The Noncommutative Geometry of the Quantum Projective Plane

We study the spectral geometry of the quantum projective plane CP^2_q, a deformation of the complex projective plane CP^2, the simplest example of a spin^c manifold which is not spin. In particular, we construct a Dirac operator D which gives a 0^+ summable spectral triple, equivariant under U_q(su(3)). The square of D is a central element for which left and right actions on spinors coincide, a fact that is exploited to compute explicitly its spectrum.Comment: v2: 26 pages. Paper completely reorganized; no major change, several minor one

Giant reflection band and anomalous negative transmission in a resonant dielectric grating slab: application to a planar cavity

The fundamental optical effects that are at basis of giant reflection band and anomalous negative transmission in a self-sustained rectangular dielectric grating slab in P polarization and for incidence angle not very far from the Brewster's angle of the equivalent slab, are investigated. Notice, that the self sustained dielectric grating slab is the simplest system that, due to the Bragg diffraction, can show both the former optical effects. A systematic study of its optical response is performed by an analytical exact solution of the Maxwell equations for a general incidence geometry. At variance of the well known broad reflection bands in high contrast dielectric grating slab in the sub-wavelength regime, obtained by the destructive interference between the travelling fundamental wave and the first diffracted wave (a generalization of the so called second kind Wood's anomalies), the giant reflection band is a subtle effect due to the interplay, as well as among the travelling fundamental wave and the first quasi-guided diffracted one, also among the higher in-plane wave- vector components of the evanescent/divergent waves. To better describe this effect we will compare the optical response of the self-sustained high contrast dielectric grating slab with a system composed by an equivalent homogeneous slab with a thin rectangular high contrast dielectric grating engraved in one of the two surfaces, usually taken as a prototype for the second kind Wood's anomalies generation. Finally, the electromagnetic field confinement in a patterned planar cavity, where the mirrors are two self-sustained rectangular dielectric grating slabs, is briefly discussed.Comment: 14 pages, 12 figures, submitted to Phys. Rev.

Polariton-polariton scattering in microcavities: A microscopic theory

We apply the fermion commutation technique for composite bosons to polariton-polariton scattering in semiconductor planar microcavities. Derivations are presented in a simple and physically transparent fashion. A procedure of orthogonolization of the initial and final two-exciton state wavefunctions is used to calculate the effective scattering matrix elements and the scattering rates. We show how the bosonic stimulation of the scattering appears in this full fermionic approach whose equivalence to the bosonization method is thus demonstrated in the regime of low exciton density. We find an additional contribution to polariton-polariton scattering due to the exciton oscillator strength saturation, which we analyze as well. We present a theory of the polariton-polariton scattering with opposite spin orientations and show that this scattering process takes place mainly via dark excitonic states. Analytical estimations of the effective scattering amplitudes are given.Comment: Theoretical paper on polariton-polariton scattering in planar microcavities. The new version contains a slightly modified abstract and a revised introduction. Typos have been corrected wherever spotted. 16 page

Prognostic significance of primary-tumor extension, stage and grade of nuclear differentiation in patients with renal cell carcinoma

Surgery remains the preferred therapy for renal cell carcinoma. The various adjunctive or complementary therapies currently yield disappointing results. Identifying reliable prognostic factors could help in selecting patients most likely to benefit from postoperative adjuvant therapies. We reviewed the surgical records of 78 patients who had undergone radical nephrectomy with lymphadenectomy for renal cell carcinoma, matched for type of operation and histology. According to staging (TNM), 5.1% of the patients were classified as stage I, 51.3% as stage II, 29.5% as stage III and 14.5% as stage IV. Of the 78 patients 40 were T2N0 and 21 T3aN0. Tumor grading showed that 39.7% of the patients had well-differentiated tumors(G1), 41.1% moderately-differentiated (G2), and 19.2% poorly-differentiated tumors (G3). Overall actuarial survival at 5 and 10 years was 100% for stage 1; 91.3% at 5 years and 83.1% at 10 years for stage II; 45.5% and 34.1% for stage III; and 29.1% and nil for stage IV (stage II vs stage III p = 0.0001). Patients with tumors confined to the kidney (pT2N0) had better 5- and 10-year survival rates than patients with tumors infiltrating the perirenal fat (pT3aN0) (p = 0.000006). Survival differed according to nuclear grading (G1 vs G3 ; p = 0.000005; G2 vs G3; p = 0.0009). In conclusion our review identified tumor stage, primary-tumor extension, and the grade of nuclear differentiation as reliable prognostic factors in patients with renal cell carcinomas

Active Control of an Axial Flow Compressor via Pulsed Air Injection

This paper presents the use of pulsed air injection to control the onset of rotating stall in a low-speed, axial flow compressor. By measuring the unsteady pressures near the rotor face, a control algorithm determines the magnitude and phase of the first mode of rotating stall and controls the injection of air in the front of the rotor face. Experimental results show that this technique slightly extends the stall point of the compressor and eliminates the hysteresis loop normally associated with rotating stall. A parametric study is used to determine the optimal control parameters for suppression of stall. Analytic results---using a low-dimensional model developed by Moore and Greitzer combined with an unsteady shift in the compressor characteristic to model the injectors---give further insights into the operation of the controller. Based on this model, we show that the behavior of the experiment can be explained as a change in the bifurcation behavior of the system under nonlinear feedback. A higher fidelity simulation model is then used to further verify some of the specific performance characteristics that are observed in experiments

