On the homomorphism order of labeled posets

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This universal order is a distributive lattice. We investigate some other properties, namely the infinite distributivity, the computation of infinite suprema and infima, and the complexity of certain decision problems involving the homomorphism order of k-posets. Sublattices are also examined.Comment: 14 page

Super-resolution provided by the arbitrarily strong superlinearity of the blackbody radiation

Blackbody radiation is a fundamental phenomenon in nature, and its explanation by Planck marks a cornerstone in the history of Physics. In this theoretical work, we show that the spectral radiance given by Planck's law is strongly superlinear with temperature, with an arbitrarily large local exponent for decreasing wavelengths. From that scaling analysis, we propose a new concept of super-resolved detection and imaging: if a focused beam of energy is scanned over an object that absorbs and linearly converts that energy into heat, a highly nonlinear thermal radiation response is generated, and its point spread function can be made arbitrarily smaller than the excitation beam focus. Based on a few practical scenarios, we propose to extend the notion of super-resolution beyond its current niche in microscopy to various kinds of excitation beams, a wide range of spatial scales, and a broader diversity of target objects

Measurement of focusing properties for high numerical aperture optics using an automated submicron beamprofiler

The focusing properties of three aspheric lenses with numerical aperture (NA) between 0.53 and 0.68 were directly measured using an interferometrically referenced scanning knife-edge beam profiler with sub-micron resolution. The results obtained for two of the three lenses tested were in agreement with paraxial gaussian beam theory. It was also found that the highest NA aspheric lens which was designed for 830nm was not diffraction limited at 633nm. This process was automated using motorized translation stages and provides a direct method for testing the design specifications of high numerical aperture optics.Comment: 6 pages 4 figure

Ultrastructural anatomy of nodes of Ranvier in the peripheral nervous system as revealed by STED microscopy.

We used stimulated emission depletion (STED) superresolution microscopy to analyze the nanoscale organization of 12 glial and axonal proteins at the nodes of Ranvier of teased sciatic nerve fibers. Cytoskeletal proteins of the axon (betaIV spectrin, ankyrin G) exhibit a high degree of one-dimensional longitudinal order at nodal gaps. In contrast, axonal and glial nodal adhesion molecules [neurofascin-186, neuron glial-related cell adhesion molecule (NrCAM)] can arrange in a more complex, 2D hexagonal-like lattice but still feature a ∼190-nm periodicity. Such a lattice-like organization is also found for glial actin. Sodium and potassium channels exhibit a one-dimensional periodicity, with the Nav channels appearing to have a lower degree of organization. At paranodes, both axonal proteins (betaII spectrin, Caspr) and glial proteins (neurofascin-155, ankyrin B) form periodic quasi–one-dimensional arrangements, with a high degree of interdependence between the position of the axonal and the glial proteins. The results indicate the presence of mechanisms that finely align the cytoskeleton of the axon with the one of the Schwann cells, both at paranodal junctions (with myelin loops) and at nodal gaps (with microvilli). Taken together, our observations reveal the importance of the lateral organization of proteins at the nodes of Ranvier and pave the way for deeper investigations of the molecular ultrastructural mechanisms involved in action potential propagation, the formation of the nodes, axon–glia interactions, and demyelination diseases

Dynamic L-type CaV1.2 channel trafficking facilitates CaV1.2 clustering and cooperative gating.

L-type CaV1.2 channels are key regulators of gene expression, cell excitability and muscle contraction. CaV1.2 channels organize in clusters throughout the plasma membrane. This channel organization has been suggested to contribute to the concerted activation of adjacent CaV1.2 channels (e.g. cooperative gating). Here, we tested the hypothesis that dynamic intracellular and perimembrane trafficking of CaV1.2 channels is critical for formation and dissolution of functional channel clusters mediating cooperative gating. We found that CaV1.2 moves in vesicular structures of circular and tubular shape with diverse intracellular and submembrane trafficking patterns. Both microtubules and actin filaments are required for dynamic movement of CaV1.2 vesicles. These vesicles undergo constitutive homotypic fusion and fission events that sustain CaV1.2 clustering, channel activity and cooperative gating. Our study suggests that CaV1.2 clusters and activity can be modulated by diverse and unique intracellular and perimembrane vesicular dynamics to fine-tune Ca2+ signals