Orientable closed 3-manifolds with surface-complexity one

After a short summary of known results on surface-complexity of closed 3-manifolds, we will classify all closed orientable 3-manifolds with surface-complexity one.Comment: 9 pages, 3 figures, 1 table; minor changes: appendix on a theorem stated in arXiv:0804.0695 adde

Non-orientable 3-manifolds of small complexity

We classify all closed non-orientable P2-irreducible 3-manifolds having complexity up to 6 and we describe some having complexity 7. We show in particular that there is no such manifold with complexity less than 6, and that those having complexity 6 are precisely the 4 flat non-orientable ones and the filling of the Gieseking manifold, which is of type Sol. The manifolds having complexity 7 we describe are Seifert manifolds of type H2 x S1 and a manifold of type Sol.Comment: 27 pages, 12 figures. Two mistakes contained in the previous version are fixed: there is a Sol manifold with complexity 6, and the examples with complexty 7 are Sol and H2xS1 (see the abstract

Modularity and Optimality in Social Choice

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M^3 log M) time (where M is the number of social outcomes).Social rule, modularity, object, optimum, hyperplane arrangement, tournament, algorithm

Branched Spines of 3-Manifolds and Reidemeister Torsion of Euler Structures

We consider homotopy classes of non-singular vector fields on three-manifolds with boundary and we define for these classes torsion invariants of Reidemeister type. We show that torsion is well-defined and equivariant under the action of the appropriate homology group using an elementary and self-contained technique. Namely, we use the theory of branched standard spines to express the difference between two homotopy classes as a combination of well-understood elementary catastrophes. As a special case we are able to reproduce Turaev’s theory of Reidemeister torsion for Euler structures on closed manifolds of dimension three

Modularity and Optimality in Social Choice

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M^3 logM) time (where M is the number of social outcomes).Comment: 42 pages, 4 figures, 8 tables, 1 algorithm

No Efficacy of the Combination of Lopinavir/Ritonavir Plus Hydroxychloroquine Versus Standard of Care in Patients Hospitalized With COVID-19: A Non-Randomized Comparison

Objectives: No specific treatment has been approved for COVID-19. Lopinavir/ritonavir (LPV/r) and hydroxychloroquine (HCQ) have been used with poor results, and a trial showed advantages of combined antiviral therapy vs. single antivirals. The aim of the study was to assess the effectiveness of the combination of antivirals (LPV/r and HCQ) or their single use in COVID-19 hospitalized patients vs. standard of care (SoC). Methods: Patients ≥18 years with SARS-CoV-2 infection, defined as positive RT-PCR from nasal/oropharyngeal (NP/OP) swab or positive serology, admitted at L. Spallanzani Institute (Italy) were included. Primary endpoint: time to invasive ventilation/death. Secondary endpoint: time to two consecutive negative SARS-CoV-2 PCRs in NP/OP swabs. In order to control for measured confounders, a marginal Cox regression model with inverse probability weights was used. Results: A total of 590 patients were included in the analysis: 36.3% female, 64 years (IQR 51-76), and 91% with pneumonia. Cumulative probability of invasive ventilation/death at 14 days was 21.2% (95% CI 17.6, 24.7), without difference between SOC, LPV/r, hydroxychloroquine, HCQ + LPV/r, and SoC. The risk of invasive ventilation/death in the groups appeared to vary by baseline ratio of arterial oxygen partial pressure to fractional inspired oxygen (PaO2/FiO2). Overall cumulative probability of confirmed negative nasopharyngeal swabs at 14 days was 44.4% (95% CI 38.9, 49.9), without difference between groups. Conclusion: In this retrospective analysis, we found no difference in the rate of invasive ventilation/death or viral shedding by different strategies, as in randomized trials performed to date. Moreover, even the combination HCQ + LPV/r did not show advantages vs. SoC

ITALIAN CANCER FIGURES - REPORT 2015: The burden of rare cancers in Italy = I TUMORI IN ITALIA - RAPPORTO 2015: I tumori rari in Italia