Control of rotating stall in a low-speed axial flow compressor using pulsed air injection: modeling, simulations, and experimental validation

Previous results in the use of pulsed air injection for active control of rotating stall have suggested that air injectors have the effect of shifting the steady state compressor characteristic. In this paper we analyze the effect of a compressor characteristic actuation scheme for the three state Moore Greitzer compression system model. It is shown that closed loop feedback based on the square magnitude of the first rotating stall mode can be used to decrease the hysteresis region associated with the transition from unstalled to stalled and back to unstalled operation. The compressor characteristic shifting idea is then applied to a higher fidelity distributed model in which the characteristic shifting has phase content in addition to the magnitude content captured by the three state model. The optimal phasing of the air injection relative to the sensed position of the stall cell is determined via simulation and the results found to agree with those obtained via an experimental parametric study on the Caltech low-speed axial flow compressor

Minimal length in quantum space and integrations of the line element in Noncommutative Geometry

We question the emergence of a minimal length in quantum spacetime, comparing two notions that appeared at various points in the literature: on the one side, the quantum length as the spectrum of an operator L in the Doplicher Fredenhagen Roberts (DFR) quantum spacetime, as well as in the canonical noncommutative spacetime; on the other side, Connes' spectral distance in noncommutative geometry. Although on the Euclidean space the two notions merge into the one of geodesic distance, they yield distinct results in the noncommutative framework. In particular on the Moyal plane, the quantum length is bounded above from zero while the spectral distance can take any real positive value, including infinity. We show how to solve this discrepancy by doubling the spectral triple. This leads us to introduce a modified quantum length d'_L, which coincides exactly with the spectral distance d_D on the set of states of optimal localization. On the set of eigenstates of the quantum harmonic oscillator - together with their translations - d'_L and d_D coincide asymptotically, both in the high energy and large translation limits. At small energy, we interpret the discrepancy between d'_L and d_D as two distinct ways of integrating the line element on a quantum space. This leads us to propose an equation for a geodesic on the Moyal plane.Comment: 29 pages, 2 figures. Minor corrections to match the published versio

Immunodepletion in xenotransplantation

Xenograft transplantation is perhaps the most immunologically difficult problem in transplantation today. An overwhelming hyperacute rejection reaction (HAR) occurs within minutes of organ implantation. Preformed antibodies are thought to initiate this process. We used a pig-to-dog renal xenograft transplant model and investigated methods of decreasing the severity of hyperacute rejection. Female pigs weighing 15-20 kg were used as donors. Recipients were mongrel dogs weighing 15-25 kg. Experimental dogs were all given a number of treatments of IgG depletion using an antibody removal system (Dupont-Excorim). This machine immunoadsorbs plasma against a column containing immobilized staphylococcal protein A, which is known to bind the IgG Fc receptor. An 84% reduction in the IgG levels and a 71% reduction in IgM levels was achieved. Postoperative assessment was made of urine output, time to onset of HAR, and histopathological examination of the rejected kidneys. Although cross-matches between donor lymphocytes and recipient sera remained strongly positive in the treated dogs, there was a two- to fourfold reduction in the titers. The time to onset of HAR was prolonged in the experimental group, and the urine output was increased slightly. The histopathologic changes in the experimental group generally showed signs of HAR, but of less intensity than in the nonimmunodepleted control group. © 1990 Informa UK Ltd All rights reserved: reproduction in whole or part not permitted

Assignment of the binding site for Haptoglobin on Apolipoprotein A-I

Haptoglobin (Hpt) was previously found binding the high-density lipoprotein (HDL) Apolipoprotein A-I (ApoA-I) and able to inhibit the ApoA-I-dependent activity of the enzyme Lecithin:Cholesterol Acyl-Transferase (LCAT), which plays a major role in the reverse cholesterol transport. The ApoA-I structure was analyzed for detecting the site bound by Hpt. ApoA-I was treated by cyanogen bromide or hydroxylamine and the resulting fragments, separated by electrophoresis or gel filtration, were tested by Western blotting or ELISA for their ability to bind Hpt. The ApoA-I sequence from Glu113 to Asn184 harbored the binding site for Hpt. Biotinylated peptides were synthesized overlapping such a sequence, and their Hpt binding activity was determined by avidin-linked peroxidase. The highest activity was exhibited by the peptide P2a, containing the ApoA-I sequence from Leu141 to Ala164. Such a sequence contains an ApoA-I domain required for binding cells, promoting cholesterol efflux, and stimulating LCAT. The peptide P2a effectively prevented both binding of Hpt to HDL-coated plastic wells and Hpt-dependent inhibition of LCAT, measured by anti-Hpt antibodies and cholesterol esterification activity respectively. The enzyme activity was not influenced, in the absence of Hpt, by P2a. Differently from ApoA-I or HDL, the peptide did not compete with Hemoglobin for Hpt binding in ELISA experiments. The results suggest that Hpt might mask the ApoA-I domain required for LCAT stimulation, thus impairing the HDL function. Synthetic peptides, able to displace Hpt from ApoA-I without altering its property of binding Hemoglobin, might be used for treatment of diseases associated with defective LCAT function