The QUEST-La Silla AGN Variability Survey: selection of AGN candidates through optical variability

We used data from the QUEST-La Silla Active Galactic Nuclei (AGN) variability survey to construct light curves for 208,583 sources over $\sim 70$ deg$^2$, with a a limiting magnitude $r \sim 21$. Each light curve has at least 40 epochs and a length of $\geq 200$ days. We implemented a Random Forest algorithm to classify our objects as either AGN or non-AGN according to their variability features and optical colors, excluding morphology cuts. We tested three classifiers, one that only includes variability features (RF1), one that includes variability features and also $r-i$ and $i-z$ colors (RF2), and one that includes variability features and also $g-r$, $r-i$, and $i-z$ colors (RF3). We obtained a sample of high probability candidates (hp-AGN) for each classifier, with 5,941 candidates for RF1, 5,252 candidates for RF2, and 4,482 candidates for RF3. We divided each sample according to their $g-r$ colors, defining blue ($g-r\leq 0.6$) and red sub-samples ($g-r>0.6$). We find that most of the candidates known from the literature belong to the blue sub-samples, which is not necessarily surprising given that, unlike for many literature studies, we do not cut our sample to point-like objects. This means that we can select AGN that have a significant contribution from redshifted starlight in their host galaxies. In order to test the efficiency of our technique we performed spectroscopic follow-up, confirming the AGN nature of 44 among 54 observed sources (81.5\% of efficiency). From the campaign we concluded that RF2 provides the purest sample of AGN candidates.Comment: Accepted for publication in The Astrophysical Journal Supplement Serie

Hierarchy of the Selberg zeta functions

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.Comment: 14 page

Fourier Transforms of Lorentz Invariant Functions

Fourier transforms of Lorentz invariant functions in Minkowski space, with support on both the timelike and the spacelike domains are performed by means of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in detail, and the results for 1+n dimensions are given.Comment: 15 pages, 1 figur

On graviton production in braneworld cosmology

We study braneworlds in a five dimensional bulk, where cosmological expansion is mimicked by motion through AdS$_5$. We show that the five dimensional graviton reduces to the four dimensional one in the late time approximation of such braneworlds. Inserting a fixed regulator brane far from the physical brane, we investigate quantum graviton production due to the motion of the brane. We show that the massive Kaluza-Klein modes decouple completely from the massless mode and they are not generated at all in the limit where the regulator brane position goes to infinity. In the low energy limit, the massless four dimensional graviton obeys the usual 4d equation and is therefore also not generated in a radiation-dominated universe.Comment: 9 pages, minor changes, references correcte

Recursion relations and branching rules for simple Lie algebras

The branching rules between simple Lie algebras and its regular (maximal) simple subalgebras are studied. Two types of recursion relations for anomalous relative multiplicities are obtained. One of them is proved to be the factorized version of the other. The factorization property is based on the existence of the set of weights $\Gamma$ specific for each injection. The structure of $\Gamma$ is easily deduced from the correspondence between the root systems of algebra and subalgebra. The recursion relations thus obtained give rise to simple and effective algorithm for branching rules. The details are exposed by performing the explicit decomposition procedure for $A_{3} \oplus u(1) \to B_{4}$ injection.Comment: 15p.,LaTe

Nature of singularities in anisotropic string cosmology

We study nature of singularities in anisotropic string-inspired cosmological models in the presence of a Gauss-Bonnet term. We analyze two string gravity models-- dilaton-driven and modulus-driven cases-- in the Bianchi type-I background without an axion field. In both scenarios singularities can be classified in two ways- the determinant singularity where the main determinant of the system vanishes and the ordinary singularity where at least one of the anisotropic expansion rates of the Universe diverges. In the dilaton case, either of these singularities inevitably appears during the evolution of the system. In the modulus case, nonsingular cosmological solutions exist both in asymptotic past and future with determinant $D=+\infty$ and D=2, respectively. In both scenarios nonsingular trajectories in either future or past typically meet the determinant singularity in past/future when the solutions are singular, apart from the exceptional case where the sign of the time-derivative of dilaton is negative. This implies that the determinant singularity may play a crucial role to lead to singular solutions in an anisotropic background.Comment: 21 pages, 8 figure

Tachyonic perturbations in AdS5_5 orbifolds

We show that scalar as well as vector and tensor metric perturbations in the Randall-Sundrum II braneworld allow normalizable tachyonic modes, i.e., possible instabilities. These instabilities require nonvanishing initial anisotropic stresses on the brane. We show with a specific example that within the Randall-Sundrum II model, even though the tachyonic modes are excited, no instability develops. We argue, however, that in the cosmological context instabilities might in principle be present. We conjecture that the tachyonic modes are due to the singularity of the orbifold construction. We illustrate this with a simple but explicit toy model.Comment: 11 pages, matches published versio

Univalent Foundations and the UniMath Library

We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (section 2). This leads us to a general discussion about the links between architecture and mathematics where a meeting of minds is revealed between architects and mathematicians (section 3). On the way our odyssey from the foundations to the "horizon" of mathematics will lead us to meet the mathematicians David Hilbert and Nicolas Bourbaki as well as the architect Christopher Alexander