In this article we introduce mathematical morphology on hypergraphs. We first define lattice structures and then mathematical morphology operators on hypergraphs. We show some relations between these operators and the hypergraph structure, considering in particular duality and similarity aspects.

" Motivation Limited Domain relations (LD-relations) " What happens for out of domain arguments? Difficulty parsing complex mathematical specifications " What does that do, again? " Objective Clear, formal representation of requirements specifications in a tabular format " Mathematic foundation " Possible for both human and machine parsing " Better partitioned specifications " Techniques Used M...

Automata are simple mathematical objects with unexpected computational, mathematical, modelling and explanatory capabilities. This paper examines some relations between automata and physics. Automata will be used to model quantum uncertainty and quantum computation. Finally, mathematical proofs will be discussed from the perspective of quantum automata. 1 Modelling Quantum Uncertainty with Auto...

Semantic relations among objects are primary semantic factors, which play the most important role for human and smart systems /machines to understand and control the situation in the context of connected systems. However, few existing works focus on the study of semantic relations from the mathematical view, though it would be the basis for further research on semantics. Existing research works...

Mathematical ability is related to both activation of the prefrontal cortex in neuroimaging studies of adults and to executive functions in school-age children. The purpose of this study was to determine whether executive functions were related to emergent mathematical proficiency in preschool children. Preschool children (N = 96) were administered an executive function battery that was reduced...

At first glance Mizar attributes look like unary predicates over mathematical objects enabling a more natural writing and reading. Attributes in Mizar, however, serve additional, more important purposes concerning typing of mathematical objects: Using attributes not only new (sub)types can be introduced, but also the user can characterize further relations between types and in this way make ava...

The concept of alliance or preferably ‘alignment’, as I shall explain below – is central to the conduct of international politics, and thus the discipline of International Relations (IR). Duffield et al. (2008: 291) identify that ‘Alliances are one of the most significant phenomena in security studies and world politics more generally’, while Modelski (1963: 773) considers them ‘one of a dozen ...

In this article I locate some of the fundamental problems of self-determination within the context of an evolving international society. First, I argue that one particular manifestation of self-determination, that of national self-determination, is both a solution to the enduring problem of territorial legitimation in international relations as well as the source of subsequent challenges to ter...

In many domains of information processing, both vagueness, or imprecision, and bipolarity, encompassing positive and negative parts of information, are core features of the information to be modeled and processed. This led to the development of the concept of bipolar fuzzy sets, and of associated models and tools. Here we propose to extend these tools by defining algebraic relations between bip...

Historically, issues of gender, race and the environment have received little attention in mainstream International Relations (IR) scholarship. Great strides have been made, however, in interrogating the inadequacies of the field in these areas and, similarly, in demonstrating the necessity of expanded definitions of security and violence in IR. Despite these strides, mainstream environmental s...