Oplax Hopf Algebras

We introduce the notion of an oplax Hopf monoid in any braided monoidal bicategory, generalizing that of a Hopf monoid in a braided monoidal category in an appropriate way. We show that Hopf V-categories introduced in [BCV16] are a particular type of oplax Hopf monoids in the monoidal bicategory Span|V described in [B\"oh17]. Finally, we introduce Frobenius V-categories as the Frobenius objects in the same monoidal bicategory.Comment: 42 pages; numerous substantial changes and additions throughout the paper, to appear in `Higher Structures

Design of Anisotropic Diffusion Hardware Fiber Phantoms

A gold standard for the validation of diffusion weighted magnetic resonance imaging (DW-MRI) in brain white matter (WM) is essential for clinical purposes but still not available. Synthetic anisotropic fiber bundles are proposed as phantoms for the validation of DW-MRI because of their well-known structure, their long preservability and the possibility to create complex geometries such as curved and fiber crossings. A crucial question is how the different material properties and size of the fiber phantoms influence the outcome of the DW-MRI experiment. Several fiber materials are compared in this study. The effect of surface relaxation and internal gradients on the SNR is evaluated. In addition, the dependency of the fiber density and fiber radius on the diffusion properties is investigated

Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI

We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational invariants and their expansion in the powers of diffusion weighting, we analytically uncover the nontrivial topology of the parameter estimation landscape, showing that multiple branches of parameters describe the measurement almost equally well, with only one of them corresponding to the biophysical reality. A comprehensive acquisition shows that the branch choice varies across the brain. Our framework reveals hidden degeneracies in MRI parameter estimation for neuronal tissue, provides microstructural and orientational maps in the whole brain without constraints or priors, and connects modern biophysical modeling with clinical MRI.Comment: 25 pages, 12 figures, elsarticle two-colum

Methodological Reflections on Studying Gender‐Sensitive Parliaments Cross‐Nationally: A "Most Significant Change" Approach

Whilst cross-national comparative analyses provide distinct opportunities for the study of gender-sensitive parliaments, the inherent challenge in conducting comparisons necessitates a continued search for innovative methods. This article responds to this need by proposing the "most significant change" (MSC) approach (Davies & Dart, 2005), which centres on collecting and analysing "stories of significant change." Drawing on our own application of MSC in an international study commissioned by INTER PARES, we show that MSC's bottom-up, inductive, and participatory approach proved valuable in uncovering hitherto unknown instances of gender-sensitive changes across countries, illuminating the broader impact of such changes beyond parliaments and incorporating practitioners' perspectives. The flexibility of MSC also enabled context-specific applications, which we illustrate through three examples from Cyprus, Germany, and Trinidad & Tobago. By offering a complementary approach to compare parliaments' gender sensitivity across countries, our study provides a novel perspective for future comparative analyses in the field