Invariants of spin networks with boundary in Quantum Gravity and TQFT's

The search for classical or quantum combinatorial invariants of compact n-dimensional manifolds (n=3,4) plays a key role both in topological field theories and in lattice quantum gravity. We present here a generalization of the partition function proposed by Ponzano and Regge to the case of a compact 3-dimensional simplicial pair $(M^3, \partial M^3)$. The resulting state sum $Z[(M^3, \partial M^3)]$ contains both Racah-Wigner 6j symbols associated with tetrahedra and Wigner 3jm symbols associated with triangular faces lying in $\partial M^3$. The analysis of the algebraic identities associated with the combinatorial transformations involved in the proof of the topological invariance makes it manifest a common structure underlying the 3-dimensional models with empty and non empty boundaries respectively. The techniques developed in the 3-dimensional case can be further extended in order to deal with combinatorial models in n=2,4 and possibly to establish a hierarchy among such models. As an example we derive here a 2-dimensional closed state sum model including suitable sums of products of double 3jm symbols, each one of them being associated with a triangle in the surface.Comment: 9 page

Hierarchies of invariant spin models

In this paper we present classes of state sum models based on the recoupling theory of angular momenta of SU(2) (and of its q-counterpart $U_q(sl(2))$, q a root of unity). Such classes are arranged in hierarchies depending on the dimension d, and include all known closed models, i.e. the Ponzano-Regge state sum and the Turaev-Viro invariant in dimension d=3, the Crane-Yetter invariant in d=4. In general, the recoupling coefficient associated with a d-simplex turns out to be a $\{3(d-2)(d+1)/2\}j$ symbol, or its q-analog. Each of the state sums can be further extended to compact triangulations $(T^d,\partial T^d)$ of a PL-pair $(M^d,\partial M^d)$, where the triangulation of the boundary manifold is not keeped fixed. In both cases we find out the algebraic identities which translate complete sets of topological moves, thus showing that all state sums are actually independent of the particular triangulation chosen. Then, owing to Pachner's theorems, it turns out that classes of PL-invariant models can be defined in any dimension d.Comment: 42 pages, 25 figure

Quantum states of elementary three-geometry

We introduce a quantum volume operator $K$ in three--dimensional Quantum Gravity by taking into account a symmetrical coupling scheme of three SU(2) angular momenta. The spectrum of $K$ is discrete and defines a complete set of eigenvectors which is alternative with respect to the complete sets employed when the usual binary coupling schemes of angular momenta are considered. Each of these states, that we call quantum bubbles, represents an interference of extended configurations which provides a rigorous meaning to the heuristic notion of quantum tetrahedron. We study the generalized recoupling coefficients connecting the symmetrical and the binary basis vectors, and provide an explicit recursive solution for such coefficients by analyzing also its asymptotic limit.Comment: 15 pages, LaTe

Colorectal Cancer Stage at Diagnosis Before vs During the COVID-19 Pandemic in Italy

IMPORTANCE Delays in screening programs and the reluctance of patients to seek medical attention because of the outbreak of SARS-CoV-2 could be associated with the risk of more advanced colorectal cancers at diagnosis. OBJECTIVE To evaluate whether the SARS-CoV-2 pandemic was associated with more advanced oncologic stage and change in clinical presentation for patients with colorectal cancer. DESIGN, SETTING, AND PARTICIPANTS This retrospective, multicenter cohort study included all 17 938 adult patients who underwent surgery for colorectal cancer from March 1, 2020, to December 31, 2021 (pandemic period), and from January 1, 2018, to February 29, 2020 (prepandemic period), in 81 participating centers in Italy, including tertiary centers and community hospitals. Follow-up was 30 days from surgery. EXPOSURES Any type of surgical procedure for colorectal cancer, including explorative surgery, palliative procedures, and atypical or segmental resections. MAIN OUTCOMES AND MEASURES The primary outcome was advanced stage of colorectal cancer at diagnosis. Secondary outcomes were distant metastasis, T4 stage, aggressive biology (defined as cancer with at least 1 of the following characteristics: signet ring cells, mucinous tumor, budding, lymphovascular invasion, perineural invasion, and lymphangitis), stenotic lesion, emergency surgery, and palliative surgery. The independent association between the pandemic period and the outcomes was assessed using multivariate random-effects logistic regression, with hospital as the cluster variable. RESULTS A total of 17 938 patients (10 007 men [55.8%]; mean [SD] age, 70.6 [12.2] years) underwent surgery for colorectal cancer: 7796 (43.5%) during the pandemic period and 10 142 (56.5%) during the prepandemic period. Logistic regression indicated that the pandemic period was significantly associated with an increased rate of advanced-stage colorectal cancer (odds ratio [OR], 1.07; 95%CI, 1.01-1.13; P = .03), aggressive biology (OR, 1.32; 95%CI, 1.15-1.53; P < .001), and stenotic lesions (OR, 1.15; 95%CI, 1.01-1.31; P = .03). CONCLUSIONS AND RELEVANCE This cohort study suggests a significant association between the SARS-CoV-2 pandemic and the risk of a more advanced oncologic stage at diagnosis among patients undergoing surgery for colorectal cancer and might indicate a potential reduction of survival for these patients

