Peaked and low action solutions of NLS equations on graphs with terminal edges

We consider the nonlinear Schroedinger equation with focusing power-type nonlinearity on compact graphs with at least one terminal edge, i.e., an edge ending with a vertex of degree 1. On the one hand, we introduce the associated action functional, and we provide a profile description of positive low action solutions at large frequencies, showing that they concentrate on one terminal edge, where they coincide with suitable rescaling of the unique solution to the corresponding problem on the half-line. On the other hand, a Lyapunov-Schmidt reduction procedure is performed to construct one-peaked and multipeaked positive solutions with sufficiently large frequency, exploiting the presence of one or more terminal edges

Determination of carbonyl compounds in exhaled breath by on-sorbent derivatization coupled with thermal desorption and gas chromatography-tandem mass spectrometry

A reliable method for the determination of carbonyl compounds in exhaled breath based on on-sorbent derivatization coupled with thermal desorption and gas chromatography-tandem mass spectrometry is described. The analytical performances were optimized for a mixture of C2-C9 aldehydes and C3-C9 ketones, particularly interesting for clinical applications, by using an internal standard and applying a 2^3 full factorial design. A volume of sample (250 ml) was loaded at 50 ml min-1 into a Tenax GR sorbent tube containing 130 nmol of O-(2,3,4,5,6-pentafluorobenzyl)hydroxylamine hydrochloride. All compounds showed a limit of detection lower than 200 pptv. The yield of the derivatization procedure was normalized by adding to the sample a known amount of 6D-acetone as an internal standard. This allowed halving the relative standard deviation to 10% and 15% for the mono-and di-carbonyl compounds, respectively, thus improving reliability. The optimized method was applied to the determination of carbonyl compounds in 12 breath samples collected from four patients suffering from heart failure during hospitalization

Comparison of sampling bags for the analysis of volatile organic compounds in breath

Nalophan, Tedlar and Cali-5-Bond polymeric bags were compared to determine the most suitable type for breath sampling and storage when volatile organic compounds are to be determined. Analyses were performed by thermal desorption gas chromatography mass spectrometry. For each bag, the release of contaminants and the chemical stability of a gaseous standard mixture containing eighteen organic compounds, as well as the CO2 partial pressure were assessed. The selected compounds were representative of breath constituents and belonged to different chemical classes (i.e. hydrocarbons, ketones, aldehydes, aromatics, sulfurs and esters). In the case of Nalophan, the influence of the surface-to-volume ratio, related to the bag's filling degree, on the chemical stability was also evaluated. Nalophan bags were found to be the most suitable in terms of contaminants released during storage (only 2-methyl-1,3-dioxalane), good sample stability (up to 24 h for both dry and humid samples), and very limited costs (about 1 for a 20 liter bag). The (film) surface-to-(sample) volume ratio was found to be an important factor affecting the stability of selected compounds, and therefore we recommended to fill the bag completely

Multi-solitary waves for the nonlinear Klein-Gordon equation

International audienceWe consider the nonlinear Klein-Gordon equation in $\R^d$. We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the composing boosted standing waves are stable. It is obtained by solving the equation backward in time around a sequence of approximate multi-solitary waves and showing convergence to a solution with the desired property. The main ingredients of the proof are finite speed of propagation, variational characterizations of the profiles, modulation theory and energy estimates

On the Dynamics of solitons in the nonlinear Schroedinger equation

We study the behavior of the soliton solutions of the equation i((\partial{\psi})/(\partialt))=-(1/(2m)){\Delta}{\psi}+(1/2)W_{{\epsilon}}'({\psi})+V(x){\psi} where W_{{\epsilon}}' is a suitable nonlinear term which is singular for {\epsilon}=0. We use the "strong" nonlinearity to obtain results on existence, shape, stability and dynamics of the soliton. The main result of this paper (Theorem 1) shows that for {\epsilon}\to0 the orbit of our soliton approaches the orbit of a classical particle in a potential V(x).Comment: 29 page

On the stability of standing waves of Klein-Gordon equations in a semiclassical regime

We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.Comment: 9 page

Predicting Heart Failure Patient Events by Exploiting Saliva and Breath Biomarkers Information

The aim of this work is to present a machine learning based method for the prediction of adverse events (mortality and relapses) in patients with heart failure (HF) by exploiting, for the first time, measurements of breath and saliva biomarkers (Tumor Necrosis Factor Alpha, Cortisol and Acetone). Data from 27 patients are used in the study and the prediction of adverse events is achieved with high accuracy (77%) using the Rotation Forest algorithm. As in the near future, biomarkers can be measured at home, together with other physiological data, the accurate prediction of adverse events on the basis of home based measurements can revolutionize HF management

MS-based targeted profiling of oxylipins in COVID-19: A new insight into inflammation regulation

The key role of inflammation in COVID-19 induced many authors to study the cytokine storm, whereas the role of other inflammatory mediators such as oxylipins is still poorly understood. IMPRECOVID was a monocentric retrospective observational pilot study with COVID-19 related pneumonia patients (n = 52) admitted to Pisa University Hospital between March and April 2020. Our MS-based analytical platform permitted the simultaneous determination of sixty plasma oxylipins in a single run at ppt levels for a comprehensive characterisation of the inflammatory cascade in COVID-19 patients. The datasets containing oxylipin and cytokine plasma levels were analysed by principal component analysis (PCA), computation of Fisher's canonical variable, and a multivariate receiver operating characteristic (ROC) curve. Differently from cytokines, the panel of oxylipins clearly differentiated samples collected in COVID-19 wards (n = 43) and Intensive Care Units (ICUs) (n = 27), as shown by the PCA and the multivariate ROC curve with a resulting AUC equal to 0.92. ICU patients showed lower (down to two orders of magnitude) plasma concentrations of anti-inflammatory and pro-resolving lipid mediators, suggesting an impaired inflammation response as part of a prolonged and unsolvable pro-inflammatory status. In conclusion, our targeted oxylipidomics platform helped shedding new light in this field. Targeting the lipid mediator class switching is extremely important for a timely picture of a patient's ability to respond to the viral attack. A prediction model exploiting selected lipid mediators as biomarkers seems to have good chances to classify patients at risk of severe COVID-19