Dual Isomonodromic Deformations and Moment Maps to Loop Algebras

The Hamiltonian structure of the monodromy preserving deformation equations of Jimbo {\it et al } is explained in terms of parameter dependent pairs of moment maps from a symplectic vector space to the dual spaces of two different loop algebras. The nonautonomous Hamiltonian systems generating the deformations are obtained by pulling back spectral invariants on Poisson subspaces consisting of elements that are rational in the loop parameter and identifying the deformation parameters with those determining the moment maps. This construction is shown to lead to ``dual'' pairs of matrix differential operators whose monodromy is preserved under the same family of deformations. As illustrative examples, involving discrete and continuous reductions, a higher rank generalization of the Hamiltonian equations governing the correlation functions for an impenetrable Bose gas is obtained, as well as dual pairs of isomonodromy representations for the equations of the Painleve transcendents $P_{V}$ and $P_{VI}$.Comment: preprint CRM-1844 (1993), 28 pgs. (Corrected date and abstract.

Fluctuations in viscous fingering

Our experiments on viscous (Saffman-Taylor) fingering in Hele-Shaw channels reveal finger width fluctuations that were not observed in previous experiments, which had lower aspect ratios and higher capillary numbers Ca. These fluctuations intermittently narrow the finger from its expected width. The magnitude of these fluctuations is described by a power law, Ca^{-0.64}, which holds for all aspect ratios studied up to the onset of tip instabilities. Further, for large aspect ratios, the mean finger width exhibits a maximum as Ca is decreased instead of the predicted monotonic increase.Comment: Revised introduction, smoothed transitions in paper body, and added a few additional minor results. (Figures unchanged.) 4 pages, 3 figures. Submitted to PRE Rapi

Moduli Stabilization from Fluxes in a Simple IIB Orientifold

We study novel type IIB compactifications on the T^6/Z_2 orientifold. This geometry arises in the T-dual description of Type I theory on T^6, and one normally introduces 16 space-filling D3-branes to cancel the RR tadpoles. Here, we cancel the RR tadpoles either partially or fully by turning on three-form flux in the compact geometry. The resulting (super)potential for moduli is calculable. We demonstrate that one can find many examples of N=1 supersymmetric vacua with greatly reduced numbers of moduli in this system. A few examples with N>1 supersymmetry or complete supersymmetry breaking are also discussed.Comment: 49 pages, harvmac big; v2, corrected some typo

Confusing the extragalactic neutrino flux limit with a neutrino propagation limit

We study the possible suppression of the extragalactic neutrino flux due to a nonstandard interaction during its propagation. In particular, we study neutrino interaction with an ultra-light scalar field dark matter. It is shown that the extragalactic neutrino flux may be suppressed by such an interaction, leading to a new mechanism to reduce the ultra-high energy neutrino flux. We study both the cases of non-self-conjugate as well as self-conjugate dark matter. In the first case, the suppression is independent of the neutrino and dark matter masses. We conclude that care must be taken when explaining limits on the neutrino flux through source acceleration mechanisms only, since there could be other mechanisms for the reduction of the neutrino flux.Comment: 15 pages, 4 figures. Important changes implemented. Abstract modified. Conclusions remain. To be published in JCA

Gaugino Condensation and Nonperturbative Superpotentials in Flux Compactifications

There are two known sources of nonperturbative superpotentials for K\"ahler moduli in type IIB orientifolds, or F-theory compactifications on Calabi-Yau fourfolds, with flux: Euclidean brane instantons and low-energy dynamics in D7 brane gauge theories. The first class of effects, Euclidean D3 branes which lift in M-theory to M5 branes wrapping divisors of arithmetic genus 1 in the fourfold, is relatively well understood. The second class has been less explored. In this paper, we consider the explicit example of F-theory on $K3 \times K3$ with flux. The fluxes lift the D7 brane matter fields, and stabilize stacks of D7 branes at loci of enhanced gauge symmetry. The resulting theories exhibit gaugino condensation, and generate a nonperturbative superpotential for K\"ahler moduli. We describe how the relevant geometries in general contain cycles of arithmetic genus $\chi \geq 1$ (and how $\chi > 1$ divisors can contribute to the superpotential, in the presence of flux). This second class of effects is likely to be important in finding even larger classes of models where the KKLT mechanism of moduli stabilization can be realized. We also address various claims about the situation for IIB models with a single K\"ahler modulus.Comment: 24 pages, harvmac, no figures, references adde

