Speeding up Cylindrical Algebraic Decomposition by Gr\"obner Bases

Gr\"obner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a mixed system of equalities and inequalities, it is possible to apply Gr\"obner bases to the (conjoined) equalities before invoking CAD. We see that this is, quite often but not always, a beneficial preconditioning of the CAD problem. It is also possible to precondition the (conjoined) inequalities with respect to the equalities, and this can also be useful in many cases.Comment: To appear in Proc. CICM 2012, LNCS 736

Campholenic aldehyde ozonolysis: a mechanism leading to specific biogenic secondary organic aerosol constituents

In the present study, campholenic aldehyde ozonolysis was performed to investigate pathways leading to specific biogenic secondary organic aerosol (SOA) marker compounds. Campholenic aldehyde, a known α-pinene oxidation product, is suggested to be a key intermediate in the formation of terpenylic acid upon α-pinene ozonolysis. It was reacted with ozone in the presence and absence of an OH radical scavenger, leading to SOA formation with a yield of 0.75 and 0.8, respectively. The resulting oxidation products in the gas and particle phases were investigated employing a denuder/filter sampling combination. Gas-phase oxidation products bearing a carbonyl group, which were collected by the denuder, were derivatised by 2,4-dinitrophenylhydrazine (DNPH) followed by liquid chromatography/negative ion electrospray ionisation time-of-flight mass spectrometry analysis and were compared to the gas-phase compounds detected by online proton-transfer-reaction mass spectrometry. Particle-phase products were also analysed, directly or after DNPH derivatisation, to derive information about specific compounds leading to SOA formation. Among the detected compounds, the aldehydic precursor of terpenylic acid was identified and its presence was confirmed in ambient aerosol samples from the DNPH derivatisation, accurate mass data, and additional mass spectrometry (MS² and MS³ fragmentation studies). Furthermore, the present investigation sheds light on a reaction pathway leading to the formation of terpenylic acid, involving α-pinene, α-pinene oxide, campholenic aldehyde, and terpenylic aldehyde. Additionally, the formation of diaterpenylic acid acetate could be connected to campholenic aldehyde oxidation. The present study also provides insights into the source of other highly functionalised oxidation products (e.g. <i>m</i> / <i>z</i> 201, C₉H₁₄O₅ and <i>m</i> / <i>z</i> 215, C₁₀H₁₆O₅), which have been observed in ambient aerosol samples and smog chamber-generated monoterpene SOA. The <i>m</i> / <i>z</i> 201 and 215 compounds were tentatively identified as a C₉- and C₁₀-carbonyl-dicarboxylic acid, respectively, based on reaction mechanisms of campholenic aldehyde and ozone, as well as detailed interpretation of mass spectral data, in conjunction with the formation of corresponding DNPH derivatives

Parity of the Pairing Bosons in a High-Temperature Superconductor

We report the observation of a novel effect in the bilayer Pb-Bi2212 high-TC superconductor by means of angle-resolved photoemission with circularly polarized excitation. Different scattering rates, determined as a function of energy separately for the bonding and antibonding copper-oxygen bands, strongly imply that the dominating scattering channel is odd with respect to layer exchange within a bilayer. This is inconsistent with a phonon-mediated scattering and favours the participation of the odd collective spin excitations in the scattering mechanism in near-nodal regions of the k-space, suggesting a magnetic nature of the pairing mediator.Comment: 5 RevTex pages, 4 eps figure

Measurements of Collision Offsets and Difference in vertical Dispersion at the LEP Interaction Points

The beam overlap at the EP interaction points is optimized by monitoring the change in the Bhabha rate during the variation of an electrostatic bump amplitude. A new method has been developed and implemented to measure the difference of the residual vertical dispersion of electrons and positrons at the interaction points based on beam separation measurements at two different beam energies

