On nonsingularity of combinations of three group invertible matrices and three tripotent matrices

Let T=c1T1+c2T2+c3T3- c4(T1T2+T3T1+T2T3), where T1, T2, T3 are three n x n tripotent matrices and c1, c2, c3, c4 are complex numbers with c1, c2, c3 nonzero. In this article, necessary and sufficient conditions for the nonsingularity of such combinations are established and some formulae for the inverses of them are obtained. Some of these results are given in terms of group invertible matrices.We would like to thank the referee for his/her careful reading. The first author was supported by the Vicerrectorado de Investigacion U.P.V. PAID 06-2010-2285.Benítez López, J.; Sarduvan, M.; Ülker, S.; Özdemir, H. (2013). On nonsingularity of combinations of three group invertible matrices and three tripotent matrices. Linear and Multilinear Algebra. 61(4):463-481. https://doi.org/10.1080/03081087.2012.689986S463481614Baksalary, J. K., & Baksalary, O. M. (2004). Nonsingularity of linear combinationsof idempotent matrices. Linear Algebra and its Applications, 388, 25-29. doi:10.1016/j.laa.2004.02.025Baksalary, J. K., Baksalary, O. M., & Özdemir, H. (2004). A note on linear combinations of commuting tripotent matrices. Linear Algebra and its Applications, 388, 45-51. doi:10.1016/j.laa.2004.01.011Benítez, J., Liu, X., & Zhu, T. (2010). Nonsingularity and group invertibility of linear combinations of twok-potent matrices. Linear and Multilinear Algebra, 58(8), 1023-1035. doi:10.1080/03081080903207932Benítez, J., & Thome, N. (2006). {k}-Group Periodic Matrices. SIAM Journal on Matrix Analysis and Applications, 28(1), 9-25. doi:10.1137/s0895479803437384Gross, J., & Trenkler, G. (2000). Nonsingularity of the Difference of Two Oblique Projectors. SIAM Journal on Matrix Analysis and Applications, 21(2), 390-395. doi:10.1137/s0895479897320277Horn, R. A., & Johnson, C. R. (1985). Matrix Analysis. doi:10.1017/cbo9780511810817Koliha, J. J., & Rakočević, V. (2006). The nullity and rank of linear combinations of idempotent matrices. Linear Algebra and its Applications, 418(1), 11-14. doi:10.1016/j.laa.2006.01.011Koliha, J. ., Rakočević, V., & Straškraba, I. (2004). The difference and sum of projectors. Linear Algebra and its Applications, 388, 279-288. doi:10.1016/j.laa.2004.03.008Liu, X., Wu, S., & Benítez, J. (2011). On nonsingularity of combinations of two group invertible matrices and two tripotent matrices. Linear and Multilinear Algebra, 59(12), 1409-1417. doi:10.1080/03081087.2011.558843Meyer, C. (2000). Matrix Analysis and Applied Linear Algebra. doi:10.1137/1.9780898719512Mitra, S. K. (1987). On group inverses and the sharp order. Linear Algebra and its Applications, 92, 17-37. doi:10.1016/0024-3795(87)90248-5Mitra, S. K., & Bhimasankaram, P. (2010). MATRIX PARTIAL ORDERS, SHORTED OPERATORS AND APPLICATIONS. SERIES IN ALGEBRA. doi:10.1142/9789812838452Zhang, F. (1999). Matrix Theory. Universitext. doi:10.1007/978-1-4757-5797-2Zuo, K. (2010). Nonsingularity of the difference and the sum of two idempotent matrices. Linear Algebra and its Applications, 433(2), 476-482. doi:10.1016/j.laa.2010.03.01

Analysis of proliferative activity in oral gingival epithelium in immunosuppressive medication induced gingival overgrowth

BACKGROUND: Drug-induced gingival overgrowth is a frequent adverse effect associated principally with administration of the immunosuppressive drug cyclosporin A and also certain antiepileptic and antihypertensive drugs. It is characterized by a marked increase in the thickness of the epithelial layer and accumulation of excessive amounts of connective tissue. The mechanism by which the drugs cause gingival overgrowth is not yet understood. The purpose of this study was to compare proliferative activity of normal human gingiva and in cyclosporine A-induced gingival overgrowth. METHODS: Gingival samples were collected from 12 generally healthy individuals and 22 Cyclosporin A-medicated renal transplant recipients. Expression of proliferating cell nuclear antigen was evaluated in formalin-fixed, paraffin-embedded gingival samples using an immunoperoxidase technique and a monoclonal antibody for this antigen. RESULTS: There were differences between the Cyclosporin A group and control group in regard to proliferating cell nuclear antigen and epithelial thickness. In addition, the degree of stromal inflammation was higher in the Cyclosporin A group when compared with the control group. CONCLUSION: The results suggest that the increased epithelial thickness observed in Cyclosporin A-induced gingival overgrowth is associated with increased proliferative activity in keratinocytes

