Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal algebras $so(p,q)$ starting from the one corresponding to $so(N+1)$. It allows to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for the cases $N=2,3,4$. All Lie bialgebra contractions studied in this paper define Hopf algebra contractions for the Drinfel'd-Jimbo deformations $U_z so(p,q)$. They are explicitly used to generate new non-semisimple quantum algebras as it is the case for the Euclidean, Poincar\'e and Galilean algebras.Comment: 26 pages LATE

Quasars: from the Physics of Line Formation to Cosmology

Quasars accreting matter at very high rates (known as extreme Population A [xA] or super-Eddington accreting massive black holes) provide a new class of distance indicators covering cosmic epochs from the present-day Universe up to less than 1 Gyr from the Big Bang. The very high accretion rate makes it possible that massive black holes hosted in xA quasars radiate at a stable, extreme luminosity-to-mass ratio. This in turns translates into stable physical and dynamical conditions of the mildly ionized gas in the quasar low-ionization line emitting region. In this contribution, we analyze the main optical and UV spectral properties of extreme Population A quasars that make them easily identifiable in large spectroscopic surveys at low-z (z < 1) and intermediate-z (2 < z < 2.6), and the physical conditions that are derived for the formation of their emission lines. Ultimately, the analysis supports the possibility of identifying a virial broadening estimator from low-ionization line widths, and the conceptual validity of the redshift-independent luminosity estimates based on virial broadening for a known luminosity-to-mass ratio.Comment: 13 pages, 5 figures. Invited lecture at SPIG 2018, Belgrade. To appear in Ato

Errors and Artefacts in Agent-Based Modelling

The objectives of this paper are to define and classify different types of errors and artefacts that can appear in the process of developing an agent-based model, and to propose activities aimed at avoiding them during the model construction and testing phases. To do this in a structured way, we review the main concepts of the process of developing such a model – establishing a general framework that summarises the process of designing, implementing, and using agent-based models. Within this framework we identify the various stages where different types of errors and artefacts may appear. Finally we propose activities that could be used to detect (and hence eliminate) each type of error or artefact.Verification, Replication, Artefact, Error, Agent-Based Modelling, Modelling Roles

Black hole mass estimates in quasars - A comparative analysis of high- and low-ionization lines

The inter-line comparison between high- and low-ionization emission lines has yielded a wealth of information on the quasar broad line region (BLR) structure and dynamics, including perhaps the earliest unambiguous evidence in favor of a disk + wind structure in radio-quiet quasars. We carried out an analysis of the CIV 1549 and Hbeta line profiles of 28 Hamburg-ESO high luminosity quasars and of 48 low-z, low luminosity sources in order to test whether the high-ionization line CIV 1549 width could be correlated with Hbeta and be used as a virial broadening estimator. We analyze intermediate- to high-S/N, moderate resolution optical and NIR spectra covering the redshifted CIV and H$\beta$ over a broad range of luminosity log L ~ 44 - 48.5 [erg/s] and redshift (0 - 3), following an approach based on the quasar main sequence. The present analysis indicates that the line width of CIV 1549 is not immediately offering a virial broadening estimator equivalent to H$\beta$. At the same time a virialized part of the BLR appears to be preserved even at the highest luminosities. We suggest a correction to FWHM(CIV) for Eddington ratio (using the CIV blueshift as a proxy) and luminosity effects that can be applied over more than four dex in luminosity. Great care should be used in estimating high-L black hole masses from CIV 1549 line width. However, once corrected FWHM(CIV) values are used, a CIV-based scaling law can yield unbiased MBH values with respect to the ones based on H$\beta$ with sample standard deviation ~ 0.3 dex.Comment: 43 pages, 15 Figures, submitted to A&

Quantization of Lie-Poisson structures by peripheric chains

The quantization properties of composite peripheric twists are studied. Peripheric chains of extended twists are constructed for U(sl(N)) in order to obtain composite twists with sufficiently large carrier subalgebras. It is proved that the peripheric chains can be enlarged with additional Reshetikhin and Jordanian factors. This provides the possibility to construct new solutions to Drinfeld equations and, thus, to quantize new sets of Lie-Poisson structures. When the Jordanian additional factors are used the carrier algebras of the enlarged peripheric chains are transformed into algebras of motion of the form G_{JB}^{P}={G}_{H}\vdash {G}_{P}. The factor algebra G_{H} is a direct sum of Borel and contracted Borel subalgebras of lower dimensions. The corresponding omega--form is a coboundary. The enlarged peripheric chains F_{JB}^{P} represent the twists that contain operators external with respect to the Lie-Poisson structure. The properties of new twists are illustrated by quantizing r-matrices for the algebras U(sl(3)), U(sl(4)) and U(sl(7)).Comment: 24 pages, LaTe

