Subresultants in multiple roots: an extremal case

We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x-\alpha)^m and (x-\beta)^n with respect to the set of Bernstein polynomials \{(x-\alpha)^j(x-\beta)^{d-j}, \, 0\le j\le d\}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.Comment: 18 pages, uses elsart. Revised version accepted for publication at Linear Algebra and its Application

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

Regulation of T cell lymphokine production by killer cell inhibitory receptor recognition of self HLA class I alleles.

The killer cell inhibitory receptors (KIRs) are surface glycoproteins expressed by natural killer (NK) and T cells that specifically recognize defined groups of polymorphic human histocompatibility leukocyte antigen (HLA) class I molecules. Interactions between KIRs on NK or T cells and major histocompatibility complex (MHC) class I molecules on potential target cells inhibit cell-mediated cytotoxicity, presumably by delivering a negative signal preventing lymphocyte activation. In this study we examined whether KIRs also regulate cytokine production induced in response to T cell receptor-dependent T cell activation. CD4+ and CD8+ T cell clones were stimulated by bacterial superantigens in the presence or absence of monoclonal antibodies (mAbs) against the KIR NKB1 or MHC class I molecules, and production of tumor necrosis factor alpha and interferon gamma was evaluated. When bacterial superantigen was presented by an autologous antigen-presenting cell (APC) to a KIR+ T cell clone, cytokine production was always enhanced in the presence of anti-MHC class I mAb. Similarly, anti-KIR mAb also augmented cytokine production, provided that the APC expressed a HLA class I allele recognized by the KIR. These results suggest that recognition of autologous MHC class I molecules by KIR+ T cells provides a regulatory mechanism acting to modulate the potency of their responses to antigenic challenge

Finiteness and orbifold Vertex Operator Algebras

In this paper, I investigate the ascending chain condition of right ideals in the case of vertex operator algebras satisfying a finiteness and/or a simplicity condition. Possible applications to the study of finiteness of orbifold VOAs is discussed.Comment: 12 pages, comments are welcom

Wick Rotation and Fermion Doubling in Noncommutative Geometry

In this paper, we discuss two features of the noncommmutative geometry and spectral action approach to the Standard Model: the fact that the model is inherently Euclidean, and that it requires a quadrupling of the fermionic degrees of freedom. We show how the two issues are intimately related. We give a precise prescription for the Wick rotation from the Euclidean theory to the Lorentzian one, eliminating the extra degrees of freedom. This requires not only projecting out mirror fermions, as has been done so far, and which leads to the correct Pfaffian, but also the elimination of the remaining extra degrees of freedom. The remaining doubling has to be removed in order to recover the correct Fock space of the physical (Lorentzian) theory. In order to get a Spin(1,3) invariant Lorentzian theory from a Spin(4) invariant Euclidean theory such an elimination must be performed after the Wick rotation. Differences between the Euclidean and Lorentzian case are described in detail, in a pedagogical way.Comment: Minor changes. To appear in PRD. 25 page

La riforma del bicameralismo italiano al traino dell’inesistente federalismo ovvero quando il bluff delle parole è smascherato dal niente dei fatti

Lo scritto, muovendo da una ricostruzione delle ragioni storiche del bicameralismo perfetto italiano (riconducibili all’esigenza di ampliare i “luoghi” e i “modi” attraverso i quali potesse esprimersi la rappresentanza politica nazionale, nonché alla preoccupazione di dotare l’ordinamento di un quadro procedurale che assicurasse la maggiore ponderazione possibile dell’indirizzo politico di maggioranza), mette in luce come l’attuale crisi del Parlamento non dipenda dalla presenza di due Camere dotate dei medesimi poteri. Lo svilimento della forma di governo parlamentare prevista dal dettato costituzionale è invece il frutto di una esaltazione del ruolo del Governo impostosi in via di prassi (nonostante la ricorrente “lamentela” secondo cui nel nostro ordinamento, se non si cambia il dettato costituzionale, sono destinati ad operare solo Governi “deboli”) e dell’assenza di rappresentatività delle Camere dovuta alla legge elettorale vigente (c.d. porcellum), in ragione della quale i deputati e i senatori non sono selezionati dagli elettori ma fiduciari dei loro capi-partito, che ne influenzano l’attività. Il problema che si impone con urgenza nel nostro ordinamento è dunque la rivitalizzazione dell’organo parlamentare che passa esclusivamente dal superamento dell’attuale, vergognoso sistema elettorale. Una volta che si riuscisse a ritornare ad una funzione genuinamente rappresentativa delle Assemblee elettive, sarebbe probabilmente utile al rilancio del Parlamento italiano correggere l’attuale bicameralismo partendo da una Camera delle Regioni, portando così a degno completamento il coraggioso disegno regionalistico dei Costituenti (al quale nemmeno il modello proposto dalla Lega Nord nel nome addirittura del “federalismo”, peraltro mai concretizzatosi in Italia, si avvicinava). La proposta attualmente in discussione al Senato di ripensamento del bicameralismo con riguardo al procedimento legislativo è una proposta di modifica “minimale” dell’attuale assetto costituzionale, probabilmente inutile al fine di una semplificazione e velocizzazione dell’iter legis, che, ove fosse approvata, produrrebbe piuttosto un rafforzamento delle prerogative dell’Esecutivo da usare in Parlamento, senza tuttavia variare nella sostanza la struttura organizzativa delle Camere e l’attuale sistema bicamerale

Usefulness of image guidance in the surgical treatment of petrous apex cholesterol granuloma

The petrous apex is a pyramid-shaped structure, located medial to the inner ear and the intrapetrous segment of the internal carotid artery. Lesions of the petrous apex can be surgically treated through different surgical routes. Because of the important neurovascular structures located inside the temporal bone, anatomical 3D knowledge is paramount. For this reason, image-guided surgery could represent a useful tool. We report the case of a young woman who came to our observation for a trigeminal neuralgia due to a petrous apex cholesterol granuloma. The lesion was treated through the placement of a drainage tube via an infracochlear approach, with the aid of neuronavigation and intraoperative MRI. Preoperative CT scan images and intraoperative MRI images were fused for surgical planning. The accuracy of the neuronavigation system has proved to be good, and the safety of the procedure was enhanced. Therefore, neuronavigation and intraoperative MRI, though not available in all neurootological centres, should be considered useful tools in these challenging procedures

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