Community-Aware Graph Signal Processing

The emerging field of graph signal processing (GSP) allows to transpose classical signal processing operations (e.g., filtering) to signals on graphs. The GSP framework is generally built upon the graph Laplacian, which plays a crucial role to study graph properties and measure graph signal smoothness. Here instead, we propose the graph modularity matrix as the centerpiece of GSP, in order to incorporate knowledge about graph community structure when processing signals on the graph, but without the need for community detection. We study this approach in several generic settings such as filtering, optimal sampling and reconstruction, surrogate data generation, and denoising. Feasibility is illustrated by a small-scale example and a transportation network dataset, as well as one application in human neuroimaging where community-aware GSP reveals relationships between behavior and brain features that are not shown by Laplacian-based GSP. This work demonstrates how concepts from network science can lead to new meaningful operations on graph signals.Comment: 21 pages, 4 figures, Accepted to Signal Processing Magazine: Special Issue on Graph Signal Processing: Foundations and Emerging Direction

Unveiling Relations in the Industry 4.0 Standards Landscape based on Knowledge Graph Embeddings

Industry~4.0 (I4.0) standards and standardization frameworks have been proposed with the goal of \emph{empowering interoperability} in smart factories. These standards enable the description and interaction of the main components, systems, and processes inside of a smart factory. Due to the growing number of frameworks and standards, there is an increasing need for approaches that automatically analyze the landscape of I4.0 standards. Standardization frameworks classify standards according to their functions into layers and dimensions. However, similar standards can be classified differently across the frameworks, producing, thus, interoperability conflicts among them. Semantic-based approaches that rely on ontologies and knowledge graphs, have been proposed to represent standards, known relations among them, as well as their classification according to existing frameworks. Albeit informative, the structured modeling of the I4.0 landscape only provides the foundations for detecting interoperability issues. Thus, graph-based analytical methods able to exploit knowledge encoded by these approaches, are required to uncover alignments among standards. We study the relatedness among standards and frameworks based on community analysis to discover knowledge that helps to cope with interoperability conflicts between standards. We use knowledge graph embeddings to automatically create these communities exploiting the meaning of the existing relationships. In particular, we focus on the identification of similar standards, i.e., communities of standards, and analyze their properties to detect unknown relations. We empirically evaluate our approach on a knowledge graph of I4.0 standards using the Trans$^*$ family of embedding models for knowledge graph entities. Our results are promising and suggest that relations among standards can be detected accurately.Comment: 15 pages, 7 figures, DEXA2020 Conferenc

Synthesis of Attributed Feature Models From Product Descriptions: Foundations

Feature modeling is a widely used formalism to characterize a set of products (also called configurations). As a manual elaboration is a long and arduous task, numerous techniques have been proposed to reverse engineer feature models from various kinds of artefacts. But none of them synthesize feature attributes (or constraints over attributes) despite the practical relevance of attributes for documenting the different values across a range of products. In this report, we develop an algorithm for synthesizing attributed feature models given a set of product descriptions. We present sound, complete, and parametrizable techniques for computing all possible hierarchies, feature groups, placements of feature attributes, domain values, and constraints. We perform a complexity analysis w.r.t. number of features, attributes, configurations, and domain size. We also evaluate the scalability of our synthesis procedure using randomized configuration matrices. This report is a first step that aims to describe the foundations for synthesizing attributed feature models

Towards MKM in the Large: Modular Representation and Scalable Software Architecture

MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM "in the small" is well-studied, so the real problem is to scale up to large, highly interconnected corpora: "MKM in the large". We contend that advances in two areas are needed to reach this goal. We need representation languages that support incremental processing of all primitive MKM operations, and we need software architectures and implementations that implement these operations scalably on large knowledge bases. We present instances of both in this paper: the MMT framework for modular theory-graphs that integrates meta-logical foundations, which forms the base of the next OMDoc version; and TNTBase, a versioned storage system for XML-based document formats. TNTBase becomes an MMT database by instantiating it with special MKM operations for MMT.Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 201

Mathematical Foundations of Consciousness

We employ the Zermelo-Fraenkel Axioms that characterize sets as mathematical primitives. The Anti-foundation Axiom plays a significant role in our development, since among other of its features, its replacement for the Axiom of Foundation in the Zermelo-Fraenkel Axioms motivates Platonic interpretations. These interpretations also depend on such allied notions for sets as pictures, graphs, decorations, labelings and various mappings that we use. A syntax and semantics of operators acting on sets is developed. Such features enable construction of a theory of non-well-founded sets that we use to frame mathematical foundations of consciousness. To do this we introduce a supplementary axiomatic system that characterizes experience and consciousness as primitives. The new axioms proceed through characterization of so- called consciousness operators. The Russell operator plays a central role and is shown to be one example of a consciousness operator. Neural networks supply striking examples of non-well-founded graphs the decorations of which generate associated sets, each with a Platonic aspect. Employing our foundations, we show how the supervening of consciousness on its neural correlates in the brain enables the framing of a theory of consciousness by applying appropriate consciousness operators to the generated sets in question