On the characterization of trace class representations and Schwartz operators

In this note we collect several characterizations of unitary representations $(\pi, \mathcal{H})$ of a finite dimensional Lie group $G$ which are trace class, i.e., for each compactly supported smooth function $f$ on $G$, the operator $\pi(f)$ is trace class. In particular we derive the new result that, for some $m \in \mathbb{N}$, all operators $\pi(f)$, $f \in C^m_c(G)$, are trace class. As a consequence the corresponding distribution character $\theta_\pi$ is of finite order. We further show $\pi$ is trace class if and only if every operator $A$, which is smoothing in the sense that $A\mathcal{H}\subseteq \mathcal{H}^\infty$, is trace class and that this in turn is equivalent to the Fr\'echet space $\mathcal{H}^\infty$ being nuclear, which in turn is equivalent to the realizability of the Gaussian measure of $\mathcal{H}$ on the space $\mathcal{H}^{-\infty}$ of distribution vectors. Finally we show that, even for infinite dimensional Fr\'echet-Lie groups, $A$ and $A^*$ are smoothing if and only if $A$ is a Schwartz operator, i.e., all products of $A$ with operators from the derived representation are bounded

Polyphonic sonification of electrocardiography signals for diagnosis of cardiac pathologies

Kather JN, Hermann T, Bukschat Y, Kramer T, Schad LR, Zöllner FG. Polyphonic sonification of electrocardiography signals for diagnosis of cardiac pathologies. Scientific Reports. 2017;7(1): 44549.Electrocardiography (ECG) data are multidimensional temporal data with ubiquitous applications in the clinic. Conventionally, these data are presented visually. It is presently unclear to what degree data sonification (auditory display), can enable the detection of clinically relevant cardiac pathologies in ECG data. In this study, we introduce a method for polyphonic sonification of ECG data, whereby different ECG channels are simultaneously represented by sound of different pitch. We retrospectively applied this method to 12 samples from a publicly available ECG database. We and colleagues from our professional environment then analyzed these data in a blinded. Based on these analyses, we found that the sonification technique can be intuitively understood after a short training session. On average, the correct classification rate for observers trained in cardiology was 78%, compared to 68% and 50% for observers not trained in cardiology or not trained in medicine at all, respectively. These values compare to an expected random guessing performance of 25%. Strikingly, 27% of all observers had a classification accuracy over 90%, indicating that sonification can be very successfully used by talented individuals. These findings can serve as a baseline for potential clinical applications of ECG sonification

Maleimide-functionalised platinum(IV) complexes as synthetic platform for targeted drug delivery

Maleimide-functionalised Pt(IV) complexes with highly selective binding properties to thiol groups were synthesised as precursors for binding of thiol-containing tumour targeting molecules like human serum albumi

Equatorial Pacific forcing of western Amazonian precipitation during Heinrich Stadial 1

Abundant hydroclimatic evidence from western Amazonia and the adjacent Andes documents wet conditions during Heinrich Stadial 1 (HS1, 18–15 ka), a cold period in the high latitudes of the North Atlantic. This precipitation anomaly was attributed to a strengthening of the South American summer monsoon due to a change in the Atlantic interhemispheric sea surface temperature (SST) gradient. However, the physical viability of this mechanism has never been rigorously tested. We address this issue by combining a thorough compilation of tropical South American paleorecords and a set of atmosphere model sensitivity experiments. Our results show that the Atlantic SST variations alone, although leading to dry conditions in northern South America and wet conditions in northeastern Brazil, cannot produce increased precipitation over western Amazonia and the adjacent Andes during HS1. Instead, an eastern equatorial Pacific SST increase (i.e., 0.5–1.5 °C), in response to the slowdown of the Atlantic Meridional Overturning Circulation during HS1, is crucial to generate the wet conditions in these regions. The mechanism works via anomalous low sea level pressure over the eastern equatorial Pacific, which promotes a regional easterly low-level wind anomaly and moisture recycling from central Amazonia towards the Andes

Evaluating stratospheric ozone and water vapour changes in CMIP6 models from 1850 to 2100

