Marginal deformations and defect anomalies

We deform a defect conformal field theory by an exactly marginal bulk operator and we consider the dependence on the marginal coupling of flat and spherical defect expectation values. For even dimensional spherical defects we find a logarithmic divergence which can be related to a $a$-type defect anomaly coefficient. This coefficient, for defect theories, is not invariant on the conformal manifold and its dependence on the coupling is controlled to all orders by the one-point function of the associated exactly marginal operator. For odd-dimensional defects, the flat and spherical case exhibit different qualitative behaviors, generalizing to arbitrary dimensions the line-circle anomaly of superconformal Wilson loops. Our results also imply a non-trivial coupling dependence for the recently proposed defect $C$-function. We finally apply our general result to a few specific examples, including superconformal Wilson loops and R\'enyi entropy.Comment: 8 pages, v2: derivation on coupling independence for superconformal surface defects adde

Strenght prediction of the glulam beams based on the information of knots in single lamellas

In this thesis the effect of knots on the structural behaviour in terms of stiffness and strength was studied, in a linear elastic analysis, using Abaqus. Test setups from European standard EN 408 and tests performed in the research centre “Holzforschung München” were modelled, in order to compute mechanical properties and have a qualitative and quantitative estimation of the effect of knots. The attention was then led to the effect of the adhesive layer on the numerical model, for which there is little available literature. Different types of adhesive were used in the modelling procedure to study their effects on the mechanical behaviour of wood. It is shown that the adhesive effect is generally negligible and failure is occurring in wood. All tests results and simulations are referred to thin layers of adhesive. The last part of the study focused on the effect of stress concentrations next to knots. The maximum longitudinal stress was used to predict the glulam strength through the correlation between stress from analysis and strength from tests on single boards. The accuracy of results is not high for slightly defected boards, because other different phenomena outer than knots should be taken into account (fiber deviation, microcracks ecc.). However, predictions are relatively good for the boards with knots and not clusters. The objective of this study was finding an estimation of strength starting from a computationally efficient model, in which few input data are required. Other researches in literature developed tools and models for an accurate analysis of strength, however the required computational resources and input parameters are sensitively increasing

Perturbation theory for string sigma models

In this thesis we investigate quantum aspects of the Green-Schwarz superstring in various AdS backgrounds relevant for the AdS/CFT correspondence, providing several examples of perturbative computations in the corresponding integrable sigma-models. We start by reviewing in details the supercoset construction of the superstring action in $AdS_5 \times S^5$, pointing out the limits of this procedure for $AdS_4$ and $AdS_3$ backgrounds. For the $AdS_4 \times CP^3$ case we give a thorough derivation of an alternative action, based on the double-dimensional reduction of eleven-dimensional super-membranes. We then consider the expansion about the BMN vacuum and the S-matrix for the scattering of worldsheet excitations in the decompactification limit. To evaluate its elements efficiently we describe a unitarity-based method resulting in a very compact formula yielding the cut-constructible part of any one-loop two-dimensional S-matrix. In the second part of this review we analyze the superstring action on $AdS_4 \times CP^3$ expanded around the null cusp vacuum. The free energy of this model, whose computation we reproduce up to two-loops at strong coupling, is related to the cusp anomalous dimension of the ABJM theory and, indirectly, to a non-trivial effective coupling $h(\lambda)$ featuring all integrability-based calculations in $AdS_4/CFT_3$. Finally, we extensively discuss the comparison of the perturbative results and the integrability predictions for the one-loop dispersion relation of GKP excitations. Our results provide valuable data in support of the quantum consistency of the string actions - often debated due to possible issues with cancellation of UV divergences and the lack of manifest power-counting renormalizability - and furnish non-trivial stringent tests for the quantum integrability of the analyzed models.Comment: 198 pages. Based on the author's PhD thesis and on the publications arXiv:1304.1798, arXiv:1401.0448, arXiv:1405.7947, arXiv:1407.4788, arXiv:1505.0078

More on microstate geometries of 4d black holes

We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in $\mathbb{R}^3$. Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.Comment: 25 page

Time series kernel similarities for predicting Paroxysmal Atrial Fibrillation from ECGs

We tackle the problem of classifying Electrocardiography (ECG) signals with the aim of predicting the onset of Paroxysmal Atrial Fibrillation (PAF). Atrial fibrillation is the most common type of arrhythmia, but in many cases PAF episodes are asymptomatic. Therefore, in order to help diagnosing PAF, it is important to design procedures for detecting and, more importantly, predicting PAF episodes. We propose a method for predicting PAF events whose first step consists of a feature extraction procedure that represents each ECG as a multi-variate time series. Successively, we design a classification framework based on kernel similarities for multi-variate time series, capable of handling missing data. We consider different approaches to perform classification in the original space of the multi-variate time series and in an embedding space, defined by the kernel similarity measure. We achieve a classification accuracy comparable with state of the art methods, with the additional advantage of detecting the PAF onset up to 15 minutes in advance