Words without Near-Repetitions

We find an infinite word w on four symbols with the following property: Two occurrences of any block in w must be separated by more than the length of the block. That is, in any subword of w of the form xyx, the length of y is greater than the length of x. This answers a question of C. Edmunds connected to the Burnside problem for groups.The research of the first author was supported by an NSERC Operating Grant. The second author was supported by an NSERC Undergraduate Summer Research Award.https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/words-without-nearrepetitions/F86509D865F222F1FC63ACA8545C069

Preventing type 1 diabetes in childhood

Type 1 diabetes (T1D) is an autoimmune disease in which the insulin-producing β cells of the pancreas are destroyed by T lymphocytes. Recent studies have demonstrated that monitoring for pancreatic islet autoantibodies, combined with genetic risk assessment, can identify most children who will develop T1D when they still have sufficient β cell function to control glucose concentrations without the need for insulin. In addition, there has been recent success in secondary prevention using immunotherapy to delay the progression of preclinical disease, and primary prevention approaches to inhibiting the initiating autoimmune process have entered large-scale clinical trials. By changing the focus of T1D management from late diagnosis and insulin replacement to early diagnosis and β cell preservation, we can anticipate a future without the need for daily insulin injections for children with T1D