Search results for "quantization"
showing 10 items of 253 documents
Integrable systems and moduli spaces of curves
2016
This document has the purpose of presenting in an organic way my research on integrable systems originating from the geometry of moduli spaces of curves, with applications to Gromov-Witten theory and mirror symmetry. The text contains a short introduction to the main ideas and prerequisites of the subject from geometry and mathematical physics, followed by a synthetic review of some of my papers (listed below) starting from my PhD thesis (October 2008), and with some open questions and future developements. My results include: • the triple mirror symmetry among P 1-orbifolds with positive Euler characteristic , the Landau-Ginzburg model with superpotential −xyz + x p + y q + z r with 1 p + …
Numerical stochastic perturbation theory in the Schrödinger functional
2013
The Schr\"odinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.
A robust blind 3-D mesh watermarking based on wavelet transform for copyright protection
2019
Nowadays, three-dimensional meshes have been extensively used in several applications such as, industrial, medical, computer-aided design (CAD) and entertainment due to the processing capability improvement of computers and the development of the network infrastructure. Unfortunately, like digital images and videos, 3-D meshes can be easily modified, duplicated and redistributed by unauthorized users. Digital watermarking came up while trying to solve this problem. In this paper, we propose a blind robust watermarking scheme for three-dimensional semiregular meshes for Copyright protection. The watermark is embedded by modifying the norm of the wavelet coefficient vectors associated with th…
Hybrid blind robust image watermarking technique based on DFT-DCT and Arnold transform
2018
In this paper, a robust blind image watermarking method is proposed for copyright protection of digital images. This hybrid method relies on combining two well-known transforms that are the discrete Fourier transform (DFT) and the discrete cosine transform (DCT). The motivation behind this combination is to enhance the imperceptibility and the robustness. The imperceptibility requirement is achieved by using magnitudes of DFT coefficients while the robustness improvement is ensured by applying DCT to the DFT coefficients magnitude. The watermark is embedded by modifying the coefficients of the middle band of the DCT using a secret key. The security of the proposed method is enhanced by appl…
A Robust Blind 3-D Mesh Watermarking Technique Based on SCS Quantization and Mesh Saliency for Copyright Protection
2019
Due to the recent demand of 3-D meshes in a wide range of applications such as video games, medical imaging, film special effect making, computer-aided design (CAD), among others, the necessity of implementing 3-D mesh watermarking schemes aiming to protect copyright has increased in the last decade. Nowadays, the majority of robust 3-D watermarking approaches have mainly focused on the robustness against attacks while the imperceptibility of these techniques is still a serious challenge. In this context, a blind robust 3-D mesh watermarking method based on mesh saliency and scalar Costa scheme (SCS) for Copyright protection is proposed. The watermark is embedded by quantifying the vertex n…
Robustness Analysis of DCE-MRI-Derived Radiomic Features in Breast Masses: Assessing Quantization Levels and Segmentation Agreement
2022
Featured Application The use of highly robust radiomic features is fundamental to reduce intrinsic dependencies and to provide reliable predictive models. This work presents a study on breast tumor DCE-MRI considering the radiomic feature robustness against the quantization settings and segmentation methods. Machine learning models based on radiomic features allow us to obtain biomarkers that are capable of modeling the disease and that are able to support the clinical routine. Recent studies have shown that it is fundamental that the computed features are robust and reproducible. Although several initiatives to standardize the definition and extraction process of biomarkers are ongoing, th…
Interaction-induced spin polarization in quantum dots.
2010
The electronic states of lateral many electron quantum dots in high magnetic fields are analyzed in terms of energy and spin. In a regime with two Landau levels in the dot, several Coulomb blockade peaks are measured. A zig-zag pattern is found as it is known from the Fock-Darwin spectrum. However, only data from Landau level 0 show the typical spin-induced bimodality, whereas features from Landau level 1 cannot be explained with the Fock-Darwin picture. Instead, by including the interaction effects within spin-density-functional theory a good agreement between experiment and theory is obtained. The absence of bimodality on Landau level 1 is found to be due to strong spin polarization.
Geometric quantization in the presence of an electromagnetic field
1983
Some aspects of the formalism of geometric quantization are described emphasizing the role played by the symmetry group of the quantum system which, for the free particle, turns out to be a central extensionG(m) of the Galilei groupG. The resulting formalism is then applied to the case of a particle interacting with the electromagnetic field, which appears as a necessary modification of the connection 1-form of the quantum bundle when its invariance group is generalized to alocal extension ofG. Finally, the quantization of the electric charge in the presence of a Dirac monopole is also briefly considered.
Topological Hopf Algebras, Quantum Groups and Deformation Quantization
2019
After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologi es on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and their doubles explains their dualities a nd provides a comprehensive framework. Relations with deformation quantization and applications to the deformation quantization of symmetric spaces are described.
Relativistic wave equations from supergroup quantization
1983
A formalism of geometric quantization recently introduced which is based on the consideration of Lie groups which are central extensions by U(1) is applied to the relativistic case by using the N-2 super Poincare group with a central charge.