Overview of the LHC dynamic aperture studies

The dynamic aperture (D.A.) of the LHC is estimated by tracking a thin-lens model of the lattice over a real machine time of 9 seconds. This raw result is then processed to predict the D.A. over longer times and realistic conditions. We discuss the reliability and limits of the method, the phenomena limiting the D.A. and scaling laws used for fast estimates. The long-term dynamic aperture at injection is close to the requirements, with prospects of further improvements

Recent Results on Energy Calibration at LEP

The determination of the centre-of-mass energy at the four experiments installed on the CERN Large Electron Positron (LEP) collider is one of the major ingredients in the Standard Model investigations being carried on in the context of the experimental programme. Several depolarising effects at beam energies beyond 60 GeV limit the application of the Resonant Depolarisation (RD) method, which provi des an energy uncertainty of about ±1 MeV at the Z0 resonance. Extrapolation techniques from magnetic field measurements are used to obtain beam energies in the W-pair region, aiming at a total energy error £15 MeV. Consistency checks over a large range of precisely calibrated energies are mandatory to contain systematic errors from extrapolation. Progress obtained in extending the polarisable ener gy range in the 1997 LEP Run and the preliminary extrapolation errors are reported

Culturally sensitive stepped care for adolescent refugees: efficacy and cost–utility of a multicentric randomized controlled trial

Adolescent refugees and asylum seekers (ARAS) are highly vulnerable to mental health problems. Stepped care models (SCM) and culturally sensitive therapies offer promising treatment approaches to effectively provide necessary medical and psychological support. To our knowledge, we were the first to investigate whether a culturally sensitive SCM will reduce symptoms of depression and PTSD in ARAS more effectively and efficiently than treatment as usual (TAU). We conducted a multicentric, randomized, controlled and rater-blinded trial across Germany with ARAS between the ages of 14 to 21 years. Participants (N = 158) were stratified by their level of depressive symptom severity and then equally randomized to either SCM or TAU. Depending on their severity level, SCM participants were allocated to tailored interventions. Symptom changes were assessed for depression (PHQ) and PTSD (CATS) at four time points, with the primary end point at post-intervention after 12 weeks. Based on an intention-to-treat sample, we used a linear mixed model approach for the main statistical analyses. Further evaluations included cost–utility analyses, sensitivity analyses, follow-up-analyses, response and remission rates and subgroup analysis. We found a significant reduction of PHQ (d = 0.52) and CATS (d = 0.27) scores in both groups. However, there was no significant difference between SCM and TAU. Cost–utility analyses indicated that SCM generated greater cost–utility when measured as quality-adjusted life years compared to TAU. Subgroup analysis revealed different effects for the SCM interventions depending on the outcome measure. Although culturally sensitive, SCMs did not prove to be more effective in symptom change and represent a more cost-effective treatment alternative for mentally burdened ARAS. Our research contributes to the optimization of clinical productivity and the improvement of therapeutic care for ARAS. Disorder-specific interventions should be further investigated

Calibration of centre-of-mass energies at LEP1 for precise measurements of Z properties

The determination of the centre-of-mass energies from the LEP1 data for 1993, 1994 and 1995 is presented. Accurate knowledge of these energies is crucial in the measurement of the Z resonance param eters. The improved understanding of the LEP energy behaviour accumulated during the 1995 energy scan is detailed, while the 1993 and 1994 measurements are revised. For 1993 these supersede the pr eviously published values. Additional instrumentation has allowed the detection of an unexpectedly large energy rise during physics fills. This new effect is accommodated in the modelling of the beam-energy in 1995 and propagated to the 1993 and 1994 energies. New results are reported on the magnet temperature behaviour which constitutes one of the major corrections to the average LEP ene rgy. The 1995 energy scan took place in conditions very different from the previous years. In particular the interaction-point specific corrections to the centre-of-mass energy in 1995 are more complicated than previously: these arise from the modified radiofrequency-system configuration and from opposite-sign vertical dispersion induced by the bunch-train mode of LEP operation. Finall y an improved evaluation of the LEP centre-of-mass energy spread is presented. This significantly improves the precision on the Z width