The subgroup growth spectrum of virtually free groups

For a finitely generated group $\Gamma$ denote by $\mu(\Gamma)$ the growth coefficient of $\Gamma$, that is, the infimum over all real numbers $d$ such that $s_n(\Gamma)<n!^d$. We show that the growth coefficient of a virtually free group is always rational, and that every rational number occurs as growth coefficient of some virtually free group. Moreover, we describe an algorithm to compute $\mu$

Molecular architecture of polycomb repressive complexes

The polycomb group (PcG) proteins are a large and diverse family that epigenetically repress the transcription of key developmental genes. They form three broad groups of polycomb repressive complexes (PRCs) known as PRC1, PRC2 and Polycomb Repressive DeUBiquitinase, each of which modifies and/or remodels chromatin by distinct mechanisms that are tuned by having variable compositions of core and accessory subunits. Until recently, relatively little was known about how the various PcG proteins assemble to form the PRCs; however, studies by several groups have now allowed us to start piecing together the PcG puzzle. Here, we discuss some highlights of recent PcG structures and the insights they have given us into how these complexes regulate transcription through chromatin

Blocking D2/D3 dopamine receptors in male participants increases volatility of beliefs when learning to trust others

The ability to learn about other people is crucial for human social functioning. Dopamine has been proposed to regulate the precision of beliefs, but direct behavioural evidence of this is lacking. In this study, we investigate how a high dose of the D2/D3 dopamine receptor antagonist sulpiride impacts learning about other people’s prosocial attitudes in a repeated Trust game. Using a Bayesian model of belief updating, we show that in a sample of 76 male participants sulpiride increases the volatility of beliefs, which leads to higher precision weights on prediction errors. This effect is driven by participants with genetically conferred higher dopamine availability (Taq1a polymorphism) and remains even after controlling for working memory performance. Higher precision weights are reflected in higher reciprocal behaviour in the repeated Trust game but not in single-round Trust games. Our data provide evidence that the D2 receptors are pivotal in regulating prediction error-driven belief updating in a social context

Pair production in laser fields oscillating in space and time

The production of electron-positron pairs from vacuum by counterpropagating laser beams of linear polarization is calculated. In contrast to the usual approximate approach, the spatial dependence and magnetic component of the laser field are taken into account. We show that the latter strongly affects the creation process at high laser frequency: the production probability is reduced, the kinematics is fundamentally modified, the resonant Rabi-oscillation pattern is distorted and the resonance positions are shifted, multiplied and split.Comment: 5 pages, 5 figure

Chasing the hare - Evaluating the phylogenetic utility of a nuclear single copy gene region at and below species level within the species rich group Peperomia (Piperaceae)

Background: The rapidly increasing number of available plant genomes opens up almost unlimited prospects for biology in general and molecular phylogenetics in particular. A recent study took advantage of this data and identified a set of nuclear genes that occur in single copy in multiple sequenced angiosperms. The present study is the first to apply genomic sequence of one of these low copy genes, agt1, as a phylogenetic marker for species-level phylogenetics. Its utility is compared to the performance of several coding and non-coding chloroplast loci that have been suggested as most applicable for this taxonomic level. As a model group, we chose Tildenia, a subgenus of Peperomia (Piperaceae), one of the largest plant genera. Relationships are particularly difficult to resolve within these species rich groups due to low levels of polymorphisms and fast or recent radiation. Therefore, Tildenia is a perfect test case for applying new phylogenetic tools. Results: We show that the nuclear marker agt1, and in particular the agt1 introns, provide a significantly increased phylogenetic signal compared to chloroplast markers commonly used for low level phylogenetics. 25% of aligned characters from agt1 intron sequence are parsimony informative. In comparison, the introns and spacer of several common chloroplast markers (trnK intron, trnK-psbA spacer, ndhF-rpl32 spacer, rpl32-trnL spacer, psbA-trnH spacer) provide less than 10% parsimony informative characters. The agt1 dataset provides a deeper resolution than the chloroplast markers in Tildenia. Conclusions: Single (or very low) copy nuclear genes are of immense value in plant phylogenetics. Compared to other nuclear genes that are members of gene families of all sizes, lab effort, such as cloning, can be kept to a minimum. They also provide regions with different phylogenetic content deriving from coding and non-coding parts of different length. Thus, they can be applied to a wide range of taxonomic levels from family down to population level. As more plant genomes are sequenced, we will obtain increasingly precise information about which genes return to single copy most rapidly following gene duplication and may be most useful across a wide range of plant groups

Computational Complexity of Iterated Maps on the Interval (Extended Abstract)

The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the computational complexity is analyzed. As a main result, the computational complexity measure considered here is related to the Ljapunow exponent of the dynamical system under consideration

Detection of metastable electronic states by Penning trap mass spectrometry

State-of-the-art optical clocks achieve fractional precisions of $10^{-18}$ and below using ensembles of atoms in optical lattices or individual ions in radio-frequency traps. Promising candidates for novel clocks are highly charged ions (HCIs) and nuclear transitions, which are largely insensitive to external perturbations and reach wavelengths beyond the optical range, now becoming accessible to frequency combs. However, insufficiently accurate atomic structure calculations still hinder the identification of suitable transitions in HCIs. Here, we report on the discovery of a long-lived metastable electronic state in a HCI by measuring the mass difference of the ground and the excited state in Re, the first non-destructive, direct determination of an electronic excitation energy. This result agrees with our advanced calculations, and we confirmed them with an Os ion with the same electronic configuration. We used the high-precision Penning-trap mass spectrometer PENTATRAP, unique in its synchronous use of five individual traps for simultaneous mass measurements. The cyclotron frequency ratio $R$ of the ion in the ground state to the metastable state could be determined to a precision of $\delta R=1\cdot 10^{-11}$, unprecedented in the heavy atom regime. With a lifetime of about 130 days, the potential soft x-ray frequency reference at $\nu=4.86\cdot 10^{16}\,\text{Hz}$ has a linewidth of only $\Delta \nu\approx 5\cdot 10^{-8}\,\text{Hz}$, and one of the highest electronic quality factor ($Q=\frac{\nu}{\Delta \nu}\approx 10^{24}$) ever seen in an experiment. Our low uncertainty enables searching for more HCI soft x-ray clock transitions, needed for promising precision studies of fundamental physics in a thus far unexplored frontier