Graphical statistics to explore the natural and anthropogenic processes influencing the inorganic quality of drinking water, ground water and surface water

Plots of cumulative distribution functions (CDF) are a simple but powerful exploratory data analysis (EDA) tool to evaluate and compare statistical data distributions. Here, empirical CDF plots are used to compare results of four large (476 to 884 samples) national- to continental-scale inorganic water chemistry data sets: (1) European surface water, (2) European tap water, (3) European bottled waters as a proxy for groundwater and (4) Norwegian crystalline bedrock rock groundwater, all analysed at the same laboratory, albeit at different times. For many parameters (e.g., Ba, Cl-, K, SO4 2-) median values and ranges are, given the differing origins and, in some cases, treatment processes of the waters, surprisingly comparable. Unusually high concentrations of some other elements (e.g., B, Be, Br, Cs, F-, Ge, Li, Rb, Te and Zr) appear to be characteristic of deeper-seated, mature groundwaters. Other influences that can be inferred include contamination from well construction or plumbing materials (Cu, Pb, Zn – in tap waters, bottled waters and Norwegian groundwaters), water treatment (Fe, Mn – in tap- and Norwegian groundwater), bottle materials (Sb - bottled waters). The empirical CDF plots also reveal analytical issues for some elements (excessive rounding, element interferences). The best reference for natural and uncontaminated ’water’ is probably provided by the mineral water samples, representing ’deep groundwater’ at the European scale

Radiative Symmetry Breaking of the Minimal Left-Right Symmetric Model

Under the assumption of classical conformal invariance, we study the Coleman-Weinberg symmetry breaking mechanism in the minimal left-right symmetric model. This model is attractive as it provides a natural framework for small neutrino masses and the restoration of parity as a good symmetry of nature. We find that, in a large fraction of the parameter space, the parity symmetry is maximally broken by quantum corrections in the Coleman-Weinberg potential, which are a consequence of the conformal anomaly. As the left-right symmetry breaking scale is connected to the Planck scale through the logarithmic running of the dimensionless couplings of the scalar potential, a large separation of the two scales can be dynamically generated. The symmetry breaking dynamics of the model was studied using a renormalization group analysis. Electroweak symmetry breaking is triggered by the breakdown of left-right symmetry, and the left-right breaking scale is therefore expected in the few TeV range. The phenomenological implications of the symmetry breaking mechanism are discussed.Comment: 23 pages, 1 figure; version as published in journal; title changed, changes in abstract, introduction and conclusion

The Flavor Structure of the Three-Site Higgsless Model

We study the flavor structure of the three-site Higgsless model and evaluate the constraints on the model arising from flavor physics. We find that current data constrain the model to exhibit only minimal flavor violation at tree level. Moreover, at the one-loop level, by studying the leading chiral logarithmic corrections to chirality-preserving Delta F = 1 and Delta F = 2 processes from new physics in the model, we show that the combination of minimal flavor violation and ideal delocalization ensures that these flavor-changing effects are sufficiently small that the model remains phenomenologically viable.Comment: 23 pages, 22 pdf figures include

Z to b bbar and Chiral Currents in Higgsless Models

In this note we compute the flavor-dependent chiral-logarithmic corrections to the decay Z to b bbar in the three site Higgsless model. We compute these corrections diagrammatically in the "gaugeless" limit in which the electroweak couplings vanish. We also compute the chiral-logarithmic corrections to the decay Z to b bbar using an RGE analysis in effective field theory, and show that the results agree. In the process of this computation, we compute the form of the chiral current in the gaugeless limit of the three-site model, and consider the generalization to the N-site case. We elucidate the Ward-Takahashi identities which underlie the gaugeless limit calculation in the three-site model, and describe how the result for the Z to b bbar amplitude is obtained in unitary gauge in the full theory. We find that the phenomenological constraints on the three-site Higgsless model arising from measurements of Z to b bbar are relatively mild, requiring only that the heavy Dirac fermion be heavier than 1 TeV or so, and are satisfied automatically in the range of parameters allowed by other precision electroweak data.Comment: 19 pages, 7 embedded eps figures (additional reference added

Minimum Degree up to Local Complementation: Bounds, Parameterized Complexity, and Exact Algorithms

The local minimum degree of a graph is the minimum degree that can be reached by means of local complementation. For any n, there exist graphs of order n which have a local minimum degree at least 0.189n, or at least 0.110n when restricted to bipartite graphs. Regarding the upper bound, we show that for any graph of order n, its local minimum degree is at most 3n/8+o(n) and n/4+o(n) for bipartite graphs, improving the known n/2 upper bound. We also prove that the local minimum degree is smaller than half of the vertex cover number (up to a logarithmic term). The local minimum degree problem is NP-Complete and hard to approximate. We show that this problem, even when restricted to bipartite graphs, is in W[2] and FPT-equivalent to the EvenSet problem, which W[1]-hardness is a long standing open question. Finally, we show that the local minimum degree is computed by a O*(1.938^n)-algorithm, and a O*(1.466^n)-algorithm for the bipartite graphs

Baryon masses at O(a^2) in chiral perturbation theory

The chiral Lagrangian for the Symanzik action through O(a^2) for baryons is obtained. We consider two flavor unquenched and partially quenched lattice theories, allowing for mixed actions in the latter. As an application, we calculate masses to O(a^2) for the nucleons and deltas, and investigate the corrections due to the violation of O(4) rotational invariance. These results are contrasted with those in the meson sector for lattice simulations using mixed and unmixed actions of Wilson and Ginsparg-Wilson quarks.Comment: 27 pages, 2 figures, revise