Normal Inverse Gaussian Approximation for Arrival Time Difference in Flow-Induced Molecular Communications

In this paper, we consider molecular communications in one-dimensional flow-induced diffusion channels with a perfectly absorbing receiver. In such channels, the random propagation delay until the molecules are absorbed follows an inverse Gaussian (IG) distribution and is referred to as first hitting time. Knowing the distribution for the difference of the first hitting times of two molecules is very important if the information is encoded by a limited set of molecules and the receiver exploits their arrival time and/or order. Hence, we propose a moment matching approximation by a normal inverse Gaussian (NIG) distribution and we derive an expression for the asymptotic tail probability. Numerical evaluations showed that the NIG approximation matches very well with the exact solution obtained by numerical convolution of the IG density functions. Moreover, the asymptotic tail probability outperforms state-of-the-art tail approximations.Comment: This paper has been submitted to IEEE Transactions on Molecular, Biological and Multi-Scale Communication

On Reliability of a Double Redundant Renewable System with a Generally Distributed Life and Repair Times

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Trees classification based on Fourier coefficients of the sapflow density flux

In this paper we study the possibility to use the artificial neural networks for trees classification based on real and approximated values of the sap flow density flux describing water transport in trees. The data sets were generated by means of a new tree monitoring system TreeTalker. The Fourier series-based model is used for fitting the data sets with periodic patterns. The multivariate regression model defines the functional dependencies between sap flow density and temperature time series. The paper shows that Fourier coefficients can be successfully used as elements of the feature vectors required to solve different classification problems. Here we train multilayer neural networks to classify the trees according to different types of classes. The quality of the developed model for prediction and classification is verified by numerous numerical examples

Trees classification based on Fourier coefficients of the sapflow density flux

In this paper we study the possibility to use the artificial neural networks for trees classification based on real and approximated values of the sap flow density flux describing water transport in trees. The data sets were generated by means of a new tree monitoring system TreeTalker. The Fourier series-based model is used for fitting the data sets with periodic patterns. The multivariate regression model defines the functional dependencies between sap flow density and temperature time series. The paper shows that Fourier coefficients can be successfully used as elements of the feature vectors required to solve different classification problems. Here we train multilayer neural networks to classify the trees according to different types of classes. The quality of the developed model for prediction and classification is verified by numerous numerical examples

Normal inverse Gaussian approximation for arrival time difference in flow-induced molecular communications

The inverse Gaussian (IG) distribution is a well- established distribution for the first hitting time in flow-induced diffusion molecular communications. However, the distribution of the difference between two independent IG-distributed random variables has not been derived yet, although it is very important for the analysis of many molecular communication systems. For example, for deriving crossover probabilities or characterizing the noise in time between release modulation. In this letter, we propose an approximation by a normal inverse Gaussian (NIG) distribution and derive an asymptotic tail approximation. Numerical evaluations showed that the NIG approximation matches very well with the solution obtained through numerical integration, in particular for the tails. Moreover, the asymptotic tail approximation converges very quickly to the actual probability and outperforms state-of-the-art tail approximations

An algorithmic approach to analysing the reliability of a controllable unreliable queue with two heterogeneous servers

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