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Rhythmic and sequential subdivision of the elongating vertebrate embryonic body axis into morphological somites is controlled by an oscillating multicellular genetic network termed the segmentation clock. This clock operates in the…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the…
Neural field equations offer a continuous description of the dynamics of large populations of synaptically coupled neurons. This makes them a convenient tool to describe various neural processes, such as working memory, motion perception,…
A theoretical study of delayed feedback in spin-torque nano-oscillators is presented. A macrospin geometry is considered, where self-sustained oscillations are made possible by spin transfer torques associated with spin currents flowing…
The brain is formed by cortical regions that are associated with different cognitive functions. Neurons within the same region are more likely to connect than neurons in distinct regions, making the brain network to have characteristics of…
This series of papers models the dynamics of a large set of interacting neurons within the framework of statistical field theory. The system is described using a two-field model. The first field represents the neuronal activity, while the…
A general scheme for construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the…
Walking animals, like stick insects, cockroaches or ants, demonstrate a fascinating range of locomotive abilities and complex behaviors. The locomotive behaviors can consist of a variety of walking patterns along with adaptation that allow…
This paper presents a rigorous analytical model of traffic dynamics on a circular track, demonstrating the emergence of standing oscillations resulting from microscopic driver behaviour, delay responses, and proximity pressure. Without…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
This technical note introduces parametric dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow…
We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…
Biological neurons can detect complex spatio-temporal features in spiking patterns via their synapses spread across across their dendritic branches. This is achieved by modulating the efficacy of the individual synapses, and by exploiting…
Representational drift refers to an unstable mapping between neural activity and input sensory or output behavioral variables. While much work has focused on the effect of representational drift on single, simple external variables, we…
Current Deep Learning methods for environment segmentation and velocity estimation rely on Convolutional Recurrent Neural Networks to exploit spatio-temporal relationships within obtained sensor data. These approaches derive scene dynamics…
Macroscopic oscillations of different brain regions show multiple phase relationships that are persistent across time and have been implicated routing information. Various cellular level mechanisms influence the network dynamics and…
Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to…
To model time series accurately is important within a wide range of fields. As the world is generally too complex to be modelled exactly, it is often meaningful to assess the probability of a dynamical system to be in a specific state. This…