相关论文: Counting interval sizes in the poset of monotone B…
This paper consists of two independent, but related parts. In the first part we show how to use symbolic computation to derive explicit expressions for the first few moments of the number of implicants that a random Boolean function has, or…
We study the values of the M\"obius function $\mu$ of intervals in the containment poset of permutations. We construct a sequence of permutations $\pi_n$ of size $2n-2$ for which $\mu(1,\pi_n)$ is given by a polynomial in $n$ of degree 7.…
We present a two term formula for the M\"obius function of intervals in the poset of all permutations, ordered by pattern containment. The first term in this formula is the number of so called normal occurrences of one permutation in…
We describe a new algorithm for answering a given set of range queries under $\epsilon$-differential privacy which often achieves substantially lower error than competing methods. Our algorithm satisfies differential privacy by adding noise…
We consider a probability distribution on the set of Boolean functions in n variables which is induced by random Boolean expressions. Such an expression is a random rooted plane tree where the internal vertices are labelled with connectives…
A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we…
The aim of this note is to provoke discussion concerning arithmetic properties of function $p_{d}(n)$ counting partitions of an positive integer $n$ into $d$-th powers, where $d\geq 2$. Besides results concerning the asymptotic behavior of…
In a recent paper by Jonasson and Steif, definitions to describe the volatility of sequences of Boolean functions, \( f_n \colon \{ -1,1 \}^n \to \{ -1,1 \} \) were introduced. We continue their study of how these definitions relate to…
Recent research has shown that interval estimators with good coverage properties are achievable for some functions of quantiles, even when sample sizes are not large. Motivated by this, we consider interval estimators for the ratios of…
Decision Diagrams(DDs) are one of the most popular representations for boolean functions. They are widely used in the design and verification of circuits. Different types of DDs have been proven to represent important functions in…
Deep learning has achieved impressive performance on many tasks in recent years. However, it has been found that it is still not enough for deep neural networks to provide only point estimates. For high-risk tasks, we need to assess the…
We present a simple variant of the Gaussian mechanism for answering differentially private queries when the sensitivity space has a certain common structure. Our motivating problem is the fundamental task of answering $d$ counting queries…
This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for the space of Boolean n-tuples is introduced. Stochastic boolean vectors and…
In the applications of Boolean networks to modeling biological systems, an important computational problem is the detection of the fixed points of these networks. This is an NP-complete problem in general. There have been various attempts…
We study an interval ordering problem introduced by D\"urr et al. [Discrete Appl. Math. 2012] which is motivated by applications in bioinformatics. The task is to order a given set of n intervals with the goal of minimizing a certain…
Confidence intervals for the population mean of normally distributed data are some of the most standard statistical outputs one might want from a database. In this work we give practical differentially private algorithms for this task. We…
Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an…
In biomedical studies, researchers are often interested in assessing the association between one or more ordinal explanatory variables and an outcome variable, at the same time adjusting for covariates of any type. The outcome variable may…
In this paper, building on previous work, we extend the thermodynamic formalism for random open dynamical systems generated by piecewise monotone interval maps with countably many branches. Under summable and contracting assumptions on the…
The scheme of divided differences is widely used in many approximation and interpolation problems. Computing the Newton coefficients of the interpolating polynomial is the first step of the Bj\"{o}rck and Pereyra algorithm for solving…