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Background: By the mid-20th century, cardiovascular disease (CVD) had become an important cause of mortality and morbidity in developed countries. The aim was to set up a pilot study to screen citizens aged 45–59 in order to identify modifiable risk factors (RFs). Methods: Our study was conducted from February 2019 to February 2020 on citizens of a population of central Italy, aged 45–59, contacted by letter. The variables evaluated were lipid profile, glycemia, anthropometric parameters, lifestyle and utility of screening. Results: It is important to underline that from the comparison with Italian national data, our results showed that blood pressure and lipid profile had better values. On the contrary, there were some alarm bells: a high percentage (57%) of smokers (63.9 in men and 37.1 in women), a sedentary lifestyle (24.5%), and a significantly higher waist circumference than the reference cut-offs for both men and women. The organization of the screening was considered excellent by 56.3% of women and 48.4% of men, and good by 37.5% of women and 46.5% of men. Conclusions: Our study provides a picture to stakeholders of the state of the health of citizens in the area under study, in the immediate pre-pandemic period; however, it is important to underline that their state of health may be modified after the pandemic period. Furthermore, cardiovascular (CV) screening was perceived by the citizens to be important for health care.

Background and Objective: The presence of multiple chronic diseases is associated with an increase in mortality when related to COVID-19 infection. The aims of our study were: (i) to evaluate the association between the severity of the COVID-19 disease, defined as symptomatic hospitalized in prison or symptomatic hospitalized out of prison, and the presence of one or more comorbidities in two prisons in central Italy: L’Aquila and Sulmona; (ii) to describe the profiles of inmates using multiple correspondence analysis (MCA). Methods: A database was created including age, gender and clinical variables. The database containing anonymized data was password-protected. The Kruskal–Wallis test was used to evaluate a possible association between diseases and the severity of COVID-19 stratified by age groups. We used MCA to describe a possible characteristic profile of inmates. Results: Our results show that in the 25–50-year-old age group (COVID-19-negative) in the L’Aquila prison, 19/62 (30.65%) were without comorbidity, 17/62 (27.42%) had 1–2 comorbidities and only 3.23% had >2 diseases. It is interesting to note that in the elderly group, the frequency of 1–2 or >2 pathologies was higher than in the younger group, and only 3/51 (5.88%) inmates did not have comorbidities and were COVID-19 negative (p = 0.008). The MCA identified the following profiles: the prison of L’Aquila showed a group of women over 60 with diabetes, cardiovascular and orthopedic problems, and hospitalized for COVID-19; the Sulmona prison presented a group of males over 60 with diabetes, cardiovascular, respiratory, urological, gastrointestinal and orthopedic problems, and hospitalized or symptomatic due to COVID-19. Conclusions: our study has demonstrated and confirmed that advanced age and the presence of concomitant pathologies have played a significant role in the severity of the disease: symptomatic hospitalized in the prison; symptomatic hospitalized out of the prison.

Following the pandemic scenario, researchers from all over the world, including Italians, have undertaken fervent research activity using the epidemiological data available on the sites of government and national and international research institutes. The objectives of our study were: (1) to analyze the load and trend of the COVID-19 pandemic in Italy, from the beginning to October 2021; (2) to analyze vaccination coverage by age groups and types of vaccines administered and check how the vaccination campaign has influenced the course of the disease and deaths; (3) to evaluate the Italian situation in the European context, comparing the incidence and mortality of Italy with respect to European countries; (4) finally, to evaluate how much vaccination coverage may have had an effect on mortality in the various European countries. Databases were structured to archive Italian and European COVID-19 data provided by Our World in Data, and data came from the Ministry of Health, to evaluate percentage of vaccines administered. The monthly trend of the cumulative incidence per 100,000 inhabitants in the period January 2020–October 2021 was evaluated. It is important to underline 3 peaks of incidence and mortality rates that occurred during the three waves of COVID-19: March–April–May 2020, October–November–December 2020, and March–April–May 2021. There is a slight increase in incidence in August 2021 and in mortality in September 2021. The three mortality rate peaks, related to the three waves of COVID-19, are always higher in Italy than in Europe, particularly in April 2020, December 2020, and March 2021. From May 2021 to October 2021, the mortality trend reversed, and it turned out to be higher in Europe than in Italy. Regarding vaccination, Italy currently has an important coverage, not only in the most fragile population, where it exceeds 90%, but also in the 12–19 age group, with percentages above 65%. The Pfizer/BioNTech vaccine was used widely in all age groups (first and second dose), with highest administration in 12–19 age groups and 80+, while the lowest was recorded in the 70–79 age group. In conclusion, these data confirm the importance of vaccination in the management of the COVID-19 pandemic.

