Further properties on the core partial order and other matrix partial orders

This paper carries further the study of core partial order initiated by Baksalary and Trenkler [Core inverse of matrices, Linear Multilinear Algebra. 2010;58:681-697]. We have extensively studied the core partial order, and some new characterizations are obtained in this paper. In addition, simple expressions for the already known characterizations of the minus, the star (and one-sided star), the sharp (and one-sided sharp) and the diamond partial orders are also obtained by using a Hartwig-Spindelbck decomposition.This author was partially supported by Ministry of Education of Spain [grant number DGI MTM2010-18228] and by Universidad Nacional de La Pampa, Argentina, Facultad de Ingenieria [grant number Resol. No 049/11].Malik, SB.; Rueda, LC.; Thome, N. (2014). Further properties on the core partial order and other matrix partial orders. Linear and Multilinear Algebra. 62(12):1629-1648. https://doi.org/10.1080/03081087.2013.839676S162916486212Mitra, S. K., & Bhimasankaram, P. (2010). MATRIX PARTIAL ORDERS, SHORTED OPERATORS AND APPLICATIONS. SERIES IN ALGEBRA. doi:10.1142/9789812838452Baksalary, J. K., & Hauke, J. (1990). A further algebraic version of Cochran’s theorem and matrix partial orderings. Linear Algebra and its Applications, 127, 157-169. doi:10.1016/0024-3795(90)90341-9Baksalary, O. M., & Trenkler, G. (2010). Core inverse of matrices. Linear and Multilinear Algebra, 58(6), 681-697. doi:10.1080/03081080902778222Baksalary, J. K., Baksalary, O. M., & Liu, X. (2003). Further properties of the star, left-star, right-star, and minus partial orderings. Linear Algebra and its Applications, 375, 83-94. doi:10.1016/s0024-3795(03)00609-8Groβ, J., Hauke, J., & Markiewicz, A. (1999). Partial orderings, preorderings, and the polar decomposition of matrices. Linear Algebra and its Applications, 289(1-3), 161-168. doi:10.1016/s0024-3795(98)10108-8Mosić, D., & Djordjević, D. S. (2012). Reverse order law for the group inverse in rings. Applied Mathematics and Computation, 219(5), 2526-2534. doi:10.1016/j.amc.2012.08.088Patrício, P., & Costa, A. (2009). On the Drazin index of regular elements. Open Mathematics, 7(2). doi:10.2478/s11533-009-0015-6Rakić, D. S., & Djordjević, D. S. (2012). Space pre-order and minus partial order for operators on Banach spaces. Aequationes mathematicae, 85(3), 429-448. doi:10.1007/s00010-012-0133-2Tošić, M., & Cvetković-Ilić, D. S. (2012). Invertibility of a linear combination of two matrices and partial orderings. Applied Mathematics and Computation, 218(9), 4651-4657. doi:10.1016/j.amc.2011.10.052Hartwig, R. E., & Spindelböck, K. (1983). Matrices for whichA∗andA†commute. Linear and Multilinear Algebra, 14(3), 241-256. doi:10.1080/03081088308817561Baksalary, O. M., Styan, G. P. H., & Trenkler, G. (2009). On a matrix decomposition of Hartwig and Spindelböck. Linear Algebra and its Applications, 430(10), 2798-2812. doi:10.1016/j.laa.2009.01.015Mielniczuk, J. (2011). Note on the core matrix partial ordering. Discussiones Mathematicae Probability and Statistics, 31(1-2), 71. doi:10.7151/dmps.1134Meyer, C. (2000). Matrix Analysis and Applied Linear Algebra. doi:10.1137/1.978089871951

The Midwives Service Scheme in Nigeria

Seye Abimbola and colleagues describe and evaluate their programme in Nigeria of recruiting midwives to rural areas to provide skilled attendance at birth, which is much poorer than in urban areas

Delivering at Home or in a Health Facility? Health-Seeking Behaviour of Women and the Role of Traditional birth attendants in Tanzania.

