Related papers: Dynamical Theory for Adaptive Systems

We present a theoretical analysis of some popular adaptive Stochastic Gradient Descent (SGD) methods in the small learning rate regime. Using the stochastic modified equations framework introduced by Li et al., we derive effective…

Mobile robots, such as ground vehicles and quadrotors, are becoming increasingly important in various fields, from logistics to agriculture, where they automate processes in environments that are difficult to access for humans. However, to…

Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…

We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific scales of the biological framework of adaptive dynamics.…

We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model by a low-dimensional system of equations permitting analytical…

Although many phenotypic traits are determined by a large number of genetic variants, how a polygenic trait adapts in response to the changes in the environment is still poorly understood. Here we study the adaptation dynamics of a…

Evolution in changing environments is an important, but little studied aspect of the theory of evolution. The idea of adaptive walks in fitness landscapes has triggered a vast amount of research and has led to many important insights about…

Adaptive networks are a versatile approach to model phenomena such as contagion and spreading dynamics, critical transitions and structure formation that emerge from the dynamic coevolution of complex network structure and node states.…

We consider the problem of learning the dynamics of autonomous linear systems (i.e., systems that are not affected by external control inputs) from observations of multiple trajectories of those systems, with finite sample guarantees.…

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node…

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…

Network routing approaches are widely used to study the evolution in time of self-adapting systems. However, few advances have been made for problems where adaptation is governed by time-dependent inputs. In this work we study a dynamical…

To explain day-to-day (DTD) route-choice behaviors and traffic dynamics observed in a series of lab experiments, Part I of this research proposed a discrete choice-based analytical dynamic model (Qi et al., 2023). Although the deterministic…

In adaptive dynamical networks, the dynamics of the nodes and the edges influence each other. We show that we can treat such systems as a closed feedback loop between edge and node dynamics. Using recent advances on the stability of…

In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…

Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…

What can we learn about controlling a system solely from its underlying network structure? Here we adapt a recently developed framework for control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic…

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…

This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian…

In order to robustly execute a task under environmental uncertainty, a robot needs to be able to reactively adapt to changes arising in its environment. The environment changes are usually reflected in deviation from expected sensory…