Related papers: A Measure of data-collapse for scaling
Data depths are score functions that quantify in an unsupervised fashion how central is a point inside a distribution, with numerous applications such as anomaly detection, multivariate or functional data analysis, arising across various…
Data clustering is the process of identifying natural groupings or clusters within multidimensional data based on some similarity measure. Clustering is a fundamental process in many different disciplines. Hence, researchers from different…
Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise…
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…
The standard approach to quantum measurements is to assume that they lead to effectively instantaneous collapse of the quantum state. However, if we assume that we are unable to enforce at what exact moment of time the measurement occurs…
Two-phase sampling designs are frequently employed in epidemiological studies and large-scale health surveys. In such designs, certain variables are exclusively collected within a second-phase random subsample of the initial first-phase…
We propose a finite-size scaling analysis of binary stochastic processes $X(t)\in \{0,1\}$ based on the second moment correlation length $\xi$ for the autocorrelation function $C(t)$. The purpose is to clarify the critical properties and…
Early fault detection using instrumented sensor data is one of the promising application areas of machine learning in industrial facilities. However, it is difficult to improve the generalization performance of the trained fault-detection…
Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can…
This paper introduces {\em fusion subspace clustering}, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. The main idea is to assign each datum to a subspace of its own, and minimize…
Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and Dynamical reduction models propose a…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Inelastic collapse is found in a two-dimensional system of inelastic hard disks confined between two walls which act as an energy source. As the coefficient of restitution is lowered, there is a transition between a state containing small…
The paper presents a construction of a quantitative measure of variability for parameter estimates in the data fitting problem under interval uncertainty. It shows the degree of variability and ambiguity of the estimate, and the need for…
We explore a collapsing cosmology driven by a scalar field which is minimally coupled to gravity in a spatially at and spherically symmetric, isotropic and homogeneous space-time, with a variable timescale that avoids the final singularity.…
The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation…
This paper proposes an experiment designed to distinguish between competing interpretations of quantum mechanics: those that involve wave function collapse and those that assume purely unitary evolution. The experiment tests whether an…
Certain frustrated systems, including spin ice and dimer models, exhibit a Coulomb phase at low temperatures, with power-law correlations and fractionalized monopole excitations. Transitions out of this phase, at which the effective gauge…
Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. For most applications, applying clustering is only appropriate when cluster structure is present. As such, the study of clusterability,…
This work is devoted to the study of the scaling, and the consequent power-law behavior, of the correlation function in a mutation-replication model known as the expansion-modification system. The latter is a biology inspired random…