Natural Intrinsic Geometrical Symmetries

A proposal is made for what could well be the most natural symmetrical Riemannian spaces which are homogeneous but not isotropic, i.e. of what could well be the most natural class of symmetrical spaces beyond the spaces of constant Riemannian curvature, that is, beyond the spaces which are homogeneous and isotropic, or, still, the spaces which satisfy the axiom of free mobility

Ideally embedded space-times

Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we extend the notion of ideal embeddings from Riemannian geometry to the indefinite case. Ideal embeddings are such that the embedded manifold receives the least amount of tension from the surrounding space. Then it is shown that the de Sitter spaces, a Robertson-Walker space-time and some anisotropic perfect fluid metrics can be ideally embedded in a five-dimensional pseudo-Euclidean space.Comment: layout changed and typos corrected; uses revtex

Hydration free energies in the FreeSolv database calculated with polarized iterative Hirshfeld charges

Computer simulations of biomolecular systems often use force fields, which are combinations of simple empirical atom-based functions to describe the molecular interactions. Even though polarizable force fields give a more detailed description of intermolecular interactions, nonpolarizable force fields, developed several decades ago, are often still preferred because of their reduced computation cost. Electrostatic interactions play a major role in biomolecular systems and are therein described by atomic point charges. In this work, we address the performance of different atomic charges to reproduce experimental hydration free energies in the FreeSolv database in combination with the GAFF force field. Atomic charges were calculated by two atoms-in-molecules approaches, Hirshfeld-I and Minimal Basis Iterative Stockholder (MBIS). To account for polarization effects, the charges were derived from the solute’s electron density computed with an implicit solvent model, and the energy required to polarize the solute was added to the free energy cycle. The calculated hydration free energies were analyzed with an error model, revealing systematic errors associated with specific functional groups or chemical elements. The best agreement with the experimental data is observed for the AM1-BCC and the MBIS atomic charge methods. The latter includes the solvent polarization and presents a root-mean-square error of 2.0 kcal mol–1 for the 613 organic molecules studied. The largest deviation was observed for phosphorus-containing molecules and the molecules with amide, ester and amine functional groups

Do we still need animals? Surveying the role of animal-free models in Alzheimer’s and Parkinson’s disease research

The use of animals in neuroscience and biomedical research remains controversial. Policy is built around the “3R” principle of “Refining, Reducing and Replacing” animal experiments, and across the globe, different initiatives stimulate the use of animal-free methods. Based on an extensive literature screen to map the development and adoption of animal-free methods in Alzheimer's and Parkinson's disease research, we find that at least two in three examined studies rely on animals or on animal-derived models. Among the animal-free studies, the relative contribution of innovative models that may replace animal experiments is limited. We argue that the distinction between animal research and alternative models presents a false dichotomy, as the role and scientific value of both animal and animal-free approaches are intertwined. Calls to halt all animal experiments appear premature, as insufficient non-animal-based alternatives are available and their development lags behind. In light of this, we highlight the need for objective, unprejudiced monitoring, and more robust performance indicators of animal-free approaches

A Computational Model of Visual Anisotropy

Visual anisotropy has been demonstrated in multiple tasks where performance differs between vertical, horizontal, and oblique orientations of the stimuli. We explain some principles of visual anisotropy by anisotropic smoothing, which is based on a variation on Koenderink's approach in [1]. We tested the theory by presenting Gaussian elongated luminance profiles and measuring the perceived orientations by means of an adjustment task. Our framework is based on the smoothing of the image with elliptical Gaussian kernels and it correctly predicted an illusory orientation bias towards the vertical axis. We discuss the scope of the theory in the context of other anisotropies in perception