Semiclassical low energy scattering for one-dimensional Schr\"odinger operators with exponentially decaying potentials

We consider semiclassical Schr\"odinger operators on the real line of the form $$H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)$$ with $\hbar>0$ small. The potential $V$ is assumed to be smooth, positive and exponentially decaying towards infinity. We establish semiclassical global representations of Jost solutions $f_\pm(\cdot,E;\hbar)$ with error terms that are uniformly controlled for small $E$ and $\hbar$, and construct the scattering matrix as well as the semiclassical spectral measure associated to $H(\hbar)$. This is crucial in order to obtain decay bounds for the corresponding wave and Schr\"odinger flows. As an application we consider the wave equation on a Schwarzschild background for large angular momenta $\ell$ where the role of the small parameter $\hbar$ is played by $\ell^{-1}$. It follows from the results in this paper and \cite{DSS2}, that the decay bounds obtained in \cite{DSS1}, \cite{DS} for individual angular momenta $\ell$ can be summed to yield the sharp $t^{-3}$ decay for data without symmetry assumptions.Comment: 44 pages, minor modifications in order to match the published version, will appear in Annales Henri Poincar

Memetic Multilevel Hypergraph Partitioning

Hypergraph partitioning has a wide range of important applications such as VLSI design or scientific computing. With focus on solution quality, we develop the first multilevel memetic algorithm to tackle the problem. Key components of our contribution are new effective multilevel recombination and mutation operations that provide a large amount of diversity. We perform a wide range of experiments on a benchmark set containing instances from application areas such VLSI, SAT solving, social networks, and scientific computing. Compared to the state-of-the-art hypergraph partitioning tools hMetis, PaToH, and KaHyPar, our new algorithm computes the best result on almost all instances

Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption

We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy at most slightly above that of the ground state.Comment: 40 page

Physical and chemical properties of urban aerosols in São Paulo, Brazil: links between composition and size distribution of submicron particles

In this work, the relationships between size and composition of submicron particles (PM1) were analyzed at an urban site in the Metropolitan Area of São Paulo (MASP), a megacity with about 21 million inhabitants. The measurements were carried out from 20 December 2016 to 15 March 2017. The chemical composition was measured with an Aerodyne Aerosol Chemical Speciation Monitor and size distribution with a TSI Scanning Mobility Particle Sizer 3082. PM1 mass concentrations in the MASP had an average mass concentration of 11.4 µg m−3. Organic aerosol (OA) dominated the PM1 composition (56 %), followed by sulfate (15 %) and equivalent black carbon (eBC, 13 %). Four OA classes were identified using positive matrix factorization: oxygenated organic aerosol (OOA, 40 % of OA), biomass burning organic aerosol (BBOA, 13 %), and two hydrocarbon-like OA components (a typical HOA related to vehicular emissions (16 %) and a second HOA (21 %) representing a mix of anthropogenic sources). Particle number concentrations averaged 12 100±6900 cm−3, dominated by the Aitken mode. The accumulation mode increased under relatively high-PM1 conditions, suggesting an enhancement of secondary organic aerosol (SOA) production. Conversely, the contribution of nucleation-mode particles was less dependent on PM1 levels, consistent with vehicular emissions. The relationship between aerosol size modes and PM1 composition was assessed by multilinear regression (MLR) models. Secondary inorganic aerosols were partitioned between Aitken and accumulation modes, related to condensation particle growth processes. Submicron mass loading in the accumulation mode was mostly associated with highly oxidized OOA and also traffic-related emissions. To the authors' knowledge, this is the first work that uses the MLR methodology to estimate the chemical composition of the different aerosol size modes. The chemical composition with size-dependent PM provides innovative information on the properties of both primary and secondary organic aerosols, as well as inorganic aerosols in a complex urban environment. The results emphasize the relevance of vehicular emissions to the air quality at MASP and highlight the key role of secondary processes on the PM1 ambient concentrations in the region since 56 % of PM1 mass loading was attributed to SOA and secondary inorganic aerosol.</p

Effectiveness of ammonia reduction on control of fine particle nitrate

In some regions, reducing aerosol ammonium nitrate (NH4NO3) concentrations may substantially improve air quality. This can be accomplished by reductions in precursor emissions, such as nitrogen oxides (NOx) to lower nitric acid (HNO3) that partitions to the aerosol, or reductions in ammonia (NH3) to lower particle pH and keep HNO3 in the gas phase. Using the ISORROPIA-II thermodynamic aerosol model and detailed observational data sets, we explore the sensitivity of aerosol NH4NO3 to gas-phase NH3 and NOx controls for a number of contrasting locations, including Europe, the United States, and China. NOx control is always effective, whereas the aerosol response to NH3 control is highly nonlinear and only becomes effective at a thermodynamic sweet spot. The analysis provides a conceptual framework and fundamental evaluation on the relative value of NOx versus NH3 control and demonstrates the relevance of pH as an air quality parameter. We find that, regardless of the locations examined, it is only when ambient particle pH drops below an approximate critical value of 3 (slightly higher in warm and slightly lower in cold seasons) that NH3 reduction leads to an effective response in PM2.5 mass. The required amount of NH3 reduction to reach the critical pH and efficiently decrease NH4NO3 at different sites is assessed. Owing to the linkage between NH3 emissions and agricultural productivity, the substantial NH3 reduction required in some locations may not be feasible. Finally, controlling NH3 emissions to increase aerosol acidity and evaporate NH4NO3 will have other effects, beyond reduction of PM2.5 NH4NO3, such as increasing aerosol toxicity and potentially altering the deposition patterns of nitrogen and trace nutrients.</p

