A note on rectangular partially massless fields

We study a class of non-unitary so(2,d) representations (for even values of d), describing mixed-symmetry partially massless fields which constitute natural candidates for defining higher-spin singletons of higher order. It is shown that this class of so(2,d) modules obeys of natural generalisation of a couple of defining properties of unitary higher-spin singletons. In particular, we find out that upon restriction to the subalgebra so(2,d-1), these representations branch onto a sum of modules describing partially massless fields of various depths. Finally, their tensor product is worked out in the particular case of d=4, where the appearance of a variety of mixed-symmetry partially massless fields in this decomposition is observed.Comment: 31 pages, 4 figures; v2: typos corrected and references adde

Structure constants of shs[λ][\lambda]: the deformed-oscillator point of view

We derive and spell out the structure constants of the $\mathbb{Z}_2$-graded algebra $\mathfrak{shs}[\lambda]\,$ by using deformed-oscillators techniques in $Aq(2;\nu)\,$, the universal enveloping algebra of the Wigner-deformed Heisenberg algebra in 2 dimensions. The use of Weyl ordering of the deformed oscillators is made throughout the paper, via the symbols of the operators and the corresponding associative, non-commutative star product. The deformed oscillator construction was used by Vasiliev in order to construct the higher spin algebras in three spacetime dimensions. We derive an expression for the structure constants of $\mathfrak{shs}[\lambda]\,$ and show that they must obey a recurrence relation as a consequence of the associativity of the star product. We solve this condition and show that the $\mathfrak{hs}[\lambda]\,$ structure constants are given by those postulated by Pope, Romans and Shen for the Lone Star product.Comment: 22 pages, no figures. Contribution to the proceedings of the workshop "About various kinds of interactions", 4-5 June 2015 at UMONS, in honour of Philippe Spindel; v2: references and comments on Moyal product added; v3: Expanded version of the proceedings, covering the fermionic sector of $Aq(2;\nu)$. 1+27 pages, no figure

A note about a pure spin-connection formulation of General Relativity and spin-2 duality in (A)dS

We investigate the problem of finding a pure spin-connection formulation of General Relativity with non-vanishing cosmological constant. We first revisit the problem at the linearised level and find that the pure spin-connection, quadratic Lagrangian, takes a form reminiscent to Weyl gravity, given by the square of a Weyl-like tensor. Upon Hodge dualisation, we show that the dual gauge field in (A)dS$_D$ transforms under $GL(D)$ in the same representation as a massive graviton in the flat spacetime of the same dimension. We give a detailed proof that the physical degrees of freedom indeed correspond to a massless graviton propagating around the (anti-) de Sitter background and finally speculate about a possible nonlinear pure-connection theory dual to General Relativity with cosmological constant.Comment: 21 page

Character Integral Representation of Zeta function in AdSd+1_{d+1}: II. Application to partially-massless higher-spin gravities

We compute the one-loop free energies of the type-A$_\ell$ and type-B$_\ell$ higher-spin gravities in $(d+1)$-dimensional anti-de Sitter (AdS$_{d+1}$) spacetime. For large $d$ and $\ell$, these theories have a complicated field content, and hence it is difficult to compute their zeta functions using the usual methods. Applying the character integral representation of zeta function developed in the companion paper arXiv:1805.05646 to these theories, we show how the computation of their zeta function can be shortened considerably. We find that the results previously obtained for the massless theories ($\ell=1$) generalize to their partially-massless counterparts (arbitrary $\ell$) in arbitrary dimensions.Comment: 39 pages; v2: references and subsection 6.3 on SU(N) matrix model added; v3: typo corrected in subsection 5.3.

Using Posters to Recommend Anime and Mangas in a Cold-Start Scenario

Item cold-start is a classical issue in recommender systems that affects anime and manga recommendations as well. This problem can be framed as follows: how to predict whether a user will like a manga that received few ratings from the community? Content-based techniques can alleviate this issue but require extra information, that is usually expensive to gather. In this paper, we use a deep learning technique, Illustration2Vec, to easily extract tag information from the manga and anime posters (e.g., sword, or ponytail). We propose BALSE (Blended Alternate Least Squares with Explanation), a new model for collaborative filtering, that benefits from this extra information to recommend mangas. We show, using real data from an online manga recommender system called Mangaki, that our model improves substantially the quality of recommendations, especially for less-known manga, and is able to provide an interpretation of the taste of the users.Comment: 6 pages, 3 figures, 1 table, accepted at the MANPU 2017 workshop, co-located with ICDAR 2017 in Kyoto on November 10, 201

Potassic late orogenic Stephanian volcanism in the South West french Massif Central (Decazeville, Figeac, Lacapelle-Marival basins): an example for mantle metasomatism along strike-slip faults?

International audienceIn the Southwestern part of the French Massif central (Decazeville basin, at the Sillon Houiller fault termination; Figeac and Lacapelle-Marival basins along the Argentat fault), Stephanian volcanism exhibits shoshonitic affinities. Their chondrite-normalized Rare Earth Element (REE) patterns are enriched in light REE, but almost flat for heavy REE, with marked negative Eu anomalies. Primitive mantle-normalized element spectra show negative Nb, Ta, P, Sm, Ti, and positive Th, U, Pb anomalies, respectively. εNd values are negative and homogeneous (-6 to -4). This volcanism shares the same geochemical patterns as the late-orogenic Stephanian-Permian magmatism from the southern part of the Variscan belt (Pyrénées, Alps, Sardinia). We explain these geochemical characteristics as resulting from the partial melting of a metasomatised mantle. We propose a new mechanism to explain this melting process: horizontal displacement along the main late-orogenic strike-slip faults might bring into contact a hydrated lower crust with the lithospheric mantle. Mantle metasomatism within the strike-slip fault zone may then induce partial meltin

Identifying Cultural and Cognitive Proximity between Managers and Customers in Tornio and Haparanda Cross Border Region

Daily intercultural interactions in cross-border regions such as those between customers and managers can be a source of knowledge and ideas. However, such interactions can pose distinctive constraints and opportunities for learning and exchange of ideas. This study adopts a relatively fine–grained quantitative approach to study elements of cognitive and cultural proximity which have a major impact on these interactions. It is based on a survey of 91 managers of small service firms and 312 customers in the twin city of Tornio and Haparanda on the border between Finland and Sweden. Seven elements of proximity were identified and measured. Six elements of perceived cognitive and cultural proximity including values, conservative values towards new ideas, knowledge and use of technology, use of a foreign language, sufficiently focusing or providing specific details and ways of solving problems were found significant in terms of shaping perceptions of Swedish and Finnish managers and customers, which shape these interactions. The results enhance our understanding of how daily cross-border intercultural can be examined in the context of cross-border regional knowledge transfer