An update of the Worldwide Integrated Assessment (WIA) on systemic insecticides. Part 2: impacts on organisms and ecosystems

New information on the lethal and sublethal effects of neonicotinoids and fipronil on organisms is presented in this review, complementing the previous WIA in 2015. The high toxicity of these systemic insecticides to invertebrates has been confirmed and expanded to include more species and compounds. Most of the recent research has focused on bees and the sublethal and ecological impacts these insecticides have on pollinators. Toxic effects on other invertebrate taxa also covered predatory and parasitoid natural enemies and aquatic arthropods. Little, while not much new information has been gathered on soil organisms. The impact on marine coastal ecosystems is still largely uncharted. The chronic lethality of neonicotinoids to insects and crustaceans, and the strengthened evidence that these chemicals also impair the immune system and reproduction, highlights the dangers of this particular insecticidal classneonicotinoids and fipronil. , withContinued large scale – mostly prophylactic – use of these persistent organochlorine pesticides has the potential to greatly decreasecompletely eliminate populations of arthropods in both terrestrial and aquatic environments. Sublethal effects on fish, reptiles, frogs, birds and mammals are also reported, showing a better understanding of the mechanisms of toxicity of these insecticides in vertebrates, and their deleterious impacts on growth, reproduction and neurobehaviour of most of the species tested. This review concludes with a summary of impacts on the ecosystem services and functioning, particularly on pollination, soil biota and aquatic invertebrate communities, thus reinforcing the previous WIA conclusions (van der Sluijs et al. 2015)

Global Impact of the COVID-19 Pandemic on Cerebral Venous Thrombosis and Mortality

Background and purpose: Recent studies suggested an increased incidence of cerebral venous thrombosis (CVT) during the coronavirus disease 2019 (COVID-19) pandemic. We evaluated the volume of CVT hospitalization and in-hospital mortality during the 1st year of the COVID-19 pandemic compared to the preceding year. Methods: We conducted a cross-sectional retrospective study of 171 stroke centers from 49 countries. We recorded COVID-19 admission volumes, CVT hospitalization, and CVT in-hospital mortality from January 1, 2019, to May 31, 2021. CVT diagnoses were identified by International Classification of Disease-10 (ICD-10) codes or stroke databases. We additionally sought to compare the same metrics in the first 5 months of 2021 compared to the corresponding months in 2019 and 2020 (ClinicalTrials.gov Identifier: NCT04934020). Results: There were 2,313 CVT admissions across the 1-year pre-pandemic (2019) and pandemic year (2020); no differences in CVT volume or CVT mortality were observed. During the first 5 months of 2021, there was an increase in CVT volumes compared to 2019 (27.5%; 95% confidence interval [CI], 24.2 to 32.0; P<0.0001) and 2020 (41.4%; 95% CI, 37.0 to 46.0; P<0.0001). A COVID-19 diagnosis was present in 7.6% (132/1,738) of CVT hospitalizations. CVT was present in 0.04% (103/292,080) of COVID-19 hospitalizations. During the first pandemic year, CVT mortality was higher in patients who were COVID positive compared to COVID negative patients (8/53 [15.0%] vs. 41/910 [4.5%], P=0.004). There was an increase in CVT mortality during the first 5 months of pandemic years 2020 and 2021 compared to the first 5 months of the pre-pandemic year 2019 (2019 vs. 2020: 2.26% vs. 4.74%, P=0.05; 2019 vs. 2021: 2.26% vs. 4.99%, P=0.03). In the first 5 months of 2021, there were 26 cases of vaccine-induced immune thrombotic thrombocytopenia (VITT), resulting in six deaths. Conclusions: During the 1st year of the COVID-19 pandemic, CVT hospitalization volume and CVT in-hospital mortality did not change compared to the prior year. COVID-19 diagnosis was associated with higher CVT in-hospital mortality. During the first 5 months of 2021, there was an increase in CVT hospitalization volume and increase in CVT-related mortality, partially attributable to VITT

The prognostic significance of tumour-stroma ratio in endometrial carcinoma.

