The Opinion procedure under Article 218(11) TFEU: Reflections in the light of Opinion 1/17

This paper explores aspects of Opinion 1/17, handed down by the Court of Justice on 30 April 2019, as an example of the specific procedure of Article 218(11) TFEU and the Court’s evolving practice. The prior Opinion procedure serves to prevent the complications that would arise, both internally and externally, if an international treaty were concluded by the EU and then subsequently found to be incompatible with primary EU law. Opinion 1/17 raised issues of institutional and substantive compatibility, in the form of the principle of autonomy and compliance with the Charter of Fundamental Rights. In handling both, the Court’s approach was characterised by its insistence on the reciprocal nature of the CETA relationship, the separation of the CETA system from EU law, the ability of the EU to engage with such independent and reciprocal dispute settlement processes, and its assessment of the way in which the agreement would be implemented. The Opinion represents an example of the explanatory or didactic form of reasoning typical of recent Opinions, as well as breaking new ground in its conception of an ‘envisaged’ agreement

What is the probability that a random integral quadratic form in nn variables has an integral zero?

We show that the density of quadratic forms in $n$ variables over $\mathbb Z_p$ that are isotropic is a rational function of $p$, where the rational function is independent of $p$, and we determine this rational function explicitly. When real quadratic forms in $n$ variables are distributed according to the Gaussian Orthogonal Ensemble (GOE) of random matrix theory, we determine explicitly the probability that a random such real quadratic form is isotropic (i.e., indefinite). As a consequence, for each $n$, we determine an exact expression for the probability that a random integral quadratic form in $n$ variables is isotropic (i.e., has a nontrivial zero over $\mathbb Z$), when these integral quadratic forms are chosen according to the GOE distribution. In particular, we find an exact expression for the probability that a random integral quaternary quadratic form has an integral zero; numerically, this probability is approximately $98.3\%$.Comment: 17 pages. This article supercedes arXiv:1311.554

Familial hypercholesterolemia in cardiac rehabilitation: a new field of interest

Familial hypercholesterolemia (FH) is a frequently undiagnosed genetic disease characterized by substantial elevations of low-density lipoprotein cholesterol (LDL-C). The prevalence of heterozygous FH (HeFH) in the general population is 1:500 inhabitants, while the prevalence of homozygous FH (HoFH) is 1:1,000,000. If FH is not identified and aggressively treated at an early age, affected individuals have a 20-fold increased lifetime risk of coronary heart disease compared with the general population. This narrative review provide a concise overview of recommendations for diagnosis and treatment of adults and children with FH, and discuss the utility of considering FH as a comorbidity at the entry of cardiac rehabilitation programme

Computing automorphic forms on Shimura curves over fields with arbitrary class number

We extend methods of Greenberg and the author to compute in the cohomology of a Shimura curve defined over a totally real field with arbitrary class number. Via the Jacquet-Langlands correspondence, we thereby compute systems of Hecke eigenvalues associated to Hilbert modular forms of arbitrary level over a totally real field of odd degree. We conclude with two examples which illustrate the effectiveness of our algorithms.Comment: 15 pages; final submission to ANTS I

Pape satan aleppe...

Ġabra ta’ poeżiji u proża li tinkludi: Il-Għanja taċ-ċaqliq ta’ A. Buttigieg – Kelb xiħ tal-għassa ta’ A. Cremona – Il-fergħa tas-sagħtar ta’ George Zammit – L-infern tal-midneb! ta’ Karmenu Vassallo – Pape satan aleppe... ta’ Albert M. Cassola.N/

Small angle x-ray scattering with edge-illumination

Sensitivity to sub-pixel sample features has been demonstrated as a valuable capability of phase contrast x-ray imaging. Here, we report on a method to obtain angular-resolved small angle x-ray scattering distributions with edge-illumination- based imaging utilizing incoherent illumination from an x-ray tube. Our approach provides both the three established image modalities (absorption, differential phase and scatter strength), plus a number of additional contrasts related to unresolved sample features. The complementarity of these contrasts is experimentally validated by using different materials in powder form. As a significant application example we show that the extended complementary contrasts could allow the diagnosis of pulmonary emphysema in a murine model. In support of this, we demonstrate that the properties of the retrieved scattering distributions are consistent with the expectation of increased feature sizes related to pulmonary emphysema. Combined with the simplicity of implementation of edge-illumination, these findings suggest a high potential for exploiting extended sub-pixel contrasts in the diagnosis of lung diseases and beyond

Limiting modular symbols and their fractal geometry

In this paper we use fractal geometry to investigate boundary aspects of the first homology group for finite coverings of the modular surface. We obtain a complete description of algebraically invisible parts of this homology group. More precisely, we first show that for any modular subgroup the geodesic forward dynamic on the associated surface admits a canonical symbolic representation by a finitely irreducible shift space. We then use this representation to derive an `almost complete' multifractal description of the higher--dimensional level sets arising from Manin--Marcolli's limiting modular symbols.Comment: 20 pages, 1 figur

Galois Theory, discriminants and torsion subgroups of elliptic curves

We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown using some characterizations for the squareness of the discriminant of the elliptic curve.Comment: New version, some typos fixed and the proof of the lemma in the Appendix has been expande

Disconnection clauses: an inevitable symptom of regionalism?

‘Disconnection clauses’ are legal provisions inserted into multilateral conventions to ensure that certain parties to the convention are not required to apply the rules of the convention because other relevant rules have already been agreed to among themselves. A disconnection clause can also be described more generally as a ‘conflict clause’ because it signals to all parties that parallel and potentially conflicting treaty obligations exist. This paper presents a discussion of the disconnection clause which argues that while these clauses make it possible for a limited group of parties to enhance the objectives of a treaty by taking measures that correspond to their special circumstance, this practice also creates a possibility that the inter se agreement will undermine the original treaty regime. The actual impact of a particular disconnection clause depends on how the clause is crafted, along with the changing nature of the regime that it refers to. The potential for a disconnection clause to undermine the object and purpose of the original treaty can therefore be removed during its design. Nevertheless, without full disclosure when negotiating the convention, any clause that seeks to replace treaty provisions with an alternative regime that would be applicable only between certain parties may, at worst, be creating different standards for different parties and, at best, be opaque and incoherent. This paper first describes the various types of disconnection clause, focusing on their purpose and development. It then assesses the main legal and political controversies surrounding these clauses before assessing whether these clauses could potentially create more legal problems than they are intended to solve or whether they are simply a practical response to deepening regionalism