Pre-Euclidean geometry and Aeginetan coin design: some further remarks

Some ancient Greek coins from the island state of Aegina depict peculiar geometric designs. Hitherto they have been interpreted as anticipations of some Euclidean propositions. But this paper proposes geometrical constructions which establish connections to pre-Euclidean treatments of incommensurability. The earlier Aeginetan coin design from about 500 bc onwards appears as an attempt not only to deal with incommensurability but also to conceal it. It might be related to Plato’s dialogue Timaeus. The newer design from 404 bc onwards reveals incommensurability, namely in the context of ‘doubling the square’. It thereby covers the same topic but a different geometry as passages in Plato’s dialogue Meno (385 bc). This coin design incorporates important elements of ancient Greek geometrical analysis of the fifth century bc like the gnomon, Hippocrates’ squaring of the lunule (ca. 430 bc), and a geometrical version of monetary equivalence. Through this venue, the design’s conceptual lineage might be traced as far back as Heraclitus’ cosmology of about 500 bc.     

Fructose transport-deficient Staphylococcus aureus reveals important role of epithelial glucose transporters in limiting sugar-driven bacterial growth in airway surface liquid

Hyperglycaemia as a result of diabetes mellitus or acute illness is associated with increased susceptibility to respiratory infection with Staphylococcus aureus. Hyperglycaemia increases the concentration of glucose in airway surface liquid (ASL) and promotes the growth of S. aureus in vitro and in vivo. Whether elevation of other sugars in the blood, such as fructose, also results in increased concentrations in ASL is unknown and whether sugars in ASL are directly utilised by S. aureus for growth has not been investigated. We obtained mutant S. aureus JE2 strains with transposon disrupted sugar transport genes. NE768(fruA) exhibited restricted growth in 10 mM fructose. In H441 airway epithelial-bacterial co-culture, elevation of basolateral sugar concentration (5–20 mM) increased the apical growth of JE2. However, sugar-induced growth of NE768(fruA) was significantly less when basolateral fructose rather than glucose was elevated. This is the first experimental evidence to show that S. aureus directly utilises sugars present in the ASL for growth. Interestingly, JE2 growth was promoted less by glucose than fructose. Net transepithelial flux of d-glucose was lower than d-fructose. However, uptake of d-glucose was higher than d-fructose across both apical and basolateral membranes consistent with the presence of GLUT1/10 in the airway epithelium. Therefore, we propose that the preferential uptake of glucose (compared to fructose) limits its accumulation in ASL. Pre-treatment with metformin increased transepithelial resistance and reduced the sugar-dependent growth of S. aureus. Thus, epithelial paracellular permeability and glucose transport mechanisms are vital to maintain low glucose concentration in ASL and limit bacterial nutrient sources as a defence against infection.     

Evolution of the Cdk-activator Speedy/RINGO in vertebrates

Successful completion of the cell cycle relies on the precise activation and inactivation of cyclin-dependent kinases (Cdks) whose activity is mainly regulated by binding to cyclins. Recently, a new family of Cdk regulators termed Speedy/RINGO has been discovered, which can bind and activate Cdks but shares no apparent amino acid sequence homology with cyclins. All Speedy proteins share a conserved domain of approximately 140 amino acids called “Speedy Box”, which is essential for Cdk binding. Speedy/RINGO proteins display an important role in oocyte maturation in Xenopus. Interestingly, a common feature of all Speedy genes is their predominant expression in testis suggesting that meiotic functions may be the most important physiological feature of Speedy genes. Speedy homologs have been reported in mammals and can be traced back to the most primitive clade of chordates (Ciona intestinalis). Here, we investigated the evolution of the Speedy genes and have identified a number of new Speedy/RINGO proteins. Through extensive analysis of numerous species, we discovered diverse evolutionary histories: the number of Speedy genes varies considerably among species, with evidence of substantial gains and losses. Despite the interspecies variation, Speedy is conserved among most species examined. Our results provide a complete picture of the Speedy gene family and its evolution.     

Investigations of the coordinates in Ptolemy’s Geographike Hyphegesis Book 8

In Book 8 of his Geographike Hyphegesis Ptolemy gives coordinates for ca. 360 so-called noteworthy cities. These coordinates are the time difference to Alexandria, the length of the longest day, and partly the ecliptic distance from the summer solstice. The supposable original conversions between the coordinates in Book 8 and the geographical coordinates in the location catalogue of Books 2–7 including the underlying parameters and tabulations are here reconstructed. The results document the differences between the ${\Omega}$ - and ${\Xi}$ -recension. The known difference in the longitude of Alexandria underlying the conversion of the longitudes is examined more closely. For the ecliptic distances from the summer solstice of the ${\Omega}$ -recension, it is revealed that they were originally computed by means of a so far undiscovered approximate, linear conversion. Further it is shown that the lengths of the longest day could be based on a linear interpolation of the data in the Mathematike Syntaxis 2.6.     

