The mathematical life of Cauchy's group theorem

AbstractCauchy's theorem on the order of finite groups is a fixture of elementary course work in abstract algebra today: its proof is a straightforward exercise in the application of general mathematical tools. The initial proof by Cauchy, however, was unprecedented in its complex computations involving permutational group theory and contained an egregious error. A direct inspiration to Sylow's theorem, Cauchy's theorem was reworked by R. Dedekind, G.F. Frobenius, C. Jordan, and J.H. McKay in ever more natural, concise terms. Its most succinct form employs just the structure lacking in Cauchy's original proof—the wreath product

Characterization of ISP Traffic: Trends, User Habits, and Access Technology Impact

In the recent years, the research community has increased its focus on network monitoring which is seen as a key tool to understand the Internet and the Internet users. Several studies have presented a deep characterization of a particular application, or a particular network, considering the point of view of either the ISP, or the Internet user. In this paper, we take a different perspective. We focus on three European countries where we have been collecting traffic for more than a year and a half through 5 vantage points with different access technologies. This humongous amount of information allows us not only to provide precise, multiple, and quantitative measurements of "What the user do with the Internet" in each country but also to identify common/uncommon patterns and habits across different countries and nations. Considering different time scales, we start presenting the trend of application popularity; then we focus our attention to a one-month long period, and further drill into a typical daily characterization of users activity. Results depict an evolving scenario due to the consolidation of new services as Video Streaming and File Hosting and to the adoption of new P2P technologies. Despite the heterogeneity of the users, some common tendencies emerge that can be leveraged by the ISPs to improve their servic

A Formal Approach to Exploiting Multi-Stage Attacks based on File-System Vulnerabilities of Web Applications (Extended Version)

Web applications require access to the file-system for many different tasks. When analyzing the security of a web application, secu- rity analysts should thus consider the impact that file-system operations have on the security of the whole application. Moreover, the analysis should take into consideration how file-system vulnerabilities might in- teract with other vulnerabilities leading an attacker to breach into the web application. In this paper, we first propose a classification of file- system vulnerabilities, and then, based on this classification, we present a formal approach that allows one to exploit file-system vulnerabilities. We give a formal representation of web applications, databases and file- systems, and show how to reason about file-system vulnerabilities. We also show how to combine file-system vulnerabilities and SQL-Injection vulnerabilities for the identification of complex, multi-stage attacks. We have developed an automatic tool that implements our approach and we show its efficiency by discussing several real-world case studies, which are witness to the fact that our tool can generate, and exploit, complex attacks that, to the best of our knowledge, no other state-of-the-art-tool for the security of web applications can find

Strengthening measurements from the edges: application-level packet loss rate estimation

Network users know much less than ISPs, Internet exchanges and content providers about what happens inside the network. Consequently users cannot either easily detect network neutrality violations or readily exercise their market power by knowledgeably switching ISPs. This paper contributes to the ongoing efforts to empower users by proposing two models to estimate -- via application-level measurements -- a key network indicator, i.e., the packet loss rate (PLR) experienced by FTP-like TCP downloads. Controlled, testbed, and large-scale experiments show that the Inverse Mathis model is simpler and more consistent across the whole PLR range, but less accurate than the more advanced Likely Rexmit model for landline connections and moderate PL

Subtitling Neapolitan Dialect in “My Brilliant Friend”: Linguistic Choices and Sociocultural Implications in the Screen Adaptation of Elena Ferrante’s Best-selling Novel.

n the screen adaptation of Elena Ferrante’s best-selling novel “My Brilliant Friend”, the first foreign language co-production of the American pay-cable network HBO with the Italian public broadcaster RAI, as a specific requirement of the American producers, the Italian of the main characters has been transformed into Neapolitan, a thick regional dialect mostly appropriate to tell the story of a life-long friendship on the backdrop of the 1950s poor outskirts of Naples, the main city of southern Italy. Starting from some background theories of cultural aspects of translation together with audiovisual translation, the aim of this presentation is that of analysing how English subtitlers have faced the translation of the dialectal elements in such a culture-bound audiovisual text and to what extent their choices depend on those made by Italian subtitlers, then discussing about the sociocultural implications of the solutions adopted. The data have been organized and presented with reference to the extralinguistic and the intralinguistic levels (in terms of syntactical, lexico-semantic and crosscultural pragmatic elements)

Dimensioning Renewable Energy Systems to Power Mobile Networks

To face the huge increase in the mobile traffic demand, denser cellular access networks are extensively deployed by mobile operators, entailing high cost for energy supply. Hence, renewable energy (RE) sources are often adopted to power base stations (BSs), in order to make them more self-sufficient and reduce the energy bill. Nevertheless, sizing an RE generation system is a critical task, and the dimensioning methods available in the literature are based on simulation or optimization approaches, hence resulting time consuming or computationally complex. This paper proposes and validates a simple still effective analytical method that, based on the location dependent mean value and variance of RE production, allows to find feasible combinations of photovoltaic (PV) panel and battery sizes, suitable to power a BS and decrease the storage depletion probability below a target threshold. Furthermore, the application of this method highlights the role of RE production variance. Higher values of the variance require larger PV panels, almost doubled with respect to locations with low variance. However, only locations with higher variance benefit from increasing the battery size and relaxing the constraint on energy self-sufficiency, with the scope of reducing the required PV panel capacity and the capital expenditures

A collaborative caching over PLC for remote areas

Power line communication (PLC) technology has emerged to foster ease of reach for broadband access network in remote or developing areas at lower costs by making use of existing wired power infrastructure for electricity distribution. The increase in data demand, pushed by the popularity of communication services, poses an overwhelming burden on the underlying PLC technology, especially for backhaul links. To confront this issue, edge server deployed at the access network improves data processing and reduces network delays and also helps better provisioning of resources which are crucial for PLC networks. Moreover, data caching at specialized nodes such as edge servers brings forth efficient retrieving, storing and processing of data.In this work, we propose a distributed data caching scenario jointly based on edge server (ES) and edge devices (EDs) that are equipped with caching facility and are communicating via PLC in a remote area. We develop a framework to test the mutual collaboration between ES and EDs for content fetching to minimize the use of cloud resources and relieve the load on possibly congested PLC backhaul links. Results reveal that a collaborative caching would boost effective utilization of low bandwidth PLC links and the shift of most popular contents at user premises is crucial to improve socio-economic growth and digital learning platforms for unconnected part of the world