OBJECTIVES: This collaborative study, based on data collected by the network of Italian Cancer Registries (AIRTUM), describes the burden of rare cancers in Italy. Estimated number of new rare cancer cases yearly diagnosed (incidence), proportion of patients alive after diagnosis (survival), and estimated number of people still alive after a new cancer diagnosis (prevalence) are provided for about 200 different cancer entities. MATERIALS AND METHODS: Data herein presented were provided by AIRTUM population- based cancer registries (CRs), covering nowadays 52% of the Italian population. This monograph uses the AIRTUM database (January 2015), which includes all malignant cancer cases diagnosed between 1976 and 2010. All cases are coded according to the International Classification of Diseases for Oncology (ICD-O-3). Data underwent standard quality checks (described in the AIRTUM data management protocol) and were checked against rare-cancer specific quality indicators proposed and published by RARECARE and HAEMACARE (www.rarecarenet.eu; www.haemacare.eu). The definition and list of rare cancers proposed by the RARECAREnet "Information Network on Rare Cancers" project were adopted: rare cancers are entities (defined as a combination of topographical and morphological codes of the ICD-O-3) having an incidence rate of less than 6 per 100,000 per year in the European population. This monograph presents 198 rare cancers grouped in 14 major groups. Crude incidence rates were estimated as the number of all new cancers occurring in 2000-2010 divided by the overall population at risk, for males and females (also for gender-specific tumours).The proportion of rare cancers out of the total cancers (rare and common) by site was also calculated. Incidence rates by sex and age are reported. The expected number of new cases in 2015 in Italy was estimated assuming the incidence in Italy to be the same as in the AIRTUM area. One- and 5-year relative survival estimates of cases aged 0-99 years diagnosed between 2000 and 2008 in the AIRTUM database, and followed up to 31 December 2009, were calculated using complete cohort survival analysis. To estimate the observed prevalence in Italy, incidence and follow-up data from 11 CRs for the period 1992-2006 were used, with a prevalence index date of 1 January 2007. Observed prevalence in the general population was disentangled by time prior to the reference date (≤2 years, 2-5 years, ≤15 years). To calculate the complete prevalence proportion at 1 January 2007 in Italy, the 15-year observed prevalence was corrected by the completeness index, in order to account for those cancer survivors diagnosed before the cancer registry activity started. The completeness index by cancer and age was obtained by means of statistical regression models, using incidence and survival data available in the European RARECAREnet data. RESULTS: In total, 339,403 tumours were included in the incidence analysis. The annual incidence rate (IR) of all 198 rare cancers in the period 2000-2010 was 147 per 100,000 per year, corresponding to about 89,000 new diagnoses in Italy each year, accounting for 25% of all cancer. Five cancers, rare at European level, were not rare in Italy because their IR was higher than 6 per 100,000; these tumours were: diffuse large B-cell lymphoma and squamous cell carcinoma of larynx (whose IRs in Italy were 7 per 100,000), multiple myeloma (IR: 8 per 100,000), hepatocellular carcinoma (IR: 9 per 100,000) and carcinoma of thyroid gland (IR: 14 per 100,000). Among the remaining 193 rare cancers, more than two thirds (No. 139) had an annual IR <0.5 per 100,000, accounting for about 7,100 new cancers cases; for 25 cancer types, the IR ranged between 0.5 and 1 per 100,000, accounting for about 10,000 new diagnoses; while for 29 cancer types the IR was between 1 and 6 per 100,000, accounting for about 41,000 new cancer cases. Among all rare cancers diagnosed in Italy, 7% were rare haematological diseases (IR: 41 per 100,000), 18% were solid rare cancers. Among the latter, the rare epithelial tumours of the digestive system were the most common (23%, IR: 26 per 100,000), followed by epithelial tumours of head and neck (17%, IR: 19) and rare cancers of the female genital system (17%, IR: 17), endocrine tumours (13% including thyroid carcinomas and less than 1% with an IR of 0.4 excluding thyroid carcinomas), sarcomas (8%, IR: 9 per 100,000), central nervous system tumours and rare epithelial tumours of the thoracic cavity (5%with an IR equal to 6 and 5 per 100,000, respectively). The remaining (rare male genital tumours, IR: 4 per 