Quantum Hall Effect and Noncommutative Geometry

We study magnetic Schrodinger operators with random or almost periodic electric potentials on the hyperbolic plane, motivated by the quantum Hall effect in which the hyperbolic geometry provides an effective Hamiltonian. In addition we add some refinements to earlier results. We derive an analogue of the Connes-Kubo formula for the Hall conductance via the quantum adiabatic theorem, identifying it as a geometric invariant associated to an algebra of observables that turns out to be a crossed product algebra. We modify the Fredholm modules defined in [CHMM] in order to prove the integrality of the Hall conductance in this case.Comment: 18 pages, paper rewritte

Spectral flow invariants and twisted cyclic theory from the Haar state on SU_q(2)

In [CPR2], we presented a K-theoretic approach to finding invariants of algebras with no non-trivial traces. This paper presents a new example that is more typical of the generic situation. This is the case of an algebra that admits only non-faithful traces, namely SU_q(2), and also KMS states. Our main results are index theorems (which calculate spectral flow), one using ordinary cyclic cohomology and the other using twisted cyclic cohomology, where the twisting comes from the generator of the modular group of the Haar state. In contrast to the Cuntz algebras studied in [CPR2], the computations are considerably more complex and interesting, because there are nontrivial `eta' contributions to this index.Comment: 25 pages, 1 figur

Principal Bundles and the Dixmier Douady Class

A systematic consideration of the problem of the reduction and extension of the structure group of a principal bundle is made and a variety of techniques in each case are explored and related to one another. We apply these to the study of the Dixmier-Douady class in various contexts including string structures, U-res bundles and other examples motivated by considerations from quantum field theory.Comment: 28 pages, latex, no figures, uses amsmath, amsthm, amsfonts. Revised version - only change a lot of irritating typos remove

The mechanism of infection and decay of window joinery

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Quantum Hall Effect on the Hyperbolic Plane

In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables. We define a twisted analogue of the Kasparov map, which enables us to use the pairing between $K$-theory and cyclic cohomology theory, to identify this geometric invariant with a topological index, thereby proving the integrality of the Hall conductivity in this case.Comment: AMS-LaTeX, 28 page

Maternal Factors Related to Parenting Young Children with Congenital Heart Disease

The purpose of this study was to compare the early child-rearing practices between mothers of young children with congenital heart disease (CHD) and mothers of healthy children. In addition, maternal stress, parental developmental expectations, and the early behavioral and emotional development of their children were explored. Maccoby’s (1992) socialization theory emphasizing the reciprocal nature of mother-child interactions provided the framework for this study. Findings from quantitative self-report measures and videotaped parent-child interactions showed a remarkable similarity between mothers of children with CHD and mothers of healthy children. In contrast, qualitative data revealed important differences with mothers of CHD children reporting high levels of vigilance with their children. The important role of promoting the principle of normalization among mothers of children with CHD and ensuring a sufficient support system is discussed

Aquatic Nitrate Retention at River Network Scales Across Flow Conditions Determined Using Nested In Situ Sensors

Nonpoint pollution sources are strongly influenced by hydrology and are therefore sensitive to climate variability. Some pollutants entering aquatic ecosystems, e.g., nitrate, can be mitigated by in‐stream processes during transport through river networks. Whole river network nitrate retention is difficult to quantify with observations. High frequency, in situ nitrate sensors, deployed in nested locations within a single watershed, can improve estimates of both nonpoint inputs and aquatic retention at river network scales. We deployed a nested sensor network and associated sampling in the urbanizing Oyster River watershed in coastal New Hampshire, USA, to quantify storm event‐scale loading and retention at network scales. An end member analysis used the relative behavior of reactive nitrate and conservative chloride to infer river network fate of nitrate. In the headwater catchments, nitrate and chloride concentrations are both increasingly diluted with increasing storm size. At the mouth of the watershed, chloride is also diluted, but nitrate tended to increase. The end member analysis suggests that this pattern is the result of high retention during small storms (51–78%) that declines to zero during large storms. Although high frequency nitrate sensors did not alter estimates of fluxes over seasonal time periods compared to less frequent grab sampling, they provide the ability to estimate nitrate flux versus storm size at event scales that is critical for such analyses. Nested sensor networks can improve understanding of the controls of both loading and network scale retention, and therefore also improve management of nonpoint source pollution