We give new q-(1+q)-analogue of the Gaussian coefficient, also know as the q-binomial which, like the original q-binomial [ n k ] q , is symmetric in k and n− k. We show this q-(1 + q)-binomial is more compact than the one discovered by Fu, Reiner, Stanton and Thiem. Underlying our q-(1 + q)-analogue is a Boolean algebra decomposition of an associated poset. These ideas are extended to the Birk...

Let f(x1, . . . , xk) be a polynomial over a field K. This paper considers such questions as the enumeration of the number of nonzero coefficients of f or of the number of coefficients equal to α ∈ K∗. For instance, if K = Fq then a matrix formula is obtained for the number of coefficients of fn that are equal to α ∈ Fq , as a function of n. Many additional results are obtained related to such ...

Abstract: Bivariate (or pairwise) information measures such as mutual information or correlation are heavily used in variable selection and network inference algorithms mainly because they are faster and require fewer samples than multivariate (or multidimensional) strategies. This paper proposes a new relevance measure that aims at improving the detection of relevant variables based on pairwis...

Accommodation coefficient of HOBr on deliquescent sodium bromide aerosol particles M. Wachsmuth1,2, H. W. Gäggeler1,2, R. von Glasow3,*, and M. Ammann1 1Paul Scherrer Institut, Laboratory for Radioand Environmental Chemistry, Villigen, Switzerland 2Also at Department of Chemistry and Biochemistry, University of Bern, Bern, Switzerland 3Max-Planck-Institut für Chemie, Abt. Chemie der Atmosphäre,...

Similarity measures are essential to solve many pattern recognition problems such as classification, clustering, and retrieval problems. Various similarity measures are categorized in both syntactic and semantic relationships. In this paper we present a novel similarity, Unilateral Jaccard Similarity Coefficient (uJaccard), which doesn’t only take into consideration the space among two points b...

This paper studies a general class of nonlinear varying coefficient time series models with possible nonstationarity in both the regressors and the varying coefficient components. The model accommodates a cointegrating structure and allows for endogeneity with contemporaneous correlation among the regressors, the varying coefficient drivers, and the residuals. This framework allows for a mixtur...

We are interested in learning causal relationships between pairs of random variables, purely from observational data. To effectively address this task, the state-of-the-art relies on strong assumptions on the mechanisms mapping causes to effects, such as invertibility or the existence of additive noise, which only hold in limited situations. On the contrary, this short paper proposes to learn h...

Elements in a sample date are demonstrated based on their characteristics and in turn the characteristics are represented by variables. Identifying the relationship between these variables is crucial for prediction, hypothesis testing, and decision making. The relation between two variables is often quantified using a correlation factor. Once correlation is known it can be used to make predicti...