Normalizations of Eisenstein integrals for reductive symmetric spaces

We construct minimal Eisenstein integrals for a reductive symmetric space G/H as matrix coefficients of the minimal principal series of G. The Eisenstein integrals thus obtained include those from the \sigma-minimal principal series. In addition, we obtain related Eisenstein integrals, but with different normalizations. Specialized to the case of the group, this wider class includes Harish-Chandra's minimal Eisenstein integrals.Comment: 66 pages. Minor revisions. To be published in Journal of Functional Analysi

KK-invariant cusp forms for reductive symmetric spaces of split rank one

Let $G/H$ be a reductive symmetric space of split rank $1$ and let $K$ be a maximal compact subgroup of $G$. In a previous article the first two authors introduced a notion of cusp forms for $G/H$. We show that the space of cusp forms coincides with the closure of the $K$-finite generalized matrix coefficients of discrete series representations if and only if there exist no $K$-spherical discrete series representations. Moreover, we prove that every $K$-spherical discrete series representation occurs with multiplicity $1$ in the Plancherel decomposition of $G/H$.Comment: 12 page

Vortex trapping and expulsion in thin-film YBCO strips

A scanning SQUID microscope was used to image vortex trapping as a function of the magnetic induction during cooling in thin-film YBCO strips for strip widths W from 2 to 50 um. We found that vortices were excluded from the strips when the induction Ba was below a critical induction Bc. We present a simple model for the vortex exclusion process which takes into account the vortex - antivortex pair production energy as well as the vortex Meissner and self-energies. This model predicts that the real density n of trapped vortices is given by n=(Ba-BK)/Phi0 with BK = 1.65Phi0/W^2 and Phi0 = h/2e the superconducting flux quantum. This prediction is in good agreement with our experiments on YBCO, as well as with previous experiments on thin-film strips of niobium. We also report on the positions of the trapped vortices. We found that at low densities the vortices were trapped in a single row near the centers of the strips, with the relative intervortex spacing distribution width decreasing as the vortex density increased, a sign of longitudinal ordering. The critical induction for two rows forming in the 35 um wide strip was (2.89 + 1.91-0.93)Bc, consistent with a numerical prediction

Mutant generation by allelic exchange and genome resequencing of the biobutanol organism Clostridium acetobutylicum ATCC 824

BackgroundClostridium acetobutylicum represents a paradigm chassis for the industrial production of the biofuel biobutanol and a focus for metabolic engineering. We have previously developed procedures for the creation of in-frame, marker-less deletion mutants in the pathogen Clostridium difficile based on the use of pyrE and codA genes as counter selection markers. In the current study we sought to test their suitability for use in C. acetobutylicum.ResultsBoth systems readily allowed the isolation of in-frame deletions of the C. acetobutylicum ATCC 824 spo0A and the cac824I genes, leading to a sporulation minus phenotype and improved transformation, respectively. The pyrE-based system was additionally used to inactivate a putative glycogen synthase (CA_C2239, glgA) and the pSOL1 amylase gene (CA_P0168, amyP), leading to lack of production of granulose and amylase, respectively. Their isolation provided the opportunity to make use of one of the key pyrE system advantages, the ability to rapidly complement mutations at appropriate gene dosages in the genome. In both cases, their phenotypes were restored in terms of production of granulose (glgA) and amylase (amyP). Genome re-sequencing of the ATCC 824 COSMIC consortium laboratory strain used revealed the presence of 177 SNVs and 49 Indels, including a 4916-bp deletion in the pSOL1 megaplasmid. A total of 175 SNVs and 48 Indels were subsequently shown to be present in an 824 strain re-acquired (Nov 2011) from the ATCC and are, therefore, most likely errors in the published genome sequence, NC_003030 (chromosome) and NC_001988 (pSOL1).ConclusionsThe codA or pyrE counter selection markers appear equally effective in isolating deletion mutants, but there is considerable merit in using a pyrE mutant as the host as, through the use of ACE (Allele-Coupled Exchange) vectors, mutants created (by whatever means) can be rapidly complemented concomitant with restoration of the pyrE allele. This avoids the phenotypic effects frequently observed with high copy number plasmids and dispenses with the need to add antibiotic to ensure plasmid retention. Our study also revealed a surprising number of errors in the ATCC 824 genome sequence, while at the same time emphasising the need to re-sequence commonly used laboratory strains

Operation of a high-Tc_{c} SQUID gradiometer with a two-stage Joule-Thomson micro-cooler

