scholarly journals An Optimal Method for Diffusion Parameters of Nonlinear Diffusion Problem of Drug Releasing in 2D-Disc Device by Separate Variable Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Youyun Li ◽  
Jinhui Ouyang ◽  
Jiaohua Qin ◽  
Yingli Gao
Keyword(s):  
Nonlinear Problem ◽  
Nonlinear Diffusion ◽  
Diffusion Problem ◽  
Control Model ◽  
Least Square ◽  
Computational Method ◽  
Variable Method ◽  
Linear Diffusion ◽  
Separate Variable ◽  
Diffusion Parameters

An optimization control model and the corresponding computational method drawing the diffusion parameters of the nonlinear problem for the drug releasing in the 2D-disc device were given in this paper. Firstly, based on the nonlinear diffusion equation of the drug releasing in the 2D-disc device, we used the linear diffusion problem to discrete the nonlinear diffusion problem with the discrete space and the discrete time. Then, by the separate variable method, the solution of the linear problem was given. Next, the least square method based on the separate variable idea (LSMSV) was used to estimate the nonlinear appropriate diffusion parameters. Finally, a numerical example was presented to show that the control model and the numerical method were valid for computing the diffusion coefficient of the nonlinear problem for the drug releasing in the 2D-disc device.

scholarly journals IILLS: predicting virus-receptor interactions based on similarity and semi-supervised learning

2019 ◽  
Vol 20 (S23) ◽  
Author(s):  
Cheng Yan ◽  
Guihua Duan ◽  
Fang-Xiang Wu ◽  
Jianxin Wang
Keyword(s):  
Infectious Diseases ◽  
Cross Validation ◽  
Sequence Similarity ◽  
Least Square ◽  
Computational Method ◽  
Receptor Interaction ◽  
Virus Receptor ◽  
Receptor Interactions ◽  
Leave One Out ◽  
Fold Cross Validation

Abstract Background Viral infectious diseases are the serious threat for human health. The receptor-binding is the first step for the viral infection of hosts. To more effectively treat human viral infectious diseases, the hidden virus-receptor interactions must be discovered. However, current computational methods for predicting virus-receptor interactions are limited. Result In this study, we propose a new computational method (IILLS) to predict virus-receptor interactions based on Initial Interaction scores method via the neighbors and the Laplacian regularized Least Square algorithm. IILLS integrates the known virus-receptor interactions and amino acid sequences of receptors. The similarity of viruses is calculated by the Gaussian Interaction Profile (GIP) kernel. On the other hand, we also compute the receptor GIP similarity and the receptor sequence similarity. Then the sequence similarity is used as the final similarity of receptors according to the prediction results. The 10-fold cross validation (10CV) and leave one out cross validation (LOOCV) are used to assess the prediction performance of our method. We also compare our method with other three competing methods (BRWH, LapRLS, CMF). Conlusion The experiment results show that IILLS achieves the AUC values of 0.8675 and 0.9061 with the 10-fold cross validation and leave-one-out cross validation (LOOCV), respectively, which illustrates that IILLS is superior to the competing methods. In addition, the case studies also further indicate that the IILLS method is effective for the virus-receptor interaction prediction.

scholarly journals Regularity, Asymptotic Solutions and Travelling Waves analysis in a porous medium system to model the interaction between invasive and invaded species

2021 ◽  
Author(s):  
José Díaz ◽  
Antonio Naranjo
Keyword(s):  
Porous Medium ◽  
Travelling Waves ◽  
Stationary Solutions ◽  
Uniqueness Of Solutions ◽  
Linear Diffusion ◽  
Diffusion Parameters ◽  
Medium System ◽  
Topological Argument ◽  
And Diffusion ◽  
Stable Connection

This work provides an analytical approach to characterize and determine solutions to a porous medium system of equations with views in applications to invasive-invaded biological dynamics. Firstly, the existence and uniqueness of solutions are proved. Afterwards, profiles of solutions are obtained making use of the selfsimilar structure that permits to show the existence of a diffusive front. The solutions are then studied within the Travelling Waves (TW) domain showing the existence of potential and exponential profiles in the stable connection that converges to the stationary solutions in which the invasive specie predominates. The TW profiles are shown to exist based on the geometry perturbation theory together with an analytical-topological argument in the phase plane. The finding of an exponential decaying rate (related with the advection and diffusion parameters) in the invaded specie TW is not trivial in the non-linear diffusion case and reflects the existence of a TW trajectory governed by the invaded specie runaway (in the direction of the advection) and the diffusion (acting along a finite speed front or support).

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