Related papers: Parisi Phase in a Neuron
Broken-symmetry-induced order parameters account for many phenomena in condensed matter physics. For spin glasses, such a framework dictates its theoretical construction, whereas experiments have only established dynamical behaviors such as…
We consider the dynamics of a diluted mean-field spin glass model in the aging regime. The model presents a particularly rich heterogeneous behavior. In order to catch this behavior, we perform a **spin-by-spin analysis** for a **given…
Active inference is a normative framework for explaining behaviour under the free energy principle -- a theory of self-organisation originating in neuroscience. It specifies neuronal dynamics for state-estimation in terms of a descent on…
This paper is divided into two parts. The first part concerns several standard scenarios for how short-range spin glasses might behave at low temperature. Earlier theorems of the authors are reviewed, and some new results presented,…
We study the collective dynamics of a Leaky Integrate and Fire network in which precise relative phase relationship of spikes among neurons are stored, as attractors of the dynamics, and selectively replayed at differentctime scales. Using…
Glassy behavior is one of the main open problems in condensed matter physics. In this thesis, we approach the problem by studying spin-glasses and colloids, using several complementary strategies. From the point of view of model building,…
The description of activated relaxation of glassy systems in the multidimensional configurational space is a long-standing open problem. We develop a phenomenological description of the out-of-equilibrium dynamics of a model with a rough…
Short-term plasticity (STP) is a mechanism that stores decaying memories in synapses of the cerebral cortex. In computing practice, STP has been used, but mostly in the niche of spiking neurons, even though theory predicts that it is the…
While the Gibbs states of spin glass models have been noted to have an erratic dependence on temperature, one may expect the mean over the disorder to produce a continuously varying ``quenched state''. The assumption of such continuity in…
The full structuration of light in the transverse plane, including intensity, phase and polarization, holds the promise of unprecedented capabilities for applications in classical optics as well as in quantum optics and information…
We consider a stochastic model describing the spiking activity of a countable set of neurons spatially organized into a homogeneous tree of degree $d$, $d \geq 2$; the degree of a neuron is just the number of connections it has. Roughly,…
Motivated by understanding the emergence of thermodynamic restoring forces and oscillations, we develop a quantum-mechanical model of a bath of spins coupled to the elasticity of a material. We show our model reproduces the behavior of a…
Bayesian inference provides a principled framework for understanding brain function, while neural activity in the brain is inherently spike-based. This paper bridges these two perspectives by designing spiking neural networks that simulate…
In this paper, we extend the full replica symmetry breaking scheme to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity method, providing a…
Memory information in the brain is commonly believed to be stored in the synapse. However, a recent groundbreaking electrophysiology research has raised the possibility that memory information may actually be stored inside the neuron…
I discuss results from numerical simulations of finite dimensional spin glass models, and show that they show all signatures of a mean field like behavior, basically coinciding with the one of the Parisi solution. I discuss the Binder…
We propose a microscopic model without energy barriers in order to explain some generic features observed in structural glasses. The statics can be exactly solved while the dynamics has been clarified using Monte Carlo calculations.…
The Sherrington-Kirkpatrick spin-glass model used the replica symmetry method to find the phase transition of the system. In 1979-1980, Parisi proposed a solution based on replica symmetry breaking (RSB), which allowed him to identify the…
Generic glass formers exhibit at least two characteristic changes in their relaxation behavior, first to an Arrhenius-type relaxation at some characteristic temperature, and then at a lower characteristic temperature to a super-Arrhenius…
We introduce the use of neural networks as classifiers on classical disordered systems with no spatial ordering. In this study, we implement a convolutional neural network trained to identify the spin-glass state in the three-dimensional…