Background: High tumour stromal content has been found to predict adverse clinical outcome in a range of epithelial tumours. The aim of this study was to assess the prognostic significance of tumour-stroma ratio (TSR) in endometrial adenocarcinomas and investigate its relationship with other clinicopathological parameters. Methods: Clinicopathological and 5-year follow-up data were obtained for a retrospective series of endometrial adenocarcinoma patients (n = 400). TSR was measured using a morphometric approach (point counting) on digitised histologic hysterectomy specimens. Inter-observer agreement was determined using Cohen’s Kappa statistic. TSR cut-offs were optimised using log-rank functions and prognostic significance of TSR on overall survival (OS) and disease-free survival (DFS) were determined using Cox Proportional Hazards regression analysis and Kaplan-Meier curves generated. Associations of TSR with other clinicopathological parameters were determined using non-parametric tests followed by Holm-Bonferroni correction for multiple comparisons. Results: TSR as a continuous variable associated with worse OS (P = 0.034) in univariable Cox-regression analysis. Using the optimal cut-off TSR value of 1.3, TSR-high (i.e. low stroma) was associated with worse OS (HR = 2.51; 95 % CI = 1.22–5.12; P = 0.021) and DFS (HR = 2.19; 95 % CI = 1.15–4.17; P = 0.017) in univariable analysis. However, TSR did not have independent prognostic significance in multivariable analysis, when adjusted for known prognostic variables. A highly significant association was found between TSR and tumour grade (P < 0.001) and lymphovascular space invasion (P < 0.001), both of which had independent prognostic significance in this study population. Conclusions: Low tumour stromal content associates with both poor outcome and with other adverse prognostic indicators in endometrial cancer, although it is not independently prognostic. These findings contrast with studies on many - although not all - cancers and suggest that the biology of tumour-stroma interactions may differ amongst cancer types

Global Impact of the COVID-19 Pandemic on Cerebral Venous Thrombosis and Mortality.

BACKGROUND AND PURPOSE: Recent studies suggested an increased incidence of cerebral venous thrombosis (CVT) during the coronavirus disease 2019 (COVID-19) pandemic. We evaluated the volume of CVT hospitalization and in-hospital mortality during the 1st year of the COVID-19 pandemic compared to the preceding year. METHODS: We conducted a cross-sectional retrospective study of 171 stroke centers from 49 countries. We recorded COVID-19 admission volumes, CVT hospitalization, and CVT in-hospital mortality from January 1, 2019, to May 31, 2021. CVT diagnoses were identified by International Classification of Disease-10 (ICD-10) codes or stroke databases. We additionally sought to compare the same metrics in the first 5 months of 2021 compared to the corresponding months in 2019 and 2020 (ClinicalTrials.gov Identifier: NCT04934020). RESULTS: There were 2,313 CVT admissions across the 1-year pre-pandemic (2019) and pandemic year (2020); no differences in CVT volume or CVT mortality were observed. During the first 5 months of 2021, there was an increase in CVT volumes compared to 2019 (27.5%; 95% confidence interval [CI], 24.2 to 32.0; P<0.0001) and 2020 (41.4%; 95% CI, 37.0 to 46.0; P<0.0001). A COVID-19 diagnosis was present in 7.6% (132/1,738) of CVT hospitalizations. CVT was present in 0.04% (103/292,080) of COVID-19 hospitalizations. During the first pandemic year, CVT mortality was higher in patients who were COVID positive compared to COVID negative patients (8/53 [15.0%] vs. 41/910 [4.5%], P=0.004). There was an increase in CVT mortality during the first 5 months of pandemic years 2020 and 2021 compared to the first 5 months of the pre-pandemic year 2019 (2019 vs. 2020: 2.26% vs. 4.74%, P=0.05; 2019 vs. 2021: 2.26% vs. 4.99%, P=0.03). In the first 5 months of 2021, there were 26 cases of vaccine-induced immune thrombotic thrombocytopenia (VITT), resulting in six deaths. CONCLUSIONS: During the 1st year of the COVID-19 pandemic, CVT hospitalization volume and CVT in-hospital mortality did not change compared to the prior year. COVID-19 diagnosis was associated with higher CVT in-hospital mortality. During the first 5 months of 2021, there was an increase in CVT hospitalization volume and increase in CVT-related mortality, partially attributable to VITT