This thesis is devoted to the exploration of the complexity of some mathematical problems using the framework of computable analysis and descriptive set theory. We will especially focus on Weihrauch reducibility as a means to compare the uniform computational strength of problems. After a short introduction of the relevant background notions, we investigate the uniform computational content of problems arising from theorems that lie at the higher levels of the reverse mathematics hierarchy.We first analyze the strength of the open and (...) clopen Ramsey theorems. Since there is not a canonical way to phrase these theorems as multi-valued functions, we identify eight different multi-valued functions and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility.We then discuss some new operators on multi-valued functions and study their algebraic properties and the relations with other previously studied operators on problems. In particular, we study the first-order part and the deterministic part of a problem f, capturing the Weihrauch degree of the strongest multi-valued problem that is reducible to f and that, respectively, has codomain $\mathbb {N}$ or is single-valued.These notions proved to be extremely useful when exploring the Weihrauch degree of the problem $\mathsf {DS}$ of computing descending sequences in ill-founded linear orders. They allow us to show that $\mathsf {DS}$, and the Weihrauch equivalent problem $\mathsf {BS}$ of finding bad sequences through non-well quasi-orders, while being very “hard” to solve, are rather weak in terms of uniform computational strength. We then generalize $\mathsf {DS}$ and $\mathsf {BS}$ by considering $\boldsymbol {\Gamma }$ -presented orders, where $\boldsymbol {\Gamma }$ is a Borel pointclass or $\boldsymbol {\Delta }^1_1$, $\boldsymbol {\Sigma }^1_1$, $\boldsymbol {\Pi }^1_1$. We study the obtained $\mathsf {DS}$ -hierarchy and $\mathsf {BS}$ -hierarchy of problems in comparison with the Baire hierarchy and show that they do not collapse at any finite level.Finally, we work in the context of geometric measure theory and we focus on the characterization, from the point of view of descriptive set theory, of some conditions involving the notions of Hausdorff/Fourier dimension and Salem sets. We first work in the hyperspace $\mathbf {K}$ 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 $\mathbf {K}$. We also 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 $\mathbf {F}$ with the Fell topology. A similar result holds also for the Vietoris topology.We conclude by analyzing the same notions from the point of view of effective descriptive set theory and Type-2 Theory of Effectivity, and show that the complexities remain the same also in the lightface case. In particular, we show that the family of all the closed Salem sets is $\Pi ^0_3$ -complete. We furthermore characterize the Weihrauch degree of the functions computing Hausdorff and Fourier dimension of closed sets.prepared by Manlio Valenti.E-mail:[email protected]. (shrink)

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 $\mathrm {ATR_0}$ from the point of view of reverse mathematics, there is not a canonical way to phrase them as multivalued functions. We identify eight different multivalued functions 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 $\mathrm {ATR}_0$. (shrink)

In this work we investigate the Weihrauch degree of the problem Decreasing Sequence of finding an infinite descending sequence through a given ill-founded linear order, which is shared by the problem Bad Sequence of finding a bad sequence through a given non-well quasi-order. We show that $\mathsf {DS}$, despite being hard to solve, is rather weak in terms of uniform computational strength. To make the latter precise, we introduce the notion of the deterministic part of a Weihrauch degree. We then (...) generalize $\mathsf {DS}$ and $\mathsf {BS}$ by considering $\boldsymbol {\Gamma }$ -presented orders, where $\boldsymbol {\Gamma }$ is a Borel pointclass or $\boldsymbol {\Delta }^1_1$, $\boldsymbol {\Sigma }^1_1$, $\boldsymbol {\Pi }^1_1$. We study the obtained $\mathsf {DS}$ -hierarchy and $\mathsf {BS}$ -hierarchy of problems in comparison with the Baire hierarchy and show that they do not collapse at any finite level. (shrink)

Inquieta anche il fatto che i nuovi giardini tendano ad assomigliare in modo impressionante a quei “rendering”, anch’essi uno standard, che si trovano esposti nelle vetrine delle sempre più numerose agenzie immobiliari che impestano la periferia diffusa. Ne avevo una vicino a casa qualche trasloco fa, quando abitavo in un appartamento di due stanze con bagno nel quartiere di Santa Lucia.Vitaliano Trevisan, Tristissimi giardini, pp. 46-47 Dopo la mela biblica consumata in un giardino terrestre...

Inquieta anche il fatto che i nuovi giardini tendano ad assomigliare in modo impressionante a quei “rendering”, anch’essi uno standard, che si trovano esposti nelle vetrine delle sempre più numerose agenzie immobiliari che impestano la periferia diffusa. Ne avevo una vicino a casa qualche trasloco fa, quando abitavo in un appartamento di due stanze con bagno nel quartiere di Santa Lucia.Vitaliano Trevisan, Tristissimi giardini, pp. 46-47 Dopo la mela biblica consumata in un giardino terrestre...

