Monomial transformations of the projective space

We prove that, over any field, the dimension of the indeterminacy locus of a rational transformation $f$ of $P^n$ which is defined by monomials of the same degree $d$ with no common factors is at least $(n-2)/2$, provided that the degree of $f$ as a map is not divisible by $d$. This implies upper bounds on the multidegree of $f$

Symbolic powers of monomial ideals and Cohen-Macaulay vertex-weighted digraphs

In this paper we study irreducible representations and symbolic Rees algebras of monomial ideals. Then we examine edge ideals associated to vertex-weighted oriented graphs. These are digraphs having no oriented cycles of length two with weights on the vertices. For a monomial ideal with no embedded primes we classify the normality of its symbolic Rees algebra in terms of its primary components. If the primary components of a monomial ideal are normal, we present a simple procedure to compute its symbolic Rees algebra using Hilbert bases, and give necessary and sufficient conditions for the equality between its ordinary and symbolic powers. We give an effective characterization of the Cohen--Macaulay vertex-weighted oriented forests. For edge ideals of transitive weighted oriented graphs we show that Alexander duality holds. It is shown that edge ideals of weighted acyclic tournaments are Cohen--Macaulay and satisfy Alexander dualityComment: Special volume dedicated to Professor Antonio Campillo, Springer, to appea

The variable mass loss of the AGB star WX Psc as traced by the CO J=1-0 through 7-6 lines and the dust emission

Low and intermediate mass stars lose a significant fraction of their mass through a dust-driven wind during the Asymptotic Giant Branch (AGB) phase. Recent studies show that winds from late-type stars are far from being smooth. Mass-loss variations occur on different time scales, from years to tens of thousands of years. The variations appear to be particularly prominent towards the end of the AGB evolution. The occurrence, amplitude and time scale of these variations are still not well understood. The goal of our study is to gain insight into the structure of the circumstellar envelope (CSE) of WX Psc and map the possible variability of the late-AGB mass-loss phenomenon. We have performed an in-depth analysis of the extreme infrared AGB star WX Psc by modeling (1) the CO J=1-0 through 7-6 rotational line profiles and the full spectral energy distribution (SED) ranging from 0.7 to 1300 micron. We hence are able to trace a geometrically extended region of the CSE. Both mass-loss diagnostics bear evidence of the occurrence of mass-loss modulations during the last ~2000 yr. In particular, WX Psc went through a high mass-loss phase (Mdot~5e-5 Msun/yr) some 800 yr ago. This phase lasted about 600 yr and was followed by a long period of low mass loss (Mdot~5e-8 Msun/yr). The present day mass-loss rate is estimated to be ~6e-6 Msun/yr. The AGB star WX Psc has undergone strong mass-loss rate variability on a time scale of several hundred years during the last few thousand years. These variations are traced in the strength and profile of the CO rotational lines and in the SED. We have consistently simulated the behaviour of both tracers using radiative transfer codes that allow for non-constant mass-loss rates.Comment: 12 pages, accepted for publication in A&

The Waldschmidt constant for squarefree monomial ideals

Given a squarefree monomial ideal $I \subseteq R =k[x_1,\ldots,x_n]$, we show that $\widehat\alpha(I)$, the Waldschmidt constant of $I$, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of $I$. By applying results from fractional graph theory, we can then express $\widehat\alpha(I)$ in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of $I$. Moreover, expressing $\widehat\alpha(I)$ as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on $\widehat\alpha(I)$, thus verifying a conjecture of Cooper-Embree-H\`a-Hoefel for monomial ideals in the squarefree case. As an application, we compute the Waldschmidt constant and the resurgence for some families of squarefree monomial ideals. For example, we determine both constants for unions of general linear subspaces of $\mathbb{P}^n$ with few components compared to $n$, and we find the Waldschmidt constant for the Stanley-Reisner ideal of a uniform matroid.Comment: 26 pages. This project was started at the Mathematisches Forschungsinstitut Oberwolfach (MFO) as part of the mini-workshop "Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems" held in February 2015. Comments are welcome. Revised version corrects some typos, updates the references, and clarifies some hypotheses. To appear in the Journal of Algebraic Combinatoric

