We explore the tree limits recently defined by Elek and Tardos. In particular, we find tree limits for many classes of random trees. We give general theorems for three classes of conditional Galton–Watson trees and simply generated trees, for split trees and generalized split trees (as defined here), and for trees defined by a continuous-time branching process. These general results include, for example, random labelled trees, ordered trees, random recursive trees, preferential attachment trees, and binary search trees.

Renal Replacement Therapies generally associated to the Artificial Kidney (AK) are membrane-based treatments that assure the separation functions of the failing kidney in extracorporeal blood circulation. Their progress from conventional hemodialysis towards high-flux hemodialysis (HFHD) through the introduction of ultrafiltration membranes characterized by high convective permeation fluxes intensified the need of elucidating the effect of the membrane fluid removal rates on the increase of the potentially blood-traumatizing shear stresses developed adjacently to the membrane. The AK surrogate consisting of two-compartments separated by an ultrafiltration membrane is set to have water circulation in the upper chamber mimicking the blood flow rates and the membrane fluid removal rates typical of HFHD. Pressure drop mirrors the shear stresses quantification and the modification of the velocities profiles. The increase on pressure drop when comparing flows in slits with a permeable membrane and an impermeable wall is ca. 512% and 576% for $ \mathrm{CA}22/5\%{\mathrm{SiO}}_2 $ and $ \mathrm{CA}30/5\%{\mathrm{SiO}}_2 $ membranes, respectively.

Target date funds (TDFs) are becoming increasingly popular investment choices among investors with long-term prospects. Examples include members of superannuation funds seeking to save for retirement at a given age. TDFs provide efficient risk exposures to a diversified range of asset classes that dynamically match the risk profile of the investment payoff as the investors age. This is often achieved by making increasingly conservative asset allocations over time as the retirement date approaches. Such dynamically evolving allocation strategies for TDFs are often referred to as glide paths. We propose a systematic approach to the design of optimal TDF glide paths implied by retirement dates and risk preferences and construct the corresponding dynamic asset allocation strategy that delivers the optimal payoffs at minimal costs. The TDF strategies we propose are dynamic portfolios consisting of units of the growth-optimal portfolio (GP) and the risk-free asset. Here, the GP is often approximated by a well-diversified index of multiple risky assets. We backtest the TDF strategies with the historical returns of the S&P500 total return index serving as the GP approximation.

To assess the relationship between the neutrophil-to-lymphocyte ratio (NLR) and related parameters to the severity of coronavirus disease 2019 (COVID-19) symptoms. Clinical data from 38 COVID-19 patients who were diagnosed, treated and discharged from the Qishan Hospital in Yantai over the period from January to February 2020 were analysed. NLR and procalcitonin (PCT) were determined in the first and fourth weeks after their admission, along with the clinical characteristics and laboratory test results of these patients. Based on results as obtained on the first and fourth weeks after admission, five indices consisting of NLR, white blood cells, neutrophils, lymphocytes (LY) and monocytes (MON) were selected to generate receiver operating characteristic curves, while optimal cutoff values, sensitivities and specificities were obtained according to the Yuden index. Statistically significant differences in neutrophils, LY and the NLR were present in the severe vs. moderate COVID-19 group from the first to the fourth week of their hospitalisation. The cut-off value of NLR for predicting the severity of COVID-19 was 4.425, with a sensitivity of 0.855 and a specificity of 0.979. A statistically significant positive correlation was present between PCT and NLR in the severe group as determined within the first week of admission. NLR can serve as a predictor of COVID-19 disease severity as patients' progress from the first to the fourth week of their hospitalisation. The statistically significant positive correlation between levels of NLR and PCT in severe patients indicated that increases in NLR were accompanied with gradual increases in PCT.

In this paper, the optimal insurance design is studied from the perspective of an insured, who faces an insurable risk and a background risk. For the reduction of ex post moral hazard, alternative insurance contracts are asked to satisfy the principle of indemnity and the incentive-compatible condition. As in the literature, it is assumed that the insurer calculates the insurance premium solely on the basis of the expected indemnity. When the insured has a general mean-variance preference, an explicit form of optimal insurance is derived explicitly. It is found that the stochastic dependence between the background risk and the insurable risk plays a critical role in the insured’s risk transfer decision. In addition, the optimal insurance policy can often change significantly once the incentive-compatible constraint is removed.