Traditional birth attendants retain an important role in reproductive and maternal health in Tanzania. The Tanzanian Government promotes TBAs in order to provide maternal and neonatal health counselling and initiating timely referral, however, their role officially does not include delivery attendance. Yet, experience illustrates that most TBAs still often handle complicated deliveries. Therefore, the objectives of this research were to describe (1) women's health-seeking behaviour and experiences regarding their use of antenatal (ANC) and postnatal care (PNC); (2) their rationale behind the choice of place and delivery; and to learn (3) about the use of traditional practices and resources applied by traditional birth attendants (TBAs) and how they can be linked to the bio-medical health system. Qualitative and quantitative interviews were conducted with over 270 individuals in Masasi District, Mtwara Region and Ilala Municipality, Dar es Salaam, Tanzania. The results from the urban site show that significant achievements have been made in terms of promoting pregnancy- and delivery-related services through skilled health workers. Pregnant women have a high level of awareness and clearly prefer to deliver at a health facility. The scenario is different in the rural site (Masasi District), where an adequately trained health workforce and well-equipped health facilities are not yet a reality, resulting in home deliveries with the assistance of either a TBA or a relative. Instead of focusing on the traditional sector, it is argued that more attention should be paid towards (1) improving access to as well as strengthening the health system to guarantee delivery by skilled health personnel; and (2) bridging the gaps between communities and the formal health sector through community-based counselling and health education, which is provided by well-trained and supervised village health workers who inform villagers about promotive and preventive health services, including maternal and neonatal health

Quality Of Antenatal Care In Rural Southern Tanzania: A Reality Check.

Counselling on the danger signs of unpredictable obstetric complications and the appropriate management of such complications are crucial in reducing maternal mortality. The objectives of this study were to identify gaps in the provision of ANC services and knowledge of danger signs as well as the quality of care women receive in case of complications. The study took place in the Rufiji District of Tanzania in 2008 and was conducted in seven health facilities. The study used (1) observations from 63 antenatal care (ANC) sessions evaluated with an ANC checklist, (2) self-assessments of 11 Health workers, (3) interviews with 28 pregnant women and (4) follow-up of 12 women hospitalized for pregnancy-related conditions.Blood pressure measurements and abdominal examinations were common during ANC visits while urine testing for albumin or sugar or haemoglobin levels was rare which was often explained as due to a lack of supplies. The reasons for measuring blood pressure or abdominal examinations were usually not explained to the women. Only 15/28 (54%) women were able to mention at least one obstetric danger sign requiring medical attention. The outcomes of ten complicated cases were five stillbirths and three maternal complications. There was a considerable delay in first contact with a health professional or the start of timely interventions including checking vital signs, using a partograph, and detailed record keeping. Linking danger signs to clinical and laboratory examination results during ANC with the appropriate follow up and avoiding delays in emergency obstetric care are crucial to the delivery of coordinated, effective care interventions

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

Staff experiences of Providing Maternity Services in Rural Southern Tanzania -- A Focus on Equipment, Drug and Supply Issues.

The poor maintenance of equipment and inadequate supplies of drugs and other items contribute to the low quality of maternity services often found in rural settings in low- and middle-income countries, and raise the risk of adverse maternal outcomes through delaying care provision. We aim to describe staff experiences of providing maternal care in rural health facilities in Southern Tanzania, focusing on issues related to equipment, drugs and supplies. Focus group discussions and in-depth interviews were conducted with different staff cadres from all facility levels in order to explore experiences and views of providing maternity care in the context of poorly maintained equipment, and insufficient drugs and other supplies. A facility survey quantified the availability of relevant items. The facility survey, which found many missing or broken items and frequent stock outs, corroborated staff reports of providing care in the context of missing or broken care items. Staff reported increased workloads, reduced morale, difficulties in providing optimal maternity care, and carrying out procedures that carried potential health risks to themselves as a result. Inadequately stocked and equipped facilities compromise the health system's ability to reduce maternal and neonatal mortality and morbidity by affecting staff personally and professionally, which hinders the provision of timely and appropriate interventions. Improving stock control and maintaining equipment could benefit mothers and babies, not only through removing restrictions to the availability of care, but also through improving staff working conditions

