Related papers: Pair correlation functions for identifying spatial…
This paper introduces a predictive control barrier function (PCBF) framework for enforcing state constraints in discrete-time systems with unknown relative degree, which can be caused by input delays or unmodeled input dynamics. Existing…
Canonical correlation analysis (CCA) is a classical and important multivariate technique for exploring the relationship between two sets of continuous variables. CCA has applications in many fields, such as genomics and neuroimaging. It can…
The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
Causal discovery is the subfield of causal inference concerned with estimating the structure of cause-and-effect relationships in a system of interrelated variables, as opposed to quantifying the strength or describing the form of causal…
The three-point correlation function (3PCF) of the spin-2 fields, the cosmic shear and cosmic microwave background polarization fields, is a statistical measure of non-Gaussian signals. At each vertex of a triangle, the shear field has two…
Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in…
Aims. Our goal is to find the relation between the two-point correlation functions (CFs) of projected and spatial density fields of galaxies in the context of the cosmic web. Methods. To investigate relations between spatial (3D) and…
We investigate whether neighbor-density-weighted marked correlation functions (MCFs) can extract cosmological information beyond the standard redshift-space two-point correlation function (2PCF). Using the Kun suite of 129 $w_0w_a$CDM$+\sum…
We analyze the quasar two-point correlation function (2pCF) within the redshift interval $0.8<z<2.2$ using a sample of 52303 quasars selected from the recent 7th Data Release of the Sloan Digital Sky Survey. Our approach to 2pCF uses a…
The classical Canonical Correlation Analysis (CCA) identifies the correlations between two sets of multivariate variables based on their covariance, which has been widely applied in diverse fields such as computer vision, natural language…
As modern systems become ever more connected with complex dynamic coupling relationships, developing safe control methods becomes paramount. In this paper, we discuss the relationship of node-level safety definitions for individual agents…
Recently, the theory concerning piecewise smooth vector fields (PSVFs for short) have been undergoing important improvements. In fact, many results obtained do not have an analogous for smooth vector fields. For example, the chaoticity of…
We propose a methodology to explore and measure the pairwise correlations that exist between variables in a dataset. The methodology leverages copulas for encoding dependence between two variables, state-of-the-art optimal transport for…
Researchers develop models to explain the unknowns. These models typically involve parameters that capture tangible quantities, the estimation of which is desired. Parameter identifiability investigates the recoverability of the unknown…
Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…
The timing analysis of transient events allows for investigating numerous still open areas of modern astrophysics. The article explores all the mathematical and physical tools required to estimate delays and associated errors between two…
Probability generating functionals (PGFLs) are efficient and powerful tools for tracking independent objects in clutter. It was shown that PGFLs could be used for the elegant derivation of practical multi-object tracking algorithms, e.g.,…
Accurate modelling of redshift-space distortions (RSD) is challenging in the non-linear regime for two-point statistics e.g. the two-point correlation function (2PCF). We take a different perspective to split the galaxy density field…
This paper presents MPC-CDF, a new approach integrating control density functions (CDFs) within a model predictive control (MPC) framework to ensure safety-critical control in nonlinear dynamical systems. By using the dual formulation of…