相关论文: Emergent Properties in Structurally Dynamic Disord…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the…
Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a class of ' cellular networks'…
As in an earlier paper we start from the hypothesis that physics on the Planck scale should be described by means of concepts taken from ``discrete mathematics''. This goal is realized by developing a scheme being based on the dynamical…
We study the effects of spatial constraints on the structural properties of networks embedded in one or two dimensional space. When nodes are embedded in space, they have a well defined Euclidean distance $r$ between any pair. We assume…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
Previous study of cellular automata and random Boolean networks has shown emergent behavior occurring at the edge of chaos where the randomness (disorder) of internal connections is set to an intermediate critical value. The value at which…
Neural Cellular Automata (NCA) models are trainable variations of traditional Cellular Automata (CA). Emergent motion in the patterns created by NCA has been successfully applied to synthesize dynamic textures. However, the conditions…
We study networks representing the dynamics of elementary 1-d cellular automata (CA) on finite lattices. We analyze scaling behaviors of both local and global network properties as a function of system size. The scaling of the largest node…
The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links, the average eccentricity and…
In the framework of coupled cell systems, a coupled cell network describes graphically the dynamical dependencies between individual dynamical systems, the cells. The fundamental network of a network reveals the hidden symmetries of that…
Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a '{\it cellular network}'…
Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
A cell's behavior is a consequence of the complex interactions between its numerous constituents, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes,…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and PDE trajectories. Our method is designed to identify underlying…
Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…
Fluorescence microscopy has led to impressive quantitative models and new insights gained from richer sets of biomedical imagery. However, there is a dearth of rigorous and established bioimaging strategies for modeling spatiotemporal…