In a study, scientists compared the skin microbiomes of infants who developed eczema and those who did not. Skin microbes were sampled from both groups in early infancy. The microbiome was less diverse in infants who later developed eczema, compared to the more diverse skin microbiome found in infants who remained eczema-free. According to some studies, mothers' skin secretions during birth and early skin contact transfer a modified set of protective lipids to the newborn. This is not used by the infant for its own energy needs. However, the bacteria colonising the infant's skin thrive on these lipids, which serve as their food. Mothers with skin conditions like eczema themselves have been shown to have lower levels of these protective lipids. Consequently, the skin microbiomes of their infants fail to diversify properly. That, in turn, leads to a higher risk of eczema in the infant.

On the basis of the above passage, the following assumptions have been made:

1. Topical probiotic creams are a solution to treat infants at risk of eczema due to an immature skin microbiome.

2. Infants of mothers who have eczema themselves generally tend to be at higher risk of eczema.

Which of the above assumptions is/are valid?