Modern Stochastics: Theory and Applications

The study aimed to assess the impact of ketosis in cows during early lactation, immediately postpartum, on the development of mastitis as a secondary disease and its potential role as a risk factor for recurrent mastitis. This was achieved by monitoring affected udders throughout one lactation period. The research involved N = 156 Holstein Friesian and Simmental cows, divided into three groups of N = 52: the first group included cows with primary postpartum ketosis and secondary mastitis, the second group consisted of cows with mastitis but no ketosis, and the third served as a healthy control group. Ketosis was diagnosed through laboratory analysis of blood, milk, and urine samples for the presence of ketone bodies. Mastitis detection involved clinical evaluation of the udder and microbiological identification of causative pathogens from milk samples. Cows in the first group were monitored throughout lactation to determine the prevalence of recurrent mastitis and identify key risk factors contributing to its recurrence. The findings revealed that recurrent mastitis was diagnosed in 24 cows across both mastitis-affected groups, with Staphylococcus aureus identified as the primary pathogen responsible for recurrence in 87.5% of cases. Additionally, a statistically significant difference in milk yield was observed between the control group and the mastitis-affected groups (P < 0.05). These results suggest that metabolic disorders may contribute to the recurrence of mastitis caused by common pathogens and that mastitis has a significant impact on milk yield in dairy cows.

It seems obvious that intelligent ranking algorithms should outperform recommendations generated at random. But how can we measure how much better they work? In this article, we have established the expected value and variance of the average accuracy at k (AP@k), as they can be used as a foundation for efficiency criteria for MAP@k. Here, we considered two widely used evaluation models: offline and online, together with corresponding randomization models for them, and calculated the expected value and variance of AP@k in both cases. The numerical study for different scenarios was also performed.