Global attractors and extinction dynamics of cyclically competing species

Transitions to absorbing states are of fundamental importance in nonequilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three cyclically interacting species. The interaction scheme comprises both direct competition between species as in the cyclic Lotka-Volterra model, and separated selection and reproduction processes as in the May-Leonard model. We show that the dynamic processes leading to the transient maintenance of biodiversity are closely linked to attractors of the nonlinear dynamics for the overall species' concentrations. The characteristics of these global attractors change qualitatively at certain threshold values of the mobility and depend on the relative strength of the different types of competition between species. They give information about the scaling of extinction times with the system size and thereby the stability of biodiversity. We define an effective free energy as the negative logarithm of the probability to find the system in a specific global state before reaching one of the absorbing states. The global attractors then correspond to minima of this effective energy landscape and determine the most probable values for the species' global concentrations. As in equilibrium thermodynamics, qualitative changes in the effective free energy landscape indicate and characterize the underlying nonequilibrium phase transitions. We provide the complete phase diagrams for the population dynamics and give a comprehensive analysis of the spatio-temporal dynamics and routes to extinction in the respective phases

Curvature-enhanced Neural Subdivision

Subdivision is an important and widely used technique for obtaining dense meshes from coarse control (triangular) meshes for modelling and animation purposes. Most subdivision algorithms use engineered features (subdivisionrules). Recently, neural subdivision successfully applied machine learning to the subdivision of a triangular mesh. It uses a simple neural network to learn an optimal vertex positioning during a subdivision step. We propose an extension to the neural subdivision algorithm that introduces explicit curvature informationinto the network. This makes a larger amount of relevant information accessible which allows the network to yield better results. We demonstrate that this modification yields significant improvement over the original algorithm, in terms of both Hausdorff distance and mean squared error

Curvature-enhanced Neural Subdivision

Subdivision is an important and widely used technique for obtaining dense meshes from coarse control (triangular) meshes for modelling and animation purposes. Most subdivision algorithms use engineered features (subdivisionrules). Recently, neural subdivision successfully applied machine learning to the subdivision of a triangular mesh. It uses a simple neural network to learn an optimal vertex positioning during a subdivision step. We propose an extension to the neural subdivision algorithm that introduces explicit curvature informationinto the network. This makes a larger amount of relevant information accessible which allows the network to yield better results. We demonstrate that this modification yields significant improvement over the original algorithm, in terms of both Hausdorff distance and mean squared error

Visual Analysis of Popping in Progressive Visualization

Progressive visualization allows users to examine intermediate results while they are further refined in the background. This makes them increasingly popular when dealing with large data and computationally expensive tasks. The characteristics of how preliminary visualizations evolve over time are crucial for efficient analysis; in particular unexpected disruptive changes betweeniterations can significantly hamper the user experience. This paper proposes a visualization framework to analyze the refinement behavior of progressive visualization. We particularly focus on sudden significant changes between the iterations, which we denote as popping artifacts, in reference to undesirable visual effects in the context of level of detail representations in computergraphics. Our visualization approach conveys where in image space and when during the refinement popping artifacts occur. It allows to compare across different runs of stochastic processes, and supports parameter studies for gaining further insights and tuning the algorithms under consideration. We demonstrate the application of our framework and its effectiveness via twodiverse use cases with underlying stochastic processes: adaptive image space sampling, and the generation of grid layouts

Curvature-enhanced Neural Subdivision

Subdivision is an important and widely used technique for obtaining dense meshes from coarse control (triangular) meshes for modelling and animation purposes. Most subdivision algorithms use engineered features (subdivisionrules). Recently, neural subdivision successfully applied machine learning to the subdivision of a triangular mesh. It uses a simple neural network to learn an optimal vertex positioning during a subdivision step. We propose an extension to the neural subdivision algorithm that introduces explicit curvature informationinto the network. This makes a larger amount of relevant information accessible which allows the network to yield better results. We demonstrate that this modification yields significant improvement over the original algorithm, in terms of both Hausdorff distance and mean squared error

Curvature-enhanced Neural Subdivision

Subdivision is an important and widely used technique for obtaining dense meshes from coarse control (triangular) meshes for modelling and animation purposes. Most subdivision algorithms use engineered features (subdivisionrules). Recently, neural subdivision successfully applied machine learning to the subdivision of a triangular mesh. It uses a simple neural network to learn an optimal vertex positioning during a subdivision step. We propose an extension to the neural subdivision algorithm that introduces explicit curvature informationinto the network. This makes a larger amount of relevant information accessible which allows the network to yield better results. We demonstrate that this modification yields significant improvement over the original algorithm, in terms of both Hausdorff distance and mean squared error

Curvature-enhanced Neural Subdivision

Subdivision is an important and widely used technique for obtaining dense meshes from coarse control (triangular) meshes for modelling and animation purposes. Most subdivision algorithms use engineered features (subdivisionrules). Recently, neural subdivision successfully applied machine learning to the subdivision of a triangular mesh. It uses a simple neural network to learn an optimal vertex positioning during a subdivision step. We propose an extension to the neural subdivision algorithm that introduces explicit curvature informationinto the network. This makes a larger amount of relevant information accessible which allows the network to yield better results. We demonstrate that this modification yields significant improvement over the original algorithm, in terms of both Hausdorff distance and mean squared error

Curvature-enhanced Neural Subdivision

Subdivision is an important and widely used technique for obtaining dense meshes from coarse control (triangular) meshes for modelling and animation purposes. Most subdivision algorithms use engineered features (subdivisionrules). Recently, neural subdivision successfully applied machine learning to the subdivision of a triangular mesh. It uses a simple neural network to learn an optimal vertex positioning during a subdivision step. We propose an extension to the neural subdivision algorithm that introduces explicit curvature informationinto the network. This makes a larger amount of relevant information accessible which allows the network to yield better results. We demonstrate that this modification yields significant improvement over the original algorithm, in terms of both Hausdorff distance and mean squared error