Mathematics, metaphor and economic visualisability

The mathematisation of economic theory is an issue that has been discussed many times. These discussions have been dominated by debate about the appropriateness of the deductive method for economics. This rather narrow focus has pushed a number of important methodological issues regarding the nature of mathematical economics aside. In this paper, it is argued that mathematical economics involves the construction of metaphor and is therefore metaphorical in nature. Whilst mathematical economics has been responsible for what are generally regarded to be notable theoretical achievements and retains a place in economics as an apparatus for the development of economic science, the meaning of mathematical economics is restricted to those elements of economic reality that may be talked about in terms of mathematical objects and there is a danger of declining economic visualisability as the metaphors of mathematical economics become less vivid

Conceptual combination with PUNC

Noun-noun compounds play a key role in the growth of language. In this article we present a system for producing and understanding noun-noun compounds (PUNC). PUNC is based on the Constraint theory of conceptual combination and the C-3 model. The new model incorporates the primary constraints of the Constraint theory in an integrated fashion, creating a cognitively plausible mechanism of interpreting noun-noun phrases. It also tries to overcome algorithmic limitations of the C-3 model in being more efficient in its computational complexity, and deal with a wider span of empirical phenomena, such as dimensions of word familiarity. We detail the model, including knowledge representation and interpretation production mechanisms. We show that by integrating the constraints of the Constraint theory of conceptual combination and prioritizing the knowledge available within a concept's representation, PUNC can not only generate interpretations that reflect those produced by people, but also mirror the differences in processing times for understanding familiar, similar and novel word combinations

FGF21 underlies a hormetic response to metabolic stress in methylmalonic acidemia

Methylmalonic acidemia (MMA), an organic acidemia characterized by metabolic instability and multiorgan complications, is most frequently caused by mutations in methylmalonyl-CoA mutase (MUT). To define the metabolic adaptations in MMA in acute and chronic settings, we studied a mouse model generated by transgenic expression of Mut in the muscle. Mut-/-;TgINS-MCK-Mut mice accurately replicate the hepatorenal mitochondriopathy and growth failure seen in severely affected patients and were used to characterize the response to fasting. The hepatic transcriptome in MMA mice was characterized by the chronic activation of stress-related pathways and an aberrant fasting response when compared with controls. A key metabolic regulator, Fgf21, emerged as a significantly dysregulated transcript in mice and was subsequently studied in a large patient cohort. The concentration of plasma FGF21 in MMA patients correlated with disease subtype, growth indices, and markers of mitochondrial dysfunction but was not affected by renal disease. Restoration of liver Mut activity, by transgenesis and liver-directed gene therapy in mice or liver transplantation in patients, drastically reduced plasma FGF21 and was associated with improved outcomes. Our studies identify mitocellular hormesis as a hepatic adaptation to metabolic stress in MMA and define FGF21 as a highly predictive disease biomarker

Apatite and titanite from the Karrat Group, Greenland; implications for charting the thermal evolution of crust from the U-Pb geochronology of common Pb bearing phases

Titanite and apatite have Pb closure temperatures of ~700 °C and 450–550 °C, respectively, allowing different points on a cooling trajectory to be determined. However, both phases typically accommodate moderate to significant quantities of common Pb. Understanding the thermal diffusivity of a specific isotopic system in different minerals along with their apparent U-Pb age allows modelling of regional cooling trends. Such cooling trends may provide key evidence for correct interpretation of the measured geochronometer. Specifically, thermal history reconstruction may address questions related to the interpretation of an isotopic date as the time of crystallization versus cooling, or alternatively, as a resetting age. In this work, a case study from metavolcanic rocks of the Karrat Group, West Greenland, is used to inform the U-Pb geochronology of common Pb bearing phases, thermal modelling, and also the regional geology. Magmatic apatite yields a reset U-Pb age of 1826 ± 9 Ma, whereas titanite yields a mean U-Pb age of 1768 ± 8 Ma. The apatite age is interpreted as the time of total resetting during a > 485 °C event. In contrast, the titanite age is interpreted as the time of metamorphic crystallization, consistent with its REE chemistry. Thermal modelling indicates this metamorphic event did not exceed 452 °C. The resetting of the U-Pb system in magmatic apatite is interpreted as a response to the collision between the Rae Craton and the Superior Craton during the Trans-Hudson Orogeny. However, subsequent metamorphic titanite growth is interpreted as distal evidence of an event shared with the Nagssugtoqidian Orogen. The modelled thermal history implies over 100 million years of communal tectonic history between the Nagssugtoqidian and Rinkian Orogens. Of great significance is the fact that both apatite and titanite show distinctly different common Pb compositions. Apatite retains common Pb with a composition similar to ancient common Pb, whereas titanite retains common Pb with a lower 207 Pb/ 206 Pb ratio implying it was influenced also by Pb from recrystallized precursor U bearing minerals. The common Pb signature in minerals may assist in interpretation of the growth mechanism of the dated phase