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We compare two standard approaches to defining lower Ricci curvature bounds for Riemannian metrics of regularity below $C^2$. These are, on the one hand, the synthetic definition via weak displacement convexity of entropy functionals in the framework of optimal transport, and the distributional one based on non-negativity of the Ricci-tensor in the sense of Schwartz. It turns out that distributional bounds imply entropy bounds for metrics of class $C^1$ and that the converse holds for $C^{1,1}$-metrics under an additional convergence condition on regularizations of the metric.
New occurrences of flask-shaped and envelope-bearing microfossils, including the predominantly Cambrian taxon Granomarginata, are reported from new localities, as well as from earlier in time (Ediacaran) than previously known. The stratigraphic range of Granomarginata extends into the Cambrian System, where it had a cosmopolitan distribution. This newly reported Ediacaran record includes areas from Norway (Baltica), Newfoundland (Avalonia) and Namibia (adjacent to the Kalahari Craton), and puts the oldest global occurrence of Granomarginata in the Indreelva Member (< 563 Ma) of the Stáhpogieddi Formation on the Digermulen Peninsula, Arctic Norway. Although Granomarginata is rare within the assemblage, these new occurrences together with previously reported occurrences from India and Poland, suggest a potentially widespread palaeogeographic distribution of Granomarginata through the middle–late Ediacaran interval. A new flask-shaped microfossil Lagoenaforma collaris gen. et sp. nov. is also reported in horizons containing Granomarginata from the Stáhpogieddi Formation in Norway and the Dabis Formation in Namibia, and flask-shaped fossils are also found in the Gibbett Hill Formation in Newfoundland. The Granomarginata–Lagoenaforma association, in addition to a low-diversity organic-walled microfossil assemblage, occurs in the strata postdating the Shuram carbon isotope excursion, and may eventually be of use in terminal Ediacaran biostratigraphy. These older occurrences of Granomarginata add to a growing record of body fossil taxa spanning the Ediacaran–Cambrian boundary.
Ediacara-type fossils are found in a diverse array of preservational styles, implying that multiple taphonomic mechanisms might have been responsible for their preservational expression. For many Ediacara fossils, the “death mask” model has been invoked as the primary taphonomic pathway. The key to this preservational regime is the replication or sealing of sediments around the degrading organisms by microbially induced precipitation of authigenic pyrite, leading toward fossil preservation along bedding planes. Nama-style preservation, on the other hand, captures Ediacaran organisms as molds and three-dimensional casts within coarse-grained mass flow beds, and has been previously regarded as showing little or no evidence of a microbial preservational influence. To further understand these two seemingly distinct taphonomic pathways, we investigated the three-dimensionally preserved Ediacaran fossil Pteridinium simplex from mass flow deposits of the upper Kliphoek Member, Dabis Formation, Kuibis Subgroup, southern Namibia. Our analysis, using a combination of petrographic and micro-analytical methods, shows that Pteridinium simplex vanes are replicated with minor pyrite, but are most often represented by open voids that can be filled with secondary carbonate material; clay minerals are also found in association with the vanes, but their origin remains unresolved. The scarcity of pyrite and the development of voids are likely related to oxidative weathering and it is possible that microbial activities and authigenic pyrite may have contributed to the preservation of Pteridinium simplex; however, any microbes growing on P. simplex vanes within mass flow deposits were unlikely to have formed thick mats as envisioned in the death mask model. Differential weathering of replicating minerals and precipitation of secondary minerals greatly facilitate fossil collection and morphological characterization by allowing Pteridinium simplex vanes to be parted from the massive hosting sandstone.
Vitamin D and folate are associated with decreased colorectal cancer risk and their association with colorectal cancer prognosis is under investigation. We assessed the levels of plasma 25-hydroxyvitamin D3 (25(OH)D3), folate and vitamin B12 in an international pilot study in order to determine variability of these biomarkers based on geographical location. Plasma 25(OH)D3, folate and vitamin B12 concentrations were measured in 149 invasive, newly diagnosed colorectal cancer cases from Heidelberg (Germany), Seattle (WA, USA), and Tampa (FL, USA) and in ninety-one age- and sex-matched controls. Their associations with potential predictors were assessed using multivariate linear regression analyses. Plasma 25(OH)D3, folate and vitamin B12 concentrations differed by location. Other predictors were season for 25(OH)D3 and tumour stage (vitamin B12). Season-corrected average 25(OH)D3 concentrations were higher in Heidelberg (31·7 ng/ml; range 11·0–83·0 ng/ml) than in Seattle (23·3 ng/ml; range 4·0–80·0 ng/ml) and Tampa (21·1 ng/ml; range 4·6–51·6 ng/ml). In Heidelberg, a strong seasonal variation was observed. Folate (11·1 ng/ml) and vitamin B12 (395 pg/ml) concentrations in Heidelberg were lower than those in Seattle (25·3 ng/ml and 740 pg/ml, respectively) and Tampa (23·8 ng/ml and 522 pg/ml, respectively). Differences in plasma 25(OH)D3 and folate concentrations between Heidelberg and the US sites were observed, probably reflecting variation in outdoor activities and sun-avoidance behaviour during summer as well as in folic acid fortification and supplement use. Intra-site differences at each study location were greater than between-location variability, suggesting that individual health behaviours play a significant role. Nevertheless, the intra-site differences we observed may be due to chance because of the limited sample size. Our pilot study illustrates the value of an international cohort in studying colorectal cancer prognosis to discern geographical differences in a broad range of exposures.
