Related papers: Scale-invariance underlying the logistic equation …

Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…

Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…

Nowadays there is an increasing interest of physicists in finding regularities related to social phenomena. This interest is clearly motivated by applications that a statistical mechanical description of the human behavior may have in our…

The logistics of urban areas are becoming more sophisticated due to the fast city population growth. The stakeholders are faced with the challenges of the dynamic complexity of city logistics(CL) systems characterized by the uncertainty…

A system is invariant with respect to an input transformation if we can transform any dynamic input by this function and obtain the same output dynamics after adjusting the initial conditions appropriately. Often, the set of all such input…

A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence…

Local scale invariance (LSI) has been recently proposed as a possible extension of the dynamical scaling in systems at the critical point and during phase ordering. LSI has been applied inter alia to provide predictions for the scaling…

Scale invariance is a hallmark of criticality in complex dynamical systems. While random external inputs or tunable stochastic interactions are typically required to produce critical behavior, it remains unclear whether scale-invariant…

Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced.…

There is a contradiction at the heart of our current understanding of individual and collective mobility patterns. On one hand, a highly influential stream of literature on human mobility driven by analyses of massive empirical datasets…

Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy…

We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the…

Human behaviors are often driven by human interests. Despite intense recent efforts in exploring the dynamics of human behaviors, little is known about human-interest dynamics, partly due to the extreme difficulty in accessing the human…

The logistic map is a nonlinear difference equation well studied in the literature, used to model self-limiting growth in certain populations. It is known that, under certain regularity conditions, the stochastic logistic map, where the…

Mean field equilibrium (MFE) has emerged as a computationally tractable solution concept for large dynamic games. However, computing MFE remains challenging due to nonlinearities and the absence of contraction properties, limiting its…

Modeling human dynamics responsible for the formation and evolution of the so-called social networks - structures comprised of individuals or organizations and indicating connectivities existing in a community - is a topic recently…

Computer simulations of first-order relaxation processes show that the spatial configurations of the system acquire an invariant shape once the stationary regime is attained. Inspired by them we find that, in any first-order relaxation…

Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…

Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and…

We study a class of heterogeneous agent-based models which are based on a basic set of principles, and the most fundamental operations of an economic system: trade and product transformations. A basic guiding principle is scale invariance,…