Related papers: The arrow of time, complexity and the scale free a…
We show that in a broad class of processes that show a $1/f^{\alpha}$ spectrum, the power also explicitly depends on the characteristic time scale. Despite an enormous amount of work, this generic behavior remains so far overlooked and…
The concept of time series irreversibility -- the degree by which the statistics of signals are not invariant under time reversal -- naturally appears in non-equilibrium physics in stationary systems which operate away from equilibrium and…
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and…
A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…
Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a…
The explanations of large language models have recently been shown to be sensitive to the randomness used for their training, creating a need to characterize this sensitivity. In this paper, we propose a characterization that questions the…
A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being…
We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative weights in a given time series. Two different tools have been advanced in the literature to such effect, namely, i) the…
Temporal irreversibility, often referred to as the arrow of time, is a fundamental concept in statistical mechanics. Markers of irreversibility also provide a powerful characterisation of information processing in biological systems.…
The existence of higher derivative discontinuous solutions to a first order ordinary differential equation is shown to reveal a nonlinear SL(2,R) structure of analysis in the sense that a real variable $t$ can now accomplish changes not…
The dynamics of coupled 2D chaotic maps with time-delay on a scalefree-tree is studied, with different types of the collective behaviors already been reported for various values of coupling strength [1]. In this work we focus on the…
The renormalization group equations for large-scale structure (RG-LSS) describe how the bias and stochastic (noise) parameters -- both of matter and biased tracers such as galaxies -- evolve as a function of the cutoff $\Lambda$ of the…
This paper re-examines the use of response time to infer problem complexity. It revisits a canonical Wald model of optimal stopping, taking signal-to-noise ratio as a measure of problem complexity. While choice quality is monotone in…
Recurrence analysis is a well settled method allowing to discern chaos from order, and determinism from noise. We apply this tool to study time series representing geodesic and inspiraling motion of a test particle in a deformed Kerr…
Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as…
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data.…
We present a new, scalable alternative to the structured singular value, which we call $\nu$, provide a convex upper bound, study their properties and compare them to $\ell_1$ robust control. The analysis relies on a novel result on the…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order's omnipresence has long been recognized by the scientific…