Dengue during pregnancy and live birth outcomes: a cohort of linked data from Brazil

OBJECTIVES: Dengue is the most common viral mosquito-borne disease, and women of reproductive age who live in or travel to endemic areas are at risk. Little is known about the effects of dengue during pregnancy on birth outcomes. The objective of this study is to examine the effect of maternal dengue severity on live birth outcomes. // DESIGN AND SETTING: We conducted a population-based cohort study using routinely collected Brazilian data from 2006 to 2012. // PARTICIPATING: We linked birth registration records and dengue registration records to identify women with and without dengue during pregnancy. Using multinomial logistic regression and Firth method, we estimated risk and ORs for preterm birth (<37 weeks' gestation), low birth weight (<2500 g) and small for gestational age (<10thcentile). We also investigated the effect of time between the onset of the disease and each outcome. // RESULTS: We included 16 738 000 live births. Dengue haemorrhagic fever was associated with preterm birth (OR=2.4; 95% CI 1.3 to 4.4) and low birth weight (OR=2.1; 95% CI 1.1 to 4.0), but there was no evidence of effect for small for gestational age (OR=2.1; 95% CI 0.4 to 12.2). The magnitude of the effects was higher in the acute disease period. // CONCLUSION: This study showed an increased risk of adverse birth outcomes in women with severe dengue during pregnancy. Medical intervention to mitigate maternal risk during severe acute dengue episodes may improve outcomes for infants born to exposed mothers

Behavioural Determinants of Hand Washing and Glove Recontamination before Aseptic Procedures at Birth: A Time-and-Motion Study and Survey in Zanzibar Labour Wards

© 2020 by the authors. Recent research calls for distinguishing whether the failure to comply with World Health Organisation hand hygiene guidelines is driven by omitting to rub/wash hands, or subsequently recontamination of clean hands or gloves prior to a procedure. This study examined the determinants of these two behaviours. Across the 10 highest-volume labour wards in Zanzibar, we observed 103 birth attendants across 779 hand hygiene opportunities before aseptic procedures (time-and-motion methods). They were then interviewed using a structured cross-sectional survey. We used mixed-effect multivariable logistic regressions to investigate the independent association of candidate determinants with hand rubbing/washing and avoiding glove recontamination. After controlling for confounders, we found that availability of single-use material to dry hands (OR:2.9; CI:1.58–5.14), a higher workload (OR:29.4; CI:12.9–67.0), more knowledge about hand hygiene (OR:1.89; CI:1.02–3.49), and an environment with more reminders from colleagues (OR:1.20; CI:0.98–1.46) were associated with more hand rubbing/washing. Only the length of time elapsed since donning gloves (OR:4.5; CI:2.5–8.0) was associated with avoiding glove recontamination. We identified multiple determinants of hand washing/rubbing. Only time elapsed since washing/rubbing was reliably associated with avoiding glove recontamination. In this setting, these two behaviours require different interventions. Future studies should measure them separately.The project was funded by the Medical Research Council–PHIND scheme. Award number MR/N015975/1. The Soapbox Collaborative also contributed by funding staff involved in this project. This award is jointly funded by the UK Medical Research Council (MRC) and the UK Department for International Development (DFID) under the MRC/DFID Concordat agreement and is also part of the EDCTP2 programme supported by the European Union. The writing up of this paper provided part of the background needed for the CLEAN Study funded by the UK Joint Global Health Trials (Wellcome, MRC, DFID and DOH). Award number: MR/R019274/1. SN is supported by an award jointly funded by the UK Medical Research Council (MRC) and the UK Department for International Development (DFID) under the MRC/DFID Concordat agreement, which is also part of the EDCTP2 programme supported by the European Union. Award number: MR/R010161/

