• Proceedings of the National Institute of Ecology of the Republic of Korea
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• v.3 no.3
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• pp.149-153
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• 2022

The degree distribution of the plant-pollinator network was identified by analyzing the data in the ecosystem and reproduced by a model of the growing bipartite mutualistic networks. The degree distribution of pollinator shows power law or stretched exponential distribution, while plant usually shows stretched exponential distribution. In the growth model, the plant and the pollinator are selected with probability P_p and P_A=1-P_p, respectively. The number of incoming links for the plant and the pollinator is l_p and l_A, respectively. The probability that the link of the plant selects the pollinator of the existing network given as $A_{k_i}=k^{{\lambda}_A}_i/{\sum}_i\;k^{{\lambda}_A}_i$, and the probability that the pollinator selects the plant is $P_{k_i}=k^{{\lambda}_p}_i/{\sum}_i\;k^{{\lambda}_p}_i$. When the nonlinear growth index is 𝛌_X=1 (X=A or P), the degree distribution follows a power law, and if 0≤𝛌_X<1, the degree distribution follows a stretched exponential distribution. The cumulative degree distributions of plants and pollinators of 14 empirical plant-pollinators included in Interaction Web Database were calculated. A set of parameters (P_A,P_P,l_A,l_P) that reproduces these cumulative degree distributions and a growth index 𝛌_X (X=A or P) were obtained. We found that animal takes very heterogenous connections, whereas plant takes a more flexible connection network.

• The Korean Journal of Applied Statistics
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• v.29 no.3
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• pp.425-435
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• 2016

In this paper, we analyze the inverse statistics of rainfall for 12 regions from 1973 to 2014. We obtain a probability density function f(x) of daily rainfall x, and $f({\tau}_{\rho})$ of the first passage time ${\tau}_{\rho}$ for a given ${\rho}$. Lastly, we derive the relation between ${\rho}$ and ${\tau}_{mean}({\rho})$, i.e., the averaged value of ${\tau}_{\rho}$. The analyses result in the x and ${\tau}_{\rho}$ have stretched exponential distributions. Also, ${\tau}_{mean}({\rho})$ has the form of a stretched exponential function. We derive the shape parameter ${\beta}$ of the distribution, and analyze the characteristics of 12 regional rainfalls.

• Journal of the Korean Magnetic Resonance Society
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• v.17 no.1
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• pp.19-23
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• 2013

The temperature dependences of the NMR spectrum and the spin-lattice relaxation times in $KH_2PO_4$ were investigated via single-crystal NMR and MAS NMR. The stretched-exponential relaxation that occurred because of the distribution of correlation times was indicative of the degree of the distribution of the double-well potential on the hydrogen bond. The behaviors responsible for the strong temperature dependences of the $^1H$ and $^{31}P$ spin-lattice relaxation times in the rotating frame $T_{1{\rho}}$ in $KH_2PO_4$ are likely related to the reorientational motion of the hydrogen-bond geometry and the $PO_4$ tetrahedral distortion.