Related papers: Strong dependence, weight, and measure

Let $\mathcal{N}$ be the $\sigma$-ideal of the null sets of reals. We introduce a new property of forcing notions that enable control of the additivity of $\mathcal{N}$ after finite support iterations. This is applied to answer some open…

I propose a flexible structural model to estimate peer effects across various quantiles of the peer outcome distribution. The model allows peers with low, intermediate, and high outcomes to exert distinct influences, thereby capturing more…

We introduce the notion of effective Axiom A and use it to show that some popular tree forcings are Suslin+. We introduce transitive nep and present a simplified version of Shelah's "preserving a little implies preserving much": If I is a…

We generalize the Unstable Formula Theorem characterization of stable theories from \citep{sh78}: that a theory $T$ is stable just in case any infinite indiscernible sequence in a model of $T$ is an indiscernible set. We use a generalized…

We investigate the cofinality of the strong measure zero ideal for $\kappa$ inaccessible, and show that it is independent of the size of $2^\kappa$.

Let (X,T) be a dynamical system, where X is a compact metric space and T a continuous onto map. For weak Gibbs measures we prove large deviations estimates.

We argue that robustness of explanations---i.e., that similar inputs should give rise to similar explanations---is a key desideratum for interpretability. We introduce metrics to quantify robustness and demonstrate that current methods do…

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…

We conduct an axiomatic study of the problem of estimating the strength of a known causal relationship between a pair of variables. We propose that an estimate of causal strength should be based on the conditional distribution of the effect…

Assessing the stability of a multiple testing procedure under dependence is important but very challenging. Even for multiple testing which among a set of Normal random variables have mean zero, which we refer to as the "Normal means…

We study some dynamical aspects of the action of automorphisms in model theory in particular in the presence of invariant measures. We give some characterizations for NIP theories in terms of dynamics of automorphisms and invariant measures…

In this paper, we prove a $p$-Hardy inequality on the discrete half-line with weights $n^{\alpha}$ for all real $p > 1$. Building on the work of Miclo for $p = 2$ and Muckenhoupt in the continuous settings, we develop a quantitative…

This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the…

It is known that strongly nilpotent matrices over a division ring are linearly triangularizable. We describe the structure of such matrices in terms of the strong nilpotency index. We apply our results on quasi-translation x + H such that…

We introduce a robust belief-based measure of complexity. The idea is that task A is deemed more complex than task B if the probability of solving A correctly is smaller than the probability of solving B correctly regardless of the reward.…

Strong monads are important for several applications, in particular, in the denotational semantics of effectful languages, where strength is needed to sequence computations that have free variables. Strength is non-trivial: it can be…

In exploratory data analysis, we are often interested in identifying promising pairwise associations for further analysis while filtering out weaker, less interesting ones. This can be accomplished by computing a measure of dependence on…

We define the notion $\phi(x,y)$ has $NIP$ in $A$, where $A$ is a subset of a model, and give some equivalences by translating results from [1]. Using additional material from [11] we discuss the number of coheirs when $A$ is not…

We suggest a dependence coefficient between a categorical variable and some general variable taking values in a metric space. We derive important theoretical properties and study the large sample behaviour of our suggested estimator.…

In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…