On the reliability of mass-loss-rate estimates for AGB stars

In the recent literature there has been some doubt as to the reliability of CO multi-transitional line observations as a mass-loss-rate estimator for AGB stars. Mass-loss rates for 10 intermediate- to high-mass-loss-rate AGB stars are derived using a detailed non-LTE, non-local radiative transfer code based on the Monte-Carlo method to model the CO radio line intensities. The circumstellar envelopes are assumed to be spherically symmetric and formed by constant mass-loss rates. The energy balance is solved self-consistently and the effects of dust on the radiation field and thermal balance are included. An independent estimate of the mass-loss rate is also obtained from the combination of dust radiative transfer modelling with a dynamical model of the gas and dust particles. We find that the CO radio line intensities and shapes are successfully reproduced for the majority of our objects assuming a constant mass-loss rate. Moreover, the CO line intensities are only weakly dependent on the adopted micro-turbulent velocity, in contrast to recent claims in the literature. The two methods used in the present work to derive mass-loss-rates are consistent within a factor of ~3 for intermediate- to high-mass-loss-rate objects, indicating that this is a lower limit to the uncertainty in present mass-loss-rate estimates. We find a tentative trend with chemistry. Mass-loss rates from the dust/dynamical model are systematically higher than those from the CO model for the carbon stars and vice versa for the M-type stars. This could be ascribed to a discrepancy in the adopted CO/H_2-abundance ratio, but we caution that the sample is small and systematic errors cannot be excluded.Comment: 18 pages, 17 figures, accepted for publication in A&

What are they thinking? Consumer attitudes to meat production in Australia

Meat production has come under increasing scrutiny from consumers and citizens who feel that certain practices are unethical and negatively affect farm-animal welfare. Animal welfare can be viewed as both a scientific and social concept, and purchasing products with animal welfare claims can be considered an act of ‘ethical consumption’. The present paper reviews research that examines consumer attitudes to animal welfare and highlights tensions between consumer and citizen attitudes and behaviours, and assumptions that are made within these studies. We present our own research into motivations to purchase free-range eggs as an example of research that attempts to unpack these assumptions, in particular, that such purchases are made out of concern for animal welfare. We present a further example of our own research that attempts to identify how attitudes to meat production are socially constructed. We conclude with recommended strategies to engage the broader community in discussions about animal production, so as to improve industry–community communication about farm-animal welfare in meat-production industries.H. J. Bray, E. A. Buddle and R. A. Anken

Extending Landsat 8: Retrieval of an Orange contra-Band for Inland Water Quality Applications

The Operational Land Imager (OLI) onboard Landsat 8 has found successful application in inland and coastal water remote sensing. Its radiometric specification and high spatial resolution allows quantification of water-leaving radiance while resolving small water bodies. However, its limited multispectral band set restricts the range of water quality parameters that can be retrieved. Identification of cyanobacteria biomass has been demonstrated for sensors with a band centered near 620 nm, the absorption peak of the diagnostic pigment phycocyanin. While OLI lacks such a band in the orange region, superposition of the available multispectral and panchromatic bands suggests that it can be calculated by a scaled difference. A set of 428 in situ spectra acquired in diverse lakes in Belgium and The Netherlands was used to develop and test an orange contra-band retrieval algorithm, achieving a mean absolute percentage error of 5.39 % and a bias of −0.88 % in the presence of sensor noise. Atmospheric compensation error propagated to the orange contra-band was observed to maintain about the same magnitude (13 % higher) observed for the red band and thus results in minimal additional effects for possible base line subtraction or band ratio algorithms for phycocyanin estimation. Generality of the algorithm for different reflectance shapes was tested against a set of published average coastal and inland Optical Water Types, showing robust retrieval for all but relatively clear water types (Secchi disk depth > 6 m and chlorophyll a < 1.6 mg m−3). The algorithm was further validated with 79 matchups against the Ocean and Land Colour Imager (OLCI) orange band for 10 globally distributed lakes. The retrieved band is shown to convey information independent from the adjacent bands under variable phycocyanin concentrations. An example application using Landsat 8 imagery is provided for a knowncyanobacterialbloominLakeErie,US.ThemethodisdistributedintheACOLITEatmospheric correction code. The contra-band approach is generic and can be applied to other sensors with overlapping bands. Recommendations are also provided for development of future sensors with broad spectral bands with the objective to maximize the accuracy of possible spectral enhancement