Memories may be encoded in the brain via strongly interconnected groups of neurons, called assemblies. The concept of Hebbian plasticity suggests that these assemblies are generated through synaptic plasticity, strengthening the recurrent connections within select groups of neurons that receive correlated stimulation. To remain stable in absence of such stimulation, the assemblies need to be self-reinforcing under the plasticity rule. Previous models of such assembly maintenance require additional mechanisms of fast homeostatic plasticity often with biologically implausible timescales. Here we provide a model of neuronal assembly generation and maintenance purely based on spike-timing-dependent plasticity (STDP) between excitatory neurons. It uses irregularly and stochastically spiking neurons and STDP that depresses connections of uncorrelated neurons. We find that assemblies do not grow beyond a certain size, because temporally imprecise spike correlations dominate the plasticity in large assemblies. Assemblies in the model can be learned or spontaneously emerge. The model allows for prominent, stable overlap structures between static assemblies. Further, assemblies can drift, particularly according to a novel, transient overlap-based mechanism. Finally the model indicates that assemblies grow in the aging brain, where connectivity decreases.

Networks in the brain consist of different types of neurons. Here we investigate the influence of neuron diversity on the dynamics, phase space structure and computational capabilities of spiking neural networks. We find that already a single neuron of a different type can qualitatively change the network dynamics and that mixed networks may combine the computational capabilities of ones with a single neuron type. We study inhibitory networks of concave leaky (LIF) and convex "antileaky" (XIF) integrate-and-fire neurons that generalize irregularly spiking non-chaotic LIF neuron networks. Endowed with simple conductance-based synapses for XIF neurons, our networks can generate a balanced state of irregular asynchronous spiking as well. We determine the voltage probability distributions and self-consistent firing rates assuming Poisson input with finite size spike impacts. Further, we compute the full spectrum of Lyapunov exponents (LEs) and the covariant Lyapunov vectors (CLVs) specifying the corresponding perturbation directions. We find that there is approximately one positive LE for each XIF neuron. This indicates in particular that a single XIF neuron renders the network dynamics chaotic. A simple mean-field approach, which can be justified by properties of the CLVs, explains the finding. As an application, we propose a spike-based computing scheme where our networks serve as computational reservoirs and their different stability properties yield different computational capabilities.

Memories may be encoded in the brain via strongly interconnected groups of neurons, called assemblies. The concept of Hebbian plasticity suggests that these assemblies are generated through synaptic plasticity, strengthening the recurrent connections within select groups of neurons that receive correlated stimulation. To remain stable in absence of such stimulation, the assemblies need to be self-reinforcing under the plasticity rule. Previous models of such assembly maintenance require additional mechanisms of fast homeostatic plasticity often with biologically implausible timescales. Here we provide a model of neuronal assembly generation and maintenance purely based on spike-timing-dependent plasticity (STDP) between excitatory neurons. It uses irregularly and stochastically spiking neurons and STDP that depresses connections of uncorrelated neurons. We find that assemblies do not grow beyond a certain size, because temporally imprecisely correlated spikes dominate the plasticity in large assemblies. Assemblies in the model can be learned or spontaneously emerge. The model allows for prominent, stable overlap structures between static assemblies. Further, assemblies can drift, particularly according to a novel, transient overlap-based mechanism. Finally the model indicates that assemblies grow in the aging brain, where connectivity decreases.

We study gravity coupled to a cosmological constant and a scale but not conformally invariant sector. In Minkowski vacuum, scale invariance is spontaneously broken. We consider small fluctuations around the Minkowski vacuum. At the linearised level we find that the trace of metric perturbations receives a positive or negative mass squared contribution. However, only for the Fierz-Pauli combination the theory is free of ghosts. The mass term for the trace of metric perturbations can be cancelled by explicitly breaking scale invariance. This reintroduces fine-tuning. Models based on four form field strength show similarities with explicit scale symmetry breaking due to quantisation conditions.