Oxygen is critical for optimal bone regeneration. While axolotls and salamanders have retained the ability to regenerate whole limbs, mammalian regeneration is restricted to the distal tip of the digit (P3) in mice, primates, and humans. Our previous study revealed the oxygen microenvironment during regeneration is dynamic and temporally influential in building and degrading bone. Given that regeneration is dependent on a dynamic and changing oxygen environment, a better understanding of the effects of oxygen during wounding, scarring, and regeneration, and better ways to artificially generate both hypoxic and oxygen replete microenvironments are essential to promote regeneration beyond wounding or scarring. To explore the influence of increased oxygen on digit regeneration in vivo daily treatments of hyperbaric oxygen were administered to mice during all phases of the entire regenerative process. Micro-Computed Tomography (μCT) and histological analysis showed that the daily application of hyperbaric oxygen elicited the same enhanced bone degradation response as two individual pulses of oxygen applied during the blastema phase. We expand past these findings to show histologically that the continuous application of hyperbaric oxygen during digit regeneration results in delayed blastema formation at a much more proximal location after amputation, and the deposition of better organized collagen fibers during bone formation. The application of sustained hyperbaric oxygen also delays wound closure and enhances bone degradation after digit amputation. Thus, hyperbaric oxygen shows the potential for positive influential control on the various phases of an epimorphic regenerative response.

Sorted L-One Penalized Estimation (SLOPE, Bogdan et al., 2013, 2015) is a relatively new convex optimization procedure which allows for adaptive selection of regressors under sparse high dimensional designs. Here we extend the idea of SLOPE to deal with the situation when one aims at selecting whole groups of explanatory variables instead of single regressors. Such groups can be formed by clustering strongly correlated predictors or groups of dummy variables corresponding to different levels of the same qualitative predictor. We formulate the respective convex optimization problem, gSLOPE (group SLOPE), and propose an efficient algorithm for its solution. We also define a notion of the group false discovery rate (gFDR) and provide a choice of the sequence of tuning parameters for gSLOPE so that gFDR is provably controlled at a prespecified level if the groups of variables are orthogonal to each other. Moreover, we prove that the resulting procedure adapts to unknown sparsity and is asymptotically minimax with respect to the estimation of the proportions of variance of the response variable explained by regressors from different groups. We also provide a method for the choice of the regularizing sequence when variables in different groups are not orthogonal but statistically independent and illustrate its good properties with computer simulations. Finally, we illustrate the advantages of gSLOPE in the context of Genome Wide Association Studies. package with an implementation of our method is available on CRAN.

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Reducing the number of false discoveries is presently one of the most pressing issues in the life sciences. It is of especially great importance for many applications in neuroimaging and genomics, where data sets are typically high-dimensional, which means that the number of explanatory variables exceeds the sample size. The false discovery rate (FDR) is a criterion that can be employed to address that issue. Thus it has gained great popularity as a tool for testing multiple hypotheses. Canonical correlation analysis (CCA) is a statistical technique that is used to make sense of the cross-correlation of two sets of measurements collected on the same set of samples (e.g., brain imaging and genomic data for the same mental illness patients), and sparse CCA extends the classical method to high-dimensional settings. Here, we propose a way of applying the FDR concept to sparse CCA, and a method to control the FDR. The proposed FDR correction directly influences the sparsity of the solution, adapting it to the unknown true sparsity level. Theoretical derivation as well as simulation studies show that our procedure indeed keeps the FDR of the canonical vectors below a user-specified target level. We apply the proposed method to an imaging genomics data set from the Philadelphia Neurodevelopmental Cohort. Our results link the brain connectivity profiles derived from brain activity during an emotion identification task, as measured by functional magnetic resonance imaging, to the corresponding subjects' genomic data.