When a binary liquid is confined by a strongly repulsive wall, the local density is depleted near the wall and an interface similar to that between the liquid and its vapor is formed. This analogy suggests that the composition of the binary liquid near this interface should exhibit spatial modulation similar to that near a liquid-vapor interface even if the interactions of the wall with the two...

Abstract relation types (ART) are developed to represent, describe and establish a computational framework for a system. An abstract relation type is closely related to and builds upon two fundamental ideas. The first idea is the binary relation and structural modeling techniques developed by John N. Warfield. The second idea is the concept of abstract data types. These two ideas are combined t...

We show that the Confusion Entropy, a measure of performance in multiclass problems has a strong (monotone) relation with the multiclass generalization of a classical metric, the Matthews Correlation Coefficient. Analytical results are provided for the limit cases of general no-information (n-face dice rolling) of the binary classification. Computational evidence supports the claim in the gener...

We weaken the implicit assumption of rational choice theory that imposes that preferences do not depend on the choice set. We concentrate on the cases where the preferences change monotonically when the choice set expands. We show that rationalizability is then equivalent to state the usual strong axiom of revealed preferences to the binary relation of "revealed reversals of preferences".

The foundation of an algebraic theory of binary relations was laid by C. S. Peirce, building on earlier work of Boole and De Morgan. The basic universe of discourse of this theory is a collection of binary relations over some set, and the basic operations on these relations are those of forming unions, complements, relative products (i.e., compositions), and converses (i.e., inverses). There is...

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...