Nonexistence of Certain Skew-symmetric Amorphous Association Schemes

An association scheme is amorphous if it has as many fusion schemes as possible. Symmetric amorphous schemes were classified by A. V. Ivanov [A. V. Ivanov, Amorphous cellular rings II, in Investigations in algebraic theory of combinatorial objects, pages 39--49. VNIISI, Moscow, Institute for System Studies, 1985] and commutative amorphous schemes were classified by T. Ito, A. Munemasa and M. Yamada [T. Ito, A. Munemasa and M. Yamada, Amorphous association schemes over the Galois rings of characteristic 4, European J. Combin., 12(1991), 513--526]. A scheme is called skew-symmetric if the diagonal relation is the only symmetric relation. We prove the nonexistence of skew-symmetric amorphous schemes with at least 4 classes. We also prove that non-symmetric amorphous schemes are commutative.Comment: 10 page

Detecting anomalies in heterogeneous population-scale VAT networks

Anomaly detection in network science is the method to determine aberrant edges, nodes, subgraphs or other network events. Heterogeneous networks typically contain information going beyond the observed network itself. Value Added Tax (VAT, a tax on goods and services) networks, defined from pairwise interactions of VAT registered taxpayers, are analysed at a population-scale requiring scalable algorithms. By adopting a quantitative understanding of the nature of VAT-anomalies, we define a method that identifies them utilising information from micro-scale, meso-scale and global-scale patterns that can be interpreted, and efficiently implemented, as population-scale network analysis. The proposed method is automatable, and implementable in real time, enabling revenue authorities to prevent large losses of tax revenues through performing early identification of fraud within the VAT system.Comment: 14 pages, 5 figures, 3 table