Quasipolynomial Computation of Nested Fixpoints

It is well-known that the winning region of a parity game with n nodes and k priorities can be computed as a k-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires $$\mathcal {O}(n^{\frac{k}{2}})$$ O ( n k 2 ) iterations of the function. Calude et al.’s recent quasipolynomial-time parity game solving algorithm essentially shows how to compute the same fixpoint in only quasipolynomially many iterations by reducing parity games to quasipolynomially sized safety games. Universal graphs have been used to modularize this transformation of parity games to equivalent safety games that are obtained by combining the original game with a universal graph. We show that this approach naturally generalizes to the computation of solutions of systems of any fixpoint equations over finite lattices; hence, the solution of fixpoint equation systems can be computed by quasipolynomially many iterations of the equations. We present applications to modal fixpoint logics and games beyond relational semantics. For instance, the model checking problems for the energy $$\mu $$ μ -calculus, finite latticed $$\mu $$ μ -calculi, and the graded and the (two-valued) probabilistic $$\mu $$ μ -calculus – with numbers coded in binary – can be solved via nested fixpoints of functions that differ substantially from the function for parity games but still can be computed in quasipolynomial time; our result hence implies that model checking for these $$\mu $$ μ -calculi is in $$\textsc {QP}$$ QP . Moreover, we improve the exponent in known exponential bounds on satisfiability checking.

La compleja cohabitación jurídica del catalán y el francés en el Rosellón: análisis de políticas lingüísticas en el ámbito educativo

The article describes the legal configuration of France as a monolingual state and analyzes the specific case of the educational system. A certain accommodation of regional languages as a means of instruction has been accomplished, either in time-parity bilingual sections or in immersion schools. In this respect, the data provided by the literature on the case of Catalan in the historic territory of Roussillon are reviewed. The sources analyzed show two main conclusions: (1) the breakdown of intergenerational transmission, which means that there are practically no dialect speakers and that the standard language can only be learned at school; and (2) the enrollment rate either in time-parity bilingual sections or immersion schools is too low to be able to reverse language shift.

56 Impact of Electronically-Controlled Cooling Pads on Physiological Signs of Heat Stress in Early Lactation Sows

The study objective was to evaluate the impact of electronically controlled cooling pads on physiological measurements of heat stress during early lactation. Twelve sows (d 3 to 11 of lactation) were provided with a specially designed cooling pad. Sows randomly received no cooling (CONTROL, n=6) or pads set to flush 2L cool water every 30s when aluminum plate reached 29.5°C (TREAT, n=6). Respiration rates (RR), rectal temperatures (RT) and skin temperatures (ST, 15 cm posterior to the ear) were recorded daily (0700 and 1500 h) for seven days of early lactation. Feed intake (DFI) was measured daily at 0700 h. RR, RT, and ST were fitted to a model that included the effects of day, time, parity, cooling pad treatment, and interactions. DFI was fitted to the same model, excluding time of day. For RR: treatment, day, time, treatment by day, treatment by time, and day by time interactions were significant (P< 0.0004, CONTROL=49, TREAT= 30). Pad treatment had greater impact on RR during the first two days of the trial when the temperature was greater (32°C maximum CONTROL mean=66 vs. TREAT mean=30) than the following five days: 42, and 30 respectively). There was greater treatment impact on RR at 1500 versus 0700 h (0700 h: CONTROL= 35, TREAT= 25; 1500 h: CONTROL= 61, TREAT= 36). For RT: treatment, day, time, parity and interaction of day by time were significant (P< 0.01, CONTROL= 37, treat= 35.). For ST: treatment, day, time, parity and the interactions of time by parity, treatment by time, and day by time were significant (P< 0.0006, mean CONTROL=36.5, TREAT= 35.1). For DFI: day and the interaction of day by treatment were significant. The difference in feed intake between treatments increased as day increased. The use of electronically controlled cooling pads reduced measures of heat stress in early lactating sows.

Estimating Breeding values for milk production and mastitis traits for Holstein cattle in Egypt

<p class="abstrak2">This study was carried out to evaluate the sires and dams genetically for milk production and mastitis traits in Egyptian 12 herds of Holstein cattle using Best Linear Unbiased Prediction via MTDFREML program. The data was obtained from a commercial farm called Dena, located in Cairo-Alex Desert Road (80 Km), Menofia, Egypt. Data included 4791 cows, 4227 dams and 248 sires that represented the period from 2007 to 2014. Estimating breeding values for milk production traits as cumulative milk yield at 90 days (90-DM), cumulative milk yield at 180 days (180-DM), cumulative milk yield at 270 days (270-DM), cumulative milk yield at 305 days (305-DM), and number of mastitis infection around the season of lactation (MAST). The averages of the 90-DM, 180-DM, 270-DM, 305-DM and MAST were 3026.3±655.1 kg, 5873.3±1081.1 kg, 7891.1±2692.2 kg, 9611.2±1897.9 kg, and 0.712±1.2 time/parity, respectively. Estimates of heritability for the previous traits were 0.11±0.016, 0.15±0.014, 0.18±0.012, 0.22±0.015, and 0.09±0.029, respectively; genetic variance were 47206.2 kg, 175300.6 kg, 1304654.4 kg, 792411.6 kg and 0.12 time/parity, respectively; and phenotypic variance were 429147.6 kg, 1168670.6 kg, 7248079.9 kg, 3601870.9 kg, and 1.35 time/parity, respectively. The EBV values as average, SD, (Min: Max) for sires were 0.0±0.179 (-0.4: 0.66) for MAST, 0.0±86.176 (-263.1: 245.4) for 90-DM, 0.0±227.523 (-600.3: 800.3) for 180-DM, 0.0±413.48 (-323.3: 1277.7) for 270-DM and 0.0±440.26 (-1280.9: 1565.1) for 305-DM. Also, The EBVs for dams were 0.0±0.055 (-0.14: 0.45) for MAST, 0.033±26.24 (-142.8: 103.0) for 90-DM, 0.074±76.81 (-360.2: 289.6) for 180-DM, -0.045±139.66 (-591.9: 529.2) for 270-DM and 0.266±154.1 (-666.3: 617.6) for 305-DM. These results provide that the selection of sires and dams will improve the traits of milk production and mastitis in this herd because of the wide differences in genetic potential among sires and dams.</p>