Detailed phenotypic and genotypic characterization of bietti crystalline dystrophy

OBJECTIVE: To provide a detailed phenotype/genotype characterization of Bietti crystalline dystrophy (BCD). DESIGN: Observational case series. PARTICIPANTS: Twenty patients from 17 families recruited from a multiethnic British population. METHODS: Patients underwent color fundus photography, near-infrared (NIR) imaging, fundus autofluorescence (FAF) imaging, spectral domain optical coherence tomography (SD-OCT), and electroretinogram (ERG) assessment. The gene CYP4V2 was sequenced. MAIN OUTCOME MEASURES: Clinical, imaging, electrophysiologic, and molecular genetics findings. RESULTS: Patients ranged in age from 19 to 72 years (median, 40 years), with a visual acuity of 6/5 to perception of light (median, 6/12). There was wide intrafamilial and interfamilial variability in clinical severity. The FAF imaging showed well-defined areas of retinal pigment epithelium (RPE) loss that corresponded on SD-OCT to well-demarcated areas of outer retinal atrophy. Retinal crystals were not evident on FAF imaging and were best visualized with NIR imaging. Spectral domain OCT showed them to be principally located on or in the RPE/Bruch's membrane complex. Disappearance of the crystals, revealed by serial recording, was associated with severe disruption and thinning of the RPE/Bruch's membrane complex. Cases with extensive RPE degeneration (N = 5) had ERGs consistent with generalized rod and cone dysfunction, but those with more focal RPE atrophy showed amplitude reduction without delay (N = 3), consistent with restricted loss of function, or that was normal (N = 2). Likely disease-causing variants were identified in 34 chromosomes from 17 families. Seven were novel, including p.Met66Arg, found in all 11 patients from 8 families of South Asian descent. This mutation appears to be associated with earlier onset (median age, 30 years) compared with other substitutions (median age, 41 years). Deletions of exon 7 were associated with more severe disease. CONCLUSIONS: The phenotype is highly variable. Several novel variants are reported, including a highly prevalent substitution in patients of South Asian descent that is associated with earlier-onset disease. Autofluorescence showed sharply demarcated areas of RPE loss that coincided with abrupt edges of outer retinal atrophy on SD-OCT; crystals were generally situated on or in the RPE/Bruch's complex but could disappear over time with associated RPE disruption. These results support a role for the RPE in disease pathogenesis

Percolation and epidemics in a two-dimensional small world

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of "shortcuts" in the small-world network. Our results agree with scaling hypotheses and numerical simulations for the same model.Comment: 7 pages, 3 figures, 2 table

Assessing environmental pollution in birds: a new methodological approach for interpreting bioaccumulation of trace elements in feather shafts using geochemical sediment data

Environmental trace element composition can have an important impact on ecosystem and population health as well individual fitness. Therefore, carefully assessing bioaccumulation of trace elements is central to studies investigating the ecological impact of pollution. Colonial birds are important bioindicators since non-invasive sampling can easily be achieved through sampling of chick feathers, which controls for some confounding factors of variability (age and environmental heterogeneity). However, an additional confounding factor, external contamination (ExCo), which remains even after washing feathers, has frequently been overlooked in the literature. We developed a new method to reliably interpret bioaccumulation of 10 trace elements (As, Cd, Cr, Cu, Hg, Ni, Pb, Se, Sn and Zn) in feathers using chicks of a colonial species: the Greater Flamingo, Phoenicopterus roseus. First, only shafts were used to remove ExCo retained in vanes. Secondly, we applied a thorough washing procedure. Thirdly, we applied a new analytical method to control for ExCo, which assumes that ExCo is mainly due to adhered sediment particles and that the relative concentration of each trace element will be similar to the sediment geochemical composition of sampling sites. We validated this new methodology by comparing trace element composition and particle composition (by scanning electron microscopy and mass spectrometry) of washed and unwashed feathers. The washing procedure removed >99% of K indicating that most of the ExCo from salt was removed. Scanning electron microscopy and mass spectrometry revealed that some sediment particles remained after washing, especially clays which are likely to severely bias bioaccumulation interpretation. We successfully controlled for ExCo by calculating the ratio of ExCo due to sediment using the geochemical fingerprint of sediment samples. Our methodology leads to conservative estimates of bioaccumulation for As, Cd, Cr, Cu, Hg, Ni, Pb, Se, Sn and Zn. We have validated a new more reliable method of analysing trace element concentrations in feathers, which effectively controls for ExCo, if geochemical sediment data can be meaningfully compared to ExCo of feathers. We have demonstrated that overlooking ExCo leads to potentially erroneous conclusions, and we urge that the method applied in this study be considered in future studies.Peer Reviewe

