a b s t r a c tA complete and user-friendly directory of tails of Archimedean copulas is presented which can be used in the selection and construction of appropriate models with desired properties. The results are synthesized in the form of a decision tree: Given the values of some readily computable characteristics of the Archimedean generator, the upper and lower tails of the copula are classified into one of three classes each, one corresponding to asymptotic dependence and the other two to asymptotic independence. For a long list of single-parameter families, the relevant tail quantities are computed so that the corresponding classes in the decision tree can easily be determined. In addition, new models with tailor-made upper and lower tails can be constructed via a number of transformation methods. The frequently occurring category of asymptotic independence turns out to conceal a surprisingly rich variety of tail dependence structures.
A new magnetic resonance (MR) technique, gadolinium-enhanced subtraction MR imaging, was developed to evaluate the response of patients with osteosarcoma to chemotherapy. Ten patients, who had received chemotherapy for osteosarcoma of the lower extremity, underwent MR imaging 3 days before surgery. After routine MR imaging was performed, subtraction MR was performed in the plane in which the tumor was best visualized. With gadopentetate dimeglumine (0.1 mmol per kilogram) on a standard MR console, subtraction images were created by subtracting precontrast images from gadolinium-enhanced T1-weighted images. The time of maximal tumoral vascular uptake was 1 1/2 minutes after injection, and, therefore, the subtracted image obtained at this time was used for evaluation of viable tumor. Independently, radiologists and histopathologists examined their respective studies for viable tumor to differentiate responders from nonresponders. Four of 10 osteosarcomas were classified as good responders because they appeared as nonenhancing masses, with or without enhancing thin lines, or small nodules (< or = 3 mm wide). At histopathologic examination, all were good responders with less than 3% viable tumor. Six of 10 osteosarcomas were classified as nonresponders because they appeared as enhancing high-signal-intensity masses measuring more than 3 mm in width. Five tumors had between 18% and 43% viable tumor cells.
We consider here an extended model, including several features of the recent COVID-19 outbreak: in particular the infected and recovered individuals can either be detected (+) or undetected (-) and we also integrate an intensive care unit (ICU) capacity. Our model enables a tractable quantitative analysis of the optimal policy for the control of the epidemic dynamics using both lockdown and detection intervention levers. With parametric specification based on literature on COVID-19, we investigate the sensitivities of various quantities on the optimal strategies, taking into account the subtle trade-off between the sanitary and the socio-economic cost of the pandemic, together with the limited capacity level of ICU. We identify the optimal lockdown policy as an intervention structured in 4 successive phases: First a quick and strong lockdown intervention to stop the exponential growth of the contagion; second a short transition phase to reduce the prevalence of the virus; third a long period with full ICU capacity and stable virus prevalence; finally a return to normal social interactions with disappearance of the virus. The optimal scenario hereby avoids the second wave of infection, provided the lockdown is released sufficiently slowly. We also provide optimal intervention measures with increasing ICU capacity, as well as optimization over the effort on detection of infectious and immune individuals. Whenever massive resources are introduced to detect infected individuals, the pressure on social distancing can be released, whereas the impact of detection of immune individuals reveals to be more moderate.
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