Crossings, Motzkin paths and Moments

Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain $q$-analogues of Laguerre and Charlier polynomials. The moments of these orthogonal polynomials have combinatorial models in terms of crossings in permutations and set partitions. The aim of this article is to prove simple formulas for the moments of the $q$-Laguerre and the $q$-Charlier polynomials, in the style of the Touchard-Riordan formula (which gives the moments of some $q$-Hermite polynomials, and also the distribution of crossings in matchings). Our method mainly consists in the enumeration of weighted Motzkin paths, which are naturally associated with the moments. Some steps are bijective, in particular we describe a decomposition of paths which generalises a previous construction of Penaud for the case of the Touchard-Riordan formula. There are also some non-bijective steps using basic hypergeometric series, and continued fractions or, alternatively, functional equations.Comment: 21 page

Costs Associated with Low Birth Weight in a Rural Area of Southern Mozambique

BACKGROUND: Low Birth Weight (LBW) is prevalent in low-income countries. Even though the economic evaluation of interventions to reduce this burden is essential to guide health policies, data on costs associated with LBW are scarce. This study aims to estimate the costs to the health system and to the household and the Disability Adjusted Life Years (DALYs) arising from infant deaths associated with LBW in Southern Mozambique. METHODS AND FINDINGS: Costs incurred by the households were collected through exit surveys. Health system costs were gathered from data obtained onsite and from published information. DALYs due to death of LBW babies were based on local estimates of prevalence of LBW (12%), very low birth weight (VLBW) (1%) and of case fatality rates compared to non-LBW weight babies [for LBW (12%) and VLBW (80%)]. Costs associated with LBW excess morbidity were calculated on the incremental number of hospital admissions in LBW babies compared to non-LBW weight babies. Direct and indirect household costs for routine health care were 24.12 US$(CI 95$ (CI 95% 6.33; 10.72). Of the 3,322 live births that occurred in one year in the study area, health system costs associated to LBW (routine health care and excess morbidity) and DALYs were 169,957.61 US$ (CI 95% 144,900.00; 195,500.00) and 2,746.06, respectively. CONCLUSIONS: This first cost evaluation of LBW in a low-income country shows that reducing the prevalence of LBW would translate into important cost savings to the health system and the household. These results are of relevance for similar settings and should serve to promote interventions aimed at improving maternal care

Use of tandem mass spectrometry as a tool for proteomics studies in aging and degeneration processes of the intervertebral disc

International Society for the Study of the Lumbar Spine (ISSLS) - Biochemistry: Poster Presentation: no. P24

Transcriptome of the human intervertebral disc in health and disease

Symposium 2 - Disc degeneration mechanisms: S2.9The 2010 World Forum for Spine Research (WFSR 2010): The Intervertebral Disc, Montreal, Canada, 5-8 July 2010

Mechanistic insight into chondrocyte adaptation to ER stress

Oral Presentation - Session 2: Reproduction & Development, Musculoskeletal System and Cell Biology: 2.17The 15th Research Postgraduate Symposium (RPS 2010), the University of Hong Kong, Hong Kong, China, 1-2 December 2010

Cholesterol biosynthesis is a potential pathway involved in the degeneration of the annulus fibrosus

Posters: P1060The 2010 World Forum for Spine Research (WFSR 2010): The Intervertebral Disc, Montreal, Canada, 5-8 July 2010