Bases in Lie and Quantum Algebras

Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for some arbitrary conventions. The situation is much more involved in the context of quantum algebras, where inside the quantum universal enveloping algebra, we have not enough primitive elements that allow for a privileged set of generators and all basic sets are equivalent. In this paper we discuss how the Drinfeld double structure underlying every simple Lie bialgebra characterizes uniquely a particular basis without any freedom, completing the Cartan program on simple algebras. By means of a perturbative construction, a distinguished deformed basis (we call it the analytical basis) is obtained for every quantum group as the analytical prolongation of the above defined Lie basis of the corresponding Lie bialgebra. It turns out that the whole construction is unique, so to each quantum universal enveloping algebra is associated one and only one bialgebra. In this way the problem of the classification of quantum algebras is moved to the classification of bialgebras. In order to make this procedure more clear, we discuss in detail the simple cases of su(2) and su_q(2).Comment: 16 pages, Proceedings of the 5th International Symposium on Quantum Theory and Symmetries QTS5 (July 22-28, 2007, Valladolid (Spain)

Non-linear Dependence of L(B) on L(FIR) and M(H2) among Spiral Galaxies and Effects of Tidal Interaction

Through the study of a carefully selected sample of isolated spiral galaxies, we have established that two important global physical quantities for tracing star forming activities, L(FIR) and M(H2), have non-linear dependence on another commonly cited global quantity L(B). Furthermore we show that simple power law relations can effectively describe these non-linear relations for spiral galaxies spanning four orders of magnitude in FIR and M(H2) and nearly three orders of magnitude in L(B). While the existence of non-linear dependence of M(H2) (assuming a constant CO-to-H2 conversion) and L(FIR) on optical luminosity L(B) has been previously noted in the literature, an improper normalization of simple scaling by L(B) has been commonly used in many previous studies to claim enhanced molecular gas content and induced activities among tidally interacting and other types of galaxies. We remove these non-linear effects using the template relations derived from the isolated galaxy sample and conclude that strongly interacting galaxies do not have enhanced molecular gas content, contrary to previous claims. With these non-linear relations among L(B), L(FIR) and M(H2) properly taken into account, we confirm again that the FIR emission and the star formation efficiency L(FIR)/M(H2) are indeed enhanced by tidal interactions. Virgo galaxies show the same level of M(H2) and L(FIR) as isolated galaxies. We do not find any evidence for enhanced star forming activity among barred galaxies.Comment: 19 pages and 5 figures, requires AAS style files, ApJ, accepte

Reproducibility of experiments in recommender systems evaluation

© IFIP International Federation for Information Processing 2018 Published by Springer International Publishing AG 2018. All Rights Reserved. Recommender systems evaluation is usually based on predictive accuracy metrics with better scores meaning recommendations of higher quality. However, the comparison of results is becoming increasingly difficult, since there are different recommendation frameworks and different settings in the design and implementation of the experiments. Furthermore, there might be minor differences on algorithm implementation among the different frameworks. In this paper, we compare well known recommendation algorithms, using the same dataset, metrics and overall settings, the results of which point to result differences across frameworks with the exact same settings. Hence, we propose the use of standards that should be followed as guidelines to ensure the replication of experiments and the reproducibility of the results

The functional anatomy of schizophrenia: A dynamic causal modeling study of predictive coding.

This paper tests the hypothesis that patients with schizophrenia have a deficit in selectively attending to predictable events. We used dynamic causal modeling (DCM) of electrophysiological responses - to predictable and unpredictable visual targets - to quantify the effective connectivity within and between cortical sources in the visual hierarchy in 25 schizophrenia patients and 25 age-matched controls. We found evidence for marked differences between normal subjects and schizophrenia patients in the strength of extrinsic backward connections from higher hierarchical levels to lower levels within the visual system. In addition, we show that not only do schizophrenia subjects have abnormal connectivity but also that they fail to adjust or optimize this connectivity when events can be predicted. Thus, the differential intrinsic recurrent connectivity observed during processing of predictable versus unpredictable targets was markedly attenuated in schizophrenia patients compared with controls, suggesting a failure to modulate the sensitivity of neurons responsible for passing sensory information of prediction errors up the visual cortical hierarchy. The findings support the proposed role of abnormal connectivity in the neuropathology and pathophysiology of schizophrenia