Edge Currents in Non-commutative Chern-Simons Theory from a New Matrix Model

This paper discusses the formulation of the non-commutative Chern-Simons (CS) theory where the spatial slice, an infinite strip, is a manifold with boundaries. As standard star products are not correct for such manifolds, the standard non-commutative CS theory is not also appropriate here. Instead we formulate a new finite-dimensional matrix CS model as an approximation to the CS theory on the strip. A work which has points of contact with ours is due to Lizzi, Vitale and Zampini where the authors obtain a description for the fuzzy disc. The gauge fields in our approach are operators supported on a subspace of finite dimension N+\eta of the Hilbert space of eigenstates of a simple harmonic oscillator with N, \eta \in Z^+ and N \neq 0. This oscillator is associated with the underlying Moyal plane. The resultant matrix CS theory has a fuzzy edge. It becomes the required sharp edge when N and \eta goes to infinity in a suitable sense. The non-commutative CS theory on the strip is defined by this limiting procedure. After performing the canonical constraint analysis of the matrix theory, we find that there are edge observables in the theory generating a Lie algebra with properties similar to that of a non-abelian Kac-Moody algebra. Our study shows that there are (\eta+1)^2 abelian charges (observables) given by the matrix elements (\cal A_i)_{N-1 N-1} and (\cal A_i)_{nm} (where n or m \geq N) of the gauge fields, that obey certain standard canonical commutation relations. In addition, the theory contains three unique non-abelian charges, localized near the N^th level. We show that all non-abelian edge observables except these three can be constructed from the abelian charges above. Using the results of this analysis we discuss the large N and \eta limit.Comment: LaTeX, 16 pages and 2 figures. Comments added in sections 4 and 5. A minor error corrected in section 4. Figures replaced for clarity. Typos correcte

Bailing Out the Milky Way: Variation in the Properties of Massive Dwarfs Among Galaxy-Sized Systems

Recent kinematical constraints on the internal densities of the Milky Way's dwarf satellites have revealed a discrepancy with the subhalo populations of simulated Galaxy-scale halos in the standard CDM model of hierarchical structure formation. This has been dubbed the "too big to fail" problem, with reference to the improbability of large and invisible companions existing in the Galactic environment. In this paper, we argue that both the Milky Way observations and simulated subhalos are consistent with the predictions of the standard model for structure formation. Specifically, we show that there is significant variation in the properties of subhalos among distinct host halos of fixed mass and suggest that this can reasonably account for the deficit of dense satellites in the Milky Way. We exploit well-tested analytic techniques to predict the properties in a large sample of distinct host halos with a variety of masses spanning the range expected of the Galactic halo. The analytic model produces subhalo populations consistent with both Via Lactea II and Aquarius, and our results suggest that natural variation in subhalo properties suffices to explain the discrepancy between Milky Way satellite kinematics and these numerical simulations. At least ~10% of Milky Way-sized halos host subhalo populations for which there is no "too big to fail" problem, even when the host halo mass is as large as M_host = 10^12.2 h^-1 M_sun. Follow-up studies consisting of high-resolution simulations of a large number of Milky Way-sized hosts are necessary to confirm our predictions. In the absence of such efforts, the "too big to fail" problem does not appear to be a significant challenge to the standard model of hierarchical formation. [abridged]Comment: 12 pages, 3 figures; accepted by JCAP. Replaced with published versio