Sphere packing bounds in the Grassmann and Stiefel manifolds

Applying the Riemann geometric machinery of volume estimates in terms of curvature, bounds for the minimal distance of packings/codes in the Grassmann and Stiefel manifolds will be derived and analyzed. In the context of space-time block codes this leads to a monotonically increasing minimal distance lower bound as a function of the block length. This advocates large block lengths for the code design.Comment: Replaced with final version, 11 page

Space Frequency Codes from Spherical Codes

A new design method for high rate, fully diverse ('spherical') space frequency codes for MIMO-OFDM systems is proposed, which works for arbitrary numbers of antennas and subcarriers. The construction exploits a differential geometric connection between spherical codes and space time codes. The former are well studied e.g. in the context of optimal sequence design in CDMA systems, while the latter serve as basic building blocks for space frequency codes. In addition a decoding algorithm with moderate complexity is presented. This is achieved by a lattice based construction of spherical codes, which permits lattice decoding algorithms and thus offers a substantial reduction of complexity.Comment: 5 pages. Final version for the 2005 IEEE International Symposium on Information Theor

Geometrical relations between space time block code designs and complexity reduction

In this work, the geometric relation between space time block code design for the coherent channel and its non-coherent counterpart is exploited to get an analogue of the information theoretic inequality $I(X;S)\le I((X,H);S)$ in terms of diversity. It provides a lower bound on the performance of non-coherent codes when used in coherent scenarios. This leads in turn to a code design decomposition result splitting coherent code design into two complexity reduced sub tasks. Moreover a geometrical criterion for high performance space time code design is derived.Comment: final version, 11 pages, two-colum

Local Prescribed Mean Curvature foliations in cosmological spacetimes

A theorem about local in time existence of spacelike foliations with prescribed mean curvature in cosmological spacetimes will be proved. The time function of the foliation is geometrically defined and fixes the diffeomorphism invariance inherent in general foliations of spacetimes. Moreover, in contrast to the situation of the more special constant mean curvature foliations, which play an important role in the global analysis of spacetimes, this theorem overcomes the existence problem arising from topological restrictions for surfaces of constant mean curvature.Comment: 23 pages, no figure

Differential Release of Exocytosis Marker Dyes Indicates Stimulation-Dependent Regulation of Synaptic Activity

There is a general consensus that synaptic vesicular release by a full collapse process is the primary machinery of synaptic transmission. However, competing view suggests that synaptic vesicular release operates via a kiss-and-run mechanism. By monitoring the release dynamics of a synaptic vesicular marker, FM1-43 from individual synapses in hippocampal neurons, we found evidence that the release of synaptic vesicle was delayed by several seconds after the start of field stimulation. This phenomenon was associated with modified opening kinetics of fusion pores. Detailed analysis revealed that some synapses were completely inactive for a few seconds after stimulation, despite immediate calcium influx. This delay in vesicular release was modulated by various stimulation protocols and different frequencies, indicating an activity-dependent regulation mechanism for neurotransmitter exocytosis. Staurosporine, a drug known to induce “kiss-and-run” exocytosis, increased the proportion of delayed synapses as well as the delay duration, while fluoxetine acted contrarily. Besides being a serotonin reuptake inhibitor, it directly enhanced vesicle mobilization and reduced synaptic fatigue. Exocytosis was never delayed, when it was monitored with pH-sensitive probes, synaptopHlourin and αSyt-CypHerE5 antibody, indicating an instantaneous formation of a fusion pore that allowed rapid equilibration of vesicular lumenal pH but prevented FM1-43 release because of its slow dissociation from the inner vesicular membrane. Our observations suggest that synapses operate via a sequential “kiss-and-run” and “full-collapse” exocytosis mechanism. The initially narrow vesicular pore allows the equilibration of intravesicular pH which then progresses toward full fusion, causing FM1-43 release

Microfluidic chamber design for controlled droplet expansion and coalescence

The defined formation and expansion of droplets are essential operations for droplet-based screening assays. The volumetric expansion of droplets causes a dilution of the ingredients. Dilution is required for the generation of concentration graduation which is mandatory for many different assay protocols. Here, we describe the design of a microfluidic operation unit based on a bypassed chamber and its operation modes. The different operation modes enable the defined formation of sub-µL droplets on the one hand and the expansion of low nL to sub-µL droplets by controlled coalescence on the other. In this way the chamber acts as fluidic interface between two fluidic network parts dimensioned for different droplet volumes. Hence, channel confined droplets of about 30–40 nL from the first network part were expanded to cannel confined droplets of about 500 to about 2500 nL in the second network part. Four different operation modes were realized: (a) flow rate independent droplet formation in a self-controlled way caused by the bypassed chamber design, (b) single droplet expansion mode, (c) multiple droplet expansion mode, and (d) multiple droplet coalescence mode. The last mode was used for the automated coalescence of 12 droplets of about 40 nL volume to produce a highly ordered output sequence with individual droplet volumes of about 500 nL volume. The experimental investigation confirmed a high tolerance of the developed chamber against the variation of key parameters of the dispersed-phase like salt content, pH value and fluid viscosity. The presented fluidic chamber provides a solution for the problem of bridging different droplet volumes in a fluidic networ

Induction Heating in Underwater Wet Welding—Thermal Input, Microstructure and Diffusible Hydrogen Content

Hydrogen-assisted cracking is a major challenge in underwater wet welding of high-strength steels with a carbon equivalent larger than 0.4 wt%. In dry welding processes, post-weld heat treatment can reduce the hardness in the heat-affected zone while simultaneously lowering the diffusible hydrogen concentration in the weldment. However, common heat treatments known from atmospheric welding under dry conditions are non-applicable in the wet environment. Induction heating could make a difference since the heat is generated directly in the workpiece. In the present study, the thermal input by using a commercial induction heating system under water was characterized first. Then, the effect of an additional induction heating was examined with respect to the resulting microstructure of weldments on structural steels with different strength and composition. Moreover, the diffusible hydrogen content in weld metal was analyzed by the carrier gas hot extraction method. Post-weld induction heating could reduce the diffusible hydrogen content by −34% in 30 m simulated water depth

Chip-based duplex real-time PCR for water quality monitoring concerning Legionella pneumophila and Legionella spp.

Based on biomolecular methods, rapid and selective identification of human pathogenic water organisms becomes an important issue. Legionella spp., are pathogenic water bacteria with worldwide significance. Prevalent detection methods for these microorganisms are time and/or cost intensive. We describe a detection setup and relating DNA assay. A miniaturized real-time polymerase chain reaction (real-time PCR) for direct on-line discrimination of Legionella pneumophila and Legionella spp. was established and integrated into a real-time PCR-chip-system. The PCR-chip device combines a temperature controlling unit and a fluorescence intensity measurement. It was designed to achieve rapid amplification, using an approach of real-time fluorescence read out with the intercalating dye EvaGreen® and melting curve analysis, without requiring multiple probes. The presented results exhibit reproducibility and good sensitivity, showing that the setup is suitable for robust, rapid and cost-efficient detection and monitoring of a variety of Legionella spp.in urban water samples