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We present a unified field-theoretic framework for the dynamics of activity and connectivity in interacting neuronal systems. Building upon previous works, where a field approach to activity--connectivity dynamics, formation of collective…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
Machine learning has become increasingly popular for efficiently modelling the dynamics of complex physical systems, demonstrating a capability to learn effective models for dynamics which ignore redundant degrees of freedom. Learned…
Traditional Smooth Transition Autoregressive (STAR) models offer an effective way to model these dynamics through smooth regime changes based on specific transition variables. In this paper, we propose a novel approach by drawing an analogy…
In this letter we announce rigorous results on the phenomenon of aging in the Glauber dynamics of the random energy model and their relation to Bouchaud's 'REM-like' trap model. We show that, below the critical temperature, if we consider a…
This paper proposes a neural network hybrid modeling framework for dynamics learning to promote an interpretable, computationally efficient way of dynamics learning and system identification. First, a low-level model will be trained to…
Many human social phenomena, such as cooperation, the growth of settlements, traffic dynamics and pedestrian movement, appear to be accessible to mathematical descriptions that invoke self-organization. Here we develop a model of pedestrian…
Complex networks are a great tool for simulating the outcomes of different strategies used within the iterated prisoners' dilemma game. However, because the strategies themselves rely on the connection between nodes, then initial network…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
We propose a framework for constructing microscopic traffic models from microscopic acceleration patterns that can in principle be experimental measured and proper averaged. The exact model thus obtained can be used to justify the…
Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with…
One of the aims of systems biology is to build multiple layered and multiple scale models of living systems which can efficiently describe phenomena occurring at various level of resolution. Such models should consist of layers of various…
For real-world complex system constantly enduring perturbation, to achieve survival goal in changing yet unknown environments, the central problem is constantly adapting themself to external environments according to environmental feedback.…
Motivated by the dynamics of particles embedded in active gels, both in-vitro and inside the cytoskeleton of living cells, we study an active generalization of the classical trap model. We demonstrate that activity leads to dramatic…
We consider systems that are well modelled as a networks that evolve in time, which we call {\it Moving Neighborhood Networks}. These models are relevant in studying cooperative behavior of swarms and other phenomena where emergent…
We present a structured neural network architecture that is inspired by linear time-varying dynamical systems. The network is designed to mimic the properties of linear dynamical systems which makes analysis and control simple. The…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…
The Glauber dynamics of various models (REM-like trap models, Brownian motion, BM model, Ising chain and SK model) is analyzed in relation with the existence of ageing. From a finite size Glauber matrix, we calculate a time $\tau_w(N)$…
For autonomous driving, traversability analysis is one of the most basic and essential tasks. In this paper, we propose a novel LiDAR-based terrain modeling approach, which could output stable, complete and accurate terrain models and…
Continuous "bump" attractors are an established model of cortical working memory for continuous variables and can be implemented using various neuron and network models. Here, we develop a generalizable approach for the approximation of…