A weak group inverse for rectangular matrices

[EN] In this paper, we extend the notion of weak group inverse to rectangular matrices (called WweightedWGinverse) by using the weighted core EP inverse recently investigated. This new generalized inverse also generalizes the well-known weighted group inverse given by Cline and Greville. In addition, we give several representations of the W-weighted WG inverse, and derive some characterizations and properties.First author was partially supported by UNRC (Grant PPI 18/C472) and CONICET (Grant PIP 112-201501-00433CO). Third author was partially supported by Ministerio de Economia, Industria y Competitividad of Spain (Grants DGI MTM2013-43678-P and Red de Excelencia MTM2017-90682-REDT).Ferreyra, DE.; Orquera, V.; Thome, N. (2019). A weak group inverse for rectangular matrices. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(4):3727-3740. https://doi.org/10.1007/s13398-019-00674-9S372737401134Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, New York (2003)Baksalary, O.M., Trenkler, G.: Core inverse of matrices. Linear Multilinear Algebra 58, 681–697 (2010)Baksalary, O.M., Trenkler, G.: On a generalized core inverse. Appl. Math. Comput. 236, 450–457 (2014)Bajodah, A.H.: Servo-constraint generalized inverse dynamics for robot manipulator control design. Int. J. Robot. Autom. 25, (2010). https://doi.org/10.2316/Journal.206.2016.1.206-3291Campbell, S.L., Meyer Jr., C.D.: Generalized Inverses of Linear transformations. SIAM, Philadelphia (2009)Cline, R.E., Greville, T.N.E.: A Drazin inverse for rectangular matrices. Linear Algebra Appl. 29, 53–62 (1980)Dajić, A., Koliha, J.J.: The weighted g-Drazin inverse for operators. J. Aust. Math. Soc. 2, 163–181 (2007)Doty, K.L., Melchiorri, C., Bonivento, C.: A theory of generalized inverses applied to robotics. Int. J. Rob. Res. 12, 1–19 (1993)Drazin, M.P.: Pseudo-inverses in associate rings and semirings. Am. Math. Mon. 65, 506–514 (1958)Ferreyra, D.E., Levis, F.E., Thome, N.: Revisiting of the core EP inverse and its extension to rectangular matrices. Quaest. Math. 41, 265–281 (2018)Ferreyra, D.E., Levis, F.E., Thome, N.: Maximal classes of matrices determining generalized inverses. Appl. Math. Comput. 333, 42–52 (2018)Gigola, S., Lebtahi, L., Thome, N.: The inverse eigenvalue problem for a Hermitian reflexive matrix and the optimization problem. J. Comput. Appl. Math. 291, 449–457 (2016)Hartwig, R.E.: The weighted $$*$$ ∗ -core-nilpotent decomposition. Linear Algebra Appl. 211, 101–111 (1994)Kirkland, S.J., Neumann, M.: Group inverses of M-matrices and their applications. Chapman and Hall/CRC, London (2013)Malik, S., Thome, N.: On a new generalized inverse for matrices of an arbitrary index. Appl. Math. Comput. 226, 575–580 (2014)Male $${{\check{\rm s}}}$$ s ˇ ević, B., Obradović, R., Banjac, B., Jovović, I., Makragić, M.: Application of polynomial texture mapping in process of digitalization of cultural heritage. arXiv:1312.6935 (2013). Accessed 14 June 2018Manjunatha Prasad, K., Mohana, K.S.: Core EP inverse. Linear Multilinear Algebra 62, 792–802 (2014)Mehdipour, M., Salemi, A.: On a new generalized inverse of matrices. Linear Multilinear Algebra 66, 1046–1053 (2018)Meng, L.S.: The DMP inverse for rectangular matrices. Filomat 31, 6015–6019 (2017)Mosić, D.: The CMP inverse for rectangular matrices. Aequaetiones Math. 92, 649–659 (2018)Penrose, R.: A generalized inverse for matrices. Proc. Cambrid. Philos. Soc. 51, 406–413 (1955)Soleimani, F., Stanimirović, P.S., Soleymani, F.: Some matrix iterations for computing generalized inverses and balancing chemical equations. Algorithms 8, 982–998 (2015)Xiao, G.Z., Shen, B.Z., Wu, C.K., Wong, C.S.: Some spectral techniques in coding theory. Discrete Math. 87, 181–186 (1991)Wang, H.: Core-EP decomposition and its applications. Linear Algebra Appl. 508, 289–300 (2016)Wang, H., Chen, J.: Weak group inverse. Open Math. 16, 1218–1232 (2018)Wei, Y.: A characterization for the $$W$$ W -weighted Drazin inverse and a Crammer rule for the $$W$$ W -weighted Drazin inverse solution. Appl. Math. Comput. 125, 303–310 (2002

Traditional medicinal plant use in Northern Peru: tracking two thousand years of healing culture

