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The value problem for knowledge is the problem of explaining why knowledge is more valuable than mere true belief. The problem arises for reliabilism in particular, i.e., the externalist view that knowledge amounts to reliably acquired true belief. Goldman and Olsson argue that knowledge, in this sense, is more valuable than mere true belief due to the higher likelihood of future true beliefs (produced by the same reliable process) in the case of knowledge. They maintain that their solution works given four empirical assumptions, which they claim hold “normally.” However, they do not show that their assumptions are externalistically acceptable; nor do they provide detailed evidence for their normality claim. We address these remaining gaps in Goldman and Olsson’s solution in a constructive spirit. In particular, we suggest an externalist interpretation of the assumptions such that they essentially spell out what it means for a broad range of organisms capable of belief-like representations to be epistemically adapted to their environment. Our investigation also sheds light on the circumstances in which the assumptions fail to hold and knowledge therefore fails to have extra value in Goldman and Olsson’s sense. The upshot is a deeper understanding of their solution as a contribution to naturalized epistemology and a strengthened case for its empirical validity.

In molecular dynamics (MD) simulations, free-energy differences are often calculated using free energy perturbation or thermodynamic integration (TI) methods. However, both techniques are only suited to calculate free-energy differences between two end states. Enveloping distribution sampling (EDS) presents an attractive alternative that allows to calculate multiple free-energy differences in a single simulation. In EDS, a reference state is simulated which "envelopes" the end states. The challenge of this methodology is the determination of optimal reference-state parameters to ensure equal sampling of all end states. Currently, the automatic determination of the reference-state parameters for multiple end states is an unsolved issue that limits the application of the methodology. To resolve this, we have generalised the replica-exchange EDS (RE-EDS) approach, introduced by Lee et al. [J. Chem. Theory Comput. 10, 2738 (2014)] for constant-pH MD simulations. By exchanging configurations between replicas with different reference-state parameters, the complexity of the parameter-choice problem can be substantially reduced. A new robust scheme to estimate the reference-state parameters from a short initial RE-EDS simulation with default parameters was developed, which allowed the calculation of 36 free-energy differences between nine small-molecule inhibitors of phenylethanolamine N-methyltransferase from a single simulation. The resulting free-energy differences were in excellent agreement with values obtained previously by TI and two-state EDS simulations.

Recent advances in imaging technology now provide us with 3D images of developing organs. These can be used to extract 3D geometries for simulations of organ development. To solve models on growing domains, the displacement fields between consecutive image frames need to be determined. Here we develop and evaluate different landmark-free algorithms for the determination of such displacement fields from image data. In particular, we examine minimal distance, normal distance, diffusion-based, and uniform mapping algorithms and test these algorithms with both synthetic and real data in 2D and 3D. We conclude that in most cases, the normal distance algorithm is the method of choice and wherever it fails, diffusion-based mapping provides a good alternative.