100,000; tumours of eye, IR: 0.7 per 100,000; neuroendocrine tumours, IR: 4 per 100,000; embryonal tumours, IR: 0.4 per 100,000; rare skin tumours and malignant melanoma of mucosae, IR: 0.8 per 100,000) each constituted <4% of all solid rare cancers. Patients with rare cancers were on average younger than those with common cancers. Essentially, all childhood cancers were rare, while after age 40 years, the common cancers (breast, prostate, colon, rectum, and lung) became increasingly more frequent. For 254,821 rare cancers diagnosed in 2000-2008, 5-year RS was on average 55%, lower than the corresponding figures for patients with common cancers (68%). RS was lower for rare cancers than for common cancers at 1 year and continued to diverge up to 3 years, while the gap remained constant from 3 to 5 years after diagnosis. For rare and common cancers, survival decreased with increasing age. Five-year RS was similar and high for both rare and common cancers up to 54 years; it decreased with age, especially after 54 years, with the elderly (75+ years) having a 37% and 20% lower survival than those aged 55-64 years for rare and common cancers, respectively. We estimated that about 900,000 people were alive in Italy with a previous diagnosis of a rare cancer in 2010 (prevalence). The highest prevalence was observed for rare haematological diseases (278 per 100,000) and rare tumours of the female genital system (265 per 100,000). Very low prevalence (<10 prt 100,000) was observed for rare epithelial skin cancers, for rare epithelial tumours of the digestive system and rare epithelial tumours of the thoracic cavity. COMMENTS: One in four cancers cases diagnosed in Italy is a rare cancer, in agreement with estimates of 24% calculated in Europe overall. In Italy, the group of all rare cancers combined, include 5 cancer types with an IR>6 per 100,000 in Italy, in particular thyroid cancer (IR: 14 per 100,000).The exclusion of thyroid carcinoma from rare cancers reduces the proportion of them in Italy in 2010 to 22%. Differences in incidence across population can be due to the different distribution of risk factors (whether environmental, lifestyle, occupational, or genetic), heterogeneous diagnostic intensity activity, as well as different diagnostic capacity; moreover heterogeneity in accuracy of registration may determine some minor differences in the account of rare cancers. Rare cancers had worse prognosis than common cancers at 1, 3, and 5 years from diagnosis. Differences between rare and common cancers were small 1 year after diagnosis, but survival for rare cancers declined more markedly thereafter, consistent with the idea that treatments for rare cancers are less effective than those for common cancers. However, differences in stage at diagnosis could not be excluded, as 1- and 3-year RS for rare cancers was lower than the corresponding figures for common cancers. Moreover, rare cancers include many cancer entities with a bad prognosis (5-year RS <50%): cancer of head and neck, oesophagus, small intestine, ovary, brain, biliary tract, liver, pleura, multiple myeloma, acute myeloid and lymphatic leukaemia; in contrast, most common cancer cases are breast, prostate, and colorectal cancers, which have a good prognosis. The high prevalence observed for rare haematological diseases and rare tumours of the female genital system is due to their high incidence (the majority of haematological diseases are rare and gynaecological cancers added up to fairly high incidence rates) and relatively good prognosis. The low prevalence of rare epithelial tumours of the digestive system was due to the low survival rates of the majority of tumours included in this group (oesophagus, stomach, small intestine, pancreas, and liver), regardless of the high incidence rate of rare epithelial cancers of these sites. This AIRTUM study confirms that rare cancers are a major public health problem in Italy and provides quantitative estimations, for the first time in Italy, to a problem long known to exist. This monograph provides detailed epidemiologic indicators for almost 200 rare cancers, the majority of which (72%) are very rare (IR<0.5 per 100,000). These data are of major interest for different stakeholders. Health care planners can find useful information herein to properly plan and think of how to reorganise health care services. Researchers now have numbers to design clinical trials considering alternative study designs and statistical approaches. Population-based cancer registries with good quality data are the best source of information to describe the rare cancer burden in a population