Situations often arise in which the matrix of independent variables is not of full column rank. That is, there are one or more linear dependencies among the independent variables. This paper covers in detail the situation in which the rank is one less than full column rank and extends this coverage to include cases of even greater rank deficiency. The emphasis is on the row geometry of the solutions based on the normal equations. The author shows geometrically how constrained-regression/generalized-inverses work in this situation to provide a solution in the face of rank deficiency.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3378569 | PMC |
| http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0038923 | PLOS |
Publication Analysis
Top Keywords
Similar Publications
Buqi-Tongluo Decoction inhibits osteoclastogenesis and alleviates bone loss in ovariectomized rats by attenuating NFATc1, MAPK, NF-κB signaling.
Chin J Nat Med
January 2025
The First Clinical Academy, Guangzhou University of Chinese Medicine, Guangzhou 510405, China; The First Affiliated Hospital of Guangzhou University of Chinese Medicine, Guangzhou 510407, China; Lingnan Medical Research Center of Guangzhou University of Chinese Medicine, Guangzhou 510405, China. Electronic address:
Osteoporosis is a prevalent skeletal condition characterized by reduced bone mass and strength, leading to increased fragility. Buqi-Tongluo (BQTL) decoction, a traditional Chinese medicine (TCM) prescription, has yet to be fully evaluated for its potential in treating bone diseases such as osteoporosis. To investigate the mechanism by which BQTL decoction inhibits osteoclast differentiation in vitro and validate these findings through in vivo experiments.
View Article and Find Full Text PDFIncidence and predictors of mortality among HIV positive children on anti-retroviral therapy in the selected health facilities of West Wollega Zone, Western Ethiopia: Retrospective cohort study.
PLoS One
January 2025
Departments of Public Health, Institute of Health Sciences, Wollega University, Ethiopia.
Introduction: The mortality rate among Human immunodeficiency Virus (HIV) who have started antiretroviral therapy (ART) continues to be increased in resource-limited countries, despite a decline in developed nations. Furthermore, research within this age group is limited and has not previously been conducted in the study area. Consequently, this study aimed to determine the incidence of mortality and its predictors among HIV-positive children who have been receiving ART at public health facilities in West Wollega.
View Article and Find Full Text PDFEffects of HIV exposure on anemia and vitamin D nutritional status in children aged 6-24 months: a hospital-based cross-sectional study.
Sci Rep
January 2025
Department of Maternal Health Care, Hunan Provincial Maternal and Child Health Care Hospital, Changsha, 410008, Hunan, China.
There is little research on anemia and vitamin D deficiency in HIV-exposed uninfected (HEU) children. This study was aimed to describe and compare the prevalence of anemia and vitamin D inadequacy in HEU children and HIV-unexposed uninfected (HUU) children, and to examine the associations of HIV exposure with anemia and vitamin D inadequacy. This was a hospital-based descriptive cross-sectional study nested within the Prevention of Mother-to-Child Transmission (PMTCT) of HIV program in Hunan Province during July and September 2022.
View Article and Find Full Text PDFMiniaturized spectral sensing with a tunable optoelectronic interface.
Sci Adv
January 2025
QTF Centre of Excellence, Department of Electronics and Nanoengineering, Aalto University, Espoo FI-00076 Aalto, Finland.
Reconstructive optoelectronic spectroscopy has generated substantial interest in the miniaturization of traditional spectroscopic tools, such as spectrometers. However, most state-of-the-art demonstrations face fundamental limits of rank deficiency in the photoresponse matrix. In this work, we demonstrate a miniaturized spectral sensing system using an electrically tunable compact optoelectronic interface, which generates distinguishable photoresponses from various input spectra, enabling accurate spectral identification with a device footprint of 5 micrometers by 5 micrometers.
View Article and Find Full Text PDFEfficacy and safety of Jianpi Qinghua granules for non-erosive reflux disease with spleen deficiency and damp-heat syndrome: a multicenter, randomized, double-blind, placebo-controlled clinical trial.
Front Nutr
January 2025
Peking University Traditional Chinese Medicine Clinical Medical School (Xiyuan), Peking University Health Science Center, Beijing, China.
Background: Non-erosive reflux disease (NERD), the most frequent phenotype of gastroesophageal reflux disease, presents without visible esophageal mucosal damage but significantly impacts patients' quality of life. Current treatments like proton pump inhibitors show limited efficacy for many NERD patients, necessitating alternative approaches. Jianpi Qinghua (JQ) granules, a traditional Chinese medicine, have shown promise in treating NERD by targeting symptoms of spleen deficiency and damp-heat syndrome.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!