Length of Stay After Childbirth in 92 Countries and Associated Factors in 30 Low- and Middle-Income Countries: Compilation of Reported Data and a Cross-sectional Analysis from Nationally Representative Surveys

Background: Following childbirth, women need to stay sufficiently long in health facilities to receive adequate care. Little is known about length of stay following childbirth in low- and middle-income countries or its determinants. Methods and Findings: We described length of stay after facility delivery in 92 countries. We then created a conceptual framework of the main drivers of length of stay, and explored factors associated with length of stay in 30 countries using multivariable linear regression. Finally, we used multivariable logistic regression to examine the factors associated with stays that were “too short” (<24 h for vaginal deliveries and <72 h for cesarean-section deliveries). Across countries, the mean length of stay ranged from 1.3 to 6.6 d: 0.5 to 6.2 d for singleton vaginal deliveries and 2.5 to 9.3 d for cesarean-section deliveries. The percentage of women staying too short ranged from 0.2% to 83% for vaginal deliveries and from 1% to 75% for cesarean-section deliveries. Our conceptual framework identified three broad categories of factors that influenced length of stay: need-related determinants that required an indicated extension of stay, and health-system and woman/family dimensions that were drivers of inappropriately short or long stays. The factors identified as independently important in our regression analyses included cesarean-section delivery, birthweight, multiple birth, and infant survival status. Older women and women whose infants were delivered by doctors had extended lengths of stay, as did poorer women. Reliance on factors captured in secondary data that were self-reported by women up to 5 y after a live birth was the main limitation. Conclusions: Length of stay after childbirth is very variable between countries. Substantial proportions of women stay too short to receive adequate postnatal care. We need to ensure that facilities have skilled birth attendants and effective elements of care, but also that women stay long enough to benefit from these. The challenge is to commit to achieving adequate lengths of stay in low- and middle-income countries, while ensuring any additional time is used to provide high-quality and respectful care

An assessment of opportunities and challenges for public sector involvement in the maternal health voucher program in Uganda

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background: Continued inequities in coverage, low quality of care, and high out-of-pocket expenses for health services threaten attainment of Millennium Development Goals 4 and 5 in many sub-Saharan African countries. Existing health systems largely rely on input-based supply mechanisms that have a poor track record meeting the reproductive health needs of low-income and underserved segments of national populations. As a result, there is increased interest in and experimentation with results-based mechanisms like supply-side performance incentives to providers and demand-side vouchers that place purchasing power in the hands of low-income consumers to improve uptake of facility services and reduce the burden of out-of-pocket expenditures. This paper describes a reproductive health voucher program that contracts private facilities in Uganda and explores the policy and implementation issues associated with expansion of the program to include public sector facilities. Methods: Data presented here describes the results of interviews of six district health officers and four health facility managers purposefully selected from seven districts with the voucher program in southwestern Uganda. Interviews were transcribed and organized thematically, barriers to seeking RH care were identified, and how to address the barriers in a context where voucher coverage is incomplete as well as opportunities and challenges for expanding the program by involving public sector facilities were investigated. Results: The findings show that access to sexual and reproductive health services in southwestern Uganda is constrained by both facility and individual level factors which can be addressed by inclusion of the public facilities in the program. This will widen the geographical reach of facilities for potential clients, effectively addressing distance related barriers to access of health care services. Further, intensifying ongoing health education, continuous monitoring and evaluation, and integrating the voucher program with other services is likely to address some of the barriers. The public sector facilities were also seen as being well positioned to provide voucher services because of their countrywide reach, enhanced infrastructure, and referral networks. The voucher program also has the potential to address public sector constraints such as understaffing and supply shortages.Conclusions: Accrediting public facilities has the potential to increase voucher program coverage by reaching a wider pool of poor mothers, shortening distance to service, strengthening linkages between public and private sectors through public-private partnerships and referral systems as well as ensuring the awareness and buy-in of policy makers, which is crucial for mobilization of resources to support the sustainability of the programs. Specifically, identifying policy champions and consulting with key policy sectors is key to the successful inclusion of the public sector into the voucher program