Results of the ontology alignment evaluation initiative 2019

The Ontology Alignment Evaluation Initiative (OAEI) aims at comparing ontology matching systems on precisely defined test cases. These test cases can be based on ontologies of different levels of complexity (from simple thesauri to expressive OWL ontologies) and use different evaluation modalities (e.g., blind evaluation, open evaluation, or consensus). The OAEI 2019 campaign offered 11 tracks with 29 test cases, and was attended by 20 participants. This paper is an overall presentation of that campaign

Quantum deformations of associative algebras and integrable systems

Quantum deformations of the structure constants for a class of associative noncommutative algebras are studied. It is shown that these deformations are governed by the quantum central systems which has a geometrical meaning of vanishing Riemann curvature tensor for Christoffel symbols identified with the structure constants. A subclass of isoassociative quantum deformations is described by the oriented associativity equation and, in particular, by the WDVV equation. It is demonstrated that a wider class of weakly (non)associative quantum deformations is connected with the integrable soliton equations too. In particular, such deformations for the three-dimensional and infinite-dimensional algebras are described by the Boussinesq equation and KP hierarchy, respectively.Comment: Numeration of the formulas is correcte

Menelaus relation and Fay's trisecant formula are associativity equations

It is shown that the celebrated Menelaus relation and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional algebra.Comment: Talk given at the Conference " Mathematics and Physics of Solitons and Integrable Systems", Dijon, 28.6-2.7, 2009. Minor misprints correcte

The structure of 2D semi-simple field theories

I classify all cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their effect on the Gromov-Witten potential is described by Givental's Fock space formulae. This leads to the reconstruction of Gromov-Witten invariants from the quantum cup-product at a single semi-simple point and from the first Chern class, confirming Givental's higher-genus reconstruction conjecture. The proof uses the Mumford conjecture proved by Madsen and Weiss.Comment: Small errors corrected in v3. Agrees with published versio

On the Genus Two Free Energies for Semisimple Frobenius Manifolds

We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so-called "genus two G-function". Conjecturally the genus two G-function vanishes for a series of important examples of Frobenius manifolds associated with simple singularities as well as for ${\bf P}^1$-orbifolds with positive Euler characteristics. We explain the reasons for such Conjecture and prove it in certain particular cases.Comment: 37 pages, 3 figures, V2: the published versio

Infinite hierarchies of nonlocal symmetries of the Chen--Kontsevich--Schwarz type for the oriented associativity equations

We construct infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using solutions of associated vector and scalar spectral problems. The symmetries in question generalize those found by Chen, Kontsevich and Schwarz (arXiv:hep-th/0508221) for the WDVV equations. As a byproduct, we obtain a Darboux-type transformation and a (conditional) B\"acklund transformation for the oriented associativity equations.Comment: 18 pages, LaTeX; two minor typos in Corollary 5 fixed; to appear in J. Phys. A: Math. Theor.

The XMM-LSS survey: the Class 1 cluster sample over the initial 5 square degrees and its cosmological modelling

We present a sample of 29 galaxy clusters from the XMM-LSS survey over an area of some 5deg2 out to a redshift of z=1.05. The sample clusters, which represent about half of the X-ray clusters identified in the region, follow well defined X-ray selection criteria and are all spectroscopically confirmed. For all clusters, we provide X-ray luminosities and temperatures as well as masses. The cluster distribution peaks around z=0.3 and T =1.5 keV, half of the objects being groups with a temperature below 2 keV. Our L-T(z) relation points toward self-similar evolution, but does not exclude other physically plausible models. Assuming that cluster scaling laws follow self-similar evolution, our number density estimates up to z=1 are compatible with the predictions of the concordance cosmology and with the findings of previous ROSAT surveys. Our well monitored selection function allowed us to demonstrate that the inclusion of selection effects is essential for the correct determination of the evolution of the L-T relation, which may explain the contradictory results from previous studies. Extensive simulations show that extending the survey area to 10deg2 has the potential to exclude the non-evolution hypothesis, but that constraints on more refined ICM models will probably be limited by the large intrinsic dispersion of the L-T relation. We further demonstrate that increasing the dispersion in the scaling laws increases the number of detectable clusters, hence generating further degeneracy [in addition to sigma8, Omega_m, L(M,z) and T(M,z)] in the cosmological interpretation of the cluster number counts. We provide useful empirical formulae for the cluster mass-flux and mass-count-rate relations as well as a comparison between the XMM-LSS mass sensitivity and that of forthcoming SZ surveys.Comment: Accepted for publication by MNRAS. Full resolution images as well as additional cluster data are available through a dedicated database at http://l3sdb.in2p3.fr:8080/l3sdb

Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence

We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan, Jarvis and Ruan following ideas of Witten. Moreover, on both sides, we highlight two remarkable integral local systems arising from the common formalism of Gamma-integral structures applied to the derived category of the hypersurface {W=0} and to the category of graded matrix factorizations of W. In this setup, we prove that the analytic continuation matches Orlov equivalence between the two above categories.Comment: 72pages, v2: Appendix B and references added. Typos corrected, v3: several mistakes corrected, final versio