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

Neurotransmitter profile of saccadic omnipause neurons in nucleus raphe interpositus

Saccadic omnipause neurons (OPNs) are essential for the generation of saccadic eye movements. In primates OPNs are located near the midline within the nucleus raphe interpositus (rip). In the present study we used several different neuroanatomical methods to investigate the transmitters associated with OPNs in the monkey. Immunolabeling for the calcium-binding protein parvalbumin was employed to mark OPNs in the monkey and define the homologous cell group in cat and human. The use of antibodies against GABA, glycine (GLY), glutamate (GLU), serotonin (5-HT), and tyrosine hydroxylase revealed that the somata of OPNs are GLY immunoreactive, but they are devoid of GABA and 5-HT immunostaining. In situ hybridization with the GAD67 mRNA probe confirmed the negative GABA immunostaining of OPNs. 3H-GLY was injected into a projection field of OPNs, the rostral interstitial nucleus of the medial longitudinal fascicle (riMLF)--the vertical saccadic burst neuron area. This resulted in selective retrograde labeling of the OPNs in rip, while no labeling was found in the superior colliculus, which sends an excitatory projection to the riMLF. The somata and dendrites of putative burst neurons in the riMLF were contacted by numerous GLY- immunoreactive terminals. The quantitative analysis of immunoreactive terminal-like structures contacting OPNs revealed a strong input from GLY- and GABA-positive terminals on somata and dendrites, whereas GLU- positive puncta were mainly confined to the dendrites. Very few 5-HT and catecholaminergic terminals contacted OPN somata. Our findings suggest that OPNs use GLY as a neurotransmitter, and they receive numerous contacts from GABAergic, glycinergic, and glutaminergic afferents, and significantly fewer from monoaminergic inputs.</jats:p

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

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

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

CorDeep and the Sacrobosco Dataset: Detection of Visual Elements in Historical Documents

Recent advances in object detection facilitated by deep learning have led to numerous solutions in a myriad of fields ranging from medical diagnosis to autonomous driving. However, historical research is yet to reap the benefits of such advances. This is generally due to the low number of large, coherent, and annotated datasets of historical documents, as well as the overwhelming focus on Optical Character Recognition to support the analysis of historical documents. In this paper, we highlight the importance of visual elements, in particular illustrations in historical documents, and offer a public multi-class historical visual element dataset based on the Sphaera corpus. Additionally, we train an image extraction model based on YOLO architecture and publish it through a publicly available web-service to detect and extract multi-class images from historical documents in an effort to bridge the gap between traditional and computational approaches in historical studies

Stable Magnetostatic Solitons in Yttrium Iron Garnet Film Waveguides for Tilted in-Plane Magnetic Fields

The possibility of nonlinear pulses generation in Yttrium Iron Garnet thin films for arbitrary direction between waveguide and applied static in-plane magnetic field is considered. Up to now only the cases of in-plane magnetic fields either perpendicular or parallel to waveguide direction have been studied both experimentally and theoretically. In the present paper it is shown that also for other angles (besides 0 or 90 degrees) between a waveguide and static in-plane magnetic field the stable bright or dark (depending on magnitude of magnetic field) solitons could be created.Comment: Phys. Rev. B (accepted, April 1, 2002

Super-resolving multi-photon interferences with independent light sources

We propose to use multi-photon interferences from statistically independent light sources in combination with linear optical detection techniques to enhance the resolution in imaging. Experimental results with up to five independent thermal light sources confirm this approach to improve the spatial resolution. Since no involved quantum state preparation or detection is required the experiment can be considered an extension of the Hanbury Brown and Twiss experiment for spatial intensity correlations of order N>2