Symplectic connections and Fedosov's quantization on supermanifolds

A (biased and incomplete) review of the status of the theory of symplectic connections on supermanifolds is presented. Also, some comments regarding Fedosov's technique of quantization are made.Comment: Submitted to J. of Phys. Conf. Se

Supercoherent States, Super K\"ahler Geometry and Geometric Quantization

Generalized coherent states provide a means of connecting square integrable representations of a semi-simple Lie group with the symplectic geometry of some of its homogeneous spaces. In the first part of the present work this point of view is extended to the supersymmetric context, through the study of the OSp(2/2) coherent states. These are explicitly constructed starting from the known abstract typical and atypical representations of osp(2/2). Their underlying geometries turn out to be those of supersymplectic OSp(2/2) homogeneous spaces. Moment maps identifying the latter with coadjoint orbits of OSp(2/2) are exhibited via Berezin's symbols. When considered within Rothstein's general paradigm, these results lead to a natural general definition of a super K\"ahler supermanifold, the supergeometry of which is determined in terms of the usual geometry of holomorphic Hermitian vector bundles over K\"ahler manifolds. In particular, the supergeometry of the above orbits is interpreted in terms of the geometry of Einstein-Hermitian vector bundles. In the second part, an extension of the full geometric quantization procedure is applied to the same coadjoint orbits. Thanks to the super K\"ahler character of the latter, this procedure leads to explicit super unitary irreducible representations of OSp(2/2) in super Hilbert spaces of $L^2$ superholomorphic sections of prequantum bundles of the Kostant type. This work lays the foundations of a program aimed at classifying Lie supergroups' coadjoint orbits and their associated irreducible representations, ultimately leading to harmonic superanalysis. For this purpose a set of consistent conventions is exhibited.Comment: 53 pages, AMS-LaTeX (or LaTeX+AMSfonts

Projective Fourier Duality and Weyl Quantization

The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras.Comment: LaTeX 2.09 with NFSS or AMSLaTeX 1.1. 102Kb, 44 pages, no figures. requires subeqnarray.sty, amssymb.sty, amsfonts.sty. Final version with text improvements and crucial typos correction

Obstruction Results in Quantization Theory

We define the quantization structures for Poisson algebras necessary to generalise Groenewold and Van Hove's result that there is no consistent quantization for the Poisson algebra of Euclidean phase space. Recently a similar obstruction was obtained for the sphere, though surprising enough there is no obstruction to the quantization of the torus. In this paper we want to analyze the circumstances under which such obstructions appear. In this context we review the known results for the Poisson algebras of Euclidean space, the sphere and the torus.Comment: 34 pages, Latex. To appear in J. Nonlinear Scienc

Biliary tract visualization using near-infrared imaging with indocyanine green during laparoscopic cholecystectomy: results of a systematic review

Contains fulltext : 174508.pdf (publisher's version ) (Open Access)BACKGROUND: Near-infrared imaging with indocyanine green (ICG) has been extensively investigated during laparoscopic cholecystectomy (LC). However, methods vary between studies, especially regarding patient selection, dosage and timing. The aim of this systematic review was to evaluate the potential of the near-infrared imaging technique with ICG to identify biliary structures during LC. METHODS: A comprehensive systematic literature search was performed. Prospective trials examining the use of ICG during LC were included. Primary outcome was biliary tract visualization. Risk of bias was assessed using ROBINS-I. Secondly, a meta-analysis was performed comparing ICG to intraoperative cholangiography (IOC) for identification of biliary structures. GRADE was used to assess the quality of the evidence. RESULTS: Nineteen studies were included. Based upon the pooled data from 13 studies, cystic duct (Lusch et al. in J Endourol 28:261-266, 2014) visualization was 86.5% (95% CI 71.2-96.6%) prior to dissection of Calot's triangle with a 2.5-mg dosage of ICG and 96.5% (95% CI 93.9-98.4%) after dissection. The results were not appreciably different when the dosage was based upon bodyweight. There is moderate quality evidence that the CD is more frequently visualized using ICG than IOC (RR 1.16; 95% CI 1.00-1.35); however, this difference was not statistically significant. CONCLUSION: This systematic review provides equal results for biliary tract visualization with near-infrared imaging with ICG during LC compared to IOC. Near-infrared imaging with ICG has the potential to replace IOC for biliary mapping. However, methods of near-infrared imaging with ICG vary. Future research is necessary for optimization and standardization of the near-infrared ICG technique

