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Dynamic multilayer networks frequently represent the structure of multiple co-evolving relations; however, statistical models are not well-developed for this prevalent network type. Here, we propose a new latent space model for dynamic…
The aging dynamics of a simple model glass is numerically investigated observing how it takes place in the potential energy landscape $V$. Partitioning the landscape in basins of minima of $|\nabla V|^2$, we are able to elucidate some…
The thermally activated creep motion of an elastic interface weakly driven on a disordered landscape is one of the best examples of glassy universal dynamics. Its understanding has evolved over the last 30 years thanks to a fruitful…
We propose a physical model for developmental process at cellular level to discuss the mechanism of epigenetic landscape. In our simplified model, a minimal model, the network of the interaction among cells generates the landscape…
In evolution theory the concept of a fitness landscape has played an important role, evolution itself being portrayed as a hill-climbing process on a rugged landscape. In this article it is shown that in general, in the presence of other…
We use Langevin dynamics simulations to study dynamical behaviour of a dense planar layer of active semi-flexible filaments. Using the strength of active force and the thermal persistence length as parameters, we map a detailed phase…
In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…
Threshold rules of spreading in binary-state networks lead to cascades. We study persistent cascade-recovery dynamics on quasi-robust networks, i.e., networks which are robust against small trigger but may collapse for larger one. It is…
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…
Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…
Networks observed in real world like social networks, collaboration networks etc., exhibit temporal dynamics, i.e. nodes and edges appear and/or disappear over time. In this paper, we propose a generative, latent space based, statistical…
For prediction of interacting agents' trajectories, we propose an end-to-end trainable architecture that hybridizes neural nets with game-theoretic reasoning, has interpretable intermediate representations, and transfers to downstream…
Coupled natural systems are generally modeled at multiple abstraction levels. Both structural scale and behavioral complexity of these models are determinants in the kinds of questions that can be posed and answered. As scale and complexity…
In this paper, a computationally efficient data-driven hybrid automaton model is proposed to capture unknown complex dynamical system behaviors using multiple neural networks. The sampled data of the system is divided by valid partitions…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
It is analyzed whether the potential energy landscape of a glass-forming system can be effectively mapped on a random model which is described in statistical terms. For this purpose we generalize the simple trap model of Bouchaud and…
Models that can simulate how environments change in response to actions can be used by agents to plan and act efficiently. We improve on previous environment simulators from high-dimensional pixel observations by introducing recurrent…
We propose an information-based model for network dynamics in which imperfect information leads to networks where the different vertices have widely different number of edges to other vertices, and where the topology has hierarchical…
We propose an approach to online model adaptation and control in the challenging case of hybrid and discontinuous dynamics where actions may lead to difficult-to-escape "trap" states, under a given controller. We first learn dynamics for a…
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…