相关论文: Neutral stability, rate propagation, and critical …
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers…
In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probability of 2\%, 20\% of neurons are inhibitory and 80\% are excitatory. These common values are based on…
To gain a deeper understanding of the behavior and learning dynamics of (deep) artificial neural networks, it is valuable to employ mathematical abstractions and models. These tools provide a simplified perspective on network performance…
We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some…
An Ashkin-Teller neural network, allowing for two types of neurons is considered in the case of low loading as a function of the strength of the respective couplings between these neurons. The storage and retrieval of embedded patterns…
The neural mechanism of memory has a very close relation with the problem of representation in artificial intelligence. In this paper a computational model was proposed to simulate the network of neurons in brain and how they process…
In this work we study the detection of weak stimuli by spiking neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present…
Complex networks have certain properties that distinguish them from their respective uniform or regular counterparts. One of these properties is the variation of topological properties along different hierarchical levels. In this work, we…
The way in which different types of dynamics unfold in complex networks is intrinsically related to the propagation of activation along nodes, which is strongly affected by the network connectivity. In this work we investigate to which…
Molecular networks guide the biochemistry of a living cell on multiple levels: its metabolic and signalling pathways are shaped by the network of interacting proteins, whose production, in turn, is controlled by the genetic regulatory…
Diffusion dynamics in multiplex networks can model a diverse number of real-world processes. In some specific configurations of these systems, the super-diffusion phenomenon arises, in which the diffusion is faster in the multiplex network…
Social movements, neurons in the brain or even industrial suppliers are best described by agents evolving on networks with basic interaction rules. In these real systems, the connectivity between agents corresponds to the a critical state…
Neural circuits exhibit structured connectivity, including an overrepresentation of reciprocal connections between neuron pairs. Despite important advances, a full understanding of how such partial symmetry in connectivity shapes neural…
Mathematical models of stem cell differentiation are commonly based upon the concept of subsequent cell fate decisions, each controlled by a gene regulatory network. These networks exhibit a multistable behavior and cause the system to…
Chemical and electrical synapses shape the dynamics of neuronal networks. Numerous theoretical studies have investigated how each of these types of synapses contributes to the generation of neuronal oscillations, but their combined effect…
The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but with more…
The synergy between spiking neural networks and neuromorphic hardware holds promise for the development of energy-efficient AI applications. Inspired by this potential, we revisit the foundational aspects to study the capabilities of…
Deep learning (DL) has big-data processing capabilities that are as good, or even better, than those of humans in many real-world domains, but at the cost of high energy requirements that may be unsustainable in some applications and of…
A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we…