Cryopreservation provides a critical tool for dairy herd genetics management. Due to widely varying inter- and within-bull post thaw fertility, recent research on cryoprotectant extender medium has not dramatically improved suboptimal post-thaw recovery in industry. This progress is stymied by the interactions between samples and the many components of extender media and is often compounded by industry irrelevant sample sizes. To address these challenges, here we demonstrate blank-slate optimization of bull sperm cryopreservation media by supervised machine learning. We considered two supervised learning models: artificial neural networks and Gaussian process regression (GPR). Eleven media components and initial concentrations were identified from publications in bull semen cryopreservation, and an initial 200 extender-post-thaw motility pairs were used to train and 32 extender-post-thaw motility pairs to test the machine learning algorithms. The median post-thaw motility after coupling differential evolution with GPR the increased from 52.6 ± 6.9% to 68.3 ± 6.0% at generations 7 and 17 respectively, with several media performing dramatically better than control media counterparts. This is the first study in which machine learning was used to determine the best combination of constituents to optimize bull sperm cryopreservation media, and provides a template for optimization in other cell types.

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The set of primes where a hypergeomeric series with rational parameters is padically bounded is known by [10] to have a Dirichlet density. We establish a formula for this Dirichlet density and conjecture that it is rare for the density to be large. We prove this conjecture for hypergeometric series whose parameters have denominators equal to a prime of the form p = 2q r + 1, where q is an odd prime, by establishing an upper bound on the density of bounded primes in this case. The general case remains open. This paper is the output of an undergraduate research course taught by the first listed author in the winter semester of 2018.