Backpropagation-optimized artificial neural networks, while precise, lack robustness, leading to unforeseen behaviors that affect their safety. Biological neural systems do solve some of these issues already. Unlike a...
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We explore the use of quantum generative adversarial networks QGANs for modeling eye movement velocity data. We assess whether the advanced computational capabilities of QGANs can enhance the modeling of complex stoch...
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In this article, panel (b) of Fig. 6 was inadvertently printed in black and white instead of colour;the figure should have appeared as shown below. (Figure presented.) Norm of the Jacobian of latent activations h^ (up...
Hippocampal place cells are known for their spatially selective firing patterns, which has led to the suggestion that they encode an animal's location. However, place cells also respond to contextual cues, such as...
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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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.
Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular network...
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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).
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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