相关论文: Instabilities in associative memory model with syn…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
Seizure activity is a ubiquitous and pernicious pathophysiology that, in principle, should yield to mathematical treatments of (neuronal) ensemble dynamics - and therefore interventions on stochastic chaos. A seizure can be characterised as…
We consider a large network of Izhikevich neurons. Each neuron has a quadratic integrate-and-fire type model with a recovery variable modelling spike frequency adaptation (SFA). We introduce a biologically motivated synaptic current…
We study the statistical properties of the stationary firing-rate states of a neural network model with quenched disorder. The model has arbitrary size, discrete-time evolution equations and binary firing rates, while the topology and the…
The dynamics of the domains is studied in a two-dimensional model of the microphase separation of diblock copolymers in the vicinity of the transition. A criterion for the validity of the mean field theory is derived. It is shown that at…
The synchronous dynamics and the stationary states of a recurrent attractor neural network model with competing synapses between symmetric sequence processing and Hebbian pattern reconstruction is studied in this work allowing for the…
Rich out of equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular or colloidal systems,…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…
We study associative memory based on temporal coding in which successful retrieval is realized as an entrainment in a network of simple phase oscillators with distributed natural frequencies under the influence of white noise. The memory…
We study the interplay of disorder with pumping and decay in coupled qubit-cavity arrays, the Jaynes-Cummings-Hubbard model. We find that relatively weak disorder can wash out the bistability present in the clean pumped system, and that…
Single trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory…
We study the two-dimensional paramagnetic Anderson-Hubbard model using an extension of dynamical mean-field theory that allows us to treat disorder and strong electronic correlations on equal footing. We investigate the scaling of the…
Reward processing and derangements thereof, such as drug addiction, involve the coordinated activity of many brain areas. Prior work has identified many behavioral, molecular biological and single neuron changes throughout the…
Learning shared structure across environments facilitates rapid learning and adaptive behavior in neural systems. This has been widely demonstrated and applied in machine learning to train models that are capable of generalizing to novel…
In the present work we investigate the existence of multiple nonequilibrium steady states in a coherently driven XY lattice of dissipative two-level systems. A commonly used mean-field ansatz, in which spatial correlations are neglected,…
Learning requires the traversal of inherently distinct cognitive states to produce behavioral adaptation. Yet, tools to explicitly measure these states with non-invasive imaging -- and to assess their dynamics during learning -- remain…
Our brain is a complex information processing network in which the nervous system receives information from the environment to quickly react to incoming events or learns from experience to sharp our memory. In the nervous system, the brain…
The impairment of cognitive function in Alzheimer's is clearly correlated to synapse loss. However, the mechanisms underlying this correlation are only poorly understood. Here, we investigate how the loss of excitatory synapses in sparsely…
We review a recent approach to the mean-field limits in neural networks that takes into account the stochastic nature of input current and the uncertainty in synaptic coupling. This approach was proved to be a rigorous limit of the network…