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.

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

Excitonic Effects in Quantum Wires

We review the effects of Coulomb correlation on the linear and non-linear optical properties of semiconductor quantum wires, with emphasis on recent results for the bound excitonic states. Our theoretical approach is based on generalized semiconductor Bloch equations, and allows full three-dimensional multisubband description of electron-hole correlation for arbitrary confinement profiles. In particular, we consider V- and T-shaped structures for which significant experimental advances were obtained recently. Above band gap, a very general result obtained by this approach is that electron-hole Coulomb correlation removes the inverse-square-root single-particle singularity in the optical spectra at band edge, in agreement with previous reports from purely one-dimensional models. Strong correlation effects on transitions in the continuum are found to persist also at high densities of photoexcited carriers. Below bandgap, we find that the same potential- (Coulomb) to kinetic-energy ratio holds for quite different wire cross sections and compositions. As a consequence, we identify a shape- and barrier-independent parameter that governs a universal scaling law for exciton binding energy with size. Previous indications that the shape of the wire cross-section may have important effects on exciton binding are discussed in the light of the present results.Comment: Proc. OECS-5 Conference, G\"ottingen, 1997 (To appear in Phys. Stat. Sol. (b)

Impaired haematopoietic stem cell differentiation and enhanced skewing towards myeloid progenitors in aged caspase-2-deficient mice

The apoptotic cysteine protease caspase-2 has been shown to suppress tumourigenesis in mice and its reduced expression correlates with poor prognosis in some human malignancies. Caspase-2-deficient mice develop normally but show ageing-related traits and, when challenged by oncogenic stimuli or certain stress, show enhanced tumour development, often accompanied by extensive aneuploidy. As stem cells are susceptible to acquiring age-related functional defects because of their self-renewal and proliferative capacity, we examined whether loss of caspase-2 promotes such defects with age. Using young and aged Casp2−/− mice, we demonstrate that deficiency of caspase-2 results in enhanced aneuploidy and DNA damage in bone marrow (BM) cells with ageing. Furthermore, we demonstrate for the first time that caspase-2 loss results in significant increase in immunophenotypically defined short-term haematopoietic stem cells (HSCs) and multipotent progenitors fractions in BM with a skewed differentiation towards myeloid progenitors with ageing. Caspase-2 deficiency leads to enhanced granulocyte macrophage and erythroid progenitors in aged mice. Colony-forming assays and long-term culture-initiating assay further recapitulated these results. Our results provide the first evidence of caspase-2 in regulating HSC and progenitor differentiation, as well as aneuploidy, in vivo.Swati Dawar, Nur Hezrin Shahrin, Nikolina Sladojevic, Richard J D, Andrea, Loretta Dorstyn, Devendra K Hiwase and Sharad Kuma

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

Particle Physics from Almost Commutative Spacetimes

Our aim in this review article is to present the applications of Connes' noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical audience, in this article we introduce the ideas and concepts from noncommutative geometry using physicists' terminology, gearing towards the predictions that can be derived from the noncommutative description. Focusing on a light package of noncommutative geometry (so-called 'almost commutative manifolds'), we shall introduce in steps: electrodynamics, the electroweak model, culminating in the full Standard Model. We hope that our approach helps in understanding the role noncommutative geometry could play in describing particle physics models, eventually unifying them with Einstein's (geometrical) theory of gravity.Comment: 104 pages, 5 figures, version 2 (minor changes and some additional references

Diffuse optical tomography by using time-resolved single pixel camera

International audienc

Comparison of relativity theories with observer-independent scales of both velocity and length/mass

We consider the two most studied proposals of relativity theories with observer-independent scales of both velocity and length/mass: the one discussed by Amelino-Camelia as illustrative example for the original proposal (gr-qc/0012051) of theories with two relativistic invariants, and an alternative more recently proposed by Magueijo and Smolin (hep-th/0112090). We show that these two relativistic theories are much more closely connected than it would appear on the basis of a naive analysis of their original formulations. In particular, in spite of adopting a rather different formal description of the deformed boost generators, they end up assigning the same dependence of momentum on rapidity, which can be described as the core feature of these relativistic theories. We show that this observation can be used to clarify the concepts of particle mass, particle velocity, and energy-momentum-conservation rules in these theories with two relativistic invariants.Comment: 21 pages, LaTex. v2: Andrea Procaccini (contributing some results from hia Laurea thesis) is added to the list of authors and the paper provides further elements of comparison between DSR1 and DSR2, including the observation that both lead to the same formula for the dependence of momentum on rapidit