The Tadpole Pupil: Case Series With Review of the Literature and New Considerations.

Tadpole pupil is a rare phenomenon in which segmental spasm of the iris dilator muscle results in a tadpole-shaped pupil. The pupillary distortion is usually unilateral, lasts several minutes, and can recur in clusters. Any segment of the iris can be affected; thus, for some patients, a different-shaped tadpole pupil is noticed from episode to episode. Tadpole pupil most commonly appears spontaneously in young women. Tadpole pupil is not associated with any systemic disorders, but an ipsilateral Horner syndrome is noted in 46% of patients. In this article, we have reviewed the existing literature of tadpole pupil, compiling all the published cases in a table and reporting four additional cases to re-examine the clinical profile of this disorder and to consider the different purported mechanisms as means to understand its possible etiology and treatment. The common denominator in the pathophysiology of tadpole pupil is a focal excessive contraction (segmental spasm) of the iris dilator muscle. Based on various proposed pathophysiologic mechanism of tadpole pupil, we can consider potential forms of treatment

2+1 Dimensional Georgi-Glashow Instantons in Weyl Gauge

Semiclassical instanton solutions in the 3D SU(2) Georgi-Glashow model are transformed into the Weyl gauge. This illustrates the tunneling interpretation of these instantons and provides a smooth regularization of the singular unitary gauge. The 3D Georgi-Glashow model has both instanton and sphaleron solutions, in contrast to 3D Yang-Mills theory which has neither, and 4D Yang-Mills theory which has instantons but no sphaleron, and 4D electroweak theory which has a sphaleron but no instantons. We also discuss the spectral flow picture of fundamental fermions in a Georgi-Glashow instanton background.Comment: 22 pages, 8 figures, revtex4; v2 - references and comments adde

Fredholm Indices and the Phase Diagram of Quantum Hall Systems

The quantized Hall conductance in a plateau is related to the index of a Fredholm operator. In this paper we describe the generic ``phase diagram'' of Fredholm indices associated with bounded and Toeplitz operators. We discuss the possible relevance of our results to the phase diagram of disordered integer quantum Hall systems.Comment: 25 pages, including 7 embedded figures. The mathematical content of this paper is similar to our previous paper math-ph/0003003, but the physical analysis is ne

Fractal spectral triples on Kellendonk's C∗C^*-algebra of a substitution tiling

We introduce a new class of noncommutative spectral triples on Kellendonk's $C^*$-algebra associated with a nonperiodic substitution tiling. These spectral triples are constructed from fractal trees on tilings, which define a geodesic distance between any two tiles in the tiling. Since fractals typically have infinite Euclidean length, the geodesic distance is defined using Perron-Frobenius theory, and is self-similar with scaling factor given by the Perron-Frobenius eigenvalue. We show that each spectral triple is $\theta$-summable, and respects the hierarchy of the substitution system. To elucidate our results, we construct a fractal tree on the Penrose tiling, and explicitly show how it gives rise to a collection of spectral triples.Comment: Updated to agree with published versio

Macular Microcysts in Mitochondrial Optic Neuropathies: Prevalence and Retinal Layer Thickness Measurements.

PurposeTo investigate the thickness of the retinal layers and to assess the prevalence of macular microcysts (MM) in the inner nuclear layer (INL) of patients with mitochondrial optic neuropathies (MON).MethodsAll patients with molecularly confirmed MON, i.e. Leber's Hereditary Optic Neuropathy (LHON) and Dominant Optic Atrophy (DOA), referred between 2010 and 2012 were enrolled. Eight patients with MM were compared with two control groups: MON patients without MM matched by age, peripapillary retinal nerve fiber layer (RNFL) thickness, and visual acuity, as well as age-matched controls. Retinal segmentation was performed using specific Optical coherence tomography (OCT) software (Carl Zeiss Meditec). Macular segmentation thickness values of the three groups were compared by one-way analysis of variance with Bonferroni post hoc corrections.ResultsMM were identified in 5/90 (5.6%) patients with LHON and 3/58 (5.2%) with DOA. The INL was thicker in patients with MON compared to controls regardless of the presence of MM [133.1±7μm vs 122.3±9μm in MM patients (p<0.01) and 128.5±8μm vs. 122.3±9μm in no-MM patients (p<0.05)], however the outer nuclear layer (ONL) was thicker in patients with MM (101.4±1mμ) compared to patients without MM [77.5±8mμ (p<0.001)] and controls [78.4±7mμ (p<0.001)]. ONL thickness did not significantly differ between patients without MM and controls.ConclusionThe prevalence of MM in MON is low (5-6%), but associated with ONL thickening. We speculate that in MON patients with MM, vitreo-retinal traction contributes to the thickening of ONL as well as to the production of cystic spaces

