Related papers: Dependence of functions on their variables
We wish to test whether a real-valued variable $Z$ has explanatory power, in addition to a multivariate variable $X$, for a binary variable $Y$. Thus, we are interested in testing the hypothesis $\mathbb{P}(Y=1\, | \, X,Z)=\mathbb{P}(Y=1\,…
The paper presents an elaboration of some results on Lin's conditions. A new proof of the fact that if densities of independent random variables $\xi_1$ and $\xi_2$ satisfy Lin's condition, the same is true for their product is presented.…
When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…
We provide sufficient conditions on the components of a vector field, which ensure the existence of Dulac functions depending on special functions for such vector field. We also present some applications and examples in order to illustrate…
We consider the question as to whether the exponent of a computably presentable Lebesgue space whose dimension is at least 2 must be computable. We show this very natural conjecture is true when the exponent is at least 2 or when the space…
Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…
We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. The Kac-Kubilius model suggests that the distribution of values of a given additive function can…
In this note we prove a large deviation bound on the sum of random variables with the following dependency structure: there is a dependency graph $G$ with a bounded chromatic number, in which each vertex represents a random variable.…
Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic…
The object of this paper is to study relationship between successive coefficients of some subclasses of the class of univalent functions in the unit disk. the result obtained is sharp, and is used to provide a new, short proof of the…
We compute the motivic nearby cycles of functions obtained by composition of two functions with distinct sets of variables with a two variable function
We give necessary and sufficient conditions for a function in a naturally appearing functional space to be a fixed point of the Ruelle-Thurston operator associated to a rational function, see Lemma 2.1. The proof uses essentially a recent…
We answer two questions from {\it V.Bykov, On Baire class one functions on a product space, Topol. Appl. {199} (2016) 55--62,} and prove that every Baire one function on a subspace of a countable perfectly normal product is the pointwise…
In this paper, we show that a partitioned formula \phi is dependent if and only if \phi has uniform definability of types over finite partial order indiscernibles. This generalizes our result from a previous paper [1]. We show this by…
In the current versions of the Dempster-Shafer theory, the only essential restriction on the validity of the rule of combination is that the sources of evidence must be statistically independent. Under this assumption, it is permissible to…
We show that for any semilinear partial differential equation of order m, the infinitesimals of the independent variables depend only on the independent variables and, if m>1 and the equation is also linear in its derivatives of order m-1…
Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…
This paper presents two general criteria to determine spaceability results in the complements of unions of subspaces. The first criterion applies to countable unions of subspaces under specific conditions and is closely related to the…
We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional…
We give a combinatorial proof of the result of Kahn, Kalai, and Linial, which states that every balanced boolean function on the $n$-dimensional boolean cube has a variable with influence of at least Omega(\frac{log n}{n}). The methods of…