The crocodilia have multiple interesting characteristics that affect their population dynamics. They are among several reptile species which exhibit temperature-dependent sex determination (TSD) in which the temperature of egg incubation determines the sex of the hatchlings. Their life parameters, specifically birth and death rates, exhibit strong age-dependence. We develop delay-differential equation (DDE) models describing the evolution of a crocodilian population. In using the delay formulation, we are able to account for both the TSD and the age-dependence of the life parameters while maintaining some analytical tractability. In our single-delay model we also find an equilibrium point and prove its local asymptotic stability. We numerically solve the different models and investigate the effects of multiple delays on the age structure of the population as well as the sex ratio of the population. For all models we obtain very strong agreement with the age structure of crocodilian population data as reported in Smith and Webb (Aust. Wild. Res. 12, 541-554, 1985). We also obtain reasonable values for the sex ratio of the simulated population.

Multitarget-Multisensor tracking metrics have been studied extensively in recent years. These tracking metrics require a unique assignment of tracks to truth objects at each scoring time. There are two typical approaches to address this track-to-truth assignment problem. The first approach involves developing content vectors for the measurements (i.e., vectors indicating the percentage of each truth object content in a measurement) and tracing through the computer simulations and tracking algorithms the contribution of each truth object to the tracks via the content vectors. The second approach involves the kinematic assignment of tracks to the truth objects. This second approach does not require any special design considerations in the computer simulation, and it can be used with flight test data. In this paper, a multiple hypothesis or multiple frame approach is taken to the kinematic assignment of tracks to truth, and a minimum constraint is placed on the sojourn time of those assignments to eliminate artificial switches when tracks on closely spaced and possibly unresolved objects are scored. The multiple frame approach to track-to-truth assignment is applied to simulated data and the results are compared to assignment results from single frame assignment with no constraint on the sojourn time and content vectors.

Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their properties. In particular, we formulate a theory of transport duals for probabilistic frames and prove certain properties of this class. We also investigate paths of probabilistic frames, identifying conditions under which geodesic paths between two such measures are themselves probabilistic frames. In the discrete case this is related to ranks of convex combinations of matrices, while in the continuous case this is related to the continuity of the optimal transport plan.

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In this paper we bring together some of the key ideas and methods of two very lively fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular, we construct gradient flows in the Wasserstein space P 2`ǫ pR d q for potentials of interest in frame theory.