Approximation of holomorphic mappings on strongly pseudoconvex domains

Let D be a relatively compact strongly pseudoconvex domain in a Stein manifold, and let Y be a complex manifold. We prove that the set A(D,Y), consisting of all continuous maps from the closure of D to Y which are holomorphic in D, is a complex Banach manifold. When D is the unit disc in C (or any other topologically trivial strongly pseudoconvex domain in a Stein manifold), A(D,Y) is locally modeled on the Banach space A(D,C^n)=A(D)^n with n=dim Y. Analogous results hold for maps which are holomorphic in D and of class C^r up to the boundary for any positive integer r. We also establish the Oka property for sections of continuous or smooth fiber bundles over the closure of D which are holomorphic over D and whose fiber enjoys the Convex approximation property. The main analytic technique used in the paper is a method of gluing holomorphic sprays over Cartan pairs in Stein manifolds, with control up to the boundary, which was developed in our paper "Holomorphic curves in complex manifolds" (Duke Math. J. 139 (2007), no. 2, 203--253)

Cost analysis in oral cavity and oropharyngeal reconstructions with microvascular and pedicled flaps.

Reconstructive surgery of the head and neck region has undergone tremendous advancement over the past three decades, and the success rate of free tissue transfers has risen to greater than 95\%. It must always be considered that not all patients are ideal candidates for free flap reconstruction, and also that not every defect strictly requires a free flap transfer to achieve good functional results. At our institution, free flap reconstruction is first choice, although we use pedicled alternative flaps for most weak patients suffering from severe comorbidities, and for pretreated patients presenting a second primary or a recurrent cancer. From July 2006 to May 2010, 54 consecutive patients underwent soft tissue reconstruction of oral cavity and oropharyngeal defects. We divided the cohort in three groups: Group 1 (G1): 16 patients in good general conditions that received free radial forearm flap reconstruction; Group 2 (G2): 18 high-risk patients that received a reconstruction with infrahyoid flap; Group 3 (G3): 20 patients that received temporal flap (10 cases) or pectoral flap (10 cases) reconstruction. We must highlight that pedicled alternative flaps were used in elderly, unfavourable and weak patients, where usually the medical costs tend to rise rather than decrease. We compared the healthcare costs of the three groups, calculating real costs in each group from review of medical records and operating room registers, and calculating the corresponding DRG system reimbursement. For real costs, we found a statistically significant difference among groups: in G1 the average total cost per patient was € 22,924, in G2 it was € 18,037 and in G3 was € 19,872 (p = 0.043). The amount of the refund, based on the DRG system, was € 7,650 per patient, independently of the type of surgery. Our analysis shows that the use of alternative non-microvascular techniques, in high-risk patients, is functionally and oncologically sound, and can even produce a cost savings. In particular, the infrahyoid flap (G2) ensures excellent functional results, accompanied by the best economic savings in the worst group of patients. Our data reflect a large disconnection between the DRG system and actual treatment costs.Abstract available from the publisher

Tobacco exposure and complications in conservative laryngeal surgery.

Smoking is an important risk factor in the development of head and neck cancer. However, little is known about its effects on postoperative complications in head and neck cancer surgery. We performed a retrospective analysis on 535 consecutive laryngeal cancer patients submitted to open partial laryngectomy at the Otolaryngology-Head and Neck Surgery Department of Florence University to evaluate a possible correlation between smoking and surgical complications. Patients were grouped in non smokers and smokers and evaluated for airway, swallowing, local and fistula complications by multivariate analysis: 507 (95\%) patients were smokers, 69\% presented supraglottic, 30\% glottic and 1\% transglottic cancer. The most common operation was supraglottic horizontal laryngectomy in 58\%, followed by supracricoid partial laryngectomy in 27\% and frontolateral hemilaryngectomy in 15\% of cases. The incidence of overall complications was 30\%, airway complications representing the most frequent (14\%), followed by swallowing (7\%), local (6\%) and fistula complications (3\%). Smokers developed more local complications (p = 0.05, univariate, p = 0.04, multivariate analysis) and pharyngocutaneous fistula (p = 0.01, univariate, p = 0.03, multivariate analysis)

Scheme for sub-shot-noise transmission measurement using a time multiplexed single-photon source

A promising result from optical quantum metrology is the ability to achieve sub-shot-noise performance in transmission or absorption measurements. This is due to the significantly lower uncertainty in light intensity of quantum beams with respect to their classical counterparts. In this work, we simulate the outcome of an experiment that uses a multiplexed single-photon source based on pair generation by continuous spontaneous parametric down conversion (SPDC) followed by a time multiplexing set-up with a binary temporal division strategy, considering several types of experimental losses. With such source, the sub-Poissonian statistics of the output signal is the key for achieving sub-shot-noise performance. We compare the numerical results with two paradigmatic limits: the shot-noise limit (achieved using coherent sources) and the quantum limit (obtained with an ideal photon-number Fock state as the input source). We also investigate conditions in which threshold detectors can be used, and the effect of input light fluctuations on the measurement error. Results show that sub-shot-noise performance can be achieved, even without using number-resolving detectors, with improvement factors that range from 1.5 to 2. This technique would allow measurements of optical absorption of a sample with reasonable uncertainty using ultra-low light intensity and minimum disruption of biological or other fragile specimens.Comment: 10 pages, 8 figure

