For computing the exact value of the halfspace depth of a point w.r.t. a data cloud of n points in arbitrary dimension, a theoretical framework is suggested. Based on this framework a whole class of algorithms can be derived. In all of these algorithms the depth is calculated as the minimum over a finite number of depth values w.r.t. proper projections of the data cloud. Three variants of this class are studied in more detail. All of these algorithms are capable of dealing with data that are not in general position and even with data that contain ties. As is shown by simulations, all proposed algorithms prove to be very efficient.
The demographic shift in the human population reflects an aging society-over 20% of Europeans are predicted to be 65 or over by the year 2025 (Riera & Dillin, 2015). Aging is the major risk factor for developing chronic diseases, such as cancer, Alzheimer's disease, and cardiovascular complications (Partridge et al., 2018).Unfortunately, humans spend on average one-fifth of their lifetime in poor health suffering from one or multiple age-related chronic diseases (Partridge et al., 2018). However, the onset of age-related pathologies is not fixed, and the rate of aging was shown to be malleable. The goal of biomedical research on aging or geroscience is to identify interventions that compress late-life morbidity to increase the period spent healthy and free from disease.
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