Stratospheric ozone and water vapour are key components of the Earth system, and past and future changes to both have important impacts on global and regional climate. Here, we evaluate long-term changes in these species from the pre-industrial period (1850) to the end of the 21st century in Coupled Model Intercomparison Project phase 6 (CMIP6) models under a range of future emissions scenarios. There is good agreement between the CMIP multi-model mean and observations for total column ozone (TCO), although there is substantial variation between the individual CMIP6 models. For the CMIP6 multi-model mean, global mean TCO has increased from ∼300 DU in 1850 to ∼ 305 DU in 1960, before rapidly declining in the 1970s and 1980s following the use and emission of halogenated ozone-depleting substances (ODSs). TCO is projected to return to 1960s values by the middle of the 21st century under the SSP2-4.5, SSP3-7.0, SSP4-3.4, SSP4-6.0, and SSP5-8.5 scenarios, and under the SSP3-7.0 and SSP5-8.5 scenarios TCO values are projected to be ∼ 10 DU higher than the 1960s values by 2100. However, under the SSP1-1.9 and SSP1-1.6 scenarios, TCO is not projected to return to the 1960s values despite reductions in halogenated ODSs due to decreases in tropospheric ozone mixing ratios. This global pattern is similar to regional patterns, except in the tropics where TCO under most scenarios is not projected to return to 1960s values, either through reductions in tropospheric ozone under SSP1-1.9 and SSP1-2.6, or through reductions in lower stratospheric ozone resulting from an acceleration of the Brewer-Dobson circulation under other Shared Socioeconomic Pathways (SSPs). In contrast to TCO, there is poorer agreement between the CMIP6 multi-model mean and observed lower stratospheric water vapour mixing ratios, with the CMIP6 multi-model mean underestimating observed water vapour mixing ratios by ∼ 0.5 ppmv at 70 hPa. CMIP6 multi-model mean stratospheric water vapour mixing ratios in the tropical lower stratosphere have increased by ∼ 0.5 ppmv from the pre-industrial to the present-day period and are projected to increase further by the end of the 21st century. The largest increases (∼ 2 ppmv) are simulated under the future scenarios with the highest assumed forcing pathway (e.g. SSP5-8.5). Tropical lower stratospheric water vapour, and to a lesser extent TCO, shows large variations following explosive volcanic eruptions. © Author(s) 2021

Evaluating stratospheric ozone and water vapour changes in CMIP6 models from 1850 to 2100

Stratospheric ozone and water vapour are key components of the Earth system, and past and future changes to both have important impacts on global and regional climate. Here, we evaluate long-term changes in these species from the pre-industrial period (1850) to the end of the 21st century in Coupled Model Intercomparison Project phase 6 (CMIP6) models under a range of future emissions scenarios. There is good agreement between the CMIP multi-model mean and observations for total column ozone (TCO), although there is substantial variation between the individual CMIP6 models. For the CMIP6 multi-model mean, global mean TCO has increased from ∼300 DU in 1850 to ∼ 305 DU in 1960, before rapidly declining in the 1970s and 1980s following the use and emission of halogenated ozone-depleting substances (ODSs). TCO is projected to return to 1960s values by the middle of the 21st century under the SSP2-4.5, SSP3-7.0, SSP4-3.4, SSP4-6.0, and SSP5-8.5 scenarios, and under the SSP3-7.0 and SSP5-8.5 scenarios TCO values are projected to be ∼ 10 DU higher than the 1960s values by 2100. However, under the SSP1-1.9 and SSP1-1.6 scenarios, TCO is not projected to return to the 1960s values despite reductions in halogenated ODSs due to decreases in tropospheric ozone mixing ratios. This global pattern is similar to regional patterns, except in the tropics where TCO under most scenarios is not projected to return to 1960s values, either through reductions in tropospheric ozone under SSP1-1.9 and SSP1-2.6, or through reductions in lower stratospheric ozone resulting from an acceleration of the Brewer-Dobson circulation under other Shared Socioeconomic Pathways (SSPs). In contrast to TCO, there is poorer agreement between the CMIP6 multi-model mean and observed lower stratospheric water vapour mixing ratios, with the CMIP6 multi-model mean underestimating observed water vapour mixing ratios by ∼ 0.5 ppmv at 70 hPa. CMIP6 multi-model mean stratospheric water vapour mixing ratios in the tropical lower stratosphere have increased by ∼ 0.5 ppmv from the pre-industrial to the present-day period and are projected to increase further by the end of the 21st century. The largest increases (∼ 2 ppmv) are simulated under the future scenarios with the highest assumed forcing pathway (e.g. SSP5-8.5). Tropical lower stratospheric water vapour, and to a lesser extent TCO, shows large variations following explosive volcanic eruptions