Practical applications of high-T$_{c}$ SQUIDs require cheap, simple in operation, and cryogen-free cooling. Mechanical cryo-coolers are generally not suitable for operation with SQUIDs due to their inherent magnetic and vibrational noise. In this work, we utilized a Joule-Thomson microfluidic cooling system to operate our high-T$_{c}$ SQUIDs [1]. The micro-cooler system is based on a commercial desktop CryoLab unit from DEMCON kryoz [2]. It contains a two-stage MEMS micro-cooler with a base temperature of 75 K, gross cooling power of 75 mW@80 K, and temperature stability ± 50 mK. Our high-TC dc SQUID gradiometers were fabricated from YBa$_{2}$Cu$_{3}$O$_{7-x}$ thin films grown by pulsed laser deposition on 10 mm × 10 mm SrTiO$_{3}$ bicrystal substrates with 24° misorientation angle. The SQUID chip was glued onto a 0.3 mm thick silicon wafer chip carrier that was attached to the second stage of the cold head. The vacuum housing of the cold stage was made from non-magnetic material (polyethylene terephthalate, PET) and evacuated to a base pressure below 2x10$^{-3}$ mbar. The vacuum chamber features a 0.3 mm thick sapphire window that is placed above the sensor/cold stage. We demonstrated that the equivalent magnetic flux noise of the high-T$_{c}$ SQUID gradiometer is largely unaffected by the micro-cooler setup. The cut-off frequency of the 1/f noise in our SQUID measured on the micro-cooler was around 10 Hz. This indicates that the micro-cooler does not introduce significant magnetic fields in the vicinity of the cold stage. We thus demonstrate that such a microfluidic cooling system is a promising technology for cooling of high-T$_{c}$ SQUIDs in practical applications. We also used the micro-cooler system to build a prototype a magnetic ac susceptibility (ACS) system for detection of specific binding reactions between DNA target molecules and functionalized magnetic nanoparticles (fMNP) in liquid solution. The detection principle relies on changes in Brownian rotation dynamics of fMNPs. We present the results of experiments with various concentrations of magnetic nanoparticles and discuss further development of the portable magnetic bioassay system for detection of influenza virus using oligonucleotide-tagged magnetic nanoparticles with sub-picomolar sensitivity. [1] A. Kalabukhov et al., Supercond. Sci. Technol. 29 095014 (2016). [2] http://kryoz.nl/portfolio-item/cryolab-msg

Disruption of the acetate kinase (ack) gene of Clostridium acetobutylicum results in delayed acetate production

In microorganisms, the enzyme acetate kinase (AK) catalyses the formation of ATP from ADP by de-phosphorylation of acetyl phosphate into acetic acid. A mutant strain of Clostridium acetobutylicum lacking acetate kinase activity is expected to have reduced acetate and acetone production compared to the wild type. In this work, a C. acetobutylicum mutant strain with a selectively disrupted ack gene, encoding AK, was constructed and genetically and physiologically characterized. The ack− strain showed a reduction in acetate kinase activity of more than 97% compared to the wild type. The fermentation profiles of the ack− and wild-type strain were compared using two different fermentation media, CGM and CM1. The latter contains acetate and has a higher iron and magnesium content than CGM. In general, fermentations by the mutant strain showed a clear shift in the timing of peak acetate production relative to butyrate and had increased acid uptake after the onset of solvent formation. Specifically, in acetate containing CM1 medium, acetate production was reduced by more than 80% compared to the wild type under the same conditions, but both strains produced similar final amounts of solvents. Fermentations in CGM showed similar peak acetate and butyrate levels, but increased acetoin (60%), ethanol (63%) and butanol (16%) production and reduced lactate (−50%) formation by the mutant compared to the wild type. These findings are in agreement with the proposed regulatory function of butyryl phosphate as opposed to acetyl phosphate in the metabolic switch of solventogenic clostridia

Measurement of the tt̄W and tt̄Z production cross sections in pp collisions at √s = 8 TeV with the ATLAS detector

The production cross sections of top-quark pairs in association with massive vector bosons have been measured using data from pp collisions at s√ = 8 TeV. The dataset corresponds to an integrated luminosity of 20.3 fb−¹ collected by the ATLAS detector in 2012 at the LHC. Final states with two, three or four leptons are considered. A fit to the data considering the tt̄W and tt̄Z processes simultaneously yields a significance of 5.0σ (4.2σ) over the background-only hypothesis for tt¯Wtt¯W (tt̄Z) production. The measured cross sections are σtt̄W = 369 + 100−91 fb and σtt̄Z = 176 + 58−52 fb. The background-only hypothesis with neither tt̄W nor tt̄Z production is excluded at 7.1σ. All measurements are consistent with next-to-leading-order calculations for the tt̄W and tt̄Z processes