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The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links, the average eccentricity and…
We develop the neural network based "learning from regression uncertainty" approach for automated detection of phases of matter in nonequilibrium active systems. Taking the flocking phase transition of self-propelled active particles…
According to the Kibble-Zurek mechanism (KZM), the density of topological defects created during a second-order phase transition is determined by the correlation length at the freeze-out time. This suggests that the final configuration of…
The transfer learning of a neural network is one of its most outstanding aspects and has given supervised learning with neural networks a prominent place in data science. Here we explore this feature in the context of strongly interacting…
A network of optical parametric oscillators is used to simulate classical Ising and XY spin chains. The collective nonlinear dynamics of this network, driven by quantum noise rather than thermal fluctuations, seeks out the Ising / XY ground…
The aim of this paper is to illustrate that generalized two-dimensional XY models (proposed by Romano and Zagrebnov) may also support a first-order phase transition. Two approaches are employed to accurately determine the critical parameter…
Nonlinear dynamical systems such as Lorenz63 equations are known to be chaotic in nature and sensitive to initial conditions. As a result, a small perturbation in the initial conditions results in deviation in state trajectory after a few…
High temperature series expansions of the spin-spin correlation function for the plane rotator (or XY) model on the square lattice are extended by three terms through order $\beta^{20}$. Tables of the expansion coefficients are reported for…
Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning…
In recent years, machine learning has been adopted to complex networks, but most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition…
A wavelet-based machine learning method is proposed for predicting the time evolution of homogeneous isotropic turbulence where vortex tubes are preserved. Three-dimensional convolutional neural networks and long short-term memory are…
The search for materials with topological properties is an ongoing effort. In this article we propose a systematic statistical method supported by machine learning techniques that is capable of constructing topological models for a generic…
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…
We investigate the mechanism by which topological defects form in first order phase transitions with a charged order parameter. We show how thick superconductor vortices and heavy cosmic strings form by trapping of magnetic flux. In an…
Machine learning methods are powerful in distinguishing different phases of matter in an automated way and provide a new perspective on the study of physical phenomena. We train a Restricted Boltzmann Machine (RBM) on data constructed with…
Despite continued efforts to improve classification accuracy, it has been reported that offline accuracy is a poor indicator of the usability of pattern recognition-based myoelectric control. One potential source of this disparity is the…
The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is…
A Kosterlitz-Thouless phase transition in the ground state of an antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain with nearest and next-nearest-neighbor interactions is re-investigated from a different perspective: An unequivocal…
Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…
Phase transitions mark qualitative reorganizations of collective behavior, yet identifying their boundaries remains challenging whenever analytic solutions are absent and conventional simulations fail. Here we introduce learnability as a…