The Hodge--Poincar\'e polynomial of the moduli spaces of stable vector bundles over an algebraic curve

Let X be a nonsingular complex projective variety that is acted on by a reductive group $G$ and such that $X^{ss} \neq X_{(0)}^{s}\neq \emptyset$. We give formulae for the Hodge--Poincar\'e series of the quotient $X_{(0)}^s/G$. We use these computations to obtain the corresponding formulae for the Hodge--Poincar\'e polynomial of the moduli space of properly stable vector bundles when the rank and the degree are not coprime. We compute explicitly the case in which the rank equals 2 and the degree is even.Comment: Final published version. arXiv admin note: text overlap with arXiv:math/0305346, arXiv:math/0305347 by other author

Factors affecting nitrate distribution in shallow groundwater under a beef farm in South Eastern Ireland

peer-reviewedGroundwater contamination was characterised using a methodology which combines shallow groundwater geochemistry data from 17 piezometers over a 2 yr period in a statistical framework and hydrogeological techniques. Nitrate–N (NO3-N) contaminant mass flux was calculated across three control planes (rows of piezometers) in six isolated plots. Results showed natural attenuation occurs on site although the method does not directly differentiate between dilution and denitrification. It was further investigated whether NO3-N concentration in shallow groundwater (<5 m below ground level) generated from an agricultural point source on a 4.2 ha site on a beef farm in SE Ireland could be predicted from saturated hydraulic conductivity (Ksat) measurements, ground elevation (m Above Ordnance Datum), elevation of groundwater sampling (screen opening interval) (m AOD) and distance from a dirty water point pollution source. Tobit regression, using a background concentration threshold of 2.6 mg NO3-N L−1 showed, when assessed individually in a step wise procedure, Ksat was significantly related to groundwater NO3-N concentration. Distance of the point dirty water pollution source becomes significant when included with Ksat in the model. The model relationships show areas with higher Ksat values have less time for denitrification to occur, whereas lower Ksat values allow denitrification to occur. Areas with higher permeability transport greater NO3-N fluxes to ground and surface waters. When the distribution of Cl− was examined by the model, Ksat and ground elevation had the most explanatory power but Ksat was not significant pointing to dilution having an effect. Areas with low NO3 concentration and unaffected Cl− concentration points to denitrification, low NO3 concentration and low Cl− chloride concentration points to dilution and combining these findings allows areas of denitrification and dilution to be inferred. The effect of denitrification is further supported as mean groundwater NO3-N was significantly (P < 0.05) related to groundwater N2/Ar ratio, redox potential (Eh), dissolved O2 and N2 and was close to being significant with N2O (P = 0.08). Calculating contaminant mass flux across more than one control plane is a useful tool to monitor natural attenuation. This tool allows the identification of hot spot areas where intervention other than natural attenuation may be needed to protect receptors.Research Stimulus Fund, Department of Agriculture Fisheries and Food (Ireland

How many invariant polynomials are needed to decide local unitary equivalence of qubit states?

Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if two states can be connected by local unitary operations. Interestingly, this number is not the same for every collection of the spectra. Some spectra require less polynomials to solve LU equivalence problem than others. The result is obtained using geometric methods, i.e. by calculating the dimensions of reduced spaces, stemming from the symplectic reduction procedure.Comment: 22 page

Stratifying quotient stacks and moduli stacks

Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X/H], where X is a projective scheme and H is a linear algebraic group with internally graded unipotent radical acting linearly on X, in such a way that each stratum [S/H] has a geometric quotient S/H. This leads to stratifications of moduli stacks (for example, sheaves over a projective scheme) such that each stratum has a coarse moduli space.Comment: 25 pages, submitted to the Proceedings of the Abel Symposium 201

Matrix String Theory and its Moduli Space

The correspondence between Matrix String Theory in the strong coupling limit and IIA superstring theory can be shown by means of the instanton solutions of the former. We construct the general instanton solutions of Matrix String Theory which interpolate between given initial and final string configurations. Each instanton is characterized by a Riemann surface of genus h with n punctures, which is realized as a plane curve. We study the moduli space of such plane curves and find out that, at finite N, it is a discretized version of the moduli space of Riemann surfaces: instead of 3h-3+n its complex dimensions are 2h-3+n, the remaining h dimensions being discrete. It turns out that as $N$ tends to infinity, these discrete dimensions become continuous, and one recovers the full moduli space of string interaction theory.Comment: 30 pages, LaTeX, JHEP.cls class file, minor correction

