Correction: Multi-layer 3D printed dipeptide-based low molecular weight gels.

Correction for 'Multi-layer 3D printed dipeptide-based low molecular weight gels' by Max J. S. Hill et al., Soft Matter, 2022, 18, 5960-5965, https://doi.org/10.1039/D2SM00663D.

Maximum Likelihood Estimation for Unrooted 3-Leaf Trees: An Analytic Solution for the CFN Model.

Maximum likelihood estimation is among the most widely-used methods for inferring phylogenetic trees from sequence data. This paper solves the problem of computing solutions to the maximum likelihood problem for 3-leaf trees under the 2-state symmetric mutation model (CFN model). Our main result is a closed-form solution to the maximum likelihood problem for unrooted 3-leaf trees, given generic data; this result characterizes all of the ways that a maximum likelihood estimate can fail to exist for generic data and provides theoretical validation for predictions made in Parks and Goldman (Syst Biol 63(5):798-811, 2014). Our proof makes use of both classical tools for studying group-based phylogenetic models such as Hadamard conjugation and reparameterization in terms of Fourier coordinates, as well as more recent results concerning the semi-algebraic constraints of the CFN model. To be able to put these into practice, we also give a complete characterization to test genericity.

Effect of Imposing Spatial Constraints on Low Molecular Weight Gels.

We outline the effect of imposing spatial constraints during gelation on hydrogels formed by dipeptide-based low molecular weight gelators. The gels were formed via either a solvent switch or a change in pH and formed in different sized vessels to produce gels of different thickness while maintaining the same volume. The different methods of gelation led to gels with different underlying microstructure. Confocal microscopy was used to visualize the resulting microstructures, while the corresponding mechanical properties were probed via cavitation rheology. We show that solvent-switch-triggered gels are sensitive to imposed spatial constraints, in both altered microstructure and mechanical properties, while their pH-triggered equivalents are not. These results are significant because it is often necessary to form gels of different thicknesses for different analytical techniques. Also, gels of different thicknesses are utilized between various applications of these materials. Our data show that it is important to consider the spatial constraints imposed in these situations.

Multi-layer 3D printed dipeptide-based low molecular weight gels.

We describe the direct 3D printing of dipeptide hydrogels, forming layers from gels prepared from different dipeptides. The dipeptides self-assemble into fibres that lead to very different microstructures letting us differentiate between the gels. We show how the mechanical properties of the overall 3D printed structures are affected by the composition of each of the layers, allowing us to build up structures with different microstructure and stiffness. We also discuss the interface between layers formed from different gelators, showing that the gels remain independent from neighbouring printed material, even when prepared in very close proximity.

Inconsistency of Triplet-Based and Quartet-Based Species Tree Estimation under Intralocus Recombination.

We consider species tree estimation from multiple loci subject to intralocus recombination. We focus on R∗, a summary coalescent-based method using rooted triplets, as well as a related quartet-based inference method. We demonstrate analytically that in both cases, intralocus recombination gives rise to an inconsistency zone, in which correct inference is not assured even in the limit of infinite amount of data. In addition, we validate and characterize this inconsistency zone through a simulation study, which suggests that differential rates of recombination between closely related taxa can amplify the effect of incomplete lineage sorting and contribute to inconsistency.