Cotangent bundle quantization: Entangling of metric and magnetic field

For manifolds $\cal M$ of noncompact type endowed with an affine connection (for example, the Levi-Civita connection) and a closed 2-form (magnetic field) we define a Hilbert algebra structure in the space $L^2(T^*\cal M)$ and construct an irreducible representation of this algebra in $L^2(\cal M)$. This algebra is automatically extended to polynomial in momenta functions and distributions. Under some natural conditions this algebra is unique. The non-commutative product over $T^*\cal M$ is given by an explicit integral formula. This product is exact (not formal) and is expressed in invariant geometrical terms. Our analysis reveals this product has a front, which is described in terms of geodesic triangles in $\cal M$. The quantization of $\delta$-functions induces a family of symplectic reflections in $T^*\cal M$ and generates a magneto-geodesic connection $\Gamma$ on $T^*\cal M$. This symplectic connection entangles, on the phase space level, the original affine structure on $\cal M$ and the magnetic field. In the classical approximation, the $\hbar^2$-part of the quantum product contains the Ricci curvature of $\Gamma$ and a magneto-geodesic coupling tensor.Comment: Latex, 38 pages, 5 figures, minor correction

Video-based surgical quality assessment of minimally invasive right hemicolectomy by medical students after specific training

BACKGROUND: Recently, a competency assessment tool has been developed within the RIGHT project, a national quality improvement program for minimally invasive right hemicolectomy in patients with colon cancer. This study aimed to evaluate whether trained medical students can reliably evaluate minimally invasive right hemicolectomy videos using a competency assessment tool.METHODS: Nine expert colorectal surgeons, 13 trained medical students, and 17 untrained medical students assessed the surgical quality of 6 full-length minimally invasive right hemicolectomy videos with the competency assessment tool. The expert surgeons were trained using the competency assessment tool by the RIGHT project leaders, who were also involved in the development and validation of the competency assessment tool. Training for medical students included anatomy, step-by-step procedure explanation, and competency assessment tool review with 2 supervised video assessments. The untrained students were taught only anatomy and minimally invasive right hemicolectomy steps. The intraclass correlation coefficient was calculated to determine inter-rater reliability, and analysis of variance with the Bonferroni correction for multiple testing was used to assess potential differences between the groups per video.RESULTS: The trained students demonstrated an overall excellent inter-rater reliability (intraclass correlation coefficient score of 0.885). When their scores were combined with those of the expert surgeons, a high inter-rater reliability was also demonstrated (intraclass correlation coefficient score of 0.945). Trained students consistently aligned with surgeons' mean total scores, also accurately identifying lower quality surgeries. Untrained students assigned statistically significantly higher scores to the 3 lower quality surgeries as compared with expert surgeons and trained students.CONCLUSION: Among trained students, excellent inter-rater reliability and concordance with expert colorectal surgeons was found. The study highlights the potential to engage trained medical students for objective minimally invasive right hemicolectomy video assessment.</p

Local recurrence at the site of the Lone Star device through implantation of exfoliated cells during local excision for early rectal cancer:A case report

Introduction: Invasive procedures for colorectal cancer can cause iatrogenic tumor cell seeding. Implantation of these exfoliated cells in the surrounding tissue can result in locoregional cancer recurrence. This has been described in endoscopic procedures and major surgical resections, however recurrence in iatrogenic lesions of the anal canal during minimal invasive rectal surgery has not been shown in literature yet. This is the first reported case of recurrent rectal cancer that developed into an anal metastasis at the site where hooks of the Lone Star Retractor disrupted the epithelial lining of the anal canal during a local excision of early rectal cancer using TAMIS. Presentation of case: A 57 year old male was diagnosed with a high risk early stage rectal adenocarcinoma. He was treated with transanal minimally invasive surgery (TAMIS) with the use of a Lone Star retractor and he received subsequent chemo-radiotherapy. 23 months later the patient developed a bleeding mass bulging out of the anus. A true cut and incision biopsy was performed and the pathology report revealed localization of adenocarcinoma at the anal canal which was similar to the earlier diagnosed rectal carcinoma. The patient underwent an abdominal perineal resection and left-sided lymph node dissection. Discussion and conclusion: This shows that local recurrence through implantation of exfoliated tumor cells can occur in iatrogenic lesions of the anal canal not only in major but also in minimal invasive rectal surgery. Careful tissue handling and rectal washout may reduce the chance of this implantation metastasis.</p