Homogeneous manifolds from noncommutative measure spaces

Let M be a finite von Neumann algebra with a faithful normal trace τ. In this paper we study metric geometry of homogeneous spaces O of the unitary group UM of M, endowed with a Finsler quotient metric induced by the p-norms of τ, ‖x‖p = τ (|x|p)1/p, p ≥ 1. The main results include the following. The unitary group carries on a rectifiable distance dp induced by measuring the length of curves with the p-norm. If we identify O as a quotient of groups, then there is a natural quotient distance over dp that metrizes the quotient topology. On the other hand, the Finsler quotient metric defined in O provides a way to measure curves, and therefore, there is an associated rectifiable distance dO, p. We prove that the distances over dp and dO, p coincide. Based on this fact, we show that the metric space (O, dp) is a complete path metric space. The other problem treated in this article is the existence of metric geodesics, or curves of minimal length, in O. We give two abstract partial results in this direction. The first concerns the initial values problem and the second the fixed endpoints problem. We show how these results apply to several examples. In the process, we improve some results about the metric geometry of UM with the p-norm.Facultad de Ciencias Exacta

Weak Riemannian manifolds from finite index subfactors

Let $N\subset M$ be a finite Jones' index inclusion of II$_1$ factors, and denote by $U_N\subset U_M$ their unitary groups. In this paper we study the homogeneous space $U_M/U_N$, which is a (infinite dimensional) differentiable manifold, diffeomorphic to the orbit $${\cal O}(p) =\{u p u^*: u\in U_M\}$$ of the Jones projection $p$ of the inclusion. We endow ${\cal O}(p)$ with a Riemannian metric, by means of the trace on each tangent space. These are pre-Hilbert spaces (the tangent spaces are not complete), therefore ${\cal O}(p)$ is a weak Riemannian manifold. We show that ${\cal O}(p)$ enjoys certain properties similar to classic Hilbert-Riemann manifolds. Among them, metric completeness of the geodesic distance, uniqueness of geodesics of the Levi-Civita connection as minimal curves, and partial results on the existence of minimal geodesics. For instance, around each point $p_1$ of ${\cal O}(p)$, there is a ball $\{q\in {\cal O}(p):\|q-p_1\|<r\}$ (of uniform radius $r$) of the usual norm of $M$, such that any point $p_2$ in the ball is joined to $p_1$ by a unique geodesic, which is shorter than any other piecewise smooth curve lying inside this ball. We also give an intrinsic (algebraic) characterization of the directions of degeneracy of the submanifold inclusion ${\cal O}(p)\subset {\cal P}(M_1)$, where the last set denotes the Grassmann manifold of the von Neumann algebra generated by $M$ and $p$.Comment: 19 page

Two-stage hepatectomy with radioembolization for bilateral colorectal liver metastases: A case report

BACKGROUND Two-stage hepatectomy (TSH) is a well-established surgical technique, used to treat bilateral colorectal liver metastases (CRLM) with a small future liver remnant (FLR). However, in classical TSH, drop-out is reported to be around 25%- 40%, due to insufficient FLR increase or progression of disease. Trans-arterial radioembolization (TARE) has been described to control locally tumor growth of liver malignancies such as hepatocellular carcinoma, but it has been also reported to induce a certain degree of contralateral liver hypertrophy, even if at a lower rate compared to portal vein embolization or ligation. CASE SUMMARY Herein we report the case of a 75-year-old female patient, where TSH and TARE were combined to treat bilateral CRLM. According to computed tomography (CT)-scan, the patient had a hepatic lesion in segment VI-VII and two other confluent lesions in segment II-III. Therefore, one-stage posterior right sectionectomy plus left lateral sectionectomy (LLS) was planned. The liver volumetry estimated a FLR of 38% (segments I-IV-V-VIII). However, due to a more than initially planned, extended right resection, simultaneous LLS was not performed and the patient underwent selective TARE to segments II-III after the first surgery. The CT-scan performed after TARE showed a reduction of the treated lesion and a FLR increase of 55%. Carcinoembryonic antigen and CA 19.9 decreased significantly. Nearly three months later after the first surgery, LLS was performed and the patient was discharged without any postoperative complications. CONCLUSION According to this specific experience, TARE was used to induce liver hypertrophy and simultaneously control cancer progression in TSH settings for bilateral CRLM

Infinite dimensional non-positively curved symmetric spaces of finite rank

This paper concerns a study of three families of non-compact type symmetric spaces of infinite dimension. Although they have infinite dimension they have finite rank. More precisely, we show they have finite telescopic dimension. We also show the existence of Furstenberg maps for some group actions on these spaces. Such maps appear as a first step toward superrigidity results.Comment: Some references have been adde

Inclusive production of ρ0(770),f0(980)\rho^{0}(770), f_0(980) and f2(1270)f_2(1270) mesons in νμ\nu_{\mu} charged current interactions

The inclusive production of the meson resonances $\rho^{0}(770)$, $f_0(980)$ and $f_2(1270)$ in neutrino-nucleus charged current interactions has been studied with the NOMAD detector exposed to the wide band neutrino beam generated by 450 GeV protons at the CERN SPS. For the first time the $f_{0}(980)$ meson is observed in neutrino interactions. The statistical significance of its observation is 6 standard deviations. The presence of $f_{2}(1270)$ in neutrino interactions is reliably established. The average multiplicity of these three resonances is measured as a function of several kinematic variables. The experimental results are compared to the multiplicities obtained from a simulation based on the Lund model. In addition, the average multiplicity of $\rho^{0}(770)$ in antineutrino - nucleus interactions is measured.Comment: 23 pages, 14 figures, 8 tables. To appear in Nucl. Phys.