The aim of this article is to identify the main factors of the current crisis of the nation-state and to demonstrate how many of the voids left by this crisis are filled by religions. The main characteristic of the nation-state is the principle of sovereignty. The apogee of the nation-state is the political form of industrialization. National identity is possible only when the state proves to its citizens that the fact of being a member of it carries benefits and privileges (...) and will always bring more. Today, the majority of nation-states, in particular the oldest great powers, no longer have this capability. The weakening of the nation-state began at the end of the 19th century. The first wave of globalization multiplied the cases of reciprocal interferences and trespassed on the theoretical impermeability of the sovereign states. The outcome of the First World War, with the creation of the first supranational body, and much more the outcome of the Second World War, were two important steps of this crisis. The birth of the United Nations, and of other supranational bodies, as well as the creation of the first court called to judge an entire political class, were an assault on the principle of sovereignty. The second wave of globalization, characterized by the free circulation of goods, money, people and cultures, did the rest. Moreover, the countries that ‘invented’ the principle of sovereignty are today in relative decline as new powers are emerging. The nation-state is no longer able to keep its promises. The less effective states become at offering their citizens both meaning and social services, the more do religions tend to reoccupy the public stage. The less national and political legitimacy they have, the more powers use the religious tool against one another. (shrink)

Fostering research integrity (RI) increasingly focuses on normative guidance and supportive measures within institutions. To be successful, the implementation of support should be informed by stakeholders’ experiences of RI support. This study aims to explore experiences of RI support in Dutch, Spanish and Croatian universities. In total, 59 stakeholders (Netherlands n = 25, Spain n = 17, Croatia n = 17) participated in 16 focus groups in three European countries. Global themes on RI support experiences were identified by thematic analysis. (...) Themes identified were: ‘RI governance and institutional implementation’, ‘RI roles and structures’, ‘RI education and supervision’, and ‘Infrastructure, technology and tools supporting daily practice’. Experiences of support differed between countries in relation to: the efforts to translate norms into practice; the extent to which RI oversight was a responsibility of RE structures, or separate RI structures; and the availability of support close to research practice, such as training, responsible supervision, and adequate tools and infrastructure. The study reinforces the importance of a whole institutional approach to RI, embedded within local jurisdictions, rules, and practices. A whole institutional approach puts the emphasis of responsibility on institutions rather than individual researchers. When such an approach is lacking, some stakeholders look for intervention by authorities, such as funders, outside of the university. (shrink)

Since 2002, legislation in Spain has allowed for the creation and documentation of end-of-life decisionmaking. Over the intervening years, the actual implementation of such documents is very low. Through extensive analysis of the literature, this article explores the current status of the use of and attitudes toward advance directives in Spain and then proposes strategies for improvement in their implementation.

Una prima parte del saggio sintetizza le linee principali di un recente libro dell’autore: Per un paradigma del corpo: una rifondazione filosofica dell’ecologia, Quodlibet, Macerata, 2019. Viene sostenuto un paradigma in cui corpo e biologia mantengano la loro irriducibilità nei confronti della cultura e in cui il cosiddetto “linguistic turn”, che ha dominato la filosofia del XX secolo, viene fortemente criticato; in coerenza con questo, la riflessione di Merleau-Ponty sul concetto di natura viene considerata lo strumento più adeguato e più (...) attuale per ripensare la questione ecologica; ne vengono esaminate le conseguenze nel campo della filosofia della tecnologia e del problema del soggetto. Una seconda parte del saggio, che si concentra sull’incontro che ebbe luogo nel 1961 fra Adorno e Merleau-Ponty, cerca di abbozzare un paradigma materialistico per l’ecologia, correggendo l’avvicinamento che alla fine della sua vita vi fu fra Merleau-Ponty e Heidegger. (shrink)

The emergence of ecology as a fundamental horizon not only of politics, but also of contemporary philosophy, pushes us to rethink the relationship that currents of thought such as Kuturkritik and phenomenology, especially the phenomenology of Maurice Merleau-Ponty, can maintain with it. After a preliminary consideration of post-structuralist and postmodern positions from this perspective, the essay focuses on the French philosopher, and in particular on his courses on Nature and on his elaboration of the Husserlian concept of Stiftung. This results (...) in Merleau-Ponty’s original position on the Kultur – Civilization alternative: critique of unlimited productivism, respect for the environment, and, at the same time, defense of the variety of cultures and traditions from a homogenizing globalization are valuable tools that his philosophy offers to the debates of our time. (shrink)

Environmental journalism has been criticized by various special interest groups and some editors for advocacy and faulted for inaccuracies. Sources, in turn, many from the science communities, have been accused of inaccessibility, and public relations representatiws from both industry and environmental organizations are regularly blamed for unethical behaviors rangingfrom hyperbole to more serious discussion or omission of factual information. This article reports a preliminary study of ethical decision making among members of the Society of Environmental Journalists, identifying ethical motivation diljerences (...) using the Ethical Motivation Scale. The implications of the reported dominant extrinsic guides are discussed in light of a proposed protocol for ethical environmental communication. (shrink)

Community-based mental health care providers are increasingly contacted by external researchers for research study recruitment. Unfortunately, many do not possess the resources or personn...

Depuis longtemps, les médecins se sont intéressés au phénomène de la menstruation, qui renvoie au mystère de l’» éternel féminin ». À la fin du XIXe siècle, le discours médical sur les règles recoupe encore sur bien des points les préjugés populaires, notamment en ce qui concerne l’impureté du sang menstruel. Les médecins toutefois ne sont pas unanimes : perçue par certains comme un garant de l’équilibre féminin, une « saignée naturelle » indispensable à la bonne santé de la femme, (...) la menstruation est stigmatisée par d’autres comme un état pathologique induisant chez la femme indisposée des troubles aussi bien physiologiques que psychologiques. La question des règles est ainsi révélatrice d’a priori qui sont tout autant masculins que médicaux, et le discours des médecins ne fait qu’apporter une caution qui se veut scientifique à la perception de la femme comme une éternelle malade, étroitement soumise à son destin biologique. (shrink)