Short-term morbidity and mortality after right hemicolectomy:an update of national performance in the Netherlands

Aim: The purpose of this Dutch retrospective population-based study was to evaluate how short-term outcomes and inter-hospital variability after right hemicolectomy for colon cancer have evolved between 2012 and 2020. Method: Patients who underwent right hemicolectomy for primary solitary colon cancer between 1 January 2012 and 31 December 2020 and were registered in the Dutch Colorectal Audit were included. Surgical characteristics and outcomes were assessed during three time periods (2012–2014, 2015–2017, 2018–2020). Complications and mortality were the primary outcomes, and reintervention, readmission and length of stay secondary outcomes. Results: In total, 29 274 patients were included. Significant increase in minimally invasive surgery (51.1% 2012–2014, 73.2% 2015–2017, 85.0% 2018–2020), increase in conversion (6.6%, 7.8%, 9.1%, P &lt; 0.001) and decrease in acute/urgent resections (15.9%, 11.7%, 10.9%, P &lt; 0.001) were found. The overall complication rate was slightly lower in the third period (30.9%, 30.6%, 28.8%, P = 0.004), primarily because of decreasing non-surgical complications (19.7%, 20.6%, 17.6%, P &lt; 0.001), while surgical complications remained unchanged (17.5%, 18.3%, 18.2%, P = 0.277). Postoperative mortality was 3.4%, 2.3% and 3.5%, respectively. Reintervention rate slightly decreased (9.4%, 8.3%, 8.6%, P &lt; 0.001). The proportion of patients admitted for more than 6 days decreased over time (54.3%, 42.4%, 34.3%, P &lt; 0.001), with an increase in readmission rate (7.4%, 6.8%, 9.3%, P &lt; 0.001). Inter-hospital variability decreased over time for complications, length of stay and conversion. Conclusion: This study shows a national decreasing inter-hospital variability in clinical outcomes after right hemicolectomy and a decrease in postoperative complications. Despite increasing use of laparoscopy, surgical complications and mortality remained stable over time.</p

Local recurrence at the site of the Lone Star device through implantation of exfoliated cells during local excision for early rectal cancer:A case report

Introduction: Invasive procedures for colorectal cancer can cause iatrogenic tumor cell seeding. Implantation of these exfoliated cells in the surrounding tissue can result in locoregional cancer recurrence. This has been described in endoscopic procedures and major surgical resections, however recurrence in iatrogenic lesions of the anal canal during minimal invasive rectal surgery has not been shown in literature yet. This is the first reported case of recurrent rectal cancer that developed into an anal metastasis at the site where hooks of the Lone Star Retractor disrupted the epithelial lining of the anal canal during a local excision of early rectal cancer using TAMIS. Presentation of case: A 57 year old male was diagnosed with a high risk early stage rectal adenocarcinoma. He was treated with transanal minimally invasive surgery (TAMIS) with the use of a Lone Star retractor and he received subsequent chemo-radiotherapy. 23 months later the patient developed a bleeding mass bulging out of the anus. A true cut and incision biopsy was performed and the pathology report revealed localization of adenocarcinoma at the anal canal which was similar to the earlier diagnosed rectal carcinoma. The patient underwent an abdominal perineal resection and left-sided lymph node dissection. Discussion and conclusion: This shows that local recurrence through implantation of exfoliated tumor cells can occur in iatrogenic lesions of the anal canal not only in major but also in minimal invasive rectal surgery. Careful tissue handling and rectal washout may reduce the chance of this implantation metastasis.</p