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

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

Nonlinear integral equations for finite volume excited state energies of the O(3) and O(4) nonlinear sigma-models

We propose nonlinear integral equations for the finite volume one-particle energies in the O(3) and O(4) nonlinear sigma-models. The equations are written in terms of a finite number of components and are therefore easier to solve numerically than the infinite component excited state TBA equations proposed earlier. Results of numerical calculations based on the nonlinear integral equations and the excited state TBA equations agree within numerical precision.Comment: numerical results adde

An overview on molecular characterization of thymic tumors: Old and new targets for clinical advances

Thymic tumors are a group of rare mediastinal malignancies that include three different histological subtypes with completely different clinical behavior: the thymic carcinomas, the thymomas, and the rarest thymic neuroendocrine tumors. Nowadays, few therapeutic options are available for relapsed and refractory thymic tumors after a first-line platinum-based chemotherapy. In the last years, the deepening of knowledge on thymus’ biological characterization has opened possibilities for new treatment options. Several clinical trials have been conducted, the majority with disappointing results mainly due to inaccurate patient selection, but recently some encouraging results have been presented. In this review, we summarize the molecular alterations observed in thymic tumors, underlying the great biological differences among the different histology, and the promising targeted therapies for the future

Sigma models as perturbed conformal field theories

We show that two-dimensional sigma models are equivalent to certain perturbed conformal field theories. When the fields in the sigma model take values in a space G/H for a group G and a maximal subgroup H, the corresponding conformal field theory is the $k\to\infty$ limit of the coset model $(G/H)_k$, and the perturbation is related to the current of G. This correspondence allows us for example to find the free energy for the "O(n)" (=O(n)/O(n-1)) sigma model at non-zero temperature. It also results in a new approach to the CP^{n} model.Comment: 4 pages. v2: corrects typos (including several in the published version

Update on enantiomeric composition of (1R)-(+) and (1S)-(-) camphor in essential oil by enantioselettive gas chromatography

The enantiomeric ratios of camphor have been determined in authentic essential oils, using heptakis(6-O-t-butylsilyl-2,3-di-O-ethyl)-beta-cyclodextrin as the chiral stationary phase. An enantiomeric excess of (1S)-(-) within 72-75% is characteristic of coriander oil (Coriandrum sativum L.). Contrary, an enantiomeric excess of (1R)-(+) characterizes the essential oil of sage (> 90% for Salvia sclarea L. and 50-70% for Salvia officinalis L.) and of basil (> 94% for Ocimum basilicum L.)

Identification of observables in quantum toboggans

Quantum systems with real energies generated by an apparently non-Hermitian Hamiltonian may re-acquire the consistent probabilistic interpretation via an ad hoc metric which specifies the set of observables in the updated Hilbert space of states. The recipe is extended here to quantum toboggans. In the first step the tobogganic integration path is rectified and the Schroedinger equation is given the generalized eigenvalue-problem form. In the second step the general double-series representation of the eligible metric operators is derived.Comment: 25 p

The Dressing Factor and Crossing Equations

We utilize the DHM integral representation for the BES dressing factor of the world-sheet S-matrix of the AdS_5xS^5 light-cone string theory, and the crossing equations to fix the principal branch of the dressing factor on the rapidity torus. The results obtained are further used, in conjunction with the fusion procedure, to determine the bound state dressing factor of the mirror theory. We convincingly demonstrate that the mirror bound state S-matrix found in this way does not depend on the internal structure of a bound state solution employed in the fusion procedure. This welcome feature is in perfect parallel to string theory, where the corresponding bound state S-matrix has no bearing on bound state constituent particles as well. The mirror bound state S-matrix we found provides the final missing piece in setting up the TBA equations for the AdS_5xS^5 mirror theory.Comment: LaTex, 48 pages, 10 figures; v2: a new section added where the dressing factor of the mirror theory is found; v3: formula (6.12) is corrected, a new figure is added, accepted for publication in J.Phys.

Psi clustering for the assessment of underground infrastructure deterioration

Remote sensing images find application in several different domains, such as land cover or land usage observation, environmental monitoring, and urbanization. This latter field has recently witnessed an interesting development with the use of remote sensing for infrastructural monitoring. In this work, we present an analysis of Sentinel-1 images, which were used to monitor the Italian provinces of Bologna and Modena located at the Emilia Region Apennines foothill. The goal of this study was the development of a machine learning-based detection system to monitor the deterioration of public aqueduct infrastructures based on Persistent Scatterer Interferometry (PSI). We evaluated the land deformation over a temporal range of five years; these series feed a k-means clustering algorithm to separate the pixels of the region according to different deformation patterns. Furthermore, we defined the critical areas as those areas where different patterns collided or overlapped. The proposed approach provides an informative tool for the structural health monitoring of underground infrastructures

Lattice fermion models with supersymmetry

We investigate a family of lattice models with manifest N=2 supersymmetry. The models describe fermions on a 1D lattice, subject to the constraint that no more than k consecutive lattice sites may be occupied. We discuss the special properties arising from the supersymmetry, and present Bethe ansatz solutions of the simplest models. We display the connections of the k=1 model with the spin-1/2 antiferromagnetic XXZ chain at \Delta=-1/2, and the k=2 model with both the su(2|1)-symmetric tJ model in the ferromagnetic regime and the integrable spin-1 XXZ chain at \Delta=-1/\sqrt{2}. We argue that these models include critical points described by the superconformal minimal models.Comment: 28 pages. v2: added new result on mapping to XXZ chai