Come together: firm boundaries and delegation

Little is known theoretically, and even less empirically, about the relationship between firm boundaries and the allocation of decision rights within firms. We develop a model in which firms choose which suppliers to integrate and whether to delegate decisions to integrated suppliers. We test the predictions of the model using a novel dataset that combines measures of vertical integration and delegation for a large set of firms from many countries and industries. In line with the model’s predictions, we obtain three main results: (i) integration and delegation co-vary positively; (ii) producers are more likely to integrate suppliers in input sectors with greater productivity variation (as the option value of integration is greater); and (iii) producers are more likely to integrate suppliers of more important inputs and to delegate decisions to them

A super massive black hole binary in 3C66B: future observational perspectives

Supermassive black hole binaries (SMBHBs) may exist in the centers of galaxies and active galactic nuclei (AGN) and are expected to be fairly common in the Universe as a consequence of merging processes between galaxies. The existence of SMBHBs can be probed by looking for double nuclei in galaxy centers or, more easily, detecting periodic behavior in the observed radio light curves. In a recent paper, Sudou et al. \cite{sudou2003} announced the first direct observation of an SMBHB. Using VLBI observations they found that the unresolved radio core of the radio galaxy 3C66B shows a well defined elliptical motion with a period of $1.05\pm 0.03$ yrs, implying the presence of a couple of massive black holes in the center of the galaxy. In the present paper we study the astrophysical implications of the existence of such an SMBHB in 3C66B. In particular we focus on the information that can be obtained from detecting a signal periodicity either in the $X$-ray and/or $\gamma$-ray light curves as a consequence of the motion of the black holes. These observations could be used to extract further information on the physical parameters of the SMBHB and partially solve the system parameter degeneracy. The detection of the gravitational wave spectrum emitted by such system may be used to completely determine the physical parameters of the binary system.Comment: 8 pages, 8 figures, in Press on Astronomy & Astrophysic

Quantum lump dynamics on the two-sphere

It is well known that the low-energy classical dynamics of solitons of Bogomol'nyi type is well approximated by geodesic motion in M_n, the moduli space of static n-solitons. There is an obvious quantization of this dynamics wherein the wavefunction evolves according to the Hamiltonian H_0 equal to (half) the Laplacian on M_n. Born-Oppenheimer reduction of analogous mechanical systems suggests, however, that this simple Hamiltonian should receive corrections including k, the scalar curvature of M_n, and C, the n-soliton Casimir energy, which are usually difficult to compute, and whose effect on the energy spectrum is unknown. This paper analyzes the spectra of H_0 and two corrections to it suggested by work of Moss and Shiiki, namely H_1=H_0+k/4 and H_2=H_1+C, in the simple but nontrivial case of a single CP^1 lump moving on the two-sphere. Here M_1=TSO(3), a noncompact kaehler 6-manifold invariant under an SO(3)xSO(3) action, whose geometry is well understood. The symmetry gives rise to two conserved angular momenta, spin and isospin. A hidden isometry of M_1 is found which implies that all three energy spectra are symmetric under spin-isospin interchange. The Casimir energy is found exactly on the zero section of TSO(3), and approximated numerically on the rest of M_1. The lowest 19 eigenvalues of H_i are found for i=0,1,2, and their spin-isospin and parity compared. The curvature corrections in H_1 lead to a qualitatively unchanged low-level spectrum while the Casimir energy in H_2 leads to significant changes. The scaling behaviour of the spectra under changes in the radii of the domain and target spheres is analyzed, and it is found that the disparity between the spectra of H_1 and H_2 is reduced when the target sphere is made smaller.Comment: 35 pages, 3 figure

Topological Phases near a Triple Degeneracy

We study the pattern of three state topological phases that appear in systems with real Hamiltonians and wave functions. We give a simple geometric construction for representing these phases. We then apply our results to understand previous work on three state phases. We point out that the ``mirror symmetry'' of wave functions noticed in microwave experiments can be simply understood in our framework.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let