Plane quartics: the universal matrix of bitangents

Aronhold's classical result states that a plane quartic can be recovered by the configuration of any Aronhold systems of bitangents, i.e. special $7$-tuples of bitangents such that the six points at which any sub-triple of bitangents touches the quartic do not lie on the same conic in the projective plane. Lehavi (cf. \cite{lh}) proved that a smooth plane quartic can be explicitly reconstructed from its $28$ bitangents; this result improved Aronhold's method of recovering the curve. In a 2011 paper \cite{PSV} Plaumann, Sturmfels and Vinzant introduced an $8 \times 8$ symmetric matrix that parametrizes the bitangents of a nonsingular plane quartic. The starting point of their construction is Hesse's result for which every smooth quartic curve has exactly $36$ equivalence classes of linear symmetric determinantal representations. In this paper we tackle the inverse problem, i.e. the construction of the bitangent matrix starting from the 28 bitangents of the plane quartic, and we provide a Sage script intended for computing the bitangent matrix of a given curve

GIS-based expeditious assessments in the field of water protection

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Am I guilty or not? Deontological guilt, uncertainty, and checking behavior

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Egas Moniz: 90 years (1927-2017) from cerebral angiography

In June 2017 we celebrate the 90th anniversary of the pioneer discovery of cerebral angiography, the seminal imaging technique used for visualizing cerebral blood vessels and vascular alterations as well as other intracranial disorders. Egas Moniz (1874-1955) was the first to describe the use of this revolutionary technique which, until 1975 (when computed tomography, CT, scan was introduced in the clinical practice), was the sole diagnostic tool to provide an imaging of cerebral vessels and therefore alterations due to intracranial pathology. Moniz introduced in the clinical practice this fundamental and important diagnostic tool. The present contribution wishes to pay a tribute to the Portuguese neurosurgeon, who was also a distinguished neurologist and statesman. Despite his tremendous contribution in modern brain imaging, Egas Moniz was awarded the Nobel Prize in Physiology or Medicine in 1949 for prefrontal leucotomy, the neurosurgical intervention nowadays unacceptable, but should rather be remembered for his key contribution to modern brain imaging. KEYWORDS

Oleic acid is a potent inhibitor of fatty acid and cholesterol synthesis in C6 glioma cells.

Glial cells play a pivotal role in brain fatty acid metabolism and membrane biogenesis. However, the potential regulation of lipogenesis and cholesterologenesis by fatty acids in glial cells has been barely investigated. Here, we show that physiologically relevant concentrations of various saturated, monounsaturated, and polyunsaturated fatty acids significantly reduce [1-(14)C]acetate incorporation into fatty acids and cholesterol in C6 cells. Oleic acid was the most effective at depressing lipogenesis and cholesterologenesis; a decreased label incorporation into cellular palmitic, stearic, and oleic acids was detected, suggesting that an enzymatic step(s) of de novo fatty acid biosynthesis was affected. To clarify this issue, the activities of acetyl-coenzyme A carboxylase (ACC) and FAS were determined with an in situ digitonin-permeabilized cell assay after incubation of C6 cells with fatty acids. ACC activity was strongly reduced ( approximately 80%) by oleic acid, whereas no significant change in FAS activity was observed. Oleic acid also reduced the activity of 3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGCR). The inhibition of ACC and HMGCR activities is corroborated by the decreases in ACC and HMGCR mRNA abundance and protein levels. The downregulation of ACC and HMGCR activities and expression by oleic acid could contribute to the reduced lipogenesis and cholesterologenesis

Classical theta constants vs. lattice theta series, and super string partition functions

Recently, various possible expressions for the vacuum-to-vacuum superstring amplitudes has been proposed at genus $g=3,4,5$. To compare the different proposals, here we will present a careful analysis of the comparison between the two main technical tools adopted to realize the proposals: the classical theta constants and the lattice theta series. We compute the relevant Fourier coefficients in order to relate the two spaces. We will prove the equivalence up to genus 4. In genus five we will show that the solutions are equivalent modulo the Schottky form and coincide if we impose the vanishing of the cosmological constant.Comment: 21 page