JHC772798_Supplemental_Material – Supplemental material for Immunolocalization of Advanced Glycation End Products, Mitogen Activated Protein Kinases, and Transforming Growth Factor-β/Smads in Pelvic Organ Prolapse

<p>Supplemental material, JHC772798_Supplemental_Material for Immunolocalization of Advanced Glycation End Products, Mitogen Activated Protein Kinases, and Transforming Growth Factor-β/Smads in Pelvic Organ Prolapse by Antonella Vetuschi, Simona Pompili, Anna Gallone, Angela D’Alfonso, Maria Gabriella Carbone, Gaspare Carta, Claudio Festuccia, Eugenio Gaudio, Alessandro Colapietro and Roberta Sferra in Journal of Histochemistry & Cytochemistry</p

Effect of centre volume on pathological outcomes and postoperative complications after surgery for colorectal cancer: results of a multicentre national study

Background: The association between volume, complications and pathological outcomes is still under debate regarding colorectal cancer surgery. The aim of the study was to assess the association between centre volume and severe complications, mortality, less-than-radical oncologic surgery, and indications for neoadjuvant therapy.Methods: Retrospective analysis of 16,883 colorectal cancer cases from 80 centres (2018-2021). Outcomes: 30-day mortality; Clavien-Dindo grade >2 complications; removal of >= 12 lymph nodes; non-radical resection; neoadjuvant therapy. Quartiles of hospital volumes were classified as LOW, MEDIUM, HIGH, and VERY HIGH. Independent predictors, both overall and for rectal cancer, were evaluated using logistic regression including age, gender, AJCC stage and cancer site.Results: LOW-volume centres reported a higher rate of severe postoperative complications (OR 1.50, 95% c.i. 1.15-1.096, P = 0.003). The rate of >= 12 lymph nodes removed in LOW-volume (OR 0.68, 95% c.i. 0.56-0.85, P = 12 lymph nodes removed was lower in LOW-volume than in VERY HIGH-volume centres (OR 0.57, 95% c.i. 0.41-0.80, P = 0.001). A lower rate of neoadjuvant chemoradiation was associated with HIGH (OR 0.66, 95% c.i. 0.56-0.77, P < 0.001), MEDIUM (OR 0.75, 95% c.i. 0.60-0.92, P = 0.006), and LOW (OR 0.70, 95% c.i. 0.52-0.94, P = 0.019) volume centres (vs. VERY HIGH).Conclusion: Colorectal cancer surgery in low-volume centres is at higher risk of suboptimal management, poor postoperative outcomes, and less-than-adequate oncologic resections. Centralisation of rectal cancer cases should be taken into consideration to optimise the outcomes

Tocilizumab for patients with COVID-19 pneumonia. The single-arm TOCIVID-19 prospective trial

BackgroundTocilizumab blocks pro-inflammatory activity of interleukin-6 (IL-6), involved in pathogenesis of pneumonia the most frequent cause of death in COVID-19 patients.MethodsA multicenter, single-arm, hypothesis-driven trial was planned, according to a phase 2 design, to study the effect of tocilizumab on lethality rates at 14 and 30 days (co-primary endpoints, a priori expected rates being 20 and 35%, respectively). A further prospective cohort of patients, consecutively enrolled after the first cohort was accomplished, was used as a secondary validation dataset. The two cohorts were evaluated jointly in an exploratory multivariable logistic regression model to assess prognostic variables on survival.ResultsIn the primary intention-to-treat (ITT) phase 2 population, 180/301 (59.8%) subjects received tocilizumab, and 67 deaths were observed overall. Lethality rates were equal to 18.4% (97.5% CI: 13.6-24.0, P=0.52) and 22.4% (97.5% CI: 17.2-28.3, P&lt;0.001) at 14 and 30 days, respectively. Lethality rates were lower in the validation dataset, that included 920 patients. No signal of specific drug toxicity was reported. In the exploratory multivariable logistic regression analysis, older age and lower PaO2/FiO2 ratio negatively affected survival, while the concurrent use of steroids was associated with greater survival. A statistically significant interaction was found between tocilizumab and respiratory support, suggesting that tocilizumab might be more effective in patients not requiring mechanical respiratory support at baseline.ConclusionsTocilizumab reduced lethality rate at 30 days compared with null hypothesis, without significant toxicity. Possibly, this effect could be limited to patients not requiring mechanical respiratory support at baseline.Registration EudraCT (2020-001110-38); clinicaltrials.gov (NCT04317092)