Improved Hartree--Fock resummations and spontaneous symmetry breaking

The standard Hartree--Fock approximation of the $O(N)-$invariant $\phi^4$ model suffers from serious renormalization problems. In addition, when the symmetry is spontaneously broken, another shortcoming appears in relation to the Goldstone bosons: they fail to be massless in the intermediate states. In this work, within the framework of out--of--equilibrium Quantum Field Theory, we propose a class of systematic improvements of the Hartree--Fock resummation which overcomes all the above mentioned difficulties while ensuring also exact Renormalization--Group invariance to one loop.Comment: 42 pages, 9 figure

The renormalized and Renormalization-Group invariant Hartree-Fock approximation

We study the renormalization problem for the Hartree--Fock approximation of the $O(N)-$invariant $\phi^4$ model in the symmetric phase and show how to systematically improve the corresponding diagrammatic resummation to achieve the correct renormalization properties of the effective field equations, including Renormalization--Group invariance with the one--loop beta function. These new Hartree--Fock dynamics is still of mean field type but includes memory effects which are generically nonlocal also in space.Comment: 32 pages, 13 figure

The spectral dimension of random trees

We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new scaling hypothesis for the Gaussian model on generic bounded graphs and in favor of a previously conjectured exact relation between spectral and connectivity dimensions on more general tree-like structures.Comment: 14 pages, 2 eps figures, revtex4. Revised version: changes in section I

The statistical geometry of scale-free random trees

The properties of scale-free random trees are investigated using both preconditioning on non-extinction and fixed size averages, in order to study the thermodynamic limit. The scaling form of volume probability is found, the connectivity dimensions are determined and compared with other exponents which describe the growth. The (local) spectral dimension is also determined, through the study of the massless limit of the Gaussian model on such trees.Comment: 21 pages, 2 figures, revtex4, minor changes (published version

Spectral partitions on infinite graphs

Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic behaviour at macroscopic scales. This phenomenon is of geometrical origin and may be properly described in terms of spectral partitions into subgraphs with well defined spectral dimensions and spectral weights. These subgraphs are shown to be thermodynamically homogeneous and effectively decoupled.Comment: 8 pages, to appear on Journal of Physics

Properties of the Scale Invariant O(g4)O(g^4) Lipatov Kernel

We study the scale-invariant $O(g^4)$ kernel which appears as an infra-red contribution in the BFKL evolution equation and is constructed via multiparticle $t$-channel unitarity. We detail the variety of Ward identity constraints and infra-red cancellations that characterize its infrared behaviour. We give an analytic form for the full non-forward kernel. For the forward kernel controlling parton evolution at small-x, we give an impact parameter representation, derive the eigenvalue spectrum, and demonstrate a holomorphic factorisation property related to conformal invariance. The results show that, at next-to-leading-order, the transverse momentum infra-red region may produce a strong reduction of the BFKL small-x behavior.Comment: 41 pages in latex, 16 figs. in a uu-encoded ps-fil

Segmental transverse colectomy. Minimally invasive versus open approach: results from a multicenter collaborative study

