On Combining Lensing Shear Information from Multiple Filters

We consider the possible gain in the measurement of lensing shear from imaging data in multiple filters. Galaxy shapes may differ significantly across filters, so that the same galaxy offers multiple samples of the shear. On the other extreme, if galaxy shapes are identical in different filters, one can combine them to improve the signal-to-noise and thus increase the effective number density of faint, high redshift galaxies. We use the GOODS dataset to test these scenarios by calculating the covariance matrix of galaxy ellipticities in four visual filters (B,V,i,z). We find that galaxy shapes are highly correlated, and estimate the gain in galaxy number density by combining their shapes.Comment: 8 pages, no figures, submitted to JCA

On the Structure of the Observable Algebra of QCD on the Lattice

The structure of the observable algebra ${\mathfrak O}_{\Lambda}$ of lattice QCD in the Hamiltonian approach is investigated. As was shown earlier, ${\mathfrak O}_{\Lambda}$ is isomorphic to the tensor product of a gluonic $C^{*}$-subalgebra, built from gauge fields and a hadronic subalgebra constructed from gauge invariant combinations of quark fields. The gluonic component is isomorphic to a standard CCR algebra over the group manifold SU(3). The structure of the hadronic part, as presented in terms of a number of generators and relations, is studied in detail. It is shown that its irreducible representations are classified by triality. Using this, it is proved that the hadronic algebra is isomorphic to the commutant of the triality operator in the enveloping algebra of the Lie super algebra ${\rm sl(1/n)}$ (factorized by a certain ideal).Comment: 33 page

Weak Lensing Determination of the Mass in Galaxy Halos

We detect the weak gravitational lensing distortion of 450,000 background galaxies (20<R<23) by 790 foreground galaxies (R<18) selected from the Las Campanas Redshift Survey (LCRS). This is the first detection of weak lensing by field galaxies of known redshift, and as such permits us to reconstruct the shear profile of the typical field galaxy halo in absolute physical units (modulo H_0), and to investigate the dependence of halo mass upon galaxy luminosity. This is also the first galaxy-galaxy lensing study for which the calibration errors are negligible. Within a projected radius of 200 \hkpc, the shear profile is consistent with an isothermal profile with circular velocity 164+-20 km/s for an L* galaxy, consistent with typical disk rotation at this luminosity. This halo mass normalization, combined with the halo profile derived by Fischer et al (2000) from lensing analysis SDSS data, places a lower limit of (2.7+-0.6) x 10^{12}h^{-1} solar masses on the mass of an L* galaxy halo, in good agreement with satellite galaxy studies. Given the known luminosity function of LCRS galaxies, and the assumption that $M\propto L^\beta$ for galaxies, we determine that the mass within 260\hkpc of normal galaxies contributes $\Omega=0.16\pm0.03$ to the density of the Universe (for $\beta=1$) or $\Omega=0.24\pm0.06$ for $\beta=0.5$. These lensing data suggest that $0.6<\beta<2.4$ (95% CL), only marginally in agreement with the usual $\beta\approx0.5$ Faber-Jackson or Tully-Fisher scaling. This is the most complete direct inventory of the matter content of the Universe to date.Comment: 18 pages, incl. 3 figures. Submitted to ApJ 6/7/00, still no response from the referee after four months

Covariant spinor representation of iosp(d,2/2)iosp(d,2/2) and quantization of the spinning relativistic particle

A covariant spinor representation of $iosp(d,2/2)$ is constructed for the quantization of the spinning relativistic particle. It is found that, with appropriately defined wavefunctions, this representation can be identified with the state space arising from the canonical extended BFV-BRST quantization of the spinning particle with admissible gauge fixing conditions after a contraction procedure. For this model, the cohomological determination of physical states can thus be obtained purely from the representation theory of the $iosp(d,2/2)$ algebra.Comment: Updated version with references included and covariant form of equation 1. 23 pages, no figure

