This paper presents a method to solve an ordinal classification problem where the objects are described with a set of partially ordered features. To construct an ordinal classification model we aggregate partial orders of features by weighting the incidence matrices of partial order graphs. To describe set of possible solutions we use partial order cones corresponding to the incidence matrices ...

Over the past 15 years, Ramsey theoretic techniques and concepts have been applied with great success to partially ordered sets. In the last year alone, four new applications of Ramsey theory to posets have produced solutions to some challenging combinatorial problems. First, Kierstead and Trotter showed that dimension for interval orders can be characterized by a single ramsey trail by proving...

The search for minimal elements in partially ordered sets is a generalization of the task of finding Pareto-optimal elements in multi-criteria optimization problems. Since there are usually many minimal elements within a partially ordered set, a population-based evolutionary search is, as a matter of principle, capable of finding several minimal elements in a single run and gains therefore a st...

We investigate the generalisation of quantum search of unstructured and totally ordered sets to search of partially ordered sets (posets). Two models for poset search are considered. In both models, we show that quantum algorithms can achieve at most a quadratic improvement in query complexity over classical algorithms, up to logarithmic factors; we also give quantum algorithms that almost achi...

We consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting 0,∞ ,≤ that have constant failure rate. In spite of the minimal algebraic structure, there is a surprisingly rich theory, including moment results and results concerning ladder variables and point processes. We concentrate mostly on discrete posets, par...