Related papers: Network Psychometrics
In the Ising model, we consider the problem of estimating the covariance of the spins at two specified vertices. In the ferromagnetic case, it is easy to obtain an additive approximation to this covariance by repeatedly sampling from the…
The Ising model describes collective behaviors such as phase transitions and critical phenomena in various physical, biological, economical, and social systems. It is well-known that spontaneous phase transition at finite temperature does…
Multivariate phase relationships are important to characterize and understand numerous physical, biological, and chemical systems, from electromagnetic waves to neural oscillations. These systems exhibit complex spatiotemporal dynamics and…
Learning with an artificial neural network encodes the system behavior in a feed-forward function with a number of parameters optimized by data-driven training. An open question is whether one can minimize the network complexity without…
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…
We study phase transitions in the Ising model on random graphs using graph limits. We show that the critical temperatures are determined by the eigenvalues of the kernel operator associated with the graph limit. Bifurcation diagrams for…
We investigate the connection between the supervised learning of the binary phase classification in the ferromagnetic Ising model and the standard finite-size-scaling theory of the second-order phase transition. Proposing a minimal…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The…
In this paper we calculate the nonlinear susceptibility and the resonant Raman cross section for the paramagnetic phase of the ferromagnetic Quantum Ising model in one dimension. In this region the spectrum of the Ising model has a gap $m$.…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
There have been two separate lines of work on estimating Ising models: (1) estimating them from multiple independent samples under minimal assumptions about the model's interaction matrix; and (2) estimating them from one sample in…
Network psychometrics conceptualises psychological constructs as emergent properties of systems of interacting variables. Energy-based probabilistic models have gained popularity as models of these interactions, but their psychometric…
We investigate phase transitions in the Ising model and the ANNNI model in transverse field using the interface approach. The exact result of the Ising chain in a transverse field is reproduced. We find that apart from the interfacial…
The two-dimensional Ising model of a ferromagnet allows for many ways of computing its partition function and other properties. Each way reveals surprising features of what we might call Ising Matter. Moreover, the various ways would appear…
We extend previous mean-field approaches for non-equilibrium neural network models to estimate correlations in the system. This offers a powerful tool for approximating the system dynamics as well as a fast method to infer network…
A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity…
The antiferromagnetic Ising model in small-world networks generated from two-dimensional regular lattices has been studied. The disorder introduced by long-range connections causes frustration, which gives rise to a spin-glass phase at low…
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…
We consider the fundamental problem of learning the parameters of an undirected graphical model or Markov Random Field (MRF) in the setting where the edge weights are chosen at random. For Ising models, we show that a multiplicative-weight…