Related papers: Self-similar dynamics of morphogen gradients
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The open nonlinear electrodynamic system - nonlinear transverse non-homogeneous dielectric layer, is an example of inorganic system having the properties of self-organization, peculiar to biological systems. The necessary precondition of…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
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Diffusion models are getting popular in generative image and video synthesis. However, due to the diffusion process, they require a large number of steps to converge. To tackle this issue, in this paper, we propose to perform the diffusion…
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In this paper we give a description of the asymptotic behavior, as $\epsilon\to 0$, of the $\epsilon$-gradient flow in the finite dimensional case. Under very general assumptions we prove that it converges to an evolution obtained by…
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The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A…
Spatio-temporal biochemical signaling in a large class of protein-protein interaction networks is well modeled by a reaction-diffusion system. The global existence of the solution to the reaction-diffusion system is determined by the…
In many developmental systems, cells differentiate into a tissue by reading out morphogen concentration fields, a process fundamentally limited by noise. How much can the precision of this process be improved by nonlocal information, e.g.,…
Position determination in biological systems is often achieved through protein concentration gradients. Measuring the local concentration of such a protein with a spatially-varying distribution allows the measurement of position within the…
We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. The kernel is not necessarily symmetric or compactly…
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