Related papers: Attractor landscapes in Boolean networks with firi…
We introduce a numerical method to study random Boolean networks with asynchronous stochas- tic update. Each node in the network of states starts with equal occupation probability and this probability distribution then evolves to a steady…
Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical…
Swarming behavior continues to be a subject of immense interest because of its centrality in many naturally occurring systems in physics and biology, as well as its importance in applications such as robotics. Here we examine the effects on…
Transformers are one of the most successful architectures of modern neural networks. At their core there is the so-called attention mechanism, which recently interested the physics community as it can be written as the derivative of an…
A Boolean network is a function $f:\{0,1\}^n\to\{0,1\}^n$ from which several dynamics can be derived, depending on the context. The most classical ones are the synchronous and asynchronous dynamics. Both are digraphs on $\{0,1\}^n$, but the…
The attractors of Boolean networks and their basins have been shown to be highly relevant for model validation and predictive modelling, e.g., in systems biology. Yet there are currently very few tools available that are able to compute and…
For networks of pulse-coupled oscillators with delayed excitatory coupling, we analyze the firing behaviors depending on coupling strength and transmission delay. The parameter space consisting of strength and delay is partitioned into two…
Slow adaption processes, like synaptic and intrinsic plasticity, abound in the brain and shape the landscape for the neural dynamics occurring on substantially faster timescales. At any given time the network is characterized by a set of…
Estimating the influence that individual nodes have on one another in a Boolean network is essential to predict and control the system's dynamical behavior, for example, detecting key therapeutic targets to control pathways in models of…
We consider the effects of temporal delay in a neural feedback system with excitation and inhibition. The topology of our model system reflects the anatomy of the avian isthmic circuitry, a feedback structure found in all classes of…
Early olfactory pathway responses to the presentation of an odor exhibit remarkably similar dynamical behavior across phyla from insects to mammals, and frequently involve transitions among quiescence, collective network oscillations, and…
We investigate dynamical systems characterized by a time series of distinct semi-stable activity patterns, as they are observed in cortical neural activity patterns. We propose and discuss a general mechanism allowing for an adiabatic…
In this paper, we propose an approach for modeling and analysis of a number of phenomena of collective behavior. By collectives we mean multi-agent systems that transition from one state to another at discrete moments of time. The behavior…
We study metanetworks arising in genotype and phenotype spaces, in the context of a model population of Boolean graphs evolved under selection for short dynamical attractors. We define the adjacency matrix of a graph as its genotype, which…
Bump attractors are wandering localised patterns observed in in vivo experiments of spatially-extended neurobiological networks. They are important for the brain's navigational system and specific memory tasks. A bump attractor is…
Boolean networks (BNs) are widely used to model the qualitative dynamics of biological systems. Besides the logical rules determining the evolution of each component with respect to the state of its regulators, the scheduling of component…
Boolean networks are powerful frameworks for capturing the logic of gene-regulatory circuits, yet their combinatorial explosion hampers exhaustive analyses. Here, we present a systematic reduction of a 31-node Boolean model that describes…
Attractor neural networks consider that neural information is stored as stationary states of a dynamical system formed by a large number of interconnected neurons. The attractor property empowers a neural system to encode information…
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…
We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics,…