Fast FIR Algorithms for the Continuous Wavelet Transform From Constrained Least Squares

New algorithms for the continuous wavelet transform are developed that are easy to apply, each consisting of a single-pass finite impulse response (FIR) filter, and several times faster than the fastest existing algorithms. The single-pass filter, named WT-FIR-1, is made possible by applying constraint equations to least-squares estimation of filter coefficients, which removes the need for separate low-pass and high-pass filters. Non-dyadic two-scale relations are developed and it is shown that filters based on them can work more efficiently than dyadic ones. Example applications to the Mexican hat wavelet are presented.

Programming rumen bacterial communities in newborn Merino lambs

Establishment of the rumen microbiome can be affected by both early-life dietary measures and rumen microbial inoculation. This study used a 2 × 3 factorial design to evaluate the effects of inclusion of dietary fat type and the effects of rumen inoculum from different sources on ruminal bacterial communities present in early stages of the lambs’ life. Two different diets were fed ad libitum to 36 pregnant ewes (and their lambs) from 1 month pre-lambing until weaning. Diets consisted of chaffed lucerne and cereal hay and 4% molasses, with either 4% distilled coconut oil (CO) provided as a source of rumen-active fat or 4% Megalac® provided as a source of rumen-protected fat (PF). One of three inoculums was introduced orally to all lambs, being either (1) rumen fluid from donor ewes fed the PF diet; (2) rumen fluid from donor ewes fed CO; or (3) a control treatment of MilliQ-water. After weaning at 3 months of age, each of the six lamb treatment groups were grazed in spatially separated paddocks. Rumen bacterial populations of ewes and lambs were characterised using 454 amplicon pyrosequencing of the V3/V4 regions of the 16S rRNA gene. Species richness and biodiversity of the bacterial communities were found to be affected by the diet in ewes and lambs and by inoculation treatment of the lambs. Principal coordinate analysis and analysis of similarity (ANOSIM) showed between diet differences in bacterial community groups existed in ewes and differential bacterial clusters occurred in lambs due to both diet and neonatal inoculation. Diet and rumen inoculation acted together to clearly differentiate the bacterial communities through to weaning, however the microbiome effects of these initial early life interventions diminished with time so that rumen bacterial communities showed greater similarity 2 months after weaning. These results demonstrate that ruminal bacterial communities of newborn lambs can be altered by modifying the diet of their mothers. Moreover, the rumen microbiome of lambs can be changed by diet while they are suckling or by inoculating their rumen, and resulting changes in the rumen bacterial microbiome can persist beyond weaning.