This paper examines the traditional use of medicinal plants in Northern Peru, with special focus on the Departments of Piura, Lambayeque, La Libertad, Cajamarca, and San Martin. Northern Peru represents the center of the old Central Andean "Health Axis," stretching from Ecuador to Bolivia. The roots of traditional healing practices in this region go at least as far back as the Moche period (AC 100–800). Although about 50% of the plants in use reported in the colonial period have disappeared from the popular pharmacopoeia, the plant knowledge of the population is much more extensive than in other parts of the Andean region. 510 plant species used for medicinal purposes were collected, identified and their vernacular names, traditional uses and applications recorded. The families best represented were Asteraceae with 69 species, Fabaceae (35), Lamiaceae (25), and Solanaceae (21). Euphorbiaceae had twelve species, and Apiaceae and Poaceae 11 species. The highest number of species was used for the treatment of "magical/ritual" ailments (207 species), followed by respiratory disorders (95), problems of the urinary tract (85), infections of female organs (66), liver ailments (61), inflammations (59), stomach problems (51) and rheumatism (45). Most of the plants used (83%) were native to Peru. Fresh plants, often collected wild, were used in two thirds of all cases, and the most common applications included the ingestion of herb decoctions or the application of plant material as poultices

Health for sale: the medicinal plant markets in Trujillo and Chiclayo, Northern Peru

Traditional methods of healing have been beneficial in many countries with or without access to conventional allopathic medicine. In the United States, these traditional practices are increasingly being sought after for illnesses that cannot be easily treated by allopathic medicine. More and more people are becoming interested in the knowledge maintained by traditional healers and in the diversity of medicinal plants that flourish in areas like Northern Peru. While scientific studies of medicinal plants are underway, concern has arisen over the preservation of both the large diversity of medicinal plants and the traditional knowledge of healing methods that accompanies them. To promote further conservation work, this study attempted to document the sources of the most popular and rarest medicinal plants sold in the markets of Trujillo (Mayorista and Hermelinda) and Chiclayo (Modelo and Moshoqueque), as well as to create an inventory of the plants sold in these markets, which will serve as a basis for comparison with future inventories. Individual markets and market stalls were subjected to cluster analysis based on the diversity of the medicinal plants they carry. The results show that markets were grouped based on the presence of: (1) common exotic medicinal plants; (2) plants used by laypeople for self-medication related to common ailments ("everyday remedies"); (3) specialized medicinal plants used by curanderos or traditional healers; and (4) highly "specialized" plants used for magical purposes. The plant trade in the study areas seems to correspond well with the specific health care demands from clientele in those areas. The specific market patterns of plant diversity observed in the present study represent a foundation for comparative market research in Peru and elsewhere

Inhibition of poly(ADP-ribose) polymerase-1 attenuates the toxicity of carbon tetrachloride

Carbon tetrachloride (CCl4) is routinely used as a model compound for eliciting centrilobular hepatotoxicity. It can be bioactivated to the trichloromethyl radical, which causes extensive lipid peroxidation and ultimately cell death by necrosis. Overactivation of poly(ADP-ribose) polymerase-1 (PARP-1) can rapidly reduce the levels of (β-nicotinamide adenine dinucleotide and adenosine triphosphate and ultimately promote necrosis. The aim of this study was to determine whether inhibition of PARP-1 could decrease CCl4-induced hepatotoxicity, as measured by degree of poly(ADP-ribosyl)ation, serum levels of lactate dehydrogenase (LDH), lipid peroxidation,and oxidative DNA damage. For this purpose, male ICR mice were administered intraperitoneally a hepatotoxic dose of CCl4 with or without 6(5H)-phenanthridinone, a potent inhibitor of PARP-1. Animals treated with CCl4 exhibited extensive poly(ADP-ribosyl)ation in centrilobular hepatocytes, elevated serum levels of LDH, and increased lipid peroxidation. In contrast, animals treated concomitantly with CCl4 and 6(5H)-phenanthridinone showed significantly lower levels of poly(ADP-ribosyl) ation, serum LDH, and lipid peroxidation. No changes were observed in the levels of oxidative DNA damage regardless of treatment. These results demonstrated that the hepatotoxicity of CCl4is dependent on the overactivation of PARP-1 and that inhibition of this enzyme attenuates the hepatotoxicity of CCl4

Elevated circulating levels of succinate in human obesity are linked to specific gut microbiota

Gut microbiota-related metabolites are potential clinical biomarkers for cardiovascular disease (CVD). Circulating succinate, a metabolite produced by both microbiota and the host, is increased in hypertension, ischemic heart disease, and type 2 diabetes. We aimed to analyze systemic levels of succinate in obesity, a major risk factor for CVD, and its relationship with gut microbiome. We explored the association of circulating succinate with specific metagenomic signatures in cross-sectional and prospective cohorts of Caucasian Spanish subjects. Obesity was associated with elevated levels of circulating succinate concomitant with impaired glucose metabolism. This increase was associated with specific changes in gut microbiota related to succinate metabolism: a higher relative abundance of succinate-producing Prevotellaceae (P) and Veillonellaceae (V), and a lower relative abundance of succinate-consuming Odoribacteraceae (O) and Clostridaceae (C) in obese individuals, with the (P + V/O + C) ratio being a main determinant of plasma succinate. Weight loss intervention decreased (P + V/O + C) ratio coincident with the reduction in circulating succinate. In the spontaneous evolution after good dietary advice, alterations in circulating succinate levels were linked to specific metagenomic signatures associated with carbohydrate metabolism and energy production with independence of body weight change. Our data support the importance of microbe-microbe interactions for the metabolite signature of gut microbiome and uncover succinate as a potential microbiota-derived metabolite related to CVD risk