In this paper we address the problem of skewed class distribution in implicit discourse relation recognition. We examine the performance of classifiers for both binary classification predicting if a particular relation holds or not and for multi-class prediction. We review prior work to point out that the problem has been addressed differently for the binary and multi-class problems. We demonst...

Abstract. Following Poupard’s study of strictly ordered binary trees with respect to two parameters, namely, “end of minimal chain” and “parent of maximum leaf” a true Tree Calculus is being developed to solve a partial difference equation system and then make a joint study of those two statistics. Their joint distribution is shown to be symmetric and to be expressed in the form of an explicit ...

A method is presented for evaluating the bidimension of a finite binary relation, i.e., the number of biorders (Guttman relations) needed to yield the relation as their intersection. In case the relation is induced by a binary data matrix, the bidimension equals the minimal number of dimensions needed for a representation of the data matrix according to the conjunctive model of C. H. Coombs and...

The number of binary strings of length n containing no substrings consisting of r consecutive ones is examined and shown to be given in terms of a well known integer sequence namely, the r-Fibonacci sequence. In addition, difference equations for the number of zeros and the total number of runs within these binary strings are derived. Mathematics Subject Classification: Primary 11B39, Secondary...

The sequence A000975 in OEIS can be defined by A1 = 1, An+1 = 2An if n is odd, and An+1 = 2An + 1 if n is even. This sequence satisfies other recurrence relations, admits some closed formulas, and is known to enumerate several interesting families of objects. We provide a new interpretation of this sequence using a binary operation defined by a⊖ b := −a− b. We show that the number of distinct r...

This article is an introduction to the use of relational calculi in deriving programs. We present a derivation in a relational language of a functional program that adds one bit to a binary number. The resulting program is unsurprising, being the standard ‘column of half–adders’, but the derivation illustrates a number of points about working with relations rather than functions.

In this paper we introduce the concept of Krasner hyperring $(R,+,cdot)$together with a suitable partial order relation $le $.xle y$.  Also we consider some Krasner hyperrings and define a binary relation on them such that to become ordered Krasner hyperrings. By using the notion of pseudoorder on an ordered Krasner hyperring $(R,+,cdot,le)$, we obtain an ordered ring. Moreover, we study s...

The number b, of binary trees with n nodes is well known. Two ways to determine b, are presented in [3]. One, based on constructing them, leads to recurrence relations solved by generating functions. The other recognizes that b, is the same as the number of stack permutations and counts these permutations. In [l], a method based on well-formed sequences of parentheses is given, and the result i...

In this paper, we study the decomposition of semirings with a semilattice additive reduct. For, we introduce the notion of principal left $k$-radicals $Lambda(a)={x in S | a stackrel{l}{longrightarrow^{infty}} x}$ induced by the transitive closure $stackrel{l}{longrightarrow^{infty}}$ of the relation $stackrel{l}{longrightarrow}$ which induce the equivalence relation $lambda$. Again non-transit...