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This paper deals with detecting change of distribution in multi-dimensional data sets. For a given baseline data set and a set of newly observed data points, we define a statistical test called the density test for deciding if the observed data points are sampled from the underlying distribution that produced the baseline data set. We define a test statistic that is strictly distribution-free under the null hypothesis. Our experimental results show that the density test has substantially more power than the two existing methods for multi-dimensional change detection.

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Bruton's tyrosine kinase proteolysis-targeting chimeras (BTK-PROTACs) have emerged as a promising approach to address the limitations of BTK inhibitors. However, conducting the rational discovery of orally bioavailable BTK-PROTACs presents significant challenges. In this study, dimensionality reduction analysis and model molecule validation were utilized to identify some key structural features for improving the oral absorption of BTK-PROTACs. The results were applied to optimize the newly discovered BTK-PROTACs B1 and B2. Compound C13 was discovered with improved oral bioavailability, high BTK degradation activity, and selectivity. It exhibited inhibitory effects against different hematologic cancer cells and attenuated the BTK-related signaling pathway. The oral administration of C13 effectively reduced BTK protein levels and suppressed tumor growth. This study led to the discovery of a new orally bioavailable BTK-PROTAC for the treatment of lymphoma, and we hope that the strategy will find wide utility.