Background: Differences in the level of cognitive compromise between individuals following brain injury are thought to arise from underlying differences in cognitive reserve. The level of cognitive reserve attained by an individual is influenced by both genetic and life experience factors such as educational attainment and occupational history. The Tasmanian Healthy Brain Project (THBP) is a world-first prospective study examining the capacity of university-level education to enhance cognitive reserve in older adults and subsequently reduce age-related cognitive decline and risk for neurodegenerative disease.
Methods: Up to 1,000 adults aged 50–79 years at the time of entry into the study will be recruited to participate in the THBP. All participants will be healthy and free of significant medical, psychological, or psychiatric illness. Of the participant sample, 90% will undertake a minimum of 12 months part-time university-level study as an intervention. The remaining 10% will act as a control reference group. Participants will complete an annual comprehensive assessment of neuropsychological function, medical health, socialization, and personal well-being. Premorbid estimates of past cognitive, education, occupational, and physical function will be used to account for the mediating influence of prior life experience on outcomes. Potential contributing genetic factors will also be explored.
Results: Participant results will be assessed annually. Participants displaying evidence of dementia on the comprehensive neuropsychological assessment will be referred to an independent psycho-geriatrician for screening and diagnosis.
Conclusions: The THBP commenced in 2011 and is expected to run for 10–20 years duration. To date, a total of 383 participants have been recruited into the THBP.
Literary historians have long held the view that the plays of the Greek dramatist, Sophocles deal purely with archetypes of the heroic past and that any resemblance to contemporary events or individuals is purely coincidental. In this book Michael Vickers challenges this view and argues that Sophocles makes regular and extensive allusion to Athenian politics in his plays, especially to Alcibiades, one of the most controversial Athenian politicians of his day. Vickers shows that Sophocles was no closeted intellectual but a man deeply involved in politics and he reminds us that Athenian politics was intensely personal. He argues cogently that classical writers employed hidden meanings and that consciously or sub-consciously, Sophocles was projecting onto his plays hints of contemporary events or incidents, mostly of a political nature, hoping that his audiences passion for politics would enhance the popularity of his plays.
The attitudes of the ancient Greeks towards their material culture—so far as we can discover from their writings—was rather different from that of most modern students of the remains of classical antiquity. The Greeks esteemed gold and silver vessels, while many archaeologists still believe that they preferred painted pottery. This reversal of classical values came about through the entry of Utopian ideals into the mainstream of classical scholarship in the 18th century. Laudable in themselves, these ideals have led to a serious misunderstanding of the role of ceramic in antiquity. Prices for painted pottery were extremely low and it can hardly have been the vehicle for what the Ancients would have considered to be ‘Art’. It is ironic that the classical tradition has been subverted by many of those charged with the scholarly interpretation of the classical past.
The basic purpose of this chapter is to revive the idea first expressed in modern times by the eighteenth-century English classical scholar Samuel Musgrave, that we should perhaps see the historical figure of Alcibiades underlying Oedipus in Sophocles' Oedipus Tyrannus. Musgrave (who, according to the Oxford Dictionary of National Biography, “had few superiors” as a student of Greek) was writing in the 1770s, at a time when classical scholarship had not yet become Altertumswissenschaft. If, however, we take Dodds' dictum that “what is not mentioned in the play does not exist” at face value, we could easily observe that Alcibiades is not mentioned by name in Oedipus Tyrannus and stop at this point. There is nevertheless considerable merit in Musgrave's insight as we shall see, and although he did not spell out the reasons for his belief, a case can be made for Alcibiades underlying Oedipus in both Oedipus Tyrannus and Oedipus at Colonus.
The most famous attribute of Oedipus is, in Tom Lehrer's words, that he “loved his mother”: perhaps overmuch, by most standards ancient or modern. Now while “motherlover”, or a synonym, might be a common enough epithet in some circles, the actual phenomenon of sexual relations between a mother and a son is unusual. But without – yet at least – fully identifying Alcibiades with Oedipus it is useful to note that according to his contemporary Antisthenes it was said that Alcibiades was so debauched that “he lay with his mother, his sister and his daughter” (Antisth. 29a Caizzi ap. Ath. 5.220a).