Related papers: Information-Theoretic Measures on Lattices for Hig…
Motivated by lattice mixture identification and grain boundary detection, we present a framework for lattice pattern representation and comparison, and propose an efficient algorithm for lattice separation. We define new scale and shape…
Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns.…
Several data-driven approaches based on information theory have been proposed for analyzing high-order interactions involving three or more components of a network system. Most of these methods are defined only in the time domain and rely…
In statistical physics entropy is usually introduced as a global quantity which expresses the amount of information that would be needed to specify the microscopic configuration of a system. However, for lattice models with infinitely many…
Complex systems are characterized by multiple spatial and temporal scales. A natural framework to capture their multiscale nature is that of multilayer networks, where different layers represent distinct physical processes that often…
We analyze multivariate ordered discrete response models with a lattice structure, modeling decision makers who narrowly bracket choices across multiple dimensions. These models map latent continuous processes into discrete responses using…
We address the practical problems of estimating the information relations that characterize large networks. Building on methods developed for analysis of the neural code, we show that reliable estimates of mutual information can be obtained…
We propose a method for the determination of the interaction potential of Rydberg atoms. Specifically, we consider a laser-driven Rydberg gas confined in a one-dimensional lattice and demonstrate that the Rydberg atom number after a laser…
Identifying the origin of nonequilibrium characteristics in a generic interacting system having multiple degrees of freedom is a challenging task. In this context, information theoretic measures such as mutual information and related…
Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the…
In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…
We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…
Information theoretic measures (e.g. the Kullback Liebler divergence and Shannon mutual information) have been used for exploring possibly nonlinear multivariate dependencies in high dimension. If these dependencies are assumed to follow a…
The recent explosion of interest in multimodal applications has resulted in a wide selection of datasets and methods for representing and integrating information from different modalities. Despite these empirical advances, there remain…
One of the crucial steps in scientific studies is to specify dependent relationships among factors in a system of interest. Given little knowledge of a system, can we characterize the underlying dependent relationships through observation…
Correlation of interacting particles is studied in their dynamics and localization in ideal and disordered lattice systems with the help of numerical tools. Both 1D and 2D systems are considered. In 1D lattices with long-range hopping,…
Recent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time. These data are better described by…
We demonstrate a bipartition technique using a super-lattice architecture to access correlations between alternating planes of a mesoscopic array of spin-3 chromium atoms trapped in a 3D optical lattice. Using this method, we observe that…
Statistical mechanics explains the properties of macroscopic phenomena based on the movements of microscopic particles such as atoms and molecules. Movements of microscopic particles can be represented by large-scale interacting systems. In…
Lattice model with long-range interaction of power-law type that is connected with difference of non-integer order is suggested. The continuous limit maps the equations of motion of lattice particles into continuum equations with fractional…