Sparse sums of Lorentzians can give good approximations to functions consisting of linear combination of piecewise continuous functions. To each Lorentzian, two parameters are as- signed： translation and scale. These...Sparse sums of Lorentzians can give good approximations to functions consisting of linear combination of piecewise continuous functions. To each Lorentzian, two parameters are as- signed： translation and scale. These parameters can be found by using a method for complex fre- quency detection in the frequency domain. This method is based on an alternating projection scheme between Hankel matrices and finite rank operators, and have the advantage that it can be done in weighted spaces. The weighted spaces can be used to partially revoke the effect of finite band-width filters. Apart from frequency extrapolation the method provides a way of estimating discontinuity locations.展开更多
In stochastic modeling of infectious diseases,it has been established that variations in infectivity affect the probability of a major outbreak,but not the shape of the curves during a major outbreak,which is predicte...In stochastic modeling of infectious diseases,it has been established that variations in infectivity affect the probability of a major outbreak,but not the shape of the curves during a major outbreak,which is predicted by deterministic models(Diekmann et al.,2012).However,such conclusions are derived under idealized assumptions such as the population size tending to infinity,and the individual degree of infectivity only depending on variations in the infectiousness period.In this paper we show that the same conclusions hold true in a finite population representing a medium size city,where the degree of infectivity is determined by the offspring distribution,which we try to make as realistic as possible for SARS-CoV-2.In particular,we consider distributions with fat tails,to incorporate the existence of super-spreaders.We also provide new theoretical results on convergence of stochastic models which allows to incorporate any offspring distribution with a finite variance.展开更多
文摘Sparse sums of Lorentzians can give good approximations to functions consisting of linear combination of piecewise continuous functions. To each Lorentzian, two parameters are as- signed： translation and scale. These parameters can be found by using a method for complex fre- quency detection in the frequency domain. This method is based on an alternating projection scheme between Hankel matrices and finite rank operators, and have the advantage that it can be done in weighted spaces. The weighted spaces can be used to partially revoke the effect of finite band-width filters. Apart from frequency extrapolation the method provides a way of estimating discontinuity locations.
基金financial support from Carl Tryggers foundation and RR-ORU-2021/2022.
文摘In stochastic modeling of infectious diseases,it has been established that variations in infectivity affect the probability of a major outbreak,but not the shape of the curves during a major outbreak,which is predicted by deterministic models(Diekmann et al.,2012).However,such conclusions are derived under idealized assumptions such as the population size tending to infinity,and the individual degree of infectivity only depending on variations in the infectiousness period.In this paper we show that the same conclusions hold true in a finite population representing a medium size city,where the degree of infectivity is determined by the offspring distribution,which we try to make as realistic as possible for SARS-CoV-2.In particular,we consider distributions with fat tails,to incorporate the existence of super-spreaders.We also provide new theoretical results on convergence of stochastic models which allows to incorporate any offspring distribution with a finite variance.
