Tidal entrances constitute an important boundary condition for the coastal ocean regime. Based on data from 67 sandy entrances in Florida, morphodynamic relationships between tidal prism, entrance throat area, and ebb and flood delta volumes are revisited. The main source of sand in these deltas is the littoral zone as opposed to the river. It is found that, as a rule of thumb, the volume of a mature ebb delta is equal to one fifth of the prism at the spring range of tide. Data for the coasts of Florida taken together indicate that the volume of mature flood delta varies with one third power of the prism. The Atlantic Coast flood delta volumes by themselves do not show any correlation with the prism, presumably because entrance depths have been altered by dredging. A case study of the closure of a land barrier breach at Matanzas Inlet illustrates the application of the derived morphodynamic relationships between prism, throat area, and ebb delta volume. These relationships are useful for prediction of changes in the throat area and the ebb delta volume when morphologic changes occur over time scales consistent with the reestablishment of equilibrium.
Although the backlog of untested sexual assault kits in the United States is starting to be addressed, many municipalities are opting for selective testing of samples within a kit, where only the most probative samples are tested. We use data from the San Francisco Police Department Criminalistics Laboratory, which tests all samples but also collects information on the samples flagged by sexual assault forensic examiners as most probative, to build a standard machine learning model that predicts (based on covariates gleaned from sexual assault kit questionnaires) which samples are most probative. This model is embedded within an optimization framework that selects which samples to test from each kit to maximize the Combined DNA Index System (CODIS) yield (i.e., the number of kits that generate at least one DNA profile for the criminal DNA database) subject to a budget constraint. Our analysis predicts that, relative to a policy that tests only the samples deemed probative by the sexual assault forensic examiners, the proposed policy increases the CODIS yield by 45.4% without increasing the cost. Full testing of all samples has a slightly lower cost-effectiveness than the selective policy based on forensic examiners, but more than doubles the yield. In over half of the sexual assaults, a sample was not collected during the forensic medical exam from the body location deemed most probative by the machine learning model. Our results suggest that electronic forensic records coupled with machine learning and optimization models could enhance the effectiveness of criminal investigations of sexual assaults.
‘Context for the Disc Embedding Theorem’ explains why the theorem is the central result in the study of topological 4-manifolds. After recalling surgery theory and the proof of the s-cobordism theorem for high-dimensional manifolds, the chapter explains what goes wrong when trying to apply the same techniques in four dimensions and how to start overcoming these problems. The complete statement of the disc embedding theorem is provided. Finally the most important consequences to manifold theory are listed, including a proof of why Alexander polynomial one knots are topologically slice and the existence of exotic smooth structures on 4-dimensional Euclidean space.
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