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Oscillatory phase pattern formation and amplitude control for a linearized stochastic neuron field model was investigated by simulating coupled stochastic processes defined by stochastic differential equations. It was found, for several…
We propose a model of mass-conserving heterogeneous nucleation to describe the dynamics of ligand-receptor binding in closed cellular compartments. When the ligand dissociation rate is small, competition among receptors for free ligands…
We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
Continuous attractor neural networks generate a set of smoothly connected attractor states. In memory systems of the brain, these attractor states may represent continuous pieces of information such as spatial locations and head directions…
Little is known theoretically about the associative memory capabilities of neural networks in which information is encoded not only in the mean firing rate but also in the timing of firings. Particularly, in the case that the fraction of…
Phase separation within polymer networks plays a central role in shaping the structure and mechanics of both synthetic materials and living cells, including the formation of biomolecular condensates within cytoskeletal networks. Previous…
We study the dynamics of coupled oscillator networks with higher-order interactions and their ability to store information. In particular, the fixed points of these oscillator systems consist of two clusters of oscillators that become…
We analyse the storage and retrieval capacity in a recurrent neural network of spiking integrate and fire neurons. In the model we distinguish between a learning mode, during which the synaptic connections change according to a Spike-Timing…
Coarsening, the process where larger structures grow at the expense of smaller ones, is a fundamental aspect of multiphase systems. The cell cytoplasm exemplifies an out-of-equilibrium multiphase system, where phase-separated condensates…
The spatial localization or sequestering of motile cargo and their dispersal within cells is an important process in a number of physiological contexts. The morphology of the cytoskeletal network, along which active, motor-driven…
An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is…
We propose a network of oscillators to retrieve given patterns in which the oscillators keep a fixed phase relationship with one another. In this description, the phase and the amplitude of the oscillators can be regarded as the timing and…
We study the storage and retrieval of phase-coded patterns as stable dynamical attractors in recurrent neural networks, for both an analog and a integrate-and-fire spiking model. The synaptic strength is determined by a learning rule based…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
We consider self-organization and memory formation in a mesoscopic model of an amorphous solid subject to a random shear strain protocol confined to a strain range $\pm \varepsilon_{\rm max}$. We develop proper read-out protocols to show…
Cells contain elaborate and interconnected networks of protein polymers which make up the cytoskeleton. The cytoskeleton governs the internal positioning and movement of vesicles and organelles, and controls dynamic changes in cell…
Within a continuous-time, stochastic model of single-cell size homeostasis, we study how the structure of feedback from size to growth rates and cell-cycle progression shapes overall size dynamics, both within and across cell cycles. We…
We present large-scale dynamical simulations of electronic phase separation in the single-band double-exchange model based on deep-learning neural-network potentials trained from small-size exact diagonalization solutions. We uncover an…
We design a system of phase oscillators that is able to produce temporally periodic sequences of patterns. Patterns are cluster partitions which encode information as phase differences between phase oscillators. The architecture of our…