Recently, researchers in the artificial neural network field have focused their attention on connectionist models composed by several hidden layers. In fact, experimental results and heuristic considerations suggest that deep architectures are more suitable than shallow ones for modern applications, facing very complex problems, e.g., vision and human language understanding. However, the actual theoretical results supporting such a claim are still few and incomplete. In this paper, we propose a new approach to study how the depth of feedforward neural networks impacts on their ability in implementing high complexity functions. First, a new measure based on topological concepts is introduced, aimed at evaluating the complexity of the function implemented by a neural network, used for classification purposes. Then, deep and shallow neural architectures with common sigmoidal activation functions are compared, by deriving upper and lower bounds on their complexity, and studying how the complexity depends on the number of hidden units and the used activation function. The obtained results seem to support the idea that deep networks actually implements functions of higher complexity, so that they are able, with the same number of resources, to address more difficult problems.

Although the interest of a Web page is strictly related to its content and to the subjective readers’ cultural background, a measure of the page authority can be provided that only depends on the topological structure of theWeb. PageRank is a noticeable way to attach a score toWeb pages on the basis of the Web connectivity. In this article, we look inside PageRank to disclose its fundamental properties concerning stability, complexity of computational scheme, and critical role of parameters involved in the computation. Moreover, we introduce a circuit analysis that allows us to understand the distribution of the page score, the way different Web communities interact each other, the role of dangling pages (pages with no outlinks), and the secrets for promotion of Web pages

Background Surgery is the main modality of cure for solid cancers and was prioritised to continue during COVID-19 outbreaks. This study aimed to identify immediate areas for system strengthening by comparing the delivery of elective cancer surgery during the COVID-19 pandemic in periods of lockdown versus light restriction. Methods This international, prospective, cohort study enrolled 20 006 adult (≥18 years) patients from 466 hospitals in 61 countries with 15 cancer types, who had a decision for curative surgery during the COVID-19 pandemic and were followed up until the point of surgery or cessation of follow-up (Aug 31, 2020). Average national Oxford COVID-19 Stringency Index scores were calculated to define the government response to COVID-19 for each patient for the period they awaited surgery, and classified into light restrictions (index <20), moderate lockdowns (20–60), and full lockdowns (>60). The primary outcome was the non-operation rate (defined as the proportion of patients who did not undergo planned surgery). Cox proportional-hazards regression models were used to explore the associations between lockdowns and non-operation. Intervals from diagnosis to surgery were compared across COVID-19 government response index groups. This study was registered at ClinicalTrials.gov , NCT04384926 . Findings Of eligible patients awaiting surgery, 2003 (10·0%) of 20 006 did not receive surgery after a median follow-up of 23 weeks (IQR 16–30), all of whom had a COVID-19-related reason given for non-operation. Light restrictions were associated with a 0·6% non-operation rate (26 of 4521), moderate lockdowns with a 5·5% rate (201 of 3646; adjusted hazard ratio [HR] 0·81, 95% CI 0·77–0·84; p<0·0001), and full lockdowns with a 15·0% rate (1775 of 11 827; HR 0·51, 0·50–0·53; p<0·0001). In sensitivity analyses, including adjustment for SARS-CoV-2 case notification rates, moderate lockdowns (HR 0·84, 95% CI 0·80–0·88; p<0·001), and full lockdowns (0·57, 0·54–0·60; p<0·001), remained independently associated with non-operation. Surgery beyond 12 weeks from diagnosis in patients without neoadjuvant therapy increased during lockdowns (374 [9·1%] of 4521 in light restrictions, 317 [10·4%] of 3646 in moderate lockdowns, 2001 [23·8%] of 11 827 in full lockdowns), although there were no differences in resectability rates observed with longer delays. Interpretation Cancer surgery systems worldwide were fragile to lockdowns, with one in seven patients who were in regions with full lockdowns not undergoing planned surgery and experiencing longer preoperative delays. Although short-term oncological outcomes were not compromised in those selected for surgery, delays and non-operations might lead to long-term reductions in survival. During current and future periods of societal restriction, the resilience of elective surgery systems requires strengthening, which might include...

Coronavirus disease 2019 (COVID-19) can progress to cytokine storm that is associated with organ dysfunction and death. The purpose of the present study is to determine clinical characteristics associated with 28 day inhospital survival in patients with coronavirus disease 2019 (COVID-19) that received tocilizumab. This was a retrospective observational cohort study conducted at a five hospital health system in Michigan, United States. Adult patients with confirmed COVID-19 that were admitted to the hospital and received tocilizumab for cytokine storm from March 1, 2020 through April 3, 2020 were included. Patients were grouped into survivors and non-survivors based on 28 day in-hospital mortality. Study day 0 was defined as the day tocilizumab was administered. Factors independently associated with in-hospital survival at 28 days after tocilizumab administration were assessed. Epidemiologic, demographic, laboratory, prognostic scores, treatment, and outcome data were collected and analyzed. Clinical response was collected and defined as a decline of two levels on a six-point ordinal scale of clinical status or discharged alive from the hospital. Of the 81 patients included, the median age was 64 (58-71) years and 56 (69.1%) were male. The 28 day in-hospital mortality was 43.2%. There were 46 (56.8%) patients in the survivors and 35 (43.2%) in the non-survivors group. On study day 0 no differences were noted in demographics, clinical characteristics, severity of illness scores, or treatments received between survivors and non-survivors. C-reactive protein was significantly higher in the non-survivors compared to survivors. Compared to non-survivors, recipients of tocilizumab within 12 days of symptom onset was independently associated with survival (adjusted OR: 0.296, 95% CI: 0.098-0.889). SOFA score ≥8 on day 0 was independently associated with mortality (adjusted OR: 2.842, 95% CI: 1.042-7.753). Clinical response occurred more commonly in survivors than non-survivors (80.4% vs. 5.7%; p < 0.001). Improvements in the six-point ordinal scale and SOFA score were observed in survivors after tocilizumab. Early receipt of tocilizumab in patients with severe COVID-19 was an independent predictor for in-hospital survival at 28 days.

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