Sequences and filters of characters characterizing subgroups of compact abelian groups

Let H be a countable subgroup of the metrizable compact abelian group G and f:H -> T=R/Z a (not necessarily continuous) character of H. Then there exists a sequence (chi_n)_n of (continuous) characters of G such that lim_n chi_n(alpha) = f(alpha) for all alpha in H and (chi_n(alpha))_n does not converge whenever alpha in G\H. If one drops the countability and metrizability requirement one can obtain similar results by using filters of characters instead of sequences. Furthermore the introduced methods allow to answer questions of Dikranjan et al.Comment: laTex2e, 10 page

Leptin signalling, obesity and prostate cancer: molecular and clinical perspective on the old dilemma

The prevalence of global obesity is increasing. Obesity is associated with general cancer-related morbidity and mortality and is a known risk factor for development of specific cancers. A recent large systematic review of 24 studies based on meta-analysis of 11,149 patients with prostate cancer showed a significant correlation between obesity and the risk of advanced prostate cancer. Further, a sustained reduction in BMI correlates with a decreased risk of developing aggressive disease. On the other hand, the correlation between consuming different products and prostate cancer occurrence/risk is limited. Here, we review the role of adipose tissue from an endocrine perspective and outline the effect of adipokines on cancer metabolism, with particular focus on leptin. Leptin exerts its physiological and pathological effects through modification of intracellular signalling, most notably activating the Janus kinase (JAK) 2/signal transducer and activator of transcription (STAT) 3 pathway and recently shown sphingolipid pathway. Both high levels of leptin in circulation and leptin receptor mutation are associated with prostate cancer risk in human patients; however, the in vivo mechanistic evidence is less conclusive. Given the complexity of metabolic cancer pathways, it is possible that leptin may have varying effects on prostate cancer at different stages of its development, a point that may be addressed by further epidemiological studies

Dynamic spin-Hall effect and driven spin helix for linear spin-orbit interactions

We derive boundary conditions for the electrically induced spin accumulation in a finite, disordered 2D semiconductor channel. While for DC electric fields these boundary conditions select spatially constant spin profiles equivalent to a vanishing spin-Hall effect, we show that an in-plane ac electric field results in a non-zero ac spin-Hall effect, i.e., it generates a spatially non-uniform out-of-plane polarization even for linear intrinsic spin-orbit interactions. Analyzing different geometries in [001] and [110]-grown quantum wells, we find that although this out-of-plane polarization is typically confined to within a few spin-orbit lengths from the channel edges, it is also possible to generate spatially oscillating spin profiles which extend over the whole channel. The latter is due to the excitation of a driven spin-helix mode in the transverse direction of the channel. We show that while finite frequencies suppress this mode, it can be amplified by a magnetic field tuned to resonance with the frequency of the electric field. In this case, finite size effects at equal strengths of Rashba- and Dresselhaus SOI lead to an enhancement of the magnitude of this helix mode. We comment on the relation between spin currents and boundary conditions.Comment: 10 pages, 5 figures, added references, corrected typos, extended section V, VI

Coarse-graining collective skyrmion dynamics in confined geometries

Magnetic skyrmions are magnetic quasi-particles with enhanced stability and different manipulation mechanisms using external fields and currents making them promising candidates for future applications for instance in neuromorphic computing. Recently, several measurements and simulations have shown that thermally activated skyrmions in confined geometries, as they are necessary for device applications, arrange themselves predominantly based on commensurability effects. In this simulational study, based on the Thiele model, we investigate the enhanced dynamics and degenerate non-equilibrium steady state of a system in which the intrinsic skyrmion-skyrmion and skyrmion-boundary interaction compete with thermal fluctuations as well as current-induced spin-orbit torques. The investigated system is a triangular-shaped confinement geometry hosting four skyrmions, where we inject spin-polarized currents between two corners of the structure. We coarse-grain the skyrmion states in the system to analyze the intricacies of skyrmion arrangements of the skyrmion ensemble. In the context of neuromorphic computing, such methods address the key challenge of optimizing read-out positions in confined geometries and form the basis to understand collective skyrmion dynamics in systems with competing interactions on different scales.Comment: 11 pages, 4 figure