Related papers: Strict independence
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any…
We introduce notions of stationarily ordered types and theories; the latter generalizes weak o-minimality and the first is a relaxed version of weak o-minimality localized at the locus of a single type. We show that forking, as a binary…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
We study stable like behaviour in first order theories without the independence property. We introduce generically stable measures, give characterizatiions, and show their ubiquity. We also introduce generic compact domination. We also…
This paper builds model-theoretic tools to detect changes in complexity among the simple theories. We develop a generalization of dividing, called shearing, which depends on a so-called context c. This leads to defining c-superstability, a…
Cyclic monotone independence is an algebraic notion of noncommutative independence, introduced in the study of multi-matrix random matrix models with small rank. Its algebraic form turns out to be surprisingly close to monotone…
Entanglement witnesses provide a standard tool for the analysis of entanglement in experiments. We investigate possible nonlinear entanglement witnesses from several perspectives. First, we demonstrate that they can be used to show that the…
We investigate the notion of independence, which is at the basis of many, seemingly unrelated, properties of logic like Rational Monotony in non-monotonic logics, and interpolation theorems.
We study the coherence and conservativity of extensions of dependent type theories by additional strict equalities. By considering notions of congruences and quotients of models of type theory, we reconstruct Hofmann's proof of the…
The notion of a complete type can be generalized in a natural manner to allow assigning a value in an arbitrary Boolean algebra B to each formula. We show some basic results regarding the effect of the properties of B on the behavior of…
There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…
Mekler's construction gives an interpretation of any structure in a finite relational language in a group (nilpotent of class $2$ and exponent $p>2$, but not finitely generated in general). Even though this construction is not a…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…
We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…
In light of a gap found by Krupi\'{n}ski, we give a new proof of associativity for the Morley (or "nonforking") product of invariant measures in NIP theories.
We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
This paper mainly studies nonnegativity decision of forms based on variable substitutions. Unlike existing research, the paper regards simplex subdivisions as new perspectives to study variable substitutions, gives some subdivisions of the…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…