On the presentation of pointed Hopf algebras

We give a presentation in terms of generators and relations of Hopf algebras generated by skew-primitive elements and abelian group of group-like elements with action given via characters. This class of pointed Hopf algebras has shown great importance in the classification theory and can be seen as generalized quantum groups. As a consequence we get an analog presentation of Nichols algebras of diagonal type

The Lens-Redshift Test Revisited

Kochanek (1992) suggested that the redshifts of gravitational lens galaxies rule out a large cosmological constant. This result was questioned by Helbig & Kayser (1996), who pointed out that selection effects related to the brightness of the lens can bias the results of this test against a high lambda value; however, we did not claim that the observations favoured a high lambda value, merely that current observational data were not sufficient to say either way, using the test as proposed by Kochanek (1992) but corrected for selection effects. Kochanek (1996) pointed out that additional information (fraction of measured lens redshifts) provides additional information which restores the sensitivity of the test to the cosmological model, at least somewhat. Here, I consider three aspects. First, I examine the accuracy of the correction to the test proposed by Kochanek (1996). Second, I compare the slightly different statistical methods which have been used in connection with this test. Third, I discuss what results can be obtained today now that more and better-defined observations are available.Comment: 4 pages, LaTeX, 2 included PostScript files; to appear in the proceedings of the XXXVth Rencontres de Moriond, "L2K - Cosmological Physics with Gravitational Lensing", J.-P. Kneib, Y. Mellier, M. Moniez & J. Tran Thanh Van (eds.); see also http://terapix.iap.fr/L2K/l2k_one.htm

The mm-zz relation for Type Ia supernovae: safety in numbers or safely without worry?

The $m$-$z$ relation for Type Ia supernovae is compatible with the cosmological concordance model if one assumes that the Universe is homogeneous, at least with respect to light propagation. This could be due to the density along each line of sight being equal to the overall cosmological density, or to `safety in numbers', with variation in the density along all lines of sight averaging out if the sample is large enough. Statistical correlations (or lack thereof) between redshifts, residuals (differences between the observed distance moduli and those calculated from the best-fitting cosmological model), and observational uncertainties suggest that the former scenario is the better description, so that one can use the traditional formula for the luminosity distance safely without worry.Comment: 5 pages, 6 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society (includes small changes made while checking the proofs). Related information available at http://www.multivax.de:8000/helbig/research/publications/info/etasnia2.htm

The Current Status of CLASS

I give a brief overview of the current status of some aspects of the Cosmic Lens All-Sky Survey (CLASS): description of the survey, current list of lens systems, cosmological parameters from lensing statistics, H_0 from time delays, dark lenses, wide-separation lenses.Comment: 4 pages, LaTeX; to appear in the proceedings of the XXXVth Rencontres de Moriond, "L2K - Cosmological Physics with Gravitational Lensing", J.-P. Kneib, Y. Mellier, M. Moniez & J. Tran Thanh Van (eds.); see also http://terapix.iap.fr/L2K/l2k_one.html . Of course, such a proceedings contribution is just a snapshot of the status at the time; for more up-to-date information, follow the links from http://gladia.astro.rug.nl:8000/ceres/ceres.htm

The mm-zz relation for type Ia supernovae, locally inhomogeneous cosmological models, and the nature of dark matter

The $m$-$z$ relation for type Ia supernovae is one of the key pieces of evidence supporting the cosmological `concordance model' with $\lambda_0 \approx 0.7$ and $\Omega_0 \approx 0.3$. However, it is well known that the $m$-$z$ relation depends not only on $\lambda_0$ and $\Omega_0$ (with $H_0$ as a scale factor) but also on the density of matter along the line of sight, which is not necessarily the same as the large-scale density. I investigate to what extent the measurement of $\lambda_0$ and $\Omega_0$ depends on this density when it is characterized by the parameter $\eta$ ($0 \le \eta \le 1$), which describes the ratio of density along the line of sight to the overall density. I also discuss what constraints can be placed on $\eta$, both with and without constraints on $\lambda_0$ and $\Omega_0$ in addition to those from the $m$-$z$ relation for type~Ia supernovae.Comment: 11 pages, 17 figures, published in Monthly Notices of the Royal Astronomical Society. This version contains minor changes made while correcting proofs in order to correspond as closely as practical to the offical version. No changes in content. Related information available at http://www.astro.multivax.de:8000/helbig/research/publications/info/etasnia.htm

Challenges in Emotion Style Transfer: An Exploration with a Lexical Substitution Pipeline

We propose the task of emotion style transfer, which is particularly challenging, as emotions (here: anger, disgust, fear, joy, sadness, surprise) are on the fence between content and style. To understand the particular difficulties of this task, we design a transparent emotion style transfer pipeline based on three steps: (1) select the words that are promising to be substituted to change the emotion (with a brute-force approach and selection based on the attention mechanism of an emotion classifier), (2) find sets of words as candidates for substituting the words (based on lexical and distributional semantics), and (3) select the most promising combination of substitutions with an objective function which consists of components for content (based on BERT sentence embeddings), emotion (based on an emotion classifier), and fluency (based on a neural language model). This comparably straight-forward setup enables us to explore the task and understand in what cases lexical substitution can vary the emotional load of texts, how changes in content and style interact and if they are at odds. We further evaluate our pipeline quantitatively in an automated and an annotation study based on Tweets and find, indeed, that simultaneous adjustments of content and emotion are conflicting objectives: as we show in a qualitative analysis motivated by Scherer's emotion component model, this is particularly the case for implicit emotion expressions based on cognitive appraisal or descriptions of bodily reactions.Comment: Accepted at the SocialNLP Workshop at ACL 202

Visualising Basins of Attraction for the Cross-Entropy and the Squared Error Neural Network Loss Functions

Quantification of the stationary points and the associated basins of attraction of neural network loss surfaces is an important step towards a better understanding of neural network loss surfaces at large. This work proposes a novel method to visualise basins of attraction together with the associated stationary points via gradient-based random sampling. The proposed technique is used to perform an empirical study of the loss surfaces generated by two different error metrics: quadratic loss and entropic loss. The empirical observations confirm the theoretical hypothesis regarding the nature of neural network attraction basins. Entropic loss is shown to exhibit stronger gradients and fewer stationary points than quadratic loss, indicating that entropic loss has a more searchable landscape. Quadratic loss is shown to be more resilient to overfitting than entropic loss. Both losses are shown to exhibit local minima, but the number of local minima is shown to decrease with an increase in dimensionality. Thus, the proposed visualisation technique successfully captures the local minima properties exhibited by the neural network loss surfaces, and can be used for the purpose of fitness landscape analysis of neural networks.Comment: Preprint submitted to the Neural Networks journa