This paper studies a problem of optimal reinsurance design under asymmetric information. The insurer adopts distortion risk measures to quantify his/her risk position, and the reinsurer does not know the functional form of this distortion risk measure. The risk-neutral reinsurer maximizes his/her net profit subject to individual rationality and incentive compatibility constraints. The optimal reinsurance menu is succinctly derived under the assumption that one type of insurer has a larger willingness to pay than the other type of insurer for every risk. Some comparative analyses are given as illustrations when the insurer adopts the value at risk or the tail value at risk as preferences.

The current investigation was conducted with the objective to develop an epidemiological case definition of possible severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) re-infection and assess its magnitude in India. The epidemiological case definition for SARS-CoV-2 re-infection was developed from literature review of data on viral kinetics. For achieving second objective, the individuals who satisfied the developed case definition for SARS-CoV-2 re-infection were contacted telephonically. Taking available evidence into consideration, re-infection with SARS-CoV-2 in our study was defined as any individual who tested positive for SARS-CoV-2 on two separate occasions by either molecular tests or rapid antigen test at an interval of at least 102 days with one negative molecular test in between. In this archive based, telephonic survey, 58 out of 1300 individuals (4.5%) fulfilled the above-mentioned definition; 38 individuals could be contacted with healthcare workers (HCWs) accounting for 31.6% of the cases. A large proportion of participants was asymptomatic and had higher Ct value during the first episode. While SARS-CoV-2 re-infection is still a rare phenomenon, there is a need for epidemiological definition of re-infection for establishing surveillance systems and this study contributes to such a goal.

Severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) re-infection is an emerging concern and there is a need to define it. Therefore, working epidemiological case definition for re-infection was developed and its magnitude was explored via archive-based, telephonic survey. Re-infection with SARS-CoV-2 was defined as two positive tests at an interval of at least 102 days with one interim negative test. Thirty-eight of the 58 eligible patients could be contacted with 12 (31.6%) being HCWs. Majority of the participants were asymptomatic and had higher Ct value during their first episode. To conclude, a working epidemiological case definition of SARS-CoV-2 re-infection is important to strengthen surveillance. The present investigation contributes to this goal and records reinfection in 4.5% of SARS-CoV-2 infected individuals in India.

Control of the novel COronaVIrus Disease-2019 (COVID-19) in a hospital setting is a priority. A COVID-19-infected surgeon performed surgical activities before being tested. An exposure risk classification was applied to the identified exposed subjects and high- and medium-risk contacts underwent active symptom monitoring for 14 days at home. All healthcare professionals (HCPs) were tested for severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) at the end of the quarantine and serological tests were performed. Three household contacts and 20 HCPs were identified as high- or medium-risk contacts and underwent a 14-day quarantine. Fourteen HCPs and 19 patients were instead classified as low risk. All the contacts remained asymptomatic and all HCPs tested negative for SARS-CoV-2. About 25–28 days after their last exposure, HCPs underwent serological testing and two of them had positive IgM but negative confirmatory swabs. In a low COVID-19 burden area, the in-hospital transmission of SARS-CoV-2 from an infectious doctor did not occur and, despite multiple and frequent contacts, a hospital outbreak was avoided. This may be linked to the adoption of specific recommendations and to the use of standard personal protective equipment by HCPs.

This study aimed to identify an appropriate simple mathematical model to fit the number of coronavirus disease 2019 (COVID-19) cases at the national level for the early portion of the pandemic, before significant public health interventions could be enacted. The total number of cases for the COVID-19 epidemic over time in 28 countries was analysed and fit to several simple rate models. The resulting model parameters were used to extrapolate projections for more recent data. While the Gompertz growth model (mean R2 = 0.998) best fit the current data, uncertainties in the eventual case limit introduced significant model errors. However, the quadratic rate model (mean R2 = 0.992) fit the current data best for 25 (89%) countries as determined by R2 values of the remaining models. Projection to the future using the simple quadratic model accurately forecast the number of future total number of cases 50% of the time up to 10 days in advance. Extrapolation to the future with the simple exponential model significantly overpredicted the total number of future cases. These results demonstrate that accurate future predictions of the case load in a given country can be made using this very simple model.