real prerequisite is the level of mathematical interest, maturity and patience needed to handle abstract ideas and to read and write careful proofs. A few very capable students have taken this course before introductory analysis (even, rarely, outstanding university freshmen) and invariably they have commented later on how material eased their way into analysis.https://openscholarship.wustl.edu/books/1020/thumbnail.jp

Laser surface cleaning

Decontamination of contaminated metal and material recycle, two of 31 priority needs identified by the D&D focus group, are the most promising applications for laser ablation within the DOE complex. F2 Associates has developed a robotic laser ablation system that is capable of high contamination rates, waste volume reduction, surface pore cleaning, and real-time characterization of materials. It is being demonstrated that this system will be the most cost-effective technology for metal decontamination and material recycle

Chemical signatures of salt sources in the Maya world: implications for isotopic signals in ancient consumers

Salt is an essential nutrient, as well as a spice and a food preservative. Inland sources are rare, making it one of the most precious commodities in the world. In the Maya region, salt production sites are located in multiple places on the Pacific and Caribbean coasts and the Gulf of Mexico, but there are multiple salt sources in the interior in both Guatemala and Mexico. However, while there is archaeological evidence of salt production on a scale to suggest that salt was a major export at each of these sources, it is difficult to reconstruct the movement of salt before the Spanish conquest. This is a critical question for isotopic studies of migration, which are based on the premise that Maya communities relied on local foods, even as evidence for marketplaces emerges. Salt was a non-local food consumed by most Mayas not living in proximity to saltworks

Migration routes of the Chestnut-mandibled Toucan

This is where the abstract of this record would appear. This is only demonstration data

Selective binding of facial features reveals dynamic expression fragments

The temporal correspondence between two arbitrarily chosen pairs of alternating features can generally be reported for rates up to 3–4 Hz. This limit is however surpassed for specialised visual mechanisms that encode conjunctions of features. Here we show that this 3–4 Hz limit is exceeded for eye gaze and eyebrow pairing, but not for eye gaze and mouth pairing, suggesting combined eye and eyebrow motion constitutes a dynamic expression fragment; a building block of superordinate facial actions

Discovery and Characterization of Protein-Modifying Natural Products by MALDI Mass Spectrometry Reveal Potent SIRT1 and p300 Inhibitors

A straightforward MALDI MS method facilitates the unbiased screening and characterization of compounds that modify protein activity. This procedure can be used to circumvent analytical problems deriving from compounds with autofluorescence. Various posttranslationally active enzymes like deacetylases, acetyltransferases, kinases, phosphatases, and methyltransferases can be studied in the presented way

Amorfrutin B is an efficient natural peroxisome proliferator-activated receptor gamma (PPARgamma) agonist with potent glucose-lowering properties

AIMS/HYPOTHESIS: The nuclear receptor peroxisome proliferator-activated receptor gamma (PPARgamma) is an important gene regulator in glucose and lipid metabolism. Unfortunately, PPARgamma-activating drugs of the thiazolidinedione class provoke adverse side effects. As recently shown, amorfrutin A1 is a natural glucose-lowering compound that selectively modulates PPARgamma. In this study we aimed to characterise, in vitro, a large spectrum of the amorfrutins and similar molecules, which we isolated from various plants. We further studied in vivo the glucose-lowering effects of the so far undescribed amorfrutin B, which featured the most striking PPARgamma-binding and pharmacological properties of this family of plant metabolites. METHODS: Amorfrutins were investigated in vitro by binding and cofactor recruitment assays and by transcriptional activation assays in primary human adipocytes and murine preosteoblasts, as well as in vivo using insulin-resistant high-fat-diet-fed C57BL/6 mice treated for 27 days with 100 mg kg(-1) day(-1) amorfrutin B. RESULTS: Amorfrutin B showed low nanomolar binding affinity to PPARgamma, and micromolar binding to the isotypes PPARalpha and PPARbeta/delta. Amorfrutin B selectively modulated PPARgamma activity at low nanomolar concentrations. In insulin-resistant mice, amorfrutin B considerably improved insulin sensitivity, glucose tolerance and blood lipid variables after several days of treatment. Amorfrutin B treatment did not induce weight gain and furthermore showed liver-protecting properties. Additionally, amorfrutins had no adverse effects on osteoblastogenesis and fluid retention. CONCLUSIONS/INTERPRETATION: The application of plant-derived amorfrutins or synthetic analogues thereof constitutes a promising approach to prevent or treat complex metabolic diseases such as insulin resistance or type 2 diabetes

Northeastern Atlantic cold-water coral reefs and climate

U-series age patterns obtained on reef framework-forming cold-water corals collected over a nearly 6,000 km long continental margin sector, extending from off Mauritania to the south-western Barents Sea reveal strong climate influences on the geographical distribution and sustained development of these ecosystems. During glacial times densely populated cold-water coral reefs flourished in the temperate east Atlantic, where at present only scarce live coral occurrences exist. In contrast, climate warming induces a rapid northward colonization of cold-water coral reefs with the biogeographic limit advancing from ~45°N to ~70°N. Thus, we invoke here that north-south oscillations of the polar front during the past glacial-interglacial cycles and the consequent displacement of cold nutrient-rich intermediate waters and productivity drives the decline and expansion of cold-water coral ecosystems and its biogeographic limits in the northeast Atlantic

Sponge bioerosion accelerated by ocean acidification across species and latitudes?

In many marine biogeographic realms, bioeroding sponges dominate the internal bioerosion of calcareous substrates such as mollusc beds and coral reef framework. They biochemically dissolve part of the carbonate and liberate so-called sponge chips, a process that is expected to be facilitated and accelerated in a more acidic environment inherent to the present global change. The bioerosion capacity of the demosponge Cliona celata Grant, 1826 in subfossil oyster shells was assessed via alkalinity anomaly technique based on 4 days of experimental exposure to three different levels of carbon dioxide partial pressure (pCO(2)) at ambient temperature in the cold-temperate waters of Helgoland Island, North Sea. The rate of chemical bioerosion at present-day pCO(2) was quantified with 0.08-0.1 kg m(-2) year(-1). Chemical bioerosion was positively correlated with increasing pCO(2), with rates more than doubling at carbon dioxide levels predicted for the end of the twenty-first century, clearly confirming that C. celata bioerosion can be expected to be enhanced with progressing ocean acidification (OA). Together with previously published experimental evidence, the present results suggest that OA accelerates sponge bioerosion (1) across latitudes and biogeographic areas, (2) independent of sponge growth form, and (3) for species with or without photosymbionts alike. A general increase in sponge bioerosion with advancing OA can be expected to have a significant impact on global carbonate (re)cycling and may result in widespread negative effects, e.g. on the stability of wild and farmed shellfish populations, as well as calcareous framework builders in tropical and cold-water coral reef ecosystems