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Any collection of non-blocking four-dimensional cubes, whose total volume does not exceed 17/81, can be packed into the unit four-dimensional cube. This bound is tight for the parallel packing. [ABSTRACT FROM AUTHOR]

The aim: In this study was to determine if sigmoid colorectal cancer (SCC) and colorectal cancer (CRC) in women (W) and men (M) is accompanied by zearalenone (ZEN) mycotoxicosis and changes in selected steroid levels. Materials and Methods: This cohort study was conducted on female and male patients selected from a population based on the presence of SCC or CRC, which was accompanied by the presence or absence (control group) of ZEN in their blood. The control group consisted of 17 patients with symptoms of SCC and CRC, where ZEN and its metabolites were not detected in the peripheral blood. The experimental groups comprised a total of 16 patients with SCC and CRC, where ZEN, but not its metabolites, was detected in their peripheral blood samples. Results: In groups SCC and CRC, the ZEN levels were very high, in the range from 214 to 289 ng/mL of blood. Considerable variations were observed in the concentrations of steroid hormones. Estradiol (E2) levels ranged from 166.25 (group C) to 325 pg/mL (group CRC) in women and from 98 (group C) to 95.5 pg/mL (group CRC) in men. Progesterone (P4) levels ranged from 12.09 (group C) to 13.64 ng/mL (group SCC) in women and from 6.98 (group CRC) to 12.01 ng/mL (group C) in men. Conclusions: These results indicate that post-menopausal women and similarly aged elderly men have a high and individualized demand for estrogen that is relatively effectively met by ZEN, which triggers qualitative changes in estrogen receptors. The shortage of ZEN metabolites (values under the sensitivity of the method) confirmed the high estrogen demand in the studied subjects. The presence or absence of ZEN could have influenced the therapeutic outcomes in the analyzed patients. [ABSTRACT FROM AUTHOR]

Simple Summary: African catfish is one of the most perspective fish species in modern aquaculture. However, the main cost involved in its production is focused chiefly on the cost of feeds. The main reason for this is the behavior of this species (predatory fish) and the high rate of cannibalism in intensive culture. That is why it is essential to assess functional bioactive additives to be used in commercial feed with a positive effect on the growth and survival rates of this commercially valued fish species. In the present study, African catfish juveniles were fed diets enriched with honeybee pollen (BP) and were tested for growth, survival, intestinal microbiota, and tissue histomorphology. It has been shown that BP addition positively affected all the analyzed parameters. This research study spotlights the benefits of BP as a prebiotic supplement for improving the functionality of feeds prepared for African catfish. This study aimed to determine the dietary effects of honeybee pollen (BP) on growth parameters, intestinal microbiota, hepatic histoarchitecture, and intestinal histomorphometry of African catfish Clarias gariepinus juveniles. The feeding experiment was carried out in a recirculating aquaculture system under controlled conditions for 21 days to achieve more than a 10-fold increase in weight in fish from the control group. Fish were fed well-balanced commercial feed without any supplements and served as a reference group (group C) and other diets enriched with varying BP levels as 1% (BP1), 2% (BP2), and 3% (BP3). Results showed a significant (p < 0.05) effect of the dietary BP not only on the growth parameters (such as final body weight: 5.0 g to 6.6–7.5 g, weight gain: 0.23 g/d to 0.31–0.35 g/d, body length: 84.7 mm to 93.8–95.9 mm, and specific growth rate: 11.7%/d to 13.1–13.7%/d, group C vs. experimental groups, respectively) but also on the development of beneficially important gut microbiota, such as lactic acid-producing bacteria. In BP-enriched groups, an average of 45% higher body weight gain was observed compared to those reared in the control group. The histological analysis showed that dietary BP may have a positive effect on the development of the intestinal tract and may enhance the absorption of nutrients with the potential ability to maintain a normal hepatic histoarchitecture of the treated African catfish. The results obtained suggest the optimum level of BP additive to feed for African catfish should be 1%. [ABSTRACT FROM AUTHOR]