Complex Hadamard matrices contained in a Bose-Mesner algebra

A complex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying $HH^*= nI$, where $*$ stands for the Hermitian transpose and I is the identity matrix of order $n$. In this paper, we first determine the image of a certain rational map from the $d$-dimensional complex projective space to $\mathbb{C}^{d(d+1)/2}$. Applying this result with $d=3$, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose-Mesner algebra of a certain 3-class symmetric association scheme. In particular, we recover the complex Hadamard matrices of order 15 found by Ada Chan. We compute the Haagerup sets to show inequivalence of resulting type-II matrices, and determine the Nomura algebras to show that the resulting matrices are not decomposable into generalized tensor products.Comment: 28 pages + Appendix A + Appendix

GTRACE-RS: Efficient Graph Sequence Mining using Reverse Search

The mining of frequent subgraphs from labeled graph data has been studied extensively. Furthermore, much attention has recently been paid to frequent pattern mining from graph sequences. A method, called GTRACE, has been proposed to mine frequent patterns from graph sequences under the assumption that changes in graphs are gradual. Although GTRACE mines the frequent patterns efficiently, it still needs substantial computation time to mine the patterns from graph sequences containing large graphs and long sequences. In this paper, we propose a new version of GTRACE that enables efficient mining of frequent patterns based on the principle of a reverse search. The underlying concept of the reverse search is a general scheme for designing efficient algorithms for hard enumeration problems. Our performance study shows that the proposed method is efficient and scalable for mining both long and large graph sequence patterns and is several orders of magnitude faster than the original GTRACE

About the Chemical Evolution of dSphs (and the peculiar Globular Cluster Omega Cen)

We present three dimensional hydrodynamical simulations aimed at studying the dynamical and chemical evolution of the interstellar medium (ISM) in isolated dwarf spheroidal galaxies (dSphs). This evolution is driven by the explosion of Type II and Type Ia supernovae, whose different contribution on both the dynamics and chemical enrichment is taken into account. Radiative losses are effective in radiating away the huge amount of energy released by SNe explosions, and the dSph is able to retain most of the gas allowing a long period (>2-3 Gyr) of star formation, as usually observed in this kind of galaxies. We are able to reproduce the stellar metallicity distribution function (MDF) as well as the peculiar chemical properties of strongly O-depleted stars observed in several dSphs. The model also naturally predicts two different stellar populations, with an anti-correlation between [Fe/H] and velocity dispersion, similarly to what observed in the Sculptor and Fornax dSphs. These results derive from the inhomogeneous pollution of the SNe Ia, a distinctive characteristic of our model. We also applied the model to the peculiar globular cluster (GC) Omega Cen in the hypothesis that it is the remnant of a formerly larger stellar system, possibly a dSph.Comment: To appear in the IAU Symposium 255, "Low-Metallicity Star Formation: From the First stars to Dwarf Galaxies", contributed talk, 5 page

Iñupiaq pride: Kivgiq (Messenger Feast) on the Alaskan North Slope

This paper explores tradition as dynamics of social life, history, and power relations and its meanings for local people through the examination of a revitalised ancient festival among Iñupiat on the Alaskan North Slope. In one form or another, Iñupiaq people had celebrated Kivgiq (Messenger Feast) for many centuries. However, the earlier representations of Kivgiq were discontinued in the early 20th century due to social, economic, and environmental pressures. In 1988 after a lapse of more than 70 years, the modern Kivgiq was reconstructed with intent to provide each Iñupiaq with an even stronger collective identity and enhanced ethnic pride. The first modern Kivgiq generated more than 2,000 participants and successfully integrated ancient values into those of the modern context. Now held every second year, the revitalised tradition embodies Iñupiaq socio-economic empowerment. Kivgiq is one of the most important activities to index what contemporary Iñupiat mean by tradition. Along with many other traditional activities defined by Iñupiat, such as whaling, hunting, and dancing, the contemporary Messenger Feast is the key sphere where people regenerate, reinterpret, and renegotiate their traditions to themselves and to wider audiences.À travers l’étude d’un ancien festival revitalisé chez les Iñupiat du North Slope en Alaska, cet article explore la notion de tradition en tant que dynamique de vie sociale, d’histoire et de relation de pouvoir ainsi que ce qu’elle signifie pour les populations locales. Quelle qu’en ait été sa forme, voilà des siècles que les Iñupiat célèbrent Kivgiq (la fête du messager). Toutefois, les plus anciennes célébrations de Kivgiq ont cessé au début du 20e siècle dues à des pressions sociales, économiques et environnementales. En 1988, après plus de 70 ans, le Kigviq moderne a été recréé afin de donner à chaque Iñupiaq une identité collective encore plus forte et afin de rehausser la fierté ethnique. Le premier Kivgiq moderne a attiré plus de 2000 participants et a réussi à intégrer aux anciennes valeurs celles du contexte actuel. Ayant maintenant lieu tous les deux ans, cette tradition revitalisée incarne la réappropriation du pouvoir socio-économique des Iñupiat. Kivgiq est l’une des activités qui caractérise le mieux ce que les Iñupiat entendent par tradition. Au même titre que de nombreuses autres activités traditionnelles définies par les Iñupiat telles que la poursuite de la baleine, la chasse et la danse, la fête du messager d’aujourd’hui est la sphère clé où les gens se régénèrent, réinterprètent et renégocient leurs traditions pour eux-mêmes et pour une plus large audience

The Legal Measures against the Abuse of Separate Corporate Personality and Limited Liability by Corporate Groups: The scope of Chandler v Cape plc and Thompson v Renwick Group plc

While the scope of ‘veil lifting’ has been severely restricted in UK case law, two recent notable judgments, Chandler v Cape Plc and Thompson v Renwick Group Plc, have held that a parent company could owe tortious liability for the health and safety of its subsidiary’s employees. This article contends that the legal principle recognised in Chandler and Thompson could successfully prevent corporate group abuses of separate corporate personality and limited liability, when combined with ‘veil lifting’ and protection against misrepresentation in UK law. With reference to the theoretical justification of limited liability, there are three circumstances in which limited liability should not apply: ex ante opportunism, ex post opportunism and in relation to involuntary creditors. Most cases in the former two categories can be dealt with by applying existing UK legislation and case law concerning misrepresentation and ‘veil piercing’. The final category can be dealt with by Chandler’s direct tortious liability regime if it is appropriately refined. This paper proposes an integrated understanding of Caparo’s three requirements for establishing a duty of care, namely foreseeability, proximity and fairness, and four-group categorisation, namely reliance on superior knowledge, confusing representation, business integration and fairness for other reasons, in which the parent’s direct tortious liability should be recognised