The goal of this study is to introduce a statistical method regarding the analysis of specific latent data for regression analysis of the discrete data and to build a relation between a probit regression model (related to the discrete response) and normal linear regression model (related to the latent data of continuous response). This method provides precise inferences on binary and multinomia...

Correlations discovered between millisecond timing properties and spectral properties in neutron star x-ray binaries are described and then interpreted in relation to accretion flows in the systems. Use of joint timing and spectral observations to test for the existence of the marginally stable orbit, a key prediction of strong field general relativity, is described and observations of the neut...

Considering a binary operation as a ternary relation permits certain sections of the latter (which are functions) to be used in representing an abstract semigroup as a family of the self-maps of its underlying set under function composition. The idea is thus seen to be entirely similar to the way that the sections of a partial ordering under set inclusion represent the (abstract) partially orde...

We study the problem of finding a maximal transitive relation contained in a given binary relation. Given a binary relation of size m defined on a set of size n, we present a polynomial time algorithm that finds a maximal transitive sub-relation in time O(n + nm). We also study the problem of finding a maximum transitive relation contained in a binary relation. For the class of triangle-free re...

Galois connection in crisp binary relations has proved to be useful for several applications in computer science. Unfortunately, data is not always presented as a crisp binary relation but may be composed of fuzzy values, thus forming a fuzzy binary relation. This paper aims at defining the notion of fuzzy galois connection corresponding to a fuzzy binary relation in two steps: firstly by defin...

We define as an ’articulation point’ in a lattice an element which is comparable to all the other elements, but is not extremum. We investigate a property which holds for both the lattice of a binary relation and for the lattice of the complement relation (which we call the mirror relation): one has an articulation point if and only if the other has one also. We give efficient algorithms to gen...

In this lecture, binary granular computing (granular computing on binary relations) is re-examined. Two definitions for approximations in Rough Set Theory (one is from equivalence relation and the other from point-based topology view) were no longer equal under binary relation, the latter will have the better performance, especially when the universe is infinite. However, the point-based defini...