"Just Imagine ...": Students' perspectives on empathy tasks in secondary history education

Historical empathy can be helpful when learning history. However, we do not know what students do when completing an empathy-task or how they perceive this type of task. In the explorative study presented in this article, we recognized different types of empathy-tasks, we saw students showing cognitive as well as affective elements in their responses on an empathy task, and we learned that students think that empathy-tasks are mainly useful to remember facts. Students also mentioned comparing the past with the present and imagining other people’s lives as goals of empathy-tasks

Multiple sums and integrals as neutral BKP tau functions

We consider multiple sums and multi-integrals as tau functions of the BKP hierarchy using neutral fermions as the simplest tool for deriving these. The sums are over projective Schur functions $Q_\alpha$ for strict partitions $\alpha$. We consider two types of such sums: weighted sums of $Q_\alpha$ over strict partitions $\alpha$ and sums over products $Q_\alpha Q_\gamma$. In this way we obtain discrete analogues of the beta-ensembles ($\beta=1,2,4$). Continuous versions are represented as multiple integrals. Such sums and integrals are of interest in a number of problems in mathematics and physics.Comment: 16 page

Variational Lie algebroids and homological evolutionary vector fields

We define Lie algebroids over infinite jet spaces and establish their equivalent representation through homological evolutionary vector fields.Comment: Int. Workshop "Nonlinear Physics: Theory and Experiment VI" (Gallipoli, Italy; June-July 2010). Published v3 = v2 minus typos, to appear in: Theoret. and Mathem. Phys. (2011) Vol.167:3 (168:1), 18 page

Deep neural network-based clustering of deformation curves reveals novel disease features in PLN pathogenic variant carriers

Echocardiographic deformation curves provide detailed information on myocardial function. Deep neural networks (DNNs) may enable automated detection of disease features in deformation curves, and improve the clinical assessment of these curves. We aimed to investigate whether an explainable DNN-based pipeline can be used to detect and visualize disease features in echocardiographic deformation curves of phospholamban (PLN) p.Arg14del variant carriers. A DNN was trained to discriminate PLN variant carriers (n = 278) from control subjects (n = 621) using raw deformation curves obtained by 2D-speckle tracking in the longitudinal axis. A visualization technique was used to identify the parts of these curves that were used by the DNN for classification. The PLN variant carriers were clustered according to the output of the visualization technique. The DNN showed excellent discriminatory performance (C-statistic 0.93 [95% CI 0.87–0.97]). We identified four clusters with PLN-associated disease features in the deformation curves. Two clusters showed previously described features: apical post-systolic shortening and reduced systolic strain. The two other clusters revealed novel features, both reflecting delayed relaxation. Additionally, a fifth cluster was identified containing variant carriers without disease features in the deformation curves, who were classified as controls by the DNN. This latter cluster had a very benign disease course regarding development of ventricular arrhythmias. Applying an explainable DNN-based pipeline to myocardial deformation curves enables automated detection and visualization of disease features. In PLN variant carriers, we discovered novel disease features which may improve individual risk stratification. Applying this approach to other diseases will further expand our knowledge on disease-specific deformation patterns. Graphical abstract: [Figure not available: see fulltext.] Overview of the deep neural network-based pipeline for feature detection in myocardial deformation curves. Firstly, phospholamban (PLN) p.Arg14del variant carriers and controls were selected and a deep neural network (DNN) was trained to detect the PLN variant carriers. Subsequently, a clustering-based approach was performed on the attention maps of the DNN, which revealed 4 distinct phenotypes of PLN variant carriers with different prognoses. Moreover, a cluster without features and a benign prognosis was detected

Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets

We show that the quantum field theoretical formulation of the $\tau$-function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that i) the partial charge transformations preserving the neutral sector are Laplace transformations, ii) the basic vertex operators are Levy and adjoint Levy transformations and iii) the diagonal soliton vertex operators generate fundamental transformations. We also show that the bilinear identity for the multicomponent Kadomtsev-Petviashvili hierarchy becomes, through a generalized Miwa map, a bilinear identity for the multidimensional quadrilateral lattice equations.Comment: 28 pages, 3 Postscript figure