Related papers: Topological-numerical analysis of a two-dimensiona…
Although two-dimensional periodic structures have functioned as the primary platform for exploring topological phenomena, recent advances have substantially expanded this research boundary to include more intricate, aperiodic structures:…
A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…
The dynamics of an extremely diluted neural network with high order synapses acting as corrections to the Hopfield model is investigated. As in the fully connected case, the high order terms may strongly improve the storage capacity of the…
Long and stable timescales are often observed in complex biochemical networks, such as in emergent oscillations. How these robust dynamics persist remains unclear, given the many stochastic reactions and shorter time scales demonstrated by…
We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…
It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to self-organization of network…
The data-driven modeling of dynamical systems has become an essential tool for the construction of accurate computational models from real-world data. In this process, the inherent differential structures underlying the considered physical…
The principled design and discovery of biologically- and physically-informed models of neuronal dynamics has been advancing since the mid-twentieth century. Recent developments in artificial intelligence (AI) have accelerated this progress.…
Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology.…
This work describes a novel methodology for automatic contour extraction from 2D images of 3D neurons (e.g. camera lucida images and other types of 2D microscopy). Most contour-based shape analysis methods can not be used to characterize…
In the study of neurons, morphology influences function. The complexity in the structure of neurons poses a challenge in the identification and analysis of similar and dissimilar neuronal cells. Existing methodologies carry out structural…
Complex networks are used to depict topological features of complex systems. The structure of a network characterizes the interactions among elements of the system, and facilitates the study of many dynamical processes taking place on it.…
Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have…
The structure of a complex network plays a crucial role in determining its dynamical properties. In this work, we show that the the degree to which a network is directed and hierarchically organised is closely associated with the degree to…
We consider a distributed detection system with communication constraints, where several nodes are arranged in an arbitrary tree topology, under the assumption of conditionally independent observations. We propose a cyclic design procedure…
For years, we have been building models of gene regulatory networks, where recent advances in molecular biology shed some light on new structural and dynamical properties of such highly complex systems. In this work, we propose a novel…
Biological networks have been recently found to exhibit many topological properties of the so-called complex networks. It has been reported that they are, in general, both highly skewed and directed. In this paper, we report on the dynamics…
Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…
In this work, we present a computational framework for exploring and analyzing the macroscopic dynamics of complex agent-based network models by integrating Topological Data Analysis with the Equation-Free Method. To demonstrate the…
We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the…