Grassmannian flows and applications to nonlinear partial differential equations

We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting linear evolutionary flows on a Stiefel manifold onto a coordinate chart of the underlying Grassmann manifold. Our method relies on extending this idea to the infinite dimensional case. The key is an integral equation analogous to the Marchenko equation in integrable systems, that represents the coodinate chart map. We show explicitly how to generate such solutions to scalar partial differential equations of arbitrary order with nonlocal quadratic nonlinearities using our approach. We provide numerical simulations that demonstrate the generation of solutions to Fisher--Kolmogorov--Petrovskii--Piskunov equations with nonlocal nonlinearities. We also indicate how the method might extend to more general classes of nonlinear partial differential systems.Comment: 26 pages, 2 figure

Non-Gaussian component analysis: testing the dimension of the signal subspace

Dimension reduction is a common strategy in multivariate data analysis which seeks a subspace which contains all interesting features needed for the subsequent analysis. Non-Gaussian component analysis attempts for this purpose to divide the data into a non-Gaussian part, the signal, and a Gaussian part, the noise. We will show that the simultaneous use of two scatter functionals can be used for this purpose and suggest a bootstrap test to test the dimension of the non-Gaussian subspace. Sequential application of the test can then for example be used to estimate the signal dimension

Double Dissociation of Amygdala and Hippocampal Contributions to Trace and Delay Fear Conditioning

A key finding in studies of the neurobiology of learning memory is that the amygdala is critically involved in Pavlovian fear conditioning. This is well established in delay-cued and contextual fear conditioning; however, surprisingly little is known of the role of the amygdala in trace conditioning. Trace fear conditioning, in which the CS and US are separated in time by a trace interval, requires the hippocampus and prefrontal cortex. It is possible that recruitment of cortical structures by trace conditioning alters the role of the amygdala compared to delay fear conditioning, where the CS and US overlap. To investigate this, we inactivated the amygdala of male C57BL/6 mice with GABA A agonist muscimol prior to 2-pairing trace or delay fear conditioning. Amygdala inactivation produced deficits in contextual and delay conditioning, but had no effect on trace conditioning. As controls, we demonstrate that dorsal hippocampal inactivation produced deficits in trace and contextual, but not delay fear conditioning. Further, pre- and post-training amygdala inactivation disrupted the contextual but the not cued component of trace conditioning, as did muscimol infusion prior to 1- or 4-pairing trace conditioning. These findings demonstrate that insertion of a temporal gap between the CS and US can generate amygdala-independent fear conditioning. We discuss the implications of this surprising finding for current models of the neural circuitry involved in fear conditioning

Prognostic utility of sestamibi lung uptake does not require adjustment for stress-related variables: A retrospective cohort study

BACKGROUND: Increased (99m)Tc-sestamibi stress lung-to-heart ratio (sLHR) has been shown to predict cardiac outcomes similar to pulmonary uptake of thallium. Peak heart rate and use of pharmacologic stress affect the interpretation of lung thallium uptake. The current study was performed to determine whether (99m)Tc-sestamibi sLHR measurements are affected by stress-related variables, and whether this in turn affects prognostic utility. METHODS: sLHR was determined in 718 patients undergoing (99m)Tc-sestamibi SPECT stress imaging. sLHR was assessed in relation to demographics, hemodynamic variables and outcomes (mean follow up 5.6 ± 1.1 years). RESULTS: Mean sLHR was slightly greater in males than in females (P < 0.01) and also showed a weak negative correlation with age (P < 0.01) and systolic blood pressure (P < 0.01), but was unrelated to stress method or heart rate at the time of injection. In patients undergoing treadmill exercise, sLHR was also positively correlated with peak workload (P < 0.05) but inversely with double product (P < 0.05). The combined explanatory effect of sex, age and hemodynamic variables on sLHR was less than 10%. The risk of acute myocardial infarction (AMI) or death increased by a factor of 1.7–1.8 for each SD increase in unadjusted sLHR, and was unaffected by adjustment for sex, age and hemodynamic variables (hazard ratios 1.6–1.7). The area under the ROC curve for the unadjusted sLHR was 0.65 (95% CI 0.59–0.71, P < 0.0001) and was unchanged for the adjusted sLHR (0.65, 95% CI 0.61–0.72, P < 0.0001). CONCLUSION: Stress-related variables have only a weak effect on measured sLHR. Unadjusted and adjusted sLHR provide equivalent prognostic information for prediction of AMI or death

Selective and low temperature transition metal intercalation in layered tellurides

Layered materials embrace rich intercalation reactions to accommodate high concentrations of foreign species within their structures, and find many applications spanning from energy storage, ion exchange to secondary batteries. Light alkali metals are generally most easily intercalated due to their light mass, high charge/volume ratio and in many cases strong reducing properties. An evolving area of materials chemistry, however, is to capture metals selectively, which is of technological and environmental significance but rather unexplored. Here we show that the layered telluride T2PTe2 (T=Ti, Zr) displays exclusive insertion of transition metals (for example, Cd, Zn) as opposed to alkali cations, with tetrahedral coordination preference to tellurium. Interestingly, the intercalation reactions proceed in solid state and at surprisingly low temperatures (for example, 80?°C for cadmium in Ti2PTe2). The current method of controlling selectivity provides opportunities in the search for new materials for various applications that used to be possible only in a liquid

Jet energy measurement with the ATLAS detector in proton-proton collisions at root s=7 TeV

The jet energy scale and its systematic uncertainty are determined for jets measured with the ATLAS detector at the LHC in proton-proton collision data at a centre-of-mass energy of √s = 7TeV corresponding to an integrated luminosity of 38 pb-1. Jets are reconstructed with the anti-kt algorithm with distance parameters R=0. 4 or R=0. 6. Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate jets with transverse momenta pT≥20 GeV and pseudorapidities {pipe}η{pipe}<4. 5. The jet energy systematic uncertainty is estimated using the single isolated hadron response measured in situ and in test-beams, exploiting the transverse momentum balance between central and forward jets in events with dijet topologies and studying systematic variations in Monte Carlo simulations. The jet energy uncertainty is less than 2. 5 % in the central calorimeter region ({pipe}η{pipe}<0. 8) for jets with 60≤pT<800 GeV, and is maximally 14 % for pT<30 GeV in the most forward region 3. 2≤{pipe}η{pipe}<4. 5. The jet energy is validated for jet transverse momenta up to 1 TeV to the level of a few percent using several in situ techniques by comparing a well-known reference such as the recoiling photon pT, the sum of the transverse momenta of tracks associated to the jet, or a system of low-pT jets recoiling against a high-pT jet. More sophisticated jet calibration schemes are presented based on calorimeter cell energy density weighting or hadronic properties of jets, aiming for an improved jet energy resolution and a reduced flavour dependence of the jet response. The systematic uncertainty of the jet energy determined from a combination of in situ techniques is consistent with the one derived from single hadron response measurements over a wide kinematic range. The nominal corrections and uncertainties are derived for isolated jets in an inclusive sample of high-pT jets. Special cases such as event topologies with close-by jets, or selections of samples with an enhanced content of jets originating from light quarks, heavy quarks or gluons are also discussed and the corresponding uncertainties are determined. © 2013 CERN for the benefit of the ATLAS collaboration

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal