相关论文: Mutual Information as a Tool for Identifying Phase…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
Mutual information is an important measure of the dependence among variables. It has become widely used in statistics, machine learning, biology, etc. However, the standard techniques for estimating it often perform poorly in higher…
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure. We define such a phase…
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…
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…
The mutual information characterizes correlations between spatially separated regions of a system. Yet, in experiments we often measure dynamical correlations, which involve probing operators that are also separated in time. Here, we…
Information-theoretic quantities have received significant attention as system-independent measures of correlations in many-body quantum systems, e.g., as universal order parameters of synchronization. In this work, we present a method to…
A tipping point can be defined as an abrupt shift in the properties or behaviour of a system. Tipping points in complex systems from a wide variety of scientific disciplines have been compared to phase transitions in physics, but consistent…
We consider the problem of estimating mutual information between dependent data, an important problem in many science and engineering applications. We propose a data-driven, non-parametric estimator of mutual information in this paper. The…
Mutual Information is the metric that is used to perform link adaptation, which allows to achieve rates near capacity. The computation of adaptive transmission modes is achieved by employing the mapping between the Signal to Noise Ratio and…
To understand the phase transition phenomena, information theoretical approaches can pick up some important properties of the phenomena based on the probability distribution. In this paper, we show information theoretical aspects of the…
We simulate the Vicsek model utilising topological neighbour interactions and estimate information theoretic quantities as a function of noise, the variability in the extent to which each animal aligns with its neighbours, and the flock…
The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is…
Individual components such as cells, particles, or agents within a larger system often require detailed understanding of their relative position to act accordingly, enabling the system as a whole to function in an organised and efficient…
Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider…
Information transfer is an essential factor in determining the robustness of collective behaviour in biological systems with distributed control. The most direct way to study the information transfer mechanisms is to experimentally detect…
Cells sense environmental signals and transmit information intracellularly through changes in the abundance of molecular components. Such molecular abundances can be measured in single cells and exhibit significant heterogeneity in clonal…
We demonstrate the identification and classification of topological phase transitions from experimental data using Diffusion Maps: a nonlocal unsupervised machine learning method. We analyze experimental data from an optical system…
In the analysis of time series from nonlinear sources, mutual information (MI) is used as a nonlinear statistical criterion for the selection of an appropriate time delay in time delay reconstruction of the state space. MI is a statistic…
The existing consensus is that flocks are poised at criticality, entailing long correlation lengths and a maximal value of Shannon mutual information in the large-system limit. We show, by contrast, that for finite flocks in the long…