Measles in Italy: Viral strains and crossing borders.

In 2017, Italy experienced one of the largest outbreaks of measles in recent years, with 5404 notified cases and 4347 confirmed cases. A further 2029 cases were notified during the first 6 months of 2018, and 1516 of them were laboratory-confirmed. The B3 and D8 genotypes were identified as those responsible for the outbreak. Possible transmission routes can be established by monitoring the circulating measles virus strains in support of the national health authorities to warn people and travellers

Proof of Brlek-Reutenauer conjecture

Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u) = \sum_{n=0}^{\infty}T_u(n) in which D(u) denotes the defect of u and T_u(n) denotes C_u(n+1)-C_u(n) +2 - P_U(n+1) - P_u(n), where C_u and P_u are the factor and palindromic complexity of u, respectively. This conjecture was verified for periodic words by Brlek and Reutenauer themselves. Using their results for periodic words, we have recently proved the conjecture for uniformly recurrent words. In the present article we prove the conjecture in its general version by a new method without exploiting the result for periodic words.Comment: 9 page

Variety, Competition, and Population in Economic Growth: Theory and Empirics

We provide aggregate macroeconomic evidence on how, in the long-run, a diverse degree of production-complexity may affect not only the rate of economic growth, but also the correlation between the latter, population growth and the monopolistic (intermediate) markups. For a sample of OECD economies, we find that the losses due to more complexity in production are lower than the corresponding specialization gains. According to our theoretical model, this implies that the impact of population change on economic growth is slightly positive. Using a Finite Mixture Model, we also classify the countries in the sample and verify for each cluster the impact that the population growth rate and the intermediate sector's markups exert on the 5-year average real GDP growth rate

Invariance: a Theoretical Approach for Coding Sets of Words Modulo Literal (Anti)Morphisms

Let $A$ be a finite or countable alphabet and let $\theta$ be literal (anti)morphism onto $A^*$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under $\theta$ ($\theta$-invariant for short).We establish an extension of the famous defect theorem. Moreover, we prove that for the so-called thin $\theta$-invariant codes, maximality and completeness are two equivalent notions. We prove that a similar property holds in the framework of some special families of $\theta$-invariant codes such as prefix (bifix) codes, codes with a finite deciphering delay, uniformly synchronized codes and circular codes. For a special class of involutive antimorphisms, we prove that any regular $\theta$-invariant code may be embedded into a complete one.Comment: To appear in Acts of WORDS 201

Analysing spatiotemporal patterns of Covid-19 confirmed deaths at the NUTS-2 regional level

During the ongoing Covid-19 pandemic, understanding the spatiotemporal patterns of the virus is crucial for policymakers to intervene promptly. The relevance of spatial proximity in the spread of the pandemic necessitates adequate tools, and noisy data must be properly treated. This study proposes obtaining clusters of European regions using smoothed curves of daily deaths from March 2020-March 2022. A functional representation of the curves

Variety, Competition, and Population in Economic Growth : Theory and Empirics

We provide aggregate macroeconomic evidence on how, in the long-run, a diverse degree of complexity in production may affect not only the rate of economic growth, but also the correlation between the latter, population growth and the monopolistic (intermediate) markups. For a sample of OECD countries, we find that the impact of population change on economic growth is slightly positive. According to our the- oretical model, this implies that the losses due to more complexity in production are lower than the corresponding specialization gains. Using a Finite Mixture Model, we also classify the countries in the sample and verify for each cluster the impact that the population growth rate and the intermediate sector\u2019s markups exert on the 5-year average real GDP growth rate