Impact of the COVID-19 Pandemic on the Therapeutic Continuity among Outpatients with Chronic Cardiovascular Therapies

The COVID-19 pandemic poses major challenges to healthcare systems. We aimed to investigate the impact of the pandemic on prescription and adherence patterns of chronic cardiovascular therapies (lipid-lowering [LL], oral antidiabetic drugs [AD], and antihypertensives [AH]) using administrative pharmaceutical databases. For each treatment, two cohorts of prevalent cases in 2019 and 2020 were compared. We evaluated the percentage change in dispensed packages and treatment adherence as a proportion of days covered (PDC). For all therapies, an increase was observed during March–April 2020 (LL: +4.52%; AD: +2.72%; AH: +1.09%), with a sharp decrease in May–June 2020 (LL: −8.40%; AD: −12.09%; AH: −10.54%) compared to 2019. The impact of the COVID-19 pandemic on chronic cardiovascular treatments appears negligible on adherence: 533,414 patients showed high adherence to LL (PDC ≥ 80%) in January–February 2020, and 2.29% became poorly adherent (PDC < 20%) in the following four-month period (vs. 1.98% in 2019). A similar increase was also observed for AH (1.25% with poor adherence in 2020 vs. 0.93% in 2019). For AD, the increase was restrained (1.55% with poor adherence in 2020 vs. 1.37% in 2019). The rush to supply drugs at the beginning of lockdown preserved the continuity of chronic cardiovascular therapies

Phase transitions for suspension flows

This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function to be real analytic or to exhibit a phase transition. We also construct an example of a potential for which the pressure has countably many phase transitions.Comment: Example 5.2 expanded. Typos corrected. Section 6.1 superced the note "Thermodynamic formalism for the positive geodesic flow on the modular surface" arXiv:1009.462

Intangible capital and modern economies

The production of goods and services is central to understanding economies. The textbook description of a firm, typically in agriculture or manufacturing, focuses on its physical "tangible" capital (machines), labor (workers), and the state of "know-how." Yet real-world firms, such as Apple, Microsoft, and Google, have almost no physical capital. Instead, their main capital assets are "intangible": software, data, design, reputation, supply-chain expertise, and R&D. We discuss investment in these knowledge-based types of capital: How to measure it; how it affects macroeconomic data on investment, rates of return, and GDP; and how it relates to growth theory and practical growth accounting. We present estimates of productivity in the US and European economies in recent decades including intangibles and discuss why, despite relatively rapid growth in intangible capital and what seems to be a modern technological revolution, productivity growth has slowed since the global financial crisis

The Lyapunov spectrum is not always concave

We characterize one-dimensional compact repellers having nonconcave Lyapunov spectra. For linear maps with two branches we give an explicit condition that characterizes non-concave Lyapunov spectra

Stratification of the risk of developing severe or lethal Covid-19 using a new score from a large Italian population: A population-based cohort study

Objectives To develop a population-based risk stratification model (COVID-19 Vulnerability Score) for predicting severe/fatal clinical manifestations of SARS-CoV-2 infection, using the multiple source information provided by the healthcare utilisation databases of the Italian National Health Service. Design Retrospective observational cohort study. Setting Population-based study using the healthcare utilisation database from five Italian regions. Participants Beneficiaries of the National Health Service, aged 18-79 years, who had the residentship in the five participating regions. Residents in a nursing home were not included. The model was built from the 7 655 502 residents of Lombardy region. Main outcome measure The score included gender, age and 29 conditions/diseases selected from a list of 61 conditions which independently predicted the primary outcome, that is, severe (intensive care unit admission) or fatal manifestation of COVID-19 experienced during the first epidemic wave (until June 2020). The score performance was validated by applying the model to several validation sets, that is, Lombardy population (second epidemic wave), and the other four Italian regions (entire 2020) for a total of about 15.4 million individuals and 7031 outcomes. Predictive performance was assessed by discrimination (areas under the receiver operating characteristic curve) and calibration (plot of observed vs predicted outcomes). Results We observed a clear positive trend towards increasing outcome incidence as the score increased. The areas under the receiver operating characteristic curve of the COVID-19 Vulnerability Score ranged from 0.85 to 0.88, which compared favourably with the areas of generic scores such as the Charlson Comorbidity Score (0.60). A remarkable performance of the score on the calibration of observed and predicted outcome probability was also observed. Conclusions A score based on data used for public health management accurately predicted the occurrence of severe/fatal manifestations of COVID-19. Use of this score may help health decision-makers to more accurately identify high-risk citizens who need early preventive or treatment interventions

Natural equilibrium states for multimodal maps

This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for the geometric potentials $-t \log|Df|$, for the largest possible interval of parameters $t$. We also study the regularity and convexity properties of the pressure function, completely characterising the first order phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue measure are also obtained

Almost-additive thermodynamic formalism for countable Markov shifts

We introduce a definition of pressure for almost-additive sequences of continuous functions defined over (non-compact) countable Markov shifts. The variational principle is proved. Under certain assumptions we prove the existence of Gibbs and equilibrium measures. Applications are given to the study of maximal Lypaunov exponents of product of matrices

Large deviation principle for Benedicks-Carleson quadratic maps

Since the pioneering works of Jakobson and Benedicks & Carleson and others, it has been known that a positive measure set of quadratic maps admit invariant probability measures absolutely continuous with respect to Lebesgue. These measures allow one to statistically predict the asymptotic fate of Lebesgue almost every initial condition. Estimating fluctuations of empirical distributions before they settle to equilibrium requires a fairly good control over large parts of the phase space. We use the sub-exponential slow recurrence condition of Benedicks & Carleson to build induced Markov maps of arbitrarily small scale and associated towers, to which the absolutely continuous measures can be lifted. These various lifts together enable us to obtain a control of recurrence that is sufficient to establish a level 2 large deviation principle, for the absolutely continuous measures. This result encompasses dynamics far from equilibrium, and thus significantly extends presently known local large deviations results for quadratic maps.Comment: 23 pages, no figure, former title: Full large deviation principle for Benedicks-Carleson quadratic map

Prato: The Social Construction of an Industrial City Facing Processes of Cultural Hybridization

This chapter deals with a widely studied case, that is, Prato, a middle-sized city with rooted industrial traditions, in the Centre of Italy. Prato is a textile industrial district embedded in the so-called Third Italy—an area characterized by the presence of small firms spread throughout the territory, linked together in supply and subcontracting relationships—which, in the last twenty years, has undergone a profound transformation as a consequence of the crisis of textile and immigration, leading to the formation of a large Chinese community. The related changes brought with them problems of social cohesion and sustainable development. The authors address these issues by analyzing both academic and public discourses on Prato. Their basic idea is that common stereotypes act as drivers of a public discourse that prevents the city to re-negotiate its identity. The analysis concludes that different forms of hybridization—particularly cultural hybridization—are occurring, which would need further investigations