Application of Generalized Inverses and Circulant Matrices to Iterated Functions on Integers

After reviewing fundamental properties of matrix generalized inverses and circulant matrices, we describe a particular application in which both of these concepts play an important role. In particular, we establish the form of the Moore-Penrose generalized inverse of a type of circulant matrix that arises naturally in the study of iterated functions on integers

Catch-up growth in children with chronic kidney disease started on enteral feeding after 2 years of age

BACKGROUND: Enteral feeding by tube in chronic kidney disease (CKD) before 2 years of age improves growth. Whether it is effective after this age is unknown. We assessed whether height and weight SDS changed after tube feeding was started in children with CKD above 2 years of age. METHODS: Retrospective study of pre-transplant, pre-pubertal children (< 11 years) with CKD stages 2–5 started on nasogastric tube or gastrostomy feeds for the first time after age 2 years. Children were identified by searching dietetic records and the renal database. Children on growth hormone were excluded. Height, weight, and BMI were documented 1 year prior to and at the start of tube feeds, and after 1 and 2 years. Data collection ceased at transplantation. RESULTS: Fifty children (25 male) were included. The median (range) age at start of tube feeds was 5.6 (2.1–10.9) years. Sixteen children were dialysed (1 haemodialysis, 15 peritoneal dialysis); 34 predialysis patients had a median (range) eGFR of 22 (6–88) ml/min/1.73 m2. Overall height SDS (Ht SDS) improved from − 2.39 to − 2.27 at 1 year and − 2.18 after 2 years (p = 0.02). BMI SDS improved from − 0.72 to 0.23 after 1 year and was 0.09 after 2 years of enteral feeding (p < 0.0001). Height SDS improved more in children aged 2–6 years (− 2.13 to − 1.68, p = 0.03) and in children not on dialysis (− 2.33 to − 1.99, p = 0.002). CONCLUSIONS: Enteral tube feeding commenced after 2 years of age in prepubertal children with CKD improves height and weight SDS, with stability of BMI during the second year. Younger children and those not on dialysis had the greatest benefit

A cross-sectional survey of cardiovascular health and lifestyle habits of hospital staff in the UK: Do we look after ourselves?

Background: A high prevalence of stress-related disorders is well known among healthcare professionals. We set out to assess the prevalence of cardiovascular risk factors and compliance with national dietary and physical activity recommendations in NHS staff in the UK with comparison between clinical and non-clinical staff, and national surveys. Design: A multi-centre cross-sectional study. Methods: A web-based questionnaire was developed to include anonymised data on demographics, job role, cardiovascular risk factors and diseases, dietary habits, physical activity and barriers towards healthy lifestyle. This was distributed to staff in four NHS hospitals via emails. Results: A total of 1158 staff completed the survey (response rate 13%) with equal distribution between the clinical and non-clinical groups. Most staff were aged 26–60 years and 79% were women. Half of the staff were either overweight or obese (51%) with no difference between the groups (P = 0.176), but there was a lower prevalence of cardiovascular risk factors compared to the general population. The survey revealed a low compliance (17%) with the recommended intake of five-a-day portions of fruit and vegetables, and that of moderate or vigorous physical activity (56%), with no difference between the clinical and non-clinical staff (P = 0.6). However, more clinical staff were exceeding the alcohol recommendations (P = 0.02). Lack of fitness facilities and managerial support, coupled with long working hours, were the main reported barriers to a healthy lifestyle. Conclusions: In this survey of UK NHS staff, half were found to be overweight or obese with a lower prevalence of cardiovascular risk factors compared to the general population. There was a low compliance with the five-a-day fruit and vegetables recommendation and physical activity guidelines, with no difference between the clinical and non-clinical staff

Ex vivo detection and characterization of early dental caries by optical coherence tomography and Raman spectroscopy.

Early dental caries detection will facilitate implementation of nonsurgical methods for arresting caries progression and promoting tooth remineralization. We present a method that combines optical coherence tomography (OCT) and Raman spectroscopy to provide morphological information and biochemical specificity for detecting and characterizing incipient carious lesions found in extracted human teeth. OCT imaging of tooth samples demonstrated increased light backscattering intensity at sites of carious lesions as compared to the sound enamel. The observed lesion depth on an OCT image was approximately 290 mm matching those previously documented for incipient caries. Using Raman microspectroscopy and fiber-optic- based Raman spectroscopy to characterize the caries further, spectral changes were observed in PO 42 vibrations arising from hydroxyapa- tite of mineralized tooth tissue. Examination of various ratios of PO 42 n 2 , n 3 , n 4 vibrations against the n 1 vibration showed consistent in- creases in carious lesions compared to sound enamel. The changes were attributed to demineralization-induced alterations of enamel crystallite morphology and/or orientation. OCT imaging is useful for screening carious sites and determining lesion depth, with Raman spectroscopy providing biochemical confirmation of caries. The com- bination has potential for development into a new fiber-optic diagnos- tic tool enabling dentists to identify early caries lesions with greater sensitivity and specificity. © 2005 Society of Photo-Optical Instrumentation Engi

