Enumeration of simple random walks and tridiagonal matrices

We present some old and new results in the enumeration of random walks in one dimension, mostly developed in works of enumerative combinatorics. The relation between the trace of the $n$-th power of a tridiagonal matrix and the enumeration of weighted paths of $n$ steps allows an easier combinatorial enumeration of the paths. It also seems promising for the theory of tridiagonal random matrices .Comment: several ref.and comments added, misprints correcte

Global wealth disparities drive adherence to COVID-safe pathways in head and neck cancer surgery

Peer reviewe

Microsurgical Reconstruction of the Nose: The Aesthetic Approach to Total Defects

Background Reconstruction of complex defects involving nose and close facial units represents an aesthetic and functional challenge. Restoring satisfactory nasal shape, combining aesthetic, nasal function and patent airways is mandatory. In this paper, we describe our approach to total nose defects and we report our 20-year experience in microvascular nose reconstruction.Clinical cases are shown to illustrate different surgical techniques and the evolution of our approach. Methods Nasal reconstruction procedures were performed on 21 patients between 2000 and 2020 using the radial forearm flap (RFF) or anterolateral thigh (ALT) flap. Reported reconstructions included total/subtotal nasal defects, caused by cancer resections. The key point of our approach is the expanded forehead flap for skin coverage. Reconstruction is completed by cartilage grafts to restore nasal framework and to shape nasal tip. Ancillary procedures were needed in some cases to optimize aesthetic outcomes. Results Twenty-one patients completed the multistage nasal reconstruction. The RFF flap was used in 56% of the cases (n = 11), while the ALT flap was used in 44% (n = 10) of our case series. No difference has been detected in the number of reconstructive stages required to achieve the final result comparing RFF and ALT reconstruction (3.3 vs. 3.1 reconstructive steps). Ancillary procedures were performed in 7 patients. Conclusion Microvascular tissue transfer plays a key role in full-thickness nasal defects restoration. Comparing the two groups, both the RFF and ALT are effective and reliable options in lining reconstruction, although with different indications. Expanded forehead flap, combined to free cartilage graft, is our gold standard to provide external skin coverage to rebuild the nasal framework. According to our current approach, accurate preoperative planning, supported by modern technologic tools, multistage reconstruction, and ancillary procedures are useful to accomplish satisfactory functional and aesthetic outcomes

Abdominal wall transplantation with microsurgical technique

Many patients undergoing intestinal or multivisceral transplantation have a past history of complete midgut removal with the loss of the domain of the abdominal compartment or have severely damaged abdominal walls from repeated laparotomies, tumours or enterocutaneous fistulae. These patients may encounter severe abdominal wall closure problems at the end of transplantation, resulting in increased morbidity and mortality. It is, therefore, of paramount importance to properly cover transplanted organs in order to reduce postoperative complications. Abdominal wall transplantation was recently proposed for closure of patients undergoing both small-bowel and multivisceral transplantation: the results are encouraging. However, the technical procedure proposed requires the procurement of long segments of iliac vessels as far as the vena cava and the aorta. Since donor multiorgan procurement involves many surgical teams, the removal of these vessels, with the abdominal graft, led to their unavailability for vascular surgeons. Here we present three consecutive cases of abdominal wall transplantation in which, by taking advantage of microsurgical experience, we were able to carry out a transplantation of the abdominal wall by direct anastomosis of the epigastric vessels, obtaining a very good outcome. © 2007 The Authors

Nail-plate dystrophy of the fifth toenail: thinking outside the box

none10noA 59-year-old white woman presented with a 2-year history of a moderately painful nail-plate abnormality of the fifth toenailopenDika E.; Lambertini M.; Misciali C.; Fanti P.A.; Contedini F.; Pinto V.; Pignatti M.; Cipriani F.; Corti B.; Piraccini B.M.Dika E.; Lambertini M.; Misciali C.; Fanti P.A.; Contedini F.; Pinto V.; Pignatti M.; Cipriani F.; Corti B.; Piraccini B.M