The concept of freedom in North America in the eighteenth and nineteenth centuries with a brief comparison to the developments in Germany

'Religiöse, politische, geistige sowie wirtschaftliche Freiheit waren die Motive der nordamerikanischen Kolonisten für ihre Auswanderung aus Europa. Dort entwickelte sich rasch eine politisch-gesellschaftliche Freiheitskultur, die in der Amerikanischen Revolution ihren deutlichsten Ausdruck fand. Bis 1900 kam es zu einer Ausgestaltung des freiheitlichen demokratischen Verfassungsstaates mit einer kontinuierlichen Erweiterung der Bürgerrechte.' (Autorenreferat

Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory

We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive-definite pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio L = 0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.Comment: 19 pages, 5 figures, submitted to J. Chem. Phys; new version: minor changes in structure of pape

Poor Trail Making Test Performance Is Directly Associated with Altered Dual Task Prioritization in the Elderly – Baseline Results from the TREND Study

BACKGROUND: Deterioration of executive functions in the elderly has been associated with impairments in walking performance. This may be caused by limited cognitive flexibility and working memory, but could also be caused by altered prioritization of simultaneously performed tasks. To disentangle these options we investigated the associations between Trail Making Test performance--which specifically measures cognitive flexibility and working memory--and dual task costs, a measure of prioritization. METHODOLOGY AND PRINCIPAL FINDINGS: Out of the TREND study (Tuebinger evaluation of Risk factors for Early detection of Neurodegenerative Disorders), 686 neurodegeneratively healthy, non-demented elderly aged 50 to 80 years were classified according to their Trail Making Test performance (delta TMT; TMT-B minus TMT-A). The subjects performed 20 m walks with habitual and maximum speed. Dual tasking performance was tested with walking at maximum speed, in combination with checking boxes on a clipboard, and subtracting serial 7 s at maximum speeds. As expected, the poor TMT group performed worse when subtracting serial 7 s under single and dual task conditions, and they walked more slowly when simultaneously subtracting serial 7 s, compared to the good TMT performers. In the walking when subtracting serial 7 s condition but not in the other 3 conditions, dual task costs were higher in the poor TMT performers (median 20%; range -6 to 58%) compared to the good performers (17%; -16 to 43%; p<0.001). To the contrary, the proportion of the poor TMT performance group that made calculation errors under the dual tasking situation was lower than under the single task situation, but higher in the good TMT performance group (poor performers, -1.6%; good performers, +3%; p = 0.035). CONCLUSION: Under most challenging conditions, the elderly with poor TMT performance prioritize the cognitive task at the expense of walking velocity. This indicates that poor cognitive flexibility and working memory are directly associated with altered prioritization