On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

The problem of finding a $k \times k$ submatrix of maximum volume of a matrix $A$ is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of $A$. We show that such a submatrix can always be chosen to be a principal submatrix if $A$ is symmetric semidefinite or diagonally dominant. Then we analyze the low-rank approximation error returned by a greedy method for volume maximization, cross approximation with complete pivoting. Our bound for general matrices extends an existing result for symmetric semidefinite matrices and yields new error estimates for diagonally dominant matrices. In particular, for doubly diagonally dominant matrices the error is shown to remain within a modest factor of the best approximation error. We also illustrate how the application of our results to cross approximation for functions leads to new and better convergence results

Speeding up Krylov subspace methods for computing f(A)b via randomization

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov subspace. Such compression is usually computed by forming an orthonormal basis of the Krylov subspace using the Arnoldi method. In this work, we propose to compute (non-orthonormal) bases in a faster way and to use a fast randomized algorithm for least-squares problems to compute the compression of A onto the Krylov subspace. We present some numerical examples which show that our algorithms can be faster than the standard Arnoldi method while achieving comparable accuracy

Speeding up Krylov subspace methods for computing f(A)b via randomization

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov subspace. Such compression is usually computed by forming an orthonormal basis of the Krylov subspace using the Arnoldi method. In this work, we propose to compute (non-orthonormal) bases in a faster way and to use a fast randomized algorithm for least-squares problems to compute the compression of A onto the Krylov subspace. We present some numerical examples which show that our algorithms can be faster than the standard Arnoldi method while achieving comparable accuracy

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

The problem of finding a $k\times k$ submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix can always be chosen to be a principal submatrix if A is symmetric semidefinite or diagonally dominant. Then we analyze the low-rank approximation error returned by a greedy method for volume maximization, cross approximation with complete pivoting. Our bound for general matrices extends an existing result for symmetric semidefinite matrices and yields new error estimates for diagonally dominant matrices. In particular, for doubly diagonally dominant matrices the error is shown to remain within a modest factor of the best approximation error. We also illustrate how the application of our results to cross approximation for functions leads to new and better convergence results

Immune Checkpoint Inhibitors in Malignant Pleural Mesothelioma: A Systematic Review and Meta-Analysis

Many clinical trials have investigated the role of ICIs in PM, with contrasting results. We performed a systematic review and meta-analysis of clinical trials testing single-agent anti-Programmed Death -1 (PD-1)/Programmed Death-Ligand 1 (PD-L1), anti-Cytotoxic T-Lymphocyte Antigen 4 (CTLA-4) or combined treatment in PM patients, analyzing response and survival rate as well as safety data. We selected 17 studies including 2328 patients. Both OS and PFS rates were significantly higher with combined ICI treatments than with single agent anti-PD-1/PD-L1 (p < 0.001 and p = 0.006, respectively) or anti CTLA-4 (p < 0.001) treatments. ORR and DCR for all ICI treatments were 20% (95% CI 13–27%) and 56% (95% CI 45–67%), respectively, and they did not significantly differ between combined and single agent treatments (p = 0.088 and p = 0.058, respectively). The 12-month OS and 6-month PFS rates did not differ significantly (p = 0.0545 and p = 0.1464, respectively) among pre-treated or untreated patients. Combined ICI treatments had a significantly higher rate of Adverse Events (AEs) (p = 0.01). PD-L1-positive patients had a higher probability of response and survival. In conclusion, combined ICI treatments have higher efficacy than single agents but are limited by higher toxicity. Efficacy was independent of treatment line, so a customized sequential strategy should still be speculated. PD-L1 expression could influence response to ICIs; however, reliable biomarkers are warranted

Safety of extended interval dosing immune checkpoint inhibitors:a multicenter cohort study

BACKGROUND: Real-life spectrum and survival implications of immune-related adverse events (irAEs) in patients treated with extended interval dosing (ED) immune checkpoint inhibitors (ICIs) are unknown. METHODS: Characteristics of 812 consecutive solid cancer patients who received at least 1 cycle of ED monotherapy (pembrolizumab 400 mg Q6W or nivolumab 480 mg Q4W) after switching from canonical interval dosing (CD; pembrolizumab 200 mg Q3W or nivolumab 240 mg Q2W) or treated upfront with ED were retrieved. The primary objective was to compare irAEs patterns within the same population (before and after switch to ED). irAEs spectrum in patients treated upfront with ED and association between irAEs and overall survival were also described. RESULTS: A total of 550 (68%) patients started ICIs with CD and switched to ED. During CD, 225 (41%) patients developed any grade and 17 (3%) G3 or G4 irAEs; after switching to ED, any grade and G3 or G4 irAEs were experienced by 155 (36%) and 20 (5%) patients. Switching to ED was associated with a lower probability of any grade irAEs (adjusted odds ratio [aOR] = 0.83, 95% confidence interval [CI] = 0.64 to 0.99; P = .047), whereas no difference for G3 or G4 events was noted (aOR = 1.55, 95% CI = 0.81 to 2.94; P = .18). Among patients who started upfront with ED (n = 232, 32%), 107 (41%) developed any grade and 14 (5%) G3 or G4 irAEs during ED. Patients with irAEs during ED had improved overall survival (adjusted hazard ratio [aHR] = 0.53, 95% CI = 0.34 to 0.82; P = .004 after switching; aHR = 0.57, 95% CI = 0.35 to 0.93; P = .025 upfront). CONCLUSIONS: Switching ICI treatment from CD and ED did not increase the incidence of irAEs and represents a safe option also outside clinical trials.</p

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 &lt; .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