Structures involving a lattice and join-endomorphisms on it are ubiquitous in computer science. We study the cardinality of the set E(L) of all joinendomorphisms of a given finite lattice L. In particular, we show that when L is Mn, the discrete order of n elements extended with top and bottom, |E(L)| = n!Ln(−1) + (n + 1) 2 where Ln(x) is the Laguerre polynomial of degree n. We also study the following problem: Given a lattice L of size n and a set S ⊆ E(L) of size m, find the greatest lower bound E(L) S. The join-endomorphism E(L) S has meaningful interpretations in epistemic logic, distributed systems, and Aumann structures. We show that this problem can be solved with worst-case time complexity in O(n + m log n) for powerset lattices, O(mn 2) for lattices of sets, and O(mn + n 3) for arbitrary lattices. The complexity is expressed in terms of the basic binary lattice operations performed by the algorithm.

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This study was designed to determine whether any relationship exists between exposure to artificial long days, milk yield, maternal plasma insulin-like growth factor 1 (IGF-1) levels, and kid growth rate in goats. One group of lactating goats was maintained under naturally decreasing day length (control group; n = 19), while in another one, they were kept under artificial long days (LD group; n = 19). Milk yield was higher in goats from the LD group than that in the control group (P < 0.05). Maternal IGF-1 levels at day 57 of lactation were higher (P < 0.05) in goats from the LD group than the levels in the control group and were positively correlated with the total milk yields per goat at days 43 and 57 of lactation (r = 0.77 and r = 0.84, respectively; P < 0.01). Daily weight gain at week 4 was higher (P < 0.01) in kids from the LD group than that in kids from the control group and was correlated with total and average IGF-1 maternal levels (r = 0.60 and r = 0.60, P < 0.05). It was concluded that submitting lactating goats to artificial long days increases milk yield, plasma IGF-1 maternal levels and the growth rate of the kids.

Background: Peer methodology (PM) is an adaptation of the privileged access interviewer methodology and is (Rev Méd Chile 2009; 137: 774-84).

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Process calculi provide a language in which the structure of terms represents the structure of processes together with an operational semantics to represent computational steps. This paper uses rewriting logic for specifying and analyzing a process calculus for concurrent constraint programming (ccp), combining spatial and real-time behavior. In these systems, agents can run processes in different computational spaces (e.g., containers) while subject to real-time requirements (e.g., upper bounds in the execution time of a given operation), which can be specified with both discrete and dense linear time. The real-time rewriting logic semantics is fully executable in Maude with the help of rewriting modulo SMT: partial information (i.e., constraints) in the specification is represented by quantifier-free formulas on the shared variables of the system that are under the control of SMT decision procedures. The approach is used to symbolically analyze existential real-time reachability properties of process calculi in the presence of spatial hierarchies for sharing information and knowledge.