Isaac Newton’s ‘Of Quadrature by Ordinates’

In Of Quadrature by Ordinates (1695), Isaac Newton tried two methods for obtaining the Newton–Cotes formulae. The first method is extrapolation and the second one is the method of undetermined coefficients using the quadrature of monomials. The first method provides $n$ -ordinate Newton–Cotes formulae only for cases in which $n=3,4$ and 5. However this method provides another important formulae if the ratios of errors are corrected. It is proved that the second method is correct and provides the Newton–Cotes formulae. Present significance of each of the methods is given.     

The development of the Laplace transform, 1737–1937

This paper, the first of two, follows the development of theLaplace Transform from its earliest beginnings withEuler, usually dated at 1737, to the year 1880, whenSpitzer was its major, if himself relatively minor, protagonist. The coverage aims at completeness, and shows the state which the technique reached in the hands of its greatest exponent to that time,Petzval. A sequel will trace the development of the modern theory from its beginnings withPoincaré to its present form, due toDoetsch.     

Wnt–Notch signalling crosstalk in development and disease

The Notch and Wnt pathways are two of only a handful of highly conserved signalling pathways that control cell-fate decisions during animal development (Pires-daSilva and Sommer in Nat Rev Genet 4: 39–49, 2003). These two pathways are required together to regulate many aspects of metazoan development, ranging from germ layer patterning in sea urchins (Peter and Davidson in Nature 474: 635–639, 2011) to the formation and patterning of the fly wing (Axelrod et al in Science 271:1826–1832, 1996; Micchelli et al in Development 124:1485–1495, 1997; Rulifson et al in Nature 384:72–74, 1996), the spacing of the ciliated cells in the epidermis of frog embryos (Collu et al in Development 139:4405–4415, 2012) and the maintenance and turnover of the skin, gut lining and mammary gland in mammals (Clayton et al in Nature 446:185–189, 2007; Clevers in Cell 154:274–284, 2013; Doupe et al in Dev Cell 18:317–323, 2010; Lim et al in Science 342:1226–1230, 2013; Lowell et al in Curr Biol 10:491–500, 2000; van et al in Nature 435:959–963, 2005; Yin et al in Nat Methods 11:106–112, 2013). In addition, many diseases, including several cancers, are caused by aberrant signalling through the two pathways (Bolós et al in Endocr Rev 28: 339–363, 2007; Clevers in Cell 127: 469–480, 2006). In this review, we will outline the two signalling pathways, describe the different points of interaction between them, and cover how these interactions influence development and disease.     

On Jacobi’s transformation theory of elliptic functions

The main interpretative challenge set by the Fundamenta Nova Theoriae Functionum Ellipticarum lies in Jacobi’s transformation theory upon which the entire theoretical edifice of the treatise depends. Unfortunately, Jacobi did not convey any indication of how he attained his general formulae for rational transformations of elliptic functions. He limited himself to providing a posteriori verification of the validity of his claims. The aim of this paper is precisely to describe the heuristic path by which in 1827 Jacobi succeeded in finding these transformation formulae. The proposed historical reconstruction will hopefully shed new light upon the emergence in Jacobi’s work of the inversion process of elliptic integrals of the first kind and thus of the elliptic function sinam \(u\) itself.     

The absence of melanopsin alters retinal clock function and dopamine regulation by light

The retinal circadian clock is crucial for optimal regulation of retinal physiology and function, yet its cellular location in mammals is still controversial. We used laser microdissection to investigate the circadian profiles and phase relations of clock gene expression and Period gene induction by light in the isolated outer (rods/cones) and inner (inner nuclear and ganglion cell layers) regions in wild-type and melanopsin-knockout (Opn ₄ ^?/? ) mouse retinas. In the wild-type mouse, all clock genes are rhythmically expressed in the photoreceptor layer but not in the inner retina. For clock genes that are rhythmic in both retinal compartments, the circadian profiles are out of phase. These results are consistent with the view that photoreceptors are a potential site of circadian rhythm generation. In mice lacking melanopsin, we found an unexpected loss of clock gene rhythms and of the photic induction of Per1-Per2 mRNAs only in the outer retina. Since melanopsin ganglion cells are known to provide a feed-back signalling pathway for photic information to dopaminergic cells, we further examined dopamine (DA) synthesis in Opn ₄ ^?/? mice. The lack of melanopsin prevented the light-dependent increase of tyrosine hydroxylase (TH) mRNA and of DA and, in constant darkness, led to comparatively high levels of both components. These results suggest that melanopsin is required for molecular clock function and DA regulation in the retina, and that Period gene induction by light is mediated by a melanopsin-dependent, DA-driven signal acting on retinal photoreceptors.     

