Towards Collaborative Conceptual Exploration

In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a consortium, based on closure systems of attribute sets and the well-known attribute exploration algorithm from formal concept analysis. To this end, we introduce (weak) local experts for subdomains of a given knowledge domain. These entities are able to refute and potentially accept a given (implicational) query for some closure system that is a restriction of the whole domain. On this we build up a consortial expert and show first insights about the ability of such an expert to answer queries. Furthermore, we depict techniques on how to cope with falsely accepted implications and on combining counterexamples. Using notions from combinatorial design theory we further expand those insights as far as providing first results on the decidability problem if a given consortium is able to explore some target domain. Applications in conceptual knowledge acquisition as well as in collaborative interactive ontology learning are at hand.Comment: 15 pages, 2 figure

On the Usability of Probably Approximately Correct Implication Bases

We revisit the notion of probably approximately correct implication bases from the literature and present a first formulation in the language of formal concept analysis, with the goal to investigate whether such bases represent a suitable substitute for exact implication bases in practical use-cases. To this end, we quantitatively examine the behavior of probably approximately correct implication bases on artificial and real-world data sets and compare their precision and recall with respect to their corresponding exact implication bases. Using a small example, we also provide qualitative insight that implications from probably approximately correct bases can still represent meaningful knowledge from a given data set.Comment: 17 pages, 8 figures; typos added, corrected x-label on graph

Transcriptional activation by the Myb proteins requires a specific local promoter structure

AbstractThe biological effects of the cellular c-Myb and the viral v-Myb proteins are strikingly different. While c-Myb is indispensable for normal hematopoiesis, v-Myb induces acute leukemia. The v-Myb DNA-binding domain (DBD) differs from that of c-Myb mainly by deletion of the first of three repeats which correlates with efficient oncogenic transformation and a decrease in DNA-binding activity. To investigate the difference in DNA-binding and transcriptional activation, oligonucleotide selection and electrophoretic mobility shift assays were employed. The v-Myb DBD (R2R3) shows an intrinsic DNA-binding specificity for an AT-rich downstream extension of the Myb recognition element (MRE) PyAACT/GG for efficient binding to this site, whereas R1 within the c-Myb DBD allows for more flexibility for this downstream extension. Therefore, due to the presence of repeat R1, c-Myb can bind to a greater number of target sites. The intrinsic DNA-binding specificity of R2R3 is further supported with the results from in vivo transcriptional activation experiments which demonstrated that both the v-Myb and c-Myb DBDs require an extension of the MRE (motif #1) by a downstream T-stretch (motif #2) for full activity. Surprisingly, the T-stretch improves binding when present on either strand, but is required on a specific strand for transcriptional activation

Myb proteins inhibit fibroblast transformation by v-Rel

Genes that cause cancer have been divided into two general classes – oncogenes that act in a dominant fashion to transform normal cells into a malignant state, and tumor suppressor genes that act in a dominant fashion to prevent such transformation. In this report, we demonstrate that both the v-myb retroviral oncogene, which causes leukemic transformation of hematopoietic cells, and the c-myb proto-oncogene can also function as inhibitors of fibroblast transformation by the v-rel oncogene. These results imply that the myb genes can function either as oncogenes or as tumor suppressors in different cellular contexts

Formal concept analysis and structures underlying quantum logics

A Hilbert space $H$ induces a formal context, the Hilbert formal context $\overline H$, whose associated concept lattice is isomorphic to the lattice of closed subspaces of $H$. This set of closed subspaces, denoted $\mathcal C(H)$, is important in the development of quantum logic and, as an algebraic structure, corresponds to a so-called ``propositional system'', that is, a complete, atomistic, orthomodular lattice which satisfies the covering law. In this paper, we continue with our study of the Chu construction by introducing the Chu correspondences between Hilbert contexts, and showing that the category of Propositional Systems, PropSys, is equivalent to the category of $\text{ChuCors}_{\mathcal H}$ of Chu correspondences between Hilbert contextsUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

IrF4: From Tetrahedral Compass Model to Topological Semimetal

The intersection of topology, symmetry, and magnetism yields a rich structure of possible phases. In this work, we study theoretically the consequences of magnetism on IrF4, which was recently identified as a possible candidate topological nodal chain semimetal in the absence of magnetic order. We show that the spin-orbital nature of the Ir moments gives rise to strongly anisotropic magnetic couplings resembling a tetrahedral compass model on a diamond lattice. The predicted magnetic ground state preserves key symmetries protecting the nodal lines, such that they persist into the ordered phase at the mean-field level. The consequences for other symmetry reductions are also discussed

Discovering Implicational Knowledge in Wikidata

Knowledge graphs have recently become the state-of-the-art tool for representing the diverse and complex knowledge of the world. Examples include the proprietary knowledge graphs of companies such as Google, Facebook, IBM, or Microsoft, but also freely available ones such as YAGO, DBpedia, and Wikidata. A distinguishing feature of Wikidata is that the knowledge is collaboratively edited and curated. While this greatly enhances the scope of Wikidata, it also makes it impossible for a single individual to grasp complex connections between properties or understand the global impact of edits in the graph. We apply Formal Concept Analysis to efficiently identify comprehensible implications that are implicitly present in the data. Although the complex structure of data modelling in Wikidata is not amenable to a direct approach, we overcome this limitation by extracting contextual representations of parts of Wikidata in a systematic fashion. We demonstrate the practical feasibility of our approach through several experiments and show that the results may lead to the discovery of interesting implicational knowledge. Besides providing a method for obtaining large real-world data sets for FCA, we sketch potential applications in offering semantic assistance for editing and curating Wikidata

Clones in Graphs

Finding structural similarities in graph data, like social networks, is a far-ranging task in data mining and knowledge discovery. A (conceptually) simple reduction would be to compute the automorphism group of a graph. However, this approach is ineffective in data mining since real world data does not exhibit enough structural regularity. Here we step in with a novel approach based on mappings that preserve the maximal cliques. For this we exploit the well known correspondence between bipartite graphs and the data structure formal context $(G,M,I)$ from Formal Concept Analysis. From there we utilize the notion of clone items. The investigation of these is still an open problem to which we add new insights with this work. Furthermore, we produce a substantial experimental investigation of real world data. We conclude with demonstrating the generalization of clone items to permutations.Comment: 11 pages, 2 figures, 1 tabl

Practical Use of Formal Concept Analysis in Service-Oriented Computing

International audiencePervasive applications are encountered in a number of settings, including smart houses, intelligent buildings or connected plants. Service-Oriented Computing is today the technology of choice for implementing and exposing resources in such environments. The selection of appropriate services at the right moment in order to compose meaningful applications is however a real issue. In this paper, we propose a FCA-based solution to this problem.We have integrated FCA algorithms in our pervasive gateways and adapted them in order to allow efficient runtime selection of heterogeneous and dynamic services. This work has been applied to realistic use cases in the scope of a European project