Related papers: Scale-invariance underlying the logistic equation …
Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression,…
Understanding quantitative relationships between urban elements is crucial for a wide range of applications. The observation at the macroscopic level demonstrates that the aggregated urban quantities (e.g., gross domestic product) scale…
Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…
Ordered response scales are ubiquitous in economics, but their interpretation rests on an untested assumption: that numerical labels reflect equal psychological intervals. The contribution of this paper is to provide a systematic assessment…
Scale free dynamics are observed in a variety of physical and biological systems. These include neural activity in which evidence for scale freeness has been reported using a range of imaging modalities. Here, we derive the ways in which…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
The prevalence of many urban phenomena changes systematically with population size. We propose a theory that unifies models of economic complexity and cultural evolution to derive urban scaling. The theory accounts for the difference in…
Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including…
Scale invariance and the resulting power law behaviours are seen in diverse systems. In this work we consider translation, rotational and scale invariant systems defined on a lattice, such that the variables defining the state at every…
Critical, or scale independent, systems are so ubiquitous, that gaining theoretical insights on their nature and properties has many direct repercussions in social and natural sciences. In this report, we start from the simplest possible…
We report on the computer study of a lattice system that relaxes from a metastable state. Under appropriate nonequilibrium randomness, relaxation occurs by avalanches, i.e., the model evolution is discontinuous and displays many scales in a…
The dynamics of technological, economic and social phenomena is controlled by how humans organize their daily tasks in response to both endogenous and exogenous stimulations. Queueing theory is believed to provide a generic answer to…
The Multiscale Law of Requisite Variety is a scientific law relating, at each scale, the variation in an environment to the variation in internal state that is necessary for effective response by a system. While this law has been used to…
Measurement is a fundamental building block of numerous scientific models and their creation. This is in particular true for data driven science. Due to the high complexity and size of modern data sets, the necessity for the development of…
The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…
Force networks form the skeleton of static granular matter. They are the key ingredient to mechanical properties, such as stability, elasticity and sound transmission, which are of utmost importance for civil engineering and industrial…
There is strong expectation that cities, across time, culture and level of development, share much in common in terms of their form and function. Recently, attempts to formalize mathematically these expectations have led to the hypothesis…
Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which…
A general nonlinear logistic equation has been proposed to model long-time saturation in industrial growth. An integral solution of this equation has been derived for any arbitrary degree of nonlinearity. A time scale for the onset of…