F. Barrows

F. Sheldon

F. Caravelli

We derive dynamical equations for networks with memristors and the Lyapunov functions of purely memristive circuits to study their stability.

Network analysis of memristive device circuits: dynamics, stability and correlations

Circuits  with memory

A. Kolchinsky

Balancing memory from linear components with nonlinearities from memristors optimises the computational capacity of electronic reservoirs.

Computational capacity of  LRC, memristive and hybrid reservoirs

Optimal electronic  reservoirs

F. L. Traversa

Circuits of memristors, resistors with memory, can exhibit instabilities which allow classical tunnelling through potential energy barriers.

Global minimization via classical tunneling assisted by collective force field formation

Breaking  classical barriers

A. Zegarac

A simple solvable model of memristive networks suggests a correspondence between the asymptotic states of memristors and the Ising model.

Memristive networks: from graph theory to statistical physics

Memristive networks

P. Barucca

Exact solutions for the dynamics of interacting memristors predict whether they relax to higher or lower resistance states given random initialisations.

Exactly solvable model of memristive circuits: Lyapunov functional and mean field theory

Solvable memristive circuits

Memristive networks preserve memory and have the ability to learn according to analysis of the network’s internal memory dynamics. 

The mise en scene of memristive networks: effective memory, dynamics and learning

Memristive networks and learning

F. Traversa

M. Ventra

Exact equations of motion provide an analytical description of the evolution and relaxation properties of complex memristive circuits.

The complex dynamics of memristive circuits: analytical results and universal slow relaxation

Dynamics of memristors

L. Sindoni

F. Caccioli

C. Ududec

An extension of the Kelly criterion maximises the growth rate of multiplicative stochastic processes when limited resources are available. 

Optimal growth trajectories with finite carrying capacity

Optimal growth rates

P. Staniczenko

The community matrix of a complex ecosystem captures the population dynamics of interacting species and transitions to unstable abundances.

Bounds on transient instability for complex ecosystems

Instability in complex ecosystems

M. Bardoscia

Percolation theory shows that the formation of giant clusters of neurons relies on a few parameters that could be measured experimentally.

Emergence of strongly connected components in continuum disk-spin percolation

Clusters of neurons

L. Banchi

In an infinitely bouncing Universe, the scalar field driving the cosmological expansion and contraction carries information between phases.

Geometric phases and cyclic isotropic cosmologies

Cyclic isotropic cosmologies

A. Hamma

A local model of preferential attachment with short-term memory generates scale-free networks, which can be readily computed by memristors.

Francesco Caravelli