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

HI and CO in the circumstellar environment of the oxygen-rich AGB star RX Lep

Circumstellar shells around AGB stars are built over long periods of time that may reach several million years. They may therefore be extended over large sizes (~1 pc, possibly more), and different complementary tracers are needed to describe their global properties. In the present work, we combined 21-cm HI and CO rotational line data obtained on an oxygen-rich semi-regular variable, RX Lep, to describe the global properties of its circumstellar environment. With the SEST, we detected the CO(2-1) rotational line from RX Lep. The line profile is parabolic and implies an expansion velocity of ~4.2 km/s and a mass-loss rate ~1.7 10^-7 Msun/yr (d = 137 pc). The HI line at 21 cm was detected with the Nancay Radiotelescope on the star position and at several offset positions. The linear shell size is relatively small, ~0.1 pc, but we detect a trail extending southward to ~0.5 pc. The line profiles are approximately Gaussian with an FWHM ~3.8 km/s and interpreted with a model developed for the detached shell around the carbon-rich AGB star Y CVn. Our HI spectra are well-reproduced by assuming a constant outflow (Mloss = 1.65 10^-7 Msun/yr) of ~4 10^4 years duration, which has been slowed down by the external medium. The spatial offset of the HI source is consistent with the northward direction of the proper motion, lending support to the presence of a trail resulting from the motion of the source through the ISM, as already suggested for Mira, RS Cnc, and other sources detected in HI. The source was also observed in SiO (3 mm) and OH (18 cm), but not detected. The properties of the external parts of circumstellar shells around AGB stars should be dominated by the interaction between stellar outflows and external matter for oxygen-rich, as well as for carbon-rich, sources, and the 21-cm HI line provides a very useful tracer of these regions.Comment: 15 pages, 9 figures, 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

Measuring The Mass Loss Evolution at The Tip of The Asymptotic Giant Branch

In the final stages of stellar evolution low- to intermediate-mass stars lose their envelope in increasingly massive stellar winds. Such winds affect the interstellar medium and the galactic chemical evolution as well as the circumstellar envelope where planetary nebulae form subsequently. Characteristics of this mass loss depend on both stellar properties and properties of gas and dust in the wind formation region. In this paper we present an approach towards studies of mass loss using both observations and models, focusing on the stage where the stellar envelope is nearly empty of mass. In a recent study we measure the mass-loss evolution, and other properties, of four planetary nebulae in the Galactic Disk. Specifically we use the method of integral field spectroscopy on faint halos, which are found outside the much brighter central parts of a planetary nebula. We begin with a brief comparison between our and other observational methods to determine mass-loss rates in order to illustrate how they differ and complement each other. An advantage of our method is that it measures the gas component directly requiring no assumptions of properties of dust in the wind. Thereafter we present our observational approach in more detail in terms of its validity and its assumptions. In the second part of this paper we discuss capabilities and assumptions of current models of stellar winds. We propose and discuss improvements to such models that will allow meaningful comparisons with our observations. Currently the physically most complete models include too little mass in the model domain to permit a formation of winds with as high mass-loss rates as our observations show.Comment: 7 pages, workshop in honour of Agnes Acker, Legacies of the Macquarie/AAO/Strasbourg Halpha Planetary Nebula project, ed. Q.Parker and D.Frew, PASA, in press; clarified some parts and added some additional reference

Quantifying decadal stability of lake reflectance and chlorophyll-a from medium-resolution ocean color sensors

Multi-decadal time-series of Lake Water-Leaving Reflectance (LWLR), part of the Lakes Essential Climate Variable, have typically been interrupted for the 2012–2016 period due to lack of an ocean color sensor with ca�pabilities equivalent to MERIS (2002− 2012) and OLCI (2016 - present). Here we assess, for the first time, the suitability of MODIS/Aqua to estimate LWLR and the derived concentration of chlorophyll-a (Chla) at the global scale across optically complex water types, in an effort to fill these information gaps for climate studies. We first compare the normalized water-leaving reflectance (Rw) derived from two atmospheric correction algorithms (POLYMER and L2gen) against in situ observations. POLYMER shows superior performance, considering the agreement with in situ measurements and the number of valid outputs. An extensive assessment of nine Chla algorithms is then performed on POLYMER-corrected Rw from MODIS observations. The algorithms are tested both in original parameterizations and following calibration against in situ measurements of Chla. We find that the performance of algorithms parameterized per Optical Water Type (OWT) allows considerable improvement of the global Chla retrieval capability. Using 3 years of overlapping observations between MODIS/Aqua and MERIS (2009–2011) and OLCI (2017–2019), respectively, MODIS-derived reflectance and Chla products showed a reasonable degree of long-term stability in 48 inland water bodies. These water bodies, therefore, mark the candidates to study long-term environmental change

