The Hawking-Penrose singularity theorem for C1,1C^{1,1}-Lorentzian metrics

We show that the Hawking--Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of $C^{1, 1}$-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for $C^{1,1}$-metrics, and of $C^0$-trapped submanifolds. By regularisation, we show that, under these weak conditions, causal geodesics necessarily become non-maximising. This requires a detailed analysis of the matrix Riccati equation for the approximating metrics, which may be of independent interest.Comment: Minor amendments in v4: Removed non-equivalent condition from Def. 2.2 and adapted Lemma 3.5 and the proof of Lemma 3.

Facial expressions and personality: A kinematical investigation during an emotion induction experiment

Background/Aims: In order to elucidate the relationship between personality traits and expression of positive emotions in healthy volunteers, standardized personality inventories and kinematical analysis of facial expressions can be helpful and were applied in the present study. Methods: Markers fixed at distinct points of the face emitting ultrasonic signals at high frequency gave a direct measure of facial movements with high spatial-temporal resolution. Forty-six healthy participants (mean age: 40.7 years; 20 males, 26 females) watching a witty movie ('Mr. Bean') were investigated. Results: Speed of `laughing' was associated with higher scores on Zuckerman's Sensation Seeking Scale and NEO-FFI (Openness to Experience). Conclusion: Kinematical analysis of facial expressions seems to reflect sensation seeking and related personality styles. Higher speed of facial movements in sensation seekers suggests lowered serotonergic function. Copyright (c) 2006 S. Karger AG, Basel

What you see is where you go? Modeling dispersal in mountainous landscapes

Inter-patch connectivity can be strongly influenced by topography and matrix heterogeneity, particularly when dealing with species with high cognitive abilities. To estimate dispersal in such systems, simulation models need to incorporate a behavioral component of matrix effects to result in more realistic connectivity measures. Inter-patch dispersal is important for the persistence of capercaillie (Tetrao urogallus) in central Europe, where this endangered grouse species lives in patchy populations embedded in a mountainous landscape. We simulated capercaillie movements with an individual-based, spatially explicit dispersal model (IBM) and compared the resulting connectivity measure with distance and an expert estimation. We used a landscape comprising discrete habitat patches, temporary habitat, non-habitat forests, and non-habitat open land. First, we assumed that dispersing individuals have perfect knowledge of habitat cells within the perceptual range (null model). Then, we included constraints to perception and accessibility, i.e., mountain chains, open area and valleys (three sub-models). In a full model, all sub-models were included at once. Correlations between the different connectivity measures were high (Spearman's ρ>0.7) and connectivity based on the full IBM was closer to expert estimation than distance. For selected cases, simple distance differed strongly from the full IBM measure and the expert estimation. Connectivity based on the IBM was strongly sensitive to the size of perceptual range with higher sensitivity for the null model compared to the full model that included context dependent perceptual ranges. Our heuristic approach is adequate for simulating movements of species with high cognitive abilities in strongly structured landscapes that influence perception and permeabilit

The Importance of Spatial Scale in Habitat Models: Capercaillie in the Swiss Alps

The role of scale in ecology is widely recognized as being of vital importance for understanding ecological patterns and processes. The capercaillie (Tetrao urogallus) is a forest grouse species with large spatial requirements and highly specialized habitat preferences. Habitat models at the forest stand scale can only partly explain capercaillie occurrence, and some studies at the landscape scale have emphasized the role of large-scale effects. We hypothesized that both the ability of single variables and multivariate models to explain capercaillie occurrence would vary with the spatial scale of the analysis. To test this hypothesis, we varied the grain size of our analysis from 1 to just over 1100hectares and built univariate and multivariate habitat suitability models for capercaillie in the Swiss Alps. The variance explained by the univariate models was found to vary among the predictors and with spatial scale. Within the multivariate models, the best single-scale model (using all predictor variables at the same scale) worked at a scale equivalent to a small annual home range. The multi-scale model, in which each predictor variable was entered at the scale at which it had performed best in the univariate model, did slightly better than the best single-scale model. Our results confirm that habitat variables should be included at different spatial scales when species-habitat relationships are investigate

Dissecting Supervised Contrastive Learning

Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.Comment: ICML 2021 camera ready versio

Criminal recidivism of illegal pornography offenders in the overall population - a national cohort study of 4612 offenders in Switzerland

Convictions for taking, possessing and distributing pornographic photographs of children have increased with the growing use of the Internet. Previous studies of any progression to contact offences have been small scale and only a few of these have included an investigation of subsequent reconvictions for use of illegal and especially of child pornography. The aims of the present study are to compare reconviction rates among illegal pornography offenders with and without previous child contact offences. The former are referred to as “dual offenders”. This study is a national cohort study of all individuals in Switzerland convicted of an illegal pornography offence since 1973 and was followed-up until 1st November 2008. Reconvictions were ascertained using criminal records from the Federal Office of Justice of Switzerland, leading to a total of 4612 offenders, consisting of 4249 illegal pornography offenders and 363 dual offenders. Comparison of 3-year reconviction rates showed that only 0.2% of the illegal pornography offenders were convicted of contact child sex offences, whereas 2.6% of the dual offenders were reconvicted. The illegal pornography offenders were also significantly less likely to be convicted of further pornography offences, or indeed other sexual offences. The very low “progression rate” among illegal pornography offenders to contact child sexual offences, and their low rate of even repeat pornography offences suggests that community sentences remain appropriate. It is important, however, to bear in mind that conviction rates tend to underestimate the true offending rates, and that with greater access to the Internet, characteristics of pornography users may change over time

Genome sequencing: a systematic review of health economic evidence

Recently the sequencing of the human genome has become a major biological and clinical research field. However, the public health impact of this new technology with focus on the financial effect is not yet to be foreseen. To provide an overview of the current health economic evidence for genome sequencing, we conducted a thorough systematic review of the literature from 17 databases. In addition, we conducted a hand search. Starting with 5 520 records we ultimately included five full-text publications and one internet source, all focused on cost calculations. The results were very heterogeneous and, therefore, difficult to compare. Furthermore, because the methodology of the publications was quite poor, the reliability and validity of the results were questionable. The real costs for the whole sequencing workflow, including data management and analysis, remain unknown. Overall, our review indicates that the current health economic evidence for genome sequencing is quite poor. Therefore, we listed aspects that needed to be considered when conducting health economic analyses of genome sequencing. Thereby, specifics regarding the overall aim, technology, population, indication, comparator, alternatives after sequencing, outcomes, probabilities, and costs with respect to genome sequencing are discussed. For further research, at the outset, a comprehensive cost calculation of genome sequencing is needed, because all further health economic studies rely on valid cost data. The results will serve as an input parameter for budget-impact analyses or cost-effectiveness analyses.Marsilius KollegDF

Elastic Scattering Susceptibility of the High Temperature Superconductor Bi2Sr2CaCu2O8+x: A Comparison between Real and Momentum Space Photoemission Spectroscopies

The joint density of states (JDOS) of Bi2Sr2CaCu2O8+x is calculated by evaluating the autocorrelation of the single particle spectral function A(k,omega) measured from angle resolved photoemission spectroscopy (ARPES). These results are compared with Fourier transformed (FT) conductance modulations measured by scanning tunneling microscopy (STM). Good agreement between the two experimental probes is found for two different doping values examined. In addition, by comparing the FT-STM results to the autocorrelated ARPES spectra with different photon polarization, new insight on the form of the STM matrix elements is obtained. This shines new light on unsolved mysteries in the tunneling data.Comment: Revised now available at: Phys. Rev. Lett. 96, 067005 (2006