Related papers: Statistical measures of complexity for strongly in…
Statistical mechanical models with local interactions in $d>1$ dimension can be regarded as $d=1$ dimensional models with regular long range interactions. In this paper we study the critical properties of Ising models having $V$ sites, each…
We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…
We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is…
Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…
How complex is an Ising model? Usually, this is measured by the computational complexity of its ground state energy problem. Yet, this complexity measure only distinguishes between planar and non-planar interaction graphs, and thus fails to…
Complex networks are at the core of an intense research activity. However, in most cases, intricate and costly measurement procedures are needed to explore their structure. In some cases, these measurements rely on link queries: given two…
In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…
This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients.…
We live in a world full of complex systems which we need to improve our understanding of. To accomplish this, purely probabilistic investigations are often not enough. They are only the first step and must be followed by learning the…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
Bayesian networks are one of the most widely used classes of probabilistic models for risk management and decision support because of their interpretability and flexibility in including heterogeneous pieces of information. In any applied…
During the last few years an area of active research in the field of complex systems is that of their information storing and processing abilities. Common opinion has it that the most interesting beaviour of these systems is found ``at the…
This paper is Part II of a two-part series devoting to the study of systematic measures in a complex bio-network modeled by a system of ordinary differential equations. In this part, we quantify several systematic measures of a biological…
Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires…
We have proposed novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We have considered background of the Kolmogorov complexity and also we have discussed meaning of the…
New sensitivity-based methods are developed for determining identifiability and observability of nonsmooth input-output systems. More specifically, lexicographic calculus is used to construct nonsmooth sensitivity rank condition (SERC)…
The Normalized Maximum Likelihood (NML) codelength, or stochastic complexity, represents a principled criterion for universal coding. While recent coarea-based formulations provided a calculation method for smooth models, this framework…
We consider the problem of learning the interaction strength between the nodes of a network based on dependent binary observations residing on these nodes, generated from a Markov Random Field (MRF). Since these observations can possibly be…
Visibility graphs are spatial interpretations of time series. When derived from the time evolution of physical systems, the graphs associated with such series may exhibit properties that can reflect aspects such as ergodicity, criticality,…
While various complexity measures for deep neural networks exist, specifying an appropriate measure capable of predicting and explaining generalization in deep networks has proven challenging. We propose Neural Complexity (NC), a…