Predicting the Electron Requirement for Carbon Fixation in Seas and Oceans

Marine phytoplankton account for about 50% of all global net primary productivity (NPP). Active fluorometry, mainly Fast Repetition Rate fluorometry (FRRf), has been advocated as means of providing high resolution estimates of NPP. However, not measuring CO2-fixation directly, FRRf instead provides photosynthetic quantum efficiency estimates from which electron transfer rates (ETR) and ultimately CO2-fixation rates can be derived. Consequently, conversions of ETRs to CO2-fixation requires knowledge of the electron requirement for carbon fixation (Φe,C, ETR/CO2 uptake rate) and its dependence on environmental gradients. Such knowledge is critical for large scale implementation of active fluorescence to better characterise CO2-uptake. Here we examine the variability of experimentally determined Φe,C values in relation to key environmental variables with the aim of developing new working algorithms for the calculation of Φe,C from environmental variables. Coincident FRRf and 14C-uptake and environmental data from 14 studies covering 12 marine regions were analysed via a meta-analytical, non-parametric, multivariate approach. Combining all studies, Φe,C varied between 1.15 and 54.2 mol e- (mol C)-1 with a mean of 10.9±6.91 mol e- mol C)-1. Although variability of Φe,C was related to environmental gradients at global scales, region-specific analyses provided far improved predictive capability. However, use of regional Φe,C algorithms requires objective means of defining regions of interest, which remains challenging. Considering individual studies and specific small-scale regions, temperature, nutrient and light availability were correlated with Φe,C albeit to varying degrees and depending on the study/region and the composition of the extant phytoplankton community. At the level of large biogeographic regions and distinct water masses, Φe,C was related to nutrient availability, chlorophyll, as well as temperature and/or salinity in most regions, while light availability was also important in Baltic Sea and shelf waters. The novel Φe,C algorithms provide a major step forward for widespread fluorometry-based NPP estimates and highlight the need for further studying the natural variability of Φe,C to verify and develop algorithms with improved accuracy. © 2013 Lawrenz et al

Accuracy and reproducibility of above-water radiometry with calibrated smartphone cameras using RAW data

Consumer cameras, especially on smartphones, are popular and effective instruments for above-water radiometry. The remote sensing reflectance Rrs is measured above the water surface and used to estimate inherent optical properties and constituent concentrations. Two smartphone apps, HydroColor and EyeOnWater, are used worldwide by professional and citizen scientists alike. However, consumer camera data have problems with accuracy and reproducibility between cameras, with systematic differences of up to 40% in intercomparisons. These problems stem from the need, until recently, to use JPEG data. Lossless data, in the RAW format, and calibrations of the spectral and radiometric response of consumer cameras can now be used to significantly improve the data quality. Here, we apply these methods to above-water radiometry. The resulting accuracy in Rrs is around 10% in the red, green, and blue (RGB) bands and 2% in the RGB band ratios, similar to professional instruments and up to 9 times better than existing smartphone-based methods. Data from different smartphones are reproducible to within measurement uncertainties, which are on the percent level. The primary sources of uncertainty are environmental factors and sensor noise. We conclude that using RAW data, smartphones and other consumer cameras are complementary to professional instruments in terms of data quality. We offer practical recommendations for using consumer cameras in professional and citizen science.Horizon 2020(H2020)776480Environmental BiologyInstrumentatio

Investigating lake chlorophyll-a responses to the 2019 European double heatwave using satellite remote sensing

Compounded weather events such as sequential heatwaves are likely to increasingly impact freshwater ecosystems in the future. Satellite-derived chlorophyll-a concentration estimates for 36 European lakes during a widespread double heatwave event in the summer of 2019 show that deep and medium depth lakes at higher latitudes displayed a synchronous chlorophyll-a increase with temperature, possibly as the result of an improved light climate resulting from increased stratification. Many deep or northern lakes had a notable response to the heatwaves. Warmer, southern shallow lakes had the most asynchronous response, tending to show a greater response to subsequent low pressure or storm events than to the heatwave itself. Chlorophyll-a peaks typically occurred five days after the peak of the heatwave for shallow lakes. For some shallow lakes, the sequential cycle of several heatwaves and low pressure events was found to punctuate the seasonal pattern of chlorophyll-a. Notably, in several of these nutrient-rich lakes the response to the heatwave was dwarfed by large algal blooms occurring later during the typical cyanobacterial bloom period in early autumn, underlining the importance of timing and phenology in response to heatwaves in addition to depth, latitude and trophic state