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

Functional assessment of sodium chloride cotransporter NCC mutants in polarized mammalian epithelial cells.

The thiazide-sensitive sodium chloride cotransporter NCC is important for maintaining serum sodium (Na(+)) and, indirectly, serum potassium (K(+)) levels. Functional studies on NCC have used cell lines with native NCC expression, transiently transfected nonpolarized cell lines, or Xenopus laevis oocytes. Here, we developed the use of polarized Madin-Darby canine kidney type I (MDCKI) mammalian epithelial cell lines with tetracycline-inducible human NCC expression to study NCC activity and membrane abundance in the same system. In radiotracer assays, induced cells grown on filters had robust thiazide-sensitive and chloride dependent sodium-22 ((22)Na) uptake from the apical side. To minimize cost and maximize throughput, assays were modified to use cells grown on plastic. On plastic, cells had similar thiazide-sensitive (22)Na uptakes that increased following preincubation of cells in chloride-free solutions. NCC was detected in the plasma membrane, and both membrane abundance and phosphorylation of NCC were increased by incubation in chloride-free solutions. Furthermore, in cells exposed for 15 min to low or high extracellular K(+), the levels of phosphorylated NCC increased and decreased, respectively. To demonstrate that the system allows rapid and systematic assessment of mutated NCC, three phosphorylation sites in NCC were mutated, and NCC activity was examined. (22)Na fluxes in phosphorylation-deficient mutants were reduced to baseline levels, whereas phosphorylation-mimicking mutants were constitutively active, even without chloride-free stimulation. In conclusion, this system allows the activity, cellular localization, and abundance of wild-type or mutant NCC to be examined in the same polarized mammalian expression system in a rapid, easy, and low-cost fashion

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

Ultra-light Axions: Degeneracies with Massive Neutrinos and Forecasts for Future Cosmological Observations

A generic prediction of string theory is the existence of many axion fields. It has recently been argued that many of these fields should be light and, like the well known QCD axion, lead to observable cosmological consequences. In this paper we study in detail the effect of the so-called string axiverse on large scale structure, focusing on the morphology and evolution of density perturbations, anisotropies in the cosmic microwave background and weak gravitational lensing of distant galaxies. We quantify specific effects that will arise from the presence of the axionic fields and highlight possible degeneracies that may arise in the presence of massive neutrinos. We take particular care understanding the different physical effects and scales that come into play. We then forecast how the string axiverse may be constrained and show that with a combination of different observations, it should be possible to detect a fraction of ultralight axions to dark matter of a few percent.Comment: 24 pages, 16 figures, this version: corrected typos, some comments added, matches published versio

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

Pure O-sequences and matroid h-vectors

We study Stanley's long-standing conjecture that the h-vectors of matroid simplicial complexes are pure O-sequences. Our method consists of a new and more abstract approach, which shifts the focus from working on constructing suitable artinian level monomial ideals, as often done in the past, to the study of properties of pure O-sequences. We propose a conjecture on pure O-sequences and settle it in small socle degrees. This allows us to prove Stanley's conjecture for all matroids of rank 3. At the end of the paper, using our method, we discuss a first possible approach to Stanley's conjecture in full generality. Our technical work on pure O-sequences also uses very recent results of the third author and collaborators.Comment: Contains several changes/updates with respect to the previous version. In particular, a discussion of a possible approach to the general case is included at the end. 13 pages. To appear in the Annals of Combinatoric

The thiazide sensitive sodium chloride co-transporter NCC is modulated by site-specific ubiquitylation.

The renal sodium chloride cotransporter, NCC, in the distal convoluted tubule is important for maintaining body Na(+) and K(+) homeostasis. Endogenous NCC is highly ubiquitylated, but the role of individual ubiquitylation sites is not established. Here, we assessed the role of 10 ubiquitylation sites for NCC function. Transient transfections of HEK293 cells with human wildtype (WT) NCC or various K to R mutants identified greater membrane abundance for K706R, K828R and K909R mutants. Relative to WT-NCC, stable tetracycline inducible MDCKI cell lines expressing K706R, K828R and K909R mutants had significantly higher total and phosphorylated NCC levels at the apical plasma membrane under basal conditions. Low chloride stimulation increased membrane abundance of all mutants to similar or greater levels than WT-NCC. Under basal conditions K828R and K909R mutants had less ubiquitylated NCC in the plasma membrane, and all mutants displayed reduced NCC ubiquitylation following low chloride stimulation. Thiazide-sensitive sodium-22 uptakes were elevated in the mutants and internalization from the plasma membrane was significantly less than WT-NCC. K909R had increased half-life, whereas chloroquine or MG132 treatment indicated that K706 and K909 play roles in lysosomal and proteasomal NCC degradation, respectively. In conclusion, site-specific ubiquitylation of NCC plays alternative roles for NCC function

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’

The ABCD of usability testing

We introduce a methodology for tracking and auditing feedback, errors and suggestions for software packages. This short paper describes how we innovate on the evaluation mechanism, introducing an (Antecedent, Barrier, Consequence and Development) ABCD form, embedded within an eParticipation platform to enable end users to easily report on any usability issues. This methodology will be utilised to improve the STEP cloud eParticipation platform (part of the current STEP Horizon2020 project http://step4youth.eu. The platform is currently being piloted in real life contexts, with the participation of public authorities that are integrating the eParticipation platform into their regular decision-making practices. The project is involving young people, through engagement and motivation strategies and giving them a voice in Environmental decision making at the local level. The pilot evaluation aims to demonstrate how open engagement needs to be embedded within public sector processes and the usability methodology reported here will help to identify the key barriers for wide scale deployment of the platform

Phylogeography and Ethnogenesis of Aboriginal Southeast Asians

Studying the genetic history of the Orang Asli of Peninsular Malaysia can provide crucial clues to the peopling of Southeast Asia as a whole. We have analyzed mitochondrial DNA (mtDNAs) control-region and coding-region markers in 447 mtDNAs from the region, including 260 Orang Asli, representative of each of the traditional groupings, the Semang, the Senoi, and the Aboriginal Malays, allowing us to test hypotheses about their origins. All of the Orang Asli groups have undergone high levels of genetic drift, but phylogeographic traces nevertheless remain of the ancestry of their maternal lineages. The Semang have a deep ancestry within the Malay Peninsula, dating to the initial settlement from Africa >50,000 years ago. The Senoi appear to be a composite group, with approximately half of the maternal lineages tracing back to the ancestors of the Semang and about half to Indochina. This is in agreement with the suggestion that they represent the descendants of early Austroasiatic speaking agriculturalists, who brought both their language and their technology to the southern part of the peninsula ∼4,000 years ago and coalesced with the indigenous population. The Aboriginal Malays are more diverse, and although they show some connections with island Southeast Asia, as expected, they also harbor haplogroups that are either novel or rare elsewhere. Contrary to expectations, complete mtDNA genome sequences from one of these, R9b, suggest an ancestry in Indochina around the time of the Last Glacial Maximum, followed by an early-Holocene dispersal through the Malay Peninsula into island Southeast Asia