Related papers: Conserved Ising Model on the Human Connectome
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
Humans and other organisms make decisions choosing between different options, with the aim to maximize the reward and minimize the cost. The main theoretical framework for modeling the decision-making process has been based on the highly…
The dynamical mechanism underlying the processes of anesthesia-induced loss of consciousness and recovery is key to gaining insights into the working of the nervous system. Previous experiments revealed an asymmetry between neural signals…
In order to investigate the effects of connectivity and proximity in the specific heat, a special class of exactly solvable planar layered Ising models has been studied in the thermodynamic limit. The Ising models consist of repeated…
Interdependence is a fundamental ingredient to analyze the stability of many real-world complex systems featuring functional liasons. Yet, physical realizations of this coupling are still unknown, due to the lack of a theoretical framework…
We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like anti-ferromagnetic interaction. We compute free energy, spin correlation functions and entanglement both in the ground and in…
Recently, there have been several concerted international efforts - the BRAIN initiative, European Human Brain Project and the Human Connectome Project, to name a few - that hope to revolutionize our understanding of the connected brain.…
The Ising model, in presence of an external magnetic field, is isomorphic to a model of localized interacting particles satisfying the Fermi statistics. By using this isomorphism, we construct a general solution of the Ising model which…
This paper addresses the question of the brain's critical dynamics after an injury such as a stroke. It is hypothesized that the healthy brain operates near a phase transition (critical point), which provides optimal conditions for…
In the brain, fine-scale correlations combine to produce macroscopic patterns of activity. However, as experiments record from larger and larger populations, we approach a fundamental bottleneck: the number of correlations one would like to…
Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that…
Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in…
The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or…
We investigate a kinetic Ising model with several single-spin flip dynamics (including Metropolis and heat-bath) on quenched and annealed random regular graphs. As expected, on the quenched structures all proposed algorithms reproduce the…
The study by Glauber of the time-dependent statistics of the Ising chain is extended to the case where each spin is influenced unequally by its nearest neighbours. The asymmetry of the dynamics implies the failure of the detailed balance…
The idea that information-processing systems operate near criticality to enhance computational performance is supported by scaling signatures in brain activity. However, external signals raise the question of whether this behavior is…
We study the critical behavior and the out-of-equilibrium dynamics of a two-dimensional Ising model with non-static interactions. In our model, bonds are dynamically changing according to a majority rule depending on the set of closest…
We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e.,…
Long-range synchrony from short-range interactions is a familiar pattern in biological and physical systems, many of which share a common set of ``universal'' properties at the point of synchronization. Common biological systems of coupled…
Experiments and computer simulation studies have revealed existence of rich dynamics in the orientational relaxation of molecules in confined systems such as water in reverse micelles, cyclodextrin cavities and nano-tubes. Here we introduce…