Effects of forage source and extruded linseed supplementation on methane emissions from growing dairy cattle of differing body weights

Changes in diet carbohydrate amount and type (i.e., starch vs. fiber) and dietary oil supplements can affect ruminant methane emissions. Our objectives were to measure methane emissions, whole-tract digestibility, and energy and nitrogen utilization from growing dairy cattle at 2 body weight (BW) ranges, fed diets containing either high maize silage (MS) or high grass silage (GS), without or with supplemental oil from extruded linseed (ELS). Four Holstein-Friesian heifers aged 13 mo (BW range from start to finish of 382 to 526 kg) were used in experiment 1, whereas 4 lighter heifers aged 12 mo (BW range from start to finish of 292 to 419 kg) were used in experiment 2. Diets were fed as total mixed rations with forage dry matter (DM) containing high MS or high GS and concentrates in proportions (forage:concentrate, DM basis) of either 75:25 (experiment 1) or 60:40 (experiment 2), respectively. Diets were supplemented without or with ELS (Lintec[AU1: Add manufacturer name and location.]; 260 g of oil/ kg of DM) at 6% of ration DM. Each experiment was a 4 × 4 Latin square design with 33-d periods, with measurements during d 29 to 33 while animals were housed in respiration chambers. Heifers fed MS at a heavier BW (experiment 1) emitted 20% less methane per unit of DM intake (yield) compared with GS (21.4 vs. 26.6, respectively). However, when repeated with heifers of a lower BW (experiment 2), methane yield did not differ between the 2 diets (26.6 g/kg of DM intake). Differences in heifer BW had no overall effect on methane emissions, except when expressed as grams per kilogram of digestible organic matter (OMD) intake (32.4 vs. 36.6, heavy vs. light heifers). Heavier heifers fed MS in experiment 1 had a greater DM intake (9.4 kg/d) and lower OMD (755 g/kg), but no difference in N utilization (31% of N intake) compared with heifers fed GS (7.9 kg/d and 799 g/kg, respectively). Tissue energy retention was nearly double for heifers fed MS compared with GS in experiment 1 (15 vs. 8% of energy intake, respectively). Heifers fed MS in experiment 2 had similar DM intake (7.2 kg/d) and retention of energy (5% of intake energy) and N (28% of N intake), compared with GS-fed heifers, but OMD was lower (741 vs. 765 g/kg, respectively). No effect of ELS was noted on any of the variables measured, irrespective of animal BW, and this was likely due to the relatively low amount of supplemental oil provided. Differences in heifer BW did not markedly influence dietary effects on methane emissions. Differences in methane yield were attributable to differences in dietary starch and fiber composition associated with forage type and source.

Weak constraints in four-dimensional variational data assimilation

The formulation of four-dimensional variational data assimilation allows the incorporation of constraints into the cost function which need only be weakly satisfied. In this paper we investigate the value of imposing conservation properties as weak constraints. Using the example of the two-body problem of celestial mechanics we compare weak constraints based on conservation laws with a constraint on the background state.We show how the imposition of conservation-based weak constraints changes the nature of the gradient equation. Assimilation experiments demonstrate how this can add extra information to the assimilation process, even when the underlying numerical model is conserving.

Perspex machine VII: The universal perspex machine

The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The new arithmetic has both a positive and a negative infinity which lie at the extremes of the number line, and a number nullity that lies off the number line. We prove that nullity, 0/0, is a number. Hence a number may have one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the sign of a number in one bit, as floating-, point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the usual contradictions that follow from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." We argue that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of mind and. perhaps, the whole of mind relates to the geometrical aspects of body and, perhaps, the whole of body. We review some of Turing's writings and show that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, we read Turing as believing that his machine relates computation to geometrical bodies. We simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to pro-ram than the original perspex-machine. We then show how to map the whole of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but we make no claim that the physical universe works this way or that it has the cardinality of the perspex machine. We leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line.