Spectral estimates and preconditioning for saddle point systems arising from optimization problems

In this thesis, we consider the problem of solving large and sparse linear systems of saddle point type stemming from optimization problems. The focus of the thesis is on iterative methods, and new preconditioning srategies are proposed, along with novel spectral estimtates for the matrices involved.

Kissing stenting of aortic bifurcation for aorto-iliac obstructive disease: a comparison between bare metal stents and covered stents

INTRODUCTION Aim of this multicentric study:to compare the short-and mid-term results of bare metal stents(BMS)and covered stents(CS)in the Kissing Stent(KS)technique. METHODS Patients undertaking a KS with BMS or CS between January 2017-August 2021 included. Morphological features of plaques were classified as per the extension of calcifications and thrombosis. Every endpoint and outcome was compared in relation to BMS or CS. All patients included received dual anti-platelets DAPT)for at least one month. RESULTS Thirty-four patients enrolled,17 treated with BMS and 17 with CS. Average age 66 years. The 80% of patients were part of TASC C-D categories. DAPT was administered to 82.4%(28/34)of patients with a mean duration of 4.4±1.6 months. Mean follow-up 32.1±17.8 months. Technical Success was 100%. Immediate Clinical Success was reached in 29 cases(85.3%). Immediate and 30-day Clinical Success was higher in CS(64.7% vs 100%, p=.01). Overall Clinical Success at 1-year follow-up was 91.2%,and resulted significantly higher in CS(82.4% vs 100%,p .04). Overall Primary Patency,Assisted Patency,and Secondary Patency at 30 days were 97.1%,97.1%,and 100%,without differences between BMS and CS(94.1% vs 100%,94.1% vs 100%,and 100% vs 100%;p =.7). Two cases(5.9%)of thrombosis were registered,and both occurred within 3 months after the procedure and both in the BMS,without statistical differences with the CS group(11.8% vs 0%,p .48). Both cases of thrombosis occurred in patients who were not treated with dual antiplatelet therapy(33.3% vs 0%,p .027). Survival statistically differed only at the mean follow-up in favour of CS(70.6% and 100%,p .04). CONCLUSIONS The endovascular approach is currently safe and effective in the treatment of AIOD,and KS offers excellent results in particular if performed with CS; however,no statistically significant differences emerged between the two types of stents in terms of patency,reintervention,and complications. DAPT seems to warrant the best results in terms of patency,although there is still no consensus about the ideal duration of administration.

Omission of axillary clearance in patients with early breast cancer and positive sentinel node biopsy treated with conservative surgery: application of the ACOSOG Z011 trial in clinical practice

Background: Axillary lymph node dissection (ALND) in presence of sentinel lymph node (SLN) metastases has been the standard in breast cancer (BC) patients for many years. Today, after the publication of the ACOSOG Z0011 trial, ALND is a procedure restricted to a dwindling group of patients with a clearly metastatic axilla. Material and methods: This was a prospective observational trial involving two Italian Breast Units: Policlinico di Sant’Orsola and San Raffaele hospital. Objective was to evaluate that the omission of ALND in patients with cT1-2 cN0 BC undergoing breast conserving surgery (BCS) and histological finding of metastases in 1 or 2 SLN is not associated with a worse prognostic outcome. Primary endpoint was overall survival (OS). Secondary endpoints were disease free survival (DFS) and locoregional recurrence. All BC patients treated between the 1st of November 2020 and 31st of July 2023 with cT1-2 cN0 BC, preoperative negative axillary ultrasound and 1 or 2 metastatic SLN treated with sentinel node biopsy (SLNB) alone entered the study. Results: 795 cT1-2 cN0 BC patients underwent BCS and SLNB. Ninety patients were included. Median age was 60 (52-68) years. Seventy-five patients (83%) had T1 tumor and 15 (17%) T2. Median tumor size was 16 mm (11-19). The median SLN removed was 2 (1-3). Eighty-one patients had 1 positive SLN (90%), while 9 had 2 SLN metastasis (10%). 39 (43%) micrometastases were identified and 51 macrometastasis (57%). All patients underwent radiotherapy. Seventeen (19%) performed adjuvant chemotherapy. Two received immunotherapy with trastuzumab and pertuzumab. Endocrine therapy was given to 84 (93%). At a median follow-up of 19 months (IQR 13-23) OS and DFS were 100%. No loco-regional recurrence was seen. Conclusion: The preliminary results of our study confirm that omitting ALND in patients meeting Z011 criteria is oncologically safe and should be the standard of care.