Why are images smooth?

It is a well observed phenomenon that natural images are smooth, in the sense that nearby pixels tend to have similar values. We describe a mathematical model of images that makes no assumptions on the nature of the environment that images depict. It only assumes that images can be taken at different scales (zoom levels). We provide quantitative bounds on the smoothness of a typical image in our model, as a function of the number of available scales. These bounds can serve as a baseline against which to compare the observed smoothness of natural images

The ERA of FOLE: Superstructure

This paper discusses the representation of ontologies in the first-order logical environment FOLE (Kent 2013). An ontology defines the primitives with which to model the knowledge resources for a community of discourse (Gruber 2009). These primitives, consisting of classes, relationships and properties, are represented by the ERA (entity-relationship-attribute) data model (Chen 1976). An ontology uses formal axioms to constrain the interpretation of these primitives. In short, an ontology specifies a logical theory. This paper is the second in a series of three papers that provide a rigorous mathematical representation for the ERA data model in particular, and ontologies in general, within the first-order logical environment FOLE. The first two papers show how FOLE represents the formalism and semantics of (many-sorted) first-order logic in a classification form corresponding to ideas discussed in the Information Flow Framework (IFF). In particular, the first paper (Kent 2015) provided a "foundation" that connected elements of the ERA data model with components of the first-order logical environment FOLE, and this second paper provides a "superstructure" that extends FOLE to the formalisms of first-order logic. The third paper will define an "interpretation" of FOLE in terms of the transformational passage, first described in (Kent 2013), from the classification form of first-order logic to an equivalent interpretation form, thereby defining the formalism and semantics of first-order logical/relational database systems (Kent 2011). The FOLE representation follows a conceptual structures approach, that is completely compatible with Formal Concept Analysis (Ganter and Wille 1999) and Information Flow (Barwise and Seligman 1997)

Type-Directed Weaving of Aspects for Polymorphically Typed Functional Languages

Incorporating aspect-oriented paradigm to a polymorphically typed functional language enables the declaration of type-scoped advice, in which the effect of an aspect can be harnessed by introducing possibly polymorphic type constraints to the aspect. The amalgamation of aspect orientation and functional programming enables quick behavioral adaption of functions, clear separation of concerns and expressive type-directed programming. However, proper static weaving of aspects in polymorphic languages with a type-erasure semantics remains a challenge. In this paper, we describe a type-directed static weaving strategy, as well as its implementation, that supports static type inference and static weaving of programs written in an aspect-oriented polymorphically typed functional language, AspectFun. We show examples of type-scoped advice, identify the challenges faced with compile-time weaving in the presence of type-scoped advice, and demonstrate how various advanced aspect features can be handled by our techniques. Lastly, we prove the correctness of the static weaving strategy with respect to the operational semantics of AspectFun

Enterprise model verification and validation : an approach

This article presents a verification and validation approach which is used here in order to complete the classical tool box the industrial user may utilize in enterprise modeling and integration domain. This approach, which has been defined independently from any application domain is based on several formal concepts and tools presented in this paper. These concepts are property concepts, property reference matrix, properties graphs, enterprise modeling domain ontology, conceptual graphs and formal reasoning mechanisms

A formal verification framework and associated tools for enterprise modeling : application to UEML

The aim of this paper is to propose and apply a verification and validation approach to Enterprise Modeling that enables the user to improve the relevance and correctness, the suitability and coherence of a model by using properties specification and formal proof of properties