Extending the Latent Multinomial Model with Complex Error Processes and Dynamic Markov Bases

The latent multinomial model (LMM) model of Link et al. (2010) provided a general framework for modelling mark-recapture data with potential errors in identification. Key to this approach was a Markov chain Monte Carlo (MCMC) scheme for sampling possible configurations of the counts true capture histories that could have generated the observed data. This MCMC algorithm used vectors from a basis for the kernel of the linear map between the true and observed counts to move between the possible configurations of the true data. Schofield and Bonner (2015) showed that a strict basis was sufficient for some models of the errors, including the model presented by Link et al. (2010), but a larger set called a Markov basis may be required for more complex models. We address two further challenges with this approach: 1) that models with more complex error mechanisms do not fit easily within the LMM and 2) that the Markov basis can be difficult or impossible to compute for even moderate sized studies. We address these issues by extending the LMM to separately model the capture/demographic process and the error process and by developing a new MCMC sampling scheme using dynamic Markov bases. Our work is motivated by a study of Queen snakes (Regina septemvittata) in Kentucky, USA, and we use simulation to compare the use of PIT tags, with perfect identification, and brands, which are prone to error, when estimating survival rates

The three-state toric homogeneous Markov chain model has Markov degree two

We prove that the three-state toric homogeneous Markov chain model has Markov degree two. In algebraic terminology this means, that a certain class of toric ideals is generated by quadratic binomials. This was conjectured by Haws, Martin del Campo, Takemura and Yoshida, who proved that they are generated by degree six binomials

Spermatogonia Loss Correlates with LAMA 1 Expression in Human Prepubertal Testes Stored for Fertility Preservation

Fertility preservation for male childhood cancer survivors not yet capable of producing mature spermatozoa, relies on experimental approaches such as testicular explant culture. Although the first steps in somatic maturation can be observed in human testicular explant cultures, germ cell depletion is a common obstacle. Hence, understanding the spermatogonial stem cell (SSC) niche environment and in particular, specific components such as the seminiferous basement membrane (BM) will allow progression of testicular explant cultures. Here, we revealed that the seminiferous BM is established from 6 weeks post conception with the expression of laminin alpha 1 (LAMA 1) and type IV collagen, which persist as key components throughout development. With prepubertal testicular explant culture we found that seminiferous LAMA 1 expression is disrupted and depleted with culture time correlating with germ cell loss. These findings highlight the importance of LAMA 1 for the human SSC niche and its sensitivity to culture conditions.Peer reviewe