Stability of Functional Equations and Properties of Groups

AbstractInvestigating Hyers–Ulam stability of the additive Cauchy equation with domain in a group G, in order to obtain an additive function approximating the given almost additive one we need some properties of G, starting from commutativity to others more sophisticated. The aim of this survey is to present these properties and compare, as far as possible, the classes of groups involved

Secure Cloud-Edge Deployments, with Trust

Assessing the security level of IoT applications to be deployed to heterogeneous Cloud-Edge infrastructures operated by different providers is a non-trivial task. In this article, we present a methodology that permits to express security requirements for IoT applications, as well as infrastructure security capabilities, in a simple and declarative manner, and to automatically obtain an explainable assessment of the security level of the possible application deployments. The methodology also considers the impact of trust relations among different stakeholders using or managing Cloud-Edge infrastructures. A lifelike example is used to showcase the prototyped implementation of the methodology

Statistical properties of time-reversible triangular maps of the square

Time reversal symmetric triangular maps of the unit square are introduced with the property that the time evolution of one of their two variables is determined by a piecewise expanding map of the unit interval. We study their statistical properties and establish the conditions under which their equilibrium measures have a product structure, i.e. factorises in a symmetric form. When these conditions are not verified, the equilibrium measure does not have a product form and therefore provides additional information on the statistical properties of theses maps. This is the case of anti-symmetric cusp maps, which have an intermittent fixed point and yet have uniform invariant measures on the unit interval. We construct the invariant density of the corresponding two-dimensional triangular map and prove that it exhibits a singularity at the intermittent fixed point.Comment: 15 pages, 3 figure

On a general Hyers-Ulam stability result

In this paper, we prove two general theorems about Hyers-Ulam stability of functional equations. As particular cases we obtain many of the results published in the last ten years on the stability of the Cauchy and quadratic equation

Secure FaaS orchestration in the fog: how far are we?

AbstractFunction-as-a-Service (FaaS) allows developers to define, orchestrate and run modular event-based pieces of code on virtualised resources, without the burden of managing the underlying infrastructure nor the life-cycle of such pieces of code. Indeed, FaaS providers offer resource auto-provisioning, auto-scaling and pay-per-use billing at no costs for idle time. This makes it easy to scale running code and it represents an effective and increasingly adopted way to deliver software. This article aims at offering an overview of the existing literature in the field of next-gen FaaS from three different perspectives: (i) the definition of FaaS orchestrations, (ii) the execution of FaaS orchestrations in Fog computing environments, and (iii) the security of FaaS orchestrations. Our analysis identify trends and gaps in the literature, paving the way to further research on securing FaaS orchestrations in Fog computing landscapes

Giustizia e letteratura II

The book explores and links different cultures, disciplines and perspectives, with a far more original and broad approach to the relations between “Justice” and “Literature” than more traditional works focused on “Law” and “Literature”. The many contributions from writers, literature and movie critics, psychologists, and criminal law practitioners and scholars, draw a complex and interdisciplinary path through primary texts of Italian and international literature, with the aim of prompting readers’ reflections about core issues related to law, crime, and responsibility. Through the analysis of masterpieces of literature, theatre and cinema, this book aims at stimulating dialogue and debate, as well as critical abilities and a deep-rooted sense of justice, amongst both law professionals and citizens at large. Literature and other forms of narration are presented here as a privileged key to approach long-standing questions about (amongst other) causes and consequences of crime; victimization and coping mechanisms; the role of criminal law and criminal proceedings; legalism and equity; law and ethics; the ‘time’ of justice; freedom, responsibility, culpability and forgiveness; rules, legality, socialization and culture; language and images as mediums for justice issues; the impact of prejudice and of existing balances of power on the application of the law; social and legal mechanisms of exclusion and inclusion; gender issues and legal systems; and so on. A whole section (Part V) is devoted to crimes against humanity and how the literary testimony may be understood both as a strategy to resist injustice and to seek justice, and as a way to prevent further horrors. Through this quest for justice in literature and arts, the volume proposes a wider cultural and research project which defies traditional formalistic and retributive approaches to criminal law, in order to open new perspectives for restorative and reintegrative strategies

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

Measurements of the charge asymmetry in top-quark pair production in the dilepton final state at s √ =8 TeV with the ATLAS detector

Measurements of the top-antitop quark pair production charge asymmetry in the dilepton channel, characterized by two high-pT leptons (electrons or muons), are presented using data corresponding to an integrated luminosity of 20.3  fb−1 from pp collisions at a center-of-mass energy s√=8  TeV collected with the ATLAS detector at the Large Hadron Collider at CERN. Inclusive and differential measurements as a function of the invariant mass, transverse momentum, and longitudinal boost of the tt¯ system are performed both in the full phase space and in a fiducial phase space closely matching the detector acceptance. Two observables are studied: AℓℓC based on the selected leptons and Att¯C based on the reconstructed tt¯ final state. The inclusive asymmetries are measured in the full phase space to be AℓℓC=0.008±0.006 and Att¯C=0.021±0.016, which are in agreement with the Standard Model predictions of AℓℓC=0.0064±0.0003 and Att¯C=0.0111±0.0004

Study of the B-c(+) -> J/psi D-s(+) and Bc(+) -> J/psi D-s*(+) decays with the ATLAS detector

The decays B-c(+) -> J/psi D-s(+) and B-c(+) -> J/psi D-s*(+) are studied with the ATLAS detector at the LHC using a dataset corresponding to integrated luminosities of 4.9 and 20.6 fb(-1) of pp collisions collected at centre-of-mass energies root s = 7 TeV and 8 TeV, respectively. Signal candidates are identified through J/psi -> mu(+)mu(-) and D-s(()*()+) -> phi pi(+)(gamma/pi(0)) decays. With a two-dimensional likelihood fit involving the B-c(+) reconstructed invariant mass and an angle between the mu(+) and D-s(+) candidate momenta in the muon pair rest frame, the yields of B-c(+) -> J/psi D-s(+) and B-c(+) -> J/psi D-s*(+), and the transverse polarisation fraction in B-c(+) -> J/psi D-s*(+) decay are measured. The transverse polarisation fraction is determined to be Gamma +/-+/-(B-c(+) -> J/psi D-s*(+))/Gamma(B-c(+) -> J/psi D-s*(+)) = 0.38 +/- 0.23 +/- 0.07, and the derived ratio of the branching fractions of the two modes is B-Bc+ -> J/psi D-s*+/B-Bc+ -> J/psi D-s(+) = 2.8(-0.8)(+1.2) +/- 0.3, where the first error is statistical and the second is systematic. Finally, a sample of B-c(+) -> J/psi pi(+) decays is used to derive the ratios of branching fractions B-Bc+ -> J/psi D-s*+/B-Bc+ -> J/psi pi(+) = 3.8 +/- 1.1 +/- 0.4 +/- 0.2 and B-Bc+ -> J/psi D-s*+/B-Bc+ -> J/psi pi(+) = 10.4 +/- 3.1 +/- 1.5 +/- 0.6, where the third error corresponds to the uncertainty of the branching fraction of D-s(+) -> phi(K+ K-)pi(+) decay. The available theoretical predictions are generally consistent with the measurement