On the descriptive complexity of Salem sets

In this paper we study the notion of Salem set from the point of view of descriptive set theory. We first work in the hyperspace $\mathbf{K}([0,1])$ of compact subsets of $[0,1]$ and show that the closed Salem sets form a $\boldsymbol{\Pi}^0_3$-complete family. This is done by characterizing the complexity of the family of sets having sufficiently large Hausdorff or Fourier dimension. We also show that the complexity does not change if we increase the dimension of the ambient space and work in $\mathbf{K}([0,1]^d)$. We then generalize the results by relaxing the compactness of the ambient space, and show that the closed Salem sets are still $\boldsymbol{\Pi}^0_3$-complete when we endow the hyperspace of all closed subsets of $\mathbb{R}^d$ with the Fell topology. A similar result holds also for the Vietoris topology.Comment: Extended Lemma 3.1, fixed Lemma 5.3 and improved the presentation of the results. To appear in Fundamenta Mathematica

Effective aspects of Hausdorff and Fourier dimension

In this paper, we study Hausdorff and Fourier dimension from the point of view of effective descriptive set theory and Type-2 Theory of Effectivity. Working in the hyperspace $\mathbf{K}(X)$ of compact subsets of $X$, with $X=[0,1]^d$ or $X=\mathbb{R}^d$, we characterize the complexity of the family of sets having sufficiently large Hausdorff or Fourier dimension. This, in turn, allows us to show that family of all the closed Salem sets is $\Pi^0_3$-complete. One of our main tools is a careful analysis of the effectiveness of a classical theorem of Kaufman. We furthermore compute the Weihrauch degree of the functions computing Hausdorff and Fourier dimension of closed sets.Comment: 36 page

The open and clopen Ramsey theorems in the Weihrauch lattice

We investigate the uniform computational content of the open and clopen Ramsey theorems in the Weihrauch lattice. While they are known to be equivalent to ATR_0 from the point of view of reverse mathematics, there is not a canonical way to phrase them as multivalued functions. We identify eight di\ufb00erent multivalued functions (\ufb01ve corresponding to the open Ramsey theorem and three corresponding to the clopen Ramsey theorem) and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility. In particular one of our functions turns out to be strictly stronger than any previously studied multivalued functions arising from statements around ATR_0

The Weihrauch lattice at the level of Π11−CA0\boldsymbol{\Pi}_1^1\mathsf{-CA}_0: the Cantor-Bendixson theorem

This paper continues the program connecting reverse mathematics and computable analysis via the framework of Weihrauch reducibility. In particular, we consider problems related to perfect subsets of Polish spaces, studying the perfect set theorem, the Cantor-Bendixson theorem and various problems arising from them. In the framework of reverse mathematics these theorems are equivalent respectively to $\mathsf{ATR}_0$ and $\boldsymbol{\Pi}_1^1\mathsf{-CA}_0$, the two strongest subsystems of second order arithmetic among the so-called big five. As far as we know, this is the first systematic study of problems at the level of $\boldsymbol{\Pi}_1^1\mathsf{-CA}_0$ in the Weihrauch lattice. We show that the strength of some of the problems we study depends on the topological properties of the Polish space under consideration, while others have the same strength once the space is rich enough.Comment: 35 page

La Concertazione sociale tra <i>vecchi</i> e <i>nuovi</i> modelli

The first chapter deals with corporatism, designed as a model of representation of interests of different economic actors oligopoly based about few representative organizations of a public nature. It shows how, after the removal of some thirty years, more due to an antifascist than an actual give up completely of the concept, the term corporatism appears again in the early eighties as a result of concerted practices between government, unions and associations business. The following chapter contains the core of the thesis. Is exploring the nature of social partnership: the evolution of the model and the search for its legal foundations. Illustrates the difficulty, in the absence of specific legislative references, to find a definition of dialogue that contains all the nuances of the relations of trade union participation in negotiations with the authorities. It is clear that consultation is vague concept in both the sociological and legal terms. The interdisciplinary approach of the phenomenon defines the most varied forms of negotiation with the unions complicating the definition. In the following chapter discusses the link between consultation and collective bargaining when the State attempts to inform the social partners the lines of cost containment and level of the salary to be defined in negotiations. From this perspective we can appreciate how the social partnership has been established also in terms of help, or prepare for a negotiation response to periods of economic crisis or implementation of the information contained in the reforms of the legislation. The last part of the thesis looks at new models of social partners involvement in decision-making in the economic and social development. In particular, reference is made, first, to the model of social dialogue as it has developed at Community level, on the other hand, the idea of playing a national model of collective relations based on the need to achieve levels of competitiveness and productivity, combined with increased rates of employment. Finally are taken into account the guidelines of the White Paper on European Governance and the impact on EU and national employment law

