When does every definable nonempty set have a definable element?

The assertion that every definable set has a definable element is equivalent over $\mathsf{ZF}$ to the principle $\mathbf{V}=\mathbf{HOD}$, and indeed, we prove, so is the assertion merely that every Π₂‐definable set has an ordinal‐definable element. Meanwhile, every model of $\mathsf{ZFC}$ has a forcing extension satisfying $\mathbf{V}\ne \mathbf{HOD}$ in which every Σ₂‐definable set has an ordinal‐definable element. Similar results hold for $\mathbf{HOD}(\mathbb{R})$ and $\mathbf{HOD}({\mathrm{Ord}}^{\omega })$ and other natural instances of $\mathbf{HOD}(X)$.     

Differential evolution with enhanced diversity maintenance

Optimization Letters - Differential evolution (de) is a popular population-based meta-heuristic that has been successfully used in complex optimization problems. Premature convergence is one of the...     

Interplay of thermochemistry and Structural Chemistry,the journal (volume 29, 2018, issues 3–4) and the discipline

The contents of issues 3 and 4 of Structural Chemistry from the calendar year 2018 are summarized in the present review. A brief thermochemical commentary and recommendations for future research have been added to the summary of each paper.

     

The Challenge of Functional Magnetic Resonance Imaging

Abstract

Functional magnetic resonance imaging of the human brain in action presents large statistical and computational challenges. Here we describe those challenges and provide references to a number of other papers where detailed methods developed to meet them are reported. The first seven sections of this paper were written in 1995 when our work was in its infancy. The last four sections were written more recently, to update the earlier sections and to show the directions we have gone and the directions we intend to go.