Ecological indicators for abandoned mines, Phase 1: Review of the literature

Mine waters have been identified as a significant issue in the majority of Environment Agency draft River Basin Management Plans. They are one of the largest drivers for chemical pollution in the draft Impact Assessment for the Water Framework Directive (WFD), with significant failures of environmental quality standards (EQS) for metals (particularly Cd, Pb, Zn, Cu, Fe) in many rivers linked to abandoned mines. Existing EQS may be overprotective of aquatic life which may have adapted over centuries of exposure. This study forms part of a larger project to investigate the ecological impact of metals in rivers, to develop water quality targets (alternative objectives for the WFD) for aquatic ecosystems impacted by long-term mining pollution. The report reviews literature on EQS failures, metal effects on aquatic biota and effects of water chemistry, and uses this information to consider further work. A preliminary assessment of water quality and biology data for 87 sites across Gwynedd and Ceredigion (Wales) shows that existing Environment Agency water quality and biology data could be used to establish statistical relations between chemical variables and metrics of ecological quality. Visual representation and preliminary statistical analyses show that invertebrate diversity declines with increasing zinc concentration. However, the situation is more complex because the effects of other metals are not readily apparent. Furthermore, pH and aluminium also affect streamwater invertebrates, making it difficult to tease out toxicity due to individual mine-derived metals. The most characteristic feature of the plant communities of metal-impacted systems is a reduction in diversity, compared to that found in comparable unimpacted streams. Some species thrive in the presence of heavy metals, presumably because they are able to develop metal tolerance, whilst others consistently disappear. Effects are, however, confounded by water chemistry, particularly pH. Tolerant species are spread across a number of divisions of photosynthetic organisms, though green algae, diatoms and blue-green algae are usually most abundant, often thriving in the absence of competition and/or grazing. Current UK monitoring techniques focus on community composition and, whilst these provide a sampling and analytical framework for studies of metal impacts, the metrics are not sensitive to these impacts. There is scope for developing new metrics, based on community-level analyses and for looking at morphological variations common in some taxa at elevated metal concentrations. On the whole, community-based metrics are recommended, as these are easier to relate to ecological status definitions. With respect to invertebrates and fish, metals affect individuals, population and communities but sensitivity varies among species, life stages, sexes, trophic groups and with body condition. Acclimation or adaptation may cause varying sensitivity even within species. Ecosystem-scale effects, for example on ecological function, are poorly understood. Effects vary between metals such as cadmium, copper, lead, chromium, zinc and nickel in order of decreasing toxicity. Aluminium is important in acidified headwaters. Biological effects depend on speciation, toxicity, availability, mixtures, complexation and exposure conditions, for example discharge (flow). Current water quality monitoring is unlikely to detect short-term episodic increases in metal concentrations or evaluate the bioavailability of elevated metal concentrations in sediments. These factors create uncertainty in detecting ecological impairment in metal-impacted ecosystems. Moreover, most widely used biological indicators for UK freshwaters were developed for other pressures and none distinguishes metal impacts from other causes of impairment. Key ecological needs for better regulation and management of metals in rivers include: i) models relating metal data to ecological data that better represent influences on metal toxicity; ii) biodiagnostic indices to reflect metal effects; iii) better methods to identify metal acclimation or adaptation among sensitive taxa; iv) better investigative procedures to isolate metal effects from other pressures. Laboratory data on the effects of water chemistry on cationic metal toxicity and bioaccumulation show that a number of chemical parameters, particularly pH, dissolved organic carbon (DOC) and major cations (Na, Mg, K, Ca) exert a major influence on the toxicity and/or bioaccumulation of cationic metals. The biotic ligand model (BLM) provides a conceptual framework for understanding these water chemistry effects as a combination of the influence of chemical speciation, and metal uptake by organisms in competition with H+ and other cations. In some cases where the BLM cannot describe effects, empirical bioavailable models have been successfully used. Laboratory data on the effects of metal mixtures across different water chemistries are sparse, with implications for transferring understanding to mining-impacted sites in the field where mixture effects are likely. The available field data, although relatively sparse, indicate that water chemistry influences metal effects on aquatic ecosystems. This occurs through complexation reactions, notably involving dissolved organic matter and metals such as Al, Cu and Pb. Secondly, because bioaccumulation and toxicity are partly governed by complexation reactions, competition effects among metals, and between metals and H+, give rise to dependences upon water chemistry. There is evidence that combinations of metals are active in the field; the main study conducted so far demonstrated the combined effects of Al and Zn, and suggested, less certainly, that Cu and H+ can also contribute. Chemical speciation is essential to interpret and predict observed effects in the field. Speciation results need to be combined with a model that relates free ion concentrations to toxic effect. Understanding the toxic effects of heavy metals derived from abandoned mines requires the simultaneous consideration of the acidity-related components Al and H+. There are a number of reasons why organisms in waters affected by abandoned mines may experience different levels of metal toxicity than in the laboratory. This could lead to discrepancies between actual field behaviour and that predicted by EQS derived from laboratory experiments, as would be applied within the WFD. The main factors to consider are adaptation/acclimation, water chemistry, and the effects of combinations of metals. Secondary effects are metals in food, metals supplied by sediments, and variability in stream flows. Two of the most prominent factors, namely adaptation/ acclimation and bioavailability, could justify changes in EQS or the adoption of an alternative measure of toxic effects in the field. Given that abandoned mines are widespread in England and Wales, and the high cost of their remediation to meet proposed WFD EQS criteria, further research into the question is clearly justified. Although ecological communities of mine-affected streamwaters might be over-protected by proposed WFD EQS, there are some conditions under which metals emanating from abandoned mines definitely exert toxic effects on biota. The main issue is therefore the reliable identification of chemical conditions that are unacceptable and comparison of those conditions with those predicted by WFD EQS. If significant differences can convincingly be demonstrated, the argument could be made for alternative standards for waters affected by abandoned mines. Therefore in our view, the immediate research priority is to improve the quantification of metal effects under field circumstances. Demonstration of dose-response relationships, based on metal mixtures and their chemical speciation, and the use of better biological tools to detect and diagnose community-level impairment, would provide the necessary scientific information

