A DEIM Induced CUR Factorization

We derive a CUR approximate matrix factorization based on the discrete empirical interpolation method (DEIM). For a given matrix ${\bf A}$, such a factorization provides a low-rank approximate decomposition of the form ${\bf A} \approx \bf C \bf U \bf R$, where ${\bf C}$ and ${\bf R}$ are subsets of the columns and rows of ${\bf A}$, and ${\bf U}$ is constructed to make $\bf C\bf U \bf R$ a good approximation. Given a low-rank singular value decomposition ${\bf A} \approx \bf V \bf S \bf W^T$, the DEIM procedure uses ${\bf V}$ and ${\bf W}$ to select the columns and rows of ${\bf A}$ that form ${\bf C}$ and ${\bf R}$. Through an error analysis applicable to a general class of CUR factorizations, we show that the accuracy tracks the optimal approximation error within a factor that depends on the conditioning of submatrices of ${\bf V}$ and ${\bf W}$. For very large problems, ${\bf V}$ and ${\bf W}$ can be approximated well using an incremental QR algorithm that makes only one pass through ${\bf A}$. Numerical examples illustrate the favorable performance of the DEIM-CUR method compared to CUR approximations based on leverage scores

Accelerating the LSTRS Algorithm

In a recent paper [Rojas, Santos, Sorensen: ACM ToMS 34 (2008), Article 11] an efficient method for solvingthe Large-Scale Trust-Region Subproblem was suggested which is based on recasting it in terms of a parameter dependent eigenvalue problem and adjusting the parameter iteratively. The essential work at each iteration is the solution of an eigenvalue problem for the smallest eigenvalue of the Hessian matrix (or two smallest eigenvalues in the potential hard case) and associated eigenvector(s). Replacing the implicitly restarted Lanczos method in the original paper with the Nonlinear Arnoldi method makes it possible to recycle most of the work from previous iterations which can substantially accelerate LSTRS

Emerging contaminants in urban groundwater sources in Africa

The occurrence of emerging organic contaminants within the aquatic environment in Africa is currently unknown. This study provides early insights by characterising a broad range of emerging organic contaminants (n > 1000) in groundwater sources in Kabwe, Zambia. Groundwater samples were obtained during both the dry and wet seasons from a selection of deep boreholes and shallow wells completed within the bedrock and overlying superficial aquifers, respectively. Groundwater sources were distributed across the city to encompass peri-urban, lower cost housing, higher cost housing, and industrial land uses. The insect repellent DEET was ubiquitous within groundwater at concentrations up to 1.8 mg/L. Other compounds (n ¼ 26) were detected in less than 15% of the sources and included the bactericide triclosan (up to 0.03 mg/L), chlorination by-products e trihalomethanes (up to 50 mg/L), and the surfactant 2,4,7,9-tetramethyl-5-decyne-4,7-diol (up to 0.6 mg/L). Emerging contaminants were most prevalent in shallow wells sited in low cost housing areas. This is attributed to localised vulnerability associated with inadequate well protection, sanitation, and household waste disposal. The five-fold increase in median DEET concentration following the onset of the seasonal rains highlights that more mobile compounds can rapidly migrate from the surface to the aquifer suggesting the aquifer is more vulnerable than previously considered. Furthermore it suggests DEET is potentially useful as a wastewater tracer in Africa. There was a general absence of personal care products, life-style compounds, and pharmaceuticals which are commonly detected in the aquatic environment in the developed world. This perhaps reflects some degree of attenuation within the subsurface, but could also be a result of the current limited use of products containing emerging contaminants by locals due to unaffordability and unavailability. As development and population increases in Africa, it is likely a wider-range of emerging contaminants will be released into the environment

Disordered Hubbard Model with Attraction: Coupling Energy of Cooper Pairs in Small Clusters

We generalize the Cooper problem to the case of many interacting particles in the vicinity of the Fermi level in the presence of disorder. On the basis of this approach we study numerically the variation of the pair coupling energy in small clusters as a function of disorder. We show that the Cooper pair energy is strongly enhanced by disorder, which at the same time leads to the localization of pairs.Comment: revtex, 5 pages, 6 figure

Instream and riparian implications of weed cutting in a chalk river

Macrophyte growth is extensive in the iconic chalk streams that are concentrated in southern and eastern England. Widespread and frequent weed cutting is undertaken to maintain their key functions (e.g. flood water conveyance and maintenance of viable fisheries). In this study, a multidisciplinary approach was adopted to quantify coincident physico-chemical responses (instream and riparian) that result from weed cutting and to discuss their potential implications. Three weed cuts were monitored at a site on the River Lambourn (The CEH River Lambourn Observatory) and major instream and riparian impacts were observed. Measurements clearly demonstrated how weed cutting enhanced flood flow conveyance, reduced water levels (river and wetland), increased river velocities, and mobilised suspended sediment (with associated chemicals) and reduced the capacity for its retention within the river channel. Potential implications in relation to flood risk, water resources, downstream water quality, instream and riparian ecology, amenity value of the river, and wetland greenhouse gas emissions were considered. Provided the major influence of macrophytes on instream and riparian environments is fully understood then the manipulation of macrophytes represents an effective management tool that demonstrates the great potential of working with nature

