Structure of the Three-dimensional Quantum Euclidean Space

As an example of a noncommutative space we discuss the quantum 3-dimensional Euclidean space $R^3_q$ together with its symmetry structure in great detail. The algebraic structure and the representation theory are clarified and discrete spectra for the coordinates are found. The q-deformed Legendre functions play a special role. A completeness relation is derived for these functions.Comment: 22 pages, late

Realization of the Three-dimensional Quantum Euclidean Space by Differential Operators

The three-dimensional quantum Euclidean space is an example of a non-commutative space that is obtained from Euclidean space by $q$-deformation. Simultaneously, angular momentum is deformed to $so_q(3)$, it acts on the $q$-Euclidean space that becomes a $so_q(3)$-module algebra this way. In this paper it is shown, that this algebra can be realized by differential operators acting on $C^{\infty}$ functions on $\mathbb{R}^3$. On a factorspace of $C^{\infty}(\mathbb{R}^3)$ a scalar product can be defined that leads to a Hilbert space, such that the action of the differential operators is defined on a dense set in this Hilbert space and algebraically self-adjoint becomes self-adjoint for the linear operator in the Hilbert space. The self-adjoint coordinates have discrete eigenvalues, the spectrum can be considered as a $q$-lattice.Comment: 13 pages, late

Clec9a-mediated ablation of conventional dendritic cells suggests a lymphoid path to generating dendritic cells In Vivo

Conventional dendritic cells (cDCs) are versatile activators of immune responses that develop as part of the myeloid lineage downstream of hematopoietic stem cells. We have recently shown that in mice precursors of cDCs, but not of other leukocytes, are marked by expression of DNGR-1/CLEC9A. To genetically deplete DNGR-1-expressing cDC precursors and their progeny, we crossed Clec9a-Cre mice to Rosa-lox-STOP-lox-diphtheria toxin (DTA) mice. These mice develop signs of age-dependent myeloproliferative disease, as has been observed in other DC-deficient mouse models. However, despite efficient depletion of cDC progenitors in these mice, cells with phenotypic characteristics of cDCs populate the spleen. These cells are functionally and transcriptionally similar to cDCs in wild type control mice but show somatic rearrangements of Ig-heavy chain genes, characteristic of lymphoid origin cells. Our studies reveal a previously unappreciated developmental heterogeneity of cDCs and suggest that the lymphoid lineage can generate cells with features of cDCs when myeloid cDC progenitors are impaired

Direct measurement of plasmon propagation lengths on lithographically defined metallic waveguides on GaAs

We present optical investigations of rectangular surface plasmon polariton waveguides lithographically defined on GaAs substrates. The plasmon propagation length is directly determined using a confocal microscope, with independent polarization control in both excitation and detection channels. Surface plasmon polaritons are launched along the waveguide using a lithographically defined defect at one end. At the remote end of the waveguide they scatter into the far-field, where they are imaged using a CCD camera. By monitoring the length dependence of the intensity of scattered light from the waveguide end, we directly extract the propagation length, obtaining values ranging from LSPP = 10-40 {\mu}m depending on the waveguide width (w=2-5 {\mu}m) and excitation wavelength (760-920 nm). Results are in good accord with theoretical expectations demonstrating the high quality of the lithographically defined structures. The results obtained are of strong relevance for the development of future semiconductor based integrated plasmonic technologies

Combining laser microdissection and microRNA expression profiling to unmask microRNA signatures in complex tissues

Neglecting tissue heterogeneity during the analysis of microRNA (miRNA) levels results in average signals from an unknown mixture of different cell types that are difficult to interpret. Here we demonstrate the technical requirements needed to obtain high-quality, quantitative miRNA expression infor- mation from tumor tissue compartments obtained by laser microdissection (LMD). Furthermore, we show the significance of disentangling tumor tissue heterogeneity by applying the newly developed protocols for combining LMD of tumor tissue compartments with RT-qPCR analysis to reveal compartment- specific miRNA expression signatures. An important advantage of this strategy is that the miRNA signature can be directly linked to histopatho logy. In summary, combining LMD and RT-qPCR is a powerful approach for spatial miRNA expression analysis in complex tissues, enabling discovery of disease mechanisms, biomarkers and drug candidates