An Adaptive Analytic Continuation Method for Computing the Perturbed Two-Body Problem State Transition Matrix

In this work, the Taylor series based technique, Analytic Continuation is implemented to develop a method for the computation of the gravity and drag perturbed State Transition Matrix (STM) incorporating adaptive time steps and expansion order. Analytic Continuation has been developed for the two-body problem based on two scalar variables f and gp and their higher order time derivatives using Leibniz rule. The method has been proven to be very precise and efficient in trajectory propagation. The method is expanded to include the computation of the STM for the perturbed two-body problem. Leibniz product rule is used to compute the partials for the recursive formulas and an arbitrary order Taylor series is used to compute the STM. Four types of orbits, LEO, MEO, GTO and HEO, are presented and the simulations are run for 10 orbit periods. The accuracy of the STM is evaluated via RMS error for the unperturbed cases, symplectic check for the gravity perturbed cases and error propagation for the gravity and drag perturbed orbits. The results are compared against analytical and high order numerical solvers (ODE45, ODE113 and ODE87) in terms of accuracy. The results show that the method maintains double-precision accuracy for all test cases and 1-2 orders of magnitude improvement in linear prediction results compared to ODE87. The present approach is simple, adaptive and can readily be expanded to compute the full spherical harmonics gravity perturbations as well as the higher order state transition tensors.

The prediction for development of COVID-19 in global major epidemic areas through empirical trends in China by utilizing state transition matrix model

Background Since pneumonia caused by coronavirus disease 2019 (COVID-19) broke out in Wuhan, Hubei province, China, tremendous infected cases has risen all over the world attributed to its high transmissibility. We aimed to mathematically forecast the inflection point (IFP) of new cases in South Korea, Italy, and Iran, utilizing the transcendental model from China. Methods Data from reports released by the National Health Commission of the People’s Republic of China (Dec 31, 2019 to Mar 5, 2020) and the World Health Organization (Jan 20, 2020 to Mar 5, 2020) were extracted as the training set and the data from Mar 6 to 9 as the validation set. New close contacts, newly confirmed cases, cumulative confirmed cases, non-severe cases, severe cases, critical cases, cured cases, and death were collected and analyzed. We analyzed the data above through the State Transition Matrix model. Results The optimistic scenario (non-Hubei model, daily increment rate of − 3.87%), the cautiously optimistic scenario (Hubei model, daily increment rate of − 2.20%), and the relatively pessimistic scenario (adjustment, daily increment rate of − 1.50%) were inferred and modeling from data in China. The IFP of time in South Korea would be Mar 6 to 12, Italy Mar 10 to 24, and Iran Mar 10 to 24. The numbers of cumulative confirmed patients will reach approximately 20 k in South Korea, 209 k in Italy, and 226 k in Iran under fitting scenarios, respectively. However, with the adoption of different diagnosis criteria, the variation of new cases could impose various influences in the predictive model. If that happens, the IFP of increment will be earlier than predicted above. Conclusion The end of the pandemic is still inapproachable, and the number of confirmed cases is still escalating. With the augment of data, the world epidemic trend could be further predicted, and it is imperative to consummate the assignment of global medical resources to curb the development of COVID-19.

The Prediction for Development of COVID-19 in Global Major Epidemic Areas Through Empirical Trends in China by Utilizing State Transition Matrix Model

Background: Since pneumonia caused by coronavirus disease 2019 (COVID-19) broke out in Wuhan, Hubei province, China, tremendous infected cases has risen all over the world attributed to its high transmissibility. We aimed to mathematically forecast the inflection point (IFP) of new cases in South Korea, Italy, and Iran, utilizing the transcendental model from China. Methods: Data from reports released by the National Health Commission of the People’s Republic of China (Dec 31, 2019 to Mar 5, 2020) and the World Health Organization (Jan 20, 2020 to Mar 5, 2020) were extracted as the training set and the data from Mar 6 to 9 as the validation set. New close contacts, newly confirmed cases, cumulative confirmed cases, non-severe cases, severe cases, critical cases, cured cases, and death were collected and analyzed. We analyzed the data above through the State Transition Matrix model. Results: The optimistic scenario (non-Hubei model, daily increment rate of -3.87%), the cautiously optimistic scenario (Hubei model, daily increment rate of -2.20%), and the relatively pessimistic scenario (adjustment, daily increment rate of -1.50%) were inferred and modeling from data in China. The IFP of time in South Korea would be Mar 6 to 12, Italy Mar 10 to 24, and Iran Mar 10 to 24. The numbers of cumulative confirmed patients will reach approximately 20k in South Korea, 209k in Italy, and 226k in Iran under fitting scenarios, respectively. However, with the adoption of different diagnosis criteria, the variation of new cases could impose various influences in the predictive model. If that happens, the IFP of increment will be earlier than predicted above. Conclusion: The end of the pandemic is still inapproachable, and the number of confirmed cases is still escalating. With the augment of data, the world epidemic trend could be further predicted, and it is imperative to consummate the assignment of global medical resources to curb the development of COVID-19.

Network Security Situation Assessment Model Based on Extended Hidden Markov

A network security situation assessment system based on the extended hidden Markov model is designed in this paper. Firstly, the standard hidden Markov model is expanded from five-tuple to seven-tuple, and two parameters of network defense efficiency and risk loss vector are added so that the model can describe network security situation more completely. Then, an initial algorithm of state transition matrix was defined, observation vectors were extracted from the fusion of various system security detection data, the network state transition matrix was created and modified by the observation vectors, and a solution procedure of the hidden state probability distribution sequence based on extended hidden Markov model was derived. Finally, a method of calculating risk loss vector according to the international definition was designed and the current network risk value was calculated by the hidden state probability distribution; then the global security situation was assessed. The experiment showed that the model satisfied practical applications and the assessment result is accurate and effective.