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Fractional virus epidemic model on financial networks

100%

Balci M. A.

Open Mathematics

2016

tom 14

nr 1

1074-1086

In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.

Covariate-based stochastic parameterization of baroclinic ocean eddies

100%

Verheul N., Viebahn J., Crommelin D.

Mathematics of Climate and Weather Forecasting

2017

tom 3

nr 1

90-117

In this study we investigate a covariate-based stochastic approach to parameterize unresolved turbulent processes within a standard model of the idealised, wind-driven ocean circulation. We focus on vertical instead of horizontal coarse-graining, such that we avoid the subtle difficulties of horizontal coarsegraining. The corresponding eddy forcing is uniquely defined and has a clear physical interpretation related to baroclinic instability.We propose to emulate the baroclinic eddy forcing by sampling from the conditional probability distribution functions of the eddy forcing obtained from the baroclinic reference model data. These conditional probability distribution functions are approximated here by sampling uniformly from discrete reference values. We analyze in detail the different performances of the stochastic parameterization dependent on whether the eddy forcing is conditioned on a suitable flow-dependent covariate or on a timelagged covariate or on both. The results demonstrate that our non-Gaussian, non-linear methodology is able to accurately reproduce the first four statistical moments and spatial/temporal correlations of the stream function, energetics, and enstrophy of the reference baroclinic model.

Ograniczanie wyników

1 Mathematics of Climate and Weather Forecasting

1 Open Mathematics

1 Balci M. A.

1 Crommelin D.

1 Verheul N.

1 Viebahn J.

1 2017

1 2016

Wyniki wyszukiwania

Fractional virus epidemic model on financial networks

Covariate-based stochastic parameterization of baroclinic ocean eddies