相关论文: Statistical measures of complexity for strongly in…

The data-driven characterization of the ``complexity'' present in dynamical systems remains an open problem with broad applications across the physical sciences. We investigate the ``structural complexity'' of the 2D ferromagnetic Ising…

Monitoring is an important aspect of safely deploying Large Language Models (LLMs). This paper examines activation probes for detecting ``high-stakes'' interactions -- where the text indicates that the interaction might lead to significant…

An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally…

Multiple metrics have been developed to detect causality relations between data describing the elements constituting complex systems, all of them considering their evolution through time. Here we propose a metric able to detect causality…

There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…

The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…

We propose a metric to characterize the complex behavior of a dynamical system and to distinguish between organized and disorganized complexity. The approach combines two quantities that separately assess the degree of unpredictability of…

Complex systems have become a popular lens for analyzing cities and complexity theory has many implications for urban performance and resilience. This paper develops a typology of measures and indicators for assessing the physical…

We advance our approach of analyzing the dynamics of interacting complex systems with the nonlinear dynamics of interacting nonlinear elements. We replace the widely used lattice-like connection topology of cellular neural networks (CNN) by…

We discuss some aspects of the extension to continuous systems of a statistical measure of complexity introduced by Lopez-Ruiz, Mancini and Calbet (LMC) [Phys. Lett. A 209 (1995) 321]. In general, the extension of a magnitude from the…

We extend the definitions of complexity measures of functions to domains such as the symmetric group. The complexity measures we consider include degree, approximate degree, decision tree complexity, sensitivity, block sensitivity, and a…

Understanding the dynamical behavior of complex systems is of exceptional relevance in everyday life, from biology to economy. In order to describe the dynamical organization of complex systems, existing methods require the knowledge of the…

After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…

Reduce and control complexity is an essential practice in software design. Cyclomatic complexity (CC) is one of the most popular software metrics, applied for more than 40 years. Despite CC is an interesting metric to highlight the number…

Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply…

In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…

We consider a system of stochastic interacting particles in $\mathbb{R}^d$ and we describe large deviations asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviations principle (LDP) is established for the…

We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…

This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…

Systems whose entities interact with each other are common. In many interacting systems, it is difficult to observe the relations between entities which is the key information for analyzing the system. In recent years, there has been…