Cyclotomie et formes quadratiques dans l’œuvre arithmétique d’Augustin-Louis Cauchy (1829–1840)

Augustin-Louis Cauchy publie une majorité de ses recherches arithmétiques entre 1829 et 1840. Celles-ci ne sont pourtant qu’évoquées dans certaines histoires de la théorie des nombres centrées sur les lois de réciprocité ou sur la théorie des nombres algébriques. Elles y sont décrites comme contenant quelques résultats similaires à ceux de Gauss, Jacobi ou Dirichlet mais de manière incomplète et désordonnée. L’objectif de cet article est de présenter une analyse des textes arithmétiques de Cauchy publiés entre 1829 et 1840 pour montrer qu’ils contiennent au contraire un ensemble cohérent de résultats en lien avec les formes quadratiques $4p^{\mu }=x^2+ny^2$ , où $p$ est un nombre premier et $n$ un diviseur de $p-1$ . Nous discuterons également la forme particulière de ce corpus et la stratégie utilisée pour retrouver les lignes directrices du travail de Cauchy. Augustin-Louis Cauchy published most of his arithmetical research between 1829 and 1840. These are however only mentioned in some number theory history centered on reciprocity laws or on theory of algebraic numbers. They are described as containing some results similar to those of Gauss, Jacobi and Dirichlet but in a incomplete and disorganized way. The objective of this paper is to present an analysis of Cauchy’s arithmetical texts published between 1829 and 1840 to show that they contain a rather consistent set of results related to quadratic forms $4p^{\mu } = x ^2 + ny ^2 $ , where $p$ is a prime and $n$ a divisor of $ p-1 $ . We will also discuss the particular form of this body of texts and the strategy we used to find the guidelines of the work of Cauchy.     

Delineating multiple functions of VEGF-A in the adult brain

Vascular endothelial growth factor-A (abbreviated throughout this review as VEGF) is mostly known for its angiogenic activity, for its activity as a vascular permeability factor, and for its vascular survival activity [1]. There is a growing body of evidence, however, that VEGF fulfills additional less ‘traditional’ functions in multiple organs, both during development, as well as homeostatic functions in fully developed organs. This review focuses on the multiple roles of VEGF in the adult brain and is less concerned with the roles played by VEGF during brain development, functions described elsewhere in this review series. Most functions of VEGF that are essential for proper brain development are, in fact, dispensable in the adult brain as was clearly demonstrated using a conditional brain-specific VEGF loss-of-function (LOF) approach. Thus, in contrast to VEGF LOF in the developing brain, a process which is detrimental for the growth and survival of blood vessels and leads to massive neuronal apoptosis [2–4], continued signaling by VEGF in the mature brain is no longer required for maintaining already established cerebral vasculature and its inhibition does not cause appreciable vessel regression, hypoxia or apoptosis [4–7]. Yet, VEGF continues to be expressed in the adult brain in a constitutive manner. Moreover, VEGF is expressed in the adult brain in a region-specific manner and in distinctive spatial patterns incompatible with an angiogenic role (see below), strongly suggesting angiogenesis-independent and possibly also perfusion-independent functions. Here we review current knowledge on some of these ‘non-traditional’, often unexpected homeostatic VEGF functions, including those unrelated to its effects on the brain vasculature. These effects could be mediated directly (on non-vascular cells expressing cognate VEGF receptors) or indirectly (via the endothelium). Experimental approaches aimed at distinguishing between these possibilities for each particular VEGF function will be described. This review is only concerned with homeostatic functions of VEGF in the normal, non-injured brain. The reader is referred elsewhere in this series for a review on VEGF actions in response to various forms of brain injury and/or brain pathology.     

Thyroid hormone actions in liver cancer

The thyroid hormone 3,3′,5-triiodo-l-thyronine (T₃) mediates several physiological processes, including embryonic development, cellular differentiation, metabolism, and the regulation of cell proliferation. Thyroid hormone receptors (TRs) generally act as heterodimers with the retinoid X receptor (RXR) to regulate target genes. In addition to their developmental and metabolic functions, TRs have been shown to play a tumor suppressor role, suggesting that their aberrant expression can lead to tumor transformation. Conversely, recent reports have shown an association between overexpression of wild-type TRs and tumor metastasis. Signaling crosstalk between T₃/TR and other pathways or specific TR coregulators appear to affect tumor development. Since TR actions are complex as well as cell context-, tissue- and time-specific, aberrant expression of the various TR isoforms has different effects during diverse tumorigenesis. Therefore, elucidation of the T₃/TR signaling mechanisms in cancers should facilitate the identification of novel therapeutic targets. This review provides a summary of recent studies focusing on the role of TRs in hepatocellular carcinomas (HCCs).     

Emergence of classical trajectories in quantum systems: the cloud chamber problem in the analysis of Mott (1929)

We analyze the paper “The wave mechanics of $\alpha $ -ray tracks” Mott (Proc R Soc Lond A 126:79–84, 1929), published in 1929 by N. F. Mott. In particular, we discuss the theoretical context in which the paper appeared and give a detailed account of the approach used by the author and the main result attained. Moreover, we comment on the relevance of the work not only as far as foundations of Quantum Mechanics are concerned but also as the earliest pioneering contribution in decoherence theory.