Hopf algebras and characters of classical groups

Schur functions provide an integral basis of the ring of symmetric functions. It is shown that this ring has a natural Hopf algebra structure by identifying the appropriate product, coproduct, unit, counit and antipode, and their properties. Characters of covariant tensor irreducible representations of the classical groups GL(n), O(n) and Sp(n) are then expressed in terms of Schur functions, and the Hopf algebra is exploited in the determination of group-subgroup branching rules and the decomposition of tensor products. The analysis is carried out in terms of n-independent universal characters. The corresponding rings, CharGL, CharO and CharSp, of universal characters each have their own natural Hopf algebra structure. The appropriate product, coproduct, unit, counit and antipode are identified in each case.Comment: 9 pages. Uses jpconf.cls and jpconf11.clo. Presented by RCK at SSPCM'07, Myczkowce, Poland, Sept 200

Integrity bases for local invariants of composite quantum systems

Unitary group branchings appropriate to the calculation of local invariants of density matrices of composite quantum systems are formulated using the method of $S$-function plethysms. From this, the generating function for the number of invariants at each degree in the density matrix can be computed. For the case of two two-level systems the generating function is $F(q) = 1 + q + 4q^{2} + 6 q^{3} + 16 q^{4} + 23 q^{5} + 52 q^{6} + 77 q^{7} + 150 q^{8} + 224 q^{9} + 396 q^{10} + 583 q^{11}+ O(q^{12})$. Factorisation of such series leads in principle to the identification of an integrity basis of algebraically independent invariants. This note replaces Appendix B of our paper\cite{us} J Phys {\bf A33} (2000) 1895-1914 (\texttt{quant-ph/0001076}) which is incorrect.Comment: Latex, 4 pages, correcting Appendix B of quant-ph/0001076 Error in $F(q)$ corrected and conclusions modified accordingl

As above, so below: whole transcriptome profiling demonstrates strong molecular similarities between avian dorsal and ventral pallial subdivisions

Over the last two decades, beginning withthe Avian Brain Nomenclature Forum in2000, major revisions have been made to our understanding of the organization andnomenclature of the avian brain. However, there are still unresolved questions on avianpallial organization, particularly whether the cells above the vestigial ventricle representdistinct populations to those below it or similar populations. To test these two hypothe-ses, we profiled the transcriptomes of the major avian pallial subdivisions dorsal and ven-tral to the vestigial ventricle boundary using RNA sequencing and a new zebra finchgenome assembly containing about 22,000annotated, complete genes. We found thatthe transcriptomes of neural populations above and below the ventricle were remarkablysimilar. Each subdivision in dorsal pallium (Wulst) had a corresponding molecular counter-part in the ventral pallium (dorsal ventricularridge). In turn, each corresponding subdivi-sion exhibited shared gene co-expression modules that contained gene sets enriched infunctional specializations, such as anatomical structure development, synaptic transmis-sion, signaling, and neurogenesis. Thesefindings are more in line with the continuumhypothesis of avian brain subdivision organization above and below the vestigial ventriclespace, with the pallium as a whole consisting offour major cell populations (intercalatedpallium, mesopallium, hyper-nidopallium, andarcopallium) instead of seven (hyperpalliumapicale, interstitial hyperpallium apicale, intercalated hyperpallium, hyperpalliumdensocellare, mesopallium, nidopallium, and arcopallium). We suggest adopting a morestreamlined hierarchical naming system thatreflects the robust similarities in geneexpression, neural connectivity motifs, and function. These findings have important impli-cations for our understanding of overall vertebrate brain evolution

Polynomial super-gl(n) algebras

We introduce a class of finite dimensional nonlinear superalgebras $L = L_{\bar{0}} + L_{\bar{1}}$ providing gradings of $L_{\bar{0}} = gl(n) \simeq sl(n) + gl(1)$. Odd generators close by anticommutation on polynomials (of degree $>1$) in the $gl(n)$ generators. Specifically, we investigate `type I' super-$gl(n)$ algebras, having odd generators transforming in a single irreducible representation of $gl(n)$ together with its contragredient. Admissible structure constants are discussed in terms of available $gl(n)$ couplings, and various special cases and candidate superalgebras are identified and exemplified via concrete oscillator constructions. For the case of the $n$-dimensional defining representation, with odd generators $Q_{a}, \bar{Q}{}^{b}$, and even generators ${E^{a}}_{b}$, $a,b = 1,...,n$, a three parameter family of quadratic super-$gl(n)$ algebras (deformations of $sl(n/1)$) is defined. In general, additional covariant Serre-type conditions are imposed, in order that the Jacobi identities be fulfilled. For these quadratic super-$gl(n)$ algebras, the construction of Kac modules, and conditions for atypicality, are briefly considered. Applications in quantum field theory, including Hamiltonian lattice QCD and space-time supersymmetry, are discussed.Comment: 31 pages, LaTeX, including minor corrections to equation (3) and reference [60