Generalized boundary strata classes

We describe a generalization of the usual boundary strata classes in the Chow ring of $\overline{\mathcal{M}}_{g,n}$. The generalized boundary strata classes additively span a subring of the tautological ring. We describe a multiplication law satisfied by these classes and check that every double ramification cycle lies in this subring.Comment: For the Proceedings of the 2017 Abel Symposium, 10 page

Performance Evaluation of Vision-Based Algorithms for MAVs

An important focus of current research in the field of Micro Aerial Vehicles (MAVs) is to increase the safety of their operation in general unstructured environments. Especially indoors, where GPS cannot be used for localization, reliable algorithms for localization and mapping of the environment are necessary in order to keep an MAV airborne safely. In this paper, we compare vision-based real-time capable methods for localization and mapping and point out their strengths and weaknesses. Additionally, we describe algorithms for state estimation, control and navigation, which use the localization and mapping results of our vision-based algorithms as input.Comment: Presented at OAGM Workshop, 2015 (arXiv:1505.01065

Reactive Crystallization Kinetics of K2SO4 from Picromerite-Based MgSO4 and KCl

In this work, the kinetic parameters, the degrees of initial supersaturation (S0) and the profiles of supersaturation (S) were determined for the reactive crystallization of K2SO4 from picromerite (K2SO4.MgSO4.6H2O) and KCl. Different reaction temperatures between 5 and 45 °C were considered, and several process analytical techniques were applied. Along with the solution temperature, the crystal chord length distribution (CLD) was continuously followed by an FBRM probe, images of nucleation and growth events as well as the crystal morphology were captured, and the absorbance of the solution was measured via ATR-FTIR spectroscopy. In addition, the ion concentrations were analyzed. It was found that S0 is inversely proportional to the reactive crystallization temperature in the K+, Mg2+/Cl−, SO42−//H2O system at 25 °C, where S0 promotes nucleation and crystal growth of K2SO4 leading to a bimodal CLD. The CLD was converted to square-weighted chord lengths for each S0 to determine the secondary nucleation rate (B), crystal growth rate (G), and suspension density (MT). By correlation, from primary nucleation rate (Bb) and G with S0, the empirical parameters b = 3.61 and g = 4.61 were obtained as the order of primary nucleation and growth, respectively. B versus G and MT were correlated to the reaction temperature providing the rate constants of B and respective activation energy, E = 69.83 kJ∙mol−1. Finally, a general Equation was derived that describes B with parameters KR = 13,810.8, i = 0.75 and j = 0.71. The K2SO4 crystals produced were of high purity, containing maximal 0.51 wt% Mg impurity, and were received with ~73% yield at 5 °C

Progressive changes in microglia and macrophages in spinal cord and peripheral nerve in the transgenic rat model of amyotrophic lateral sclerosis

<p>Abstract</p> <p>Background</p> <p>The role of neuroinflammation in motor neuron death of amyotrophic lateral sclerosis (ALS) is unclear. The human mutant superoxide dismutase-1 (hmSOD1)-expressing murine transgenic model of ALS has provided some insight into changes in microglia activity during disease progression. The purpose of this study was to gain further knowledge by characterizing the immunological changes during disease progression in the spinal cord and peripheral nerve using the more recently developed hmSOD1 rat transgenic model of ALS.</p> <p>Methods</p> <p>Using immunohistochemistry, the extent and intensity of tissue CD11b expression in spinal cord, lumbar nerve roots, and sciatic nerve were evaluated in hmSOD1 rats that were pre-clinical, at clinical onset, and near disease end-stage. Changes in CD11b expression were compared to the detection of MHC class II and CD68 microglial activation markers in the ventral horn of the spinal cord, as well as to the changes in astrocytic GFAP expression.</p> <p>Results</p> <p>Our study reveals an accumulation of microglia/macrophages both in the spinal cord and peripheral nerve prior to clinical onset based on CD11b tissue expression. The microglia formed focal aggregates in the ventral horn and became more widespread as the disease progressed. Hypertrophic astrocytes were not prominent in the ventral horn until after clinical onset, and the enhancement of GFAP did not have a strong correlation to increased CD11b expression. Detection of MHC class II and CD68 expression was found in the ventral horn only after clinical onset. The macrophages in the ventral nerve root and sciatic nerve of hmSOD1 rats were observed encircling axons.</p> <p>Conclusions</p> <p>These findings describe for the first time in the hmSOD1 rat transgenic model of ALS that enhancement of microglia/macrophage activity occurs pre-clinically both in the peripheral nerve and in the spinal cord. CD11b expression is shown to be a superior indicator for early immunological changes compared to other microglia activation markers and astrogliosis. Furthermore, we suggest that the early activity of microglia/macrophages is involved in the early phase of motor neuron degeneration and propose that studies involving immunomodulation in hmSOD1transgenic models need to consider effects on macrophages in peripheral nerves as well as to microglia in the spinal cord.</p

