Properly ordered dimers, RR-charges, and an efficient inverse algorithm

The $\mathcal{N}=1$ superconformal field theories that arise in AdS-CFT from placing a stack of D3-branes at the singularity of a toric Calabi-Yau threefold can be described succinctly by dimer models. We present an efficient algorithm for constructing a dimer model from the geometry of the Calabi-Yau. Since not all dimers produce consistent field theories, we perform several consistency checks on the field theories produced by our algorithm: they have the correct number of gauge groups, their cubic anomalies agree with the Chern-Simons coefficients in the AdS dual, and all gauge invariant chiral operators satisfy the unitarity bound. We also give bounds on the ratio of the central charge of the theory to the area of the toric diagram. To prove these results, we introduce the concept of a properly ordered dimer.Comment: 33 pages, 19 figures, some corrections and clarification

Uncertainty Analysis of Feature Extraction from Expired Gas Traces

Noninvasive medical analyses are a convenient method to study several pathologies even though their indirect nature often requires a complex processing to determine the relevant health "indicators". The usefulness of such indicators depends on the employed model, but also on the uncertainty that is connected to the complex processing involved in the indicator determination. This paper deals with the problems related to the estimation of the uncertainty when the indicators are computed by means of a nontrivial processing on recorded traces of clinical parameters. The paper is focused on the analysis of expired gas traces, but the procedure can also be applied to many other cases where the processing involves manual or automatic selection of suitable "key points" on repetitive traces

Bounding Selmer groups for the Rankin--Selberg convolution of Coleman families

Let $f$ and $g$ be two cuspidal modular forms and let $\mathcal{F}$ be a Coleman family passing through $f$, defined over an open affinoid subdomain $V$ of weight space $\mathcal{W}$. Using ideas of Pottharst, under certain hypotheses on $f$ and $g$ we construct a coherent sheaf over $V \times \mathcal{W}$ which interpolates the Bloch-Kato Selmer group of the Rankin-Selberg convolution of two modular forms in the critical range (i.e. the range where the $p$-adic $L$-function $L_p$ interpolates critical values of the global $L$-function). We show that the support of this sheaf is contained in the vanishing locus of $L_p$.Comment: Final version. To appear in Canadian Jour. Mat

The first two decisions of the European Court of Justice on the law applicable to employment contracts

Abstract: The article examines the first two decisions of the Court of Justice of the EuropeanUnion on Article 6 of the Rome Convention on the law applicable to employment contracts.The author underlines the effort of the Court in giving raise to a well integrated European systemof conflict of laws and international procedure’s rules. Building on the value given by the Court to itsprevious case law on grounds for jurisdiction in employment contracts, the author then argues that sucha system is thoroughly oriented towards a substantive (not formal) construction of conflict of laws’rules,in view of attaining the aim of protection of the employee.Key words: Rome Convention on the law applicable to contractual obligation, notion of «habitualplace of work», employees performing their work in more than one State. Estratto: Il contributo esamina le prime due sentenze nelle quali la Corte di giustizia dell’Unioneeuropea interpreta l’art. 6 della Convenzione di Roma, relativo alla legge applicabile ai contratti individualidi lavoro. L’autore sottolinea lo sforzo della Corte nella ricostruzione di un sistema di dirittointernazionale privato e processuale europeo organico e ben integrato. Sulla scorta del valore attribuitodalla Corte alla propria precedente giurisprudenza sui titoli di giurisdizione in materia di contratto dilavoro, l’autore sostiene che tale sistema appare fortemente orientato verso un’interpretazione materiale(non formale) delle regole di conflitto, volta alla realizzazione della miglior tutela del lavoratore. Parole chiave: Convenzione di Roma sulla legge applicabile alle obbligazioni contrattuali,nozione di «luogo abituale di lavoro», dipendenti che prestano l’attività lavorativa in più di un Paese