none65noThe role of minimally invasive surgery in the treatment of transverse colon cancer is still controversial. The aim of this study is to investigate the advantages of a totally laparoscopic technique comparing open versus laparoscopic/robotic approach. Three hundred and eighty-eight patients with transverse colon cancer, treated with a segmental colon resection, were retrospectively analyzed. Demographic data, tumor stage, operative time, intraoperative complications, number of harvested lymph nodes and recovery outcomes were recorded. Recurrences and death were also evaluated during the follow-up. No differences were found between conventional and minimally invasive surgery, both for oncological long-term outcomes (recurrence rate p = 0.28; mortality p = 0.62) and postoperative complications (overall rate p = 0.43; anemia p = 0.78; nausea p = 0.68; infections p = 0.91; bleeding p = 0.62; anastomotic leak p = 0.55; ileus p = 0.75). Nevertheless, recovery outcomes showed statistically significant differences in favor of minimally invasive surgery in terms of time to first flatus (p = 0.001), tolerance to solid diet (p = 0.017), time to first mobilization (p = 0.001) and hospital stay (p = 0.004). Compared with laparoscopic approach, robotic surgery showed significantly better results for time to first flatus (p = 0.001), to first mobilization (p = 0.005) and tolerance to solid diet (p = 0.001). Finally, anastomosis evaluation confirmed the superiority of intracorporeal approach which showed significantly better results for time to first flatus (p = 0.001), to first mobilization (p = 0.003) and tolerance to solid diet (p = 0.001); moreover, we recorded a statistical difference in favor of intracorporeal approach for infection rate (p = 0.04), bleeding (p = 0.001) and anastomotic leak (p = 0.03). Minimally invasive approach is safe and effective as the conventional open surgery, with comparable oncological results but not negligible advantages in terms of recovery outcomes. Moreover, we demonstrated that robotic approach may be considered a valid option and an intracorporeal anastomosis should always be preferred.noneMilone, Marco; Degiuli, Maurizio; Velotti, Nunzio; Manigrasso, Michele; Vertaldi, Sara; D'Ugo, Domenico; De Palma, Giovanni Domenico; Dario Bruzzese, Giuseppe Servillo, Giuseppe De Simone, Katia Di Lauro, Silvia Sofia, Marco Ettore Allaix, Mario Morino, Rossella Reddavid, Carlo Alberto Ammirati, Stefano Scabini, Gabriele Anania, Cristina Bombardini, Andrea Barberis, Roberta Longhin, Andrea Belli, Francesco Bianco, Giampaolo Formisano, Giuseppe Giuliani, Paolo Pietro Bianchi, Davide Cavaliere, Leonardo Solaini, Claudio Coco, Gianluca Rizzo, Andrea Coratti, Raffaele De Luca, Michele Simone, Alberto Di Leo, Giovanni De Manzoni, Paola De Nardi, Ugo Elmore, Riccardo Rosati, Andrea Vignali, Paolo Delrio, Ugo Pace, Daniela Rega, Antonio Di Cataldo, Giovanni Li Destri, Annibale Donini, Luigina Graziosi, Andrea Fontana, Michela Mineccia, Sergio Gentilli, Manuela Monni, Mario Guerrieri, Monica Ortenzi, Francesca Pecchini, Micaela Piccoli, Italy. Corrado Pedrazzani, Giulia Turri, Sara Pollesel, Franco Roviello, Marco Rigamonti, Michele Zuolo, Mauro Santarelli, Federica Saraceno, Pierpaolo Sileri Giuseppe Sigismondo Sica, Luigi Siragusa Salvatore Pucciarelli, Matteo ZuinMilone, Marco; Degiuli, Maurizio; Velotti, Nunzio; Manigrasso, Michele; Vertaldi, Sara; D'Ugo, Domenico; De Palma, Giovanni Domenico; Dario Bruzzese, Giuseppe Servillo, Giuseppe De Simone, Katia Di Lauro, Silvia Sofia, Marco Ettore Allaix, Mario Morino, Rossella Reddavid, Carlo Alberto Ammirati, Stefano Scabini, Gabriele Anania, Cristina Bombardini, Andrea Barberis, Roberta Longhin, Andrea Belli, Francesco Bianco, Giampaolo Formisano, Giuseppe Giuliani, Paolo Pietro Bianchi, Davide Cavaliere, Leonardo Solaini, Claudio Coco, Gianluca Rizzo, Andrea Coratti, Raffaele De Luca, Michele Simone, Alberto Di Leo, Giovanni De Manzoni, Paola De Nardi, Ugo Elmore, Riccardo Rosati, Andrea Vignali, Paolo Delrio, Ugo Pace, Daniela Rega, Antonio Di Cataldo, Giovanni Li Destri, Annibale Donini, Luigina Graziosi, Andrea Fontana, Michela Mineccia, Sergio Gentilli, Manuela Monni, Mario Guerrieri, Monica Ortenzi, Francesca Pecchini, Micaela Piccoli, Italy. Corrado Pedrazzani, Giulia Turri, Sara Pollesel, Franco Roviello, Marco Rigamonti, Michele Zuolo, Mauro Santarelli, Federica Saraceno, Pierpaolo Sileri Giuseppe Sigismondo Sica, Luigi Siragusa Salvatore Pucciarelli, Matteo Zui