Strain-dependent variation in the early transcriptional response to CNS injury using a cortical explant system

<p>Abstract</p> <p>Background</p> <p>While it is clear that inbred strains of mice have variations in immunological responsiveness, the influence of genetic background following tissue damage in the central nervous system is not fully understood. A cortical explant system was employed as a model for injury to determine whether the immediate transcriptional response to tissue resection revealed differences among three mouse strains.</p> <p>Methods</p> <p>Immunological mRNAs were measured in cerebral cortex from SJL/J, C57BL/6J, and BALB/cJ mice using real time RT-PCR. Freshly isolated cortical tissue and cortical sections incubated in explant medium were examined. Levels of mRNA, normalized to β-actin, were compared using one way analysis of variance with pooled samples from each mouse strain.</p> <p>Results</p> <p>In freshly isolated cerebral cortex, transcript levels of many pro-inflammatory mediators were not significantly different among the strains or too low for comparison. Constitutive, baseline amounts of CD74 and antisecretory factor (ASF) mRNAs, however, were higher in SJL/J and C57BL/6J, respectively. When sections of cortical tissue were incubated in explant medium, increased message for a number of pro-inflammatory cytokines and chemokines occurred within five hours. Message for chemokines, IL-1α, and COX-2 transcripts were higher in C57BL/6J cortical explants relative to SJL/J and BALB/cJ. IL-1β, IL-12/23 p40, and TNF-α were lower in BALB/cJ explants relative to SJL/J and C57BL/6J. Similar to observations in freshly isolated cortex, CD74 mRNA remained higher in SJL/J explants. The ASF mRNA in SJL/J explants, however, was now lower than levels in both C57BL/6J and BALB/cJ explants.</p> <p>Conclusions</p> <p>The short-term cortical explant model employed in this study provides a basic approach to evaluate an early transcriptional response to neurological damage, and can identify expression differences in genes that are influenced by genetic background.</p

Optimal thickness of rectangular superconducting microtraps for cold atomic gases

We study superconducting microtraps with rectangular shapes for cold atomic gases. We present a general argument why microtraps open, if brought close to the surface of the superconductor. We show that for a given width of the strips there exists an optimal thickness under which the closest distance of the microtrap from the superconductor can be achieved. The distance can be significantly improved, if the edge enhancement of the supercurrent near edges and corners is exploited. We compare numerical calculations with results from conformal mapping and show that conformal mapping can often give useful approximate results.Comment: 5 pages, 4 figure

Imaging nonequilibrium atomic vibrations with x-ray diffuse scattering

For over a century, x-ray scattering has been the most powerful tool for determining the equilibrium structure of crystalline materials. Deviations from perfect periodicity, for example due to thermal motion of the atoms, reduces the intensity of the Bragg peaks as well as produces structure in the diffuse scattering background. Analysis of the thermal diffuse scattering (TDS) had been used to determine interatomic force constants and phonon dispersion in relatively simple cases before inelastic neutron scattering became the preferred technique to study lattice dynamics. With the advent of intense synchrotron x-ray sources, there was a renewed interest in TDS for measuring phonon dispersion. The relatively short x-ray pulses emanating from these sources also enables the measurement of phonon dynamics in the time domain. Prior experiments on nonequilibrium phonons were either limited by time-resolution and/or to relatively long wavelength excitations. Here we present the first images of nonequilibrium phonons throughout the Brillouin zone in photoexcited III-V semiconductors, indium-phosphide and indium-antimonide, using picosecond time-resolved diffuse scattering. In each case, we find that the lattice remain out of equilibrium for several hundred picoseconds up to nanoseconds after laser excitation. The non-equilibrium population is dominated by transverse acoustic phonons which in InP are directed along high-symmetry directions. The results have wide implications for the detailed study of electron-phonon and phonon-phonon coupling in solids.Comment: 10 pages, 3 figure