Effects of dietary vitamin A concentration of roasted soybean inclusion on marbling, adipose cellularity, and fatty acid composition of beef

A feedlot trial was conducted to determine the effect of dietary vitamin A concentration and roasted soybean (SB) inclusion on carcass characteristics, adipose tissue cellularity, and muscle fatty acid composition. Angus-crossbred steers (n = 168; 295 +/- 1.8 kg) were allotted to 24 pens (7 steers each). Four treatments, in a 2 x 2 factorial arrangement, were investigated: no supplemental vitamin A, no roasted soybeans (NANS); no vitamin A, roasted SB (20% of the diet on a DM basis; NASB); with supplemental (2,700 IU/kg) vitamin A, no roasted SB (WANS); and with supplemental vitamin A, roasted SB (WASB). Diets included high moisture corn, 5% corn silage, 10 to 20% supplement, and 20% roasted SB in the SB treatments on a DM basis. The calculated vitamin A concentration in the basal diet was < 1,300 IU/kg of DM. Blood samples (2 steers/pen) were collected for serum vitamin A determination. Steers were slaughtered after 168 d on feed. Carcass characteristics and LM composition were determined. Fatty acid composition of LM was analyzed, and adipose cellularity in the i.m. and s.c. depots was determined. No vitamin A x SB interactions were detected (P > 0.10) for cattle performance, carcass composition, or muscle fatty acid composition. Low vitamin A diets (NA) did not affect (P > 0.05) ADG, DMI, or G:F. Quality grade tended (P = 0.07) to be greater in NA steers. Marbling scores and the percentage of carcasses grading > or = Choice(-) were 10% greater for NA steers, although these trends were not significant (P = 0.11 and 0.13, respectively). Backfat thickness and yield grade were not affected (P > 0.26) by vitamin A supplementation. Composition of the LM was not affected (P > 0.15) by vitamin A or SB supplementation. Serum retinol at slaughter was 44% lower (P < 0.01) for steers fed NA than for steers supplemented with vitamin A (23.0 vs. 41.1 microg/dL). A vitamin A x SB interaction occurred (P < 0.05) for adipose cellularity in the i.m. depot; when no SB was fed, vitamin A supplementation decreased cell density and increased cell size. However, when SB was fed, vitamin A supplementation did not affect adipose cellularity. Adipose cellularity at the s.c. depot was not affected (P > 0.18) by vitamin A or SB treatments. Fatty acid profile of the LM was not affected by vitamin A (P > 0.05), but SB increased (P < 0.05) PUFA (7.88 vs. 4.30 g/100 g). It was concluded that feeding NA tended to increase marbling without affecting back-fat and yield grade. It appeared that NA induced hyperplasia in the i.m. but not in the s.c. fat depot.

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.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.