Necessary and sufficient conditions for realizability of point processes

We give necessary and sufficient conditions for a pair of (generali- zed) functions 1(r1) and 2(r1, r2), ri 2X, to be the density and pair correlations of some point process in a topological space X, for ex- ample, Rd, Zd or a subset of these. This is an infinite-dimensional version of the classical “truncated moment” problem. Standard tech- niques apply in the case in which there can be only a bounded num- ber of points in any compact subset of X. Without this restriction we obtain, for compact X, strengthened conditions which are necessary and sufficient for the existence of a process satisfying a further re- quirement—the existence of a finite third order moment. We general- ize the latter conditions in two distinct ways when X is not compact.

Chemical composition and fermentation characteristics of grain and different parts of the stover from maize land races harvested at different growing periods in two zones of central Mexico

The objective of this work was to determine the rumen fermentation characteristics of maize land races used as forage in central Mexico. In vitro gas production (ml per 200 mg dry matter (DM)) incubations were carried out, and cumulative gas volumes were fitted to the Krishnamoorthy et al. (1991) model. The trial used a split-plot design with cultivation practices associated with maize colour (COL) as the main plot with three levels: white, yellow and black maize; growing periods (PER) were the split plots where PER1, PER2 and PER3 represented the first, second and third periods, respectively and two contrasting zones (Z1 = valley and Z2 = mountain) were used as blocking factors. The principal effects observed were associated with the maturity of the plants and potential gas production increased (P < 0.05) in stems (PER 1 = 51.8, PER2 = 56.3, PER3 = 58.4 ml per 200 mg DM) and in whole plant (PER 1 = 60.9, PER2 = 60.8, PER3= 70.9 ml per 200 mg DM). An inverse effect was observed with fermentation rates in leaves (P < 0.01) with 0.061, 0.053 and 0.0509 (per h) and in whole plant (P < 0.05) with 0.068, 0.057, 0.050 (per h) in PER1, PER2 and PER3 respectively. The digestibility of the neutral-detergent fibre (NDF) decreased with maturity especially in leaves (P < 0.05) with values of 0.71, 0.67 and 0.66 g/kg; in rachis (P < 0.01) 0.75, 0.72, and 0.65 in PER1, PER2 and PER3 respectively. The NDF content in leaves in leaves (668, 705 and 713 g/kg DM for PER1, PER2 and PER3, respectively), stems (580, 594 and 644 g/kg DM) and, husk (663, 774 and, 808 g/kg DM) increased (P < 0.05) with increasing plant maturity, rachis were significantly different between periods (P < 0.01). The structure with-the best nutritive characteristics was the husk, because it had the lowest fibre contents, especially in acid-detergent lignin, with values of 22.6, 28.6 and 37.6 g/kg DM in PER1, PER2 and PER3, respectively.

Study of the lactation curve in dairy cattle on farms in Central Mexico

Accurate knowledge of lactation curves has an important relevance to management and research of dairy production systems. A number of equations have been proposed to describe the lactation curve, the most widely applied being the gamma equation. The objective of this work was to compare and evaluate candidate functions for their predictive ability in describing lactation curves from central Mexican dairy cows reared under 2 contrasting management systems. Five equations were considered: Gaines ( exponential decay), Wood ( gamma equation), Rook ( Michaelis-Menten x exponential), and 2 more mechanistic ones (Dijkstra and Pollott). A database consisting of 701 and 1283 records of cows in small-scale and intensive systems, respectively, was used in the analysis. Before analysis, the database was divided into 6 groups representing first, second, and third and higher parity cows in both systems. In all cases except second and above parity cows in small-scale systems, all models improved on the Gaines equation. The Wood equation explained much of the variation, but its parameters do not have direct biological interpretation. Although the Rook equation fitted the data well, some of the parameter estimates were not significant. The Dijkstra equation consistently gave better predictions, and its parameters were usually statistically significant and lend themselves to physiological interpretation. As such, the differences between systems and parity could be explained due to variations in theoretical initial milk production at parturition, specific rates of secretory cell proliferation and death, and rate of decay, all of which are parameters in the model. The Pollott equation, although containing the most biology, was found to be over-parameterized and resulted in nonsignificant parameter estimates. For central Mexican dairy cows, the Dijkstra equation was the best option to use in describing the lactation curve.

Modeling small-scale dairy farms in central Mexico using multi-criteria programming

Milk supply from Mexican dairy farms does not meet demand and small-scale farms can contribute toward closing the gap. Two multi-criteria programming techniques, goal programming and compromise programming, were used in a study of small-scale dairy farms in central Mexico. To build the goal and compromise programming models, 4 ordinary linear programming models were also developed, which had objective functions to maximize metabolizable energy for milk production, to maximize margin of income over feed costs, to maximize metabolizable protein for milk production, and to minimize purchased feedstuffs. Neither multicriteria approach was significantly better than the other; however, by applying both models it was possible to perform a more comprehensive analysis of these small-scale dairy systems. The multi-criteria programming models affirm findings from previous work and suggest that a forage strategy based on alfalfa, rye-grass, and corn silage would meet nutrient requirements of the herd. Both models suggested that there is an economic advantage in rescheduling the calving season to the second and third calendar quarters to better synchronize higher demand for nutrients with the period of high forage availability.