Scalar masses in general N=2 gauged supergravity theories

We readdress the question of whether any universal upper bound exists on the square mass m^2 of the lightest scalar around a supersymmetry breaking vacuum in generic N=2 gauged supergravity theories for a given gravitino mass m_3/2 and cosmological constant V. We review the known bounds which apply to theories with restricted matter content from a new perspective. We then extend these results to theories with both hyper and vector multiplets and a gauging involving only one generator, for which we show that such a bound exists for both V>0 and V<0. We finally argue that there is no bound for the same theories with a gauging involving two or more generators. These results imply that in N=2 supergravity theories metastable de Sitter vacua with V<<m^2_3/2 can only arise if at least two isometries are gauged, while those with V>>m^2_3/2 can also arise when a single isometry is gauged.Comment: 19 pages, 1 figure; v2 minor corrections and addition

Simple metastable de Sitter vacua in N=2 gauged supergravity

We construct a simple class of N=2 gauged supergravity theories that admit metastable de Sitter vacua, generalizing the recent work done in the context of rigid supersymmetry. The setup involves one hypermultiplet and one vector multiplet spanning suitably curved quaternionic-Kahler and special-Kahler geometries, with an Abelian gauging based on a single triholomorphic isometry, but neither Fayet-Iliopoulos terms nor non-Abelian gauge symmetries. We construct the most general model of this type and show that in such a situation the possibility of achieving metastable supersymmetry breaking vacua crucially depends on the value of the cosmological constant V relative to the gravitino mass squared m_{3/2}^2 in Planck units. In particular, focusing on de Sitter vacua with positive V, we show that metastability is only possible when V >= 2.17 m_{3/2}^2. We also derive an upper bound on the lightest scalar mass in this kind of model relative to the gravitino mass m_{3/2} as a function of the cosmological constant V, and discuss its physical implications.Comment: 26 pages, 2 figures; v2 minor corrections, some additional comments and one reference adde

On the global structure of conformal gradient solitons with nonnegative Ricci tensor

In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product $\mathbb{R}\times N^{n-1}$, or globally conformally equivalent to the Euclidean space $\mathbb{R}^{n}$ or to the round sphere $\mathbb{S}^{n}$. In particular, we show that any complete, noncompact, gradient Yamabe-type soliton with positive Ricci tensor is rotationally symmetric, whenever the potential function is nonconstant.Comment: Minor correction

Favourable outcome of coronavirus disease 2019 in a patient with anaplastic lymphoma kinase-positive non-small-cell lung cancer receiving alectinib

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Breath analysis for early detection of malignant pleural mesothelioma: Volatile organic compounds (VOCs) determination and possible biochemical pathways

Malignant pleural mesothelioma (MPM) is a rare neoplasm, mainly caused by asbestos exposure, with a high mortality rate. The management of patients with MPM is controversial due to a long latency period between exposure and diagnosis and because of non-specific symptoms generally appearing at advanced stage of the disease. Breath analysis, aimed at the identification of diagnostic Volatile Organic Compounds (VOCs) pattern in exhaled breath, is believed to improve early detection of MPM. Therefore, in this study, breath samples from 14 MPM patients and 20 healthy controls (HC) were collected and analyzed by Thermal Desorption-Gas Chromatography-Mass Spectrometry (TD-GC/MS). Nonparametric test allowed to identify the most weighting variables to discriminate between MPM and HC breath samples and multivariate statistics were applied. Considering that MPM is an aggressive neoplasm leading to a late diagnosis and thus the recruitment of patients is very difficult, a promising data mining approach was developed and validated in order to discriminate between MPM patients and healthy controls, even if no large population data are available. Three different machine learning algorithms were applied to perform the classification task with a leave-one-out cross-validation approach, leading to remarkable results (Area Under Curve AUC = 93%). Ten VOCs, such as ketones, alkanes and methylate derivates, as well as hydrocarbons, were able to discriminate between MPM patients and healthy controls and for each compound which resulted diagnostic for MPM, the metabolic pathway was studied in order to identify the link between VOC and the neoplasm. Moreover, five breath samples from asymptomatic asbestos-exposed persons (AEx) were exploratively analyzed, processed and tested by the validated statistical method as blinded samples in order to evaluate the performance for the early recognition of patients affected by MPM among asbestos-exposed persons. Good agreement was found between the information obtained by gold-standard diagnostic methods such as computed tomography CT and model output

SOME ABSTRACT PROPERTIES OF SEMIGROUPS APPEARING IN SUPERCONFORMAL THEORIES

A new type of semigroups which appears while dealing with $N=1$ superconformal symmetry in superstring theories is considered. The ideal series having unusual abstract properties is constructed. Various idealisers are introduced and studied. The ideal quasicharacter is defined. Green's relations are found and their connection with the ideal quasicharacter is established.Comment: 11 page