On the spectral properties of L_{+-} in three dimensions

This paper is part of the radial asymptotic stability analysis of the ground state soliton for either the cubic nonlinear Schrodinger or Klein-Gordon equations in three dimensions. We demonstrate by a rigorous method that the linearized scalar operators which arise in this setting, traditionally denoted by L_{+-}, satisfy the gap property, at least over the radial functions. This means that the interval (0,1] does not contain any eigenvalues of L_{+-} and that the threshold 1 is neither an eigenvalue nor a resonance. The gap property is required in order to prove scattering to the ground states for solutions starting on the center-stable manifold associated with these states. This paper therefore provides the final installment in the proof of this scattering property for the cubic Klein-Gordon and Schrodinger equations in the radial case, see the recent theory of Nakanishi and the third author, as well as the earlier work of the third author and Beceanu on NLS. The method developed here is quite general, and applicable to other spectral problems which arise in the theory of nonlinear equations

Circulating MACC1 transcripts in colorectal cancer patient plasma predict metastasis and prognosis

BACKGROUND: Metastasis is the most frequent cause of treatment failure and death in colorectal cancer. Early detection of tumors and metastases is crucial for improving treatment strategies and patient outcome. Development of reliable biomarkers and simple tests routinely applicable in the clinic for detection, prognostication, and therapy monitoring is of special interest. We recently identified the novel gene Metastasis-Associated in Colon Cancer 1 (MACC1), a key regulator of the HGF/Met-pathway. MACC1 is a strong prognostic biomarker for colon cancer metastasis and allows identification of high-risk subjects in early stages, when determined in patients' primary tumors. To overcome the limitation of a restricted number of molecular analyses in tumor tissue, the establishment of a non-invasive blood test for early identification of high-risk cancer patients, for monitoring disease course and therapy response is strongly needed. METHODOLOGY/PRINCIPAL FINDINGS: For the first time, we describe a non-invasive assay for quantification of circulating MACC1 transcripts in blood of more than 300 colorectal cancer patients. MACC1 transcript levels are increased in all disease stages of the cancer patients compared to tumor-free volunteers. Highest MACC1 levels were determined in individuals with metastases (all P<0.05). Importantly, high MACC1 levels correlate with unfavorable survival (P<.0001). Combining MACC1 with circulating transcripts of the metastasis gene S100A4, a transcriptional target of the Wnt/beta-catenin-pathway, improves survival prediction for newly diagnosed cancer patients. CONCLUSION/SIGNIFICANCE: This blood-based assay for circulating MACC1 transcripts, which can be quantitated on a routine basis, is clinically applicable for diagnosis, prognosis, and therapeutic monitoring of cancer patients. Here we demonstrate the diagnostic and prognostic value of circulating MACC1 transcripts in patient plasma for metastasis and survival. Since MACC1 represents a promising target for anti-metastatic therapies, circulating MACC1 transcripts may prove to be an ideal read-out for monitoring therapeutic response of future interventions targeting MACC1-induced metastasis in cancer patients

RAGE mediates S100A4-induced cell motility via MAPK/ERK and hypoxia signaling and is a prognostic biomarker for human colorectal cancer metastasis

Survival of colorectal cancer patients is strongly dependent on development of distant metastases. S100A4 is a prognostic biomarker and inducer for colorectal cancer metastasis. Besides exerting intracellular functions, S100A4 is secreted extracellularly. The receptor for advanced glycation end products (RAGE) is one of its interaction partners. The impact of the S100A4-RAGE interaction for cell motility and metastasis formation in colorectal cancer has not been elucidated so far. Here we demonstrate the RAGE-dependent increase in migratory and invasive capabilities of colorectal cancer cells via binding to extracellular S100A4. We show the direct interaction of S100A4 and RAGE, leading to hyperactivated MAPK/ERK and hypoxia signaling. The S100A4-RAGE axis increased cell migration (P<0.005) and invasion (P<0.005), which was counteracted with recombinant soluble RAGE and RAGE-specific antibodies. In colorectal cancer patients, not distantly metastasized at surgery, high RAGE expression in primary tumors correlated with metachronous metastasis, reduced overall (P=0.022) and metastasis-free survival (P=0.021). In summary, interaction of S100A4-RAGE mediates S100A4-induced colorectal cancer cell motility. RAGE by itself represents a biomarker for prognosis of colorectal cancer. Thus, therapeutic approaches targeting RAGE or intervening in S100A4-RAGE-dependent signaling early in tumor progression might represent alternative strategies restricting S100A4-induced colorectal cancer metastasis