Chemometric applications in Nuclear Magnetic Resonance metabonomics

The use of generalised 2D correlation spectroscopic (Gen2D) analysis techniques coupled with NMR spectroscopy has been proposed for identifying biomarkers and aiding in the modelling of biological processes. Spectral pre-processing is of paramount importance. During the analysis of dynamic 1H NMR spectra &amp;lsquo;ghost&amp;rsquo; peaks can be observed in the two-dimensional asynchronous correlation plots. These have been demonstrated here, for the first time, to be the result of minor changes in peak widths between successive spectra. Such variation in spectra is common in NMR and can be removed if spectra are synthesized with constant peak widths. Gen2D NMR correlation spectroscopy has been applied to monitoring a commercial fermentation of red wine. The synchronous matrix highlighted positively and negatively correlated spectral features and the asynchronous matrix provided information regarding the differing order of change of intensity of spectral features. These two matrices provide a diagrammatic summary of relative changes in samples over time. Two-dimensional correlation methods have also been applied to interpretation of NMR-based spectra of plasma from human subjects undertaking an exercise-dietary regimen. For the first time Gen2D, hybrid correlation analysis has been employed to monitor the metabolic effects of phosphonate in Phytophthora. In vivo 31P NMR was used to monitor changes in P-metabolites. Finally, a multivariate analysis of plasma samples&amp;rsquo; 1H- NMR spectra highlighted differences in the metabolic profiles of adult Black Bream fish exposed to a single high dose of the estrogen 17&amp;beta;-estradiol. It is concluded that NMR 2D-correlation maps can be successful in aiding interpretation of time series of data, being visually accessible

Assessing Human Error Against a Benchmark of Perfection

An increasing number of domains are providing us with detailed trace data on human decisions in settings where we can evaluate the quality of these decisions via an algorithm. Motivated by this development, an emerging line of work has begun to consider whether we can characterize and predict the kinds of decisions where people are likely to make errors. To investigate what a general framework for human error prediction might look like, we focus on a model system with a rich history in the behavioral sciences: the decisions made by chess players as they select moves in a game. We carry out our analysis at a large scale, employing datasets with several million recorded games, and using chess tablebases to acquire a form of ground truth for a subset of chess positions that have been completely solved by computers but remain challenging even for the best players in the world. We organize our analysis around three categories of features that we argue are present in most settings where the analysis of human error is applicable: the skill of the decision-maker, the time available to make the decision, and the inherent difficulty of the decision. We identify rich structure in all three of these categories of features, and find strong evidence that in our domain, features describing the inherent difficulty of an instance are significantly more powerful than features based on skill or time.Comment: KDD 2016; 10 page

Spatio-temporal development of vegetation die-off in a submerging coastal marsh

In several places around the world, coastal marsh vegetation is converting to open water through the formation of pools. This is concerning, as vegetation die-off is expected to reduce the marshes\u27 capacity to adapt to sea level rise by vegetation-induced sediment accretion. Quantitative analyses of the spatial and temporal development of marsh vegetation die-off are scarce, although these are needed to understand the bio-geomorphic feedback effects of vegetation die-off on flow, erosion, and sedimentation. In this study, we quantified the spatial and temporal development of marsh vegetation die-off with aerial images from 1938 to 2010 in a submerging coastal marsh along the Blackwater River (Maryland, U.S.A). Our results indicate that die-off begins with conversion of marsh vegetation into bare open water pools that are relatively far (\u3e 75 m) from tidal channels. As vegetation die-off continues, pools expand, and new pools emerge at shorter and shorter distances from channels. Consequently larger pools are found at larger distances from the channels. Our results suggest that the size of the pools and possibly the connection of pools with the tidal channel system have important bio-geomorphic implications and aggravate marsh deterioration. Moreover, we found that the temporal development of vegetation die-off in moderately degraded marshes is similar as the spatial die-off development along a present-day gradient, which indicates that the contemporary die-off gradient might be considered a chronosequence that offers a unique opportunity to study vegetation die-off processes

Temperature sensitivity of organic-matter decay in tidal marshes

Approximately half of marine carbon sequestration takes place in coastal wetlands, including tidal marshes, where organic matter contributes to soil elevation and ecosystem persistence in the face of sea-level rise. The long-term viability of marshes and their carbon pools depends, in part, on how the balance between productivity and decay responds to climate change. Here, we report the sensitivity of labile soil organic-matter decay in tidal marshes to seasonal and latitudinal variations in temperature measured over a 3-year period. We find a moderate increase in decay rate at warmer temperatures (3-6% per degrees C, Q(10) = 1.3-1.5). Despite the profound differences between microbial metabolism in wetlands and uplands, our results indicate a strong conservation of temperature sensitivity. Moreover, simple comparisons with organic-matter production suggest that elevated atmospheric CO2 and warmer temperatures will accelerate carbon accumulation in marsh soils, and potentially enhance their ability to survive sea-level rise

Inter-Industry Differences in Male Percentage Unemployment Compensation - A Cross Section Analysis for Irish Manufacturing Industry. Quarterly Economic Commentary Special Article, November 1976

It is widely accepted that unemployment rates vary substantially amongst industrial sectors in Ireland. However, it does not appear to be equally recognised that there are substantial inter-industry differences in the percentage of net earnings which an unemployed person receives from Unemployment and Pay-Related Benefits. These differences are accentuated by the non-uniformity of the dependency structure of the labour force in different industries. This paper, therefore, comprises two parts. Part 1 is methodological and consists of an attempt to compute, under fairly restrictive assumptions, for each of 36 manufacturing industries, the proportion of net earnings obtained from unemployment compensation. This is done for persons of differing dependency status. These proportions are then weighted by the dependency distribution of the unemployed in each industry in order to obtain a representative percentage compensation figure for each of the 36 industries. Some space is devoted to an examination of these results. In Part 2 an attempt is made to explore the hypothesis that levels of unemployment compensation may be an important factor in explaining the extent and duration of registered unemployment