Complex WKB Analysis of a PT Symmetric Eigenvalue Problem

The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied, and found to have an extremely rich structure. In this paper we present an explanation for these spectral properties in terms of quantisation conditions obtained from the complex WKB method. In particular, we consider the relation of the quantisation conditions to the reality and positivity properties of the eigenvalues. The methods are also used to examine further the pattern of eigenvalue degeneracies observed by Dorey et al. in [1,2].Comment: 22 pages, 13 figures. Added references, minor revision

On the Thermodynamic Bethe Ansatz Equation in Sinh-Gordon Model

Two implicit periodic structures in the solution of sinh-Gordon thermodynamic Bethe ansatz equation are considered. The analytic structure of the solution as a function of complex $\theta$ is studied to some extent both analytically and numerically. The results make a hint how the CFT integrable structures can be relevant in the sinh-Gordon and staircase models. More motivations are figured out for subsequent studies of the massless sinh-Gordon (i.e. Liouville) TBA equation.Comment: 32 pages, 18 figures, myart.st

The dilute A_L models and the integrable perturbations of unitary minimal CFTs

Recently, a set of thermodynamic Bethe ansatz equations is proposed by Dorey, Pocklington and Tateo for unitary minimal models perturbed by \phi_{1,2} or \phi_{2,1} operator. We examine their results in view of the lattice analogues, dilute A_L models at regime 1 and 2. Taking M_{5,6}+\phi_{1,2} and M_{3,4}+\phi_{2,1} as the simplest examples, we will explicitly show that the conjectured TBA equations can be recovered from the lattice model in a scaling limit.Comment: 14 pages, 2 figure

Machine learning for cloud detection of globally distributed sentinel-2 images

In recent years, a number of different procedures have been proposed for segmentation of remote sensing images, basing on spectral information. Model-based and machine learning strategies have been investigated in several studies. This work presents a comprehensive overview and an unbiased comparison of the most adopted segmentation strategies: Support Vector Machines (SVM), Random Forests, Neural networks, Sen2Cor, FMask and MAJA. We used a training set for learning and two different independent sets for testing. The comparison accounted for 135 images acquired from 54 different worldwide sites. We observed that machine learning segmentations are extremely reliable when the training and test are homogeneous. SVM performed slightly better than other methods. In particular, when using heterogeneous test data, SVM remained the most accurate segmentation method while state-of-the-art model-based methods such as MAJA and FMask obtained better sensitivity and precision, respectively. Therefore, even if each method has its specific advantages and drawbacks, SVM resulted in a competitive option for remote sensing applications

Development and validation of a nomogram predicting recurrence risk in women with symptomatic urinary tract infection

Objectives: To develop and externally validate a novel nomogram predicting recurrence risk probability at 12 months in women after an episode of urinary tract infection. Methods: The study included 768women from Santa Maria Annunziata Hospital, Florence, Italy, affected by urinary tract infections from January 2005 to December 2009. Another 373 women with the same criteria enrolled at Santa Chiara Hospital, Trento, Italy, from January 2010 to June 2012 were used to externally validate and calibrate the nomogram. Univariate and multivariate Cox regression models tested the relationship between urinary tract infection recurrence risk, and patient clinical and laboratory characteristics. The nomogram was evaluated by calculating concordance probabilities, as well as testing calibration of predicted urinary tract infection recurrence with observed urinary tract infections. Nomogram variables included: number of partners, bowel function, type of pathogens isolated (Grampositive/ negative), hormonal status, number of previous urinary tract infection recurrences and previous treatment of asymptomatic bacteriuria. Results: Of the original development data, 261 out of 768 women presented at least one episode of recurrence of urinary tract infection (33.9%). The nomogram had a concordance index of 0.85. The nomogram predictions were well calibrated. This model showed high discrimination accuracy and favorable calibration characteristics. In the validation group (373 women), the overall c-index was 0.83 (P = 0.003, 95% confidence interval 0.51–0.99), whereas the area under the receiver operating characteristic curve was 0.85 (95% confidence interval 0.79–0.91). Conclusions: The present nomogram accurately predicts the recurrence risk of urinary tract infection at 12 months, and can assist in identifying women at high risk of symptomatic recurrence that can be suitable candidates for a prophylactic strategy

Shannon entropy approach reveals relevant genes in Alzheimer's disease

Alzheimer's disease (AD) is the most common type of dementia and affects millions of people worldwide. Since complex diseases are often the result of combinations of gene interactions, microarray data and gene co-expression analysis can provide tools for addressing complexity. Our study aimed to find groups of interacting genes that are relevant in the development of AD. In this perspective, we implemented a method proposed in a previous work to detect gene communities linked to AD. Our strategy combined co-expression network analysis with the study of Shannon entropy of the betweenness. We analyzed the publicly available GSE1297 dataset, achieved from the GEO database in NCBI, containing hippocampal gene expression of 9 control and 22 AD human subjects. Co-expressed genes were clustered into different communities. Two communities of interest (composed by 72 and 39 genes) were found by calculating the correlation coefficient between communities and clinical features. The detected communities resulted stable, replicated on two independent datasets and mostly enriched in pathways closely associated with neuro-degenative diseases. A comparison between our findings and other module detection techniques showed that the detected communities were more related to AD phenotype. Lastly, the hub genes within the two communities of interest were identified by means of a centrality analysis and a bootstrap procedure. The communities of the hub genes presented even stronger correlation with clinical features. These findings and further explorations on the detected genes could shed light on the genetic aspects related with physiological aspects of Alzheimer's disease

Evaluation of the colorimetric tetrazolium assay for the cytotoxicity testing a commercial vanilla flavouring

The tetrazolium colorimetric assay (MTT-assay) has been used to evaluate the cytotoxicity of a vanilla flavouring found on the market. It was characterised by the use of 1,2-propylene glycol and glycerol as diluents and by the presence of vanillin, heliotropine and the corresponding 1,2-propylene and glycerol acetals. The method developed by Mosmann (J. Immunol. Methods 65, 55\u201363-1983) was used with some modifications. The same assay was applied to the diluent 1,2-propylene glycol in order to verify its possible influence on the toxic effect. This technique proved useful for preliminary screening useful to evidence doubts relating to the safety of flavouring preparations