Cap Rate as the Interpretative Variable of the Urban Real Estate Capital Asset: A Comparison of Different Sub\u2010Market Definitions in Palermo, Italy

Real estate capital is in constant competition with other capital assets due to its different and complementary economic functions such as direct use, productive investment, and speculative investment. These features and the resulting opportunities cannot be easily deduced from direct observation of the real estate markets, so some further insights need to be carried out in order to highlight the relationship between prices, rents and performances. This study aims at providing a multifaceted perspective of a specific urban real estate market to overcome the difficulties arising from opacities and informative asymmetries that hinder the decision of investors, by facilitating the comparison of different options such as capital value, income and performance. Within the mass appraisal approach, the study proposes a methodology for the analysis of the cap rate, intended as the expression of profitability and liquidity of the urban real estate capital asset. The methodology is based on a detailed survey of a sample of the housing market data, collected within a structured database, supported by statistical and territorial analyses of the sample, in order to display the range of cap rates featuring each sub\u2010market, and the related distributions. The methodology is applied to a case study of nearly 1000 properties distributed in a vast urban area of the municipality of Palermo, Italy. The consistency of the relationships between the three variables has been tested with reference to two hypotheses about the sub\u2010market definition, which has been carried out by cluster and by neighbourhood

A jump operator on the Weihrauch degrees

A partial order $(P,\le)$ admits a jump operator if there is a map $j\colon P \to P$ that is strictly increasing and weakly monotone. Despite its name, the jump in the Weihrauch lattice fails to satisfy both of these properties: it is not degree-theoretic and there are functions $f$ such that $f\equiv_{\mathrm{W}} f'$. This raises the question: is there a jump operator in the Weihrauch lattice? We answer this question positively and provide an explicit definition for an operator on partial multi-valued functions that, when lifted to the Weihrauch degrees, induces a jump operator. This new operator, called the totalizing jump, can be characterized in terms of the total continuation, a well-known operator on computational problems. The totalizing jump induces an injective endomorphism of the Weihrauch degrees. We study some algebraic properties of the totalizing jump and characterize its behavior on some pivotal problems in the Weihrauch lattice

5-Hydr­oxy-7-meth­oxy-4H-chromen-4-one

The mol­ecular conformation of the title compound, C10H8O4, isolated from Laretia acualis, is stabilized by a strong intra­molecular hydrogen bond between the hydroxyl and carbonyl groups. The crystal packing shows π–π stacking inter­actions. The chromene (4H-1-benzopyran-4-one) unit is essentially planar

Reviewing Traffic ClassificationData Traffic Monitoring and Analysis

Traffic classification has received increasing attention in the last years. It aims at offering the ability to automatically recognize the application that has generated a given stream of packets from the direct and passive observation of the individual packets, or stream of packets, flowing in the network. This ability is instrumental to a number of activities that are of extreme interest to carriers, Internet service providers and network administrators in general. Indeed, traffic classification is the basic block that is required to enable any traffic management operations, from differentiating traffic pricing and treatment (e.g., policing, shaping, etc.), to security operations (e.g., firewalling, filtering, anomaly detection, etc.). Up to few years ago, almost any Internet application was using well-known transport layer protocol ports that easily allowed its identification. More recently, the number of applications using random or non-standard ports has dramatically increased (e.g. Skype, BitTorrent, VPNs, etc.). Moreover, often network applications are configured to use well-known protocol ports assigned to other applications (e.g. TCP port 80 originally reserved for Web traffic) attempting to disguise their presence. For these reasons, and for the importance of correctly classifying traffic flows, novel approaches based respectively on packet inspection, statistical and machine learning techniques, and behavioral methods have been investigated and are becoming standard practice. In this chapter, we discuss the main trend in the field of traffic classification and we describe some of the main proposals of the research community. We complete this chapter by developing two examples of behavioral classifiers: both use supervised machine learning algorithms for classifications, but each is based on different features to describe the traffic. After presenting them, we compare their performance using a large dataset, showing the benefits and drawback of each approac