Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model.

We study the behavior of the eigenvectors associated with the smallest eigenvalues of the Laplacian matrix of temporal networks. We consider the multilayer representation of temporal networks, i.e., a set of networks linked through ordinal interconnected layers. We analyze the Laplacian matrix, known as supra-Laplacian, constructed through the supraadjacency matrix associated with the multilayer formulation of temporal networks, using a constant block Jacobi model which has closed-form solution. To do this, we assume that the interlayer weights are perturbations of the Kronecker sum of the separate adjacency matrices forming the temporal network. Thus we investigate the properties of the eigenvectors associated with the smallest eigenvalues (close to zero) of the supra-Laplacian matrix. Using arguments of perturbation theory, we show that these eigenvectors can be approximated by linear combinations of the zero eigenvectors of the individual time layers. This finding is crucial in reconsidering and generalizing the role of the Fielder vector in supra-Laplacian matrices.

Nationwide analysis of the impact of COVID-19 in patients with a cardiovascular, oncological or chronic pulmonary disease in the context of an Eastern European country with a low vaccination rate, Bulgaria: March 2020-April 2022.

OBJECTIVE: This study focused on Bulgarian patient cohorts harbouring a single documented chronic comorbidity-cardiovascular pathology, an oncological disease or a chronic pulmonary diseases (CPD) comparing the outcomes in fully vaccinated and non-vaccinated populations classified by sex and age groups in ambulatory, hospital and intensive care unit (ICU) settings at the national level. DESIGN: Retrospective analysis SETTINGS, PARTICIPANTS AND OUTCOME MEASURES: In total, 1 126 946 patients with confirmed COVID-19, on a national level, were retrospectively analysed between March 2020 and April 2022, using data from the Ministry of Health's United Information Portal, launched in March 2020. RESULTS: Of all the confirmed 247 441 hospitalised cases of COVID-19, 67 723 (27.3%) had documented cardiovascular disease (CVD), 2140 (0.9%) had confirmed solid malignancy (regardless of stage) and 3243 (1.3%) had established CPD as their only chronic pathology. The number of cumulative deaths in each subgroup was 10 165 (in-hospital=5812 and ICU=4353); 4.0% vaccinated (410/10 165, p<0.001), 344 (in-hospital=196 and ICU=148), 4.9% vaccinated (17/344, p<0.001), 494 (in-hospital=287 and ICU=207) and 5.2% vaccinated (26/494, p<0.001), respectively. Statistical significance (p<0.001) was obtained in favour of reduced ambulatory, hospitalisation and both in-hospital and ICU-related mortality in the vaccinated cohorts, and BNT162b2 was the most effective at preventing mortality in all age groups. CONCLUSIONS: This retrospective analysis shows that patients vaccinated against COVID-19 demonstrated trends of reduced hospitalisations and premature mortality in patients with CVD, solid malignancy or CPD as a single comorbidity.