Max Noether

Life and work of the mathematician Max Noether (1844-1921)

Fermat hypersurfaces and Subcanonical curves

We extend the classical Enriques-Petri Theorem to $s$-subcanonical projectively normal curves, proving that such a curve is $(s+2)$-gonal if and only if it is contained in a surface of minimal degree. Moreover, we show that any Fermat hypersurface of degree $s+2$ is apolar to an $s$-subcanonical $(s+2)$-gonal projectively normal curve, and vice versa.Comment: 18 pages; AMS-LaTe

Apolarity, Hessian and Macaulay polynomials

A result by Macaulay states that an Artinian graded Gorenstein ring R of socle dimension one and socle degree b can be realized as the apolar ring of a homogeneous polynomial f of degree b. If R is the Jacobian ring of a smooth hypersurface g=0, then b is just equal to the degree of the Hessian polynomial of g. In this paper we investigate the relationship between f and the Hessian polynomial of g.Comment: 12 pages. Improved exposition, minor correction

Formation of the postmitotic nuclear envelope from extended ER cisternae precedes nuclear pore assembly

During mitosis, the nuclear envelope merges with the endoplasmic reticulum (ER), and nuclear pore complexes are disassembled. In a current model for reassembly after mitosis, the nuclear envelope forms by a reshaping of ER tubules. For the assembly of pores, two major models have been proposed. In the insertion model, nuclear pore complexes are embedded in the nuclear envelope after their formation. In the prepore model, nucleoporins assemble on the chromatin as an intermediate nuclear pore complex before nuclear envelope formation. Using live-cell imaging and electron microscope tomography, we find that the mitotic assembly of the nuclear envelope primarily originates from ER cisternae. Moreover, the nuclear pore complexes assemble only on the already formed nuclear envelope. Indeed, all the chromatin-associated Nup 107–160 complexes are in single units instead of assembled prepores. We therefore propose that the postmitotic nuclear envelope assembles directly from ER cisternae followed by membrane-dependent insertion of nuclear pore complexes

The body in the library: adventures in realism

This essay looks at two aspects of the virtual ‘material world’ of realist fiction: objects encountered by the protagonist and the latter’s body. Taking from Sartre two angles on the realist pact by which readers agree to lend their bodies, feelings, and experiences to the otherwise ‘languishing signs’ of the text, it goes on to examine two sets of first-person fictions published between 1902 and 1956 — first, four modernist texts in which banal objects defy and then gratify the protagonist, who ends up ready and almost able to write; and, second, three novels in which the body of the protagonist is indeterminate in its sex, gender, or sexuality. In each of these cases, how do we as readers make texts work for us as ‘an adventure of the body’

Algorithms for zero-dimensional ideals using linear recurrent sequences

Inspired by Faug\`ere and Mou's sparse FGLM algorithm, we show how using linear recurrent multi-dimensional sequences can allow one to perform operations such as the primary decomposition of an ideal, by computing the annihilator of one or several such sequences.Comment: LNCS, Computer Algebra in Scientific Computing CASC 201

GSK3-mediated raptor phosphorylation supports amino acid-dependent Q2 mTORC1-directed signalling

The mammalian or mechanistic target of rapamycin (mTOR) complex 1 (mTORC1) is a ubiquitously expressed multimeric protein kinase complex that integrates nutrient and growth factor signals for the co-ordinated regulation of cellular metabolism and cell growth. Herein, we demonstrate that suppressing the cellular activity of glycogen synthase kinase-3 (GSK3), by use of pharmacological inhibitors or shRNA-mediated gene silencing, results in substantial reduction in amino acid (AA)-regulated mTORC1-directed signalling, as assessed by phosphorylation of multiple downstream mTORC1 targets. We show that GSK3 regulates mTORC1 activity through its ability to phosphorylate the mTOR-associated scaffold protein raptor (regulatory-associated protein of mTOR) on Ser(859). We further demonstrate that either GSK3 inhibition or expression of a S859A mutated raptor leads to reduced interaction between mTOR and raptor and under these circumstances, irrespective of AA availability, there is a consequential loss in phosphorylation of mTOR substrates, such as p70S6K1 (ribosomal S6 kinase 1) and uncoordinated-51-like kinase (ULK1), which results in increased autophagic flux and reduced cellular proliferation

Adherence to a Mediterranean diet and Alzheimer's disease risk in an Australian population

The Mediterranean diet (MeDi), due to its correlation with a low morbidity and mortality for many chronic diseases, has been widely recognised as a healthy eating model. We aimed to investigate, in a cross-sectional study, the association between adherence to a MeDi and risk for Alzheimer's disease (AD) and mild cognitive impairment (MCI) in a large, elderly, Australian cohort. Subjects in the Australian Imaging, Biomarkers and Lifestyle Study of Ageing cohort (723 healthy controls (HC), 98 MCI and 149 AD participants) completed the Cancer Council of Victoria Food Frequency Questionnaire. Adherence to the MeDi (0- to 9-point scale with higher scores indicating higher adherence) was the main predictor of AD and MCI status in multinominal logistic regression models that were adjusted for cohort age, sex, country of birth, education, apolipoprotein E genotype, total caloric intake, current smoking status, body mass index, history of diabetes, hypertension, angina, heart attack and stroke. There was a significant difference in adherence to the MeDi between HC and AD subjects (P < 0.001), and in adherence between HC and MCI subjects (P < 0.05). MeDi is associated with change in Mini-Mental State Examination score over an 18-month time period (P < 0.05) in HCs. We conclude that in this Australian cohort, AD and MCI participants had a lower adherence to the MeDi than HC participants.S Gardener, Y Gu, S R Rainey-Smith, J B Keogh, P M Clifton, S L Mathieson, K Taddei, A Mondal, V K Ward, N Scarmeas, M Barnes, K A Ellis, R Head, C L Masters, D Ames, S L Macaulay, C C Rowe, C Szoeke and R N Martins for the AIBL Research Grou

Quasar accretion disk sizes from continuum reverberation mapping in the DES standard-star fields

Measurements of the physical properties of accretion disks in active galactic nuclei are important for better understanding the growth and evolution of supermassive black holes. We present the accretion disk sizes of 22 quasars from continuum reverberation mapping with data from the Dark Energy Survey (DES) standard star fields and the supernova C fields. We construct continuum lightcurves with the \textit{griz} photometry that span five seasons of DES observations. These data sample the time variability of the quasars with a cadence as short as one day, which corresponds to a rest frame cadence that is a factor of a few higher than most previous work. We derive time lags between bands with both JAVELIN and the interpolated cross-correlation function method, and fit for accretion disk sizes using the JAVELIN Thin Disk model. These new measurements include disks around black holes with masses as small as $\sim10^7$ $M_{\odot}$, which have equivalent sizes at 2500\AA \, as small as $\sim 0.1$ light days in the rest frame. We find that most objects have accretion disk sizes consistent with the prediction of the standard thin disk model when we take disk variability into account. We have also simulated the expected yield of accretion disk measurements under various observational scenarios for the Large Synoptic Survey Telescope Deep Drilling Fields. We find that the number of disk measurements would increase significantly if the default cadence is changed from three days to two days or one day.Comment: 33 pages, 24 figure