The activity and dynamics of excitable cells are fundamentally regulated and moderated by extracellular and intracellular ion concentrations and their electric potentials. The increasing availability of dense reconstr...
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Mathematical models for excitable tissue with explicit representation of individual cells are highly detailed and can, unlike classical homogenized models, represent complex cellular geometries and local membrane vari...
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In this paperwe consider PDE-constrained optimization problemswhich incorporate an H_(1)regularization control *** focus on a time-dependent PDE,and consider both distributed and boundary *** problems we consider incl...
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In this paperwe consider PDE-constrained optimization problemswhich incorporate an H_(1)regularization control *** focus on a time-dependent PDE,and consider both distributed and boundary *** problems we consider include bound constraints on the state,and we use a Moreau-Yosida penalty function to handle *** propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.
A posteriori error estimates based on residuals can be used for reliable error control of numerical methods. Here, we consider them in the context of ordinary differential equations and Runge-Kutta methods. In particu...
A posteriori error estimates based on residuals can be used for reliable error control of numerical methods. Here, we consider them in the context of ordinary differential equations and Runge-Kutta methods. In particular, we take the approach of Dedner & Giesselmann (2016) and investigate it when used to select the time step size. We focus on step size control stability when combined with explicit Runge-Kutta methods and demonstrate that a standard I controller is unstable while more advanced PI and PID controllers can be designed to be stable. We compare the stability properties of residual-based estimators and classical error estimators based on an embedded Runge-Kutta method both analytically and in numerical experiments.
numerical computations of two-phase flows with surface active agents (surfactants) are highly demanded in several scientific and engineering applications. Apart from the other challenges associated with the computatio...
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ISBN:
(纸本)9783950353709
numerical computations of two-phase flows with surface active agents (surfactants) are highly demanded in several scientific and engineering applications. Apart from the other challenges associated with the computation of two-phase flows, the presence of surfactants increases the complexity. Surfactants alter the flow dynamics significantly by lowering the surface tension on the interface. Moreover, the concentration of surfactants along the interface is often not uniform and thus Marangoni forces are induced. Adsorption and desorption of surfactants between the interface and the bulk phase may take place in the case of soluble surfactants.
We prove an $$L^p(I,C^\alpha (\Omega ))$$ regularity result for a diffusion equation with mixed boundary conditions, $$L^\infty $$ coefficients and an $$L^{ q }$$ initial condition. We provide explicit control of the ...
We prove an $$L^p(I,C^\alpha (\Omega ))$$ regularity result for a diffusion equation with mixed boundary conditions, $$L^\infty $$ coefficients and an $$L^{ q }$$ initial condition. We provide explicit control of the $$L^p(I,C^\alpha (\Omega ))$$ norm with respect to the data. To prove our result, we first establish $$C^\alpha (\Omega )$$ control of the stationary equation, extending a result by Haller-Dintelmann et al. (Appl Math Optim 60(3):397–428, 2009).
Artificial and biological agents are unable to learn given completely random and unstructured data. The structure of data is encoded in the distance or similarity relationships between data points. In the context of n...
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Artificial and biological agents are unable to learn given completely random and unstructured data. The structure of data is encoded in the distance or similarity relationships between data points. In the context of neural networks, the neuronal activity within a layer forms a representation reflecting the transformation that the layer implements on its inputs. In order to utilize the structure in the data in a truthful manner, such representations should reflect the input distances and thus be continuous and isometric. Supporting this statement, recent findings in neuroscience propose that generalization and robustness are tied to neural representations being continuously differentiable. However, in machine learning, most algorithms lack robustness and are generally thought to rely on aspects of the data that differ from those that humans use, as is commonly seen in adversarial attacks. During cross-entropy classification, the metric and structural properties of network representations are usually broken both between and within classes. This side effect from training can lead to instabilities under perturbations near locations where such structure is not preserved. One of the standard solutions to obtain robustness is to train specifically by introducing perturbations in the training data. This leads to networks that are particularly robust to specific training perturbations but not necessarily to general perturbations. While adding ad hoc regularization terms to improve robustness has become common practice, to our knowledge, forcing representations to preserve the metric structure of the input data as a stabilising mechanism has not yet been introduced. In this work, we train neural networks to perform classification while simultaneously maintaining the metric structure within each class, leading to continuous and isometric within-class representations. We show that such network representations turn out to be a beneficial component for making accurate and robust
In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that ...
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The Keller-Segel model is a well-known system representing chemotaxis in living organisms. We study the convergence of a generalized nonlinear variant of the Keller-Segel to the degenerate Cahn-Hilliard system. This a...
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