Polymer electrolyte direct methanol fuel cells: an option for transportation applications

PEFCs most frequently considered for electric vehicles have been based on either hydrogen carried aboard, or steam-reforming of methanol on board to produce H2 + CO2. Direct methanol fuel cells (DMFCs), which use a liquid methanol fuel feed, completely avoid the complexity and weight penalties of the reformer, but have not been considered a serious option until recently, because of much lower power densities. Recent advances in DMFCs have been dramatic, however, with the DMFC reaching power densities which are significant fractions of those provided by reformate/air fuel cells. Use of established Pt-Ru anode electrocatalysts and Pt cathode electrocatalysts in polymer electrolyte DMFCs has resulted in enhanced DMFC performance, particularly when operated above 100 C and when catalyst layer composition and structure are optimized. The higher DMFC power densities recently achieved provide a new basis for considering DMFCs for transportation applications

Multiagency approaches to preventing sudden unexpected death in infancy (SUDI): a review and analysis of UK policies

Background Recent reviews of sudden unexpected deaths in infancy (SUDI) in England recommend a multiagency working (MAW) approach to prevention but lack clear guidance around how this might be implemented.Aims In England, local authorities commission and oversee public health services. This review examines how local authority policies address implementation of MAW for SUDI prevention to understand local variations and identify strengths and weaknesses.Methods Using a comprehensive list of all metropolitan, county, unitary councils and London boroughs in England, we systematically searched local authority websites for relevant published documents and submitted freedom of information (FOI) requests where policies or guidance for SUDI prevention had not been sourced online. We extracted data from documents using a standardised form to summarise policy contents which were then collated, described and appraised.Findings We searched the websites of 152 council and London boroughs, identifying 36 relevant policies and guidelines for staff. We submitted 116 FOI requests which yielded 64 responses including six valid documents: 45% (52/116) of local authorities did not respond. Seventeen councils shared the same guidance under safeguarding partnerships; removal of duplicates resulted in 26 unique documents. Only 15% (4/26) of the documents included a detailed plan for how MAW approaches were to be implemented despite 73% (19/26) of the documents mentioning the importance of engaging the MAW in raising awareness of safe sleep for babies with vulnerable families. Five areas of variation were identified across policies: (1) scope, (2) responsibilities, (3) training, (4) implementation and (5) evaluation.Conclusions There are discrepancies between local authorities in England in whether and how MAW for SUDI prevention is carried out. Strengths and weaknesses of approaches are identified to inform future development of MAW for SUDI prevention

The stone adze and obsidian assemblage from the Talasiu site, Kingdom of Tonga

Typological and geochemical analyses of stone adzes and other stone tools have played a significant role in identifying directionality of colonisation movements in early migratory events in the Western Pacific. In later phases of Polynesian prehistory, stone adzes are important status goods which show substantial spatial and temporal variation. However, there is a debate when standardisation of form and manufacture appeared, whether it can be seen in earliest populations colonising the Pacific or whether it is a later development. We present in this paper a stone adze and obsidian tool assemblage from an early Ancestral Polynesian Society Talasiu site on Tongatapu, Kingdom of Tonga. The site shows a wide variety of adze types; however, if raw material origin is taken into account, emerging standardisation in adze form might be detected. We also show that Tongatapu was strongly connected in a network of interaction to islands to the North, particularly Samoa, suggesting that these islands had permanent populations

Root canal morphology of primary maxillary second molars:a micro-computed tomography analysis

Aim Successful endodontic treatment of primary teeth requires comprehensive knowledge and understanding of root canal morphology. The purpose of this study was to investigate the root canal configurations of primary maxillary second molars using micro-computed tomography. Methods Extracted human primary maxillary second molars (n = 57) were scanned using micro-computed tomography and reconstructed to produce three-dimensional models. Each root canal system was analysed qualitatively according to Vertucci's classification. Results 22.8% (n = 13) of the sample presented with the fusion of the disto-buccal and palatal roots; of these, Type V was the most prevalent classification. For teeth with three separate roots (n = 44), the most common root canal type was Type 1 for the palatal canal (100%) and disto-buccal canal (77.3%) and Type V for the mesio-buccal canal (36.4%). Overall, 7% (n = 4) of mesio-buccal canals were 'unclassifiable'. Conclusion The root canal systems of primary maxillary second molars were not only complex but had a range of configurations that may contribute to unfavourable clinical outcomes after endodontic treatment