A general framework for stability analysis of gene regulatory networks with delay.
A general scheme for constructing inversion algorithms for cone beam CT.
A generalization of Osgood's test and a comparison criterion for integral equations with noise.
A generalization of the Keller-Segel system to higher dimensions from a structural viewpoint
We consider initial boundary problems of a two-chemical substances chemotaxis system. In the four-dimensional setting, it was shown that solutions exist globally in time and remain bounded if the total mass is less than , whereas the solution emanating from some initial data of large magnitude may blows up. This result can be regarded as a generalization of the well-known problem in the Keller–Segel system to higher dimensions. We will compare mathematical structures of the Keller–Segel system...
A geometrical description of visual sensation
A geometrical description of visual sensation II
A global attractor in a general diffusive food chain model.
A haplotype block model for fine mapping of quantitative trait loci regulating HIV-1 pathogenesis.
A Hopf Bifurcation Theorem for Difference Equations Approximating a Differential Equation.
A Hybrid Model Describing Different Morphologies of Tumor Invasion Fronts
The invasive capability is fundamental in determining the malignancy of a solid tumor. Revealing biomedical strategies that are able to partially decrease cancer invasiveness is therefore an important approach in the treatment of the disease and has given rise to multiple in vitro and in silico models. We here develop a hybrid computational framework, whose aim is to characterize the effects of the different cellular and subcellular mechanisms involved...
A hyperbolic model of chemotaxis on a network: a numerical study
In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the...
A hypothetical-mathematical model of acute myeloid leukaemia pathogenesis.
A kinetic model of tumor/immune system cellular interactions.
A limit set trichotomy for order-preserving systems on time scales.
A linear model for the dynamics of fish larvae.
A linear scheme to approximate nonlinear cross-diffusion systems*
This paper proposes a linear discrete-time scheme for general nonlinear cross-diffusion systems. The scheme can be regarded as an extension of a linear scheme based on the nonlinear Chernoff formula for the degenerate parabolic equations, which proposed by Berger et al. [RAIRO Anal. Numer.13 (1979) 297–312]. We analyze stability and convergence of the linear scheme. To this end, we apply the theory of reaction-diffusion system approximation. After discretizing the scheme in space, we obtain a versatile,...
A linear scheme to approximate nonlinear cross-diffusion systems*
This paper proposes a linear discrete-time scheme for general nonlinear cross-diffusion systems. The scheme can be regarded as an extension of a linear scheme based on the nonlinear Chernoff formula for the degenerate parabolic equations, which proposed by Berger et al. [RAIRO Anal. Numer.13 (1979) 297–312]. We analyze stability and convergence of the linear scheme. To this end, we apply the theory of reaction-diffusion system approximation. After discretizing the scheme in space, we obtain a versatile,...
A Logic and computer algebra approach to a decision-making problem in medicine
A Markov chain approach to randomly grown graphs.
A mathematical model describing cellular division with a proliferating phase duration depending on the maturity of cells.