Related papers: The Problematic Hoover Index
National statistical agencies are regularly required to produce estimates about various subpopulations, formed by demographic and/or geographic classifications, based on a limited number of samples. Traditional direct estimates computed…
Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…
Successful innovations achieve large geographical coverage by spreading across settlements and distances. For decades, spatial diffusion has been argued to take place along the urban hierarchy such that the innovation first spreads from…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
The geographical pattern of human dialects is a result of history. Here, we formulate a simple spatial model of language change which shows that the final result of this historical evolution may, to some extent, be predictable. The model…
Stellar population synthesis can be approached as an inverse problem. The physical information is extracted from the observations through an inverse model. The process requires the transformation of the observational errors into model…
Knowing where people live is a fundamental component of many decision making processes such as urban development, infectious disease containment, evacuation planning, risk management, conservation planning, and more. While bottom-up, survey…
Hyper-Wiener index was introduced as one of the main generalizations of the well known Wiener index. Through the years properties of the Wiener index have been extensively studied in both Mathematics and Chemistry. The Hyper-Wiener index,…
We discuss the possibility of deriving an H-theorem for the nonlinear discrete time evolution known as Ulam's redistribution of energy problem. In this model particles are paired at random and then their total energy is redistributed…
We analyze the nonlinear dynamics near the incoherent state in a mean-field model of coupled oscillators. The population is described by a Fokker-Planck equation for the distribution of phases, and we apply center-manifold reduction to…
A problem of bounding the generalization error of a classifier f in H, where H is a "base" class of functions (classifiers), is considered. This problem frequently occurs in computer learning, where efficient algorithms of combining simple…
In this work we consider the problem of extracting a set of interaction parameters from an high-dimensional dataset describing T independent configurations of a complex system composed of N binary units. This problem is formulated in the…
Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are…
A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g. reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such…
Cities can be characterised and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al have proposed that many of these urban measures…
The problem of estimation of the proportion of units with a given attribute in a~finite population is considered. From the population a sample is drawn due to the simple random sampling without replacement. There are limited funds for…
In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…
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…
In the global description of eternal inflation, probabilities for vacua are notoriously ambiguous. The local point of view is preferred by holography and naturally picks out a simple probability measure. It is insensitive to large expansion…