Summary We propose a definition for the average indirect effect of binary treatment in potential outcomes model causal inference under cross-unit interference. Our is analogous to standard direct and can be expressed without needing compare across multiple randomized experiments. show that proposed satisfies decomposition theorem stating Bernoulli trial, sum effects always corresponds policy in...

Abstract. The study of the identities of symmetry for the Bernoulli polynomials arises from the study of Gauss’s multiplication formula for the gamma function. There are many works in this direction. In the sense of p-adic analysis, the q-Bernoulli polynomials are natural extensions of the Bernoulli and Apostol-Bernoulli polynomials (see the introduction of this paper). By using the N-fold iter...

The concepts of Bernoulli numbers B n , Bernoulli polynomials B n (x), and the generalized Bernoulli numbers B n (a, b) are generalized to the one B n (x; a, b, c) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between B n , B n (x), B n (a, b), and B n (x; a, b, c) are established.

Let I1, . . . , In be independent but not necessarily identically distributed Bernoulli random variables, and let Xn = ∑n j=1 Ij . For ν in a bounded region, a local central limit theorem expansion of PI (Xn = EI Xn + ν) is developed to any given degree. By conditioning, this expansion provides information on the high order correlation structure of dependent, weighted sampling schemes of a popu...

in this study, the bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear two-dimensional integral equations. to this aim, the operational matrices of integration and the product for bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. some examples are presented to illustrate the efficien...

We derive two asymptotic formulas relating the Kolmogorov complexity of strings over a nite alphabet to the entropy of a discrete Markov information source that generates the strings. In 2], Beyer, Stein, and Ulam discussed several notions of complexity of integers and made a conjecture relating Kolmogorov complexity and information theoretic entropy. We will state this conjecture, after summar...

A central object of study in the field of algorithmic randomness are notions of randomness for sequences, i.e., infinite sequences of zeros and ones. These notions are usually defined with respect to the uniform measure on the set of all sequences, but extend canonically to other computable probability measures. This way each notion of randomness induces an equivalence relation on the computabl...

In this paper, a robust image transmission scheme based on JPEG2000 is proposed for packet erasure channels. Error resilience functionalities provided by JPEG2000 are utilized to control the source coding efficiency and the robustness according to channel conditions. Furthermore, together with the proposed interleaving scheme, some erasures can be recovered. Experimental results show the effect...

Motivated by a question of Krzysztof Oleszkiewicz we study a notion of weak tail domination of random vectors. We show that if the dominating random variable is sufficiently regular weak tail domination implies strong tail domination. In particular positive answer to Oleszkiewicz question would follow from the so-called Bernoulli conjecture. Introduction. This note is motivated by the following...