This paper concerns the folklore statement that ``entropy is a lower bound for compression''. More precisely we derive from the entropy theorem a simple proof of a pointwise inequality firstly stated by Ornstein and Shields and which is the almost-sure version of an average inequality firstly stated by Khinchin in 1953. We further give an elementary proof of original Khinchin inequality that can be used as an exercise for Information Theory students and we conclude by giving historical and technical notes of such inequality., Compared to version 1, in version 2 we added a simpler proof than the one given by Shields of a more general theorem (Theorem 4, pg. 7) presented by Ornstein and Shields. Consequently we also modified the title of the paper. In version 3 we have reordered the sections of the paper, simplified the proof of Theorem 4 (now Theorem 3) and significantly reduced the proof of Theorem 3 (now Theorem 4)

We performed an updated meta-analysis to robustly quantify admission trends of patients with ST-segment elevation MI (STEMI) and non-ST-segment elevation MI (NSTEMI) during the first wave of the pandemic and to characterize on a large basis the risk profile and early prognosis. Studies having the same observation period for the comparison between SARS-CoV-2 outbreak in 2020 versus control period in 2019 were included. Primary endpoints were the relative variation of hospital admissions, the difference of in-hospital mortality for STEMI and NSTEMI. Secondary were: mortality according to countries, income levels and data quality; cardiogenic shock, mechanical complications, door-to-balloon time, time from symptom onset to first medical contact, left ventricular ejection fraction (LVEF) and troponin. In total, 61 observational studies with 125,346 patients were included. Compared with 2019, during the pandemic for STEMI were observed: a 24% reduction of hospitalizations with an impact on early survival (OR = 1.33 in-hospital mortality); the time from symptom onset to first medical contact was 91.31 min longer, whereas door-to-balloon time was increased (+5.44 min); after STEMI, the rate of cardiogenic shock was 33% higher; LVEF at discharge was decreased (−3.46); elevated high-sensitivity troponin levels (1.52) on admission. For NSTEMI, in the COVID-19 period, we observed a 31% reduction of hospitalizations and higher in-hospital deaths (OR = 1.34). The highest mortality rates among countries were: Italy OR = 3.71 (high income), Serbia OR = 2.15 (upper middle) and Pakistan OR = 1.69 (lower middle). Later hospital presentation was associated with larger infarctions, as well as with increased cardiogenic shock and in-hospital mortality.

Flexible parsing algorithm, a two-steps-greedy parsing algorithm for text factorisation, has been proved to be an optimal parsing for LZ78-like compressors in the case of constant-cost phrases [1] , [2] . Whilst in early implementations of LZ78-like compressors the phrases have constant cost, in common modern implementations the cost of the k-th phrase is ⌈ log 2 ⁡ k + C ⌉ where C is a real constant [3] , [4] . Indeed we show examples where Flexible parsing is not optimal under the above more realistic setting. In this paper we prove that, under the assumption that the cost of a phrase is block-wise constant and non-decreasing, the Flexible parsing is almost optimal. For almost optimal we mean that, for any text T, the difference between the sizes of the compressed text obtained by using a Flexible parsing and an optimal parsing is bounded by the maximal cost of a phrase in T, i.e. it is logarithmic in practical cases. Furthermore we investigate how an optimal parsing, and hence an almost optimal parsing, affects the rate of convergence to the entropy of LZ78-like compressors. We discuss some experimental results considering the ratio between the speed of convergence to the entropy of compressors with and without an optimal parsing. This ratio presents a kind of wave effect that increases as the entropy of a memoryless source decreases but it seems always to slowly converge to one. According to the theory, this wave can be a tsunami for some families of highly compressible strings and, although the optimal (and the almost optimal) parsing does not improve the asymptotical speed of convergence to the entropy, it can improve compression ratio, and hence the decoding speed, in many practical cases.

The stable set problem is a well-known \(\mathcal{NP}\)-hard combinatorial optimization problem. As well as being hard to solve (or even approximate) in theory, it is often hard to solve in practice. The main difficulty is that upper bounds based on linear programming (LP) tend to be weak, whereas upper bounds based on semidefinite programming (SDP) take a long time to compute. We propose a new method to strengthen the LP-based upper bounds. The key idea is to take violated Chvatal-Gomory cuts and then strengthen their right-hand sides. Although the strengthening problem is itself \(\mathcal{NP}\)-hard, it can be solved reasonably quickly in practice. As a result, the overall procedure proves to be capable of yielding competitive upper bounds in reasonable computing times.