Locality and topology with fat link overlap actions

We study the locality and topological properties of fat link clover overlap (FCO) actions. We find that a small amount of fattening (2-4 steps of APE or 1 step of HYP) already results in greatly improved properties compared to the Wilson overlap (WO). We present a detailed study of the localisation of the FCO and its connection to the density of low modes of $A^\dagger A$. In contrast to the Wilson overlap, on quenched gauge backgrounds we do not find any dependence of the localization of the FCO on the gauge coupling. This suggests that the FCO remains local in the continuum limit. The FCO also faithfully reproduces the zero mode wave functions of typical lattice instantons, not like the Wilson overlap. After a general discussion of different lattice definitions of the topological charge we also show that the FCO together with the Boulder charge are likely to satisfy the index theorem in the continuum limit. Finally, we present a high statistics computation of the quenched topological susceptibility with the FCO action.Comment: 19 pages, LaTe

Online fluorescence spectroscopy for the real-time evaluation of the microbial quality of drinking water

We assessed the utility of online fluorescence spectroscopy for the real-time evaluation of the microbial quality of untreated drinking water. Online fluorimeters were installed on the raw water intake at four groundwater -derived UK public water supplies alongside existing turbidity sensors that are used to forewarn of the presence of microbial contamination in the water industry. The fluorimeters targeted fluorescent dissolved organic matter (DOM) peaks at excitation/emission wavelengths of 280/365 nm (tryptophan-like fluorescence, TLF) and 280/450 nm (humic-like fluorescence, HLF). Discrete samples were collected for Escherichia coli, total bacterial cell counts by flow cytometry, and laboratory-based fluorescence and absorbance. Both TLF and HLF were strongly correlated with E. coli (r ¼ 0.71e0.77)and total bacterial cell concentrations (r ¼ 0.73e0.76), whereas the correlations between turbidity and E. coli (r ¼ 0.48) and total bacterial cell counts (r ¼ 0.40) were much weaker. No clear TLF peak was observed at the sites and all apparent TLF was considered to be optical bleed-through from the neighbouring HLF peak. Therefore, a HLF fluorimeter alone would be sufficient to evaluate the microbial water quality at these sources. Fluorescent DOM was also influenced by site operations such as pump start-up and the precipitation of cations on the sensor windows. Online fluorescent DOM sensors are a better indicator of the microbial quality of untreated drinking water than turbidity and they have wide-ranging potential applications within the water industry

Chiral symmetry restoration and the Z3 sectors of QCD

Quenched SU(3) lattice gauge theory shows three phase transitions, namely the chiral, the deconfinement and the Z3 phase transition. Knowing whether or not the chiral and the deconfinement phase transition occur at the same temperature for all Z3 sectors could be crucial to understand the underlying microscopic dynamics. We use the existence of a gap in the Dirac spectrum as an order parameter for the restoration of chiral symmetry. We find that the spectral gap opens up at the same critical temperature in all Z3 sectors in contrast to earlier claims in the literature.Comment: 4 pages, 4 figure

Evidence Against Instanton Dominance of Topological Charge Fluctuations in QCD

The low-lying eigenmodes of the Dirac operator associated with typical gauge field configurations in QCD encode, among other low-energy properties, the physics behind the solution to the $U_A(1)$ problem (i.e. the origin of the $\eta'$ mass), the nature of spontaneous chiral symmetry breaking, and the physics of string-breaking, quark-antiquark pair production, and the OZI rule. Moreover, the space-time chiral structure of these eigenmodes reflects the space-time topological structure of the underlying gauge field. We present evidence from lattice QCD on the local chiral structure of low Dirac eigenmodes leading to the conclusion that topological charge fluctuations of the QCD vacuum are not instanton-dominated. The result supports Witten's arguments that topological charge is produced by confinement-related gauge fluctuations rather than instantons.Comment: 35 pages, 11 figure

On the Application of the Non Linear Sigma Model to Spin Chains and Spin Ladders

We review the non linear sigma model approach (NLSM) to spin chains and spin ladders, presenting new results. The generalization of the Haldane's map to ladders in the Hamiltonian approach, give rise to different values of the $\theta$ parameter depending on the spin S, the number of legs $n_{\ell}$ and the choice of blocks needed to built up the NLSM fields. For rectangular blocks we obtain $\theta = 0$ or $2 \pi S$ depending on wether $n_{\ell}$, is even or odd, while for diagonal blocks we obtain $\theta = 2 \pi S n_{\ell}$. Both results agree modulo $2 \pi$, and yield the same prediction, namely that even ( resp. odd) ladders are gapped (resp. gapless). For even legged ladders we show that the spin gap collapses exponentially with $n_{\ell}$ and we propose a finite size correction to the gap formula recently derived by Chakravarty using the 2+1 NSLM, which gives a good fit of numerical results. We show the existence of a Haldane phase in the two legged ladder using diagonal blocks and finally we consider the phase diagram of dimerized ladders.Comment: 25 pages, Latex, 7 figures in postscript files, Proc. of the 1996 El Escorial Summer School on "Strongly Correlated Magnetic and Superconducting Systems". Some more references are adde