Chiral transition and deconfinement in N_f = 2 QCD

The transition is studied by means of a disorder parameter detecting condensation of magnetic monopoles in the vacuum. The deconfining transition is found to coincide with the chiral transition and the susceptibility \rho, related to the disorder parameter, is consistent with a first order phase transition.Comment: 3 pages, 2 figures. Poster presented at Lattice2004(topology), Fermilab, June 21-26, 200

Monopoles, vortices and confinement in SU(3) gauge theory

We compute, in SU(3) pure gauge theory, the vacuum expectation value (vev) of the operator which creates a $Z_3$ vortex wrapping the lattice through periodic boundary conditions (dual Polyakov line). The technique used is the same already tested in the SU(2) case. The dual Polyakov line proves to be a good disorder parameter for confinement, and has a similar behaviour to the monopole condensate. The new features which characterise the construction of the disorder operator in SU(3) are emphasised.Comment: 8 pages, 4 eps figures, typed with elsart.cl

Color confinement and dual superconductivity of the vacuum. III

It is demonstrated that monopole condensation in the confined phase of SU(2) and SU(3) gauge theories is independent of the specific Abelian projection used to define the monopoles. Hence the dual excitations which condense in the vacuum to produce confinement must have magnetic U(1) charge in all the Abelian projections. Some physical implications of this result are discussed.Comment: 6 pages, 5 postscript figure

Adversarial Robustness Guarantees for Random Deep Neural Networks

The reliability of deep learning algorithms is fundamentally challenged by the existence of adversarial examples, which are incorrectly classified inputs that are extremely close to a correctly classified input. We explore the properties of adversarial examples for deep neural networks with random weights and biases, and prove that for any $p\ge1$, the $\ell^p$ distance of any given input from the classification boundary scales as one over the square root of the dimension of the input times the $\ell^p$ norm of the input. The results are based on the recently proved equivalence between Gaussian processes and deep neural networks in the limit of infinite width of the hidden layers, and are validated with experiments on both random deep neural networks and deep neural networks trained on the MNIST and CIFAR10 datasets. The results constitute a fundamental advance in the theoretical understanding of adversarial examples, and open the way to a thorough theoretical characterization of the relation between network architecture and robustness to adversarial perturbations

Topological aspects of QCD

We review recent results from lattice on topological aspects of QCD: most of the results refer to monopoles and to instantons. We discuss in detail the evidence for condensation of monopoles in the vacuum and confinement of colour by dual superconductivity, and the major role of monopoles in dynamics (monopole dominance). As for instantons we review the $U(1)$ problem, a possible determination of the spin content of the proton, and new lattice data relevant to instanton liquid models.Comment: 8 pages, to be published in the Proceedings of Lattice 95, uuencoded postscript file. IFUP-TH 49/9

A finite temperature investigation of dual superconductivity in the modified SO(3) lattice gauge theory

We study the SO(3) lattice gauge theory in 3+1 dimensions with the adjoint Wilson action modified by a $\mathbb{Z}_2$ monopole suppression term and by means of the Pisa disorder operator. We find evidence for a finite temperature deconfinement transition driven by the condensation of U(1) magnetic charges. A finite-size scaling test shows consistency with the critical exponents of the 3D Ising model.Comment: 14 pages, 4 figures. Layout changed, figures, text and references added. To appear on Physics Letters

SU(2) vortex configuration in Laplacian Center Gauge

We study how Laplacian Center Gauge identifies the vortex content of a thick SU(2) vortex configuration on the lattice. This configuration is a solution of the Yang-Mills classical equations of motion having vortex properties. We find that this gauge fixing procedure cleanly identifies the underlying vortex properties. We also study the monopole content of this configuration detected with this procedure. We obtain two monopole curves lying on the surface of the vortex.Comment: 22 pages, 10 PostScript figures. v2, 21 pages, 10 Postscript figures. Part of the results and part of the conclusions change in v2. v3, 13 pages, 4 Postscript figures, shortened version to appear in PL

The influence of institutional pressures on climate mitigation and adaptation strategies

Starting from institutional theory, this study aims to explore the effects of coercive, normative and mimetic pressures on businesses climate change mitigation and adaptation strategies. In order to test these hypotheses, the study relies on an econometric model by using data from 487 Italian manufacturing companies collected by a questionnaire-based survey. The empirical model based on a multivariate regression reveals that companies which perceive normative and mimetic pressures are more likely to have a higher climate change sensitivity. Moreover, companies with a higher climate change sensitivity are more likely to adopt both mitigation and adaptation strategies. The article provides several contributions. First the study contributes to the debate among institutional scholars by clarifying which institutional pressures exert a more incisive effect on pushing companies to adopt climate actions. Second, it highlights how internal factors play a mediating role between institutional pressures and business climate responses

Dual superconductivity in the SU(2) pure gauge vacuum: a lattice study

We investigate the dual superconductivity hypothesis in pure SU(2) lattice gauge theory. We focus on the dual Meissner effect by analyzing the distribution of the color fields due to a static quark-antiquark pair. We find evidence of the dual Meissner effect both in the maximally Abelian gauge and without gauge fixing. We measure the London penetration length. Our results suggest that the London penetration length is a physical gauge-invariant quantity. We put out a simple relation between the penetration length and the square root of the string tension. We find that our extimation is quite close to the extrapolated continuum limit available in the literature. A remarkable consequence of our study is that an effective Abelian theory can account for the long range properties of the SU(2) confining vacuum.Comment: 38 pages, uuencoded compressed (using GNU's gzip) tar file containing 1 LaTeX2e file (to be processed 3 times) + 16 encapsulated Postscript figures. A full Postscript version of this paper is available at http://www.ba.infn.it/disk$gruppo_4/cosmai/www/papers/195-95.P