A novel sampling theorem on the rotation group

We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by connecting the rotation group to the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to capture all of the information content of a signal band-limited at $L$, reducing the number of required samples by a factor of two compared to other equiangular sampling theorems. We present fast algorithms to compute the associated Fourier transform on the rotation group, the so-called Wigner transform, which scale as $O(L^4)$, compared to the naive scaling of $O(L^6)$. For the common case of a low directional band-limit $N$, complexity is reduced to $O(N L^3)$. Our fast algorithms will be of direct use in speeding up the computation of directional wavelet transforms on the sphere. We make our SO3 code implementing these algorithms publicly available.Comment: 5 pages, 2 figures, minor changes to match version accepted for publication. Code available at http://www.sothree.or

Entanglement measurement with discrete multiple coin quantum walks

Within a special multi-coin quantum walk scheme we analyze the effect of the entanglement of the initial coin state. For states with a special entanglement structure it is shown that this entanglement can be meausured with the mean value of the walk, which depends on the i-concurrence of the initial coin state. Further on the entanglement evolution is investigated and it is shown that the symmetry of the probability distribution is reflected by the symmetry of the entanglement distribution.Comment: 9 pages, IOP styl

The returns to education for opportunity entrepreneurs, necessity entrepreneurs, and paid employees

We assess the relevance of formal education for the productivity of the self- employed and distinguish between opportunity entrepreneurs, who voluntarily pursue a business opportunity, and necessity entrepreneurs, who lack alternative employment options. We expect differences in the returns to education between these groups because of different levels of control. We use the German Socio-economic Panel and account for the endogeneity of education and non-random selection. The results indicate that the returns to a year of education for opportunity entrepreneurs are 3.5 percentage points higher than the paid employees’ rate of 8.1%, but 6.5 percentage points lower for necessity entrepreneurs

Exploring the Relationship between Urban Form, Mobility and Social Well-Being: Towards an Interdisciplinary Field of Sustainable Urban Planning and Transport Development

This Special Issue focuses on exploring the relationship between urban form, mobility, and social well-being across neighbourhoods, cities, and regions. Understanding more about these relationships is helpful in shaping integrated sustainable urban planning and transport development strategies. There is a growing body of research examining changes in well-being in response to social and spatial interventions (e.g., inequality, social exclusion, the built environment, land use, and transport development) and behavioural changes (e.g., travel preferences). However, there is a lack of understanding of the different types of well-being (e.g., social, hedonic, eudaimonic, short-term/long-term, or individual/collective well-being, as well as the spatial nature of well-being) and the variations in their impact. Furthermore, limited attention has been paid to the standardised measurement of well-being in both quantitative and qualitative terms in the field of social sciences, particularly regarding social and eudaimonic well-being, since they are abstract concepts and thus difficult to assess accurately. Therefore, there is an urgent need to further explore the relationship between urban form, mobility, and social well-being, as well as to examine the ways in which different types of well-being can be measured by applying various advanced models and research approaches within the broad field of urban planning and transport

Theory of short-range magnetic order for the t-J model

We present a self-consistent theory of magnetic short-range order based on a spin-rotation-invariant slave-boson representation of the 2D t-J model. In the functional-integral scheme, at the nearest-neighbour pair-approximation level, the bosonized t-J Lagrangian is transformed to a classical Heisenberg model with an effective (doping-dependent) exchange interaction which takes into account the interrelation of ``itinerant'' and ``localized'' magnetic behaviour. Evaluating the theory in the saddle-point approximation, we find a suppression of antiferromagnetic and incommensurate spiral long-range-ordered phases in the favour of a paramagnetic phase with pronounced antiferromagnetic short-range correlations.Comment: 2 pages, 1 Postscript figure, LTpaper.sty, Proc. XXI Int. Conf. on Low Temp. Phys. Prague 9