The Hénon-Heiles Hamiltonian is investigated in the context of chaotic scattering, in the range of energies where escaping from the scattering region is possible. Special attention is paid to the analysis of the different nature of the orbits, and the the invariant sets, such as the stable and unstable manifolds and the chaotic saddle. Furthermore, a discussion on the average decay time associated to the typical chaotic transients, which are present in this problem, is presented. The main goal of this paper is to show, by using various computational methods, that the corresponding exit basins of this open Hamiltonian are not only fractal, but they also verify the more restrictive property of Wada. We argue that this property is verified by typical open Hamiltonian systems with three or more escapes.
Background: Prognostic factors of poor outcome in patients with hematological malignancies and COVID-19 are poorly defined. Patients and methods: This was a Spanish transplant group and cell therapy (GETH) multicenter retrospective observational study, which included a large cohort of blood cancer patients with laboratory-confirmed SARS-CoV-2 infection through PCR assays from March 1st 2020 to May 15th 2020. Results: We included 367 pediatric and adult patients with hematological malignancies, including recipients of autologous (ASCT) (n = 58) or allogeneic stem cell transplantation (allo-SCT) (n = 65) from 41 hospitals in Spain. Median age of patients was 64 years (range 1-93.8). Recipients of ASCT and allo-SCT showed lower mortality rates (17% and 18%, respectively) compared to non-SCT patients (31%) (p = 0.02). Prognostic factors identified for day 45 overall mortality (OM) by logistic regression multivariate analysis included age > 70 years [odds ratio (OR) 2.1, 95% confidence interval (CI) 1.2-3.8, p = 0.011]; uncontrolled hematological malignancy (OR 2.9, 95% CI 1.6-5.2, p < 0.0001); ECOG 3-4 (OR, 2.56, 95% CI 1.4-4.7, p = 0.003); neutropenia (< 0.5 × 10 9 /L) (OR 2.8, 95% CI 1.3-6.1, p = 0.01); and a C-reactive protein (CRP) > 20 mg/dL (OR 3.3, 95% CI 1.7-6.4, p < 0.0001). In multivariate analysis of 216 patients with very severe COVID-19, treatment with azithromycin or low dose corticosteroids was associated with lower OM (OR 0.42, 95% CI 0.2-0.89 and OR 0.31, 95% CI 0.11-0.87, respectively, p = 0.02) whereas the use of hidroxycloroquine did not show significant improvement in OM (OR 0.64, 95% CI 0.37-1.1, P = 0.1).
The reliable operation of modern infrastructures depends on computerized systems and Supervisory Control and Data Acquisition (SCADA) systems, which are also based on the data obtained from sensor networks. The inherent limitations of the sensor devices make them extremely vulnerable to cyberwarfare/cyberterrorism attacks. In this paper, we propose a reputation system enhanced with distributed agents, based on unsupervised learning algorithms (self-organizing maps), in order to achieve fault tolerance and enhanced resistance to previously unknown attacks. This approach has been extensively simulated and compared with previous proposals.
Prediction is one of the fundamental goals of science. When prediction is lost, it can be thought that one of the foundations of science is shattered. The notion of a chaotic system and the sensitive dependence on initial conditions implies a certain lack of prediction on the time evolution along an orbit. However we do not speak here about this temporal prediction, but about an extreme dependence on the initial conditions that fractal structures in phase space impose, and that obstructs the prediction of the final state of the system.
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